Enzymatic reactor (Michaelis-Menten) simulation

1 inlet -> 1 outlet (substrate + pH-branched dual products)

Governing equations

The exact equations the solver works for a enzymatic reactor (michaelis-menten) — the same math shown in the app's "Theory" panel, not a black box.

$S$

substrate concentration [mol/m³]

$S_{in}$

substrate fed

$S_{out}$

substrate leaving (and, in a CSTR, the concentration the reaction actually sees)

$v(S)$

reaction rate [mol/m³/s]

$V_{max}$

maximum rate when the enzyme is saturated [mol/m³/s]

$K_m$

Michaelis constant [mol/m³] — the substrate level at half V_max; low K_m means a tight-binding enzyme

$\tau$

residence time V/V̇ [s]

$V$

reactor volume [m³]

$\dot V$

volumetric flow [m³/s]

$\mathrm{pH}$

operating pH — here it selects *which* product forms

$\mathrm{p}K_a$

pKa of the ionizable group doing the selecting

$f_{low}, f_{high}$

fraction of consumed substrate routed to each product pathway

Parameters

substrate (feed component), volume [m^3], vmax [mol/(m^3*s)], km [mol/m^3], ph, pka_switch [pH-dependent product-branching switch point]; optional product_low_ph [default 'product_low_ph'], product_high_ph [default 'product_high_ph'], pressure_drop [Pa]. Michaelis-Menten CSTR; substrate consumed splits between the two products via a single-ionizable-group pH-titration switch

Example flowsheets that use it