Formulation of an Almost Band Algorithm

For the case where one or more reactions occur on each stage of an absorber or distillation column and the vapor and liquid phases form highly nonideal mixtures, a formulation of the Almost Band Algorithm is recommended. In the present formulation for the case where one or more chemical reactions occur on each stage of an absorber, the following choice of N(2c + 1 + r) independent variables and N(2c 4-1 + r) independent functions are made. In particular, for the case of one chemical reaction per stage, the independent variables and functions are taken to be 

The enthalpy balance functions are given by Eq. (8-42). Use of the characteristics of homogeneous functions of degree zero and the approximations presented in Chap. 5 make it possible to regard the mixtures as ideal solutions in the partial differentiation of the G/s. This amounts to neglecting the dependencies of the enthalpies //7i, h on compositions. Column scaling followed by row scaling is recommended. It is anticipated that an internal loop would be required. This loop would be similar to the one used above in the N(r + 2) formulation in which the solution set / , is found on the basis of the assumed sets /,, and 7J.  

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