Theoretical Analysis Of Miscible Displacement In Fractured Porous Media By A One-Dimensional Model: Part I -- Theory

Abstract

Abstract A one-dimensional model is formulated to describe miscible displacement in fractured porous media. Four parameters, R1 (normalized fracture capacity), B (productivity capacity ratio), M (viscosity ratio), and Ngr (gravity number) that characterize the process are identified. No-crossflow and crossflow equilibrium assumptions are made, and solution methods for both cases are provided. In the case of crossflow equilibrium, the flow is balanced by the viscous and gravity forces. Three branches of solution characteristics are discovered. These are:dominant viscous crossflow,moderate gravity crossflow, andstrong gravity crossflow. The criterion for each case is given in terms of viscosity ratio and gravity number. Depending on the magnitude of viscosity ratio and gravity number, crossflow direction changes along the length of matrix-fracture interface. Introduction One of the main characteristics of a fractured petroleum reservoiris high rate wells in the early life of the field. Depending on the drainage rate. the high rate can continue for a long time for some fractured reservoirs and for a very short period for others, Fractures increase the effective single phase permeability of the combined matrix-fracture porous media. The magnitude of the increase of effective single phase permeability depends on the (kA)r/(kA)m ratio (fractures are assumed perpendicular to the well). For most naturally fractured reservoirs, (kA)r/(kA)m is in the range of 10 to 100. Therefore, wells could produce at rates of 10 to 100 times more than a nonfractured matrix. The above picture of a fractured petroleum reservoir changes for the two phase gas-oil now process. The oil drained from the matrix to the fracture could partly or totally reinfiltrate to the blocks underneath due to capillary and gravity forces(1,2). The reinfiltration process, therefore, substantially reduces the rate of oil production in the two-phase gas-oil region. Another parameter which could lower the rate of drainage in fractured porous media is the fracture gasoil capillary pressure. Visual observations have revealed that the oil now in the fractures for the gas-oil immiscible system is mainly film now, and higher fracture aperture (i.e., fracture capillary pressure effect) reduces the liquid film flow across the matrix blocks(3). Both the reinfiltration process and the capillary pressure contrast between the matrix and fracture lower the rate of drainage. In other words, the rate of drainage from fractured porous media, when the oil is derived from the matrix. is less than in an unfractured medium with the same matrix permeability, provided oil compressibility effects and fracture storage are negligible. After an infinite lime period due to capillary continuity, the ultimate recovery will be the same for both fractured and unfractured porous media. The key to drainage rate enhancement for fractured porous media is:to increase gas-oil gravity drainage rate, andto reduce rein filtration rate.