SC Simultaneous Correction Method

A brief description of this procedure is abstracted from the fuller treatment of Henley and Seader (1981). The MESH equations (13.182)-(13.186) in terms of mol fractions are transformed into equations with molal flow rates of individual components in the liquid phase ltJ and vapor phase vif as the primary variables. The relations between the transformed variables are in this list  

The balance equations become three groups totalling N(2C +1) in number  

Evaluate the discrepancy function made up of deviations from zero of the mass M, equilibrium E, and enthalpy H functions of Eqs. (13.214)-(13.216)  

The total flow rates are found by summing up the component flow rates 

Evaluate condenser and reboiler loads by heat balances if they have not been specified. 

It will ensure that the converged variables will be accurate to generally at least four significant figures. 

Initial estimates of the stage temperatures are taken from linear variations between estimated overhead dewpoint and bottoms bubblepoint temperatures. Those of the vapor rates are based on the assumption of constant molal overflow with due regard to sidestreams, and those of the liquid rates are made consistent with the material flow balances. 

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SC (simultaneous correction) method. The MESH equations are reduced to a set of N(2C +1) nonlinear equations in the mass flow rates of liquid components ltJ and vapor components and the temperatures 2J. The enthalpies and equilibrium constants Kg are determined by the primary variables lijt vtj, and Tf. The nonlinear equations are solved by the Newton-Raphson method. A convergence criterion is made up of deviations from material, equilibrium, and enthalpy balances simultaneously, and corrections for the next iterations are made automatically. The method is applicable to distillation, absorption and stripping in single and multiple columns. The calculation flowsketch is in Figure 13.19. A brief description of the method also will be given. The availability of computer programs in the open literature was cited earlier in this section. 

Figure 13.20. Algorithm of the SC (simultaneous correction) method for all multistage separations of fluid mixtures [Naphthati and Sandholm, AIChE J. 17, 148 (1971), Henley and Seader, 1981].

Multicomponent distillation, 393 absorption factor method, 398 azeotropic, 420-426 bubblepoint (BP) method, 406-409 computer program references. 404 concentration profiles, 394 distribution of non-kevs. 395 Edmister method, 398,399 extractive, 412, 417-422 feed tray location, 397 free variables, number of 395 Lewis-Matheson method 404 MESH eauations. 405-407 molecular, 425-427 nomenclature, 405 number of theoretical trays, 397 packed towers, 433-439 petroleum, 411-415 reflux, minimum, 397 reflux, operating, 397 SC (simultaneous correction) method, 408-411... 

SC (simultaneous correction) method. The MESH equations are reduced to a set of A(2C + 1) nonlinear equations in the mass flow rates of liquid components ly and vapor components Vij and the temperatures 7. The enthalpies and equilibrium constants Ky are determined by the primary variables lij, Vij, and Tj. The nonlinear equations are solved by the... 

Separations 404 Specifications 405 The MESH Equations 405 The Wang-Henke Bubblepoint Method 408 The SR (Sum-Rates) Method 409 SC (Simultaneous Correction) Method 410... 

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