Dynamic Gas Slippage: A Unique Dual-Mechanism Approach to the Flow of Gas in Tight Formations

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.

Comparative Study on Flow Characteristics in Deep Marine and Marine-Continental Transitional Shale in the Southeastern Sichuan Basin, China

Permeability is a significant characteristic of porous media and a crucial parameter for shale gas development. This study focuses on deep marine and marine-continental transitional shale in the southeastern Sichuan area using the gas pulse decay testing method to systematically analyze the gas permeability, stress sensitivity, and gas transport mechanisms of shale under different pressure conditions and directions. The results show that the porosity and gas permeability of the deep marine shale are greater compared to those of the marine-continental transitional shale. The elevated fluid pressure in the deep marine shale offers superior conditions for the preservation of nanopores, while the high quartz content provides advantageous conditions for fluid transport in nanopore channels. The permeability and stress sensitivity of the deep marine shale are greater than those of the marine-continental transitional shale, and the stress sensitivity is greater in the perpendicular bedding direction than in the parallel bedding direction, possibly related to the mineral composition of shale and the compaction it has undergone. The flow mechanism of the deep marine shale is transition flow and Knudsen flow, while that of the marine-continental transitional shale is transition flow. The deep marine shale possesses smaller nanopore sizes and a higher quantity of micropores, which create advantageous conditions for gas transport within nanopores. During the process of extracting shale gas, the extraction of gas causes a decrease in pore pressure and an increase in effective stress, resulting in a reduction in permeability. However, when the pore pressure reaches a specific value, the enhanced slippage effect leads to an increase in permeability, which is advantageous for gas extraction. In the later stage of shale gas well production, intermittent production plans can be developed considering the strength of the slippage effect, leading to a significant improvement in production efficiency.

Multiple Gas Seepage Mechanisms and Production Development Research for Shale Gas Reservoirs from Experimental Techniques and Theoretical Models

Shale gas seepage theory provides a scientific basis for dynamically analyzing the physical gas flow processes involved in shale gas extraction and for estimating shale gas production. Conventional experimental techniques and theoretical methods applied in seepage research are unable to accurately illustrate shale gas mass transfer processes at the micro- and nanoscale. In view of these scientific issues, the knowledge of seepage mechanisms and production development design was improved from the perspective of experimental techniques and theoretical models in the paper. First, multiple techniques (e.g., focused ion beam scanning electron microscopy and a combination of mercury intrusion porosimetry and adsorption measurement techniques) were integrated to characterize the micro- and nanopore distribution in shales. Then, molecular dynamics simulations were carried out to analyze the microscale distribution of gas molecules in nanopores. In addition, an upscaled gas flow model for the shale matrix was developed based on molecular dynamics simulations. Finally, the coupled flow and productivity models were set up according to a long-term production physical simulation to identify the production patterns for adsorbed and free gas. The research results show that micropores (diameter: <2 nm) and mesopores (diameter: 2-50 nm) account for more than 70% of all the pores in shales and that they are the primary space hosting adsorbed gas. Molecular simulations reveal that microscopic adsorption layers in organic matter nanopores can be as thick as 0.7 nm and that desorption and diffusion are the main mechanisms behind the migration of gas molecules. An apparent permeability model that comprehensively accounts for adsorption, diffusion, and seepage was developed to address the deficiency of Darcy's law in characterizing gas flowability in shale reservoirs. The productivity model results for a certain gas well show that the production in the first three years accounts for more than 50% of its estimated ultimate recovery and that adsorbed gas contributes more to the annual production than free gas in the eighth year. These research results provide theoretical and technical support for improving the theoretical understanding of shale gas seepage and optimizing shale gas extraction techniques in China.

