The application of mass transfer boundary layer theory to spatially periodic flows is investigated. Numerical methods are used to solve the flow problems, and the solutions are used in conjunction with mass transfer boundary layer theory to predict mass transfer rates. This approach is advantageous because at large Schmidt numbers numerical solution for the concentration profiles requires very high numerical resolution in the boundary layer region. For the two prototype flows investigated, tube bank flow and Taylor-Couette flow, the predictions agree reasonably well with the experimental results. As a result, this approach should be useful for preliminary design calculations in spatially periodic systems.