A novel continuous biodrying reactor has been developed for drying pulp and paper mixed sludge to raise the dry solids levels so that the dried sludge can be combusted economically in a biomass boiler for energy recovery. A two-dimensional (2D) model was proposed that takes into account coupled mass, heat, and biological transport processes for both gas and solids flow directions. This model was solved numerically using the finite element method. The predicted temperatures reflect the two-dimensionality of the transport phenomena in the biodrying reactor. Despite some discrepancies between the temperature predicted by this model and the experimental data, the estimated water removal rates are in good agreement with measured ones. It was found that only one third of the total water removal takes place in the convection-dominated zone of the reactor, whereas the removal of remaining water takes place in its bioheat-and mass diffusion-dominated zone. It was also found that conduction heat transfer has only a minor impact on the matrix temperature, relative to the bioheat source term and evaporative heat sink term, which play important roles.