Chemical and Reactive Transport Processes Associated with Hydraulic Fracturing of Unconventional Oil/Gas Shales

Hydraulic fracturing of unconventional oil/gas shales has changed the energy landscape of the U.S. Recovery of hydrocarbons from tight, hydraulically fractured shales is a highly inefficient process, with estimated recoveries of <25% for natural gas and <5% for oil. This review focuses on the complex chemical interactions of additives in hydraulic fracturing fluid (HFF) with minerals and organic matter in oil/gas shales. These interactions are intended to increase hydrocarbon recovery by increasing porosities and permeabilities of tight shales. However, fluid-shale interactions result in the dissolution of shale minerals and the release and transport of chemical components. They also result in mineral precipitation in the shale matrix, which can reduce permeability, porosity, and hydrocarbon recovery. Competition between mineral dissolution and mineral precipitation processes influences the amounts of oil and gas recovered. We review the temporal/spatial origins and distribution of unconventional oil/gas shales from mudstones and shales, followed by discussion of their global and U.S. distributions and compositional differences from different U.S. sedimentary basins. We discuss the major types of chemical additives in HFF with their intended purposes, including drilling muds. Fracture distribution, porosity, permeability, and the identity and molecular-level speciation of minerals and organic matter in oil/gas shales throughout the hydraulic fracturing process are discussed. Also discussed are analysis methods used in characterizing oil/gas shales before and after hydraulic fracturing, including permeametry and porosimetry measurements, X-ray diffraction/Rietveld refinement, X-ray computed tomography, scanning/transmission electron microscopy, and laboratory- and synchrotron-based imaging/spectroscopic methods. Reactive transport and spatial scaling are discussed in some detail in order to relate fundamental molecular-scale processes to fluid transport. Our review concludes with a discussion of potential environmental impacts of hydraulic fracturing and important knowledge gaps that must be bridged to achieve improved mechanistic understanding of fluid transport in oil/gas shales.

Sustainable Production from Shale Gas Resources through Heat-Assisted Depletion

Advancements in drilling and production technologies have made exploiting resources, which for long time were labeled unproducible such as shales, as economically feasible. In particular, lateral drilling coupled with hydraulic fracturing has created means for hydrocarbons to be transported from the shale matrix through the stimulated network of microcracks, natural fractures, and hydraulic fractures to the wellbore. Because of the degree of confinement, the ultimate recovery is just a small fraction of the total hydrocarbons in place. Our aim was to investigate how augmented pressure gradient through hydraulic fracturing when coupled with another derive mechanism such as heating can improve the overall recovery for more sustainable exploitation of unconventional resources. Knowledge on how hydrocarbons are stored and transported within the shale matrix is uncertain. Shale matrix, which consists of organic and inorganic constituents, have pore sizes of few nanometers, a degree of confinement at which our typical reservoir engineering models break down. These intricacies hinder any thorough investigations of hydrocarbon production from shale matrix under the influence of pressure and thermal gradients. Kerogen, which represents the solid part of the organic materials in shales, serves as form of nanoporous media, where hydrocarbons are stored and then expelled after shale stimulation procedure. In this work, a computational representation of a kerogen–hydrocarbon system was replicated to study the depletion process under coupled mechanisms of pressure and temperature. The extent of production enhancement because of increasing temperature was shown. Moreover, heating requirements to achieve the enhancement at reservoir scale was also presented to assess the sustainability of the proposed method.

Pore Network Modeling Study of Gas Transport Temperature Dependency in Tight Formations

Temperature's effects on rock permeability are ambiguous; both positive and negative correlations have been reported in the literature. Temperature can affect the geomechanical behavior of porous media, as well as influence the mode of fluid transport. Rocks are subject to deformation, compaction, and chemical alteration at elevated temperatures. Conversely, confined fluids can undergo augmented non-Darcian mechanisms. In this research, a multiscale, multiphysical study of temperature's effects on gas permeability in tight formations is presented.

