X
GO
Advanced Ethanol Fermentation Simulator – FermAxiom LLC

Advanced Ethanol Fermentation Simulator

2026

The Advanced Ethanol Fermentation Simulator is FermAxiom LLC's calibrated mechanistic platform for resolving
anaerobic Saccharomyces cerevisiae kinetics across the four industrial operating regimes: Batch, Semi-batch,
Fed-batch, and Continuous. The Advanced suite integrates four tabs: a steady-state Medium Calculator,
a dynamic Time-Course Simulator, a Fit Model to Experimental Data tab, and a Model Notes
reference. The simulator advances a fifteen-element ODE state vector resolving starch,
glucose, dextrins, biomass, ethanol, glycerol, lactic and acetic acids, dissolved CO2,
ergosterol cellular quota, broth volume, and adiabatic temperature with calibrated
treatment of Hill-form ethanol inhibition, Liebig's-minimum nutrient coupling
(FAN, Mg, Zn, ergosterol, oleate), two-step starch hydrolysis, pH-stress
cell death, and enzyme inactivation. Strain presets — Ethanol Red,
S288c, CEN.PK — prime parameters in one click; the Model Exp.
Data tab fits HPLC time-courses via Nelder–Mead simplex.
Adiabatic Qmetab/Qcool tracking forecasts cooling loads.
In depth application guidance is further available under
Industrial Bioprocess Technology Platforms and E-Modules

Basic Ethanol Fermentation
Simulation Advanced Ethanol Fermentation
Simulation Industrial Ethanol Fermentation
Simulation
FermAxiom Ethanol Fermentation Suite v26.93 — Yield · Medium · Inoculation · Simulator · Model Data

Ethanol Yield Calculator

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Stoichiometric Yield Design Grains · Tubers · Molasses  |  v26.93

Feedstock-to-ethanol sizing on a dry-basis composition, with saccharification and fermentation efficiencies set independently and co-products credited back to the mass balance.

Primary SubstrateMASS · COMPOSITION
Feedstock sets composition defaults & moisture
Weight Unit
Feedstock Weight
Test Weight i
Feedstock Moisture i
Dry Mass
▶ Detailed composition (% dry basis · editable) Corn — whole kernel
Bio-Process & Fermentation TechnologyPROCESS
Theoretical reports the Gay-Lussac stoichiometric maximum with no efficiency losses. Dry grind is the predominant US fuel-ethanol process (residue → DDGS, optional back-end corn oil). Wet grind is used by integrated corn refineries producing co-products (oil → corn oil, gluten → CGM, fiber → CGF).
All ingredients are charged in the initial batch medium at t = 0. (Informational — fermentation mode does not change the stoichiometric yield computed here.)
Industrial ethanol-producing strains differ in fermentation efficiency. Selecting a strain auto-fills Fermentation Efficiency in Conversion Constants.
Ethanol YieldOUTPUT
Glucose Generated i
Ethanol Mass i
Ethanol Volume
CO2 Generated i
Yield (per grain unit)
Co-Product RecoveryDDGS / CGM / CGF

Conversion Constants

▶

Reference Comparison — capture & compare runs

▶

Results Validation Test — stoichiometric verification

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Conceptual tool for rapid what-if analysis.

User Guide

Purpose and scope

This calculator sizes ethanol output from a given mass of feedstock (corn, wheat, barley, cassava, molasses, and other starch/sugar sources) using hydrolysis and fermentation stoichiometry on a dry-basis composition. It models three industrial process types:

  • Theoretical — Gay-Lussac stoichiometric maximum. No efficiency losses. Reports each grain component individually.
  • Dry-Grind — the dominant US corn-ethanol process (~90% of US production). Whole grain ground, cooked, saccharified, fermented; non-ethanol residue reports as DDGS, with optional back-end corn oil extraction.
  • Wet-Grind — corn wet-milling. Grain steeped and components physically separated before fermentation: germ → corn oil, gluten → CGM, residual → CGF.

Tabs at a glance

  • Yield Analysis — enter feedstock and read ethanol, co-product, glucose and CO₂ results.
  • Economics — per-batch revenue, cost of goods sold and margin from the current run, with selectable currency and units.
  • Sustainability — carbon intensity, water and energy for the current run, with selectable unit system.
  • Instructions / Science / References — this guide, the underlying equations, and source citations.

Workflow

  1. Select feedstock and process type.
  2. Enter feedstock weight (in your chosen unit) and moisture percentage. For each input, the value is entered first and its unit is chosen in the dropdown to its right.
  3. Enter dry-basis composition for the seven major components. They should sum to ~100%.
  4. Adjust process parameters in Conversion Constants if needed (Fermentation Efficiency, Saccharification Efficiency, Starch Recovery, Corn Oil Extraction).
  5. Read the calculated yields and co-products in the right-hand cards.

Key inputs

  • Test Weight (only when entering bushels) — USDA standard 56 lb/bu corn, 60 lb/bu wheat, 48 lb/bu barley.
  • Moisture — storage-spec corn is ~14%; mash-ready may be lower.
  • Composition — should close to 100% dry basis.
  • Efficiencies — Saccharification Efficiency (starch→glucose) is set by the Bio-Process Technology; Fermentation Efficiency (glucose→ethanol) is set by the Yeast Strain. Both default to 100% for theoretical runs.

Economics tab

  • Currency — choose USD ($) or EUR (€). When you switch, an editable FX-rate field (€ per $) appears and all entered prices auto-convert.
  • Units — each price row has its own unit dropdown. Selecting EUR defaults the rows to metric (€/L ethanol, €/tonne co-products, €/kg oil, €/tonne grain); USD defaults to US units. You can still override any single row.
  • The Per-batch economics card reports revenue, co-product credits, COGS, net margin and the net ethanol cost-basis — with the value and its unit shown in separate columns, updating live as you change Calculator inputs or prices.

Sustainability tab

  • Unit system — toggle US or Metric. Metric uses MJ/L process energy, kWh/L electricity and L/L water; carbon intensity stays gCO₂e/MJ. Switching converts the entered values and flips each row's unit.
  • Defaults by process — carbon intensity, water and energy defaults populate from the selected Process Type. Use "Reset to process defaults" to restore them; override with measured plant data when available.
  • The Per-batch totals card reports CO₂e emitted, the reduction versus a 94 gCO₂e/MJ gasoline baseline, and total water, energy and electricity.

Validation & reference tools

On the Yield Analysis tab, two collapsible panels sit below the results:

  • Results Validation Test — runs automated stoichiometric and benchmark checks. Click "Run all tests" to see a pass/fail summary; tests temporarily set inputs and restore your current state on completion.
  • Reference Comparison — click "Generate Reference" to capture the current run as a baseline, then change inputs to see the change (Δ) versus the saved reference for ethanol, glucose, CO₂ and yield. "Clear reference" discards the baseline.
Biochemical Pathway · Starch → Glucose → Ethanol
Starch
(C6H10O5)n
Amylose & amylopectin
Glucose
C6H12O6
Fermentable sugar
Ethanol
C2H5OH + CO2↑
Hydrolysis
α-amylase & glucoamylase
+ H2O
x1.11 mass factor
Fermentation
S. cerevisiae (yeast)
anaerobic
x0.511 yield factor
(C6H10O5)n + nH2O → nC6H12O6 α-amylase + glucoamylase C6H12O6 → 2C2H5OH + 2CO2 S. cerevisiae

Mathematical Formulations

Dry mass

All downstream stoichiometry runs on dry-basis mass:

mdry [kg] = mas-received × (1 − M)

where M is moisture mass fraction.

Hydrolysis: starch → glucose

Polymeric starch (anhydroglucose, MW 162.14) is enzymatically converted to free glucose (MW 180.16). Each cleavage adds one water molecule, so glucose mass exceeds starch mass:

hydrolysis factor = 180.16 / 162.14 ≈ 1.11

Fermentation: glucose → ethanol

The Gay-Lussac stoichiometry C6H12O6 → 2 C2H5OH + 2 CO2 sets the upper bound:

ethanol yield factor = (2 × 46.07) / 180.16 ≈ 0.511 CO2 fraction = 1 − 0.511 = 0.489

Process efficiency factors

Real industrial plants run below the maximum. The model uses two independent efficiency stages plus two co-product factors:

etasacch — saccharification efficiency (starch→glucose), set by Bio-Process Technology: Theoretical 100%, Dry Grind 95%, Wet Grind 98% etaferm — fermentation efficiency (glucose→ethanol), set by Yeast Strain: Theoretical Gay-Lussac 100%, real strains 88-93% eta_starch_rec — wet-grind starch recovery to co-products (default 95%) eta_oil_DG — back-end oil extraction, dry-grind only (default 50%)

Process-aware mass balance

mglucose = mdry × (Xstarch × etasacch × 1.11 + Xsugars) methanol = mglucose × etaferm × 0.511 mCO2 = mglucose × etaferm × 0.489

Dry-Grind co-products

m_cornoil_DG = mdry × Xoil × eta_oil_DG mDDGS = mdry × (1 − (Xstarch + Xsugars) × etaferm) − m_cornoil_DG

Wet-Grind co-products

m_cornoil_WG = mdry × Xoil × 0.85 mCGM = mdry × Xprotein × 0.50 mCGF = mdry × ( Xfiber + Xash + Xother + Xstarch × (1 − etastarch) + Xoil × (1 − 0.85) + Xprotein × (1 − 0.50) )

Economic analysis

Revenue, cost of goods sold (COGS) and margin are computed per batch from the current run. Prices may be entered in USD or EUR and in US or metric units; each price is converted to a canonical USD-per-US-unit basis before the math, then results are displayed in the selected currency.

revenueethanol = Vethanol[gal] × priceethanol revenuecoprod = Σ (massi × pricei) revenuetotal = revenueethanol + revenuecoprod costfeed = grain[bu-equiv] × pricefeedstock costconv = Vethanol[gal] × priceconversion COGS = costfeed + costconv margin = revenuetotal − COGS costbasis = (COGS − revenuecoprod) / Vethanol

Currency conversion uses an editable FX rate r (euros per dollar): price€ = price$ × r, and outputs convert back by the same factor. Unit conversions to the canonical basis use 1 gal = 3.78541 L, 1 short ton = 2000 lb, 1 tonne = 2204.62 lb, 1 kg = 2.20462 lb, and grain bushel weights of 56 (corn), 60 (wheat) and 48 (barley) lb/bu.

Sustainability & lifecycle

Carbon, water and energy totals scale with ethanol energy output. Ethanol lower-heating-value energy is taken as 80 MJ/gal:

Eethanol[MJ] = Vethanol[gal] × 80 CO2e[kg] = CI[gCO2e/MJ] × Eethanol / 1000 reduction_vs_gasoline = (1 − CI / 94) × 100% water = waterintensity × Vethanol energy = energyintensity × Vethanol electricity = elecintensity × Vethanol

The 94 gCO₂e/MJ gasoline baseline follows CARB/GREET convention. Carbon intensity is already metric (gCO₂e/MJ); the US/Metric toggle converts the volume-based intensities using 1 gal = 3.78541 L, 1 BTU = 0.00105506 MJ, so BTU/gal → MJ/L and kWh/gal → kWh/L, while the water ratio (gal/gal = L/L) is unit-invariant.

Scientific References

Stoichiometry and grain composition

  1. Watson, S. A., & Ramstad, P. E. (1987). Corn: Chemistry and Technology. AACC.
  2. BeMiller, J. N., & Whistler, R. L. (2009). Starch: Chemistry and Technology (3rd ed.). Academic Press.
  3. Bothast, R. J., & Schlicher, M. A. (2005). Biotechnological processes for conversion of corn into ethanol. Applied Microbiology and Biotechnology, 67(1), 19–25.

Industrial dry-grind ethanol and DDGS

  1. Ingledew, W. M. (2009). The Alcohol Textbook (5th ed.). Nottingham University Press.
  2. Kwiatkowski, J. R., et al. (2006). Modeling the corn dry-grind ethanol process. Industrial Crops and Products, 23(3), 288–296.
  3. Belyea, R. L., Rausch, K. D., & Tumbleson, M. E. (2004). Composition of corn and DDGS from dry-grind. Bioresource Technology, 94(3), 293–298.
  4. Liu, K. (2011). Chemical composition of distillers grains, a review. J. Agric. Food Chem., 59(5), 1508–1526.

Back-end corn oil extraction

  1. Wang, H., et al. (2008). Decantation method to recover oil and protein from thin stillage. JAOCS, 85(11), 1077–1085.
  2. Moreau, R. A., et al. (2011). Distribution changes in dry-grind ethanol process. JAOCS, 88(7), 911–917.

Wet-milling and corn refining

  1. Johnson, L. A., & May, J. B. (2003). Wet milling: corn biorefineries. In Corn: Chemistry and Technology, 449–494.
  2. Rausch, K. D., & Belyea, R. L. (2006). Co-products from corn processing. Applied Biochemistry and Biotechnology, 128(1), 47–86.
  3. Singh, V., & Eckhoff, S. R. (1996). Germ recovery parameters in wet milling. Cereal Chemistry, 73(6), 716–720.

Economic Analysis

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Per-batch revenue · COGS · margin  |  Prices reference CBOT · ICE · Euronext · USDA AMS

Live revenue, cost-of-goods-sold, and margin for the current Calculator run, with co-product credits and per-bushel-equivalent breakdown. Adjusts as you change Calculator inputs.

Revenue, cost-of-goods-sold (COGS), and net margin from the current calculator run, using user-supplied commodity prices. Co-product credits reduce the effective ethanol cost-basis. Default prices are illustrative — adjust to your contract/market.

Prices (user input)$ INPUT
Currency
FX rate i
€ per $
Ethanol price ($/gal)
DDGS price ($/ton)
Corn oil price ($/lb)
CGM price ($/ton)
CGF price ($/ton)
Feedstock cost ($/bu) i
Conversion cost ($/gal EtOH) i
Per-batch economics$ OUTPUT
Ethanol volume–gal
Grain (equivalent)–bu
Ethanol revenue–$
Co-product revenue–$
Total revenue–$
Feedstock cost–$
Conversion cost–$
Total COGS–$
Net margin–$
Margin per grain unit–$/bu
Net ethanol cost-basis i–$/gal

Co-product values reflect the current Calculator run. Adjusting prices here updates these figures live; adjusting calculator inputs (Calculator tab) cascades through.

Sustainability & Lifecycle Metrics

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Carbon · Water · Energy  |  Defaults from Argonne GREET · CARB CA-GREET literature

Carbon intensity, water use, and process energy for the current Calculator run. Defaults adjust automatically with Process Type; override with measured plant data when available.

Carbon intensity, water consumption, and process energy for the current run. Defaults adjust automatically when you change Process Type on the Calculator tab; override with measured plant data when available.

Process intensity (user-editable)US UNITS
Unit system
Carbon intensity (gCO₂e/MJ) i
gCO₂e/MJ
Water consumption (gal H₂O/gal) i
Process energy (BTU/gal) i
Electricity (kWh/gal)
Per-batch totalsOUTPUT
Ethanol volume–gal
Ethanol energy content (LHV)–MJ
Total CO₂e emitted–kg
vs. gasoline (94 gCO₂e/MJ)–% redux
Total water–gal
Total process energy–MMBtu
Total electricity–kWh

LHV ethanol = 80 MJ/gal (76,300 BTU/gal). RFS pathway: corn-starch ethanol qualifies as D6 Renewable Fuel; advanced/cellulosic categories require alternate feedstocks. Defaults are illustrative; for compliance-grade analysis use plant-measured data and a CARB CA-GREET or Argonne GREET model run.

Yeast Inoculum & Seed Train Calculator — Ethanol Fermentation

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Inoculum Design S. cerevisiae  |  v26.90 · Performance Mode

Staged seed-train sizing — Fermentation (direct inoculation) · Pre-Fermentation · HDYC — with viability, transfer efficiency, costs, sensitivity analysis, strain comparison, and exportable batch records.

Commercial Yeast Inoculum — Format & Quality
Sets Total Volume below from the Medium Formulations tab's working volume and this tab's working-volume %.
Ethanol Fermentation Ferm
Fermenter Fill Cycle & Yeast Transfer
Fermentation Yeast Growth
Ethanol Fermentation Ferm
▼Sensitivity — Viability & Cells/g

Strain Comparison

Strain A

Namei
Formati
Viable Cellsi
Moisturei
Viabilityi
Cost/kg ($)i
Mass Requiredi
Total Cost ($)i

Strain B

Namei
Formati
Viable Cellsi
Moisturei
Viabilityi
Cost/kg ($)i
Mass Requiredi
Total Cost ($)i

Seed-Train Summary

Inoculum & Seed Train Calculator — User Guide Guide

Purpose

Sizes yeast inoculation across three seed-train topologies for industrial S. cerevisiae ethanol fermentation — direct-inoculation, propagation, and staged HDYC → Pre-Fermentation → Fermentation. Includes realistic production considerations: viability, transfer efficiency between stages, three growth-kinetic models (Logistic / Gompertz / Exponential) with model-aware specific-growth-rate definitions, an oxygen-regime-dependent carrying capacity entered directly in cells/mL, in-fermenter growth prediction during the 18–22 h active growth window, fill-cycle geometry for semi-batch operation, strain-to-strain cost comparison, and full batch-record export.

Core workflow

  1. Select Technology — Direct inoculation, Propagation, or HDYC + Pre-Fermentation (staged).
  2. Select Mode — five modes (detailed below): Fermentation Baseline Design, HDYC Forward, Capacity, HDYC Performance, and HDYC Bioreactor Design. The last three are available only in the HDYC topology.
  3. Set commercial yeast format — ADY (dry) or CmY (cream). The carrying capacity is entered in cells/mL (format-independent); only the derived g/L display changes with format (ADY:CmY ≈ 1:5.5).
  4. Enter fermenter geometry — total volume and working-volume %. Set Process Strategy: Semi-Batch (progressive fill with pulsed inoculation — Fill Cycle section active) or Batch (instantaneous charge and inoculation — Fill Cycle hidden).
  5. Expand the Fermentation Yeast Growth section. Set Calculations Mode (Diagnostic / Target), Growth Kinetics (Logistic / Gompertz / Exponential), and kinetic parameters (µ, tgrowth, Carrying Capacity Xmax, λ if Gompertz).
  6. Set Inoculum Target Xi — lives inside the Yeast Growth section. In Diagnostic mode Xi is user-editable; in Target mode enter a Target Xf (end-of-growth density) and Xi becomes derived.
  7. Tune upstream stages (Propagation or HDYC + Pre-Ferm). Each stage independently sets Process Type, Process Strategy, time, µ, transfer efficiency η, kinetic model, carrying capacity (cells/mL), and λ.
  8. Review outputs — stage masses, Z generation counts with color gauge, Xmax utilization, verdict banner on end-of-growth density (healthy range 1–3×10⁸ cells/mL), fed-batch feed profile, per-stage sensitivity tables, fill-cycle peak Xi and dilution factor.
  9. Export — CSV or print-ready batch record.

The five calculation modes

  • Fermentation Baseline Design (default; all topologies) — you know the target Xi and fermenter volume; back-calculate up the seed train to find commercial yeast required. Transfer efficiency and kinetics at each upstream stage scale the demand. Yeast Growth forward-models what Xi becomes after the 18–22 h growth window (Diagnostic), or back-calculates Xi from a target Xf (Target).
  • HDYC Forward (HDYC only) — the inverse of Design. You know the physical assets: commercial seed culture mass, HDYC / Pre-Ferm / Fermenter volumes, and kinetics. Forward-compute the resulting Xi at the fermenter. Answers "given these tanks and this commercial purchase, what inoculum density will I actually achieve?" HDYC Seed Culture becomes editable; Ferm Xi becomes derived.
  • Capacity (all applicable topologies) — you know your commercial yeast inventory and target Xi; compute the maximum fermenter working volume that inventory can support. Yeast mass becomes the input, working volume the output.
  • HDYC Performance (max Xi, ferm) (HDYC only) — drives every stage to its carrying-capacity ceiling (Xmax) to find the highest achievable fermenter Xi, and reports the commercial HDYC inoculum required to reach that maximum. Requires a ceiling model (Logistic or Gompertz) — Exponential has no ceiling and is rejected.
  • HDYC Bioreactor Design (HDYC only) — the full process-design mode. Maximizes biomass at HDYC and Pre-Ferm (like Performance), and adds two Pre-Ferm behaviors: a viability balance readout (viability declines as the stage is pushed to its ceiling — reports biomass, resulting viability, and viable transfer mass) and a conditioning factor C (0–1; computed from Pre-Ferm Process Type + residence time, user-overridable). Conditioning auto-adjusts the fermentation-stage kinetics: λferm = λbase·(1 − C) and µferm = µbase·(1 + 0.20·C). Also requires Logistic or Gompertz.

Fermentation Yeast Growth

Forward-models (or back-calculates) yeast growth during the active growth window of ethanol fermentation — typically the first 18–22 h when cells divide. After this window, ethanol accumulation (~5–8% v/v) and substrate/nutrient depletion halt cell division even though ethanol production continues for another 30–50 h in stationary phase.

  • Diagnostic mode (default) — enter an Assumed Xi at completed yeast transfer; the model runs it forward to the end-of-growth density and flags whether that lands in the industrial healthy range (1–3×10⁸ cells/mL). The Inoculum Target row echoes the Xi in use.
  • Target mode — you specify Target Xf (desired end-of-growth density); back-calc the required Xi so the seed train sizes to produce that inoculum. Target Xf row appears; top-of-section Xi becomes read-only and derived.
  • Three kinetic models — Logistic (sigmoidal approach to Xmax, default); Gompertz (Logistic + explicit lag phase λ for rehydration / anaerobic adaptation); Exponential (no ceiling — a rough comparison case, used only with an average µ over the full window).
  • In HDYC Forward, HDYC Performance, and HDYC Bioreactor Design modes, Target is disabled (Xi is already determined by the forward chain or by driving to maximum biomass).

Carrying capacity (Xmax) — entered in cells/mL, regime-dependent

Each stage's carrying capacity is the maximum viable cell density it can sustain at stationary phase — the ceiling the Logistic/Gompertz models approach. It is entered directly in cells/mL (matching the cell-density basis of the targets), and the equivalent g/L product-mass value is shown read-only beside it. Because cells are cells regardless of product form, the cells/mL value does not change with ADY/CmY format — only the g/L display does.

Carrying capacity depends on the oxygen regime (the stage's Process Type): aerobic respiratory growth sustains the highest density, Fermento-Respiratory intermediate, anaerobic fermentation the lowest. The default carrying capacity adapts to the selected Process Type (aerobic ≈ 1.2×10⁹, Fermento-Respiratory ≈ 1.0–0.8×10⁹, fermentation ≈ 0.5×10⁹ cells/mL); custom values you enter are preserved when the regime changes.

Model-aware specific growth rate (µ)

The meaning of µ differs by model, so the symbol and callout update with the selected kinetics:

  • Logistic → µi (intrinsic) — the rate at low density in dX/dt = µ·X·(1 − X/Xmax); the realized rate declines toward zero as biomass nears Xmax.
  • Gompertz → µmax — the maximum specific growth rate, the slope at the curve's inflection point (Zwietering parameterization).
  • Exponential → µavg — the average rate over the full window, µavg = ln(Xf/Xi)/t. Not a peak rate; use the realized average (typically well below the Logistic/Gompertz peak).

Switching model auto-adjusts the µ default to a model-appropriate value (peak for Logistic/Gompertz, lower average for Exponential); a custom µ you typed is preserved.

Fill cycle (Semi-Batch only)

The Fill Cycle collapsible section (below Yeast Growth, collapsed by default) describes how the fermenter fills while yeast is pulsed in as a short transfer. Outputs include Peak Xi during fill (when all cells are in but the tank isn't yet full) and Fill Dilution Factor. Not relevant for Batch strategy — section hides when Strategy = Batch since the inoculation is instantaneous.

Kinetic models per stage

Propagation, Pre-Fermentation, HDYC, and Fermentation Yeast Growth each have their own independent kinetics dropdown (Logistic / Gompertz / Exponential), carrying capacity (cells/mL), and λ inputs — full parity across stages. Choose Logistic when a biomass ceiling is realistic (all staged-production vessels); add Gompertz lag when rehydrated ADY needs 1–3 h to ramp up; use Exponential only as a no-ceiling comparison with an average µ.

Typical defaults (Logistic kinetics)

  • Fermentation Yeast Growth: µi = 0.30 hr⁻¹, tgrowth = 20 h, carrying capacity = 3.0×10⁸ cells/mL (15 g DCW/L), λ = 2 h — industrial-strain anaerobic grain ferm. The fermenter carrying capacity is expressed as dry-cell-weight (DCW), format-independent.
  • Propagation: µi = 0.35 hr⁻¹, t = 8 h, carrying capacity ≈ 0.8×10⁹ cells/mL (Fermento-Respiratory), λ = 1 h.
  • Pre-Fermentation: µi = 0.35 hr⁻¹, t = 8 h, carrying capacity ≈ 0.8×10⁹ cells/mL (Fermento-Respiratory), λ = 1 h.
  • HDYC: µi = 0.25 hr⁻¹, t = 8 h, carrying capacity ≈ 1.2×10⁹ cells/mL (aerobic fed-batch), λ = 1.5 h.
  • Fill cycle: tfill = 8 h, txferStart = 0.5 h, txferDuration = 45 min, heel = 0% — typical dry-grind semi-batch.

Common pitfalls

  • Growth-window duration ≠ fermentation duration. The 20 h default is the active cell-division window, NOT the 48–72 h full ferm run. Cells divide early; ethanol-production output continues long after division stops.
  • Viability only applies at the commercial-yeast purchase point. In direct inoculation, that's the Ferm inoculum; in staged modes, it's the upstream-most starter (Propagation or HDYC). Intermediate stages use viable biomass with no further viability scaling.
  • Transfer efficiency stacks. In staged modes, each boundary multiplies demand by 1/η. Three stages at 99% each = 1.0304× multiplier relative to ideal.
  • Kinetic ceiling matters. If Xi ≥ Xmax for a Logistic/Gompertz stage, back-calc is infeasible. Raise carrying capacity, raise working volume, or lower demand.
  • Carrying capacity is a physical cell density. Enter it in cells/mL; it does not change with ADY/CmY format. The default adapts to the stage's Process Type (oxygen regime); custom values are preserved on regime change.
  • Performance and Bioreactor Design need a ceiling model. They drive stages to Xmax, which Exponential lacks — those modes require Logistic or Gompertz and reject Exponential.
  • Match µ to the model. µ means the intrinsic rate (Logistic), the inflection-point maximum (Gompertz), or the full-window average (Exponential) — the symbol shows which.

