Numerical Simulation of Water Imbibition in Fractured Cores

Abstract

Original manuscript received in Society f Petroleum Engineers office Sept. 15, 1977. Paper accepted for publication June 9, 1978. Revised manuscript received Feb. 19, 1979. Paper (SPE 6890) first presented at the SPE-AIME 52nd Annual Fall Technical Conference and Exhibition, held in Denver, Oct. 9-12, 1977. Abstract A two-dimensional, two-phase, semi-implicit, numerical simulator was used to simulate water imbibition and oil recovery in artificially fractured and unfractured cores. Experimental results were matched satisfactorily by the numerical simulator. These results provide evidence of the reliability of the concepts underlying an earlier numerical simulator, which was tailored specifically for field applications. We show that the flow equations used to match the laboratory data reduce to the equations used in the field simulator. In addition, the experiments themselves were conducted quite differently from those commonly used in imbibition experiments and provide added insight into oil recovery from fractured reservoirs. Introduction Previously, we reported on the development of a Previously, we reported on the development of a numerical reservoir simulator for use in field applications. In this paper, we examine the reliability of the concepts underlying the numerical simulation by matching experimental results of fractured and unfractured cores with a simulator that accounts for the fracture and the matrix components. The simulator is a conventional two-dimensional, two-phase, semi-implicit simulator, but we show that it reduces to the formulation used in the field simulator. Several studies have reported on water imbibition in fractured media. These studies were concerned primarily with the imbibition aspects of the flow primarily with the imbibition aspects of the flow mechanism in the matrix rather than the total flow problem in the fracture-matrix system. Mattax and problem in the fracture-matrix system. Mattax and Kyte developed equations for scaling up imbibition effects. Parsons and Chaney used these equations to study imbibition effects in carbonate rocks. Iffly et al., in addition to experimental work, used a one-dimensional, two-phase, semi-implicit mathematical model to match oil recoveries from the matrix. A similar mathematical model in two dimensions was used by Kleppe and Morse to match the results of their imbibition experiments. While the last two papers show that imbibition oil recovery can be simulated numerically, the total concept of fluid flow in fracture-matrix systems has not been investigated adequately either numerically or experimentally. Mathematical Model The porous media used here were cylindrical cores or rectangular blocks cut along the long axis. The flow experiments were conducted so that the fracture plane and the entire core were horizontal. Therefore, the fractured cores were simulated by a layered two-dimensional simulator. The core halves were simulated as two matrix layers having the properties of the original core. The fracture was simulated as a very thin, high-permeability, and high-flow-capacity layer, where capillary pressure was essentially zero. The basic flow equations, assuming imcompressible flow, are w w----- wx ------ + ----- wz --------x x x zax az Sw+ qw Bw (X - Xo) = -------................(1)at t o o------ ox------ + ------ oz -------qoBo (X-Xo)x x z z So= ---------..................................(2)t Sw + So = 1.....................................(3) Pc(Sw) = po - pw....................................(4) kxkrwwx = 0.006328 -----------,......................(5)w SPEJ P. 175