Gas Multiple Flow Mechanisms and Apparent Permeability Evaluation in Shale Reservoirs

Gas flow mechanisms and apparent permeability are important factors for predicating gas production in shale reservoirs. In this study, an apparent permeability model for describing gas multiple flow mechanisms in nanopores is developed and incorporated into the COMSOL solver. In addition, a dynamic permeability equation is proposed to analyze the effects of matrix shrinkage and stress sensitivity. The results indicate that pore size enlargement increases gas seepage capacity of a shale reservoir. Compared to conventional reservoirs, the ratio of apparent permeability to Darcy permeability is higher by about 1–2 orders of magnitude in small pores (1–10 nm) and at low pressures (0–5 MPa) due to multiple flow mechanisms. Flow mechanisms mainly include surface diffusion, Knudsen diffusion, and skip flow. Its weight is affected by pore size, reservoir pressure, and temperature, especially pore size ranging from 1 nm to 5 nm and reservoir pressures below 5 MPa. The combined effects of matrix shrinkage and stress sensitivity induce nanopores closure. Therefore, permeability declines about 1 order of magnitude compare to initial apparent permeability. The results also show that permeability should be adjusted during gas production to ensure a better accuracy.

Flow of methane in shale nanopores at low and high pressure by molecular dynamics simulations

Flow in shale nanopores may be vastly different from that in the conventional permeable media. In large pores and fractures, flow is governed by viscosity and pressure-driven. Convection describes the process. Pores in some shale media are in nanometer range. At this scale, continuum flow mechanism may not apply. Knudsen diffusion and hydrodynamic expressions such as the Hagen-Poiseuille equation and their modifications have been used to compute flow in nanopores. Both approaches may have drawbacks and can significantly underestimate molecular flux in nanopores. In this work, we use the dual control volume-grand canonical molecular dynamics simulations to investigate methane flow in carbon nanopores at low and high pressure conditions. Our simulations reveal that methane flow in a slit pore width of 1-4 nm can be more than one order of magnitude greater than that from Knudsen diffusion at low pressure and the Hagen-Poiseuille equation at high pressure. Knudsen diffusion and Hagen-Poiseuille equations do not account for surface adsorption and mobility of the adsorbed molecules, and inhomogeneous fluid density distributions. Mobility of molecules in the adsorbed layers significantly increases molecular flux. Molecular velocity profiles in nanopores deviate significantly from the Navier-Stokes hydrodynamic predictions. Our molecular simulation results are in agreement with the enhanced flow measurements in carbon nanotubes.

Simulation of Gas Transport in Tight/Shale Gas Reservoirs by a Multicomponent Model Based on PEBI Grid

The ultra-low permeability and nanosize pores of tight/shale gas reservoir would lead to non-Darcy flow including slip flow, transition flow, and free molecular flow, which cannot be described by traditional Darcy’s law. The organic content often adsorbs some gas content, while the adsorbed amount for different gas species is different. Based on these facts, we develop a new compositional model based on unstructured PEBI (perpendicular bisection) grid, which is able to characterize non-Darcy flow including slip flow, transition flow, and free molecular flow and the multicomponent adsorption in tight/shale gas reservoirs. With the proposed model, we study the effect of non-Darcy flow, length of the hydraulic fracture, and initial gas composition on gas production. The results show both non-Darcy flow and fracture length have significant influence on gas production. Ignoring non-Darcy flow would underestimate 67% cumulative gas production in lower permeable gas reservoirs. Gas production increases with fracture length. In lower permeable reservoirs, gas production increases almost linearly with the hydraulic fracture length. However, in higher permeable reservoirs, the increment of the former gradually decreases with the increase in the latter. The results also show that the presence of CO2in the formation would lower down gas production.

Pore structure and limit pressure of gas slippage effect in tight sandstone

Gas slip effect is an important mechanism that the gas flow is different from liquid flow in porous media. It is generally considered that the lower the permeability in porous media is, the more severe slip effect of gas flow will be. We design and then carry out experiments with the increase of backpressure at the outlet of the core samples based on the definition of gas slip effect and in view of different levels of permeability of tight sandstone reservoir. This study inspects a limit pressure of the gas slip effect in tight sandstones and analyzes the characteristic parameter of capillary pressure curves. The experimental results indicate that gas slip effect can be eliminated when the backpressure reaches a limit pressure. When the backpressure exceeds the limit pressure, the measured gas permeability is a relatively stable value whose range is less than 3% for a given core sample. It is also found that the limit pressure increases with the decreasing in permeability and has close relation with pore structure of the core samples. The results have an important influence on correlation study on gas flow in porous medium, and are beneficial to reduce the workload of laboratory experiment.