Inoculum & Seed Train — Mathematical Formulations Science

Viability — applied only at the commercial purchase point

Viability is a specification of commercial yeast (ADY or CmY): the fraction of total cells/g that are metabolically active. Dead cells don't multiply during propagation and don't ferment. Viability therefore affects one thing only — how much commercial yeast must be purchased to deliver the required number of viable cells to the stage that receives it.

Fermenter cell concentration is determined by inoculum target Xi and working volume V alone, not by the commercial viability spec.

Direct inoculation (Ferm is the purchase point):
mcommercial (g) = (Xi · Vw,mL) / (ncells/g · vviability)
Staged (propagation or HDYC chain):
mFerm inoculum, viable (g) = (Xi · Vw,mL) / ncells/g ← no viability

The biomass arriving at Ferm is fresh propagate from the upstream stage — assumed essentially 100% viable. Viability of commercial yeast enters only at the most upstream stage (the seed culture that IS purchased).

mcommercial seed culture (g) = mstage initial, viable / vviability

Three kinetic models per stage

Propagation, Pre-Fermentation, HDYC, and Fermentation Yeast Growth each independently select from Logistic, Gompertz, or Exponential (full parity across all stages). Each has a forward (Xi → Xf) and inverse (Xf → Xi) formulation used by Design back-calc, Target back-calc, and the forward/performance modes.

Model-aware specific growth rate (µ)

µ is not the same quantity in every model, so the calculator labels it accordingly:

  • µi (Logistic) — intrinsic/initial rate; the maximum the culture achieves, at low density.
  • µmax (Gompertz) — maximum specific growth rate, the tangent slope at the inflection point (Zwietering form).
  • µavg (Exponential) — time-averaged rate over the full window, µavg = ln(Xf/Xi)/t.
Exponential (no ceiling — average µ)
Xf = Xi · exp(µavg · t) ⟺ Xi = Xf / exp(µavg · t)

A no-ceiling comparison case. It is only honest when µ is the average rate over the full growth time (µavg = ln(Xf/Xi)/t) — feeding it a peak/intrinsic rate over the full window overshoots reality. It does not apply to the HDYC Performance or Bioreactor Design modes, which require a finite ceiling.

Logistic (default)

Sigmoidal growth toward an empirical ceiling Xmax that lumps ethanol inhibition, substrate depletion, oxygen limitation, and nutrient exhaustion:

dX/dt = µi · X · (1 − X / Xmax)

Closed-form forward and inverse solutions:

X(t) = X0 · Xmax / [ X0 + (Xmax − X0) · exp(−µ·t) ]
X0 = Xf / [ exp(µ·t) − (Xf/Xmax)·(exp(µ·t) − 1) ]
Gompertz (Zwietering modified)

Adds an explicit lag phase λ before exponential entry — captures rehydration, anaerobic adaptation, or stress recovery. µ here is the inflection-point maximum µmax:

X(t) = X0 · (Xmax/X0)G(t), G(t) = exp(−exp(µmax·e · (λ − t)/A + 1)), A = ln(Xmax/X0)

The forward function is monotone in X0; the inverse is solved by bisection on X0 ∈ (0, Xf] to machine precision (no closed form exists).

Generation count Z

Z = log2(Xf / Xi)

Valid across all three kinetic models. For Exponential reduces to Z = µavg·t / ln(2).

Fermentation Yeast Growth

The active growth window is the first 18–22 h of fermentation when cells divide; after this the culture is stationary-phase and ethanol production continues without further division for another 30–50 h. The calculator forward-models (Diagnostic) or back-calculates (Target) this window only.

Mass ⇄ cell-density conversion
Mkg = Xcells/mL · VL / ncells/g ⟺ Xcells/mL = Mkg · ncells/g / VL

For the seed-train stages, biomass is tracked in the format-consistent product-mass basis (kg ADY or kg CmY) and ncells/g is format-aware via the Yeast Format selector. For Fermentation Yeast Growth, biomass is tracked in dry-cell-weight (DCW) using the fixed dry-cell reference, so the in-fermenter growth result is the same regardless of which product is purchased.

Diagnostic mode (forward)

Given Xi at completed yeast transfer, forward-model to end-of-growth density Xf,growth. Verdict compares Xf,growth against the healthy industrial range 1–3×10⁸ cells/mL.

Target mode (back-calc)

User specifies Target Xf (desired end-of-growth density); inverse kinetic solves for required Xi, which then drives upstream seed-train sizing. Infeasibility is flagged when Target Xf ≥ Xmax,ferm.

HDYC Forward chain (HDYC topology)

Given commercial seed culture mass and HDYC/Pre-Ferm/Ferm volumes + kinetics, forward-compute through the chain:

X0,HDYC = mcomm · vviab
Xend,HDYC = forward(X0,HDYC, µHDYC, tHDYC, Xmax,HDYC, λHDYC)
X0,PF = Xend,HDYC · ηHDYC
Xend,PF = forward(X0,PF, µPF, tPF, Xmax,PF, λPF)
mpitch,ferm = Xend,PF · ηPF
Xi,ferm = mpitch,ferm · ncells/g / Vferm,L

Infeasibility at any stage (X0 ≥ Xmax) halts the chain with a descriptive error. Saturation (Xend > 0.98·Xmax) triggers a soft warning — the stage has no headroom and more time won't yield more biomass.

Transfer efficiency

ηk captures physical losses (residual in lines, transfer pumps, etc.) at stage boundary k. In back-calc direction, upstream viable biomass demand scales by 1/η. In forward direction, transferred mass scales by η directly.

Capacity mode (reverse direction)

Given available yeast mass mavailable and target Xi:

Vw,max (mL) = (mavailable (g) · ncells/g · vviab,eff) / Xi

vviab,eff is commercial viability in direct-inoculation mode, 1 in staged modes (where the available mass represents propagated biomass).

Fill-cycle geometry (Semi-Batch only)

Fermenter fills linearly from Vheel to Vworking over tfill hours. Yeast is pulsed in over txfer starting at txferStart. Peak cell density occurs at transfer-complete (all cells in, minimum volume):

Vfill-frac(t) = Vheel + (1 − Vheel) · t / tfill
V@xferEnd = Vworking · Vfill-frac(txferStart + txfer)
Peak Xi = (Xi,target · Vworking) / V@xferEnd
Dilution factor = Vworking / V@xferEnd = Peak Xi / Xi,target

At Batch strategy the fill cycle is instantaneous; this section is hidden and values display em-dashes. Current model treats growth during fill as negligible — realistic for short transfers and dilute early-fill conditions; a µfill overlay could be added in a future build.

Fed-batch feed profile (staged modes)

For biomass balance dX/dt = µ·X at constant µ:

F(t) = µ · V · Xviable(t) / (Yx/s · Sfeed)

Peak feed rate is at t = tend. Total sugar delivered:

Stotal = Xi,viable · V · (eµt − 1) / Yx/s

Process Type and Process Strategy (all stages user-controlled)

Each upstream stage (Propagation, Pre-Fermentation, HDYC) exposes a user-selected Process Type (oxygen regime: aerobic / Fermento-Respiratory / fermentation) and Process Strategy (Batch / Semi-Batch / Fed-Batch). The Process Type sets the carrying-capacity default for that stage's oxygen regime; the Process Strategy controls the fed-batch feed-profile panel. None of these is auto-classified from µ — they are physically determined by operator choice, so the calculator leaves them under user control.

For reference, the respirofermentative transition for S. cerevisiae sits near a critical specific growth rate µcrit ≈ 0.27 hr⁻¹ (Crabtree-on above, substrate-limited respiratory below) — useful when choosing an aerobic fed-batch feed rate, but applied as guidance, not an automatic switch.

Ethanol yield vs biomass yield — metabolic mode and feeding strategy

Ethanol and biomass compete for the same carbon, so the useful design ratio is ethanol produced per unit biomass formed, Yp/x = Yp/s ÷ Yx/s. Which metabolic mode dominates — and therefore where Yp/x lands — is set by the residual glucose concentration the cells experience, with oxygen as a permissive (not forcing) factor. The feeding strategy is simply the lever that controls glucose.

Yield ranges by metabolic mode
  • Fully fermentative (anaerobic) — Yx/s ≈ 0.08–0.12 g DCW/g glucose (little carbon to cells); Yp/s ≈ 0.42–0.48 g EtOH/g glucose (90–95% of the 0.511 theoretical max). Ethanol per biomass ≈ 4–6 g EtOH/g DCW (higher in optimized VHG systems where biomass is deliberately minimized).
  • Fermento-respiratory (micro-aerobic, mixed) — Yx/s ≈ 0.15–0.30 g DCW/g glucose (more carbon to cells); Yp/s ≈ 0.25–0.40 g EtOH/g glucose (some carbon fully oxidized to CO₂). Ethanol per biomass ≈ 1–2.5 g EtOH/g DCW.

In round terms, fully fermentative metabolism yields roughly 2–4× more ethanol per unit biomass than fermento-respiratory — the reason production fermenters run anaerobically while oxygen is confined to the propagation / seed train, where biomass is the goal.

Critical concentration parameters
  • Glucose — Crabtree threshold ≈ 0.1–0.15 g/L (~0.5–1 mM). Above this residual glucose, S. cerevisiae ferments to ethanol even under full aeration (overflow metabolism — respiratory capacity is saturated and excess flux spills to ethanol). Below it, the cell respires fully and makes biomass. Aerobic fed-batch biomass production is fundamentally an exercise in feeding glucose to keep residual concentration under this threshold; the associated critical rate is µcrit ≈ 0.25–0.28 hr⁻¹.
  • Oxygen — dissolved O₂ and transfer rate. Respiratory (biomass) metabolism needs DO above ~5–20% of saturation and an oxygen transfer rate (OTR / kLa) high enough to meet the cells' uptake at the target density — high-density culture is usually OTR-limited. Critically, oxygen alone does not force respiration: high glucose overrides high oxygen via the Crabtree effect, so you need both low glucose and adequate O₂. For ethanol production O₂ is kept near zero, though trace micro-aeration is sometimes supplied because the yeast needs a little O₂ to synthesize sterols and unsaturated fatty acids for membrane integrity and ethanol tolerance — exactly the fermento-respiratory niche, trading a little ethanol yield for more robust cells.
Summary — feeding system, metabolic mode, and ethanol/biomass
SystemGlucose regimeO₂ regimeDominant metabolismEtOH/biomass (g/g)
BatchHigh throughoutLow (anaerobic)Fermentative~4–6
Semi-BatchVaries with fillLow–microMostly fermentative~3–6
Fed-BatchHeld below ~0.1 g/LAerated (high OTR)RespiratoryLow; ~1–2
Fed-Batch, micro-aeratedLow–moderateTrace / microFermento-respiratory~1.5–2.5

Unifying principle: glucose concentration sets the metabolic mode via the Crabtree threshold; oxygen enables (but does not force) respiration; the feeding system is the lever for controlling glucose. Ethanol-per-biomass is maximized by keeping glucose high and oxygen low (batch / anaerobic); biomass is maximized by keeping glucose low and oxygen high (aerobic fed-batch). Values are literature-typical ranges for S. cerevisiae — they shift with strain, temperature, gravity, and nutrient status, so calibrate against plant-specific data for design.

Batch vs Semi-Batch strategy (Fermentation)

  • Semi-Batch — fermenter fills over tfill while yeast is pulsed in. Fill Cycle section active.
  • Batch — full charge at t=0, instantaneous inoculation. Fill Cycle section hidden; Xi is the inoculum density at t=0. This is the one case where Xi and XEF coincide, because the transfer completes at the full working volume.

Yeast Growth math is identical in both strategies — the distinction affects fill dynamics, not post-fill growth.

Carrying capacity Xmax — cells/mL primary, regime-dependent

Each stage's carrying capacity is entered as a viable cell density (cells/mL) and is the ceiling the Logistic/Gompertz models approach. The g/L product-mass equivalent is derived and shown read-only:

g/L (product) = Xmax,cells/mL · 1000 / ncells/g

Because ncells/g is format-aware, the displayed g/L changes with ADY/CmY (≈1:5.5) while the cells/mL value — a physical density — stays fixed. The default carrying capacity adapts to the stage's oxygen regime (Process Type):

  • Aerobic ≈ 1.2×10⁹ cells/mL · Fermento-Respiratory ≈ 1.0–0.8×10⁹ · Fermentation ≈ 0.5×10⁹

Custom values are preserved when the regime changes (only recognized regime defaults auto-swap).

Fermenter carrying capacity in dry-cell-weight (DCW)

The Fermentation Yeast Growth carrying capacity is internally a dry-cell-weight density (g DCW/L) using the fixed dry-cell reference (≈2×10¹⁰ cells/g dry), so the in-fermenter growth model is independent of whether ADY or CmY is purchased — a fermenter's living-biomass ceiling is a physical quantity, not a product-mass quantity. The cells/mL ⇄ g DCW/L conversion uses that fixed reference, not the format-aware product cells/g.

HDYC Performance and Bioreactor Design (drive-to-maximum modes)

Both modes drive each stage to a high fraction (99%) of its carrying capacity and chain forward to the fermenter, reporting the maximum achievable Xi and the commercial HDYC inoculum required. They require a finite ceiling (Logistic or Gompertz) — Exponential is rejected.

Bioreactor Design adds Pre-Ferm conditioning and viability balance:

viabilityPF = v0 · (1 − K · util²), util = Xend/Xmax (K ≈ 0.12)
C = conditioning factor ∈ [0,1] (computed from Pre-Ferm regime × residence-time, or user override)
λferm = λbase · (1 − C)
µferm = µbase · (1 + 0.20 · C)

Conditioning models fermentative adaptation: a well-conditioned inoculum (C→1) enters the fermenter with reduced lag and a higher early rate. These relationships are gentle, monotonic engineering correlations — tunable in one constants block — not a mechanistic metabolic model.

Sig-fig display

Outputs use 3 significant figures: formatSigFigs(1556.73, 3) = "1560", formatSigFigs(0.00423, 3) = "0.00423". Avoids misleading 2-decimal precision across 6 orders of magnitude.

Tolerant number parser

The inoculum input accepts: 10E6, 1e7, 10M, 10,000,000, 10 000 000, 1.0e+07. Internal canonical: scientific notation with uppercase E.

Sensitivity analysis

Per-stage sensitivity tables vary ±10% and ±20% on one parameter (µ or t) holding all else fixed, reporting the corresponding change in Xi mass in the display convention for that stage (commercial purchase for the upstream-most stage, viable biomass for intermediate). Intended as quick-and-dirty "how sensitive am I to this choice?" not a full Monte-Carlo.

Scope and caveats

  • Kinetic models are lumped — Xmax absorbs ethanol inhibition, substrate depletion, O2 limitation, and nutrient exhaustion empirically without modeling them separately. For full mechanistic modeling (Monod, Levenspiel product inhibition, Yx/s-vs-µ Crabtree coupling), use the FermAxiom Ethanol Time-Course Simulator.
  • Yeast Growth assumes cells stop dividing at tgrowth (default 20 h) — consistent with industrial observation that ethanol accumulation halts division by hour 18–22. The rest of the ferm run is stationary-phase and not modeled here.
  • Fill cycle treats biomass as purely volumetric (no growth during fill). Realistic for short transfers; a µfill kinetic overlay would refine this if needed.
  • Fed-batch feed profile assumes constant µ throughout the stage — in reality, µ may drift.
  • Strain comparison is mass/cost only; physiological differences (stress tolerance, flocculation, byproduct profile) are not modeled.
  • Fresh propagate is assumed ~100% viable; real propagated biomass typically has 95%+ viability but the commercial-viability specification does not apply to it.

Scientific References References

This calculator's formulations, default values, and physiological assumptions draw on the peer-reviewed literature and standard industry references below. Entries are grouped by topic and ordered by date within each group.

Growth kinetics — exponential, logistic, Gompertz

  1. Monod, J. (1949). The growth of bacterial cultures. Annual Review of Microbiology, 3(1), 371–394.
  2. Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & van 't Riet, K. (1990). Modeling of the bacterial growth curve. Applied and Environmental Microbiology, 56(6), 1875–1881.
  3. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583.
  4. Verhulst, P. F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique, 10, 113–121. (Original logistic-growth formulation.)
  5. Buchanan, R. L., Whiting, R. C., & Damert, W. C. (1997). When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiology, 14(4), 313–326.

Saccharomyces cerevisiae physiology and fermentation

  1. Pirt, S. J. (1975). Principles of Microbe and Cell Cultivation. Blackwell Scientific Publications, Oxford. (Classic text for maintenance coefficient, biomass yield YX/S, specific growth rate µ.)
  2. Bailey, J. E. & Ollis, D. F. (1986). Biochemical Engineering Fundamentals (2nd ed.). McGraw-Hill, New York.
  3. van Dijken, J. P., Weusthuis, R. A., & Pronk, J. T. (1993). Kinetics of growth and sugar consumption in yeasts. Antonie van Leeuwenhoek, 63(3–4), 343–352.
  4. Pronk, J. T., Steensma, H. Y., & van Dijken, J. P. (1996). Pyruvate metabolism in Saccharomyces cerevisiae. Yeast, 12(16), 1607–1633.
  5. Walker, G. M. (1998). Yeast Physiology and Biotechnology. John Wiley & Sons, Chichester.
  6. Walker, G. M. & Stewart, G. G. (2016). Saccharomyces cerevisiae in the production of fermented beverages. Beverages, 2(4), 30.

Crabtree effect and overflow metabolism

  1. De Deken, R. H. (1966). The Crabtree effect: a regulatory system in yeast. Journal of General Microbiology, 44(2), 149–156.
  2. Postma, E., Verduyn, C., Scheffers, W. A., & van Dijken, J. P. (1989). Enzymic analysis of the Crabtree effect in glucose-limited chemostat cultures of Saccharomyces cerevisiae. Applied and Environmental Microbiology, 55(2), 468–477.
  3. Sonnleitner, B. & Käppeli, O. (1986). Growth of Saccharomyces cerevisiae is controlled by its limited respiratory capacity: formulation and verification of a hypothesis. Biotechnology and Bioengineering, 28(6), 927–937.

Industrial ethanol fermentation — fuel ethanol, VHG, dry-grind

  1. Ingledew, W. M. (1999). Alcohol production by Saccharomyces cerevisiae: a yeast primer. In: The Alcohol Textbook (3rd ed.), Nottingham University Press, Nottingham, UK.
  2. Jacques, K. A., Lyons, T. P., & Kelsall, D. R. (eds.) (2003). The Alcohol Textbook (4th ed.). Nottingham University Press, Nottingham, UK.
  3. Bayrock, D. P. & Ingledew, W. M. (2001). Application of multistage continuous fermentation for production of fuel alcohol by very-high-gravity fermentation technology. Journal of Industrial Microbiology and Biotechnology, 27(2), 87–93.
  4. Bai, F. W., Anderson, W. A., & Moo-Young, M. (2008). Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnology Advances, 26(1), 89–105.
  5. Puligundla, P., Smogrovicova, D., Obulam, V. S. R., & Ko, S. (2011). Very high gravity (VHG) ethanolic brewing and fermentation: a research update. Journal of Industrial Microbiology and Biotechnology, 38(9), 1133–1144.
  6. Basso, L. C., Basso, T. O., & Rocha, S. N. (2011). Ethanol production in Brazil: the industrial process and its impact on yeast fermentation. In: Biofuel Production — Recent Developments and Prospects, IntechOpen, pp. 85–100.
  7. Lopes, M. L., Paulillo, S. C. L., Godoy, A., Cherubin, R. A., Lorenzi, M. S., Giometti, F. H. C., Bernardino, C. D., Amorim Neto, H. B., & Amorim, H. V. (2016). Ethanol production in Brazil: a bridge between science and industry. Brazilian Journal of Microbiology, 47(Suppl 1), 64–76.

Active dry yeast (ADY) — rehydration, viability, cells per gram

  1. Beker, M. J. & Rapoport, A. I. (1987). Conservation of yeasts by dehydration. Advances in Biochemical Engineering/Biotechnology, 35, 127–171.
  2. Attfield, P. V. (1997). Stress tolerance: the key to effective strains of industrial baker's yeast. Nature Biotechnology, 15(13), 1351–1357.
  3. Bayrock, D. P. & Ingledew, W. M. (1997). Mechanism of viability loss during fluidized bed drying of baker's yeast. Food Research International, 30(6), 417–425.
  4. Rodríguez-Porrata, B., Novo, M., Guillamón, J. M., Rozès, N., Mas, A., & Cordero Otero, R. (2008). Vitality enhancement of the rehydrated active dry wine yeast. International Journal of Food Microbiology, 126(1–2), 116–122.
  5. Pérez-Torrado, R., Gamero, E., Gómez-Pastor, R., Garre, E., Aranda, A., & Matallana, E. (2015). Yeast biomass, an optimised product with myriad applications in the food industry. Trends in Food Science & Technology, 46(2), 167–175.

Viability measurement — methylene blue, flow cytometry

  1. Lee, S. S., Robinson, F. M., & Wang, H. Y. (1981). Rapid determination of yeast viability. Biotechnology and Bioengineering Symposium, 11, 641–649.
  2. Boyd, A. R., Gunasekera, T. S., Attfield, P. V., Simic, K., Vincent, S. F., & Veal, D. A. (2003). A flow-cytometric method for determination of yeast viability and cell number in a brewery. FEMS Yeast Research, 3(1), 11–16.
  3. Kwolek-Mirek, M. & Zadrag-Tecza, R. (2014). Comparison of methods used for assessing the viability and vitality of yeast cells. FEMS Yeast Research, 14(7), 1068–1079.
  4. American Society of Brewing Chemists (ASBC) Methods of Analysis, Yeast-3: Yeast Stains; Yeast-4: Microscopic Yeast Cell Counting. (Current revision.)

Inoculum / inoculation rate — brewing and fuel-ethanol practice

  1. Verbelen, P. J., Dekoninck, T. M. L., Saerens, S. M. G., Van Mulders, S. E., Thevelein, J. M., & Delvaux, F. R. (2009). Impact of pitching rate on yeast fermentation performance and beer flavour. Applied Microbiology and Biotechnology, 82(1), 155–167.
  2. Erten, H., Tanguler, H., & Cakıroz, H. (2007). The effect of pitching rate on fermentation and flavour compounds in high gravity brewing. Journal of the Institute of Brewing, 113(1), 75–79.
  3. Briggs, D. E., Boulton, C. A., Brookes, P. A., & Stevens, R. (2004). Brewing: Science and Practice. Woodhead Publishing, Cambridge. (Standard reference for inoculation-rate calculations and seed-train design.)

Fed-batch fermentation kinetics and feed-profile design

  1. Yamanè, T. & Shimizu, S. (1984). Fed-batch techniques in microbial processes. Advances in Biochemical Engineering/Biotechnology, 30, 147–194.
  2. Fiechter, A., Fuhrmann, G. F., & Käppeli, O. (1981). Regulation of glucose metabolism in growing yeast cells. Advances in Microbial Physiology, 22, 123–183.
  3. Enfors, S.-O. (2011). Fermentation Process Engineering. Royal Institute of Technology (KTH), Stockholm. (Reference text for exponential fed-batch feed profiles F = µXV / (YX/S · Sfeed).)

Seed-train design and scale-up

  1. Humphrey, A. E. (1998). Shake flask to fermentor: what have we learned? Biotechnology Progress, 14(1), 3–7.
  2. Junker, B. H. (2004). Scale-up methodologies for Escherichia coli and yeast fermentation processes. Journal of Bioscience and Bioengineering, 97(6), 347–364.
  3. Wang, G., Haringa, C., Noorman, H., Chu, J., & Zhuang, Y. (2020). Developing a computational framework to advance bioprocess scale-up. Trends in Biotechnology, 38(8), 846–856.

Yeast biomass yield coefficients

  1. Verduyn, C., Postma, E., Scheffers, W. A., & van Dijken, J. P. (1990). Physiology of Saccharomyces cerevisiae in anaerobic glucose-limited chemostat cultures. Journal of General Microbiology, 136(3), 395–403.
  2. Verduyn, C. (1991). Physiology of yeasts in relation to biomass yields. Antonie van Leeuwenhoek, 60(3–4), 325–353.
  3. Rosenfeld, E., Beauvoit, B., Blondin, B., & Salmon, J.-M. (2003). Oxygen consumption by anaerobic Saccharomyces cerevisiae under enological conditions: effect on fermentation kinetics. Applied and Environmental Microbiology, 69(1), 113–121.

Yeast conditioning, fermentative adaptation, and high-density viability stress

  1. Boulton, C. & Quain, D. (2001). Brewing Yeast and Fermentation. Blackwell Science, Oxford. (Yeast physiological condition, oxygenation of inoculum yeast, and its effect on subsequent fermentation performance.)
  2. Verstrepen, K. J., Iserentant, D., Malcorps, P., Derdelinckx, G., Van Dijck, P., Winderickx, J., Pretorius, I. S., Thevelein, J. M., & Delvaux, F. R. (2004). Glucose and sucrose: hazardous fast-food for industrial yeast? Trends in Biotechnology, 22(10), 531–537. (Carbon-source adaptation and its impact on fermentative capacity.)
  3. Rossignol, T., Dulau, L., Julien, A., & Blondin, B. (2003). Genome-wide monitoring of wine yeast gene expression during alcoholic fermentation. Yeast, 20(16), 1369–1385. (Adaptive transcriptional shift on entry into fermentative metabolism — basis for treating conditioning as reduced lag / faster start.)
  4. Brejning, J., Jespersen, L., & Arneborg, N. (2003). Genome-wide transcriptional changes during the lag phase of Saccharomyces cerevisiae. Archives of Microbiology, 179(4), 278–294. (Molecular basis of lag-phase duration and its shortening with prior adaptation.)
  5. Gibson, B. R., Lawrence, S. J., Leclaire, J. P. R., Powell, C. D., & Smart, K. A. (2007). Yeast responses to stresses associated with industrial brewery handling. FEMS Microbiology Reviews, 31(5), 535–569. (Viability and vitality loss under high-density and accumulated-stress conditions — basis for the viability-vs-utilization balance.)
  6. Pratt, P. L., Bryce, J. H., & Stewart, G. G. (2003). The effects of osmotic pressure and ethanol on yeast viability and morphology. Journal of the Institute of Brewing, 109(3), 218–228. (Stress-driven viability decline at elevated biomass / solute load.)

