Averaging the experimental capillary pressure curves for scaling up to the reservoir condition in the imbibition process

Heterogeneity of a reservoir rock is an important factor that needs to be accounted for modeling of reservoir blocks. The rock properties are measured in the laboratory using a small core plug while in the simulation of a large scale reservoir, the size of each grid block is much larger. Hence, the rock properties of a simulation block should be obtained by averaging methods from core samples that forms the grid block. Among the rock properties, capillary pressure (P-c) is more challenging as it is a function of fluids' saturation. The most commonly used methods to average the capillary pressure data are J-function and simple curve fitting. However, these methods are not adequately precise and the heterogeneity pattern, and the physics of fluids' flow are not considered as well. In the present paper, various models were built using experimental data under different heterogeneity patterns, and then the imbibition process of the oil/water system was simulated. In this case, different Pc curves were distributed in the model based on the heterogeneity patterns. In the next step, one Pc curve, obtained from an averaging method, was assigned to the entire model and the simulation was applied again. The comparison between the simulation results of the actual model and the averaged Pc model, depicts the accuracy of the averaging method. We introduced and tested different averaging techniques for many heteronomous models and the accuracy of each technique was evaluated. The results show that the traditional techniques are inaccurate and may not represent the heterogeneous (actual) model. Based on the results obtained from many models, a new approach is proposed for the averaging of the Pc curves which can adequately predict the actual model's Pc. This method was successfully verified for a variety of models which had not been used in the development stage.