Evaluation of Matrix-Fracture Imbibition Transfer Functions for Different Types of Oil, Rock and Aqueous Phase

Abstract

Abstract Several different versions of the transfer functions evolved from classical Mattax and Kyte's dimensionless group and Aranofsky et al.'s abstract relationship were tested. Another transfer function derived analytically based on power law relationship between recoverable oil and time was also included in the testing process. The exponents in all these transfer functions reflect the strength and type of the transfer. The recovery curves obtained from the spontaneous imbibition of different aqueous phases (brine and surfactant) into cylindrical rock samples saturated with different types of oil were used to fit the transfer functions. The exponents yielding the best fit to experimental data were obtained and correlated to the effective parameters such as the viscosity of oil, matrix permeability, IFT, matrix size, and wettability using multivariable regression analysis. The correlations developed were analyzed for the rock and oil types, and IFT. It was observed that the exponential relationships were more suitable for synthetic and processed oil samples whereas the power law transfer functions were more applicable for crude oil cases. It is hoped that the analysis provided in this paper would facilitate the selection of proper transfer function type for performance estimation of naturally fractured reservoirs. Introduction Reliable description of matrix-fracture interaction is the key to an accurate simulation of naturally fractured reservoirs if matrix is heavily contributing to the production. During the injection of any material for EOR purpose, the injectant will preferably flow in the fracture. Matrix oil will be recovered by an interaction between the fracture and matrix. Obviously, the same type of transfer function is not expected to be applicable to every rock, fluid and process type. Suitable transfer functions need to be determined for particular rock and fluid properties. This entails a critical analysis and testing of matrix-fracture transfer functions that would eventually lead to a classification of them for different fluid, rock and process types. Oil in the matrix is typically recovered by capillary imbibition if the matrix is water wet and enough amount of water is supplied in the fracture. For such systems, the accuracy of the dual porosity model depends on the accurate description of matrix fracture transfer function1. A general description of matrix-fracture transfer function is difficult to propose due to complexity of the phenomenon and significant number of parameters involved in the process. In this paper, several different types of matrix-fracture interaction functions were tested for different rock and fluid properties. After an extensive review of the previously proposed matrix-fracture transfer functions, the exponents that control the rate of spontaneous imbibition in the exponential and power law transfer functions were correlated to matrix and fluid properties. Experimental data obtained using a wide variety of oil, rock and aqueous phase types were used for this purpose.