A Multiple-Porosity Method for Simulation of Naturally Fractured Petroleum Reservoirs

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Abstract
Summary. This paper describes the application of the method of "Multiple Interacting Continua" (MINC) to the simulation of oil recovery in naturally fractured reservoirs. A generalization of the double-porosity technique, the MINC method permits a fully transient description of interporosity flow by numerical methods. We present examples to demonstrate the utility of the MINC method for modeling oil-recovery mechanisms by water imbibition and field applications for five-spot waterflooding and water coning problems in fractured reservoirs. All results show that the MINC method problems in fractured reservoirs. All results show that the MINC method provides accurate predictions of the behavior of naturally fractured provides accurate predictions of the behavior of naturally fractured reservoirs, while requiring only a modest increase in computation work compared with the double-porosity method. The double-porosity method may result in large errors for matrix blocks of low permeability or large size. Introduction The study of fluid flow in naturally fractured petroleum reservoirs has been a challenging task. Considerable progress has been made since the 1960's because many fractured hydrocarbon reservoirs have been discovered and put into development in the past decades. Most papers treating flow in fractured reservoirs consider that global flow occurs primarily through the high-permeability, low-effective-porosity fracture system surrounding matrix rock blocks. The matrix blocks contain the majority of the reservoir storage volume and act as local source or sink terms to the fracture system. The fractures are interconnected and provide the main fluid flow path to injection and production wells. Because of the complexity of the pore structure of fractured reservoirs, no universal method for the simulation of reservoir behavior exists. Several different double-porosity models (DPM's) have been developed to describe single-phase and multiphase flow in fractured media. Usually, analytic approximations are introduced for the coupling between fracture and matrix continua. For example, it is commonly assumed that a quasisteady state exists in the primary-porosity matrix elements at all times. Very little work has been done so far in studying transient flow in the matrix blocks or between matrix and fracture systems either numerically or experimentally. As a generalization of the double-porosity concept, Pruess and Narasimhan developed the MINC method, which treats the multiphase and multidimensional transient flow in both fractures and matrix blocks by a numerical approach. This method was successfully applied to a number of geothermal reservoir problems. The MINC method of Pruess and Narasimhan involves discretization of matrix blocks into a sequence of nested volume elements, which are defined on the basis of distance from the block surface (Fig. 1a). In this way, it is possible to resolve in detail the gradients (of pressure, possible to resolve in detail the gradients (of pressure, temperature, etc.) that drive interporosity flow. This discretization technique was later adopted by Gilman for flow in fractured hydrocarbon reservoirs and by Neretnieks and Rasmuson for chemical transport in fractured groundwater systems. In the present paper, we apply the MINC method to study oil- recovery mechanisms in fractured reservoirs and to obtain insight into the behavior of water/oil flow during the imbibition process. Imbibition is regarded as a very important mechanism of oil production in waterflooding or water coning of fractured production in waterflooding or water coning of fractured reservoirs. For multiphase flow, pressure, viscous, gravitational, and capillary forces should all be taken into account. To understand the roles played by the three kinds of forces, we have studied the imbibition process with the MINC method, the conventional DPM, and with a detailed explicit discretization of matrix blocks. The comparison of the results from the three methods shows that the MINC method can give an accuracy of better than 1% at all times, while the DPM approximation with quasisteady interporosity flow can produce large errors, especially for matrix blocks with low permeability or large size. We also apply the MINC method to match published data of a five-spot waterfloods and the observed coning behavior of a well with bottomwater drive in a fractured oil reservoir. Satisfactory results have been obtained for the two examples. In both the imbibition study of individual matrix blocks and field-scale applications, the MINC method is found to give more reliable history matching and behavior predictions for the simulation of fractured reservoir than the conventional DPM. In most previous analytical or numerical studies of multiphase flow in porous media, it has been taken for granted that the matrix system can be treated as a single continuum with (locally) uniform pressure and fluid saturation distributions. To the best of our pressure and fluid saturation distributions. To the best of our knowledge, no studies for multiphase flow have been published concerning how much error will be introduced by this treatment and under what conditions the quasisteady approximation for interporosity flow is acceptable for engineering applications. The applicability of the DPM method is discussed by analyzing the results from individual block imbibition studies and field-scale examples with MINC and DPM in this paper. Through the work of this paper, it is found that the DPM method is often unsuitable for the paper, it is found that the DPM method is often unsuitable for the simulation of oil/water imbibition processes in naturally fractured reservoirs. Depending on reservoir fluid and rock properties, DPM may either overestimate or underestimate imbibition oil recovery from matrix blocks, especially for matrix blocks with low permeability and large size or for high oil viscosity. In some permeability and large size...