Computation of multicomponent distillation processes by the Newton-Raphson method using an implicit function

A new iterative method is presented for the rigorous simulation of multicomponent distillation processes using the Newton-Raphson method to solve the simultaneous equations, which is characterized by the use of the liquid compositions as the independent variables and analytical equations for evaluating the partial derivatives, with the vapor compositions and temperatures as the dependent variables. The analytical equations for the partial derivatives of the vapor compositions with respect to the liquid compositions are derived, using the implicit-function theorem. The advantages of the method are that a numerical differentiation of the partial derivatives is unnecessary, as is normalization of the liquid compositions. The method has excellent convergence characteristics when applied to 10 typical distillation columns of complicated structure.