Inhomogeneous Fluid Transport Modeling in Dual-Scale Porous Media Considering Fluid-Solid Interactions

Dynamics of fluid transport in ultratight reservoirs such as organic-rich shales differ from those in high-permeable reservoirs due to the complex nature of fluid transport and fluid-solid interaction in nanopores. We present a multiphase multicomponent transport model for primary production and gas injection in shale, considering the dual-scale porosity and intricate fluid-solid interactions. The pore space in the shale matrix is divided into macropores and nanopores based on pore size distribution. We employ density functional theory (DFT) to account for fluid-solid interactions and to compute the inhomogeneous fluid density distribution and phase behavior within a dual-scale matrix. The calculated fluid thermodynamic properties and transmissibility values are then integrated into the multiphase multicomponent transport model grounded in Maxwell-Stefan theory to simulate primary oil production from and gas injection into organic-rich shales. Our findings highlight DFT's adeptness in detailing the complex fluid inhomogeneities within nanopores─a critical concept that a cubic equation of state does not capture. Fluids within pores are categorized into confined and bulk states, restricted by a threshold pore width of 30 nm. Different compositions of fluid mixtures are observed in macropores and nanopores: heavier hydrocarbon components preferentially accumulate in nanopores due to their strong fluid-solid interactions. We utilize the developed model to simulate hydrocarbon production from an organic-rich shale matrix as well as CO2 injection into the matrix. During primary hydrocarbon production, strong fluid-solid interactions in nanopores impede the mobility of heavy components in the near-wall region, leading to their confinement. Consequently, heavy components mostly remain within the nanopores in the shale matrix during primary hydrocarbon production. During the CO2 injection process, the injected CO2 alters fluid composition within macropores and nanopores, promoting fluid redistribution. Injected CO2 engages in competitive fluid-solid interactions against intermediate hydrocarbons, successfully displacing a considerable number of these hydrocarbons from the nanopores.

Gas Diffusion and Flow in Shale Nanopores with Bound Water Films

Shale reservoirs are rich in nanoscale pore-microfractures, and generally contain water (especially inorganic pores) under reservoir conditions. Therefore, evaluating gas flow capacity under water-bearing conditions is of great significance for analyzing reservoir capacity and forecasting production. Based on the single-phase gas transfer theory in nanopores, we established a gas transport model in both circular pores and slit pores by considering pore-fracture patterns of actual samples. As will be shown, inorganic pore fractures are mostly slit-type, while organic pores are mostly circular. This gas transport model also uses weighting coefficients superimposed on slip flow and molecular free flow. Further, the effect of water saturation on gas flow is quantified by considering the distribution characteristics of inorganic and organic pores in shale and also by combining the pore distribution characteristics of actual samples. The flow characteristics of gas in organic and inorganic pores under water-bearing conditions in the reservoir are further compared. The study lays a theoretical foundation for the reasonable evaluation and prediction of shale gas well capacity under reservoir water conditions.

An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces

The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.

Study on Two Component Gas Transport in Nanopores for Enhanced Shale Gas Recovery by Using Carbon Dioxide Injection

Injecting carbon dioxide to enhance shale gas recovery (CO2-EGR) is a useful technique that has raised great research interests. Clear understanding of the two-component gas transport mechanisms in shale nanopores is the foundation for the efficient development of shale gas reservoir (SGR) and also the long-term geological storage of CO2. Although extensive studies on single-component gas transport and corresponding models in shale nanopores have been carried out in recent years, limited studies have been conducted on two-component or even multi-component gas transport models in shale nanopores. In this work, the shale nanopores were classified into inorganic and organic nanopores. The corresponding models for two-component gas transport were constructed. Mechanisms including Knudsen diffusion, slip flow, viscous flow, and molecular diffusion are considered in the inorganic pores. In the organic pores, due to existence of adsorption gas, surface diffusion is further considered besides the aforementioned mechanisms. Effects of pressure, temperature, fraction of organic nanopores, and gas concentration were analyzed. Results show that gas apparent permeability is negatively correlated with pressure, and positively correlated with temperature and organic nanopore fraction. As the concentration of CH4 decreases, the apparent permeability of CH4 increases continuously, while the apparent permeability of CO2 decreases. The permeability ratio of CH4 in the total permeability is negatively correlated with pressure and gas concentration ratio. Additionally, the contribution of transport mechanisms to the total gas apparent permeability has been analyzed. It is found that the surface diffusion contributes up to 5.68% to gas apparent permeability under high pressure. The contribution of molecular diffusion can reach up to 88.83% in mesopores under low pressure. Under high pressure and macropores, it contributes less than 1.41%. For all situations, the contribution of viscous flow is more than 46.36%, and its contribution can reach up to 86.07%. Results of this study not only can improve the understanding of two-component gas transport in nanochannels, but also can lay the foundation for more reliable reservoir simulation of CO2-EGR.

