A Statistical Dual-Tube Model to Analyze Gas Production from Shale Formations

Abstract

Gas flow through fractured nano-porous shale formations is complicated by a hierarchy of structural features and fluid transport mechanisms. Structural features include tight porous rock with a variety of fractures. Gas transport mechanisms include self diffusion, Knudsen diffusion, advection, gas expansion, adsorption, and slippage effects at the pore walls. In nanopores, as encountered in tight shale gas reservoirs, the effects of diffusion can overcome advection and should be included in reservoir flow calculations. As the permeability of shale is very low, conventional reservoir simulation modeling and production estimation methods, which are designed for fluid-flow processes dominated by viscous forces, may not be reliable to predict the reservoir production rate. We present a pore-based mechanistic model (the Bundle of Dual-Tube Model, BoDTM), which includes complex gas dynamics in fractured nanoporous shale formations. The pore-based model provides a quick and reliable means for modeling tight rock gas flow that includes known and uncertain reservoir properties, such as rock permeability, diffusion, pore volume, pore throat size, rock tortuosity and fracture characteristics. Gas flow is modeled in the shale matrix and production rate is estimated with a simple bundle of dual-tubes. Each dual-tube idealizes a gas pathway formed by pore bulbs and throats and is characterized by two diameters (a conductive diameter and a storage diameter) and one length. The two diameters permit modeling slow recovery of large gas volumes; the tube length takes into account the pathway length from the matrix into the fracture network, which is the length that controls the travel time and the production rate. To construct the BoDTM, a statistical estimate of the fracture-network and shale-matrix parameters is necessary. Production rate is controlled by flow from the tight shale rock matrix (which has the largest storage capacity but the lowest diffusivity) into the fracture network, and we assume that gas in the fractures is produced instantaneously. Applying statistical distribution functions, we examine the effect of model input properties on gas production. By applying the BoDTM to field data from the Barnett and Fayetteville Plays, we demonstrate that the model provides a means to quickly assess gas production rates from shale formations.