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The science
Dilute countercurrent absorption of a solute (mole ratios Y in the gas, X in the liquid, inert gas rate G, solvent rate L). Linear equilibrium with a van t Hoff temperature dependence:
Y* = m(T) X , m(T) = m25 exp[ (dH/R) (1/T - 1/298.15) ] , dH = -20 kJ/mol (illustrative)
Overall balance: G (Y_in - Y_out) = L (X_out - X_in) (operating line slope L/G)
Design with transfer units (plug flow, linear equilibrium, absorption factor A = L / (m G)):
Z = HOG · NOG , NOG = ln[ (1 - 1/A) (Y_in - m X_in)/(Y_out - m X_in) + 1/A ] / (1 - 1/A)
Y_out = m X_in + (1 - 1/A)(Y_in - m X_in) / ( e^(NOG (1 - 1/A)) - 1/A )
The simulator is a cell model: each gas cell uses the exact exponential solution Y_out = Y* + (Y_in - Y*) e^(-dz/HOG) and each liquid cell is a mixed holdup, H_c dX_i/dt = L (X_(i-1) - X_i) + G (Y_in,i - Y_out,i), so the liquid residence time (about 40 s) produces real transients. HOG follows a power law in the gas and liquid fluxes (Onda-type trend). Pressure drop uses a Leva form dP/Z = a G'^2 / rho_G · 10^(b L'); above a flooding limit of 1000 Pa/m the effective HOG grows steeply (flooded bed). The analyser has a delay and a first-order lag. The PI controller moves the L/G ratio (anti-windup, rate limit, pump lag).
Numerical checks run in the page
- Steady outlet of a 400-cell numerical column against the Colburn closed form (within 1 %).
- Overall solute balance of that steady state, G (Y_in - Y_out) = L (X_out - X_in).
- The exponential gas-cell step against RK4 integration of dY/dz = -(Y - mX)/HOG.
- The model's Henry slope ratio against the van t Hoff relation.
Honest simplifications
Isothermal column (no heat of absorption temperature profile), constant HOG within a run apart from the flux and flooding corrections, linear equilibrium (a generic solute, not a specific chemistry such as amine-CO2 chemisorption), pressure-drop constants chosen to place flooding at 1000 Pa/m rather than taken from a packing datasheet, short 5 m bed so that the dynamics are easy to watch. Educational process-engineering model, not a design tool.