Gas Transport Mechanisms Research Articles

Shale gas reservoir modeling and production evaluation considering complex gas transport mechanisms and dispersed distribution of kerogen

Stimulated shale reservoirs consist of kerogen, inorganic matter, secondary and hydraulic fractures. The dispersed distribution of kerogen within matrices and complex gas flow mechanisms make production evaluation challenging. Here we establish an analytical method that addresses kerogen-inorganic matter gas transfer, dispersed kerogen distribution, and complex gas flow mechanisms to facilitate evaluating gas production. The matrix element is defined as a kerogen core with an exterior inorganic sphere. Unlike most previous models, we merely use boundary conditions to describe kerogen-inorganic matter gas transfer without the instantaneous kerogen gas source term. It is closer to real inter-porosity flow conditions between kerogen and inorganic matter. Knudsen diffusion, surface diffusion, adsorption/desorption, and slip corrected flow are involved in matrix gas flow. Matrix-fracture coupling is realized by using a seven-region linear flow model. The model is verified against a published model and field data. Results reveal that inorganic matrices serve as a major gas source especially at early times. Kerogen provides limited contributions to production even under a pseudo-steady state. Kerogen properties’ influence starts from the late matrix-fracture inter-porosity flow regime, while inorganic matter properties control almost all flow regimes except the early-mid time fracture linear flow regime. The contribution of different linear flow regions is also documented.

The effect of lithologic heterogeneity on diffusive methane migration in hydrate systems

Short-range diffusive gas migration has been proposed as a means of supplying methane to coarse-grained, hydrate-bearing sediments. In this scenario, methane is generated microbially in fine-grained sediments and moves diffusively into adjacent coarse-grained sediments due to a dissolved methane concentration gradient caused by pore size contrasts. Previous work has shown that short-range diffusion is sufficient to supply thin, isolated sands (<1 m thickness) with enough methane to achieve high hydrate saturations (>80%) in systems with a high ratio of clay to sand. Several notable hydrate reservoirs such as those encountered at Daini-Atsumi Knoll in the Nankai Trough, and Walker Ridge Block 313 and Green Canyon Block 955 in the Gulf of Mexico exhibit tens of meters of alternating sand/silt and clay layers that are decimeters in thickness. The coarse-grained layers in these settings are typically filled with hydrate to saturations exceeding 80%. While short-range diffusion is capable of filling thin, isolated sands with hydrate, thicker sands within more heterogeneous systems require mechanisms other than, or in addition to, short-range diffusion. Using 1-D numerical simulations, we demonstrate that short-range diffusive migration of microbial methane is insufficient for reaching consistently high hydrate saturations in such systems. This work shows that a different mechanism for gas transport, such as advective migration, is necessary to achieve these observed hydrate saturations in layered systems.

Development and Calibration of a Semianalytic Model for Shale Wells with Nonuniform Distribution of Induced Fractures Based on ES-MDA Method

Given reliable parameters, a newly developed semianalytic model could offer an efficient option to predict the performance of the multi-fractured horizontal wells (MFHWs) in unconventional gas reservoirs. However, two major challenges come from the accurate description and significant parameters uncertainty of stimulated reservoir volume (SRV). The objective of this work is to develop and calibrate a semianalytic model using the ensemble smoother with multiple data assimilation (ES-MDA) method for the uncertainty reduction in the description and forecasting of MFHWs with nonuniform distribution of induced fractures. The fractal dimensions of induced-fracture spacing (dfs) and aperture (dfa) and tortuosity index of induced-fracture system (θ) are included based on fractal theory to describe the properties of SRV region. Additionally, for shale gas reservoirs, gas transport mechanisms, e.g., viscous flow with slippage, Knudsen diffusion, and surface diffusion, among multi-media including porous kerogen, inorganic matter, and fracture system are taken into account and the model is verified. Then, the effects of the fractal dimensions and tortuosity index of induced fractures on MFHWs performances are analyzed. What follows is employing the ES-MDA method with the presented model to reduce uncertainty in the forecasting of gas production rate for MFHWs in unconventional gas reservoirs using a synthetic case for the tight gas reservoir and a real field case for the shale gas reservoir. The results show that when the fractal dimensions of induced-fracture spacing and aperture is smaller than 2.0 or the tortuosity index of induced-fracture system is larger than 0, the permeability of induced-fracture system decreases with the increase of the distance from hydraulic fractures (HFs) in SRV region. The large dfs or small θ causes the small average permeability of the induced-fracture system, which results in large dimensionless pseudo-pressure and small dimensionless production rate. The matching results indicate that the proposed method could enrich the application of the semianalytic model in the practical field.