Industry practice and standards

  1. Renewable Fuels Association (RFA). Fuel Ethanol Industry Guidelines, Recommended Practices, and Specifications. (Current edition.)
  2. Kelsall, D. R. & Lyons, T. P. (2003). Management of fermentations in the production of alcohol: Moving toward 23% ethanol. In: The Alcohol Textbook (4th ed.), Ch. 11, pp. 121–135.
  3. Ingledew, W. M., Kelsall, D. R., Austin, G. D., & Kluhspies, C. (eds.) (2009). The Alcohol Textbook (5th ed.). Nottingham University Press, Nottingham, UK.

Inclusion of a reference in this list does not imply endorsement of the present calculator by any cited author or publisher. The calculator is a design and training tool; for any process-calibration decision, consult the primary literature and validate against plant-specific data.

Regression Test Suite · 20+ canonical cases

The test suite exercises core pure-calculation functions with known-good inputs and expected outputs. Click Run to verify correctness; useful after edits.

Fermentation Simulator Setup

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Anaerobic S. cerevisiae  |  Conceptual tool for rapid what-if analysis  |  v26.93

Instant rates + ODE simulation for Starch→Glucose→EtOH & Glycerol with strain presets (Ethanol Red, S288c, CEN.PK) and aeration regime.

Profile
Notes

▼ Fermentation Instant Predictions

Live state snapshot — derived from current input conditions

Sugar loaded
— g/L
St·1.11 + Dx·1.11 + S
Gay-Lussac ceiling
— g/L
sugar × 0.51142
Realistic max (95% GL)
— g/L
sugar × 0.485
Volumetric productivity
— g/L/h
rP at current state
Sugar consumption rate
— g/L/h
qS · X
Net growth rate (μ − kd)
— h⁻¹
+ = growing · − = dying
Doubling time
— h
ln 2 / μnet
Apparent YP/S
— g/g
qP / qS
Glycerol fraction
— %
qGly·YS/Gly / qS
Limiting factor
—
growth bottleneck
Dominant glycerol driver
—
largest qGly contribution
Mass-balance status
—
ethanol / theoretical max
▼Growth & substrate uptake

Specific Growth Rate (μ)

0.000 h⁻¹
anaerobic: μ = μmax·fT·fpH·(S/(Ks+S))·fE·fS,inh
aerated: μ = Yox·(qS,ox−mS) + Yred·qS,red, capped by the above

Specific Sugar Uptake (qS)

0.000 g/g/h
anaerobic: qS = μ/YX/S + mS·favail + qGly/YS/Gly
aerated: qS = qS,max·(S/(Ks+S))·fS,inh·fenv — uptake leads, growth follows

Respired fraction (fresp)

—
qS,ox / qS — 1.00 is fully respirative

Oxidative uptake (qS,ox)

—
min(qS, qS,crit, OTR/X/YO₂/S) — the binding term is named below

Effective yield (YX/S,eff)

—
(1−fresp)·YX/S + fresp·YX/S,ox

Ethanol re-uptake (qE,ox)

—
gated by glucose repression and by spare O₂

What limits the oxidative route

—
Crabtree means feeding slower helps; oxygen transfer means more kLa does
▼Ethanol production

Specific EtOH Rate (qP)

0.000 g/g/h
qP = YP/S·(qS − qGly/YS/Gly − (CX/Cglu)·μ) + α·μ + β

Volumetric EtOH Rate (rP)

0.000 g/L/h
rP = qP·X
▼CO₂ off-gas

Specific CO₂ Rate (qCO₂)

0.000 g/g/h
qCO₂ = YCO₂/S·qS

Volumetric CO₂ Rate (rCO₂)

0.000 g/L/h
rCO₂ = qCO₂·X
▼Glycerol production

Specific Glycerol Rate
(qGly)

0.000 g/g/h
growth α·μ = 0.000 base qG0 = 0.000 osmotic = 0.000 ethanol = 0.000 temp. = 0.000 pH = 0.000 N-limit = 0.000
sum × fs   (fosm=0.000, feth=0.000, fT=0.000, fpH=0.000, 1−fN=0.000)

Volumetric Glycerol Rate
(rGly)

0.000 g/L/h
rGly = qGly·X
▼Starch hydrolysis & dextrins

Starch → Dextrins → Glucose

0.000 g/L/h
rhyd = (vliq+vGA·St)·YG/St · liquef. vliq=0, sacchar. vsac=0, GA-on-St vGA·St=0 g/L/h

Yeast on Dextrins (qDx)

0.000 g/g/h
MAL pathway uptake; glucose-repression factor fglu,rep=1.000 (1=fully derepressed, 0=fully repressed)
▼Cell viability & environment

Cell Death Rate (rd)

0.000 g/L/h
rd = kd,eff·X; kd,eff = kd·(1 + kd,E·E + kd,T·max(T−Topt,0)²)

pH (CO₂-corrected)

—
pH shift from dissolved CO₂ ⇌ H⁺ + HCO₃⁻ (pKa=6.35)

Health Check

—
Quick qualitative assessment of conditions.
▼Predictions charts (vs T & pH)
Active models driving these curves: —

rP & YP/S,apparent vs Temperature

rP & YP/S,apparent vs pH

Active models driving these curves: —

μ, μ−kd,eff, kd,eff vs Temperature

μ, μ−kd,eff, kd,eff vs pH

Active models driving these curves: —

Glycerol decomposition: qGly,stress vs qGly,growthlike vs Temperature

Glycerol decomposition: qGly,stress vs qGly,growthlike vs pH

Model comparison tab — each chart overlays ALL available model options for one submodel, using the current strain/preset parameters. The curve corresponding to your currently selected model is drawn solid; alternatives are dashed for reference. Use this tab to preview what each selector in Advanced Model Parameters would do before you switch.

fT vs Temperature — Cardinal vs Gaussian

fpH vs pH — Cardinal vs Gaussian

fS vs Substrate — Haldane vs Monod × inhibition

fE vs Ethanol (growth) — Luong vs Hill vs Aiba

fE,p vs Ethanol (production) — Luong vs Hill vs Aiba

Cell-death kd,eff factors — thermal + pH decomposition

▼ Fermentation Conditions

▼Strain & operating conditions
Out of range (0–60°C)
Out of range (0–14)
▼Initial substrate concentrations
Must be ≥ 0
Must be ≥ 0
Must be ≥ 0
▼Enzyme dosing
Enzyme dose, activity and price are set in Medium Formulations → Total Required → Enzymes, alongside every other component. The values entered there drive the hydrolysis kinetics below.
▼Initial biomass & metabolites
Must be > 0
▼Gas-phase CO₂
▼Buffer system
—
Carbon balance check: —

▼ Advanced Model Parameters

▼Aeration & respiration (HDYC)
Dissolved O₂ is not integrated as a state: its time constant is seconds against hours for everything else, so the respired flux is a quasi-steady-state balance — min(available sugar, qS,crit, kLa·C*/X ÷ YO₂/S). Respired sugar leaves as CO₂ before the Gay-Lussac split and cannot also become ethanol.
▼Growth kinetics
Must be > 0
▼Substrate model
Must be > 0
Must be > 0
▼Ethanol inhibition on growth
Must be > 0
▼Ethanol inhibition on production
Must be > 0
▼Temperature model
Must be < Topt
Must be > Topt
▼pH model
Must be < pHopt
Must be > pHopt
▼Yields & stoichiometry
Must be > 0
Must be > 0
▼Glycerol model
▼Cell death model
Must be ≥ 0
▼Enzyme inactivation model
▼Starch hydrolysis model
Must be > 0
Must be > 0
Must be > 0
▼Yeast on dextrins (MAL pathway)
▼Organic acid byproducts (pH effect)
Lactic and acetic acid are produced as minor byproducts during fermentation (or by contaminating bacteria). They accumulate in the medium and lower pH via their pKa equilibria (lactic pKa = 3.86, acetic pKa = 4.76). Set yields to 0 to disable.

▼ Time-Course Simulation (ODE)

▼Active Model Configuration Summary

Active model configuration — reflects current selections

▼Inoculum Sizing

Computed inoculum — from current targets and qP

Xavg required
— g DCW/L
= P / (qP · t)
Xpitch
— g DCW/L
= Xavg · ratio
Cell density
— × 10⁷ cells/mL
≈2.1×10⁷ cells/mL per g DCW/L
Wet yeast cream
— g/L medium
30% DCW basis
▼Nutrient Coupling & Environment

Nutrient status — Monod factors at current initial concentrations

▼Trace elements & vitamins

Phosphate

Trace metals (Cu, Mn enter Liebig; Fe/Mo/Co tracked only)

Vitamins (biotin enters Liebig; others tracked only)

Typical ethanol ferm pH drops 0.5–1.0 units over a run due to ammonium assimilation releasing H+.
Final Ethanol
—
run a simulation
Peak Temperature
—
vs Tset
Total Cooling Duty
—
∫Qcool·V dt
Batch Time to 95%
—
of final ethanol
▼Time-course charts (Metabolism / Nutrients / Environment / Rates / Heat / Overview)
Limiting: —
Time cursor Drag to zoom · Ctrl+wheel to zoom · Shift+drag to pan · double-click to reset
Run a simulation to read the state at the cursor.

Concentrations vs time

Compare A/B

Theoretical vs target vs actual ethanol yield

—
Gay-Lussac ceiling
—
Target (Medium Formulations)
—
Actual (simulated)
—
—
—
How to read this: the ceiling is the stoichiometric maximum (Gay-Lussac, 0.51142 g/g) — physically impossible to exceed. The target is what the Medium Formulations tab planned for, using its YE/S slider as the planning yield (default 0.4603 g/g = ~90 % of ceiling). The actual is what the kinetic ODE produces after death, glycerol, residual sugar, and ethanol-tolerance losses. A 2–5 % gap between target and actual is normal and reflects realistic process losses; a gap larger than ~10 % usually points to a limiting nutrient, an ethanol-tolerance ceiling lower than target, or an under-sized inoculum. Actual can also sit ABOVE target — the two rest on different yields, and only the ceiling is a hard limit. The target uses the Medium tab's deliberately conservative planning YE/S; if the kinetics convert better than that, the run beats its own plan. Both yields are printed under the figures, so compare those rather than the titres: an actual above target with an achieved yield under the ceiling is a medium designed with margin, not an error.
Sensitivity

Yeast biomass & viability vs time

Yeast biomass summary & cell-count conversion

—
Inoculum
—
—
—
Peak
—
—
—
End
—
—
—
Doublings
—
log₂(Xpeak/Xpitch)
Stationary onset
—
μ = kd,eff crossover
Viability (end)
—
Xend / Xpeak
—

Nutrients vs time

Nutrient consumption & limitation

—
Final medium nutrients
—
Cellular sterol quota
—
—

Environment vs time

Process environment summary

—
Temperature
—
pH
—
Peak [CO₂(aq)]
—
Enzyme activity
—
—

Rates vs time

Productivity & kinetics summary

—
Peak rP (ethanol rate)
—
Peak μ (growth rate)
—
Avg productivity
—
Peak death kd,eff
—
—

Heat duty — Qmetab vs Qcool

Heat-balance summary

—
Peak Qmetab
—
kJ/L/h
Peak Qcool
—
kJ/L/h
Cumulative metabolic heat
—
∫Qmetab·V dt over the run
Cumulative cooling load
—
∫Qcool·V dt over the run
—

Feed flow Fk(t) per stream

Feed-stream summary

—
Stream 1 (C)
—
peak L/h
Stream 2 (N)
—
peak L/h
Stream 3 (P)
—
peak L/h
Stream 4 (Tr)
—
peak L/h
Stream 5 (V)
—
peak L/h
—
© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Conceptual tool for rapid what-if analysis.

Fermentation Simulators — Quick StartAll stages

One engine runs all three stages; they differ in configuration, not in kind. This page is the general workflow — what every stage shares. HDYC is respirative and fed-batch, Pre-Fermentation fermento-respirative and semi-batch, Fermentation anaerobic and semi-batch, and each has its own Simulation Instructions button on the stage bar covering its own setup and what to read in its run.

Start by picking the stage on the tab bar. That reads Process Type and Process Strategy from Inoculum & Seed Train and applies the regime, the aeration switch and the bioprocess mode. Geometry and composition originate there and in Medium Formulations; this tab owns kinetics and time.

  1. Pick a strain preset in the Fermentation Conditions card → Strain & Regime sub-section (Ethanol Red for industrial fuel ethanol, S288c or CEN.PK for lab strains, or Custom). One click sets μmax, yields, ethanol tolerance, glycerol base rate, and starch-hydrolysis qDx,max in one go. The strain choice also primes the Advanced Model Parameters card with strain-specific defaults.
  2. The simulator auto-syncs from the Medium Formulations tab. Any change there — feedstock, titer, starch fraction, nutrients (N, Mg, Zn, ergosterol, oleate), yield sliders — propagates immediately into the Substrate, Init Conditions, and Nutrient Coupling sub-sections of the Fermentation Conditions card. The "← Import from Medium Formulations" button is still there as a manual refresh, but you shouldn't need it for routine edits.
  3. Verify Substrate Initial Conditions in the Substrate Pools sub-section. For starchy feedstocks (corn, wheat, cassava) you'll see low initial glucose [Glucose]Initial (2–10 g/L from the small free-sugar fraction in the grain) and high [Starch]Initial (150–260 g/L for VHG); enzymes hydrolyze starch to glucose during the run via the two-step pathway (Starch → Dextrins → Glucose). For pure sugars or molasses, all the sugar-eq lands as free glucose with 0 starch.
  4. Set Duration (h) in the Time-Course Simulation card — the single source of truth for fermentation time. The Inoculum Sizing card's "Target fermentation time" field is read-only and auto-mirrors Duration (⇄ badge), so Xavg = P / (qP·Duration) stays consistent.
  5. Tune Advanced Model Parameters if needed — the Advanced Model Parameters h2 expands into 11 sub-collapsibles (Substrate & Half-Saturations, Ethanol Inhibition (Cells), Ethanol Inhibition (Production), Temperature, pH Modulation, Yield Coefficients, Glycerol Multi-Factor, Cell Death, Enzyme Inactivation, Hydrolysis & Two-Step, MAL Pathway). Each opens to its own parameter group. Any change auto-triggers a re-run with a 180 ms debounce.
  6. Read the Live State Snapshot at the top of the Fermentation Instant Predictions card. Twelve cells show derived values from the current input state: Sugar loaded, Gay-Lussac ceiling, Realistic max (95% GL), Volumetric productivity (rP), Sugar consumption rate, Net growth rate (μ−kd), Doubling time, Apparent YP/S, Glycerol fraction, Limiting factor, Dominant glycerol driver, and a color-coded Mass-balance status (✓/~/○/✖). Useful as a sanity check before clicking Run.
  7. Explore the Fermentation Instant Predictions sub-collapsibles — Growth, Ethanol, CO₂, Glycerol, Stoichiometry, Viability, and Charts. The Charts sub-section opens 6 mini-charts (3 vs Temperature, 3 vs pH) at the current operating point:
    • Ethanol — rP (primary, blue/green) + rGly (secondary, purple dashed) on dual axes.
    • Yeast (growth/death) — μ specific growth rate (primary) + kd,eff effective death rate (secondary, red dashed). Crossover T marks washout.
    • Glycerol — rGly volumetric (primary, purple) + qGly specific (secondary, orange dashed). Diagnoses osmotic / redox stress.
  8. Click "Run simulation" (or rely on the auto-debounce). The Time-Course Simulation card's Charts sub-section shows glucose, starch, dextrins, ethanol, biomass, glycerol, and CO₂ evolving over Duration.
  9. Check the "Limiting" pill above the time-course chart tab bar — it reports which nutrient f-factor (Ergosterol, N, Mg, Zn, Tween-80, or "none") bottlenecks growth in the last third of the run.
  10. Inspect the Theoretical vs Actual Yield panel below the Metabolism chart — Gay-Lussac ceiling, actual simulated ethanol, efficiency tier (✓ excellent ≥88%, ~ typical 70–88%, ⚠ stuck <70%), and a stacked carbon breakdown bar (ethanol / residual sugar / biomass / glycerol / maintenance losses).
  11. Switch time-course chart tabs (Metabolism / Yeast / Nutrients / Environment / Rates / Heat / Feed Flow / Overview) to diagnose what's happening at different stages of the run. Each tab now carries a computed summary panel beneath its chart in the same teal-accented style as the Live State Snapshot — Theoretical vs Actual yield for Metabolism, a 3×3 biomass/cells/cream grid for Yeast with DCW→cells conversion, a nutrient-consumption panel for Nutrients, a T/pH/CO₂/enzyme panel for Environment, peak-rates / average productivity / death-rate for Rates, and Qmetab vs Qcool + hero tiles (final ethanol, peak T, total cooling duty) plus a heat-balance summary (cumulative heat, peak rates, ΔT from setpoint) for Heat. Charts are 600 px tall with the container min-height locked so tab-switching never reflows the page, and the x-axis uses clean integer-hour ticks (1h / 2h / 6h / 24h step, auto-scaled to run duration).
  12. Highlight individual series or axis groups. Click any legend item to emphasise that curve (thick line; others dim to ~28% opacity); click again or click another item to switch. Click a Y-axis to highlight every series bound to that axis simultaneously — e.g., clicking the growth/death rate axis on the Yeast chart highlights μ, kd,eff, and μ−kd,eff together. The cursor changes to a pointer when hovering any Y-axis region. Pinned highlights persist through simulation re-runs.
  13. Read any hour of the run with the time cursor. The bar between the chart tabs and the chart holds one cursor shared by every time-course chart: move the pointer over a chart, drag the slider, or type an hour and press Enter, and the readout lists the state at that instant — sugars, biomass, ethanol, glycerol, CO₂, pH, T, volume, μ, qP, enzyme activity and the limiting nutrient. Click in a plot (or Pin) to hold the cursor while you switch tabs; the hour also survives a re-run, so two runs can be compared at the same instant. Hovering shows every series of the chart at that hour in one tooltip.
  14. Zoom into a window of the run. Drag across a chart to zoom to those hours, Ctrl+wheel to zoom about the pointer, Shift+drag to pan, double-click or Reset zoom to see the whole run again. The window is shared: zoom on Metabolism and the Rates, Environment and every other tab show the same hours. The Overview tab shows twelve small panels — one variable each, including V(t) — on the same cursor and window; the link on each panel opens the full chart.
  15. Save the chart on screen. Save PNG writes the visible chart with its title and legend; Save CSV writes its series over the zoomed hours only, one column per visible curve. Both name the file after the chart and the time of export. The whole run is still exported from the Run/Export row above the charts.
  16. Optionally enable Volume tracking — in Fermentation Conditions → Strain & operating conditions, a dropdown offers three modes: Constant V (default, no change), Post-proc shrink from CO₂ mass loss (ODE runs at constant V but display scales to Vfinal), and In-ODE rigorous (V integrated with the state vector; ethanol inhibition and Monod saturation feel the concentrating medium during the run). Typical VHG runs lose 5–10% volume to CO₂ outgassing. The Theoretical vs Actual yield panel adds a V0→Vfinal line when tracking is on, and both the Gay-Lussac ceiling and the actual titer are then reported on the Vfinal basis (efficiency ratio stays invariant — it's a mass-conversion number).
  17. Iterate: if stuck, switch to the Medium Formulations tab and boost the limiting nutrient. Changes propagate back automatically; watch the efficiency climb. Export the CSV when satisfied.

Every section header in the Simulator (Fermentation Conditions · Inoculum Sizing · Nutrient Coupling · Fermentation Instant Predictions · Time-Course Simulation · Advanced Model Parameters) is click-to-collapse; Inoculum Sizing and Nutrient Coupling & Environment start collapsed by default so the left column reads as a compact table of contents. The same applies to the ~25 sub-collapsibles inside them — useful once you've configured a section. The cellular DCW-to-cell-count conversion factor is derived from the ADY product spec on the Inoculum & Seed Train tab (ADY viable cells ÷ dry-matter fraction) and shown read-only in Inoculum Sizing (derived 2.13 × 1010 cells/g DCW ≈ 47 pg/cell for industrial S. cerevisiae; range 3–10 × 1010 covers strain and growth-phase variation). See the Model Notes → Science tab for the full mathematical definitions and References for primary sources.

HDYC Propagation — Simulation InstructionsHDYC

What this stage is, where its setup comes from, and what to check in the run. For the general workflow across all three stages, see the INSTRUCTIONS tab above.

  1. The setup is not yours to set here. Process Type and Process Strategy come from Inoculum & Seed Train — HDYC ships as Respirative (Aerobic) and Fed-Batch. Selecting the HDYC tab reads them and sets the regime, the aeration switch and the bioprocess mode for you. Change them upstream, not here.
  2. Vessel geometry comes from the same tab. Volume at Inoculation (V0) and the working volume set the batch/feed split: the initial charge is V0 of a Vwork stage, and the medium's nutrient split follows that ratio automatically.
  3. Carbon is the exception to that split. In fed-batch the charge is not a fraction of the total sugar — it is V0 × Initial [Sugar], deliberately dilute, and everything above it arrives with the feed. At the shipped 2,000 L and 10 g/L that is 20 kg of sugar in the charge, not the stage total.
  4. Set kLa to your vessel. Aeration & respiration → kLa, with C*O2 for the temperature. This is what decides how much sugar can be respired: qS,ox = min(qS, qS,crit, kLa·C*/X ÷ YO2/S). Too low and the culture overflows to ethanol however well it is fed.
  5. Watch the overflow, not just the biomass. A propagation that makes ethanol is being fed faster than it can respire. Ethanol on the time-course chart is the diagnostic: a respirative HDYC should make little, and re-consume what it does make once sugar stops filling the oxidative capacity.
  6. Ethanol recuperation is part of the yield. Once qS,resp falls below qS,crit, the engine oxidises accumulated ethanol back to biomass at YX/E. A large part of a real propagation's final cell mass arrives this way, so do not read the ethanol peak as lost carbon.
  7. Check the feed against the medium. The medium sizes this stage's sugar from X ÷ YX/S. If the feed strength and window cannot deliver that mass, the run will starve and the shortfall will read as a kinetic limit rather than a configuration error.
  8. What to read at the end: final biomass against the HDYC design in Medium Formulations, the respired fraction fresp, residual ethanol, and whether the limiting-nutrient pill names something other than carbon.

Pre-Fermentation — Simulation InstructionsPRE

What this stage is, where its setup comes from, and what to check in the run. For the general workflow across all three stages, see the INSTRUCTIONS tab above.

  1. Setup originates in Inoculum & Seed Train. Pre-Fermentation ships as Fermento-respirative (Micro-aeration) and Semi-Batch. The tab applies both when you select it; the profile no longer stores its own copy.
  2. Micro-aeration is the whole point of the stage. kLa is moderate by design, so oxygen — not the Crabtree ceiling — is what bounds qS,ox. Both ethanol and biomass form, which is what makes this stage fermento-respirative rather than either extreme.
  3. Semi-batch means the fill sets the substrate profile. Under Semi-Batch fill parameters, the vessel fills from Vinit to Vtarget over tfill; the fill rate, not the residual sugar, is what holds the culture near its oxidative capacity. A fill that is too fast pushes it to overflow.
  4. Inoculum timing changes the early hours. Pre-fill, in-feed and post-fill give different starting cell densities for the same final mass. Pre-fill is the default and the mildest.
  5. The medium is built for adaptation, not for titre. The Pre-Fermentation formulation carries a YX/S well below the propagator's because sugar demand here reflects ethanol and by-product formation as well as growth. Ethanol is checked against what the culture survives, not aimed at.
  6. What to read at the end: the biomass handed to the fermenter, the ethanol the culture has already seen, and whether the fill window left the run substrate-limited at any point.
  7. Known limit. Sterol and UFA status — the reserves a micro-aerated stage exists to build — are modelled as a nutrient requirement drawn from the medium, not as something this stage synthesises. A well-run and a badly-run pre-fermentation therefore hand the fermenter the same cell.

Ethanol Fermentation — Simulation InstructionsFERM

What this stage is, where its setup comes from, and what to check in the run. For the general workflow across all three stages, see the INSTRUCTIONS tab above.

  1. Setup originates in Inoculum & Seed Train. Fermentation ships as Fermentation (Anaerobic) and Semi-Batch. With aeration off, the respiratory branch is inert and the engine runs the classical fermentation model.
  2. Pick a strain preset first in Fermentation Conditions → Strain & operating conditions. One click sets μmax, the yields, ethanol tolerance, the glycerol base rate and qDx,max, and primes Advanced Model Parameters with strain-specific defaults.
  3. The substrate pools matter for starchy feedstocks. Corn, wheat and cassava start with low free glucose and high starch; enzymes hydrolyse it during the run through Starch → Dextrins → Glucose. For molasses or refined sugar it all lands as free glucose with zero starch.
  4. Semi-batch fill dominates the early hours. The vessel fills from a heel over tfill; fitting those hours at constant volume attributes dilution to kinetics. Set the heel fraction and fill duration from your own vessel.
  5. Duration is the single source of truth for time. The Inoculum Sizing card's target time mirrors it read-only.
  6. What to read at the end: final titre against the Gay-Lussac ceiling, the efficiency tier on the Theoretical vs Actual panel, the limiting-nutrient pill, and residual sugar — a stuck ferment shows as titre short of ceiling with sugar left.

