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Dynamic Distillation Column

Tray-by-tray transient composition/temperature profiles under constant-molal-overflow, fixed tray holdup, and instantaneous VLE — closes the gap where the dynamics engine could only simulate well-mixed vessels, showing a column's startup/shutdown/feed-upset transient instead of just its converged steady state.

dynamicsdistillationcolumn
Concept

Closes a real gap: until this engine, the only column model was the converged steady state — no way to see a startup, shutdown, or feed-upset transient tray by tray. Three explicit, bounded simplifying assumptions keep the ODE well-posed without a full dynamic-MESH rebuild:

  • Liquid/vapor flows per stage are fixed at the steady-state constant-molal-overflow profile — no tray hydraulics.
  • Tray liquid holdup is a fixed parameter, not a state — what evolves is each tray's liquid mole fraction, not raw moles.
  • VLE is instantaneous — every tray's temperature and vapor composition are the bubble point of its current liquid composition.
The math
Show the governing equations
Mj dxjdt=Lj−1xj−1+Vj+1yj+1−Ljxj−VjyjM_j\,\frac{dx_j}{dt} = L_{j-1}x_{j-1} + V_{j+1}y_{j+1} - L_jx_j - V_jy_j
What this genuinely captures: real transient composition/temperature profiles across every tray responding to a feed-composition or feed-rate step. What it doesn't: tray hydraulics, a dynamic energy balance, or literal flooding/draining — the documented follow-up is a rigorous dynamic MESH with vapor/liquid holdup states.
Execution

Same solve_ivp(BDF) machinery as the tank engine — a feed-composition step at a chosen time is the standard way to exercise it.