The Automatic History Matching Method To Calculate Relative Permeability

There are many important properties in the simulation of reservoir performance,where relative permeability curves are currently the most difficult to determine, theyreflected characteristics of reservoir fluids flow. As a basic data, whether for fielddevelopment program design, field development dynamic analysis, or reservoirnumerical simulation, it is indispensable. Since the relative permeability curvesobtained by original JBN method and its improved method is not smooth, and it’smonotonic can’t be guaranteed, the automatic history matching method isintroduced to address these deficiencies.The paper establishes mathematical model based on core’s centrifuge experimentin laboratory, assuming three relative permeability models and use the IMPES(saturation explicit method for solving the implicit method for solving the pressure)finite difference method to solve two-phase displacement equation; using the wetphase recovery data to establish objective function and adding penalty functions to theobjective function to confine the parameters range in relative permeability model;applying Gauss-Newton optimization method for numerical inversion of the relativepermeability by adjusting the relative permeability parameter value to make theobjective function minimized; inversion process must considers the impact ofcapillary pressure and capillary pressure data is obtained through the core centrifugeexperiments.Research shows that there are differences among the results of automatic historymatching obtained by three kinds of relative permeability model, but the relativepermeability curves are smoother compared with the explicit JBN method. Coreymodel fits best in the whole area and the resulting relative permeability curves is themost smooth; the result of B-spline function model is volatile, but basically consistentwith the experimental results, although the smoothness of the resulting relativepermeability curves is not good, it can guarantee curves’ monotonic; polynomialmodel fits well early, but later simulation results and experimental results are biased, and the trend becomes larger, and it can’t guarantee the monotonicity of relativepermeability curves. Therefore, Corey model and B-spline model can be used in coreflood experiments to inverse relative permeability data, and polynomial model shouldbe discarded.