It is known that the classical capillary pressure-saturation relationship may be deficient under non-equilibrium conditions when large saturation changes may occur. An extended relationship has been proposed in the literature which correlates the rate of change of saturation to the difference between the phase pressures and the equilibrium capillary pressure. This linear relationship contains a damping coefficient, tau, that may be a function of saturation. The extended relationship is examined at the macro-scale through simulations using the two-phase simulator MUFTE-UG. In these simulations, it is assumed that the traditional equilibrium relationship between the water saturation and the difference in fluid pressures holds locally. Steady-state and dynamic "numerical experiments" are performed where a non-wetting phase displaces a wetting phase in homogeneous and heterogeneous domains with varying boundary conditions, domain size, and soil parameters. From these simulations the damping coefficient tau can be identified as a (non-linear) function of the water saturation. It is shown that the value of tau increases with an increased domain size and/or with decreased intrinsic permeability. Also, the value of tau for a domain with a spatially correlated random distribution of intrinsic permeability is compared to a homogeneous domain with equivalent permeability; they are shown to be almost equal.