A dual-tube model for gas dynamics in fractured nanoporous shale formations

Abstract

Gas 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 transport mechanisms that differ from the standard viscous flow used in reservoir modelling. In small pores, self-diffusion becomes more important than advection; also, slippage effects and Knudsen diffusion might become relevant at low densities. We derive a nonlinear effective diffusion coefficient that describes the main transport mechanisms in shale-gas production. In dimensionless form, this coefficient depends only 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 shales, we observe that the production rate is controlled by the flow from the shale matrix (which has the smallest 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-dual-tubes model (BoDTM), in which each tube is characterized by two diameters (one for transport and the other for storage). The solution of a single tube is approximately self-similar at early time, but not at late time, when the gas flux decays exponentially owing to the finite length of the tube. To construct a BoDTM, a reliable estimate of the joint statistics of the matrix-porosity parameters is required. This can be either inferred from core measurements or postulated on the basis of some a priori assumptions when information from laboratory and field measurements is scarce. By comparison with field production data from the Barnett shale-gas field, we demonstrate that BoDTM can be calibrated to estimate structural parameters of the shale formation and to predict the cumulative production of shale gas. Our framework has enough flexibility to construct models of increasing complexity that can be employed in the presence of a complex dataset or when more information is available.

Non-equilibrium dynamics of dense gas under tight confinement

“…The MFR obtained from the Boltzmann equation is a key parameter in the generalized Reynolds equation to describe gas-film lubrication problems such as the gas slide bearing (Fukui & Kaneko 1987, 1990Cercignani, Lampis & Lorenzani 2007), as well as in the upscaling methods used to predict the gas permeability of ultra-tight shale strata (Darabi et al 2012;Mehmani, Prodanović & Javadpour 2013;Lunati & Lee 2014;Ma et al 2014).…”

Assessing the utility of FIB-SEM images for shale digital rock physics

“…GRI permeability acquisition) because it does not take into account slip flow and Knudsen (and Fickian) diffusion through the pore space and kerogen [32], [21], and [33]; however, we expect that…”

Measurement of the surface diffusion coefficient for adsorbed gas in the fine mesopores and micropores of shale organic matter

“…Further, if the porous media was a strong adsorbent and the pore diameter was nano-scale, the bulk transport of gas molecules would be strongly influenced by the adsorption potential of the walls, and surface diffusion would became dominant [17,23,29]. For pure gas diffusing in porous media [20,72], the formulas of the above three diffusion types were displayed in Eqs. (11)-(13):…”

“…Considering the large percentages of adsorbed gas, its flow behavior has become one of the key transport mechanisms which needed deep research. Reservoir simulations also demonstrated that both the well productivity and accumulative production of shale gas reservoirs would present a remarkable increase if the output of adsorbed gas were involved [19][20][21].…”