Bioreactor simulation

1 inlet -> 1 outlet (Monod fermenter)

Governing equations

The exact equations the solver works for a bioreactor — the same math shown in the app's "Theory" panel, not a black box.

$\mu$

specific growth rate [1/s]

$\mu_{max}$

maximum growth rate when substrate is plentiful

$S$

substrate concentration [mol/m³]

$S_{in}$

substrate fed

$K_s$

half-saturation constant — the substrate level at half μ_max (Monod)

$D$

dilution rate Q/V [1/s]; at steady state the cells must grow exactly this fast or wash out

$Q$

volumetric flow [m³/s]

$V$

working volume [m³]

$X$

biomass concentration [kg/m³]

$Y_{xs}$

biomass yield per unit substrate consumed

$K_i$

optional Haldane substrate-inhibition constant [mol/m³] — high S suppresses μ

Parameters

substrate (feed component), mu_max [1/s], Ks [mol/m^3], volume [m^3]; optional yield_xs, yield_px, biomass/product labels, ki [mol/m^3, Haldane substrate-inhibition constant — switches from Monod to Haldane growth kinetics when set]

Example flowsheets that use it