In this paper we develop a more general formulation for transient multiphase flow in porous media based on physics observed in core-scale and micromodel experiments. We account for non-equilibrium effects by considering redistribution time and treat saturation by evolving locally moving time-averages of the saturation. Several families of models arise from approximations to the general formulation with various degrees of accuracy. The classical Buckley-Leverett and Barenblatt expressions are special cases of these families. We explore the behaviors of a number of special cases arising from the proposed general formulation using established and novel numerical schemes that provide nonlinear physics-based preconditioning. The agreement observed between numerical and experimental results demonstrates the consistency of the proposed abstraction.