Free Monod Fermentation Kinetics & Yield Calculator

KINETIC PARAMETERS & SUBSTRATE FORMULATION

Organism & Substrate Preset

Substrate Concentration S (g/L) 1.20 g/L

Max Specific Growth μ_max (h⁻¹) 0.650 h⁻¹

Monod Constant K_s (g/L) 0.140 g/L

True Biomass Yield Y_x/s (g/g) 0.500 g/g

Maintenance Coeff m_s (g/g/h) 0.040 g/g/h

Chemostat Feed S_in (g/L) 20.0 g/L

SUBSTRATE RESPONSE & RECIPROCAL LINEARIZATION KINETIC CURVES

FERMENTATION HANDOFF ➔ STEP 5
Calculated specific growth rate μ = 0.582 h⁻¹, observed yield Y_obs = 0.472 g/g, and substrate uptake q_s = 1.204 g/g/h ready to feed into BatchCompare Golden Envelope (Step 5) to baseline batch deviation limits.

CHEMOSTAT & YIELD DIAGNOSTICS STEADY STATE

Critical Washout Dilution (D_crit)

0.645 h⁻¹

Maximum dilution before culture washout

Steady-State Biomass (X_ss)

8.87 g/L

At operating dilution D = μ = 0.582 h⁻¹

Biomass Volumetric Productivity (P_x)

5.16 g/L/h

Cell mass output flux ($P_x = D \cdot X_{ss}$)

Maintenance Energy Drain

3.32% of Substrate

Fraction of carbon routed to cellular maintenance

Substrate Saturation Margin

8.57× K_s

S / K_s ratio indicates saturated kinetics

📚 Monod Microbial Kinetics & Substrate Consumption ODE Guide Fermentation Kinetics • Step 3 of 5

Theoretical Principles & Engineering Fundamentals

The Monod model is the foundation of biochemical reaction engineering, relating specific microbial growth rate ($\mu$) to the concentration of growth-limiting substrate ($S$). Combining Monod kinetics with substrate yield ($Y_{X/S}$) and maintenance coefficients ($m_s$) provides the governing differential equations for batch, fed-batch, and chemostat reactors.

Governing Equations & Mathematical Formulations

Monod Growth Equation \mu(S) = \mu_{\max} \frac{S}{K_s + S}

Relates growth rate to substrate concentration where $K_s$ is the affinity constant.

Substrate Utilization Rate -\frac{dS}{dt} = \frac{1}{Y_{X/S}} \frac{dX}{dt} + m_s X

Incorporates both growth-coupled consumption and baseline cellular maintenance.

Luedeking-Piret Product Formation \frac{dP}{dt} = \alpha \frac{dX}{dt} + \beta X

Models growth-associated ($lpha$) and non-growth-associated ($eta$) bioproduct synthesis.

Industrial Benchmark Data & Parameter Reference

Parameter	Symbol	Typical E. coli Value	Typical Yeast Value
Max Specific Growth Rate	μ_max	0.60 – 1.00 hr⁻¹	0.35 – 0.45 hr⁻¹
Substrate Affinity Constant	K_s	0.02 – 0.05 g/L (Glucose)	0.05 – 0.15 g/L
Biomass Yield on Glucose	Y_X/S	0.45 – 0.50 g/g	0.48 – 0.52 g/g
Maintenance Coefficient	m_s	0.02 – 0.04 g/(g·hr)	0.01 – 0.03 g/(g·hr)

Frequently Asked Questions (Bioprocess Engineering FAQ)

What is the physical meaning of the affinity constant (Ks)?

$K_s$ represents the substrate concentration at which the specific growth rate reaches exactly half of its maximum value ($\mu = 0.5\,\mu_{\max}$). Low $K_s$ values indicate high enzymatic affinity for the substrate.

How does maintenance energy impact fermentation yield?

Maintenance energy ($m_s$) represents ATP expended on osmoregulation, protein turnover, and cell motility without contributing to new cell synthesis. In long fed-batch fermentations, maintenance reduces overall biomass yield.

What is a chemostat steady state?

In a continuous chemostat reactor with dilution rate $D$, the system reaches a self-regulating steady state where $\mu = D$, allowing continuous harvesting at constant substrate concentration $S^* = \frac{K_s D}{\mu_{\max} - D}$.

Free Monod Fermentation Kinetics & Biomass Yield Calculator

📚 Monod Microbial Kinetics & Substrate Consumption ODE Guide Fermentation Kinetics • Step 3 of 5

Theoretical Principles & Engineering Fundamentals

Governing Equations & Mathematical Formulations

Industrial Benchmark Data & Parameter Reference

Frequently Asked Questions (Bioprocess Engineering FAQ)

BioFlo Bioprocess Engineering Network