A nonequilibrium stage model of a multistage gas-liquid-solid reactive separation process is developed, in which the multicomponent mass and energy transfer between liquid and solid phases are taken into account. An algorithm based on a differential homotopy continuation method is demonstrated. A simulation of a catalytic stripping with a condensation of phenol with acetone to produce Bisphenol-A and water is carried out. The prediction is in good agreement with the experimental data in a pilot plant. Compared with a liquid-solid quasihomogeneous model, calculations by our model are more precise.