Applications of the Dual-tube Model to a Hydraulically Fractured Shale-gas Reservoir

Abstract

Summary Flow through fractured nanoporous shale formations is complicated by a hierarchy of structural features (ranging from nanopores to microseismic and hydraulic fractures) and by several gas-transport mechanisms that differ from standard viscous flow used in reservoir modeling. In small pores, self-diffusion becomes more important than advection, and slippage effects and Knudsen diffusion might become relevant at relatively low densities. We derive a nonlinear effective diffusion coefficient that describes the main transport mechanisms. In its dimensionless form, this coefficient only depends on a geometric factor (or dimensionless permeability) and on the kinetic model that describes the gas. To simplify the description of the complex structure of fractured shale formations, we observe that the production rate is controlled by the flow from the shale matrix (which has the largest storage capacity but the lowest diffusivity) into the fracture network, which is assumed to produce instantaneously. Therefore, we propose to model the flow in the shale matrix and estimate the production rate with a simple bundle of tube. Each tube is characterized by two diameters (conductive diameter and storage diameter), which idealizes gas pathways formed by bulbs and throats and permit to model slow recovery of large gas volumes. To construct a Bundle-of-Dual-Tube Model (BoDTM) a reliable estimate of the joint statistics of the matrix-porosity parameters is needed. This can be either inferred from core measurements or postulate on the basis of some a-priori assumption if not enough information is available. By means of simplified distributions we investigate the effects the variability and correlation of bundle-parameters on the production rate. The BoDTM, which can be easily extended to obtain bundles with a more complex statistics, entails enough flexibility to describe complex production rate from shale formations.