HDYC Propagation — Simulation ScienceHDYC

The model as it applies to this stage. One ODE system serves all three — what differs is which terms are active, and that is what this page sets out. Growth is common to all: μ = μmax·fT·fpH·S/(KS+S)·fE·fnutrients, with fnutrients a Liebig minimum — the single scarcest nutrient, not a product.

The same system, with two more terms alive

HDYC integrates the same state vector by the same fixed-step Runge–Kutta 4 as the fermentation stage — [St, Dx, S, E, Gly, X, T, … nutrients]. What is different is that two terms which are inert under anaerobic operation are now doing the work: the respiratory split of sugar uptake, and ethanol as a second substrate. Everything on the Fermentation Science page still applies underneath; this page covers what is added.

Oxygen supply is a rate, not a switch

Transfer is two-film: OTR = kLa · (C* − CL). In a propagation the cells hold dissolved O₂ near zero, so the practical ceiling is OTRmax = kLa · C*, in g O₂ per litre per hour. Divided among the cells present it becomes a specific supply, OTRmax/X — which falls as the culture grows. This is the central fact of a propagation: the oxygen demand rises with X while the supply per cell does not, so a stage that is comfortably aerobic at inoculation can be oxygen-limited by hour eight.

The bottleneck — Sonnleitner & Käppeli

Sugar uptake is split before it is spent. The oxidative route has a finite capacity, and three separate things can bound it:

qS,ox = min( qS , qS,crit , (kLa·C*/X) ÷ YO₂/S )
qS,red = qS − qS,ox

  • qS — there is nothing to respire beyond what is taken up.
  • qS,crit — the Crabtree threshold: the respiratory apparatus itself saturates, and the cell overflows to ethanol even in full air. This is the bound that governs a well-aerated propagator.
  • (kLa·C*/X) ÷ YO₂/S — the oxygen the vessel can actually deliver, converted to the sugar it can burn. This is the bound that governs an under-aerated one.

Whatever the binding term, the remainder qS,red goes to ethanol. Overflow is therefore not a failure mode bolted on — it is what is left when the oxidative route is full.

Uptake leads, growth follows

Sugar uptake is its own law, not a consequence of growth:

qS = qS,max · S/(KS+S) · fS,inh · fenv,  qS,max ≈ 2.5 g/g/h on glucose

and growth is what the split leaves:

μ = YX/S,ox·(qS,ox − mS) + YX/S·qS,red, bounded above by the environmental Monod value

The direction matters. Set μ from Monod and compute its sugar cost afterwards — which is what this model did until v26.89 — and uptake has no ceiling: it rises to absorb whatever the yield collapse demands. At the HDYC operating point that gave qS = 3.5 g/g/h, beyond anything S. cerevisiae has been measured doing, and the loop was self-reinforcing — a low effective yield raises uptake, which shrinks the respired fraction, which lowers the yield again. A propagator designed for YX/S 0.475 predicted 0.079, making ethanol faster than cells. With uptake bounded first, the same stage at its fed-batch control point (residual sugar below 0.1 g/L) runs fully respirative at YX/S,eff 0.50 with no ethanol at all.

⚠ The ceiling is physiology, so it applies anaerobically too — a transporter does not know whether the vessel is sparged. Under anaerobic operation the split is meaningless and μ keeps the classical Monod form; only the uptake cap carries over.

Respiration and fermentation of the same sugar give very different cell yields — roughly 0.5 g/g against 0.05 g/g. The effective yield the two routes produce is the flux-weighted blend:

YX/S,eff = (1 − fresp)·YX/S + fresp·YX/S,ox,  fresp = qS,ox / qS,available

and it sets the sugar cost of growth in the demand equation — qS = μ/YX/S,eff + … — not merely a cap on carbon. That is the whole point: respiration makes growth cheaper, so the same feed builds more cells.

It is also circular. The yield sets the demand; the demand sets the split; the split sets the yield. The engine resolves it as a fixed point, iterated to convergence each step rather than corrected once. One correction is not enough where it matters most — under sugar limitation the respired fraction approaches 1 while a single pass still reports a yield blended near 0.3.

Ethanol recuperation — the second carbon source

A propagation that overflows early does not lose that carbon. Once sugar stops filling the oxidative capacity, the cells oxidise the accumulated ethanol back to biomass:

qE,ox = min( qE,max · E/(KE+E) · (1 − qS,resp/qS,crit) , O₂ headroom ÷ YO₂/E )

Two gates, both real. The middle term is glucose repression — ethanol is untouched while sugar still occupies the respiratory route, which is what puts the diauxie in the right order. The second is the oxygen the sugar respiration did not claim. The contribution YX/E·qE,ox is added to μ and debited from the ethanol balance, not from sugar — charging it to the sugar carbon budget would count it twice.

Why the charge is deliberately dilute

Fed-batch carbon is not split by volume like the other nutrients. The initial charge is V0 · C0 — the volume at inoculation times the design initial sugar concentration — and everything above it arrives with the feed. Keeping C0 low is exactly what holds qS below qS,crit in the first hours. A rich charge makes ethanol before the feed has started, and no amount of aeration recovers it: the Crabtree bound is a property of the cell, not of the sparger.

The feed streams then run on their own strategies — a setpoint controller on a residual, a programmed constant flow, or a single dose — and the design objective throughout is to keep qS at or just under the oxidative ceiling.

What this model does not do at this stage

Dissolved oxygen is not a state variable: transfer is evaluated at CL → 0 rather than integrated, so a real DO trace and its lag are outside the model. kLa is a constant you supply, not a function of stirrer speed, gas flow, viscosity or antifoam — as the broth thickens in a real propagation, the true kLa falls and this one does not. There is no respiratory quotient output, no gas-phase O₂ or CO₂ balance on the off-gas, and no cell-cycle structure, so budding index and cell-size distribution are outside it. Sterol and UFA status is drawn from the medium rather than synthesised, so the aerobic advantage in membrane composition is not modelled.

Pre-Fermentation — Simulation SciencePRE

The model as it applies to this stage. One ODE system serves all three — what differs is which terms are active, and that is what this page sets out. Growth is common to all: μ = μmax·fT·fpH·S/(KS+S)·fE·fnutrients, with fnutrients a Liebig minimum — the single scarcest nutrient, not a product.

The stage between two regimes

Pre-fermentation integrates the same state vector by the same fixed-step Runge–Kutta 4 as the other two stages. Its distinction is that neither branch dominates: enough oxygen is present for a respiratory contribution, not enough to suppress overflow. Both products form throughout, which is what the name fermento-respirative means and what makes this stage the hardest of the three to reason about without a model.

Which term binds — and why it is oxygen here

The same three-way bound applies as in the propagator:

qS,ox = min( qS , qS,crit , (kLa·C*/X) ÷ YO₂/S )

but with kLa moderate by design, the third term is the smallest. That single difference changes the behaviour of the stage completely. Under a Crabtree bound, as in HDYC, overflow depends on how fast you feed. Under an oxygen bound it depends on how much biomass is present, because the specific supply is OTRmax/X and falls as the culture grows. So the respired fraction declines through the run even at constant aeration and constant feeding, and the stage drifts toward fermentative on its own.

The consequence worth internalising: ethanol is expected here. It is checked against what the culture can survive, not driven to zero. A pre-fermentation with no ethanol at all is either over-aerated or under-fed.

Growth from the blended yield

YX/S,eff = (1 − fresp)·YX/S + fresp·YX/S,ox sets the sugar cost of growth, resolved as a fixed point each step because yield, demand and split are mutually dependent. With fresp sitting partway rather than at either extreme, the effective yield lands between the fermentative and respiratory values — which is precisely why the Pre-Fermentation medium is formulated at a YX/S well below the propagator’s. Sugar demand here pays for ethanol and by-products as well as cells.

The fill is the control variable

Semi-batch adds volume during the run, so this stage has a term the others largely do not:

dC/dt = r − C · (dV/dt)/V — applied to every concentration in the state vector.

During the fill phase, medium is added from Vinit to Vtarget over tfill on a chosen profile — linear, exponential, or stepped pulses — after which the vessel continues in batch. The fill rate, not the residual sugar, is what holds the culture near its oxidative capacity: too fast and qS exceeds what the oxygen supply can burn, too slow and the stage is substrate-limited and hands over less biomass than designed.

Inoculum timing is a separate choice — pre-fill (all cells in Vinit at t=0), during the fill, or post-fill — and it changes the early specific supply materially, because OTRmax/X depends on how many cells are present when the oxygen is.

⚠ Fitting these hours at constant volume attributes dilution to kinetics, and will under-estimate μmax by roughly the fill ratio.

Ethanol recuperation is possible but usually small

The same term is active as in HDYC — qE,ox gated by glucose repression and by spare oxygen — but at this stage both gates tend to be closed. Sugar generally keeps the respiratory route occupied, and the oxygen headroom that would drive re-uptake is the same headroom the stage does not have. Expect recuperation to matter here only if the fill finishes well before the end of the run.

What this stage is for, and what the model does not capture

The stated purpose of pre-fermentation is conditioning — handing the fermenter a population already adapted to ethanol, to the temperature, and to the osmotic load, with membrane sterol and unsaturated fatty acid reserves built while oxygen was still available. Those reserves are the reason the stage is micro-aerated rather than anaerobic.

⚠ The model does not build them. Ergosterol and UFA are treated as nutrient requirements drawn from the medium: they enter μ through the Liebig minimum and dilute with growth as dErg/dt = −μ·Erg, but no synthesis term replenishes them from the oxygen this stage supplies. Nothing carries an adaptation state across the transfer either. So a well-run and a badly-run pre-fermentation hand the fermenter cells that are identical as far as the engine is concerned, differing only in number.

The rest of the exclusions from the fermentation stage apply here too: dissolved oxygen is not integrated, kLa does not respond to broth properties, there is no respiratory quotient or off-gas balance, and the vessel is one well-mixed compartment.

Ethanol Fermentation — Simulation ScienceFERM

The model as it applies to this stage. One ODE system serves all three — what differs is which terms are active, and that is what this page sets out. Growth is common to all: μ = μmax·fT·fpH·S/(KS+S)·fE·fnutrients, with fnutrients a Liebig minimum — the single scarcest nutrient, not a product.

What is actually integrated

The run is an initial-value problem solved by fixed-step Runge–Kutta 4. The state vector carried through the integration is:

[ St , Dx , S , E , Gly , X , T , … nutrients ] — starch, dextrins, glucose, ethanol, glycerol, viable biomass, broth temperature, and the nutrient pools (N, Mg, Zn, P, trace metals, vitamins, ergosterol, UFA).

Every step evaluates one rate function at the current state and returns specific rates; the balances below convert those into d/dt. Nothing is stepped forward analytically and no rate is held constant across a step — that is what separates this from the Instant Predictions card, which evaluates the same rate function once at the current inputs.

The balances

dSt/dt  = −(vliq + vga,st)
dDx/dt = vliq − vsac − qDx·X
dS/dt  = rhyd − qS·X
dE/dt  = qP·X
dGly/dt = qGly·X
dX/dt  = (μ − kd,eff)·X

Glucose is a balance, not an input: it is released by hydrolysis and drawn by the cells, so the residual sugar curve is the difference between two rates rather than a scheduled decline.

Growth

μ = μmax · fT · fpH · fS · fE · fnutrients

  • fS — Monod, S/(KS+S), or Haldane S/(KS+S+S²/Ki,S) when substrate inhibition is enabled, which matters at VHG where the initial charge itself is inhibitory.
  • fT, fpH — Gaussian about the optima, with their own widths.
  • fE — selectable, because the three published forms disagree where it matters. Hill: (1−E/Emax)n. Luong: threshold-based, (Emax−E)/(Emax−Einh) raised to n, so growth is unaffected below the threshold and reaches exactly zero at Emax. Aiba: exp(−kE·E), smooth and never quite zero.
  • fnutrients — a Liebig minimum over the nutrient pools, not a product. The scarcest single nutrient sets the ceiling; two nutrients at 80% do not give 64%.

Substrate demand

qS = μ/YX/S + mS·fenv + qGly/YS/Gly + qlipid + qDx·yglu/dx

A Pirt split: growth at the biomass yield, plus maintenance, plus what glycerol and the lipid factors draw. Maintenance is gated by fenv — a cell that is too hot or too acidic to grow is also not paying full maintenance.

Products

Ethanol follows Luedeking–Piret: qP = α·μ + β — a growth-associated term and a non-growth-associated one, which is why ethanol continues to accumulate after growth has stopped. CO₂ follows the same carbon, with a dissolved and a headspace pool rather than instant escape, so off-gas persists after the ferment ends.

Glycerol is multi-factor, not a fixed yield: a growth-coupled term αGly·μ plus osmotic, ethanol, temperature, pH and nitrogen-stress drivers. The dominant driver at each point is identified rather than assumed — that is what makes glycerol diagnostic of which stress is acting.

Saccharification — sugar is released, not given

For starchy feedstocks glucose arrives through two enzymatic steps with their own rate constants and their own thermal inactivation:

Starch → Dextrins (α-amylase, liquefaction) → Glucose (glucoamylase, saccharification)

In SSF the second step runs during the ferment, so glucose is metered by the enzyme rather than present at t=0. Yeast can also take dextrins directly through the MAL pathway, subject to glucose repression — which is why residual DP2/DP3 falls only after glucose is low. For molasses or refined sugar the whole sugar-equivalent starts as free glucose with zero starch, and the hydrolysis terms drop out.

Death and viability

kd,eff is not a constant. It rises with ethanol, with temperature stress (asymmetrically — heat kills harder than cold, since protein denaturation dominates above the optimum), with pH stress, and falls with cellular inositol status. Net growth is (μ − kd,eff)·X, so a culture can be growing and dying at once, and the biomass curve turning over does not by itself mean substrate ran out.

Volume, temperature and pH

Semi-batch adds volume during the fill, so every concentration carries a dilution term dC/dt = r − C·(dV/dt)/V. Fitting the fill hours at constant volume attributes dilution to kinetics and will mis-estimate μmax. Volume tracking offers three modes: constant, post-processed shrink from CO₂ mass loss, and in-ODE rigorous, where ethanol inhibition and Monod saturation feel the concentrating medium during the run.

In adiabatic mode dT/dt = (Qmetab − Qcool)/cp, with Qmetab from the heat of fermentation per mole of ethanol and Qcool linear to setpoint. pH is buffer chemistry referenced to the medium at inoculation, moved by organic-acid production and by the ethanol dielectric shift in pKa.

What this model does not do

No mixing or spatial gradients — the vessel is one well-mixed compartment. No bacterial contamination. No cell-cycle or population structure: X is a single lumped pool of viable biomass, so budding index and cell-size distribution are outside it. Trace metals are two-sided from v26.89 — zinc, copper, manganese and iron each limit growth when scarce and inhibit it when loaded, f = C/(K+C) · Ki/(Ki+C), and each is drawn down by growth against its own biomass quota. Copper toxicity and iron overload carry real constants; the zinc and manganese ceilings are set high enough to be inert unless you lower them. Molybdenum and cobalt are consumed and mass-balanced but still have no kinetic effect. Under anaerobic operation the respiratory branch is inert by construction — qS,ox → 0 and all flux is reduced.

Time-Course Simulator — ReferencesRefs

Primary sources for the kinetic forms, stoichiometric defaults, and engineering conventions encoded in the simulator. Implementations frequently blend or adapt the published forms; the Model Notes → Science tab gives the exact functional expressions used by the ODE. Citations below are organised by topic.

Kinetic forms

  1. Luedeking R, Piret EL (1959). A kinetic study of the lactic acid fermentation. Batch process at controlled pH. Journal of Biochemical and Microbiological Technology and Engineering 1:393–412. — Origin of the growth-associated + non-growth-associated product term qP = α·μ + β used for ethanol production.
  2. Luong JHT (1985). Kinetics of ethanol inhibition in alcohol fermentation. Biotechnology and Bioengineering 27:280–285. — Generalised ethanol-inhibition factor fE with critical tolerance Emax; the simulator's default ethanol-inhibition model.
  3. Aiba S, Shoda M, Nagatani M (1968). Kinetics of product inhibition in alcohol fermentation. Biotechnology and Bioengineering 10:845–864. — Exponential fE = exp(−kE·E); offered as a legacy alternative inhibition form.
  4. Andrews JF (1968). A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnology and Bioengineering 10:707–723. — Haldane substrate-inhibition term S/(Ks + S + S²/Ki,S) for high-gravity sugar loads.
  5. Monod J (1949). The growth of bacterial cultures. Annual Review of Microbiology 3:371–394. — Foundational S/(Ks+S) saturation form for substrate-limited growth.
  6. Pirt SJ (1965). The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society B 163:224–231. — Maintenance-energy framework underlying the mS·X carbon-drain term.

Ethanol tolerance, cell death, and glycerol overflow

  1. Casey GP, Ingledew WM (1986). Ethanol tolerance in yeasts. CRC Critical Reviews in Microbiology 13:219–280. — Classic review of membrane / Mg²⁺ / lipid mechanisms of ethanol toxicity; biochemical basis for VHG sterol and oleate supplementation.
  2. Atala DIP, Costa AC, Maciel R, Maciel Filho R (2001). Kinetics of ethanol fermentation with high biomass concentration considering the effect of temperature, sugar and ethanol. Applied Biochemistry and Biotechnology 91–93:353–365. — Cell-death rate as a function of ethanol and temperature; basis for the kd,eff(E,T) term.
  3. Pham TK, Wright PC (2008). The proteomic response of Saccharomyces cerevisiae in very high glucose conditions. Journal of Proteome Research 7:4766–4774. — Osmotic-stress glycerol overproduction; basis for the Hill term qg,osm in the seven-component glycerol decomposition.
  4. Aguilera F, Peinado RA, Millán C, Ortega JM, Mauricio JC (2006). Relationship between ethanol tolerance, H⁺-ATPase activity and the lipid composition of the plasma membrane in different wine yeast strains. International Journal of Food Microbiology 110:34–42. — Quantitative correlations between membrane sterol content, ethanol tolerance, and H⁺-ATPase activity; underpins the fE × Ergq coupling.
  5. Furukawa K, Obata H, Kitano H, Mizoguchi H, Hara S (2004). Effect of cellular inositol content on ethanol tolerance of Saccharomyces cerevisiae in sake brewing. Journal of Bioscience and Bioengineering 98:107–113. — Inositol-limited cells show a higher death-rate constant under 12–20% ethanol via reduced phosphatidylinositol and plasma-membrane H⁺-ATPase activity; basis for the inositol–ethanol toxicity coupling on kd,eff.
  6. Krause EL, Villa-García MJ, Henry SA, Walker LP (2007). Determining the effects of inositol supplementation and the opi1 mutation on ethanol tolerance of Saccharomyces cerevisiae. Industrial Biotechnology 3:260–268. — Higher membrane PI content (inositol supplementation or opi1 overproduction) improves ethanol tolerance and reduces ATPase inhibition; corroborates the inositol toxicity mechanism.
  7. You KM, Rosenfield CL, Knipple DC (2003). Ethanol tolerance in the yeast Saccharomyces cerevisiae is dependent on cellular oleic acid content. Applied and Environmental Microbiology 69:1499–1503. — Role of UFAs in ethanol tolerance; rescue of ethanol-sensitive strains by oleate supplementation.
  8. Cot M, Loret MO, François J, Benbadis L (2007). Physiological behaviour of Saccharomyces cerevisiae in aerated fed-batch fermentation for high-level production of bioethanol. FEMS Yeast Research 7:22–32. — Industrial fed-batch operation and the ergosterol dilution behaviour modelled in the Ergq dilution kinetics.

Physiology, yields, and VHG operation

  1. Verduyn C, Postma E, Scheffers WA, van Dijken JP (1990). Physiology of Saccharomyces cerevisiae in anaerobic glucose-limited chemostat cultures. Journal of General Microbiology 136:395–403. — Anaerobic YX/S ≈ 0.10 g/g, ergosterol and UFA quotas, maintenance coefficient mS; default yields used in the simulator.
  2. Lange HC, Heijnen JJ (2001). Statistical reconciliation of the elemental and molecular biomass composition of Saccharomyces cerevisiae. Biotechnology and Bioengineering 75:334–344. — Biomass elemental composition (CH1.79O0.57N0.15P0.012) used for carbon-balance closure and mass conservation checks.
  3. Bai FW, Anderson WA, Moo-Young M (2008). Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnology Advances 26:89–105. — VHG review; industrial yield benchmarks (YE/S = 0.45–0.49), feedstock yield coefficients, productivity ranges.
  4. Walker GM (2011). Pichia and Saccharomyces yeast biology. In The Yeasts: A Taxonomic Study, 5th ed., Elsevier. — Magnesium/zinc/vitamin requirements; sterol and UFA auxotrophy under anaerobiosis.
  5. Perli T, Wronska AK, Ortiz-Merino RA, Pronk JT, Daran JM (2020). Vitamin requirements and biosynthesis in Saccharomyces cerevisiae. Yeast 37:283–304; and Perli T et al. (2020), Microbial Cell Factories / bioRxiv ALE study. — Single-vitamin-omission growth-rate measurements for CEN.PK113-7D: μ reduced 95% (biotin), 57% (pantothenate), 32% (pyridoxine/B6), 22% (thiamine), 19% (inositol), with niacin, folate, and pABA showing no significant reduction after adaptation. Basis for activating pantothenate, B6, thiamine, and inositol as Liebig factors and for keeping niacin/riboflavin/folate tracked-only.
  6. Andreasen AA, Stier TJB (1953, 1954). Anaerobic nutrition of Saccharomyces cerevisiae. I. Ergosterol requirement for growth in a defined medium. Journal of Cellular and Comparative Physiology 41:23–36; II. Unsaturated fatty acid requirement for growth in a defined medium. Ibid. 43:271–281. — Original demonstration that yeast cannot grow anaerobically without exogenous sterol and UFA; biochemical basis for the Phase 2 ergosterol dilution mechanism.

Temperature, SSF, and enzyme kinetics

  1. Pham HTB, Sundstrom ER, Wright AR (2008). Kinetic modeling of ethanol fermentation from wheat flour under simultaneous saccharification and fermentation. Biotechnology Progress 24:118–126. — Two-step hydrolysis (Starch → Dextrins → Glucose); α-amylase and glucoamylase loading conventions.
  2. Stewart GG (2017). Brewing and Distilling Yeasts. Springer, Cham. — α-Amylase ~500 U/g starch; glucoamylase ~200 U/g starch; nitrogen targets (200–700 mg N/L for normal-gravity through VHG).
  3. Gancedo JM (1998). Yeast carbon catabolite repression. Microbiology and Molecular Biology Reviews 62:334–361. — Glucose repression of MAL operon; basis for the Kglu,rep/(Kglu,rep+S) gate on yeast dextrin uptake.
  4. Kosaric N, Vardar-Sukan F (2001). Potential source of energy and chemical products. In The Biotechnology of Ethanol, Wiley-VCH. — Feedstock-yield reference values for corn, wheat, cassava, and molasses (fermentable sugars per g dry feedstock).
  5. Birol G, Önsan ZI, Kırdar B, Oliver SG (1998). Mathematical description of ethanol fermentation by immobilised Saccharomyces cerevisiae. Process Biochemistry 33:763–771. — Source of several temperature-response calibration points used in the Gaussian fT factor.
Calibration anchors used in the default parameter set: YE/S = 0.4603 g/g (0.51142 × 90% efficiency) and YX/S (anaerobic) = 0.04–0.05 g/g (Bai 2008; Verduyn 1990); anaerobic mS ≈ 0.02 g/g/h (Pirt 1965; Verduyn 1990); Emax strain-specific 95–125 g/L (Casey & Ingledew 1986; Walker 2011); kd,eff(E,T) exponential form (Atala 2001); seven-component glycerol decomposition with osmotic Hill term (Pham & Wright 2008); ergosterol dilution by growth (Andreasen & Stier 1953; Cot 2007).

Model Notes

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Anaerobic S. cerevisiae  |  Workflow guide & mathematical reference  |  v26.93

Workflow guide and mathematical definitions for the combined suite

ABBREVIATED

These are abbreviated Model Notes

What follows is a working summary — enough to use the suite correctly and to understand what each number means. It is not the model documentation. The full technical manual runs to roughly 200 pages and is available on request from peter.krasucki@fermaxiom.com.

What the full manual covers that these notes do not:

  • Derivations, not just statements. Every rate expression and balance is developed from its starting assumptions, with the simplifications made at each step identified and justified. These notes quote the results.
  • The mechanistic yield model in full. How ethanol yield emerges from the carbon distribution — biomass and glycerol carbon drawn before the Gay-Lussac split — rather than being imposed as a fixed coefficient, including the closure checks that keep the carbon balance honest.
  • The glycerol model. The full component treatment, the osmotic and redox drivers, and how the dominant driver is identified at each point in a run.
  • pH dynamics. Buffer chemistry referenced to the medium at inoculation, organic-acid production, the late-fermentation recovery from lysis base release, and the ethanol dielectric shift in pKa.
  • The headspace CO2 reservoir. Gas-phase balance, dissolved-CO2 coupling, and why an instantaneous-equilibrium assumption fails to reproduce the days-long CO2 persistence seen after fermentation ends.
  • Semi-batch and fed-batch coupling. The volume and multi-stream dilution mathematics, fill profiles, inoculum timing, and the nutrient sub-streams.
  • Nutrient, enzyme and inhibition submodels — nitrogen, phosphorus, magnesium, trace metals, vitamins, ergosterol and lipid status, saccharification kinetics, and the ethanol and temperature inhibition forms.
  • Parameter identifiability. Local sensitivity analysis and Brun collinearity indices — which parameters can be estimated from which observables, which must be fixed, and why fitting a collinear pair produces confident nonsense.
  • Industrial process context. How the modelled stages map onto real plant operation: propagation, pre-fermentation, semi-batch fill, drop criteria and the measurements a plant actually takes.
  • Numerical methods and validation. Integrator choice, stiffness and step control, mass-balance closure tests, and the regression cases the engine is checked against.
  • Complete symbol table, parameter tables with units and literature ranges, and a cross-referenced figure, table and equation set.

Where these notes and the manual disagree, the manual is authoritative — it is revised alongside the engine, and a version-matched copy can be supplied for whichever build you are running.

