Simulation of multiphase flow in porous media requires knowledge of relative permeability functions. A commonly used unsteady-state method of estimating relative permeability is based on interpreting flow data collected from laboratory displacement experiments. In this paper, refinements are outlined, for improving the accuracy of estimated relative permeability pararmeters by accounting for thermal effects for produced fluids, utilizing pre breakthrough differential pressure data in cases where capillary forces are neglected, elimination of convergence problems in history-matching algorithms, and improving the reliability of injected phase relative permeability estimates.

For the gravimetric method of collecting displacement data, the existing procedure of calculating production volumes is improved to account for thermal expansion of fluids in collection vessels, both for imbibition and drainage displacement. The parameter estimation technique is used to determine relative permeability. A semi-analytical procedure, based on the JBN method, utilizes pre-breakthrough differential pressure data, in cases when capillary forces are neglected. This is especially important for low permeability samples, where post-breakthrough production data could be limited. Otherwise, capillary and gravitational forces are accounted for using a finite- difference method.

The history matching procedure requires minimizing the objective function, which is a measure of the deviation between simulated and experimental data. The simulated annealing method is used to avoid possible convergence of the minimization routine to a local, rather than the global minimum of the objective function. Interpretation of relative permeability of the injected fluid from displacement experiments is shown to be less precise than for the displaced fluid. The theoretical analysis rationalizes acquisition of more data during early phases of a displacement experiment. Optimization features discussed in this paper are incorporated in a new, relative permeability simulator.

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