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Summary Flow conditions determine the flow regimes governing gas flow in porous media. Slip-flow regime commonly occurs in laboratory gas-permeability measurements, and one must consider the physics of that when finding the absolute permeability of a sample. Accurate permeability estimates are paramount for production forecasts, financial planning, and recovery estimation. Slip flow is present in low-permeability rocks, both in the laboratory environment and at reservoir conditions. Gas flow through the matrix lies under the slip-flow regime for the majority of low-permeability-reservoir production scenarios, and accurate prediction of pressure and production rate requires a good understanding of the flow regime. In this paper, an analytical study is conducted on the dominant flow regimes under typical shale-gas reservoir conditions. A flow-regime map is produced with respect to gas pressure and matrix permeability. Steady-state gas-permeability experiments are conducted on three shale samples. An analytical model is used to match the experimental results that could explain the order-of-magnitude difference between the permeabilities of gas and liquid in shales. Experimental results are combined with further tests available in the literature to inform a discussion of the model's parameters. The results improve the accuracy of gas-flow modeling and of absolute-permeability estimates from laboratory tests. Similar tests performed at various mean effective stresses investigate the influence of mean effective stress on flow regime and apparent permeability. The results indicate that flow regime is a function of mean effective stress, and that the apparent permeability of shale rocks is a function of both flow regime and mean effective stress.
Abstract This paper introduces a robust and accurate technique for the steady-state permeability and porosity measurements in ultra-low permeability shale core samples. A laboratory set-up was designed and assembled which has a resolution of one nano-darcy for the permeability and one-hundredth cubic centimeters for pore volume measurements. Extremely accurate differential-pressure transducers are used to measure the flow of gas passing through the core sample under in-situ conditions. The in-situ conditions are achieved by maintaining isothermal conditions and the application of the confining stress on the core sample. The laboratory set-up is fully automated to eliminate any human error and more importantly maintains the temperature stable within the enclosed unit. A series of measurements were performed on a Marcellus Shale core sample under wide range of pore and confining pressures using Helium (He) as a non-adsorbent and Nitrogen (N2) and Carbon Dioxide (CO2) as adsorbent gases. The measured gas permeability under steady-state condition is generally higher than the absolute permeability due to gas slippage (Klinkenberg 1941). Recent experimental and numerical studies indicate that permeability values for organic rich shale obtained by using different gases are much larger than the absolute permeability predicted by Klinkenberg the slippage theory. In ultra-tight formations such as organic rich shale, the measured "apparent" permeability is not a linear function of reciprocal of pressure as predicted by Klinkenberg. Thus, a new method based on the double gas slippage theory in nano-capillaries has been proposed for reliable estimation of the shale absolute permeability. In this study both Klinkenberg and double slippage corrections were applied to the steady-state permeability measurements. The results indicated that application of Klinkenberg to the permeability measurements lead to negative absolute permeability for shale samples. However, the double-slippage correction resulted in physically plausible values for absolute permeability of shale samples. Finally, the measurement results with adsorbent gases indicated that the adsorbed gas layer thickness can significantly impact the gas transport and storage in organic rich shale reservoirs and needs to be considered for hydrocarbon in place calculation and production predictions.
Predicting long-term production from shale gas 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 carried out 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 (due to the resultant increase in effective confining stress) from 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 (<1000 psi) because of the slippage effects. We utilize the magnitude of the Klinkenberg effect to estimate the effective aperture of the flow paths within the samples, and compare these estimates to SEM image observations. Our results suggest effective flow paths to be on the order from tens of nanometers in most samples to 100-200 nanometers in a relatively high-permeability Eagle Ford sample. Finally, to gain insight on the scale dependence of permeability measurements, we crushed the same core plugs and measured permeability again at the particle scale. The results show much lower permeability than the intact core samples, with very little correlation to the measurements on the larger cores.
Abstract Gas flow modelling in shale and tight gas reservoirs is still challenging mainly due to different pore-scale flow regimes present in micro- and nano-pores of these reservoirs. The effect of geomechanical stress also significantly affect the measurement and prediction of apparent matrix permeability. In this study, series of experiments were designed and performed on three shale samples to study the simultaneous effects of slippage and stress at five different pore pressures and four net stresses. The experimental data were used to obtain a general slip plot, which quantifies the effect of slippage on matrix permeability. Then, the stress effect was taken into account by modifying the average pore size and non-slip permeability at each net stress based on the experimental observations. It is found that the matrix non-slip permeability and average pore size follow an exponential behaviour when changing the net stress. These two relationships are then proposed to be incorporated into the corresponding slip flow model in order to capture the effects of slippage and stress at the same time. The validity of the proposed model was also investigated (using published data in the literature), which shows that the proposed technique is able to capture the intensity of permeability reduction and enhancement due to stress and slippage, respectively. The outcomes of this study increase our knowledge of rarefied flow dynamic inside micro- and nano-pores under confining stress, which is necessary for accurate predictions of the apparent matrix permeability in unconventional reservoirs.
Natural gas produced from shale represents an important emerging energy supply not only in the United States but across the globe. Proper understanding of shale petrophysical properties is essential for accurate reserve estimations, recovery factor predictions, potential enhanced recovery techniques, and carbon sequestration. Due to matrix permeability in the range of a nanodarcy and porosity less than 10%, numerous challenges are faced to garner data in the laboratory regarding the physics and flow behavior of these shale rocks. The main question addressed here is the sensitivity of shale physical properties to the gas saturating the pore space. The paper presents apparent Klinkenberg permeability measurements at different pore and confining pressures. The advantage of using helium gas in this context is that it aids the study of slip flow without any complicating effects of gas sorption on permeability. Helium permeability and porosity are compared to nitrogen, methane, and carbon dioxide results for Barnett and Eagle Ford shale samples. The effect of sorption on permeability is inferred. Results show decreased permeability with increased sorption. Gibb's excess sorption is measured utilizing the volumetric method and confirms the impact of sorption on the storage capacity and permeability of shale. Because of the small size of helium molecules, initial speculation suggested that helium measured porosity is greater than the effective methane porosity leading to overestimated shale pore volumes. Experimental results reported here for several shale samples, however, indicate otherwise.