By modifying a mathematical model for distillation with two liquid phases so as to accommodate thermally coupled distillation with two liquid phases

this paper proposes an algorithm based upon the modified Naphtali-Sandholm method. The structures of the Jacobian matrix and its submatrices of all types

and formulae for computation of their nonzero elements are given. The multiple phase flash method

combined with a comparison of free energies for determination of the liquid phase split in stage

is employed. Separation of the butanol-water-propanol ternary system is used to corroborate the method mentioned above. Satisfactory results are obtained.