Perfusion bioreactor (cell retention) simulation

1 inlet (fresh medium) -> 2 outlets [harvest, bleed]

Governing equations

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

$D$

medium-exchange (perfusion) rate [1/s] — volumetric feed divided by working volume

$D_{eff}$

cell-specific removal rate [1/s] — the rate cells actually leave, which the retention device makes much smaller than D

$\phi$

bleed fraction — the share of the withdrawn medium taken cell-laden; this is the knob that sets cell density

$R$

cell-retention efficiency of the ATF/TFF device (1 = cell-free harvest, 0 = no retention, which collapses this unit to an ordinary chemostat)

$\mu$

specific growth rate [1/s]

$\mu_{max}$

maximum specific growth rate the cell line can reach [1/s]

$\mu_d$

specific death rate [1/s] — rises as inhibitory byproducts accumulate

$S$

limiting substrate concentration in the vessel [mol/m^3]; S_in is its feed value

$K_s$

Monod half-saturation constant [mol/m^3] — the substrate level at which growth runs at half its maximum

$I_k$

concentration of inhibitory byproduct k (lactate, ammonia) [mol/m^3]

$K_{i,k}$

inhibition constant for byproduct k [mol/m^3] — smaller inhibits more strongly

$q_S$

specific substrate uptake [mol/(mol biomass . s)] — growth demand plus maintenance

$Y_{x/s}$

biomass yield on substrate [mol biomass / mol substrate]

$m_S$

Pirt maintenance coefficient — substrate burned by non-growing cells

$X$

viable cell density [mol/m^3, biomass pseudo-component basis]

$X_d$

dead cell density [mol/m^3]; viability is X/(X+X_d)

$q_P$

specific product formation [mol product / (mol biomass . s)]

$\alpha$

growth-associated product formation [mol product / mol biomass]

$\beta$

non-growth-associated product formation — a secreted protein still made by cells that have stopped dividing

Parameters

substrate (feed component), volume [m^3], mu_max [1/s], Ks [mol/m^3], yield_xs [mol biomass/mol substrate], bleed_fraction [0-1, the fraction of the medium withdrawn cell-laden], retention [0-1, cell-retention efficiency of the ATF/TFF device; 1.0 = a cell-free harvest, 0.0 collapses this to an ordinary chemostat]; optional maintenance [mol substrate/(mol biomass*s)], death_rate [1/s], death_rate_max [1/s] + kd {inhibitor: mol/m^3}, ki {inhibitor: mol/m^3}, byproduct + byproduct_yield (or byproducts {name: yield}), product + alpha [mol product/mol biomass] + beta [mol product/(mol biomass*s)], biomass [default 'biomass'], dead_biomass, pressure_drop [Pa]. Continuous culture with cell retention: steady state sets mu - mu_d = the cell-specific removal rate, not the dilution rate, so cell density is controlled by the bleed

Example flowsheets that use it