Membrane (RO) simulation

1 feed -> permeate + retentate

Governing equations

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

$c_{f,i}$

solute concentration in the feed

$c_{p,i}$

solute concentration in the permeate — what gets through

$\sigma_i$

rejection of solute i [0..1]; 1 = perfectly retained

$r$

recovery — fraction of feed volume passing as permeate

$Q_f, Q_p$

feed and permeate volumetric flows

$\pi$

osmotic pressure [Pa] — the back-pressure you must beat

$i$

van 't Hoff factor (ions per dissolved molecule)

$C$

molar concentration

$R$

gas constant

$T$

temperature [K]

$\text{NDP}$

net driving pressure — if this goes to zero, the membrane stops, which is the real limit on recovery

Parameters

recovery [0..1 permeate/feed, default 0.5], rejection [0..1 salt rejection, default 0.98], feed_pressure [Pa]; optional solvent [default 'water'], vant_hoff [ions per solute, default 1]; osmotic-pressure feasibility checked (RO rating)

Example flowsheets that use it