Mathematical Simulation about Gas Transport in a Dual-Porosity Tight Gas Reservoir considering Multiple Effects

Threshold pressure gradient, gas slippage, and stress sensitivity have important effects on the production of a tight gas reservoir. But previous studies only focused on one or two of these effects. In this study, a mathematical model considering these three effects was established to describe gas transport in a dual-porosity tight gas reservoir. Threshold pressure gradient, gas slippage, and stress sensitivity are simultaneously considered in the velocity term of continuity equation which is mainly different from the previous research results. The partial differential equation and definite solution condition are discretized by a central difference method. A finite difference procedure was compiled and applied to solve this numerical model and predict the productivity of a production well in a dual-porosity tight gas reservoir. The difference between the predicted and tested cumulative production is less than 10%, which indicates that the proposed mathematical model can be used to describe the characteristics of gas flow in the dual-porosity tight gas reservoir. Then, gas productivity of five different scenarios considering these effects was compared. Results show that both stress sensitivity and threshold pressure gradient are negatively correlated with gas production, while gas slippage is positively correlated with gas production. Among them, stress sensitivity has the greatest impact on the production of a dual-porosity tight gas reservoir. Overall, these three effects have great influence on the development of the dual-porosity tight gas reservoir, which should be considered in the production prediction.

Real Gas Effect on Gas Slippage Phenomenon in Shale

The past decade has seen the rapid development of shale gas across the world, as the record-breaking success and on-going surge of commercial shale gas production in such unconventional reservoirs pose a tremendous potential to meet the global energy supply. However, questions have been raised about the intricate gas transport mechanisms in the shale matrix, of which the gas slippage phenomenon is one of the key mechanisms for enhancing the fluid transport capacity and, therefore, the overall gas production. Given that shale reservoirs are often naturally deposited in the deep underground formations at high pressure and temperature conditions (much deeper than most typical conventional deposits), the real gas effect cannot be ignored as gas properties may vary significantly under such conditions. The purpose of this study is thus to investigate the real gas effect on the gas slippage phenomenon in shale by taking into account the gas compressibility factor (Z) and Knudsen number (Kn). This study begins with a specific determination of Z for natural gas at various pressures and temperatures under the real gas effect, followed by several calculations of the gas molecular mean free path at in-situ conditions. Following this, the real gas effect on gas slippage phenomenon in shale is specifically analyzed by examining the change in Knudsen number. Also discussed are the permeability deviation from Darcy flux (non-Darcy flow) due to the combination of gas slippage and real gas effect and the specific range of pressure and pore size for gas slippage phenomenon in shale reservoirs. The results show that the gas molecular mean free path generally increases with decreasing pressure, especially at relatively low pressures (< 20 MPa). And, increasing temperature will cause the gas molecular mean free path to rise, also at low pressures. Knudsen number of an ideal gas is greater than that of a real gas; while lower than that of a real gas as pressure continues to rise. That is, the real gas effect suppresses the gas slippage phenomenon at low pressures, while enhancing it at high pressures. Also, Darcy’s law starts deviating when Kn > 0.01 and becomes invalid at high Knudsen numbers, and this deviation increases with decreasing pore size. No matter how pore size varies, this deviation increases with decreasing pressure, meaning that the gas slippage effect is significant at low pressures. Finally, slip flow dominates in the various gas transport mechanisms given the typical range of pressure and pore size in shale reservoirs (1 MPa < P < 80 MPa; 3 nm < d < 3000 nm). Gas transport in shale is predominantly controlled by the slippage effect that mostly occurs in micro- or meso-pores (10 to 200 nm). Moreover, considering the real gas effect would improve the accuracy for determining the specific pressure range of the gas slippage phenomenon in shale.

FRACTAL MODELS FOR GAS–WATER TRANSPORT IN SHALE POROUS MEDIA CONSIDERING WETTING CHARACTERISTICS

Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.

