Rate-based column (two-film) simulation

feed -> distillate + bottoms (multicomponent Maxwell-Stefan mass transfer)

Governing equations

The exact equations the solver works for a rate-based column (two-film) — the same math shown in the app's "Theory" panel, not a black box.

$(\mathcal{N})_j$

component transfer rate across the interface on stage j [mol/s] — the heart of a rate-based model: mass moves at a finite rate, not instantly

$[K_{OV}]$

overall mass-transfer coefficient matrix (both films combined)

$[k_V], [k_L]$

vapour- and liquid-film mass-transfer coefficient matrices

$[\Gamma]$

liquid thermodynamic factor matrix — the identity for an ideal mixture, and where non-ideality couples the components

$\gamma_i$

activity coefficient of i

$K_j$

equilibrium ratios on stage j

$x_j, y_j$

bulk liquid / vapour compositions

$y_j^I, x_j^I$

compositions right at the interface, where equilibrium *does* hold

$V, L_j$

vapour and liquid molar flows [mol/s]

$f_j$

feed to stage j [mol/s]

$\delta_{ik}$

Kronecker delta

Parameters

rigorous two-film Maxwell-Stefan rate-based column (binary OR multicomponent): n_stages, feed_stage, reflux_ratio, distillate_to_feed|distillate_rate, pressure [Pa]. Each interior stage carries separate bulk vapor/liquid + interface equilibrium; c>2 uses the MS coefficient matrices with the liquid thermodynamic factor [Gamma] from the activity model (set ideal_thermo_factor to force [Gamma]=I). energy_balance (binary) solves variable non-CMO flows + separate vapor/liquid stage temperatures. Tune via mass_transfer_scale [large = equilibrium], n_gas_tu/n_liq_tu, or efficiency_method (aiche | chan_fair for trays; onda for a PACKED bed — then set packing [random_25mm|random_50mm|pall_25mm|structured_250|...], packing_material [metal|ceramic|plastic|carbon], packing_hetp [m])

Example flowsheets that use it