Modeling of hollow fiber asymmetric membranes can provide useful guidelines to achieve desirable separations of multicomponent gas mixtures. Especially in cases of high commercial interest, such as hydrogen recovery from refinery streams, the accurate prediction of membrane separation performance is important. In this work, the appropriate model equations are solved by orthogonal collocation to approximate differential equations, and to solve the resulting system of non-linear algebraic equations by the Brown method. This technique is applied for the first time in a multicomponent gas separation by hollow fiber membranes and offers minimum computational time and effort, and improved solution stability. The predictions of the mathematical model are compared with experimental results for the separation and recovery of hydrogen from a typical gas oil desulfurization unit for various feed pressures, temperatures and stage cuts. In general, there is a very good agreement between simulation and experimental results. Further application of the developed mathematical model to various refinery gas streams of interest reveals that high permeate purity (99.95+), and high recovery (0.6-0.9), can be achieved even in a one-stage membrane unit. The reported experimental results and the theoretical analysis demonstrate the potential which polymer membrane technology has for the separation of hydrogen from refinery gas streams.