Numerical Simulation of Coning Behavior of a Single Well in a Naturally Fractured Reservoir

Chen, Huan-Zhang; Scientific Research Inst. of Petroleum Exploration and Development Abstract The history matching and predicting of an actual well in a reservoir with double porosity is performed with a new coning simulation model that gives satisfactory results. A discussion of the parameters used for matching provides some insight into the structure and parameters of provides some insight into the structure and parameters of the reservoir. Other points discussed includebottomwater rising characteristics,a comparison between the dual porosity and the single porosity (assuming that the mass transfer between the fracture and matrix is equal to zero), andthe imbibition characteristics of matrix. Introduction The mathematical equations describing fluid flow in the dual-porosity medium were presented in the 1960's. Kazemi et al. obtained the numerical solution of this problem in 1976 but did not present the solution of problem in 1976 but did not present the solution of coning, and the flow terms of matrix in the equations were neglected. Since 1977, Wu Wan-yi of Beijing U. has done extensive research on this aspect. His work-the axially symmetric water coning problem-is based on a dual-porosity-medium model and equations presented by Barenblatt and Jeltov. All the terms that should appear in the equations are included-i.e., the fluid flow between the matrix blocks has not been neglected. The harmonic average value of mobility of fissure and matrix is used as the imbibition coefficient. All nonlinear coefficients are linearized, and the semi-implicit scheme is used in the difference equations. These equations are solved by the direct solution method. We performed a further study based on these works, using an improved program to give a good history matching with an actual program to give a good history matching with an actual well behavior. Our results are discussed in detail in this paper. This method may be used to solve the problems of paper. This method may be used to solve the problems of multidimensional, two-phase fluid flow. Model Structure The structure of the model is shown in Fig. 1. It is a cylinder, which represents a part of the reservoir controlled by the well. Its axis coincides with the axis of the well, and the radius of the cylinder represents the drainage radius of the well. The top and flank of this cylinder are impervious. The bottomwater is supplied from the lower surface of the cylinder, and the pressure on this surface is maintained at a constant value. The upper part of the cylinder is oil zone, the middle is transition zone, and the lower is water zone. The well may be perforated in both oil zone and water zone or in only one of the two zones. In any given depth, there may be a horizontal thin impervious break with a changeable radius. Fluid-Flow Equations Assume that the fluids are immiscible, and that both the medium and fluids are slightly compressible. In addition to the continuous flow in fracture and matrix, there is the mass transfer between the fracture and matrix. Under these assumptions, the flow of fluids satisfies the following equations. ..........................................(1) SPEJ p. 879