A More General Capillary Pressure Curve and Its Estimation From Production Data

摘要

Capillary pressure plays a very important role in naturally fractured reservoirs. The exchange of fluids between matrix and fracture is essentially dependent on capillary pressure expressed by the capillary pressure curve. Capillary force may contribute to the displacement process through imbibition process, or may oppose it in the drainage displacement process. It is essential to represent the capillary pressure curves properly. Many capillary pressure correlations have been suggested in the literature. Capillary pressure data were normally measured using core data. However these methods suffer limitation due to the scale over which the data were collected. Therefore it will be very useful if the capillary pressure curve could be extracted from production data through the history matching process. This paper presents a simple and generalized capillary pressure model which captures both the spontaneous and forced parts of the imbibition capillary pressure curve. In addition, the capillary pressure was estimated by the production data. The sensitivities of production data with respect to capillary pressure model parameters are required when the gradient-based optimization algorithm is used to minimize the objective function. How to calculate the sensitivities of the production data with respect to the capillary pressure model parameters is provided. By minimizing the objective function which describes the mismatch of the observed and simulated production data, the water-oil capillary pressure curves are estimated. All of implementations are incorporated into a commercial simulator (ECLIPSE) and iterated in the automatic history matching scheme. The method is validated using many synthetic cases.