Gas-producing mudrock systems are playing an important role in the volatile energy industry in North America and will soon play an equally important role in Europe. Mudrocks are composed of very fine grained particles, and their pores are very small, at the scale of nanometers. Gas production from these strata is much greater than what is anticipated given their very low Darcy permeability. In this paper, images of nanopores obtained by Atomic Force Microscopy (AFM) are presented for the first time. Gas flow in nanopores cannot be described simply by the Darcy equation. Processes such as Knudsen diffusion and slip flow at the solid matrix separate gas flow behaviour from Darcy-type flow. We present a formulation for gas flow in the nanopores of mudrocks based on Knudsen diffusion and slip flow. By comparing this new gas flow formulation and Darcy flow for compressible gas, we introduce an apparent permeability term that includes the complexity of flow in nanopores, and it takes the form of the Darcy equation so that it can easily be implemented in reservoir simulators. Results show that the ratio of apparent permeability to Darcy permeability increases sharply as pore sizes reduce to smaller than 100 nm. Also, Knudsen diffusion's contributions to flow increase as pores become smaller. Unlike Darcy permeability, which is a characteristic of the rock only, permeation of gas in nanopores of mudrocks depends on rock, gas type and operating conditions. Introduction In general, very fine grained sediments (<62.5 µm) are collectively referred to as mudrocks, which show no fissility (paperlike parting) and are commonly classified as mudstones; those that show fissility are commonly classified as shales. The reader is referred to Folk(1), who developed a simple classification of mudrocks. The term mudrocks, rather than shales, for unconventional gas-producing strata is used in this paper to be in line with the scientific classification acceptable in the geosciences. The existence of nanopores in mudrocks has been revealed recently by ultra-high pressure mercury injection(2, 3) and back-scattered scanning electron microscopy(4). In this paper, for the first time we show nanopores and nanogrooves detected in mudrocks using atomic force microscopy (AFM)(5). Now that we are confident that such small pores exist in mudrocks, the challenge is to understand and develop governing equations to describe gas flow in these small pores. We present new formulations for gas flow that include some complexities that were ignored in developing the Darcy equation. At equilibrium, gas molecules are distributed throughout strata, as illustrated in Figure 1. Gas molecules occupy pores as compressed gas, cover the surface of the kerogen materials as adsorbed gas and disperse in the kerogen materials as dissolved gas. Drilling a well or inducing a fracture disturbs the equilibrium, and gas molecules start flowing toward the low pressure zone. First, the freely compressed gas in the pores is produced. Then, the gas molecules on the surface of the kerogen walls desorb and increase pore pressure(2). Gas desorption changes the concentration equilibrium between the bulk of the kerogen and its surface, as illustrated in Figure 1.

Production of gas out of low permeability shale packages is very recent in the Western Canadian Sedimentary Basin (WCSB). The process of gas release and production from shale gas sediments is not well understood. Because of adsorptive capacity of certain shale constituents, including organic carbon content, coalbed methane models are sometimes being applied to model and simulate tight shale gas production behaviour. Alternatively, conventional Darcy flow models are sometimes applied to tight shale gas. However, neither of these approaches takes into account the differences in transport mechanisms in shale due to additional nanopore networks. Hence, the application of existing models for shale results in erroneous evaluation and predictions. Our analysis shows that a combination of a nanopore network connected to a micrometre pore network controls the gas flow in shale. Mathematical modelling of gas flow in nanopores is difficult since the standard assumption of no-slip boundary conditions in the Navier-Stokes equation breaks down at the nanometre scale, while the computational times of applicable molecular-dynamics (MD) codes become exorbitant. We found that the gas flow in nanopores of the shale can be modeled with a diffusive transport regime with a constant diffusion coefficient and negligible viscous effects. The obtained diffusion coefficient is consistent with the Knudsen diffusivity which supports the slip boundary condition at the nanopore surfaces. This model can be used for shale gas evaluation and production optimization. Introduction Shale gas is a type of reservoir classified under the Unconventional Gas heading. These ‘difficult to produce’ reservoirs will play an increasingly important role in Canadian gas production because they are showing the potential to offset declining conventional gas production. Quite simply, shale gas is natural gas produced from shale sequences. Gas shales are predominantly lithified clays with organic material and detrital minerals present in varying amounts. Organic matter is an integral constituent of a productive shale gas reservoir. In addition, these fine-grained rocks are microporous, causing low permeabilities. While shale gas production has had a long history in the United States, dating back about 80 years, it is still at the very early stages of commercial production in Canada. Very little public data exists on shale gas production, yet industry interest is on the rise. A variety of estimates indicate that between 550 and 860 trillion cubic feet of gas-in-place could exist in potential shale gas formations in Western Canada(1,2). But shales can be difficult to evaluate using conventional laboratory techniques. Much of this has to do with resident clays that can have bound water either as part of their matrix or loosely bound in the interlayers in amounts of 75 to 80%. Another challenge can be the accurate measurement of in situ permeabilities, which are on the nanoscale. Core samples have often been subjected to coring induced or stress release fractures, resulting in greatly overstated permeability measurements. While some shales in Western Canada are, at this early stage, showing the proper geochemical and reservoir properties to support gas production, new techniques need to be developed to more accurately understand shale properties and their productive potential.

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.

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