Rigorous Separations — The MESH Solver

A Wang-Henke bubble-point MESH solve (tridiagonal Thomas algorithm at fixed K/flows, outer loop refreshing K and stage temperatures) is the Phase-1 column; an inside-out / Newton path and a Naphtali-Sandholm simultaneous multi-liquid-phase (VLLE) stage matrix solver extend it for tougher and heterogeneous-reflux columns.

meshdistillationnaphtali-sandholm

Concept

Every equilibrium-stage column (distillation, absorption, extraction) solves the same four equation families per stage — Material balance, Equilibrium, Summation, Heat balance — the textbook "MESH" system. The default path is a Wang-Henke bubble-point solve at constant molal overflow; an inside-out/Newton path and a Naphtali-Sandholm simultaneous solver extend it for harder and heterogeneous-reflux (VLLE) columns.

The math

Show the governing equations

M:\ L_{j-1}x_{i,j-1} + V_{j+1}y_{i,j+1} - (L_j+U_j)x_{i,j} - (V_j+W_j)y_{i,j} + F_jz_{i,j} = 0

E:\ y_{i,j} = K_{i,j}\,x_{i,j}

S:\ \sum_i x_{i,j} = 1, \quad \sum_i y_{i,j} = 1

H:\ L_{j-1}h_{L,j-1} + V_{j+1}h_{V,j+1} - (L_j+U_j)h_{L,j} - (V_j+W_j)h_{V,j} + F_jh_{F,j} - Q_j = 0

Execution

SDK

unit("COL", "distillation", n_stages=8, feed_stage=4,
     reflux_ratio=2.5, distillate_rate=3.0, pressure=101325)

NONCONVERGENCE_MAX_ITERSSuccessive substitution converges linearly — tall columns (>=12 stages) may hit the iteration cap; the column returns unconverged with a usable partial stage profile, never raises.

Launch in MaximaLabs Workspace