Forecasting Gas Production in Organic Shale with the Combined Numerical Simulation of Gas Diffusion in Kerogen, Langmuir Desorption from Kerogen Surfaces, and Advection in Nanopores

Abstract

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.

An Analysis for the Influences of Fracture Network System on Multi-Stage Fractured Horizontal Well Productivity in Shale Gas Reservoirs

“…In recent works, scholars [10][11][12] hold out that the ad-desorption theory in some shale should be described by the Brunauer-Emmett-Teller (BET) isotherm. However, in this paper, the ad-desorption law conforms to the Langmuir formula, which is proven by most observations [13][14][15][16].…”

“…According to Equation (14), when pressure declines, the higher stress sensitivity leads to higher decrease of natural fracture permeability. If we assume the stress sensitivity coefficient is 0.01, 0.05 and 0.1, after 3000 days, the recovery is 52%, 49% and 47%, respectively.…”

Fluid flow through nanopore space: discussion and proposition of a model for Polish shales

“…The next zone is called the transition zone, in which mean free path and average diameter are in the same order of magnitude and as a result, the influence of collisions between gas molecules are as important as collisions of gas molecules and pore walls. The gas transport in this regime is a combination of slippage flow and Knudsen diffusion flow [3,21]. Its boarders also depends on pressure [28,29].…”

Physical and mathematical modeling of gas production in shale matrix

“…Swami studied the contribution of Knudsen diffusion, gas slippage, gas desorption and gas diffusion from kerogen to total shale gas production by a proposed pore scale gas flow model (Swami et al, 2012). Shabro introduced a new numerical algorithm to forecast gas production in organic shale, simultaneously taking into account gas diffusion in kerogen, slip flow, Knudsen diffusion, and Langmuir desorption (Shabro et al, 2012). Alharty developed a dual-porosity and a triple-porosity finite-difference model for single-phase flow in shale including advective, diffusive, and Knudsen flow mechanisms (Alharty et al, 2012).…”