Paper-based microfluidic devices offer great potential as a low-cost platform to perform chemical and biochemical tests. Commercially available formats such as dipsticks and lateral-flow test devices are widely popular as they are easy to handle and produce fast and unambiguous results. Although these simple devices lack precise control over the flow to enable integration of complex functionality for multistep processes or the ability to multiplex several tests, intense research in this area is rapidly expanding the possibilities. Modeling and simulation is increasingly more instrumental in gaining insight into the underlying physics driving the processes inside the channels; however, simulation of flow in paper-based microfluidic devices has barely been explored to aid in the optimum design and prototyping of these devices for precise control of the flow. We implement a multiphase fluid flow model through porous media for the simulation of paper imbibition of an incompressible, Newtonian fluid such as when water, urine, or serum is employed. The formulation incorporates mass and momentum conservation equations under Stokes flow conditions and results in two coupled Darcy's law equations for the pressures and saturations of the wetting and nonwetting phases, further simplified to the Richard's equation for the saturation of the wetting fluid, which is then solved using a finite element solver. The model tracks the wetting fluid front as it displaces the nonwetting fluid by computing the time-dependent saturation of the wetting fluid. We apply this to the study of liquid transport in two-dimensional paper networks and validate against experimental data concerning the wetting dynamics of paper layouts of varying geometries.