Accurate description of mass transfer and chemical reactions in anisotropic biomass particles is crucial when formulating truly predictive biorefinery process models. Due to the natural anisotropy of biomass particles, these can be accurately modeled with partial differential equations only by considering the mass transfer in all three dimensions. However, a large amount of memory and CPU time is needed to solve this three dimensional (3D) model. In order to reduce the computational load, this article introduces a method to simplify the 3D model into a ID model. Furthermore, the traditionally used low order finite difference method is replaced by the high order moment based weighted residual method. Using the simplified ID modeling approach and the new numerical method, a much lower number of variables is needed than used when solving the 3D model with the finite difference method, meanwhile providing similar average concentration profiles as the 3D model.