Multicomponent separation calculations by linearization

TLDR

The study devises a new application of the Newton–Raphson technique to separation calculations. The method linearizes mass, energy, and equilibrium equations by stage, yielding a block‑tridiagonal system solvable with a simple technique. The approach solves diverse challenging problems in ten or fewer iterations, demonstrating practical advantages over existing techniques.

Abstract

Abstract A new approach to separation calculations has been developed which has many practical advantages. The equations of conservation of mass and energy and of equilibrium are grouped by stage and then linearized. The resulting set of equations has a block‐tridiagonal structure which permits solution by a simple technique. Thus a new way to apply the Newton‐Raphson technique to separation calculations is devised. The method has been tried on a number of problems chosen to exhibit characteristics which cause other solution technique to fail. Most problems are solved with ten iterations or less.