A New Material-Balance Equation for Naturally Fractured Reservoirs Using a Dual-System Approach

Abstract

Abstract The complexity associated to naturally fractured formations constrains reservoir engineers to use simplified versions of the Material Balance Equation for determining the initial hydrocarbon in place and predicting reservoir performance. Although in particular cases a limited variant of the MBE may end up in small volumetric errors, the risk of using it is extremely high. In this paper, a new material balance equation for naturally fractured reservoirs is presented by using an original mathematical model that considers an initially-undersaturated black-oil fluid in a porous medium composed of interdependent matrix and fracture systems. The proposed equation leads to an improved method of modeling naturally fractured reservoirs by considering the compressibility difference between fractured and matrix systems. Particularly, the analysis displays its capability in reservoirs that have similar storage capacity in matrix and fractures. Modeling separate estimates of oil accumulation have significant economic implications. Poor fracture-matrix communication will give initially high oil rates that drop quickly because oil is basically produced from the fracture network. Pore pressure reduction due to production will tend to close fractures leaving behind considerable oil reserves in the matrix system. Estimates of original oil in-place both in the matrix as well as in the fracture system will help reservoir and production engineers to decide on exploitation strategies for these complex reservoirs. Our proposed equation has been applied to synthetic as well as field examples. Synthetic examples are used to validate the approach and examine the sensitivity to the average fracture compressibility. The field example is from El Segundo field, a low porosity carbonate reservoir in Colombia. Our example includes 8 producers located along the main fracture trend of the field and illustrates the feasibility of the approach for large-scale field applications. Introduction Material balance calculations are very well established techniques that apply the law of conservation of matter to petroleum engineering. Since Schilthuis1 first presented the derivation of the volumetric material balance equation (MBE), several MBE have been presented for single-porosity reservoirs2–7. One of the basic assumptions of conventional MBE is that rock properties, such as porosity and compressibility, are uniform throughout the reservoir. For dual-porosity media, as encountered in naturally fractured reservoirs (NFR), this assumption is no longer valid. Fracture and matrix porosity values change differently with pressure changes since fractures are highly compressible compared to the matrix (Fig. 1)8. Using the uniform reservoir compressibility assumption, MBE have also been derived for coal seam gas9,10 reservoirs, which are characterized for being dual-porosity systems. In conclusion, there is not a MBE specifically derived for NFR that considers the compressibility difference between fractured and matrix systems. From a storage capacity point of view, NFR can be classified into three groups11. Reservoirs of type A have high storage capacity in the matrix system and low storage capacity in the fractured system, reservoirs of type B have about similar storage capacity in matrix and fractures, and in reservoirs of type C, the storage capacity is exclusively in the fracture network. For reservoirs of type A and C, conventional MBE are applicable since single-porosity model assumptions holds. However, there is an important number of NFR in which fractures not only assist permeability in an already producible reservoir matrix but also contribute with storage capacity. For these reservoirs of type B, a new MBE was derived.