|| This paper deals with the optimization problem of extraction processes with recycle and immiscible solvent. Gradient methods using control variable iteration require a trial and error procedure to solve process and overall
equations for this problem. A new formulation is presented to eliminate such a trial and error procedure. First order and second-order convergence gradient methods were applied to determine the optimum solvent distribution in cross-current extraction with recycle and immiscible solvent. The Fletcher-Powell method converged most rapidly in all cases.