Gas Transport Model Research Articles

Study on Apparent Permeability Model for Gas Transport in Shale Inorganic Nanopores

Inorganic nanopores occurring in the shale matrix have strong hydrophilicity and irreducible water (IW) film can be formed on the inner surface of the pores making gas flow mechanisms in the pores more complex. In this paper, the existence of irreducible water (IW) in inorganic pores is considered, and, based on the Knudsen number (Kn) correction in shale pores, a shale gas apparent permeability model of inorganic nano-pores is established. The effect of the Kn correction on the apparent permeability, the ratio of flow with pore radius and the effect of IW on the apparent permeability are assessed. The main conclusions are as follows: (1) at low pressure (less than 10 MPa) and for medium pore size (pore radius range of 10 nm–60 nm), the effect of the Kn correction should be considered; (2) considering the effect of the Kn correction, bulk phase transport replaces surface diffusion more slowly; considering the existence of IW, bulk phase transport replaces surface diffusion more slowly; (3) with increase in pressure, the IW effect on gas apparent permeability decreases. Under low pressure, the IW, where pore size is small, promotes fluid flow, while the IW in the large pores hinders fluid flow. In conditions of ultra-high pressure, the IW promotes gas flow.

Modeling of Shale Gas Transport in Multi-Scale Complex Fracture Networks Considering Fracture Hits

Modeling of Shale Gas Transport in Multi-Scale Complex Fracture Networks Considering Fracture Hits

A kinetic model for multicomponent gas transport in shale gas reservoirs and its applications

An accurate gas transport model is of vital importance to the simulation and production optimization of unconventional gas reservoirs. Although great success has been achieved in the development of single-component transport models, limited progress has been made in multicomponent systems. The major challenge of developing non-empirical multicomponent gas transport models lies in the absence of the quantification of the concentration impact on the fluid dynamic properties. To fill such a gap, this work presents a comprehensive transport model for multicomponent gas transport in shale and tight reservoirs. In developing the model, we first conducted molecular dynamic simulations to qualitatively understand the differential release of hydrocarbons from unconventional shale and tight reservoirs. It is found that the gas slippage, differential adsorption, and surface diffusion are the primary transport mechanisms in the working range of Knudsen number during reservoir production. Based on the molecular dynamic study, a quantitative transport model has been developed and validated, which extends existing models from single-component systems to multiple-component systems. The kinetic theory of gases is adopted and modified to model the multicomponent slippage effect. A generalized Maxwell–Stefan formulation with extended Langmuir adsorption isotherm is used to model the multicomponent surface diffusion process. The accuracy of the proposed model is above 90% for low to moderate Knudsen numbers in modeling the differential release phenomenon in unconventional reservoirs.

Understanding gas transport mechanisms in shale gas reservoir: Pore network modelling approach

This report summarizes the recent findings on gas transport mechanisms in shale gas reservoir by pore network modelling. Multi-scale pore network model was developed to accurately characterize the shale pore structure. The pore network single component gas transport model was established considering the gas slippage and real gas property. The gas transport mechanisms in shale pore systems were elaborated on this basis. A multicomponent hydrocarbon pore network transport model was further proposed considering the influences of capillary pressure and fluid occurrence on fugacity balance. The hydrocarbon composition and pore structure influences on condensate gas transport were analyzed. These results provide valuable insights on gas transport mechanisms in shale gas reservoir. Cited as: Song, W., Yao, J., Zhang, K., Yang, Y., Sun, H. Understanding gas transport mechanisms in shale gas reservoir: Pore network modelling approach. Advances in Geo-Energy Research, 2022, 6(4): 359-360. https://doi.org/10.46690/ager.2022.04.11

Apparent diffusion coefficient for adsorption-controlled gas transport in nanoporous media

