Calculation Procedure of Multicomponent Batch Distillation

Abstract

A stable, high-speed calculation procedure for multicomponent batch distillation with plate hold-up is presented, based upon the consideration that behavior of batch distillation is represented by several eigenvalues of small absolute value. In this procedure the differential equations are linearized for a relatively large time increment and a similarity transformation is performed on the Jacobian matrix to result in solving an eigenvalue problem of symmetric tridiagonal matrix. It is shown that this eigenvalue method is more than 20 times faster than the Runge-Kutta-Gill method, especially in the mild product period.
A new criterion to estimate the absolute value of the largest negative eigenvalue which governs both the maximum stable time increment and the accuracy of numerical integration techniques is derived. It is also shown that this criterion gives estimated values which agree satisfactorily with experimental ones.