Slippage and viscosity predictions in carbon micropores and their influence on CO2 and CH4 transport

Non-equilibrium molecular dynamics simulations of pure carbon dioxide and methane and their equimolar mixtures have been carried out with an external driving force imposed on carbon slit pores to investigate gas slippage and Klinkenberg effects. Simulations were conducted to determine the effect of pore size and exposure to an external potential on the velocity profile and slip-stick boundary conditions. The simulations indicate that molecule-wall collisions influence the velocity profile, which deviates significantly from the Navier-Stokes hydrodynamic prediction for micro- and mesopores. Also, the shape of the velocity profile is found to be independent of the applied pressure gradient in micropores. The results indicate that the velocity profile is uniform for pore sizes less than 2 nm (micropores) where the transport is mainly due to molecular streaming or Knudsen diffusion and, to a lesser extent, molecular diffusion. As pore sizes increase to 10 nm, parabolic profiles are observed due to the reduced interaction of gas molecules with the pore walls. A 3D pore network, representative of porous carbon-based materials, has been generated atomistically using the Voronoi tessellation method. Simulations have been carried out to determine the effect of the pore structure and modeled viscosity on permeability and Klinkenberg parameters. The use of the bulk-phase viscosity for estimating the permeability of CO(2) in units of Darcy in a 3D micropore network is not an appropriate assumption as it significantly underestimates the CO(2) permeability. On the other hand, since the transport properties of CH(4) are less influenced by the pore walls compared with CO(2), the use of the bulk-phase CH(4) viscosity estimates are a reasonable assumption.

Gas slippage effect on microscale porous flow using the lattice Boltzmann method

A lattice Boltzmann method is developed for gaseous slip flow at the pore scale in microscale porous geometries. Flow characteristics through various porous structures are studied for different Knudsen numbers and inlet to outlet pressure ratios. It is found that the gas permeability is larger than the absolute permeability of porous media due to the gas slippage effect. Furthermore, the rarefaction influence on the gas permeability is more evident for porous structures with low porosity. The Klinkenberg equation is confirmed for the simulated porous structures. However, the second-order term of the Knudsen number (Kn2) cannot be neglected for gaseous flow with relatively high Knudsen numbers. A model for predicting the pressure drop of the flow through microscale porous media is presented based on the Ergun equation and the Carman-Kozeny equation by taking into account the effects of gas rarefaction and compressibility.

The Unsteady-State Nature of Sorption and Diffusion Phenomena in the Micropore Structure of Coal: Part 1 - Theory and Mathematical Formulation

Summary

A single-phase, 1D mathematical formulation is developed in radial/cylindrical coordinates to examine unsteady-state micropore sorption in a composite micropore/fracture, coalbed-methane transport problem. In the formulation, the micropore transport equation accounts for unsteady-state sorption and diffusion in the primary porosity. Gas entering the fracture network is considered a source term in the fracture-transport equation. The micropore and fracture systems are coupled by equating the gas pressure at the surface of the micropore elements to the pressure in the fracture network.

Introduction

Coalbed-methane reservoirs are characterized by a dual-porosity nature. Gas molecules stored in the micropore structure by adsorption are subject to desorption from the coal grain surfaces and to diffusional transport to a well-defined, natural fracture network. Laminar flow dominates in the fracture network where methane gas flows simultaneously with formation water.

Gas transport in the micropores is generally modeled with quasisteady- or unsteady-state sorption formulations. In the first case, the matrix-to-fracture gas transfer rate is calculated from the average concentration gradient in the matrix elements over a discrete timestep. In contrast, unsteady-state formulations use a nonuniform micropore concentration gradient to determine the matrix transfer rate. Quasisteady-state models offer the advantage of simplified mathematics, which can reduce computer simulation costs.

Reservoir Characteristics of Coal Seams. Coal seams are characterized by a natural fracture network commonly referred to as cleat. The cleat system consists of two perpendicular fissures, the more predominant of which is the face cleat. The butt cleat is less continuous and often ends when it intersects the face cleat. Fig. 1 is a highly idealized representation of the physical relationship between the matrix and fracture system.