Numerical Study on Gas Transport in Shale Kerogen with Adsorption Effect Using LBM

Gas transport and storage mechanism in gas reservoirs with complex pore size distribution play a key role in gas production. In the nano-scale, during the process of density disturbance caused by depressurization development, notable output gas collides with the wall as they convey along the channel. The continuum assumption of fluid flow is therefore invalid, and taking the influence of particles to collide with solid walls into account is necessary. The effective viscosity and slip boundary conditions were introduced in the simulation. Meanwhile, because of the adsorption effect is one of the most important intrinsic properties of shale, the impact of surface adsorption on the solid wall by using Langmuir adsorption kinetics was also involved in our investigation. In this work, a unified LB model was developed for gas multiple transports and surface adsorption in nanopores. In the model, the double distribution function was employed for a coupled bulk flow and gas diffusion model. The model is valid within the range of the continuum regime to the transition regime and has been verified by the analytical solution and the results of some previously published works. The results show that (1) the driven force of the fluid, the combination coefficient of slippage and the Knudsen number of the flow have an impact on the adsorption rate, (2) adsorption effect only directly influence the local small region of the solid surface, and the induced concentration gradient makes the global concentration variation, (3) once acting the surface adsorption on the boundary, the flux falls more significant as Knudsen number increases.

A Three-Dimensional Hydro-mechanical Model for Simulation of Dilatancy Controlled Gas Flow in Anisotropic Claystone

Dilatancy controlled gas flow is characterized by a series of gas pressure-induced dilatant pathways in which the pathway aperture is a function of the effective stress within the solid matrix. In this paper, a three-dimensional hydro-mechanical model is presented to simulate the gas migration in initially saturated claystone with considerable anisotropy. The governing equations including mass conservation, momentum balance and energy conservation are presented for the unsaturated rock containing three phases, i.e., gas, water and solid grain. The constitutive model is proposed in which two conceptualized fracture sets with nonlinear mechanical behavior and cubic law controlled permeability are inserted, which have a direct effect on the hydro-mechanical behavior of the equivalent continuum. Finally, the developed model is validated against three gas injection tests on initially saturated Callovo–Oxfordian claystone. In general, the model is capable of capturing the main features of dilatancy controlled flow, i.e., anisotropic radial deformation, major gas breakthrough, and mechanical volume dilation of the sample. The proposed model offers additional insight into the relation between gas flow, solid matrix deformation and fracture opening/closure, which helps us get in-depth understanding of this gas transport mechanism.

A new triple-porosity multiscale fractal model for gas transport in fractured shale gas reservoirs

A new triple-porosity model is proposed based on the fractal properties, multiscale flow properties, multiple transport mechanisms and multilayer adsorption/desorption in organic matter pores (OMP), inorganic matter pores (IMP), and fracture network (FN). This model is validated by field gas production data and the key factors affecting gas production are explored. Results show that gas flow is of temporal and spatial multiscale. Shale gas is extracted firstly from hydraulic fractures, then FN and IMP, finally OMP. More adsorbed gases are desorbed and surface diffusion is enhanced when gas pressure decreases. Slip flow is the dominate gas transport mechanism in OMP and IMP. The surface diffusion in OMP and the Knudsen diffusion in IMP are not ignorable contributors to gas production. The OMP contributes 21% of gas production in the later stage. This new triple-porosity model is more accurate than single-porosity and dual-porosity models in gas recovery.

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.

A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

Modeling of Gas Transport through Polymer/MOF Interfaces: A Microsecond-Scale Concentration Gradient-Driven Molecular Dynamics Study.

