Equilibrium stage calculations

Iterative methods for the determination of stage temperature and interstage flow rates in the equilibrium stage problem are discussed, and the use of the Newton-Raphson method for solution of the systems of simultaneous equations is proposed. It is shown that the complete correction process can be divided into four independent parts, two of which are treated in the paper. The first is equivalent to the constant molal overflow problem in distillation and the second to the constant temperature extraction problem. For each of these cases the necessary partial derivatives describing the effects of temperature and flow rate changes on all material balance equations are developed. Sample problems are briefly discussed to demonstrate the feasibility of the calculation and the fact that quadratic convergence is obtained. Equation derivation is simplified by using matrix notation, which also has the advantage that any interstage flow pattern is allowed.