An understanding of fluid transport through porous materials is critical for the development of lateral flow assays and analytical devices based on paper microfluidics. Models of fluid transport within porous materials often assume a single capillary pressure and permeability value for the material, implying that the material comprises a single pore size and that the porous material is fully saturated behind the visible wetted front. As a result, current models can lead to inaccuracies when modeling transport over long distances and/or times. A new transport model is presented that incorporates a range of pore sizes to more accurately predict the capillary transport of fluid in porous materials. The model effectively predicts the time-dependent saturation of rectangular strips of Whatman filter no. 1 paper using the manufacturer's data, published pore-size distribution measurements, and the fluid's properties.