Membrane-based separation technologies offer a cost-effective alternative to many energy-intensive gas separation processes, such as distillation. Mixed matrix membranes (MMMs) composed of polymers and metal–organic frameworks (MOFs) have attracted a great deal of attention for being promising systems to manufacture durable and highly selective membranes with high gas fluxes and high selectivities. Therefore, understanding gas transport through these MMMs is of significant importance. There has been longstanding speculation that the gas diffusion behavior at the interface formed between the polymer matrix and MOF particles would strongly affect the global performance of the MMMs due to the potential presence of nonselective voids or other defects. To shed more light on this paradigm, we have performed microsecond long concentration gradient-driven molecular dynamics (CGD-MD) simulations that deliver an unprecedented microscopic picture of the transport of H2 and CH4 as single components and as a mixture in all regions of the PIM-1/ZIF-8 membrane, including the polymer/MOF interface. The fluxes of the permeating gases are computed and the impact of the polymer/MOF interface on the H2/CH4 permselectivity of the composite membrane is clearly revealed. Specifically, we show that the poor compatibility between PIM-1 and ZIF-8, which manifests itself by the presence of nonselective void spaces at their interface, results in a decrease of the H2/CH4 permselectivity for the corresponding composite membrane as compared to the performances simulated for PIM-1 and ZIF-8 individually. We demonstrate that CGD-MD simulations based on an accurate atomistic description of the polymer/MOF composite is a powerful tool for characterization and understanding of gas transport and separation mechanisms in MMMs.

Computational model of electrode-induced microenvironmental effects on pH measurements near a cell membrane.

The mechanism of gas transport across cell membranes remains a topic of considerable interest, particularly regarding the extent to which lipids vs. specific membrane proteins provide conduction pathways. Studies of transmembrane (CO2) transport often rely on data collected under controlled conditions, using pH-sensitive microelectrodes at the extracellular surface to record changes due to extracellular CO2 diffusion and reactions. Although recent detailed computational models can predict a qualitatively correct behavior, a mismatch between the dynamical ranges of the predicted and observed pH curves raises the question whether the discrepancy may be due to a bias introduced by the pH electrode itself. More specifically, it is reasonable to ask whether bringing the electrode tip near or in contact with the membrane creates a local microenvironment between the electrode tip and the membrane, so that the measured data refer to the microenvironment rather than to the free surface. Here, we introduce a detailed computational model, designed to address this question. We find that, as long as a zone of free diffusion exists between the tip and the membrane, the microenvironment behaves effectively as the free membrane. However, according to our model, when the tip contacts the membrane, partial quenching of extracellular diffusion by the electrode rim leads to a significant increase in the pH dynamics under the electrode, matching values measured in physiological experiments. The computational schemes for the model predictions are based on semi-discretization by a finite-element method, and an implicit-explicit time integration scheme to capture the different time scales of the system.

A review of gas transport and adsorption mechanisms in two‐component methane‐carbon dioxide system

A review of gas transport and adsorption mechanisms in two‐component methane‐carbon dioxide system

A radial differential pressure decay method with micro-plug samples for determining the apparent permeability of shale matrix

We propose a radial differential pressure decay (RDPD) method to measure the apparent permeability in shale matrix. The experimental design extends the upper limit of pressure in conventional methods. The experimental error caused by the dispersiveness of sample size and the irregularity of particle shape is reduced by utilizing precisely prepared micro-plug samples with highly uniform diameters, and the reliability of the result is improved substantially. The late-time approximate solution for cylindrical samples based on the experimental configuration is presented for data interpretation and verified with the numerical simulation. The experiments based on shale matrix samples are demonstrated. The results reveal that the RDPD method can capture a differential pressure decay curve precisely, which can be closely fitted through the late-time solution. It also has great potential for various tight porous media. This method sets the stage for the accurate investigation of gas transport mechanisms in tight porous media in future work.

