The requirements for unique estimation of the two-phase flow functions are investigated. The number of observable parameters is increased by including both the external and internal data. The flow functions are represented by global empirical functions, discrete values, and piece-wise local functions. The simulated annealing method is implemented for non-linear global optimization. Applications to unsteady-state drainage and imbibition, and steady-state core flood tests are presented. Global functional representations of the relative permeability and capillary pressure data are shown to be insufficient. Discrete representations of the flow functions yield non-smooth functions. A piece-wise functional representation is shown to lead to unique determination of the relative permeability and capillary pressure data when the transient-state internal saturation profiles and the overall pressure differentials are used together for history matching.

The method presented in this study can be used for accurate determination of the flow functions which are necessary for accurate description of flow behavior in hydrocarbon reservoirs and effective reservoir exploitation and management.

A method for simultaneous estimation of relative permeability and capillary pressure data from unsteady-state and steady-state laboratory core flow displacement data is presented. Internal core flow measurements data are incorporated into the estimation of the flow functions, and the effect of the non-Darcy flow on the flow functions is analyzed.