Finite difference and orthogonal collocation techniques are used to obtain numerical solution of the differential contactor model that represents a packed column. In the orthogonal collocation approach, polynomial approximation to the model equations results in a sparse system of equations that is much smaller in dimension than with the other methods. Exploiting this sparsity and choosing the proper order for approximating polynomial are the critical issues. Higher CPU time associated with higher order of the polynomial necessitates use of finite elements in the collocation techniques. We study the accuracy and efficiency issues underlying all these approaches with the help of hydrocarbon mixture and ethanol esterification examples. The later case study is considered with both with and without the presence of reaction.