Information flow — where each number comes from

The tab numbering suggests a left-to-right order, but that is not where the information originates. Each quantity now has exactly one owner; every other tab shows it derived and locked, with the source named under the field. If a field will not accept a value, that is the design working — the badge underneath says which tab to change instead.

Ownership

  • Inoculum & Seed Train owns geometry and inoculum: vessel volumes, seed-train ratios, transfer efficiency, yeast format and the ADY certificate. The ADY spec fixes the cells-to-DCW constant used by the simulator, the data importer and every report.
  • Medium Formulations owns composition: one formulation per stage, selected on the Formulating bar. The simulator’s nitrogen and magnesium are derived from the selected stage.
  • Fermentation Simulators owns kinetics and time: growth and death parameters, inhibition, duration, feed profile, aeration.
  • Model Data owns measurement: the imported plant data and everything computed from it.

Direction differs by stage on purpose. The fermenter is sized from the production target, so volume flows Medium → Inoculation → Simulator. The seed-train vessels are geometry, so HDYC and pre-fermenter volumes flow Inoculation → Simulator.

Stages

HDYC, pre-fermentation and fermentation share one engine and one set of controls; they differ in configuration, not in kind. A stage profile (top of Strain & operating conditions) holds one stage’s whole configuration and selects the matching medium formulation with it.

Load the stage profile before touching anything. All three stages share the same fields, so a value typed with the wrong profile loaded lands in the wrong stage. The only sign is the dirty marker beside the profile selector, which reads “modified” when the live fields have drifted from the stored profile.

Working order

  1. Inoculum & Seed Train — yeast format and ADY certificate, seed-train technology, vessel volumes. Everything downstream rests on the biomass conversion set here.
  2. Medium Formulations — pick the stage on the Formulating bar, then set that stage’s composition. HDYC and pre-fermenter media are built for biomass; only the fermentation medium is built for ethanol output.
  3. Fermentation Simulators — load the matching stage profile, then set kinetics and duration. Composition arrives with the profile; you are not re-entering it.
  4. Model Data — import the matching phase, run Statistical analysis, then Evaluate fit before fitting anything.

The Yield Calculator is optional and sits outside this order. It answers “what can this grain give” — useful when sizing from a feedstock, skippable when the fermenter and titer are already known. It is a standalone tool: nothing it computes is carried into another tab, so a production target set here has to be entered again where it is used.

Stage chain

HDYC produces the inoculum for pre-fermentation, which produces the inoculum for fermentation. Each receiving tab carries an import button that pulls from the stage before it: Import fermenter from Medium Formulations on the Inoculum tab, and Import from Inoculum Calculator in the simulator’s Inoculum Sizing card. A stage profile declares which data phase it expects, and the calibration report flags a mismatch — evaluating fermentation data against an HDYC configuration is a comparison across different vessels.

Aeration — what it does and does not do

The HDYC profile enables a respiratory branch: dissolved O2 is treated at quasi-steady state, and the respired sugar flux is the smallest of what is available, the Crabtree threshold, and what kLa·C*/X can supply. Respired carbon leaves as CO2 before the Gay-Lussac split, so it correctly reduces ethanol. It does not yet raise biomass: μ is computed upstream from Monod and inhibition, and the branch only relaxes a carbon cap. Matching plant HDYC biomass needs the bottleneck formulation, where μ follows from the flux split rather than being set independently. Use the HDYC profile for biomass trajectory work; treat its ethanol as provisional.

Getting the most out of the simulator

  • Fit only what the data can see. The Statistical analysis panel marks each parameter estimable or not. A parameter it marks ✗ will still move during training, but it is absorbing noise, not information. Biomass measured at two time points cannot support kd or mS.
  • Fix what is stoichiometric, fit what is empirical. Gay-Lussac (0.51142 g/g) is a constant and should never be a fitting target. YP/S, αGly and the acid yields are the ones worth fitting.
  • Read the residuals, not the pooled R². A single R² over a trajectory is dominated by the fact that the variable changes at all. The per-time-point table and reduced χ² say where the model disagrees.
  • Hold data back. Fit on part of the dataset, then use Evaluate fit alone on batches the optimiser never saw. A good score on training data proves only that the model has enough free parameters.
  • Calibrate the biomass conversion once. A paired DCW and cell-count measurement replaces the ADY-derived estimate and rescales every YX/S fitted from the dataset. It is the single highest-value measurement available.
  • Match the vessel before comparing to a plant. A semi-batch fermenter fitted as constant volume produces confident, wrong parameters: the fill window dilutes everything, and the model has to know it.
  • Check the volume-tracking mode. Constant, CO₂-loss and in-ODE give different final concentrations for the same chemistry. Concentrations are only comparable on the same basis.
  • Sweep before you trust. Vary a parameter across its plausible range and watch whether the fit score moves. If it does not, the data does not constrain it, and whatever value you have is an assumption wearing a decimal point.

What the suite models — and what it does not

Knowing the boundary matters more than knowing the equations. A model used outside its scope still returns a number, and the number still looks reasonable.

Represented in the engine

  • Substrate cascade: starch and dextrins hydrolysed to fermentable sugar, with saccharification running alongside fermentation (SSF), not ahead of it.
  • Growth, maintenance and death, with ethanol, temperature, pH and osmotic inhibition acting on the specific rates.
  • Carbon distribution to ethanol, biomass, glycerol, CO2 and organic acids, with apparent yield emerging from the split.
  • pH trajectory including late-run recovery; nutrient depletion and its effect on growth; ergosterol and lipid status carried from the inoculum.
  • Volume as a state: CO2 outgassing, and semi-batch or fed-batch feed addition with the associated dilution.

Not represented — know before you rely on a result

  • Spatial gradients. The vessel is treated as ideally mixed. Real large fermenters carry temperature, pH and substrate gradients that a single-point model cannot show.
  • Bacterial contamination beyond the lactic and acetic yields you supply. There is no competing organism, no infection dynamic, no antibiotic response.
  • Strain adaptation or evolution during a run, and no cell-cycle or population structure — biomass is a single lumped pool.
  • Heat transfer and cooling capacity. Temperature is an input or a simple profile, not the result of a duty balance against a cooling system.
  • Foam, CIP residue, mash rheology, mechanical or equipment effects.
  • Downstream processing. The model ends at drop; distillation, evaporation and co-product recovery are outside it.

Where the numbers come from

  • Stoichiometric constants are fixed and should never be fitted: Gay-Lussac 0.51142 g/g, the 1.11 starch hydration factor, CO2 at 88/92 of ethanol mass.
  • Default kinetic parameters are literature values for industrial S. cerevisiae on corn mash. They are a defensible starting point, not your strain and not your plant.
  • Everything else is a calibration target. The Model Data tab exists because a default is an assumption until measured data has been fitted against it.

Rule of thumb: the engine is most trustworthy for relative comparisons — this recipe against that one, this drop time against another — and least trustworthy as an absolute predictor of a plant it has never been calibrated to.

Detail: Medium Formulations → Simulator (tabs 3 and 4)

The two tools are designed to work in sequence. Use the Medium Formulations tab first to specify what you are trying to produce, then watch the Simulator tell you whether the kinetics will actually deliver it within your time budget. Values flow automatically between the two — you can keep the Simulator open as a live monitor while you iterate on the recipe.

  1. Start in the Medium Formulations tab. The calculator is a design tool — it answers "what do I need to weigh out" given "what do I want to make". It's the canonical source of truth for the recipe.
  2. Enter your process targets: target ethanol production (L by default, switchable to US gallons), target titer (% v/v default 17 = VHG; also %w/v, g/L), and a feedstock from the 10-option dropdown. Selecting a feedstock auto-fills Moisture % and the full 7-component dry-basis composition table; the feedstock's fermentable-sugar yield and t=0 starch/glucose split are computed live from composition (no separate Starch Fraction input — composition is the single source). Override any composition row or moisture if your raw material differs from the literature defaults.
  3. Click "Load Standard" in the Medium Target Concentrations card for fuel-ethanol-practice defaults on all 24 nutrient rows.
  4. Verify the recipe in the Summary card. The collapsible Summary card at the top of the right column shows three snapshot-style rows of computed values:
    • Production overview — Total Sugar Required (default kg, switchable to lbs / metric ton via the Units strip), Ethanol Produced (L abs. / US gal / kg / lbs), and Medium Volume (L / US gal / hL) with biomass-produced as the descriptor.
    • Substrate split (visible when feedstock contains starch) — Starch Needed = starchFrac × sugar ÷ 1.11; Direct Glucose = (1 − starchFrac) × sugar; Feedstock (as-received) = dry mass ÷ (1 − moisture). starchFrac is derived from composition as (starch% × 1.11) ÷ (starch% × 1.11 + sugars%).
    • Enzyme loading (same trigger) — α-Amylase @ 500 U/g starch, Glucoamylase @ 200 U/g starch, plus the combined total. Auto-formatted as U / kU / MU.
    For glucose-only feedstocks (cane / beet molasses, pure sugars), the substrate + enzyme rows hide and a small italic notice replaces them. Mass balance bar (collapsible card below) should show 95–100% closure across Ethanol / CO₂ / Glycerol / Biomass / Other. Salt list lives in the Total Required tab inside Formulation Results.
  5. Switch to the Time-Course Simulator tab. Initial glucose, starch, N, Mg, Zn, ergosterol, Tween-80, medium volume, and the target titer are already live-synced from the Medium Formulations tab — no Import click needed for routine edits. (The green "← Import from Medium Formulations" button remains as a manual refresh.)
  6. Review the Fermentation Conditions card (collapsible via its ▼ header). Pick a strain preset (Ethanol Red for industrial, S288c/CEN.PK for lab, custom for bespoke calibration). For a starchy feedstock, verify Substrate [Glucose]Initial is low (typically 2–10 g/L) and Substrate [Starch]Initial is in the 150–260 g/L range — consistent with a VHG corn mash.
  7. Set Duration (h) in the Time-Course Simulation card. Duration is the single source of truth for fermentation time — the Inoculum Sizing card's "Target fermentation time" is read-only and auto-mirrors it (⇄ badge). Adjust expected qP (0.3–0.6 VHG, 0.8–1.2 normal, 1.5+ fast) and the card computes Xpitch = Xavg · ratio from P = qP·Xavg·Duration.
  8. Click "Run Simulation" or let the 180 ms auto-debounce re-run after any parameter change. The Metabolism chart shows glucose, starch, ethanol, biomass, glycerol, and CO₂ over Duration.
  9. Inspect the Theoretical vs Actual Yield panel — ✓ excellent ≥88%, ~ typical 70–88%, ⚠ stuck <70%. The stacked carbon bar shows where missing yield went (residual sugar, biomass, glycerol, maintenance / death losses). If the Volume tracking mode (Fermentation Conditions → Strain & operating conditions) is set to anything other than Constant V, the panel adds a V0→Vfinal line reflecting medium shrink from CO₂ outgassing, and both ceiling and actual titer are expressed on the Vfinal basis so they are directly comparable.
  10. Switch time-course chart tabs — six tabs (Metabolism / Yeast / Nutrients / Environment / Rates / Heat) each carry a dedicated summary panel beneath the chart. The Yeast tab includes biomass in both g DCW/L and cells/mL, with the DCW→cells conversion factor user-editable in the Inoculum Sizing card (derived 2.13 × 1010 cells/g). The Heat tab plots Qmetab against Qcool on a single axis (kJ/L/h) with hero tiles for final ethanol, peak temperature, and total cooling duty — useful for jacket sizing in adiabatic mode and as a latent-load check in isothermal mode. Click a legend item to isolate one series or a Y-axis to highlight every series bound to that axis.
  11. Read the Environment tab for the pH and dissolved-CO2 story. A healthy run has a characteristic shape: pH starts at exactly the value you set, falls 0.3–0.5 units over the first quarter as NH4+ assimilation and organic-acid production load the medium with protons, bottoms out, then recovers through the second half as dying cells release intracellular base. If pH stays flat after the minimum, the culture is not turning over biomass — check the Yeast tab for a biomass peak followed by decline. Dissolved CO2 should saturate (~28 mmol/L at 1 atm, higher under hydrostatic head) within the first hours, hold there while gas is being evolved, and then decay slowly over days once sugar is exhausted — not crash to zero, because the headspace stays blanketed with CO2 long after bubbling stops. Both traces auto-scale to the range actually present.
  12. Set the CO2 headspace controls to match your vessel (Fermentation Conditions → buffer/CO2 sub-card). Total pressure at mid-depth adds hydrostatic head — leave at 1 atm for bench work, raise toward 1.5–2 atm for a tall industrial fermenter, which roughly doubles the dissolved CO2. Headspace volume fraction is the ullage above the broth, and headspace air-exchange rate sets how quickly the CO2 blanket is replaced by air once gassing stops: lower it for a sealed beer well, raise it for an actively vented or purged tank. The legacy fixed PCO₂ mode is retained for comparison against earlier runs.
  13. Check the byproduct line under the yield panel. Beneath the theoretical-vs-actual figures the panel reports final glycerol (with YGly/S as a percentage of sugar consumed) and net biomass (YX/S). Because ethanol yield now emerges from the carbon balance rather than being imposed, these two are where any missing yield has gone — read them together with the stacked carbon bar.
  14. Explore the Instant Predictions tabs (right column) to understand how rates depend on T and pH at your current operating point:
    • Ethanol Product — rP + rGly dual-axis vs T and pH.
    • Yeast Product — μ + kd,eff dual-axis. Crossover point = washout limit.
    • Glycerol Product — rGly volumetric + qGly specific. Osmotic / redox stress diagnostic.
  15. Check the "Limiting" pill above the time-course charts. If "Ergosterol" → raise medium ergosterol in the Medium Formulations tab. If "N" → more DAP or yeast extract. If "none" → the shortfall is kinetic, not nutrient-limited.
  16. Iterate. Go back to the Medium Formulations tab, adjust. Changes propagate back automatically; watch the simulator re-run and verify the efficiency climbs. Export the CSV when you're happy and plan your bench-scale validation.
  17. Calibrate with real data (Model Exp. Data tab). Once you have laboratory HPLC time-course data from a bench or pilot fermentation, switch to the Model Exp. Data tab. Upload your CSV/TSV file (or paste directly), then follow the calibration workflow: Statistical analysis to check data quality and identify what parameters the data supports estimating → Calculate parameters to get analytical first-pass estimates from the data → Apply to simulator → Evaluate fit to see R²/RMSE/bias per species → Train (optimise) to iteratively refine remaining parameters. The fitted model can then predict scale-up scenarios with strain-specific confidence.
  18. Read the Science sub-tab for the mathematical definitions.

Why this order matters: the Medium Formulations tab is the canonical source of truth for the recipe. It has no opinion about kinetics (it doesn't know about μmax, Emax, ergosterol dilution, or cell death), but it guarantees the mass balance. The Simulator is the kinetic check that tells you whether a mass-balanced recipe will actually ferment to completion within your target time. Using the calculator first means you never simulate a recipe that can't possibly work on paper; using the simulator second means you catch the kinetic failures (stuck fermentation, ethanol toxicity, ergosterol dilution) that pure mass balance misses. And because Medium Formulations → Simulator is auto-wired, you can edit either view and see the consequence immediately in the other.

