# Aj 0 Bj 1 Cj pj Dj qj

compositions, estimate all Kj values (for k = 1, initial estimates of stage phase compositions may be necessary if Kj values are sensitive to phase compositions).

8. Compute values of xij by solving Eqs. (13-75) through (13-79) by the tridiagonal-matrix algorithm once for each component. Unless all mesh equations are converged, "Zi xi,j ^ 1 for each stage j.

9. To force xij = 1 at each stage j, normalize values by the replacement xij = xij / Zi xij.

10. Compute a new set of values of Tj(k) tear variables by computing, one at a time, the bubble-point temperature at each stage based on the specified stage pressure and corresponding normalized xij values. The equation used is obtained by combining Eqs. (13-69) and (13-70) to eliminate yi,j to give

which is a nonlinear equation in T,(k) and must be solved iteratively by some appropriate root-finding method, such as the Newton-Raphson or the Muller method.

11. Compute values of y,, one at a time from Eq. (13-69).

12. Compute a new set of values of the V, tear variables one at a time, starting with V3, from an energy-balance equation that is obtained by combining Eqs. (13-72) and (13-74), eliminating Lj_ i and Lj to give

+ Fj - 1(HLj- 1 - HFj - 1)+ Wj - 1(HVj-1 - HLj - 1) + Qj - 1

possible convergence

13. Check to determine if the new sets of tear variables T,(k) and Vj(k) are within some prescribed tolerance of sets Tjk _1) and V( _1) used to initiate the current column iteration. A possible criterion is