Membrane distillation simulation

Governing equations

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

$J$

vapour flux across the membrane [mol/m^2/s]

$C_m$

membrane distillation coefficient — measured per module [mol/(m^2 s Pa)]

$p^{sat}$

saturation vapour pressure of the solvent [Pa]

$a_w$

water activity of the feed — salt lowers it, and with it the driving force [-]

$T_f$

bulk feed temperature [K]

$T_p$

bulk permeate temperature [K]

$T_{fm}$

temperature at the feed side of the membrane, below the bulk [K]

$T_{pm}$

temperature at the permeate side of the membrane, above the bulk [K]

$h_f$

feed-side film heat-transfer coefficient [W/m^2/K]

$h_p$

permeate-side film heat-transfer coefficient [W/m^2/K]

$k_m/\delta$

conductive loss through the membrane per unit area [W/m^2/K]

$\Delta H_{vap}$

latent heat carried by every mole that crosses [J/mol]

$\mathrm{TPC}$

temperature polarisation coefficient — the fraction of the measured driving force that reaches the membrane; real modules run 0.4-0.7 [-]

$A$

membrane area [m^2]

$\dot{n}_{dist}$

distillate rate [mol/s]

Parameters

membrane_area [m^2, REQUIRED — the module size, which cannot be inferred]; permeate_temperature [K, the cold side]; optional membrane_coefficient [mol/(m^2 s Pa), default 2.78e-5 = the mid-range literature 5e-7 kg/(m^2 s Pa)], feed_heat_transfer_coefficient / permeate_heat_transfer_coefficient [W/m^2/K, default 3000 — these set temperature polarisation and therefore the real flux], membrane_conductance [W/m^2/K, default 15, conductive loss through the membrane], solvent [default 'water']. Outlets in order: distillate, concentrate.

Example flowsheets that use it