Quantifying Pore Width Effects on Diffusivity via a Novel 3D Stochastic Approach with Input from Atomistic Molecular Dynamics Simulations

The increased production of unconventional hydrocarbons emphasizes the need to understand the transport of fluids through narrow pores. Although it is well-known that confinement affects fluids structure and transport, it is not yet possible to quantitatively predict properties such as diffusivity as a function of pore width in the range of 1-50 nm. Such pores are commonly found not only in shale rocks but also in a wide range of engineering materials, including catalysts. We propose here a novel and computationally efficient methodology to obtain accurate diffusion coefficient predictions as a function of pore width for pores carved out of common materials, such as silica, alumina, magnesium oxide, calcite, and muscovite. We implement atomistic molecular dynamics (MD) simulations to quantify fluid structure and transport within 5 nm-wide pores, with particular focus on the diffusion coefficient within different pore regions. We then use these data as input to a bespoke stochastic kinetic Monte Carlo (KMC) model, developed to predict fluid transport in mesopores. The KMC model is used to extrapolate the fluid diffusivity for pores of increasing width. We validate the approach against atomistic MD simulation results obtained for wider pores. When applied to supercritical methane in slit-shaped pores, our methodology yields data within 10% of the atomistic simulation results, with significant savings in computational time. The proposed methodology, which combines the advantages of MD and KMC simulations, is used to generate a digital library for the diffusivity of gases as a function of pore chemistry and pore width and could be relevant for a number of applications, from the prediction of hydrocarbon transport in shale rocks to the optimization of catalysts, when surface-fluid interactions impact transport.

The Influence of Micro-Fractures on the Flow in Tight Oil Reservoirs Based on Pore-Network Models

In this paper, the influence of micro-fractures on the flow of tight reservoirs is studied on the microscopic scale. Three-dimensional digital cores of fractured tight sandstone with varying fracture apertures, lengths, and dip angles are constructed using computed tomography (CT) scans. Pore-network models are built using the three-dimensional digital cores to simulate the flow in tight oil reservoirs. The effects of the micro-fracture aperture, length and dip angle on the pore-throat structure, single-phase flow, and two-phase flow for fracture surfaces with/without roughness are studied. The study demonstrates different influences of micro-fracture characteristics on the flow, and the fracture aperture has the most critical effect. Meanwhile, the roughness of the micro-fracture makes a difference in addition to the three factors of micro-fractures. This paper provides a theoretical basis for the effective development of tight sandstone reservoirs.

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.

Experimental study on flow characteristics of gas transport in micro- and nanoscale pores

Gas flow behavior in porous media with micro- and nanoscale pores has always been attracted great attention. Gas transport mechanism in such pores is a complex problem, which includes continuous flow, slip flow and transition flow. In this study, the microtubes of quartz microcapillary and nanopores alumina membrane were used, and the gas flow measurements through the microtubes and nanopores with the diameters ranging from 6.42 μm to 12.5 nm were conducted. The experimental results show that the gas flow characteristics are in rough agreement with the Hagen-Poiseuille (H-P) equation in microscale. However, the flux of gas flow through the nanopores is larger than the H-P equation by more than an order of magnitude, and thus the H-P equation considerably underestimates gas flux. The Knudsen diffusion and slip flow coexist in the nanoscale pores and their contributions to the gas flux increase as the diameter decreases. The slip flow increases with the decrease in diameter, and the slip length decreases with the increase in driving pressure. Furthermore, the experimental gas flow resistance is less than the theoretical value in the nanopores and the flow resistance decreases along with the decrease in diameter, which explains the phenomenon of flux increase and the occurrence of a considerable slip length in nanoscale. These results can provide insights into a better understanding of gas flow in micro- and nanoscale pores and enable us to exactly predict and actively control gas slip.

Quantitative Analysis of Micron-Scale and Nano-Scale Pore Throat Characteristics of Tight Sandstone Using Matlab

Based on micro-scale casting thin sections, nano-scale SEM images, and the pore distribution map identified through a binary image in Matlab, the pore size distribution and pore throat coordination number of the strata of Upper Paleozoic He8 section tight sandstone in the southeastern Ordos Basin were quantitatively analyzed with the above experimental data. In combination with a high-pressure mercury injection experiment, the pore throat distribution, the pore throat ratio, and the relationships between the characteristics, parameters, and pore permeability were investigated clearly. The results show that the tight sandstone pore space in the study area is dominated by micron-sized intergranular pores, dissolved pores, and intragranular pores. The nano-scale pore throat consisted of clay minerals, intercrystalline pores, and the flake intergranular pores of overgrowth quartz grains. Kaolinite and illite intercrystalline pores occupy the pore space below 600 nm, while the ones above 800 nm are mainly dominated by the intergranular pores of overgrowth quartz grains, and the 600–800 nm ones are transitional zones. The permeability of tight sandstone increases with the average pore throat radius, sorting coefficient, median pore throat radius, and average pore throat number. The porosity is positively correlated with the average pore radius and the average pore throat coordination number, and negatively correlated with the median pore throat radius.