This paper is aimed at investigating heat and mass transfer in regenerative heat exchangers with hygroscopic materials, such as desiccant and enthalpy wheels. However, rather than examining heat and mass transfer in a traditional two-process (dehumidification and regeneration) wheel, a multi-process operation is analyzed. A mathematical model for the given problem, based on transport phenomena with in the presence of physical adsorption, is proposed, and a proper normalization scheme - in terms of physically meaningfully dimensionless parameters - is employed. The model consists of two pairs of nonlinear coupled partialdifferential equations that describe the heat and mass transport in the flowing airstreams and solid desiccant material. Multiple inlet conditions are prescribed in order to describe the multiple process streams. The the equations are solved using the Finite Volume Method for spatial discretization, and the Method of Lines for time-integration, using the numerical routines built-in the Wolfram Mathematica system. A periodicity condition is numerically imposed by iterating the numerical solution for multiple cycles (all of which undergo all inlet conditions), until a periodic, or quasi-steady-state solution is reached. Also, a mesh verification study is carried out to determine the proper mesh for simulations. At last, simulation results of a handful of cases are presented.