Equations and assumptions

  • Temperature factor (cells): Two models, user-selectable. Cardinal (default, Rosso, Lobry & Flandrois 1993, CTMI): fT = (T−Tmax)(T−Tmin)² / [(Topt−Tmin) · ((Topt−Tmin)(T−Topt) − (Topt−Tmax)(Topt+Tmin−2T))] for Tmin < T < Tmax, and exactly 0 outside that interval. Asymmetric (long shoulder below Topt, sharp drop above), with biologically interpretable cardinal temperatures (input-field defaults Tmin=5°C, Topt=30°C, Tmax=42°C; the Ethanol Red preset shifts Topt to 32°C, the industrial fuel-ethanol value, on Load Preset). Gaussian (legacy): fT = exp(−((T−Topt)²/(2σT²))) — symmetric, never reaches zero. Useful for back-compatibility with older parameter sets.
  • pH factor (cells): Two models, user-selectable. Cardinal pH Model (default, Rosso et al. 1995): fpH = (pH−pHmax)(pH−pHmin)² / [(pHopt−pHmin) · ((pHopt−pHmin)(pH−pHopt) − (pHopt−pHmax)(pHopt+pHmin−2pH))] — asymmetric (long acidic shoulder, sharp alkaline cliff), reflecting S. cerevisiae's real pH response. Gaussian (legacy): fpH = exp(−((pH−pHopt)²/(2σpH²))).
  • Substrate kinetics (cells): Two models, user-selectable. Haldane (default, unified): muS = S / (Ks + S + S²/Ki,S). Combines Monod uptake and substrate-inhibition into one biologically-grounded expression. Monod × inhibition (legacy): Monod S/(Ks+S) multiplied by 1/(1 + S/Ki,S).
  • Ethanol inhibition (cells): Three models, user-selectable. Luong (default, 1985): fE = 1 below Einh, ((Emax−E)/(Emax−Einh))n in the inhibition range, 0 above Emax. Best empirical fit for S. cerevisiae. Hill (legacy): fE = max(0, (1 − (max(E−Einh,0))/Emax)n). Aiba (1968): fE = exp(−kE · E). Smooth exponential; never reaches zero.
  • Ethanol inhibition (production, decoupled): Same three model choices, separate parameters (Emax,p, Einh,p, np, kE,p). Only the Luedeking-Piret β term is gated by fE,p — this is the *specifically* ethanol-inhibited non-growth production contribution. Maintenance catabolism (mS, regime-adjusted ~25× higher for anaerobic than aerobic) continues regardless of E, because live cells always need ATP for maintenance. What actually terminates fermentation is cell death (kd,eff rising with E), which drives X → 0 and thus rP = qP·X → 0 — not a hard metabolic cliff.
  • Smooth substrate depletion: A soft-switch factor favail = S/(S + Ks,min) (Ks,min = 0.01 g/L) replaces the hard S=0 cutoff, ensuring rates taper smoothly as substrate runs out rather than dropping discontinuously.
  • Substrate consumption: qS = μ/YX/S + mS·favail + qGly/YS/Gly; maintenance scales with substrate availability.
  • Cell death: kd,eff = kd·(1 + kd,E·E + kd,T·[(T−Topt)²heat + fcold·(T−Topt)²cold] + kd,pH·(pH−pHopt)²). dX/dt = (μ − kd,eff) · X. Heat-stress (T > Topt) drives most thermal death; cold-stress contributes a tunable fraction fcold (default 0.3) of the same quadratic to reflect membrane/osmotic damage at low T. The pH term was added to capture real yeast mortality at extremes of acidity or alkalinity (default kd,pH=0.05 per pH-unit²).
  • Enzyme hydrolysis (two-step, Starch → Dextrins → Glucose; Pham, Sundstrom & Wright 2008): Real enzyme blends produce a sugar ladder, not pure glucose, so the suite tracks dextrins (DP 3–20) as a transient pool between starch (DP > 20) and free glucose. Three parallel reaction rates, each on the anhydroglucose mass basis (g/L/h):
    • vliq = kliq·(AA·1000)·fenv,E·Starch/(Km,St+Starch) — α-amylase liquefaction, fast endo-attack on starch → dextrins. No mass gain.
    • vsac = ksac·(GA·1000)·fenv,E·Dx/(Km,Dx+Dx) — glucoamylase saccharification, slow exo-attack on dextrin chain ends → glucose. The rate-limiter in SSF.
    • vGA·St = kGA·St·(GA·1000)·fenv,E·Starch/(Km,St+Starch) — glucoamylase acting directly on starch (slow side-reaction; kGA·St ≈ 0.1·ksac).
    Glucose production rate rhyd = (vsac + vGA·St)·YG/St, with YG/St = 1.11 g glucose / g anhydroglucose to account for the +H₂O added at hydrolysis (180/162). vliq carries no YG/St factor because dextrins are still on the anhydroglucose basis — the water is added only at the saccharification step. Shared enzyme environment factor fenv,E = fact·fT,E·fpH,E, with Gaussian fT,E centred on Topt,E=60°C and fpH,E on pHopt,E=4.5 — at typical fermentation T=32°C the enzymes operate at ~2% of their nominal rate constants, which is the kinetic price of SSF. fact is the remaining active enzyme fraction (decays via first-order inactivation, see next bullet). The dextrin pool builds up early as vliq > vsac, then drains as GA catches up; residual dextrins at end-of-run are the brewer's attenuation limit.
  • Mash pre-hydrolysis correction: When the Medium Formulations tab pushes a starch loading to the simulator via importFromMedium(), 0.9% of the starch (anhydroglucose mass) is moved into the initial free-glucose pool to model the small amount of saccharification already accomplished during mashing / liquefaction before fermentation starts. The two values together always equal the user-entered total — the correction avoids double-counting that fraction as both polymer and free sugar at t=0.
  • Yeast on dextrins (MAL pathway, glucose-repressed; Stewart 2017, Gancedo 1998): S. cerevisiae can consume short dextrins (maltose, maltotriose) via the MAL permease + maltase system, but the MAL operon is under strong glucose catabolite repression. The model gates the dextrin uptake rate by a repression factor that turns the pathway off when free glucose is abundant:
    qDx,yeast = qDx,max·(Dx/(KDx,yeast+Dx))·(Kglu,rep/(Kglu,rep+S))·fE,p
    With Kglu,rep = 2 g/L (default), uptake is throttled to ~10% of maximum while S > 20 g/L and only switches on as glucose depletes below ~5 g/L. The fE,p gate adds an ethanol-tolerance constraint — dying cells stop tapping dextrins regardless. Effective glucose-equivalent flux into the cell is qDx,yeast·Yglu/Dx with Yglu/Dx ≈ 1.05 (internal hydrolysis adds water, but less than full external hydrolysis since maltase processes only the terminal bond). This is folded into qS upstream so the free-glucose balance dS/dt = rhyd − qS·X stays exact.
  • Enzyme thermal inactivation: dfact/dt = −kinact · Q10(T−Tref)/10 · fact. Activity decays faster at higher temperatures (Q10 = 2).
  • Instant rates (cells): qS = μ/YX/S + mS·favail + qGly/YS/Gly, qP = YP/S·(qS − qGly/YS/Gly − (CX/Cglu)·μ) + α·μ + β (mechanistic carbon balance — the glycerol draw and the carbon fixed into new biomass are removed before the Gay-Lussac split, so YP/S = 0.51142 is stoichiometric and the apparent yield, typically 88–90 % of theoretical, emerges from the carbon distribution rather than being imposed as a coefficient); rP=qP·X; qGly = [αGly·μ·(1 + kVHG,Gly·fosm) + qG0 + qg,osm + qg,eth + qg,T + qg,pH + qg,N]·fS (seven additive components, substrate-gated; the earlier single-multiplier form is superseded).
  • ODEs: dStarch/dt = −(vliq + vGA·St); dDx/dt = vliq − vsac − qDx,yeast·X; dS/dt = rhyd − qS·X; dX/dt=(μ − kd,eff)·X; dEtOH/dt=qP·X; dGly/dt=qGly·X; dCO₂/dt = qCO₂·X; dfact/dt = −kinact,eff·fact; dLA/dt = YLA/S·qS·X; dAA/dt = YAA/S·qS·X; dZn/dt = (feed/dilution only); dP/dt, dCu/dt, dMn/dt, dFe/dt, dMo/dt, dCo/dt = consumption (−qn·X) + feed/dilution; dBiotin/dt, dThi/dt, dRib/dt, dNia/dt, dPan/dt, dB6/dt, dFol/dt, dIno/dt = consumption + feed/dilution. 32 state variables, integrated with RK4 (full vector: st, s, x, e, gly, co2_aq, fact, N, Mg, Ergq, T, dx, V, la, aa, Zn, P, Cu, Mn, Fe, Mo, Co, Biotin, Thi, Rib, Nia, Pan, B6, Fol, Ino, Baselys, yCO₂,headspace). qS here is the glucose-equivalent uptake rate — it absorbs the qDx,yeast·Yglu/Dx flux from the MAL pathway, so dS only debits the residual draw on the free-glucose pool. Zn, Cu, Mn and Fe are dynamic; 14 additional state variables (P + 5 trace metals + 8 vitamins) support per-stream fed-batch composition. Consumption rates use qn = μ/YX/n with published yield coefficients.
  • Aqueous chemistry and pH: pH is solved at every step by bisection on the proton charge balance rather than carried as a fixed input. Five sources contribute, and the acid strengths themselves move as ethanol accumulates.
    • Baseline. The pH you enter is the pH of the finished medium, so the buffer and whatever lactic/acetic it already contains are referenced to that set point: a run set to 4.8 starts at exactly 4.8. Only acid produced during the run, H+ from NH4+ assimilation, CO2 taken up, and base from lysis perturb it.
    • Dissolved CO2. CO2(aq) is a state variable: dCO2,aq/dt = qCO₂·X/44.01 − kLa,eff·(CO2,aq − kH(T)·PCO₂), the transfer signed so the liquid can absorb from a CO2-rich headspace as well as strip into a lean one.
    • Headspace as a real reservoir. The headspace CO2 mole fraction is itself a state: dy/dt = (Jstrip/nhs)(1 − y) − khs,exch(y − yair), with nhs = Ptot(Vgas/VL)/RT. A fermenter purges its own headspace to essentially pure CO2 while gassing (broth saturates near 1.24 g/L at 1 atm, more under hydrostatic head), and the blanket clears only by exchange with air afterwards — so dissolved CO2 decays over days, not minutes. Interfacial area collapses when bubbling stops, so kLa,eff falls from its bubbled value to a surface-only one.
    • Late-fermentation pH recovery. CO2 cannot drive it: at pH 4.1 only ~0.6 % of dissolved CO2 is bicarbonate (pKa1 = 6.35), so removing all of it is worth ~0.007 pH units. The recovery instead comes from base liberated as cells die and lyse — intracellular K+, amino acids, and the collapse of the H+-ATPase gradient — carried as a state driven by the death flux, dBase/dt = ybase,lysis·rdeath. Because the driver is death rather than sugar exhaustion, the rise appears past the biomass peak, mid-run, as observed industrially (+0.3–0.5 units).
    • Ethanol pKa shift. Ethanol lowers the medium dielectric constant, weakening every carboxylic acid present: ΔpKa = kpKa,EtOH·wEtOH (~0.0145 per wt %, so acetic moves 4.76 → ~4.93 at 12 wt %). Applied to the buffer and organic acids; strong acids are unshifted.
    • Organic acids. Lactic and acetic are produced kinetically, dLA/dt = YLA/S·qS·X (defaults 0.003 and 0.002 g/g), so they accumulate through the run and stop when sugar does.
    The solved pH feeds back into growth through fpH and into death, so the recovery measurably improves completion at high gravity.
  • Extended Liebig minimum: Eight of the 14 additional state variables enter the Liebig minimum, each with a literature-grounded Monod factor:
    Phosphate (P) — fP = P/(KP+P), KP = 5 mg/L (Albers et al. 1996). Yeast can take up phosphate down to very low residual — limitation kicks in only at high biomass densities or with very low charge.
    Copper (Cu) — fCu = Cu/(KCu+Cu), KCu = 0.02 mg/L. Cytochrome cofactor; supplementation also suppresses H₂S formation.
    Manganese (Mn) — fMn = Mn/(KMn+Mn), KMn = 0.1 mg/L. Glucoamylase activator; matters for SSF productivity. Default initial Mn = 2 mg/L (top of the 0.2–2 mg/L range, reflecting that Mn is a minor-role nutrient present in most process waters), giving fMn ≈ 0.95 when replete — Mn limits growth only if a feedstock/water assay shows a genuinely low charge.
    Biotin — fbiotin = Bio/(Kbio+Bio), Kbio = 0.001 mg/L. The canonical limiting vitamin for industrial yeast, famously absent from beet molasses (Suomalainen 1971).
    Pantothenate — fPan = Pan/(KPan+Pan), KPan = 0.25 mg/L. Coenzyme-A precursor; its omission gave the largest single-vitamin growth defect after biotin (57% lower μ; Perli et al. 2020).
    Vitamin B6 (pyridoxine) — fB6 = B6/(KB6+B6), KB6 = 0.05 mg/L. Amino-acid metabolism cofactor (32% μ defect on omission; Perli et al. 2020).
    Thiamine — fThi = Thi/(KThi+Thi), KThi = 0.1 mg/L. Pyruvate-decarboxylase cofactor — directly on the fermentation pathway (22% μ defect on omission; Perli et al. 2020).
    Inositol — fIno = Ino/(KIno+Ino), KIno = 1.3 mg/L. Phosphatidylinositol precursor (19% μ defect on omission; Perli et al. 2020). Inositol also couples to ethanol toxicity — see Cell death below.
    The K values are calibrated so that well-supplied synthetic-medium defaults give f ≈ 0.95 (no false limitation when replete) while dropping steeply as the vitamin is consumed. The extended Liebig is fnutrients = min(fN, fMg, fZn, fErg, fTw, fP, fCu, fMn, fbiotin, fPan, fB6, fThi, fIno) — 13 active factors.
    The remaining six state variables (Fe, Mo, Co, riboflavin, niacin, folate) are tracked for mass balance and feed-stream delivery but do not limit growth: S. cerevisiae is effectively prototrophic for niacin, riboflavin, and folate (no significant μ reduction on omission after adaptation; Perli et al. 2020), and Fe/Mo/Co lack published half-saturation curves under industrial ethanol conditions, so adding them to the minimum with invented K values would produce poorly-grounded predictions.
  • Inositol–ethanol toxicity coupling: Beyond its growth role, cellular inositol status modulates ethanol toxicity. A low-inositol cell synthesises less phosphatidylinositol (PI), which weakens the plasma-membrane H+-ATPase that maintains the ion barrier; under 12–20% ethanol such cells show a markedly higher death-rate constant and leak more intracellular K+, phosphate, and nucleotides (Furukawa et al. 2004; Krause et al. 2007). The model scales the ethanol term of the death rate by (1 + kino,tol·(1 − fIno)): a fully inositol-replete cell (fIno → 1) sees no penalty, while a depleted cell (fIno → 0) suffers up to (1 + kino,tol)× the baseline ethanol death rate, with kino,tol = 0.6 by default. This is distinct from the growth factor fIno above — inositol limitation slows growth and accelerates ethanol-driven death, the two mechanisms acting on different terms of dX/dt.
  • Per-stream composition: Every fed-batch stream now has independent composition fields for all 14 new species. The 5 streams × 14 species = 70 fed-batch composition fields, plus 14 fields for the semi-batch composite stream = 84 total. Most stay at industrial-realistic defaults; users typically only edit fb_c_feed_S (carbohydrate concentration in Stream 1) and fb_trace_feed_Zn (Zn in Stream 4). The unified mass-balance ODE collects feed contributions from all streams as Σk Fk·Ck,feed,i / V for each species i, then subtracts the cumulative dilution Ci·ΣkFk/V. This generalises the single-stream feed coupling to arbitrary numbers of streams without changing the form.
  • Feed-flow chart: New "Feed Flow" tab in the time-course chart area shows Fk(t) for each enabled stream (5 lines in fed-batch, 1 in semi-batch). The summary panel below reports total volume delivered per stream (∫F dt, trapezoidal) and per-stream peak flow rate, with a verdict line confirming the total flow against the final V trajectory. Useful for diagnosing controller behaviour: aggressive Kp shows up as a spiky FC(t), exponential μ-targeted shows up as a smooth rising curve, stepped trace-element feed shows up as 3 distinct pulses.
  • Mass balance check: Carbon in (glucose consumed + starch consumed) vs carbon out (ethanol + CO₂ + glycerol + biomass). Warns if balance deviates >5%.
  • Feedstock mass balance (Medium Formulations): Total fermentable sugar required is computed as sugar = ethG / YE/S, then split between two paths. Dry feedstock needed = sugar / Ysugar/feedstock, where Ysugar/feedstock is computed live from the detailed composition table as (starch% × 1.11 + sugars%) ÷ 100 — the constant 1.11 = 180/162 is the stoichiometric glucose:starch mass ratio. Picking a feedstock from the dropdown populates the composition with literature defaults (e.g. corn: 74% starch + 1.5% sugars → 0.84 g/g) along with typical moisture (grains 12–14%, molasses ~20%, purified starch ~11%, pure sugars 0%); any cell of the composition table can be edited to match an assayed lot. As-received (wet) mass = dry mass ÷ (1 − moisturefraction), so at 14% moisture, 20 kg dry corn weighs 23.3 kg as received. The starch/glucose split at t=0 is derived from composition as starchFrac = (starch% × 1.11) ÷ (starch% × 1.11 + sugars%); at t=0 the medium contains (1 − starchFrac) × sugar-eq as free glucose and (starchFrac × sugar-eq) ÷ 1.11 as solid starch; amylase enzymes (α-amylase 500 U/g starch, glucoamylase 200 U/g starch) hydrolyze the starch to glucose during fermentation.
  • Instant-Predictions dual-axis charts: three tab groups in the right column of the Simulator sample rates across temperature (0–50 °C) and pH (2–8) at the current operating point, each with two series on a primary/secondary y-axis. Ethanol Product: rP primary + rGly secondary (both volumetric, g/L/h). Yeast Product: μ primary + kd,eff secondary (both specific, h⁻¹); crossover point = washout T. Glycerol Product: rGly primary (volumetric, g/L/h) + qGly secondary (specific, g/g/h), useful for osmotic / redox stress diagnosis. All three tabs re-render on every parameter change via the 180 ms debounce.
  • Nutrient coupling (Phase 2): μ is multiplied by a Liebig's-minimum factor fnutrients = min(fN, fMg, fZn, fErg, fTween, fP, fCu, fMn, fbiotin, fPan, fB6, fThi, fIno), where each f is a Monod term on the corresponding nutrient. The full 13-factor set was activated when the four limiter-vitamins (pantothenate, B6, thiamine, inositol per Perli 2020) and the trace metals P, Cu, Mn, biotin were promoted from passive tracking to active growth limitation; see the detailed Liebig extension paragraph below. Growth slows sharply when any one nutrient falls below its half-saturation constant. The dominant limiter is reported in the "Limiting" pill above the time-course charts.
  • N depletion: dN/dt = −(μ/YX/N)·X. With YX/N ≈ 10 g DCW/g N, 700 mg/L N supports ~7 g/L biomass growth — the boundary between normal-gravity and VHG fermentation.
  • Cellular ergosterol dilution: d(Ergq)/dt = −μ · Ergq. Pure dilution — anaerobic yeast cannot synthesize sterols. The initial quota is erg_q_init + erg_init_broth / X0, so increasing either the per-cell reserve or the medium supplement shifts stuck-fermentation onset. This is the mechanism behind VHG stuck fermentations at 40–60% sugar utilisation.
  • Adiabatic heat balance (optional): When temperature mode = adiabatic, T becomes a state variable with dT/dt = (Qmetab − Qcool)/Cp, where Qmetab = rP·ΔHferm/MEtOH and Qcool = kcool·(T − Tset). Drop kcool to see runaway heating.
  • pH drift from NH₄+ assimilation (Phase 3): Each mole of ammonium taken up releases 1 mole of H+ as neutral N is incorporated into biomass. Modeled as a strong acid (pKa = −2) with cumulative concentration (Ninit − Nmedium) · hperN / MN, added to the existing aqueous-chemistry buffer solver. hperN is tunable (0 for urea-only, 1 for pure NH₄+, 0.5 for typical amino/ammonium mixtures).
  • Inoculum sizing engineering identity (Phase 3): P = qP·Xavg·t, so Xavg = P / (qP·t). The sizing card solves this for target ethanol titer (auto-synced from Medium Formulations) and fermentation time (read-only field auto-mirrored from Duration — the single source of truth for time), then converts Xavg → Xpitch via a tuneable ratio (default 0.6 for mild growth during lag + exponential phase).
  • Live coupling to Medium Formulations : calc() in the Medium Formulations tab updates window._calcCanonical with the unit-resolved totals (sugarG, ethVolL, volumeL, biomassG) on every input change, then calls importFromMedium() which is bio-process mode-aware. In Batch mode it pushes medium-target concentrations to the simulator's t=0 fields (s, st, n_init, mg_init, zn_init, erg_init_broth, tween80_init). In Semi-Batch mode it ALSO pushes sb_v_target, sb_v_heel (= batchFrac · Vtarget), and fill-mash composition (sb_feed_S, sb_feed_St, sb_feed_N, sb_feed_Mg). In Fed-Batch mode it pushes fb_v_max, fb_v_init (= batchFrac · Vmax), and stream-specific composition fields: fb_c_feed_S and fb_c_feed_St (Stream 1, carbohydrate), fb_n_feed_N (Stream 2, nitrogen), and fb_trace_feed_Zn (Stream 4, trace — pre-populated even when Stream 4 is Off, so enabling the toggle picks up the target). Control strategies, timing windows, and Fmax are NOT auto-populated — those are process choices, not concentration targets, and the user configures them per stream. All modes call syncTiterToInoculum() for the Inoculum Sizing card. A recursion guard prevents re-entry. The green "← Import from Medium Formulations" button remains as a manual refresh escape hatch.
  • Bio-Process operating modes : The simulator supports three modes through a dropdown in Strain & operating conditions, bidirectionally synced with a matching dropdown in the Medium Formulations tab. Batch (default): all ingredients charged at t=0, no flow during fermentation — original behaviour preserved exactly. Semi-Batch: initial volume (Vinit at t=0) plus a single composite fill mash F(t) added during the fill window [tfill,start, tfill,start+tfill]. Three fill profiles (linear / exponential / stepped) and three inoculum-timing modes (pre_fill / in_feed / post_fill). Fed-Batch: starts batch at Vinit, then up to FIVE independent feed streams flow during fermentation, each with its own control strategy, timing, Fmax, and composition:
    Stream 1 — Carbohydrate (C): always visible. Strategies: setpoint (P-controller on residual glucose, the industrial standard for fuel ethanol), exponential μ-targeted (F maintains μtarget by feeding substrate at the cellular consumption rate), constant flow, or off.
    Stream 2 — Nitrogen (N): always visible. Strategies: setpoint (P-controller on residual N), constant flow, one-shot pulse (smeared over ~3 min so RK4 catches it), or off.
    Stream 3 — Phosphorus (P): always visible, default Off. Strategies: constant flow, one-shot pulse, or off. Currently contributes only to volume balance (phosphate is not yet a state variable in the kinetic model — Stream 3 dilutes existing medium species but adds no kinetic effect of its own).
    Stream 5 — Trace elements (Tr): toggleable (default off). Carries dynamic Zn (the 16th state variable). Strategies: constant flow, stepped pulses (3 doses equally spaced over a duration window), or one-shot pulse. Useful for late-fermentation Zn supplementation to delay senescence in VHG ethanol.
    Stream 6 — Vitamins (V): toggleable (default off). Strategies: constant flow or one-shot pulse. Currently informational — the simulator does not track individual vitamins as state variables, so Stream 5 contributes only to volume balance (and adiabatic temperature mixing).
    Shared parameters Vinit, Vmax, tfeed,end apply globally: all streams stop when V ≥ Vmax OR t ≥ tfeed,end, whichever fires first. Per-stream Fmax hard-caps the flow rate of each individual stream.
  • Feed coupling in the ODE : Semi-Batch and Fed-Batch share a unified multi-stream dilution math:
    dV/dt += Σk Fk (total volume gain)
    dCi/dt += (1/V) · (Σk Fk · Ck,feed,i − Ci · Σk Fk) (per-species feed contribution minus dilution)
    dT/dt += (1/V) · Σk Fk·(Tk−T) (adiabatic mixed-stream heat balance)
    The sum Σk runs over 1 stream in Semi-Batch and up to 5 streams in Fed-Batch. Per-stream feed composition is tagged exactly to that stream — Stream 1 carries glucose+starch only (other species at 0 in C-stream), Stream 2 carries N only, Stream 4 carries Zn only. Most off-diagonal Ck,feed,i terms are zero by construction, so the algebra collapses to a small number of non-zero contributions per species. Species with non-zero feed composition: glucose (Stream 1), starch (Stream 1), N (Stream 2), Mg (Semi-Batch only — Mg is batch-only in Fed-Batch per the industrial convention), Zn (Stream 4). Pure-dilution species (feed=0 in all streams): ethanol, dextrins, glycerol, CO₂(aq), lactic acid, acetic acid, ergosterol, Tween-80. Intensive variables (Ergq cellular quota, fact normalized enzyme activity, T outside adiabatic) are unaffected by dilution. When neither bio-process mode is active, all Fk = 0 and the whole block contributes zero — batch behaviour preserved exactly.
  • Regime multipliers are applied relative to the strain-preset base values and are indicative only; they do not compound on repeated changes. Calibrate with your own strain data.
  • Environmental viability gate: both the maintenance term and the non-growth-associated Luedeking–Piret production are now multiplied by fenv = fT·fpH. At cardinal-model extremes where fT=0 or fpH=0, mS·fS·fE,p·fenv = 0 and β·fE,p·fenv = 0, i.e. dormant cells don't consume sugar for maintenance or produce ethanol non-growth-associatedly. Previously a ~0.5 g/L/h floor persisted at T=0 or pH=2 (physically impossible). The fix makes the rP vs T / pH charts drop cleanly to zero outside [Tmin, Tmax] and [pHmin, pHmax].
  • VHG glycerol coupling: the growth-coupled glycerol term is now qg,growth = αGly·μ·(1 + kVHG,Gly·fosm), coupling αGly to the same osmotic Hill that drives qg,osm. This reflects biochemistry: under high total osmolyte, NADH disposal during biosynthesis becomes more glycerol-intensive because the cell is already stressed. At kVHG,Gly=1 (default), full VHG (fosm→1) doubles αGly. Setting kVHG,Gly=0 recovers the legacy behaviour. qgly is now decomposed into qgly,stress (osm+eth+T+pH+N, U-shape in T/pH) and qgly,growthlike (α·μ·(1+kVHG·fosm) + qG0, Gaussian) so the two biochemically distinct mechanisms display as separate curves on the Glycerol Product instant chart.
  • Instant-prediction chart semantics: the three prediction tabs were rebuilt to show distinct information instead of three copies of the μ-Gaussian. Ethanol Product now shows rP primary + YP/S,apparent = qP/qS secondary (the effective yield after maintenance and glycerol diversions). Yeast Product now shows μ primary, μ−kd,eff (net growth, dashed purple), and kd,eff (dotted red, right axis) — the zero-crossings of the net curve mark the WASHOUT boundaries. Glycerol Product plots the two decomposition buckets described above.
  • Organic acid production & dynamic pH coupling: Lactic acid (LA) and acetic acid (AA) are now dynamic ODE state variables: dLA/dt = YLA/S·qS·X, dAA/dt = YAA/S·qS·X, with production yields defaulting to 0 (no production unless user enables or optimizer fits). Both accumulate during fermentation and feed back into the pH calculation via their pKa equilibria (lactic pKa = 3.86, acetic pKa = 4.76) through the buildDynamicAcids() function, which replaces the static initial organic acid concentrations in the pH solver at each RK4 timestep. The full pH model now includes four acid sources: CO₂ dissolution (H₂CO₃), NH₄+ assimilation H+ release, dynamic lactic acid, and dynamic acetic acid — all solved simultaneously in the bisection-based proton balance. Environment chart shows both species on a dedicated "Org. acids (g/L)" axis.
  • Model Exp. Data tab: Fourth main tab for fitting the model to observed fermentation data. Accepts all 12 standard ethanol fermentation HPLC columns: time, pH, temperature, DCW, DP4+, DP3, DP2, DP1, lactic acid, glycerol, acetic acid, ethanol. Column names are case-insensitive with multiple aliases supported (e.g. ethanol, EtOH, E all match). DP2 + DP3 are automatically summed to a dextrin pool for scoring against the model's dextrin trajectory. Replicate samples at the same time point are automatically detected and averaged to mean ± SD.
  • Model Exp. Data — four actions:
    • Statistical analysis — evaluates raw data quality: dataset overview (time points, duration, sampling density), per-species quality table (n valid, missing, min/max/range, CV% from replicates or a noise estimate from the trajectory when there are none, trend detection ↑↓→↕, quality rating ✅⚠️❌), growth-phase segmentation from ln(DCW) (lag, exponential, stationary, decline windows with point counts), outlier screening at replicate and trajectory level, mass-balance checks (observed YP/S against Gay-Lussac, carbon recovery, ethanol rising after sugar exhaustion), a phase-aware parameter estimability checklist, and data limitation warnings.
    • Evaluate fit — runs the simulator with current parameters, interpolates predictions at observation times, and reports R², RMSE, NRMSE (% of range), MAE, mean bias, reduced χ² against the replicate SEM and a runs test on the residual signs per species, plus AIC/BIC on the pooled objective. Overlays observed data as scatter points on the Metabolism chart.
    • Calculate parameters — derives kinetic parameters analytically from the time-course data: μmax (corrected: slope of ln(X) + kd,eff ÷ fproduct at operating conditions), YX/S (apparent ΔX/ΔS), YP/S (apparent ΔE/ΔS), α/β (Luedeking–Piret regression of qP vs μ), kd (apparent kd,eff from decline phase), mS (apparent stationary-phase qS), plus glycerol and organic acid yields. All parameters labeled "apparent" with explanations of entanglement with the full ODE model.
    • Train (optimise) — Nelder–Mead simplex on user-selected parameters, normalised [0,1] within bounds, async with Stop button. 14 fittable parameters across 3 groups: growth kinetics (μmax, KS, mS, kd, kd,E), yields (YX/S, YP/S, αGly, YLA/S, YAA/S), ethanol production (α, β, Emax, Einh).
    A "Next steps" panel appears after each action with contextual guidance and re-run buttons for iterative refinement.
  • Medium volume tracking from CO₂ outgassing: ethanol fermentation loses mass as C₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂ drives 0.4886 g of CO₂ out of each gram of glucose consumed. On typical VHG mashes, 5–10% of medium volume exits as gas. Three modes are available (Fermentation Conditions → Strain & operating conditions → Volume tracking): Constant V (default, no tracking); Post-proc — ODE runs at constant V, then Vfinal is computed from cumulative CO₂ mass balance and all in-solution species are rescaled by V0/Vfinal for display; In-ODE rigorous — V becomes a state variable in the 30-element vector (st, s, x, e, gly, co2_aq, fact, N, Mg, Ergq, T, dx, V, la, aa, Zn, P, Cu, Mn, Fe, Mo, Co, Biotin, Thi, Rib, Nia, Pan, B6, Fol, Ino — the 15 macro states plus the 15 nutrients made dynamic) with dV/dt = −rCO₂·V/(ρ·1000); the companion dilution term +C·rCO₂/(ρ·1000) is applied to every per-medium-volume species (starch, glucose, biomass, ethanol, glycerol, dissolved CO₂, N, Mg, dextrins, lactic acid, acetic acid), derived from the product-rule expansion d(C·V)/dt = r·V. Ergq (per-biomass mg/g DCW), fact (dimensionless), and T (intensive) do not receive the dilution term. In-ODE mode captures the nonlinear coupling where ethanol inhibition feels the rising concentration during the run — slightly lowering total ethanol mass but raising end-of-run g/L.
  • DCW → cell count conversion: cells/mL = X (g DCW/L) × fcells × 107, where fcells is derived from the ADY product spec on the Inoculum & Seed Train tab and shown read-only in the Inoculum Sizing card (field: "Cells per g DCW", units ×1010). Derived 2.13 corresponds to ~47 pg single-cell dry weight (industrial S. cerevisiae exponential phase). Published values span 3–10 (60–200 pg/cell equivalent) depending on strain, growth phase (stationary cells carry glycogen/trehalose → heavier), ethanol stress (cells shrink in VHG runs), and measurement method. The factor is used by the Inoculum Sizing cell-density readout, the Yeast chart's cells-per-mL curve, and the Yeast summary panel's Inoculum/Peak/End cell counts.

Strain presets are indicative; calibrate with your strain data. Regime modifies yields and glycerol base to mimic redox shifts.

References

Key primary sources for the kinetic, stoichiometric, and engineering choices encoded in the suite. All citations are illustrative — the implementation often blends or adapts published forms; see the bullets above for exact functional forms.

  • Luedeking, R. & Piret, E. L. (1959). A kinetic study of the lactic acid fermentation. J. Biochem. Microbiol. Technol. Eng. 1: 393–412. — Original growth-associated + non-growth product term qP = α·μ + β.
  • Luong, J. H. T. (1985). Kinetics of ethanol inhibition in alcohol fermentation. Biotechnol. Bioeng. 27: 280–285. — fE with Einh threshold and Emax; default ethanol-inhibition model in this suite.
  • Aiba, S., Shoda, M. & Nagatani, M. (1968). Kinetics of product inhibition in alcohol fermentation. Biotechnol. Bioeng. 10: 845–864. — Exponential fE = exp(−kE·E); legacy alternative.
  • Andrews, J. F. (1968). A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 10: 707–723. — Haldane substrate-inhibition term S/(Ks+S+S²/Ki,S).
  • Bai, F. W., Anderson, W. A. & Moo-Young, M. (2008). Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnol. Adv. 26: 89–105. — VHG fermentation, industrial yield benchmarks (YE/S=0.45–0.49), feedstock yield coefficients.
  • Walker, G. M. (2011). Pichia and Saccharomyces yeast biology. The Yeasts: A Taxonomic Study, 5th ed. — Magnesium / zinc / vitamin requirements, sterol & unsaturated-fatty-acid auxotrophy under anaerobiosis.
  • Casey, G. P. & Ingledew, W. M. (1986). Ethanol tolerance in yeasts. CRC Crit. Rev. Microbiol. 13: 219–280. — Membrane / Mg²⁺ / lipid mechanisms behind ethanol toxicity; basis for VHG sterol & oleate supplementation.
  • Pham, T. K. & Wright, P. C. (2008). The proteomic response of Saccharomyces cerevisiae in very high glucose conditions. J. Proteome Res. 7: 4766–4774. — Osmotic-stress glycerol overproduction; basis for the Hill term qg,osm.
  • Atala, D. I. P., Costa, A. C., Maciel, R. & Maciel Filho, R. (2001). Kinetics of ethanol fermentation with high biomass concentration. Appl. Biochem. Biotechnol. 91–93: 353–365. — Cell-death rate dependence on ethanol & temperature.
  • Verduyn, C. et al. (1990). Physiology of Saccharomyces cerevisiae in anaerobic glucose-limited chemostat cultures. J. Gen. Microbiol. 136: 395–403. — Anaerobic YX/S ≈ 0.10 g/g, ergosterol & UFA quotas, maintenance coefficient mS.
  • Cot, M., Loret, M.-O., François, J. & Benbadis, L. (2007). Physiological behaviour of Saccharomyces cerevisiae in aerated fed-batch fermentation for high-level production of bioethanol. FEMS Yeast Res. 7: 22–32. — Industrial fed-batch & ergosterol dilution behaviour.
  • Stewart, G. G. (2017). Brewing and Distilling Yeasts. Springer. — α-Amylase / glucoamylase loading conventions (≈500 U/g starch / 200 U/g starch), nitrogen targets (200–700 mg N/L for normal-gravity to VHG).
  • Pham, H. T. B., Sundstrom, E. R. & Wright, A. R. (2008). Kinetic modeling of ethanol fermentation from wheat flour under simultaneous saccharification and fermentation. Biotechnol. Prog. 24: 118–126. — Two-step starch hydrolysis kinetics (Starch → Dextrins → Glucose) with separate Km for each substrate; basis for the vliq, vsac, vGA·St rate decomposition.
  • Gancedo, J. M. (1998). Yeast carbon catabolite repression. Microbiol. Mol. Biol. Rev. 62: 334–361. — Mechanism of glucose repression of MAL gene expression; basis for the Kglu,rep/(Kglu,rep+S) gate on qDx,yeast in the dextrin uptake model.
  • Pirt, S. J. (1965). The maintenance energy of bacteria in growing cultures. Proc. R. Soc. B 163: 224–231. — Maintenance-energy framework underpinning the mS·X term.
  • Kosaric, N. & Vardar-Sukan, F. (2001). Potential source of energy and chemical products. In The Biotechnology of Ethanol, Wiley-VCH. — Feedstock-yield reference values for corn / wheat / cassava / molasses.

