Modified Thiele-Geddes Method

The entire procedure is repeated until convergence is achieved. The use of 0 to correct the component flow rates tends to guide the computations toward faster convergence by forcing an overall material balance in each iteration. Convergence is considered reached when the difference between the specified and calculated distillate rates is within a preset tolerance. 

This method also considers the stage temperatures as the independent variables. The algorithm is applied to a single-feed, two-product column with a partial condenser and reboiler. As in the original Thiele-Geddes method, the problem definition is such that the feed component flow rates, are known and fixed. The column pressure profile is also fixed, as well as its configuration, which defines the number of stages and feed location. In addition, one product rate (the distillate) and one internal flow (such as the reflux rate, Lj) are specified. The solution method, outlined below, is described in detail by Holland (1975). 

Calculate stage liquid rates by applying total material balance on each stage. 

Estimate equilibrium coefficients on the basis of a composition independent correlation. 

Combine component material balance and phase equilibrium relations to calculate vapor rates of each component on each stage. 

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A modified Thiele-Geddes method, programmed for an IBM 370-155, was used to perform the calculations needed to size each required column. Experimental activity coefficient data were used to allow for nonideal liquid phase behavior while energy balances, using estimated enthalpy data, were used to correct for non-constant molal overflow. The Theta Method was used for convergence, and all plate efficiencies were assumed to be 100%. (See Reference 7 for additional calculational details and a program listing.)... 

The modified Thiele-Geddes method was mainly designed for conventional distillation columns although it has been generalized to handle complex columns (Holland, 1963). It is limited in the types of performance specifications it can handle and could be numerically unstable, especially for wide-boiling or nonideal mixtures (Wang et al., 1980). 

The modified Thiele-Geddes method described in Section 13.2 is adapted here to liquid-liquid extraction. Reference is made to the steps described in that method. 

The updated stage temperatures are obtained by calculating the bubble point temperature on each stage on the basis of the new liquid compositions given by Equations 13.19 and 13.20. The updated compositions and temperatures are used to calculate updated total liquid and vapor flows on each stage using enthalpy balances as described in the modified Thiele-Geddes method in the next section. 

Edminster (Ref. 4) has presented a modified absorption factor method that determines the molal quantities for each component as a fraction of their values in the distillate and bottoms in a manner somewhat similar to the Thiele and Geddes equations. The geometric mean of the absorption and stripping factors at the ends of the section under consideration is employed, and empirical correction terms are applied to these averages. 

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