Lattice Boltzmann simulation of shale gas transport in organic nano-pores

Confinement Effect on Porosity and Permeability of Shales

Porosity and permeability are the key factors in assessing the hydrocarbon productivity of unconventional (shale) reservoirs, which are complex in nature due to their heterogeneous mineralogy and poorly connected nano- and micro-pore systems. Experimental efforts to measure these petrophysical properties posse many limitations, because they often take weeks to complete and are difficult to reproduce. Alternatively, numerical simulations can be conducted in digital rock 3D models reconstructed from image datasets acquired via e.g., nanoscale-resolution focused ion beam–scanning electron microscopy (FIB-SEM) nano-tomography. In this study, impact of reservoir confinement (stress) on porosity and permeability of shales was investigated using two digital rock 3D models, which represented nanoporous organic/mineral microstructure of the Marcellus Shale. Five stress scenarios were simulated for different depths (2,000–6,000 feet) within the production interval of a typical oil/gas reservoir within the Marcellus Shale play. Porosity and permeability of the pre- and post-compression digital rock 3D models were calculated and compared. A minimal effect of stress on porosity and permeability was observed in both 3D models. These results have direct implications in determining the oil-/gas-in-place and assessing the production potential of a shale reservoir under various stress conditions.

The Imaging Resolution and Knudsen Effect on the Mass Transport of Shale Gas Assisted by Multi-length Scale X-Ray Computed Tomography

The spatial resolution of 3D imaging techniques is often balanced by the achievable field of view. Since pore size in shales spans more than two orders of magnitude, a compromise between representativeness and accuracy of the 3D reconstructed shale microstructure is needed. In this study, we characterise the effect of imaging resolution on the microstructural and mass transport characteristics of shales using micro and nano-computed tomography. 3D mass transport simulation using continuum and numerical physics respectively is also compared to highlight the significance of the Knudsen effect on the reconstructed solid surface. The result shows that porosity measured by micro-CT is 25% lower than nano-CT, resulting in an overestimated pore size distribution and underestimated pore connectivity. This leads to a higher simulated intrinsic permeability. An overestimated diffusive flux and underestimated permeability are obtained from the continuum mass transport simulation compared to the numerical ones when the molecular-wall collision is accounted, evidenced by the large deviation of the measured Knudsen tortuosity factor and permeability correction factor. This study is believed to provide new knowledge in understanding the importance of imaging resolution and gas flow physics on mass transport in porous media.

Direct Simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels

The impetus of the current research is to use the direct simulation Monte Carlo (DSMC) algorithm to investigate fluid behaviour and gas transport in porous microchannels. Here, we demonstrate DSMC’s capability to simulate porous media up to 40% porosity. In this study, the porous geometry is generated by a random distribution of circular obstacles through the microchannel with no interpenetration between the obstacles. The influence of the morphology along with rarefaction and gas type on the apparent permeability is investigated. Moreover, the effects of porosity, solid particle’s diameter and specific surface area are considered. Our results demonstrate that although decreasing porosity intensifies tortuosity in the flow field, the tortuosity reduces at higher Knudsen numbers due to slip flow at solid boundaries. In addition, our study on two different gas species showed that the gas type affects slippage and apparent gas permeability. Finally, comparing different apparent permeability models showed that Beskok and Karniadakis model is valid only up to the early transition regime and at higher Knudsen numbers, the current data matches those models that take Knudsen diffusion into account as well.

New insights from shale gas production at the microscopic scale

Until recently, natural gas encountered in tight shales, which provided the source and seal of the gas, was considered uneconomical to produce. Although unconventional formations may be as porous as other reservoir rocks, their exceedingly small pore sizes and low permeability render them resistant to gas movement. Considering their importance to gas transport, we outline the characteristics of shale rocks, the mechanisms of Fickian and Knudsen diffusion as well as Klinkenberg's permeability. Given the challenges in unlocking natural gas from tight formations, various techniques such as the generation of artificial fractures and the introduction of pressurised fluids are detailed. To identify the parameters which govern natural gas production, we propose a computational porous rock model inspired from an actual image of a shale formation. The solution of the conservation of mass, momentum and energy equations appear to adequately capture the physics of gas transport at the microscopic level. Permitting the comparison between numerical and analytical gas velocity results, the validation framework we developed, demonstrates good agreement of numerical with theoretical findings. Gas pressure and velocity results point to the importance of pore throats, shale permeability and pressure maintenance in dislodging gas from the shale formations.

Gaseous microflow modeling using the Fokker-Planck equation

We present a comparative study of gaseous microflow systems using the recently introduced Fokker-Planck approach and other methods such as: direct simulation Monte Carlo, lattice Boltzmann, and variational solution of Boltzmann-BGK. We show that this Fokker-Plank approach performs efficiently at intermediate values of Knudsen number, a region where direct simulation Monte Carlo becomes expensive and lattice Boltzmann becomes inaccurate. We also investigate the effectiveness of a recently proposed Fokker-Planck model in simulations of heat transfer, as a function of relevant parameters such as the Prandtl, Knudsen numbers. Furthermore, we present simulation of shock wave as a function of Mach number in transonic regime. Our results suggest that the performance of the Fokker-Planck approach is superior to that of the other methods in transition regime for rarefied gas flow and transonic regime for shock wave.

Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model

To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results.

Numerical research on the anisotropic transport of thermal neutron in heterogeneous porous media with micron X-ray computed tomography

The anisotropic transport of thermal neutron in heterogeneous porous media is of great research interests in many fields. In this paper, it is the first time that a new model based on micron X-ray computed tomography (CT) has been proposed to simultaneously consider both the separation of matrix and pore and the distribution of mineral components. We apply the Monte Carlo method to simulate thermal neutrons transporting through the model along different directions, and meanwhile detect those unreacted thermal neutrons by an array detector on the other side of the model. Therefore, the anisotropy of pore structure can be imaged by the amount of received thermal neutrons, due to the difference of rock matrix and pore-filling fluids in the macroscopic reaction cross section (MRCS). The new model has been verified by the consistent between the simulated data and the pore distribution from X-ray CT. The results show that the evaluation of porosity can be affected by the anisotropy of media. Based on the research, a new formula is developed to describe the correlation between the resolution of array detectors and the quality of imaging. The formula can be further used to analyze the critical resolution and the suitable number of thermal neutrons emitted in each simulation. Unconventionally, we find that a higher resolution cannot always lead to a better image.

Modeling adsorption with lattice Boltzmann equation

The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied.

Micro/Nano-pore Network Analysis of Gas Flow in Shale Matrix

The gas flow in shale matrix is of great research interests for optimized shale gas extraction. The gas flow in the nano-scale pore may fall in flow regimes such as viscous flow, slip flow and Knudsen diffusion. A 3-dimensional nano-scale pore network model was developed to simulate dynamic gas flow, and to describe the transient properties of flow regimes. The proposed pore network model accounts for the various size distributions and low connectivity of shale pores. The pore size, pore throat size and coordination number obey normal distribution, and the average values can be obtained from shale reservoir data. The gas flow regimes were simulated using an extracted pore network backbone. The numerical results show that apparent permeability is strongly dependent on pore pressure in the reservoir and pore throat size, which is overestimated by low-pressure laboratory tests. With the decrease of reservoir pressure, viscous flow is weakening, then slip flow and Knudsen diffusion are gradually becoming dominant flow regimes. The fingering phenomenon can be predicted by micro/nano-pore network for gas flow, which provides an effective way to capture heterogeneity of shale gas reservoir.

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

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.