An Efficient Method for Determining Capillary Pressure and Relative Permeability Curves from Spontaneous Imbibition Data

Abstract

In this paper, a very efficient method, called single matrix block analyzer (SMBA), has been developed to determine relative permeability and capillary pressure curves from spontaneous imbibition (SI) data. SMBA mimics realistically the SI tests by appropriate boundary conditions modeling. In the proposed method, a cuboid with an identical core plug height is considered. The equal dimensions of the cuboid in x and y directions are set such that the cylindrical core plug and the cuboid have the same shape factor. Thus, by avoiding the difficulties of the cylindrical coordinates, a representative model for the core plug is established. Appropriate grid numbers in x-y and z directions are specified to the model. Furthermore, the rock and fluid properties of SI test are set in the SMBA. By supposing forms of the oil-water capillary pressure and relative permeability and comparing the oil recovery curves of SMBA and SI data, capillary pressure and relative permeability can be determined. The SMBA is demonstrated using three experimental data with different aging times. Suitable equations are employed to represent the capillary pressure and relative permeability curves. The genetic algorithm is used as the optimization tool. The obtained results, especially for capillary pressure, are in good agreement with the experimental data. Moreover, the Bayesian credible interval (P10 and P90) evaluated by the Neighborhood Bayes Algorithm (NAB) is quite satisfactory.

Keywords

• Spontaneous Imbibition
• Single Matrix Block Analyzer
• Recovery Curve
• Genetic algorithm
• Neighborhood Bayes Algorithm