Model Notes — BibliographyRefs

Master bibliography for the full suite — an organised superset of the topic-specific reference lists on the Simulator, Medium Formulations, and Model Exp. Data tabs. Grouped following Part VIII of the technical report: Primary literature, Background reading, Ergosterol dilution mechanism, and Kinetic modelling choices.

Primary literature — fuel ethanol yeast nutrition and VHG practice

  1. Ingledew WM (1993). Yeasts for production of fuel ethanol. In The Yeasts, 2nd ed., Vol. 5, pp. 245–291. Academic Press, London. — The canonical reference for fuel-ethanol yeast nutrition, FAN tier recommendations, and VHG operation. If a single source is consulted from this list, it should be this one.
  2. Bafrncová P, Šmogrovičová D, Sláviková I, Pátková J, Dömény Z (1999). Improvement of very high gravity ethanol fermentation by media supplementation using Saccharomyces cerevisiae. Biotechnology Letters 21:337–341. — Quantitative Mg, Zn, and pantothenate supplementation data for VHG; source of the calculator's micronutrient defaults.
  3. Casey GP, Ingledew WM (1986). Ethanol tolerance in yeasts. CRC Critical Reviews in Microbiology 13:219–280. — Classic review of membrane / Mg²⁺ / lipid mechanisms of ethanol toxicity; biochemical basis for VHG sterol and oleate supplementation.
  4. Jones RM, Ingledew WM (1994). Fermentation of very high gravity wheat mash prepared using fresh yeast autolysate. Bioresource Technology 50:97–101. — Defines the operational FAN tiers (normal gravity ≈200 mg/L; 15% v/v ≈400 mg/L; VHG ≈600–700 mg/L) encoded as calculator defaults.
  5. Lange HC, Heijnen JJ (2001). Statistical reconciliation of the elemental and molecular biomass composition of Saccharomyces cerevisiae. Biotechnology and Bioengineering 75:334–344. — Reference biomass elemental composition; the basis for mass-balance closure checks and the N/P/K/Mg DCW-% defaults.
  6. Andreasen AA, Stier TJB (1953). Anaerobic nutrition of Saccharomyces cerevisiae. I. Ergosterol requirement for growth in a defined medium. Journal of Cellular and Comparative Physiology 41:23–36.
  7. Andreasen AA, Stier TJB (1954). Anaerobic nutrition of Saccharomyces cerevisiae. II. Unsaturated fatty acid requirement for growth in a defined medium. Journal of Cellular and Comparative Physiology 43:271–281. — Together with [6], the original demonstration that yeast cannot grow anaerobically without exogenous sterol and UFA. Biochemical basis for the Phase 2 ergosterol dilution mechanism.

Background reading — yeast biology and bioprocess engineering

  1. Walker GM (1998). Yeast Physiology and Biotechnology. Wiley, Chichester. — Comprehensive yeast-biology textbook; chapters on growth, fermentation, stress responses, and industrial applications. Accessible to readers with basic biochemistry background.
  2. Bailey JE, Ollis DF (1986). Biochemical Engineering Fundamentals, 2nd ed. McGraw-Hill, New York. — The standard textbook on bioreactor design and bioprocess kinetics; the chapters on growth kinetics, yield coefficients, and inhibition models map directly to the simulator's mathematical framework.
  3. Doran PM (2013). Bioprocess Engineering Principles, 2nd ed. Academic Press, London. — More recent and more accessible than Bailey & Ollis. Chapters on stoichiometry, kinetics, and reactor operation cover the material needed to read this report at a deeper level.
  4. Ingledew WM, Kelsall DR, Austin GD, Kluhspies C, eds. (2009). The Alcohol Textbook, 5th ed. Nottingham University Press. — The standard reference for industrial alcohol production; detailed coverage of medium design, fermentation operation, distillation, and process economics.
  5. Stewart GG (2017). Brewing and Distilling Yeasts. Springer, Cham. — Strain selection and industrial practice; α-amylase and glucoamylase loading conventions that the calculator uses as defaults.
  6. Reed G, Nagodawithana TW (1991). Yeast Technology, 2nd ed. Van Nostrand Reinhold, New York. — Yeast extract and autolysate compositions; basis for the calculator's complex-supplement nutrient credit tables.

Ergosterol dilution mechanism

  1. Aguilera F, Peinado RA, Millán C, Ortega JM, Mauricio JC (2006). Relationship between ethanol tolerance, H⁺-ATPase activity and the lipid composition of the plasma membrane in different wine yeast strains. International Journal of Food Microbiology 110:34–42. — Quantitative correlations between membrane sterol content, ethanol tolerance, and H⁺-ATPase activity; ties the simulator's fE and Ergq terms to real biology.
  2. You KM, Rosenfield CL, Knipple DC (2003). Ethanol tolerance in the yeast Saccharomyces cerevisiae is dependent on cellular oleic acid content. Applied and Environmental Microbiology 69:1499–1503. — Role of UFAs in ethanol tolerance and the rescue of ethanol-sensitive strains by oleate supplementation.
  3. Cot M, Loret MO, François J, Benbadis L (2007). Physiological behaviour of Saccharomyces cerevisiae in aerated fed-batch fermentation for high-level production of bioethanol. FEMS Yeast Research 7:22–32. — Industrial fed-batch operation and ergosterol dilution behaviour that the dilution kinetics model.

Kinetic modelling choices

  1. Luedeking R, Piret EL (1959). A kinetic study of the lactic acid fermentation. Batch process at controlled pH. Journal of Biochemical and Microbiological Technology and Engineering 1:393–412. — Growth-associated and non-growth-associated product formation (α·μ + β).
  2. Luong JHT (1985). Kinetics of ethanol inhibition in alcohol fermentation. Biotechnology and Bioengineering 27:280–285. — Generalised ethanol-inhibition kinetics with the critical ethanol concentration.
  3. Aiba S, Shoda M, Nagatani M (1968). Kinetics of product inhibition in alcohol fermentation. Biotechnology and Bioengineering 10:845–864. — Exponential ethanol toxicity form.
  4. Andrews JF (1968). A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnology and Bioengineering 10:707–723. — Substrate-inhibition (Haldane) kinetics at high sugar.
  5. Bai FW, Anderson WA, Moo-Young M (2008). Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnology Advances 26:89–105. — VHG ethanol fermentation review and industrial yield benchmarks.
  6. Walker GM (2011). Pichia and Saccharomyces yeast biology. In The Yeasts: A Taxonomic Study, 5th ed., Elsevier. — Yeast nutritional needs and strain variability.
  7. Pham HTB, Sundstrom ER, Wright AR (2008). Kinetic modeling of ethanol fermentation from wheat flour under simultaneous saccharification and fermentation. Biotechnology Progress 24:118–126. — SSF enzyme kinetics underpinning the two-step hydrolysis model.
  8. Gancedo JM (1998). Yeast carbon catabolite repression. Microbiology and Molecular Biology Reviews 62:334–361. — Glucose repression of the MAL operon (maltose permease + maltase); the biological basis for the Kglu,rep/(Kglu,rep+S) gate on yeast dextrin uptake during high-glucose phases.
  9. Atala DIP, Costa AC, Maciel R, Maciel Filho R (2001). Kinetics of ethanol fermentation with high biomass concentration. Applied Biochemistry and Biotechnology 91–93:353–365. — Temperature- and ethanol-dependent cell-death kinetics.
  10. Verduyn C, Postma E, Scheffers WA, van Dijken JP (1990). Physiology of Saccharomyces cerevisiae in anaerobic glucose-limited chemostat cultures. Journal of General Microbiology 136:395–403. — True anaerobic YX/S chemostat values; ergosterol and UFA quotas; maintenance coefficient.
  11. Cot M, Loret MO, François J, Benbadis L (2007). Physiological behaviour of Saccharomyces cerevisiae in aerated fed-batch fermentation for high-level production of bioethanol. FEMS Yeast Research 7:22–32. — Glycerol overflow under VHG.
  12. Pirt SJ (1965). The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society B 163:224–231. — The maintenance-energy framework.
  13. Monod J (1949). The growth of bacterial cultures. Annual Review of Microbiology 3:371–394. — Saturation form S/(Ks+S) for substrate-limited growth.
  14. Nelder JA, Mead R (1965). A simplex method for function minimization. The Computer Journal 7:308–313. — The simplex-reflection algorithm driving the Model Exp. Data tab's Train action.
  15. Kosaric N, Vardar-Sukan F (2001). Potential source of energy and chemical products. In The Biotechnology of Ethanol, Wiley-VCH. — Feedstock-yield reference values.
This bibliography collates references cited across the four suite tabs. Individual tabs (Simulator, Medium Formulations, Model Exp. Data) carry topically-filtered subsets that are easier to skim while using the relevant tool. Citations here follow the organisation of Part VIII of the technical report.
© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Conceptual tool for rapid what-if analysis.

Ethanol Fermentation Medium Formulations

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Anaerobic S. cerevisiae  |  Conceptual tool for rapid what-if analysis  |  v26.93

HDYC · Pre-Fermentation · Fermentation  •  Composition-Driven for Biomass Stages  •  Batch, Semi-Batch & Fed-Batch  •  Real-time

Formulating
▼Summary

Fermentation summary — computed from current targets

Fermentation Technology
Batch
selected in Yields card
Feedstock
Corn — whole kernel
selected in Feedstock card
Total Sugar Required
17.15 kg
ethanol ÷ YE/S
Ethanol Produced
10.0 L
absolute ethanol at target titer
Biomass Produced
— g
sugar × YX/S
α-Amylase
— kU
@ 500 U/g starch (liquefaction)
Starch Needed
— kg
starchFrac × sugar ÷ 1.11
Feedstock (as-received)
— kg
dry mass ÷ (1 − moisture)
Medium Volume
82.9 L
ethanol ÷ titer
Glycerol Produced
— g
sugar × YGly/S
CO₂ Evolved
— kg
~0.957 × ethanol mass
Glucoamylase
— kU
@ 200 U/g starch (saccharification)
Stoichiometric Yields
Apparent Ethanol Yield (YE/S) 0.460 g/g
fermentation efficiency 90.0% of theoretical
0.51142 × 0.900 = 0.4603 g/g. Industrial fuel ethanol typically runs 88–91%.
Biomass Yield on Sugar (YX/S) 0.050 g/g
Glycerol Yield on Sugar (YGly/S) 0.040 g/g
Units:
▼Target Production
▼Ethanol Fermentation Targets
Target an ethanol quantity; medium volume is derived from the titer.
▼Bio-Process & Fermentation Technology
All ingredients are charged in the initial batch medium at t = 0.
% Nutrients in Initial Batch Phase 100%
▼Carbon Mass Balance
▼Primary Substrate
% w/w
▶ Detailed composition (% dry basis · editable) Corn — whole kernel
Updates automatically when feedstock changes. Edit any cell to override the literature default; Σ should close to ~100%.
Component Range Target (%)
Starch (α-amylase substrate)64–78%
Free sugars (immediately fermentable)1–3%
Protein (crude · Kjeldahl N×6.25)7–10%
Oil / fat (triglycerides)3–5%
Fiber (cellulose · hemicellulose)2–3%
Ash (mineral matter)1.3–1.5%
Other carbs (NSP · β-glucans · pentosans)~8%
Σ Composition100.0%
▶ Elemental composition (ppm dry · total × availability) Corn — whole kernel
Drives the feedstock-credit calculation. Total is the elemental content of the dry feedstock in ppm (mg per kg). Avail is the fraction the yeast can access (phytate-bound P is ~50% available; ash-released K/Mg are ~100%). Available = Total × Avail, in ppm dry. Edit either Total or Avail; Available recomputes live.
▼Medium Target Concentrations
▼Macronutrients 7 entries
Element / Factor Min. Max. Target Unit
Carbon (C) — — g/L
Nitrogen (N) 200 700 mg/L
Phosphorus (P) 150 400 mg/L
Potassium (K) 300 800 mg/L
Magnesium (Mg) 50 250 mg/L
Sulfur (S) 100 300 mg/L
Calcium (Ca) 20 100 mg/L
Sodium (Na) — 500 mg/L
▼Trace Metals 6 entries
Element / Factor Min. Max. Target Unit
Iron (Fe) 2 30 mg/L
Zinc (Zn) 0.5 5 mg/L
Manganese (Mn) 0.2 2 mg/L
Copper (Cu) 0.05 0.5 mg/L
Molybdenum (Mo) 0.02 0.2 mg/L
Cobalt (Co) 0.02 0.2 mg/L
▼Vitamins 8 entries
Element / Factor Min. Max. Target Unit
Biotin (B8) 0.05 0.3 mg/L
Thiamine (B1) 1 10 mg/L
Riboflavin (B2) 0.5 2 mg/L
Nicotinic A. (B3) 2 10 mg/L
Pantothenate (B5) 2 10 mg/L
Pyridoxine (B₆) 0.5 2 mg/L
Folic A. (B9) 0.1 0.5 mg/L
Inositol 10 50 mg/L
▼Anaerobic Lipid Factors · essential under anaerobiosis 2 entries
Element / Factor Min. Max. Target Unit
Ergosterol 5 20 mg/L
Tween-80 (oleate src) 100 1000 mg/L
© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Conceptual tool for rapid what-if analysis.
▼Formulation Results
▼Macronutrients
CompoundSalt / Note Total RequiredUnitIn medium
▼Trace Metals
CompoundSalt / NoteTotal RequiredUnitIn medium
▼Vitamins
CompoundSalt / NoteTotal RequiredUnitIn medium
▼Anaerobic Lipid Factors · essential under anaerobiosis
CompoundSalt / NoteTotal RequiredUnitIn medium
Enzymes · dosed on feedstock or broth volume
EnzymeDoseActivityTotal Required$/kgCost
Prices and activities are placeholders — replace from the supplier COA. Starch-converting enzymes are costed on the fermentation stage only.
Initial Batch Medium  ·  All nutrients added at t = 0  ·  click headers to expand/collapse
▼Carbon Source
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Nitrogen Source
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Phosphorus Source
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Micronutrients
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Trace Metals
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Vitamins
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
▼Anaerobic Lipid Factors · essential under anaerobiosis
CompoundTotal in BatchUnitIn batch
Stock sheet appears with the medium.
Initial batch — stock solutions volumes in
VHG Fed-Batch Feed  ·  Added during fermentation (only if batch % < 100)  ·  click headers to expand/collapse
Stock sheet appears with the medium.
Stock sheet appears with the medium.
Stock sheet appears with the medium.
Stock sheet appears with the medium.
Stock sheet appears with the medium.
Stock sheet appears with the medium.
▼Macronutrients
CompoundTotal to FeedUnitIn feed
Stock sheet appears with the medium.
▼Trace Metals
CompoundTotal to FeedUnitIn feed
Stock sheet appears with the medium.
▼Vitamins
CompoundTotal to FeedUnitIn feed
Stock sheet appears with the medium.
▼Anaerobic Lipid Factors · essential under anaerobiosis
CompoundTotal to FeedUnitIn feed
Stock sheet appears with the medium.
Feed streams — stock solutions volumes in
Computed with the medium.

Ethanol Fermentation — Recommended Medium Concentrations

Targets reflect typical fuel-ethanol practice and literature guidance (Ingledew, Bafrncová, Jones & Pierce, Casey & Ingledew). Unlike propagation, these are medium concentrations, not per-kg-biomass. Defined-medium work; molasses/mash already supplies much of this.
Click any header to expand/collapse.

▼Macronutrients 7 entries
Element /
Factor		Typical
target		Min.Max.UnitNotes
Nitrogen700200700mg/LFree amino nitrogen — 200–300 adequate for 12% v/v; 400–500 for 15%; 500–700 for VHG (>17% v/v). Deficiency causes sluggish fermentation and H₂S
Phosphorus (P)250150400mg/LOften co-delivered with N when DAP is used (DAP is 21% N + 23% P). Excess is harmless; deficiency rare with DAP
Potassium (K)400300800mg/LMajor intracellular cation — osmotic balance against high sugar/ethanol. Higher targets for VHG
Magnesium (Mg)10050250mg/LCritical for ethanol tolerance — stabilises membranes. Target >3 mM (≈75 mg/L) free Mg²⁺; push to 150–250 mg/L for VHG
Sulfur (S)150100300mg/LMainly cysteine/methionine biosynthesis. Usually co-delivered with (NH₄)₂SO₄ or MgSO₄; avoid excess (H₂S production)
Calcium (Ca)5020100mg/LSignalling role only — non-limiting in most media. Often already present in process water at >20 mg/L
Sodium (Na)50—500mg/LNon-essential; tolerated up to ~500 mg/L. Higher levels inhibit growth and ethanol yield
▼Trace metals 6 entries
Element /
Factor		Typical
target		Min.Max.UnitNotes
Iron (Fe)5230mg/LHeme/Fe-S clusters; often present in molasses/process water. Supplement defined media only
Zinc (Zn)20.55mg/LADH cofactor — the single most important trace for ethanol fermentation. <0.5 mg/L → stuck ferm, acetaldehyde accumulation, off-flavors
Manganese (Mn)2.00.22mg/LSOD cofactor; minor role. Present in most process waters
Copper (Cu)0.20.050.5mg/LCu/Zn-SOD; trace requirement. Toxic >5 mg/L
Molybdenum (Mo)0.050.020.2mg/LUltra-trace; usually present as contamination in macronutrient salts
Cobalt (Co)0.050.020.2mg/LUltra-trace; B₁₂ precursor. Usually adequate from molasses/corn mash
▼Vitamins 8 entries
Element /
Factor		Typical
target		Min.Max.UnitNotes
Biotin (B8)0.10.050.3mg/LEssential — yeast cannot synthesize. Cofactor for acetyl-CoA carboxylase (fatty acid synthesis); demand elevated under ethanol stress
Thiamine (B1)2110mg/LTPP cofactor for pyruvate decarboxylase — the glycolytic enzyme generating acetaldehyde for ethanol. Industrial strains often thiamine auxotrophs
Riboflavin (B2)10.52mg/LFAD/FMN cofactor; synthesized by yeast, rarely limiting in practice
Nicotinic A. (B3)5210mg/LNAD⁺/NADP⁺ precursor; synthesized from tryptophan. Boost for amino-acid-limited media
Pantothenate (B5)5210mg/LCoenzyme A precursor. Deficiency causes stuck fermentation + H₂S; strongly correlated with sluggish fermentations in fuel ethanol
Pyridoxine (B₆)10.52mg/LPLP cofactor for aminotransferases; usually synthesized adequately
Folic A. (B9)0.20.10.5mg/LOne-carbon metabolism; synthesized by yeast, rarely limiting
Inositol251050mg/LPhosphatidylinositol precursor — membrane structural role. Supplementation improves ethanol tolerance above 10% v/v
▼Anaerobic Lipid Factors · essential under anaerobiosis 2 entries
Element /
Factor		Typical
target		Min.Max.UnitNotes
Ergosterol10520mg/LEssential under anaerobiosis. Yeast cannot synthesize sterols without O₂. Fermentations lacking ergosterol stall at 40–60% sugar utilisation. Add as EtOH/Tween-80 emulsion
Tween-80 (oleate source)5001001000mg/LSupplies C18:1 unsaturated fatty acid. Anaerobic desaturation impossible → oleate must be exogenous. Standard fuel ethanol dose: 0.5 g/L Tween-80
▼Ethanol Fermentation — Process Notes 12 topics
TopicGuidance
Ethanol yield (YE/S)Theoretical Gay-Lussac max = 0.511 g EtOH/g glucose. Industrial strains achieve 0.45–0.49 g/g (88–96% of theoretical). Glycerol + biomass + organic acids account for the ~3–12% loss.
Biomass yield (YX/S)0.03–0.08 g DCW/g sugar under anaerobic conditions — an order of magnitude lower than aerobic propagation (0.45–0.55). Nitrogen and vitamin demands scale with this small biomass.
Glycerol byproduct2–5% of sugar is diverted to glycerol as a redox sink to reoxidise NADH from biosynthesis. Increases under osmotic stress (VHG, > 250 g/L sugar) to ~6–8%.
CO₂ stoichiometryC₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂ gives a CO₂/EtOH mass ratio of 88/92 = 0.957. Expect ≈0.44 g CO₂ per g sugar fermented (at YE/S=0.4603).
NitrogenTarget 200–400 mg N/L for normal gravity (12–15% v/v), 400–700 mg/L for VHG (>17% v/v). DAP is standard; supplement with yeast extract or CSL for complex N if needed.
Magnesium & ethanol toleranceMg²⁺ stabilises membranes against ethanol damage. Target > 3 mM free Mg²⁺ in medium for VHG (~75 mg/L). Critical for productivity at > 10% v/v ethanol.
Zinc & ADH activityZn²⁺ is the active-site metal of alcohol dehydrogenase (ADH). Deficiency (< 0.5 mg/L) causes sluggish fermentation and acetaldehyde accumulation. 1–2 mg/L Zn²⁺ added as ZnSO₄ is typical.
Biotin & pantothenateThese two vitamins are the most common vitamin limitations in ethanol fermentation. Pantothenate deficiency elevates H₂S production and stalls fermentation at 60–80% completion. Supplement even if yeast extract is used.
VHG operation (> 17% v/v)Use fed-batch sugar addition to avoid osmotic shock. Supplement with unsaturated fatty acids (oleate, Tween-80) and sterols (ergosterol) — anaerobic synthesis is impaired and these become essential for membrane integrity.
pH & temperatureOptimal pH 4.0–5.0 (lower than propagation — suppresses contaminants). Temperature 30–34 °C for regular strains, up to 38–40 °C for thermotolerant strains. Ethanol tolerance drops sharply > 35 °C.
Trace element stocksPrepare 1000× concentrated trace stock in dilute HCl (pH 1–2) to prevent precipitation. Autoclave or filter-sterilise separately from macronutrients and sugar to avoid Maillard reactions.
Vitamin stabilityThiamine, riboflavin, folate are heat/light-labile. Filter-sterilise (0.2 µm) and add post-autoclaving. Biotin stock (0.2% w/v) stable at 4 °C for weeks; pantothenate hydrolyses above pH 7 — keep acidic.
Test against target:
Test Medium  ·  coverage by category  ·  click headers to expand/collapse
▼Macronutrients
Compound Salt / Note Amount added Unit Coverage Max vol. (L)
▼Trace Metals
Compound Salt / Note Amount added Unit Coverage Max vol. (L)
▼Vitamins
Compound Salt / Note Amount added Unit Coverage Max vol. (L)
▼Anaerobic Lipid Factors · essential under anaerobiosis
Compound Salt / Note Amount added Unit Coverage Max vol. (L)
Enter compound amounts above to test the medium.

Medium Formulations — Quick StartAll stages

One calculator formulates all three media, but they are not built the same way, and that difference is the thing to understand first. HDYC and Pre-Fermentation make cells, so their targets are derived from cell composition and the harvest. Fermentation makes ethanol, so its targets are fermentative optima you type in. Each stage has its own Medium Instructions button on the stage bar with the derivation in full.

  1. Pick the stage first. The tab bar selects which formulation you are editing. Vessel volumes and the harvest come from Inoculum & Seed Train; this tab owns composition.
  2. Biomass stages are derived and locked. On HDYC and Pre-Fermentation the targets are computed — quota × biomass ÷ volume, less what the inoculum carries in and what the feedstock delivers, over the utilisation factor. To change a target, change what it follows from.
  3. Fermentation targets are typed within the Min./Max. specification range on each row. Nitrogen is set to what the yeast needs to reach the target cell mass and no more — surplus nitrogen buys nothing and feeds contaminants.
  4. Choose the compound per element on Total Required, then the supply grade beside it. Co-delivery is accounted for, so a salt carrying two elements reduces both.
  5. Read the split on Medium Bioprocessing. Initial Batch and Feed Streams show where each compound goes; the split follows vessel geometry and, for carbon in fed-batch, the initial sugar concentration rather than a fraction of the total.
  6. Make it up from the stock sheets. Each line card carries its own stock beside it, with the concentration factor, the volume to make up and the dose. The make-up procedure sits behind the i on the card.
  7. Then simulate. Fermentation Simulators reads this formulation for the selected stage; a medium change propagates there without re-importing.

Medium Formulations — ReferencesRefs

Primary sources for the nutrient targets, FAN tiers, element stoichiometry, feedstock yields, and complex-material compositions used by the Medium Formulations tab. Where the calculator's defaults represent a range in the literature, the citation lists both endpoints and the implemented midpoint.

FAN, yeast nutrition, and VHG operation

  1. Ingledew WM (1993). Yeasts for production of fuel ethanol. In The Yeasts, 2nd ed., Vol. 5, pp. 245–291. Academic Press, London. — The canonical reference for fuel-ethanol yeast nutrition, FAN tier recommendations, and VHG operation. The single most cited source for the calculator's default nutrient targets.
  2. Jones RM, Ingledew WM (1994). Fermentation of very high gravity wheat mash prepared using fresh yeast autolysate. Bioresource Technology 50:97–101. — Defines the operational FAN ranges encoded as the calculator's defaults: ~200 mg/L for normal gravity, ~400 mg/L for 15% v/v targets, ~600–700 mg/L for VHG.
  3. Bafrncová P, Šmogrovičová D, Sláviková I, Pátková J, Dömény Z (1999). Improvement of very high gravity ethanol fermentation by media supplementation using Saccharomyces cerevisiae. Biotechnology Letters 21:337–341. — Quantitative Mg, Zn, and pantothenate supplementation data; source of the VHG micronutrient defaults (Mg 500 mg/L, Zn 2 mg/L, pantothenate 5 mg/L).
  4. Casey GP, Ingledew WM (1986). Ethanol tolerance in yeasts. CRC Critical Reviews in Microbiology 13:219–280. — Biochemical basis for the Mg / ergosterol / UFA supplementation strategy at high titer; motivates the calculator's lipid-factor category.
  5. Thomas KC, Ingledew WM (1990). Fuel alcohol production: effects of assimilable nitrogen on fermentation of very-high-gravity wheat mashes. Applied and Environmental Microbiology 56:2046–2050. — Demonstrates FAN as the primary rate-limiting nutrient in VHG wheat mash; quantitative dose-response used in the FAN-limitation model.