Apparent permeability study of rarefied gas transport properties through ultra-tight VORONOI porous media by Discrete Velocity Method

Accurate prediction of the apparent permeability relies on deep understanding of unconventional gas transport mechanism in microscale. To achieve this goal, it is necessary to develop a controllable generation method for low porosity porous media with shale characteristics and explore advanced numerical method to study non-equilibrium phenomena in porous media. Based on the VORONOI tessellation and its topological relationship, a new method for the generation of controllable low porosity porous media is proposed. Two numerical simulation methods are adopted to study gas flow in VORONOI porous media systematically, including Multiple-Relaxation-Time Lattice Boltzmann Method for the intrinsic permeability and Linearized BGK equations via the Discrete Velocity Method for the apparent permeability influenced by the non-equilibrium effect. The results show that the effective porosity is the decisive factor affecting the intrinsic permeability. Porous media with low porosity and high tortuosity are more affected by the rarefied gas effect. The velocity contours show that velocity gradually increases in the throats perpendicular to the pressure gradient direction due to the rarefied throttling effect, which reduces the mass flow rate and apparent permeability significantly. Furthermore, by considering the influences of both porosity and tortuosity, a high-order apparent permeability correction model is proposed to fit porous media with different structures.

Understanding Gas Transport Behavior through Few-Layer Graphene Oxide Membranes Controlled by Tortuosity and Interlayer Spacing.

Here, we elucidate the gas transport behavior through few-layer graphene oxide membranes (FGOMs) that have a systematically controlled diffusion pathway, including tortuosity and channel width. The obtained unusual gas permeation order (especially, CH4 > O2 > N2) of the FGOM provides strong evidence that gas molecules can indeed penetrate through the empty voids created by horizontally assembled GO, which allows selective gas transport features. These unique transport features of the FGOM originate from its continuously connected channel structure, which is an analogue of an ultrapermeable glassy polymer with extremely large free volumes in dense films. Furthermore, variation of the channel width in the range of 0.50-0.55 nm leads to notable changes in the gas permeance orders related to CH4, indicating that there is a transition region for switching the gas transport mechanism between a molecular sieving character and the solution-diffusion model.

On the flow regime model for fast estimation of tight sandstone gas apparent permeability in high-pressure reservoirs

ABSTRACT A flow regime-based gas apparent permeability model in high-pressure tight sandstone reservoirs is established by bridging molecular kinetics, gas transport mechanisms, and apparent permeability. This model is well validated against simulation and experimental data. Results indicate that an equal-flow point tends to move to a low-pressure region with an increase in a pore diameter. As an equal-flow line is close to an isoline of a Knudsen number of 1, a flow regime is divided into three Knudsen number-based regions. Both the equal-flow line and the isoline of a Knudsen number indicate that an increasing temperature expands a Knudsen diffusion-dominated region, which further enhances the gas transport permeability. A typical curve of flow-regime gas apparent permeability provides a fast estimation of gas apparent permeability based on a Knudsen number and a pore diameter. The minimum Knudsen number line constrained by a packing fraction in a typical curve also indicates a minimum gas apparent permeability when a pore diameter is less than 100 nm.

Analytical solutions for multi-stage fractured shale gas reservoirs with damaged fractures and stimulated reservoir volumes

After performing hydraulic fracturing in shale reservoirs, the hydraulic fractures and their adjacent rocks can be damaged. Typically, the following fracture damage scenarios may occur: (1) choked fractures; (2) partially propped fractures with unpropped or poorly propped sections at the middle or tail of fractures; (3) fracture face damage; and (4) multiple damage cases. The classical fracture skin factors are derived under steady-state conditions. They are not accurate when the damaged length is relatively long and are not applicable for multiple damage and partially propped fractures. In this article, a new analytical model is established considering all above-mentioned fracture damage mechanisms, complex gas transport mechanisms, and the stimulated reservoir volume (SRV) of shale gas reservoirs.The matrix model is a spherical element model considering the slip flow, Knudsen diffusion, surface diffusion, and desorption. Natural fractures are idealized as a thin layer that evenly envelops the matrix. The reservoir-fracture flow model is a ten-region linear flow model which can handle fracture damage mechanisms. Specifically, the inner reservoir region is treated as an SRV where the secondary fracture permeability obeys a power-law decreasing trend due to the attenuate stimulation intensity.This model is validated by matching with the Marcellus Shale production data. And the degraded model's calculation matches well with that of a published linear flow model. New type curves are generated and sensitivity analyses are conducted. Results indicate that the presence of the SRV diminishes pressure and derivative values in certain flow regimes depending on the SRV properties. Different damage mechanisms all control specific flow regimes but the fracture face damage shows the slightest influence. In the multiple fracture damage case, some typical flow regimes can be easily identified except those induced by the partially propped fractures. The field application example further ensures the applicability in dealing with real field data.

