Estimation of Matrix Block Size Distribution in Naturally Fractured Reservoirs

Abstract

Abstract Interporosity flow in a naturally fractured reservoir is modelled by a new formation incorporating variability in matrix block size. Matrix block size isinversely related to fracture intensity. The size of matrix elements contributing to interporosity flow is expressed as a distribution in the source term of the diffusivity equation. The pressure transient response for uniform and bimodal distributions of block size is investigated. Both pseudo-steady state and transient models of flow are analysed. It is shown that features observed on the pressure derivative curve can yield the parameters of the distribution. Thus, observed pressure response from fractured reservoirs can be analysed to obtain the matrix block size distribution in the volume of the reservoir investigated by the test. The solution to the uniform distribution can be extended to more general distributions. Other sources of information, like logs and geological observations, can give an estimation of the shape of the distribution, and this model can be used to compute the reservoir parameters. Introduction Flow tests in naturally fractured reservoirs have been analysed using a continuum approach to model the reservoir, i.e., matrix and fracture systems are assumed continuous throughout the formation. The rock matrix has a very low permeability but stores most of the reservoir fluid in its intergranular porosity. The fracture system, on the other hand, has an extremely low porosity but provides the path of principal permeability. When a well located in such a reservoir is produced, a rapid pressure response occurs in the fracture network due to its high diffusivity. This creates a pressure difference between the matrix and the fractures, which begins to deplete the fluid from the matrix, commonly termed as interporosity flow. As flow progresses, pressures in the matrix and the fractures equilibrate and the fracture flow response is observed again, with fluid now coming from a composite storativity of the matrix and the fractures. The interaction between the matrix and the fractures is affected strongly by the geometrical distribution of the fractures. The parameters used to characterise this interaction are, matrix storativity ratio, which specifies the relative fluid distribution, and, the inter-porosity flow coefficient, which lumps the effects of the flow properties of both media and their geometry. Matrix flow can be modelled as pseudo-steady state (PSS), or unsteady state (USS). Models available in the literature assume fracturing is uniform and hence matrix block size is constant. Geologic studies have shown nonuniformity in fracture intensity in many reservoirs, from very severe fracturing to very sparse fractures. Hence, it is necessary, to model variability in flow contribution from matrix elements or blocks, depending on their size. Braester concluded block size does not significantly affect the drawdown pressure response of a fractured reservoir. Cinco et al. suggested a discrete distribution of matrix block sizes with transient interporosity flow and showed the pressure derivative is significantly affected. Jalali-Yazdi and Belani show block size variability affects the pressure response markedly.