Microfluidic paper-based analytical devices (µPADs) are a promising technology to enable accurate and quantitative in situ assays. Paper’s inherent hydrophilicity drives the fluids without the need for external pressure sources. However, controlling the flow in the porous medium has remained a challenge. This study addresses this problem from the nature of the paper substrate and its design. A computational fluid dynamic model has been developed, which couples the characteristics of the porous media (fiber length, fiber diameter and porosity) to the fluidic performance of the diffusion-based µPAD sensor. The numerical results showed that for a given porous membrane, the diffusion, and therefore the sensor performance is affected not only by the substrate nature but also by the inlets’ orientation. Given a porous substrate, the optimum performance is achieved by the lowest inlets’ angle. A diffusion-based self-referencing colorimetric sensor was built and validated according to the design. The device is able to quantify the hydronium concentration in wines by comparison to 0.1–1.0 M tartaric acid solutions with a 41.3 mM limit of detection. This research showed that by proper adjustments even the simplest µPADs can be used in quantitative assays for agri-food applications.