The flow of multiple immiscible fluids within a porous medium controls many natural and engineered systems in the environment including: geologic CO2 sequestration, enhanced oil recovery from underground reservoirs, and contaminant remediation of groundwater. The need to understand how fluids are transported and distributed in these processes is important for designing accurate models that can improve process efficiency. The research comprising this dissertation developed and utilized a fast X-ray microtomography technique that allows for three-dimensional, near real-time, investigations of multiphase flow. Constitutive relationships based on multiphase state variables (saturation, capillary pressure, interfacial area, fluid topology) are tested for accurate predictions of quasi- and non-equilibrium two-fluid flow experiments in an effort to better understand the role of fluid relaxation on these relationships and state variables. The effect of bubble generation and transport, relevant to multiphase processes such as air stripping, on these relationships is also studied. Collectively, results show the need for constitutive relationships which include all four measured state variables to uniquely predict two-fluid flow independent of flow condition or bubble generation. An empirical relationship is also developed to predict interfacial area, an important mass transfer parameter, depending on the degree of relaxation within the system. Overall, the presented findings may help design more efficient engineering practices and transport models.