Second-Order Correlation of Klinkenberg-Corrected Permeability and its Experimental Verification on Heterogeneously-Stressed Gas Shale

Shale is an extremely tight and fine-grained sedimentary rock with nanometer-scale pore sizes. The nanopore structure within a shale system contributes not only to the low to ultra-low permeability coefficients (10−18 to 10−22 m2), but also to the significant gas slippage effect. The Klinkenberg equation, a first-order correlation, offers a satisfying solution to describe this particular phenomenon for decades. However, in recent years, several scholars and engineers have found that the linear relation from the Klinkenberg equation is invalid for most gas shale reservoirs, and a need for a second-order model is, therefore, proceeding apace. In this regard, the purpose of this study was to develop a second-order approach with experimental verifications. The study involved a derivation of a second-order correlation of the Klinkenberg-corrected permeability, followed by experimental verifications on a cubic shale sample sourced from the Sichuan Basin in southwestern China. We utilized a newly developed multi-functional true triaxial geophysical (TTG) apparatus to carry out permeability measurements with the steady-state method in the presence of heterogeneous stresses. Also discussed were the effects of two gas slippage factors, Klinkenberg-corrected permeability, and heterogeneous stress. Finally, based on the second-order slip theory, we analyzed the deviation of permeability from Darcy flux. The results showed that the apparent permeability increased more rapidly as the pore pressure declined when the pore pressures are relatively low, which is a strong evidence of the gas slippage effect. The second-order model could reasonably match the experimental data, resulting in a lower Klinkenberg-corrected permeability compared with that from the linear Klinkenberg equation. That is, the second-order approach improves the intrinsic permeability estimation of gas shales with the result being closer to the liquid permeability compared with the Klinkenberg approach. Analysis of the experimental data reported that both the first-order slippage factor A and the second-order slippage factor B increased with increasing stress heterogeneity, and that A was likely to be more sensitive to stress heterogeneity compared with B. Interestingly, both A and B first slightly increased and then significantly as the permeability declined. It is recommended that when the shale permeability is below 10−18 m2, the second-order approach should be taken into account. Darcy’s law starts to deviate when Kn > 0.01 and is invalid at high Knudsen numbers. The second-order approach seems to alleviate the problem of overestimation compared with the Klinkenberg approach and is more accurate in permeability evolution.

The Role of Microfabric and Laminae on Pore Structure and Gas Transport Pathways of Marine Shales from Sichuan Basin, China

This study investigated the effects of microfabric and laminae on the pore structure and gas transport pathways of the Silurian Longmaxi shales from Sichuan Basin. 23 shale samples with varied lithofacies were comprehensively investigated by mineralogy, organic geochemistry, pycnometry, and low-pressure nitrogen adsorption analysis. The fabric and laminae of these samples were identified using petrographic microscope and scanning electron microscopy. Permeabilities were measured using the nonsteady-state method on both perpendicular and parallel to bedding shales. The effective pore diameter controlling gas transport was estimated from gas slippage factors obtained in permeability measurements. These values were also compared to those calculated using the Winland equation. Siliceous shales studied are faintly laminated to nonlaminated and have larger porosity and specific surface area. Argillaceous/siliceous mixed shales are well laminated, whereas argillaceous shales contain many oriented clay flakes along the lamination. Both porosity and surface area are positively correlated with TOC content. Unlike most conventional reservoirs, there is a negative correlation between porosity and permeability values of the samples studied. Permeabilities parallel to bedding, ranging from 0.4 to 76.6 μD, are in control of the oriented clay flakes and silty microlaminae. Permeability anisotropy values of the shales vary between 1.3 and 49.8. Samples rich in oriented clay flakes and microlaminated fabric have relatively larger permeability and permeability anisotropy values. The effective transport pore diameters derived from gas slippage measurements are slightly lower than those calculated from the Winland equation. However, both methods have shown that the effective transport pore diameters of argillaceous shales (averaging 552 nm) are significantly higher than siliceous shales (averaging 198 nm), which underlines the control of microfabric, rather than porosity, on gas transport pathways of the shales studied.