Predicting long-term production from gas shale reservoirs has been a major challenge for the petroleum industry. To better understand how production profiles are likely to evolve with time, we have conducted laboratory experiments examining the effects of confining stress and pore pressure on permeability. Experiments were conducted on intact core samples from the Barnett, Eagle Ford, Marcellus, and Montney shale reservoirs. The methodology used to measure permeability allows us to separate the reduction of permeability with depletion (because of the resultant increase in effective confining stress) and the increase in permeability associated with Knudsen diffusion and molecular slippage (also known as Klinkenberg) effects at very low pore pressure. By separating these effects, we are able to estimate the relative contribution of both Darcy and diffusive fluxes to total flow in depleted reservoirs. Our data show that the effective permeability of the rock is significantly enhanced at very low pore pressures ( []) because of the slippage effects. We use the magnitude of the Klinkenberg effect to estimate the effective aperture of the flow paths within the samples and compare these estimates to scanning electron microscopy image observations. Our results suggest effective flow paths to be on the order from tens of nanometers in most samples to 100–200 nm, in a relatively high-permeability Eagle Ford sample. Finally, to gain insight on the scale dependence of permeability measurements, the same core plugs were crushed, and permeability was again measured at the particle scale using the so-called Gas Research Institute method. The results show much lower permeability than the intact core samples, with very little correlation to the measurements on the larger scale cores.

Experimental investigation of matrix permeability of gas shales

Experimental study and modelling of methane adsorption and diffusion in shale

A Model for Multiple Transport Mechanisms Through Nanopores of Shale Gas Reservoirs with Real Gas Effect-Adsorption-Mechanic Coupling

Surface diffusion plays a key role in gas mass transfer due to the majority of adsorbed gas within abundant nanopores of organic matter in shale gas reservoirs Surface diffusion simulation is very complex as a result of high reservoir pressure, surface heterogeneity, and nonisothermal desorption in shale gas reservoirs In this paper, a new model of surface diffusion for adsorbed gas in shale gas reservoirs is established, which is based on a Hwang model derived under a low pressure condition and considers the effect of adsorbed gas coverage under high pressure Additionally, this new model considers the effects of surface heterogeneity, isosteric sorption heat, and nonisothermal gas desorption Results show that (1) the surface diffusion coefficient increases with pressure and temperature, while it decreases with activation energy and gas molecular weight; (2) contributions of viscous flow, Knudsen diffusion, and surface diffusion to the total gas mass transfer are varying during the development of shal

Model for Surface Diffusion of Adsorbed Gas in Nanopores of Shale Gas Reservoirs

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

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Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

Gas flow in ultra-tight shale strata

Physics of fluid flow in shale reservoirs cannot be predicted from standard flow or mass-transfer models because of the presence of nanopores, ranging in size from one to hundreds of nanometers, in shales. Conventional continuum-flow equations, such as Darcy’s law, greatly underestimate the fluid-flow rate when applied to nanopore-bearing shale reservoirs. As a result of the existence of nanopores in shales, the molecular mean free path becomes comparable with the characteristic geometric scale, and we hypothesize that under this condition, Knudsen diffusion, in addition to correction for the slip boundary condition, becomes the dominant mechanism. Recently, a few models have been developed that use various empirical parameters to account for these modifications (Javadpour 2009; Civan 2010; Darabi et al. 2012). This paper aims to provide a different approach to modeling apparent permeability in shale reservoirs. The proposed model is analytical, free of any empirical coefficients, and has been derived without invoking the assumption of slip flow at the pore wall. Our model of apparent permeability represented by a single analytical equation, depends only on pore size, pore geometry, temperature, gas properties, and average reservoir pressure. The proposed model is valid for Knudsen numbers less than unity and it stands up under the complete operating conditions of a shale reservoir. Our model reasonably predicts results as reported by other models. Finally, the model shows that pore-surface roughness and mineralogy have a negligible influence on gas-flow rate, whereas pore geometry and pore size play a significant role in the proportion of diffusion in total flow rate. Our study shows that a combination of Darcy flow and Knudsen flow—ignoring the Klinkenberg effect— can describe gas flow for a range of Knudsen flow applicable to a shale-gas system.

Hamed Darabi

Papers

Gas flow in ultra-tight shale strata

Nonempirical Apparent Permeability of Shale

Multiscale modeling of compartmentalized reservoirs using a hybrid clustering-based non-local approach

Modeling of Wettability Alteration Due to Asphaltene Deposition in Oil Reservoirs

Aspects of Modeling Asphaltene Deposition in a Compositional Coupled Wellbore/Reservoir Simulator