ENV-23

ADM1 growth snapshot

μ = μm S/(Ks+S) · KI/(KI+I). Monod with non-competitive inhibition.

Reading speed

BiokineticsBatstone ADM1

Governing equation

\mu=\mu_m\dfrac{S}{K_S+S}\dfrac{K_I}{K_I+I}

$S \in \left[0.01, 20\right]$

where

\mu_m: Max growth (1/d)
S: Substrate (kg/m³)
K_S: Half-saturation (kg/m³)
K_I: Inhibition KI (kg/m³)
I: Inhibitor (kg/m³)
\mu: Specific growth (1/d)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mu=\mu_m\dfrac{S}{K_S+S}\dfrac{K_I}{K_I+I}

$S \in \left[0.01, 20\right]$

$S = 0.01$ $\mu = 0.007$

Along the curve

②

Domain of the variable — blue

S_{\min} = 0.01,\quad S_{\max} = 20

$S \in \left[0.01, 20\right]$

$S = 0.01$ $S = 0.01$

Along the curve

③

Response curve — green

\mu=\mu_m\dfrac{S}{K_S+S}\dfrac{K_I}{K_I+I}

$S \in \left[0.01, 20\right]$

$S = 0.01$ $\mu = 0.007$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mu}{\mathrm{d}S}

$S \in \left[0.01, 20\right]$

$S = 0.136$ $\mu^{\prime} = 0.429$

Along the curve

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-23 — ADM1 growth snapshot) is the form associated with Batstone ADM1. Working symbols: $\mu_m$ , $S$ , $K_S$ , $K_I$ , $I$ $\rightarrow$ $\mu$ . ADM1 uses hyperbolic uptake for anaerobic digestion, multiplied by an inhibition term for pH, NH3 or H2.

Purpose

Purpose: compute

\mu

from

\mu_m

S

K_S

K_I

I

in Environmental via

\mu=\mu_m\dfrac{S}{K_S+S}\dfrac{K_I}{K_I+I}

μ = μm S/(Ks+S) · KI/(KI+I). Monod with non-competitive inhibition. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu_m = 0.400\,\mathrm{1/d}

S = 2.000\,\mathrm{kg/m^{3}}

K_S = 0.500\,\mathrm{kg/m^{3}}

K_I = 0.050\,\mathrm{kg/m^{3}}

I = 0.010\,\mathrm{kg/m^{3}}

, the governing relation

\mu=\mu_m\dfrac{S}{K_S+S}\dfrac{K_I}{K_I+I}

yields

\mu = 0.2667\,\mathrm{1/d}

. A digester, a substrate bar, an inhibitor shade. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Max growth \mu_m0.4 1/dSubstrate S2 kg/m³Half-saturation K_S0.5 kg/m³Inhibition KI K_I0.05 kg/m³Inhibitor I0.01 kg/m³

Outputs

Specific growth \mu0.2667 1/d

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

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Narration of this film

A digester, a substrate bar, an inhibitor shade.

ADM1 uses hyperbolic uptake for anaerobic digestion, multiplied by an inhibition term for pH, NH3 or H2.

Reading speed

Watch on YouTube