We combine a new pore-scale model with a reservoir simulation algorithm to predict gas production in gas-bearing shales. It includes an iterative verification method of surface mass balance to ensure real-time desorption-adsorption equilibrium with gas production. The pore-scale model quantifies macroscopic petrophysical properties of formations using an algorithm of gas transport in porous media that simultaneously considers the effects of no-slip and slip flow, Knudsen diffusion, and Langmuir desorption. Subsequently, the reservoir model populates petrophysical properties derived from the pore-scale analysis at every numerical grid and at each time-step to calculate the production history and pressure distribution in the reservoir. This approach examines the contribution of different transport processes (i.e. advective flow, Knudsen diffusion, and desorption) to quantify their corresponding contributions to overall flow. Previously, we showed that slip flow and Knudsen diffusion play a significant role in explaining the higher-than-expected permeability observed in shale-gas formations with pore-throat sizes in the range of nanometers. It is shown that Langmuir desorption from organic-matter surfaces is important in the calculation of stored gas in gas-bearing shales. Modeling results show that gas desorption maintains the reservoir pressure via the supply of gas. In comparison to conventional reservoir descriptions, the contributions of slip flow and Knudsen diffusion increase the apparent permeability of the reservoir while gas production takes place. The effects of both mechanisms explain the higher-than-expected gas production rates commonly observed in these formations.

We introduce a new numerical algorithm to forecast gas production in organic shale that simultaneously takes into account gas diffusion in kerogen, slip flow, Knudsen diffusion, and Langmuir desorption. The algorithm incorporates the effects of slip flow and Knudsen diffusion in apparent permeability, and includes Langmuir desorption as a gas source at kerogen surfaces. We use the diffusion equation to model both lateral gas flow in kerogen as well as gas supply from kerogen to surfaces.Slip flow and Knudsen diffusion account for higher-than-expected permeability in shale-gas formations, while Langmuir desorption maintains pore pressure. Simulations confirm the significance of gas diffusion in kerogen on both gas flow and stored gas. Relative contributions of these flow mechanisms to production are quantified for various cases to rank their importance under practical situations.Results indicate that apparent permeability increases while reservoir pressure decreases. Gas desorption supplies additional gas to pores, thereby maintaining reservoir pressure. However, the rate of gas desorption decreases with time. Gas diffusion enhances production in two ways: it provides gas molecules to kerogen-pore surfaces, hence it maintains the gas desorption rate while kerogen becomes a flow path for gas molecules. For a shale-gas formation with porosity of 5%, apparent permeability of 59.7 µD, total organic carbon of 29%, effective kerogen porosity of 10%, and gas diffusion coefficient of 10 -22 m 2 /s, production enhancements compared to those predicted with conventional models are: 9.6% due to slip flow and Knudsen diffusion, an extra 42.6% due to Langmuir desorption, and an additional 61.7% due to gas diffusion after 1 year of production. The method introduced in this paper for modeling gas flow indicates that the behavior of gas production with time in shale-gas formations could differ significantly from production forecasts performed with conventional models.

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We have developed a new pore-scale method to quantify petrophysical properties of hydrocarbon (HC)-bearing shale. Recent studies indicate that slip flow, Knudsen diffusion, Langmuir desorption, and diffusion in kerogen contribute to the unconventional production properties of shale-gas formations. Conventional petrophysical interpretation methods do not account for the aforementioned phenomena and are often inconclusive when estimating petrophysical properties in shale formations. We constructed a pore-scale representation of the lower Eagle Ford Shale based on focused-ion-beam–scanning-electron-microscope (FIB-SEM) images. Permeability is calculated via previously developed finite-difference methods for the cases with and without slip flow and Knudsen diffusion. The method also calculates streamlines to describe sample pore connectivity. Weighted throat-size distributions are defined based on streamlines to represent the most resistive paths for fluid flow in the FIB-SEM image. Subsequently, permeability is estimated from the dominant throat size in the weighted throat-size distribution. We used a new fluid percolation model for HC-bearing shale that expands HC from kerogen surfaces and water from grain and clay surfaces into the pore space to vary fluid saturation. Isolated pores are randomly distributed within kerogen to increase kerogen maturity in the model. Electrical resistivity is calculated with a finite-difference solution of Kirchhoff’s voltage law applied at the pore scale. A parallel conductor model was used based on Archie’s equation for water conductivity in pores and a parallel conductive path for the Stern-diffuse layer. Calculations were compared with Waxman-Smits’ and Archie’s predictions of macroscopic electric conductivity. Using practical modeling parameters, the parallel conductor model yields the most accurate prediction of pore-scale sample conductivity for various cases of water saturation and conductivity.