By M. F. Doherty
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Extra info for Perry's Chemical Engineers' Handbook. Section 13
The MESH equations form a set of nonlinear, algebraic equations (in the sense that no derivatives or integrals are involved) and must, therefore, be solved by some iterative process. There are two key steps in the development of an algorithm for solving systems of nonlinear equations: • The selection of particular numerical methods • The selection of the order in which the equations are to be solved We may identify several classes of methods for numerically solving the MESH equations: 1. Tearing methods in which the equations are divided into groups and each group is solved separately 2.
Degrees-of-Freedom Analysis and Problem Formulation Table 13-8 summarizes the equations for a single equilibrium stage (in a sequence of stages). There are 2c + 4 equations per stage, of which Variables for an Equilibrium Stage Variable Symbol Number Vapor flow rate Liquid flow rate Feed flow rate Vapor sidestream flow Liquid sidestream flow Vapor-phase mole fractions Liquid-phase mole fractions Feed composition Stage temperature Stage pressure Feed temperature Feed pressure Stage heat duty Vj Lj Fj Wj Uj yi,j xi,j zi,j Tj Pj 1 1 1 1 1 c c c 1 1 1 1 1 3c + 10 Qj 13-32 DISTILLATION The 2c + 1 Formulation An alternative form of the MESH equations is used in many algorithms.
The Kremser method is most useful for making preliminary estimates of absorbent and stripping agent flow rates or equilibrium-stage requirements. The method can also be used to extrapolate quickly results of a rigorous solution to a different number of equilibrium stages. Consider the general adiabatic countercurrent cascade of Fig. 13-33 where v and ᐉ are molar component flow rates. Regardless of whether the cascade is an absorber or a stripper, components in the entering vapor will tend to be absorbed and components in the entering liquid will tend to be stripped.
Perry's Chemical Engineers' Handbook. Section 13 by M. F. Doherty