Biomass composition and element stoichiometry

  1. Lange HC, Heijnen JJ (2001). Statistical reconciliation of the elemental and molecular biomass composition of Saccharomyces cerevisiae. Biotechnology and Bioengineering 75:334–344. — Reference elemental composition of S. cerevisiae biomass (C/H/N/O/P/S/K/Mg); basis for the calculator's N = 8.3%, P = 1.2%, K = 1.0%, Mg = 0.4% DCW defaults.
  2. Walker GM (1998). Yeast Physiology and Biotechnology. Wiley, Chichester. — Comprehensive yeast-biology textbook; source for macro/micronutrient physiological roles and trace-metal auxotrophy data.
  3. Walker GM (2011). Pichia and Saccharomyces yeast biology. In The Yeasts: A Taxonomic Study, 5th ed., Elsevier. — Mg / Zn / vitamin requirements; sterol and UFA auxotrophy under anaerobiosis; basis for the Anaerobic Lipid Factors sub-card.
  4. Verduyn C, Postma E, Scheffers WA, van Dijken JP (1990). Physiology of Saccharomyces cerevisiae in anaerobic glucose-limited chemostat cultures. Journal of General Microbiology 136:395–403. — Anaerobic biomass yield YX/S ≈ 0.10 g/g (chemostat); ergosterol and UFA quotas per g DCW; the calculator's YX/S default (0.05) is a conservative industrial value within this range.
  5. Andreasen AA, Stier TJB (1953, 1954). Anaerobic nutrition of Saccharomyces cerevisiae. I. Ergosterol requirement. J. Cell. Comp. Physiol. 41:23–36; II. Unsaturated fatty acid requirement. Ibid. 43:271–281. — Foundational demonstration that anaerobic yeast require exogenous ergosterol and oleate; basis for the 10 mg/L ergosterol and 50 mg/L Tween-80 / oleate defaults.

Feedstock yields and process engineering

  1. Kosaric N, Vardar-Sukan F (2001). Potential source of energy and chemical products. In The Biotechnology of Ethanol, Wiley-VCH. — Feedstock-yield reference values (g fermentable sugar per g dry feedstock) for corn, wheat, cassava, sorghum, and molasses; source of the dropdown defaults.
  2. Ingledew WM, Kelsall DR, Austin GD, Kluhspies C, eds. (2009). The Alcohol Textbook, 5th ed. Nottingham University Press. — Standard industrial reference for medium design, enzyme dosing (α-amylase ~500 U/g starch, glucoamylase ~200 U/g starch), and fed-batch strategies; basis for the Batch % slider's default range.
  3. Bai FW, Anderson WA, Moo-Young M (2008). Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnology Advances 26:89–105. — VHG review; industrial yield benchmarks YE/S = 0.45–0.49 g/g; calculator default 0.4603.
  4. USDA FoodData Central (2024). Agricultural Research Service, U.S. Department of Agriculture. — Reference source for feedstock composition (moisture, starch/sugar, protein, ash) used in the 10-feedstock dropdown; values are midpoints of reported ranges.
  5. Verduyn C, Postma E, Scheffers WA, van Dijken JP (1992). Effect of benzoic acid on metabolic fluxes in yeasts: a continuous-culture study on the regulation of respiration and alcoholic fermentation. Yeast 8:501–517. — The original Verduyn defined-medium recipe; salt compositions and trace-metal balance referenced by the calculator's Load Standard button.

Complex supplement compositions

  1. Reed G, Nagodawithana TW (1991). Yeast Technology, 2nd ed. Van Nostrand Reinhold, New York. — Yeast extract and yeast autolysate compositions (FAN ≈ 9% of mass, B-vitamin profile); reference for the calculator's YE and autolysate nutrient-credit tables.
  2. Ingledew WM, ed. (1999). The Alcohol Textbook, 3rd ed. Nottingham University Press. — Corn steep liquor (CSL) composition (total N ~4.5%, FAN ~2.8% of dry mass, lactic acid ~20%); basis for CSL nutrient credits in the calculator.
  3. Atkinson B, Mavituna F (1991). Biochemical Engineering and Biotechnology Handbook, 2nd ed. Stockton Press, New York. — Peptone, tryptone, and soy-hydrolysate reference compositions; source of the complex-material nutrient-credit defaults.
Calibration anchors used by Load Standard (VHG fuel-ethanol profile): FAN 500 mg/L (Jones & Ingledew 1994 tier-3); Mg 500 mg/L, Zn 2 mg/L, pantothenate 5 mg/L (Bafrncová 1999); ergosterol 10 mg/L, Tween-80 50 mg/L (Andreasen & Stier 1953, Casey & Ingledew 1986); biotin 0.1 mg/L, thiamine 1 mg/L (Ingledew 1993); biomass N content 8.3% DCW, P 1.2% DCW (Lange & Heijnen 2001). YE/S default 0.4603 g/g; YX/S default 0.05 g/g (Bai 2008, Verduyn 1990).

Fit Experimental Data

© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Parameter estimation & model calibration  |  v26.93

Parameter estimation — calibrate the model against observed fermentation data

Upload or paste time-course observations below (tab- or comma-separated). The simulator compares the current model prediction against your data, reports per-species R² and RMSE, and can optimise selected parameters (Nelder–Mead simplex) to best fit the observations. Use this to calibrate on pilot-scale runs before extrapolating to production, or to identify which strain/regime settings best explain a stuck or irregular ferment. Parameters are read from and written to the Time-Course Simulator tab — switch back there to see the fitted curves overlay on the full time-course charts.
▼Observed data
Import from a plant workbook (.xlsx / .csv)
Handles wide sheets (time across columns, one row per batch) and long sheets (time down rows). Statistics rows are skipped, blanks after the drop are treated as batch-ended rather than missing, and cell counts convert to g DCW/L using the ADY-anchored constant.
▼Supported column names
▼Parameters to fit
Check the parameters you want the optimiser to vary. Current values are read live from the Simulator tab. For a first pass, 2–4 parameters converges quickly; more than 6 risks over-fitting.

Yeast growth & substrate kinetics

—
max specific growth rate [0.05–0.7 h⁻¹]
—
half-saturation for glucose [0.1–5 g/L]
—
maintenance coefficient [0–1 g/g/h]
—
basal death rate [0.001–0.05 h⁻¹]
—
ethanol death sensitivity [0.001–0.05]

Yield coefficients

—
biomass yield [0.02–0.15 g/g]
—
ethanol yield [0.30–0.51 g/g]
—
glycerol growth-coupled [0–1.5 g/g]
—
lactic acid yield [0–0.05 g/g]
—
acetic acid yield [0–0.03 g/g]

Ethanol production (Luedeking–Piret)

—
growth-associated [0–2]
—
non-growth-associated [0–2]
—
ethanol growth-stop [60–200 g/L]
—
inhibition threshold [0–50 g/L]
▼Actions

Model calibration workflow

Prerequisite
Evaluate raw data quality: sampling density, missing values, replicate precision, monotonicity, noise, and what parameters the data can support estimating.
Step 1
Run the model with current parameters and score against data. Reports R², RMSE, bias per species.
Step 2
Derive parameters analytically from data (μmax, yields, LP coefficients). Apply to simulator as starting estimates.
Step 3
Nelder–Mead iterative refinement of checked parameters to minimise weighted SSE. Fine-tunes what Calculate started.
Time groups with more replicates and tighter agreement pull harder on the fit. Groups with a single observation have no SEM and take the species’ median weight. Weights are normalised to mean 1 per species, so the reported SSE stays on the same scale as the unweighted objective — but scores from the two modes are still not directly comparable.
Time-grouped statistics
Groups the loaded rows by sampling time and computes n, mean, SD, SEM, 95% CI and CV% for each group. Scheduled hours group cleanly; drop samples occur at their own real time, so a tolerance of 0.5–2 h is usually needed to collect them into bins that carry a statistic.
Residuals by time point
Compares the prediction against the observed mean at each sampling time, measured in units of that time’s own standard error. A pooled R² over a whole trajectory is dominated by the fact that the variable changes at all, and can look acceptable while the model is wrong everywhere. Requires Evaluate fit to have been run.
Fit per batch
Needs a batch column (the workbook importer writes one). Every batch starts from the current simulator parameters — fit the population first — and frees only the parameters ticked above; keep that to two or three. Each batch gets a short Nelder–Mead run on its own points, unweighted; the simulator is restored to the population values afterwards. The table shows the fitted value per batch and the spread across batches; the CSV carries the same for correlation with batch metadata. Forty batches at forty iterations is a few minutes; raise the cap when it looks right.
Data simulation report Nothing recorded yet.
Covers import provenance, the simulator configuration, the process set-up the model was scored under, parameter selection, the statistical analysis (distribution of the batches at each time point with the charts, interval changes and rates, batch consistency, the reference envelope, data quality, estimability), steps 1–3 (evaluate, calculate, train) and the per-batch fit, followed by findings, recommendations and the methods. Each step is captured as it finishes — the pre-fit score in particular cannot be recovered afterwards. Steps not run are reported as such.
© 2026 FermAxiom LLC · Author: Peter Krasucki · peter.krasucki@fermaxiom.com  |  Conceptual tool for rapid what-if analysis.

Model Exp. Data — Calibration WalkthroughGuide

The Model Exp. Data tab solves the inverse problem — given observed fermentation time-course data, what parameter set best explains it? The workflow has four complementary actions, designed to be run in sequence: Statistical analysis (data quality gate) → Evaluate fit (how well do current parameters match?) → Calculate parameters (analytical first-pass estimates) → Train (Nelder–Mead refinement). See Part IV of the instructional report for the full scientific background.

1. Data input — the 12-column HPLC-native schema

Upload a CSV or TSV file (or paste data directly into the textarea). A header row is required. Column names are case-insensitive with multiple aliases supported — the parser accepts the standard ethanol-fermentation HPLC-DAD or HPLC-RID analytical suite:

  • time — hours. Aliases: t, hour, hours
  • pH, temperature (°C), DCW (g/L, aliases biomass, X, cells)
  • DP4+ through DP1 — starch/dextrin DP ladder (g/L). DP2 and DP3 are automatically summed to a dextrin pool for scoring against the model's dextrin trajectory.
  • lactic acid, acetic acid, glycerol, ethanol — all in g/L.

Any subset of columns works — only matched columns are scored. Replicate samples at identical time points are auto-detected and averaged to mean ± SD.

Tip: the Generate from model button creates a synthetic dataset from the current simulator settings plus ~2% Gaussian noise. Useful for testing the optimiser's recovery of known ground-truth parameters before committing real HPLC data.

2. Statistical analysis — the data-quality gate

Before any fitting, this action evaluates whether the uploaded data is good enough to support estimation. It reports:

  • Dataset overview — time points, fermentation duration, sampling density (points per hour), and any large gaps in the time axis.
  • Per-species quality table — n valid, missing values, min/max/range, coefficient of variation from replicates (or, without replicates, a noise estimate from how far each point sits from a local fit through its neighbours), trend detection (↑ ↓ → ↕), and a quality rating (✅ / ⚠️ / ❌) that also counts outliers.
  • Distribution by time point, change per interval, batch consistency — when several batches share a sampling schedule, the statistics are organised time point first: how the batches are distributed at each time (mean ± SD, CV, median and quartiles), how much each batch changes between consecutive times (paired on the batch id the importer now writes into a batch column, with the rate per hour and whether the change is reliably non-zero), and whether a batch that runs high or low does so throughout the run (systematic share and the batches concerned). Replicate outliers (e.g. a mistyped pH of 523 among 280 batches at 5.2) are excluded from the group mean and SD by default and listed in the parse status.
  • Distribution charts — with several batches per sampling time, Statistical analysis draws every species against time: one point per batch, a box for P25–P75 with the median, whiskers at P5–P95, the mean, and the median trajectory through the time points. After Evaluate fit or Train the model trajectory is laid over the batches, so it is visible at which time point, and by how much of the batch spread, the model departs from the process. Hover a time point for its statistics, click a point to trace that batch through every panel, switch the basis to mass per final litre to take the feed dilution out, and use Save PNG for a figure. Excluded replicate outliers stay visible as red crosses.
  • Process set-up — score the model under the measured conditions — the simulator's vessel, charge and duration describe a design and are owned by Inoculum & Seed Train and Medium Formulations; a plant dataset is a measured process with its own. Once data is loaded, the Process set-up card lists the simulator's conditions next to the data's (process mode, duration, volume at the start and end, feed schedule from the tank level, the starting value of every measured species, pH, temperature) and flags each difference. Tick Score the model under the measured process conditions and every run made from this tab — Evaluate fit, Train, the per-batch loop — starts from the measured state, follows the measured tank level as its feed schedule and stops with the data. No simulator input is changed; kinetic parameters, process type and aeration remain the simulator's, so select the matching stage in Fermentation Simulators first. The feed composition is not in the data: enter feed glucose and DP4+ on the card. In the per-batch loop each batch runs under its own starting values and level trace. After such a run the simulator's charts show it, with a note; run the simulator again to return to the design.
  • The model in the statistics — after each scoring the Statistical analysis is redrawn with a Model (last scored) row in the distribution, interval-change, rates and reference-envelope tables (in the envelope: inside the best-batch band, or how far past its edge). Sections you had open and the chart and envelope choices are kept. Fit at each time point also shows the working volume, unscored: in a fed run, a volume that is not the plant's dilutes every concentration differently and no kinetic parameter can repair it.
  • Rates over each interval — Statistical analysis converts every batch to mass (C·V) and reports, interval by interval, the volumetric rate (g per litre of broth per h), the specific rate (g per g DCW per h), μ, the total sugar uptake and the ethanol and biomass yields on the sugar taken up. Enter the Feed sugar concentration for fed runs, otherwise uptake and yields are left out where the volume rises. After Evaluate fit, the section Interval rates — model against the batches puts the model's rates, computed by the same formula from its trajectory, against the batch distribution: this tests the kinetics themselves, and shows a rate that is wrong early and compensated later even when the concentrations look acceptable.
  • Reference envelope — ranks the batches on one outcome (species, time, highest or lowest; a propagation defaults to biomass, a fermentation to ethanol), takes the top share as the reference set and gives their P10–P90 band at every species × time point. Separation shows where the best batches already run differently from the rest and how early; the batch table lists the batches that ran furthest from the band, with the time and variable of their first departure (2 reference SDs past the edge). The band is drawn on the distribution charts, and a click on a batch traces it there. Batch scores CSV exports every batch.
  • Fit per batch — reading the result — below the spread table: each parameter's distribution across the batches against the population start and the bounds; the rank correlation between fitted parameters (a strongly correlated pair is not identified separately within a batch); the rank correlation of each parameter with the batch outcomes taken from the data (final biomass, ethanol, residual glucose, growth rate, productivity, yields), with scatter plots of the strongest pairs; and the batches that do not belong to the pack. When most batches end at the same bound, that is reported once as a problem of the population fit, not batch by batch.
  • Volume and fed sugar — the importer writes the litre reading of the tank level into a volume column. When it is present, interval changes, the mass balance and Calculate parameters work per final litre (C·V/Vend), so dilution by the feed is not read as consumption; entering the feed sugar concentration beside the paste box adds the fed sugar (ΔV × concentration) to the sugar consumed, which is what makes yields from a fed run valid. An impossible carbon recovery after that points at the feed concentration or the cells-to-DCW constant.
  • Growth phases — lag, exponential, stationary and decline windows located from ln(DCW), with the number of points in each and the peak specific growth rate. This is what the estimability checklist reads.
  • Outlier screening — raw replicates beyond the far-out fence of their time group (3 × IQR past the quartiles, or 3.5 robust SD for groups under 8), and — for series without replicates — time points more than 3.5 robust SD (relative to the local level) and at least 8 % of the range away from a leave-one-out local fit. Listed with time, value and expected value so the source rows can be checked.
  • Mass balance and yield checks — sugar consumed as glucose equivalents (DP1 + 1.07·dextrins + 1.11·starch), observed YP/S as a percentage of the Gay-Lussac maximum, carbon recovery across the measured products (CO2 taken as 44/46 of ethanol), and a flag when ethanol keeps rising after the measured sugar is gone. These catch unit errors and unmeasured sugar species before they are absorbed into a fitted yield.
  • Parameter estimability checklist — tells you which parameters the data can realistically identify, by counting points in the phase that carries each one: μmax needs ≥ 3 points in the exponential window, kd ≥ 3 points in the decline window, mS ≥ 2 stationary points with sugar still present, and the yield coefficients need both sugar and the product.
  • Data limitation warnings — too few points, missing key species, no replicates (so no CV available), large time gaps, or a run duration too short to see relevant dynamics.
Common data pitfalls: (1) Only three time points — you can fit a linear rate but nothing with curvature. (2) No biomass column — μmax and kd become unidentifiable; the optimiser may compensate by moving α/β arbitrarily. (3) Ethanol sampled only at endpoint — the Luedeking–Piret α/β split collapses. (4) Sampling stopped before the plateau — kd estimate will be biased low.

3. Calculate parameters — analytical first-pass estimates

Derives kinetic parameters directly from the time-course data using classical identities, without running the full ODE:

μmax ≈ max slope of ln(X) over exp-phase ÷ fproduct(E, T, pH) (ergosterol-free approximation) YX/S ≈ ΔX / ΔS (apparent, endpoint-based) YP/S ≈ ΔE / ΔS (apparent, endpoint-based) α, β from Luedeking–Piret regression: qP(t) vs μ(t) kd ≈ apparent kd,eff from post-peak ln(X) decline mS ≈ qS evaluated at μ ≈ 0 (stationary phase) YGly/S, YLA/S, YAA/S by the same ΔP/ΔS ratios

All outputs are labelled "apparent" because they are entangled with the full ODE. A measured YP/S is the observed ratio; the intrinsic value depends on how much glycerol diversion and maintenance carbon the cells incurred during the run. Click Apply on any parameter to push it to the simulator.

4. Evaluate fit — goodness of fit per species

Runs the simulator with current parameters, interpolates predictions at the observation times, and reports per matched species: R² (variance explained — dominated by the fact that the variable changes at all, so read it with the others), RMSE and MAE (errors in native units), NRMSE (RMSE as % of the observed range, comparable across species; under 10 % is good), mean bias (signed systematic offset — positive means model over-predicts), reduced χ² against the replicate SEM (about 1 means the model fits within measurement noise; well above 1 means the model is wrong, well below 1 means the noise estimate is too large), and a runs test on the residual signs (“systematic” means the model sits above the data over one stretch and below it over another, which no amount of re-scaling fixes). The pooled objective is also summarised as AIC/BIC using the number of ticked parameters, so a lower SSE bought with more free parameters can be judged. After Train, a before → after table and linearised 95 % confidence intervals for the fitted parameters are added. The first table is the fit at each time point — species × time, each cell judged on its own: predicted over observed, the residual in units of the batch SD at that time (or as % of the observed value without replicates), and the prediction's percentile among the batches. The pooled per-species metrics follow as a second, folded section. With multi-batch data a further table gives the interval agreement — the model's change over each interval against the paired observed change in units of the batch spread. Fit per batch (its own card below the fitting controls) then starts every batch from the population parameters, frees the ticked ones, and tabulates the spread of the fitted values across batches, with a CSV for correlating them against batch metadata. Observed points are simultaneously overlaid on the Metabolism time-course chart in the Simulator tab as scatter markers. A good fit typically shows R² > 0.95 for ethanol and biomass, > 0.85 for glycerol, and |bias| < 3% of the endpoint value.

5. Train (optimise) — Nelder–Mead simplex over 14 parameters

Minimises a weighted sum of squared residuals across all matched species. The optimiser operates on log-transformed parameter values (so each step is a proportional adjustment) with per-species weights scaled to the endpoint observation magnitude. Select which parameters to float from the 14-parameter pool:

  • Growth & death: μmax, kd, kd,E, kd,T
  • Stoichiometry: YX/S, YP/S, YGly/S, YLA/S, YAA/S, mS
  • Luedeking–Piret: αP, βP
  • Inhibition: Emax, Ki,S

The optimiser runs until either (a) the simplex spread falls below a tolerance, (b) the residual stops improving for N iterations, or (c) a hard iteration cap is hit. Progress is reported live. Final fitted values can be applied to the simulator with one click.

Identifiability warning: Fitting too many parameters against too few data points produces parameter sets that match the data but lack predictive power. A rough guide: float no more than ⌊(nobs × nspecies) / 10⌋ parameters at a time. Prefer fitting the stoichiometric yields first (YX/S, YP/S, YGly/S) on well-sampled species before adding kinetic parameters (μmax, Emax). Always check R² per species after training — if glycerol drops while ethanol R² stays high, the optimiser traded accuracy on one species for another.

Recommended calibration workflow

  1. Load data → run Statistical analysis. Fix data issues (add columns, extend duration, add replicates) before proceeding.
  2. Calculate parameters → inspect the analytical estimates. Apply the stoichiometric yields (YX/S, YP/S, YGly/S, YLA/S, YAA/S) to the simulator — these are the most robust first-pass values.
  3. Evaluate fit → note which species are already fitting well and which need work.
  4. Train — select 3–5 parameters (μmax, kd, Emax, αP, βP is a common first set) and let the simplex refine them. Re-evaluate.
  5. Iterate — if a species still fits poorly, add the relevant parameter(s) to the float list and train again. Save the final parameter set.
Apparent-vs-intrinsic caveat: fitted parameters should be labelled by the strain, feedstock, and operating regime they were trained against. YP/S = 0.45 fitted on a 22% v/v VHG run with Ethanol Red is not directly transferable to a 12% v/v normal-gravity run with a different strain — the glycerol diversion and maintenance-carbon partitioning differ. See §4.7 of the instructional report for the full discussion.

Model Exp. Data — ReferencesRefs

Sources for the parameter-estimation methodology, Nelder–Mead simplex optimisation, identifiability considerations, and the analytical first-pass estimates produced by Calculate parameters. Kinetic-form references (Luedeking–Piret, Luong, Monod, Pirt) are shared with the Simulator tab's References.

Optimisation algorithms

  1. Nelder JA, Mead R (1965). A simplex method for function minimization. The Computer Journal 7:308–313. — The simplex-reflection algorithm underpinning the Train action. Gradient-free, tolerant of noisy objectives, widely used for bioprocess-model calibration when gradients are unavailable.
  2. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998). Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM Journal on Optimization 9:112–147. — Convergence analysis; motivates the operational practice of floating ≤14 parameters at a time in this tool.
  3. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007). Numerical Recipes: The Art of Scientific Computing, 3rd ed. Cambridge University Press. — Chapter 10.5 gives a clear reference implementation of Nelder–Mead and discusses the robust termination conditions used here (simplex-spread tolerance plus no-improvement counter).

Bioprocess-model calibration and identifiability

  1. Seber GAF, Wild CJ (1989). Nonlinear Regression. Wiley, New York. — Statistical foundations for nonlinear parameter estimation; basis for the apparent-vs-intrinsic distinction emphasised in §4.7 of the instructional report.
  2. Walter E, Pronzato L (1997). Identification of Parametric Models from Experimental Data. Springer, London. — Structural and practical identifiability; the source of the "nobs × nspecies / 10" heuristic used as the default guidance in the Train warning.
  3. Brun R, Reichert P, Künsch HR (2001). Practical identifiability analysis of large environmental simulation models. Water Resources Research 37:1015–1030. — Practical identifiability in large ODE systems; approach adopted for flagging which parameters are identifiable from a given experimental data set.
  4. Rodriguez-Fernandez M, Egea JA, Banga JR (2006). Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics 7:483. — Comparison of local vs global optimisation strategies for kinetic-model fitting; motivates the log-transformed parameter step that this tool uses.

Kinetic forms used in the residual calculation

  1. Luedeking R, Piret EL (1959). A kinetic study of the lactic acid fermentation. Batch process at controlled pH. Journal of Biochemical and Microbiological Technology and Engineering 1:393–412. — Luedeking–Piret regression of qP vs μ that underpins the α/β analytical first-pass.
  2. Pirt SJ (1965). The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society B 163:224–231. — Maintenance coefficient mS estimated from qS in stationary phase.
  3. Monod J (1949). The growth of bacterial cultures. Annual Review of Microbiology 3:371–394. — Monod saturation that μmax analytical estimates correct for product and nutrient effects.
  4. Luong JHT (1985). Kinetics of ethanol inhibition in alcohol fermentation. Biotechnology and Bioengineering 27:280–285. — Ethanol-inhibition term needed when correcting apparent μmax from late-exponential data.

HPLC analytical methods

  1. Coote N, Kirsop BH (1976). A rapid method for the determination of ethanol and other fermentation products by HPLC. Journal of the Institute of Brewing 82:34–35. — The reference method for HPLC-RID ethanol quantitation still used industry-wide; basis for the ethanol column's expected precision (CV ~2–3%).
  2. Buckee GK, Mundy AP (1994). Determination of carbohydrates in wort and beer by HPLC — collaborative trial. Journal of the Institute of Brewing 100:57–64. — DP1–DP4+ carbohydrate ladder by HPLC-RID; defines the column aliases (DP1 = glucose, DP2 = maltose, DP3 = maltotriose, DP4+ = higher dextrins) that the data-input schema accepts.
  3. Castellari M, Versari A, Spinabelli U, Galassi S, Amati A (2000). An improved HPLC method for the analysis of organic acids, carbohydrates, and alcohols in grape musts and wines. Journal of Liquid Chromatography and Related Technologies 23:2047–2056. — Simultaneous determination of lactic, acetic, glycerol, and ethanol on a single Aminex HPX-87H column — the standard configuration assumed by the tool's 12-column schema.
The optimiser is implemented client-side in JavaScript using a standard Nelder–Mead reflection/expansion/contraction routine (Nelder & Mead 1965; Press et al. 2007) with per-parameter log-scaling for proportional step sizes. Termination: simplex spread < 10−5, or 60 iterations without improvement, or 500 total iterations (whichever comes first). Objective: weighted sum of squared residuals, per-species weights = 1 / (max observed)², so each species contributes comparable magnitude regardless of its native units.