Recent Advances in Graphene Oxide Membranes for Gas Separation Applications.

Graphene oxide (GO) can dramatically enhance the gas separation performance of membrane technologies beyond the limits of conventional membrane materials in terms of both permeability and selectivity. Graphene oxide membranes can allow extremely high fluxes because of their ultimate thinness and unique layered structure. In addition, their high selectivity is due to the molecular sieving or diffusion effect resulting from their narrow pore size distribution or their unique surface chemistry. In the first part of this review, we briefly discuss different mechanisms of gas transport through membranes, with an emphasis on the proposed mechanisms for gas separation by GO membranes. In the second part, we review the methods for GO membrane preparation and characterization. In the third part, we provide a critical review of the literature on the application of different types of GO membranes for CO2, H2, and hydrocarbon separation. Finally, we provide recommendations for the development of high-performance GO membranes for gas separation applications.

The Influence of Polymer Concentration and Formation Technique on Gas Transport and Gas Sorption Properties of Copolyetherimide-Based Composite Membranes Containing MIL-101 Filler

Composite mixed-matrix membranes for gas separation containing copolyetherimide Siltem® as the polymer matrix and metal-organic framework MIL-101 (10 wt %) as the active filler, were obtained using dry and wet-dry formation techniques. It has been found that the polymer concentration in the initial solution does not significantly affect the CO2 and CH4 permeability of the film membranes obtained by dry molding. The addition of MIL-101 increases the CO2/CH4 selectivity of the dry-formed membranes approximately by 2 times compared to the selectivity of the filler-free polymer membranes. The materials synthesized by the wet-dry formation possess increased permeability and inverted CO2/CH4 selectivity, which indicates a change in the gas transport mechanism. With the increase of polymer concentration, the selectivity of the membranes obtained by the wet-dry technique, increases significantly due to the formation of the dense selective layer.

Estimation of parameters of gas diffusion in models of microtransfactions of different type by the method of molecular dynamics

Estimation of gas transport parameters in organic nano-porous materials, such as kerogens, is important for understanding the fundamentals of the processes that co-produce natural gas. In this regard, the description and numerical parameterization of the processes of transfer of components of natural gas occurring at the micro level in organic nano-porous materials is of interest both from fundamental and practical points of view, including the search for possible ways to optimize the yield of natural gas and boost recoil. The purpose of this study is to study the methods of molecular modeling and the molecular dynamics of the mechanisms of gas transport in structures that mimic organic nano-porous materials, and the numerical evaluation of mass transfer parameters.

Simultaneous determination of permeability and diffusivity subject to dynamic sorption in gas shales

Gas storage and transport mechanisms are essential for the shale gas development, while the three critical parameters are fracture permeability, adsorption capacity, and diffusivity. However, significant errors on the measured permeability may occur due to the gas sorption in the pores during the lab tests, which also affects the in-situ pore pressure. In this paper, a new approach is proposed to simultaneously determine the permeability, adsorption capacity, and diffusivity based on a modified pressure transient technique in the shale formation. Results showed that the shale permeability would be overestimated by >27.3% for Barnett shale and 55.5% for Eagle Ford shale when ignoring the sorption effect. The factors leading to errors in the measured permeability is numerically investigated and it was found that the sorption effect on the measured permeability can be reduced by using short core samples. In addition, the volume of the reference cell should be at least 6 times larger than the pore volume of the sample in order to control the permeability error within 5%. This study provides a methodology which can be readily applied in simultaneous determination of gas permeability, gas storage, and gas diffusivity, and sheds lights on better understanding of the gas storage and transport mechanisms in gas shale reservoirs.