We present an apparent diffusion coefficient derived from a diffusion-based mass conservation equation for single-component gas transport in nanoporous media. Multiple transport and storage mechanisms have been considered, including Knudsen diffusion and viscous flow for the free phase and surface diffusion and multilayer adsorption for the sorbed phase. The real gas effect, confinement effect, and dynamic adsorption layer thickness are also considered. A pore-scale simplified local density method is utilized to obtain sorbed phase properties, such as volume fraction, concentration, and adsorption isotherm. The developed apparent diffusion coefficient is applied to investigate the effects of fluid–solid attraction, fluid–solid species, and pore sizes on the gas diffusion and adsorption in nanoporous media. The results reveal that the sorbed phase occupies a significant volume of nanopores, and the entire pore space becomes sorbed-phase volume in pores with diameters ≤ 2 nm. The total mass transport in these pores is dominated by surface diffusion, and free-phase diffusion contribution increases as the pore size increases. Furthermore, in strong adsorption systems such as CO2-coal, the apparent diffusion coefficient is up to two orders of magnitude smaller than in weak adsorption systems (e.g., N2-coal and CH4-coal). This is attributed to the reduced free-phase volume fraction and increasing adsorption capacity. The proposed apparent diffusion coefficient can be used in the diffusion-based models for gas transport in nanoporous media.

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.

Non‐Covalent Cross‐Linking Does the Job: Why PIM‐1/Silicalite‐1 Mixed Matrix Membranes Perform Well Notwithstanding Silicalite‐1

The macroscopic modeling of gas transport in mixed-matrix membranes (MMMs) made of a Polymer of Intrinsic Microporosity (PIM-1) and silicalite1 (MFI) is compared to the experimental results presented in a previous paper, which shows unexpectedly large gas separation factors, although the silicalite-1 filler is practically nonselective. The mismatch between the predictions of the Maxwell model and the experiments is zeroed by the recognition of nonideal effects, the extent of which is evaluated. The good performance of the PIM-1 MMM is explained by non-covalent cross-linking of the PIM-1 matrix. Cross-linking results from π-π stacking interactions between the 2-phenylethyl grafts on the outer surface of the MFI crystals and the aromatic ladder segments of PIM-1, in agreement with the current explanation of the good transport performance of PIM-1 MMMs containing porous aromatic fillers (e.g., PAF-1).

Numerical model for static chamber measurement of multi-component landfill gas emissions and its application

The quantitative assessment of landfill gas emissions is essential to assess the performance of the landfill cover and gas collection system. The relative error of the measured surface emission of landfill gas may be induced by the static flux chamber technique. This study aims to quantify effects of the size of the chamber, the insertion depth, pressure differential on the relative errors by using an integrated approach of in situ tests, and numerical modeling. A field experiment study of landfill gas emission is conducted by using a static chamber at one landfill site in Xi’an, Northwest China. Additionally, a two-dimensional axisymmetric numerical model for multi-component gas transport in the soil and the static chamber is developed based on the dusty-gas model (DGM). The proposed model is validated by the field data obtained in this study and a set of experimental data in the literature. The results show that DGM model has a better capacity to predict gas transport under a wider range of permeability compared to Blanc’s method. This is due to the fact that DGM model can explain the interaction among gases (e.g., CH4, CO2, O2, and N2) and the Knudsen diffusion process while these mechanisms are not included in Blanc’s model. Increasing the size and the insertion depth of static chambers can reduce the relative error for the flux of CH4 and CO2. For example, increasing the height of chambers from 0.55 to 1.1 m can decrease relative errors of CH4 and CO2 flux by 17% and 18%, respectively. Moreover, we find that gas emission fluxes for the case with positive pressure differential (∆Pin-out) are greater than that of the case without considering pressure fluctuations. The Monte Carlo method was adopted to carry out the statistical analysis for quantifying the range of relative errors. The agreement of the measured field data and predicted results demonstrated that the proposed model has the capacity to quantify the emission of landfill gas from the landfill cover systems.

Gas diffusion through variably-water-saturated zeolitic tuff: Implications for transport following a subsurface nuclear event

Noble gas transport through geologic media has important applications in the characterization of underground nuclear explosions (UNEs). Without accurate transport models, it is nearly impossible to distinguish between xenon signatures originating from civilian nuclear facilities and UNEs. Understanding xenon transport time through the earth is a key parameter for interpreting measured xenon isotopic ratios. One of the most challenging aspects of modeling gas transport time is accounting for the effect of variable water saturation of geological media. In this study, we utilize bench-scale laboratory experiments to characterize the diffusion of krypton, xenon, and sulfur hexafluoride (SF6) through intact zeolitic tuff under different saturations. We demonstrate that the water in rock cores with low partial saturation dramatically affects xenon transport time compared to that of krypton and SF6 by blocking sites in zeolitic tuff that preferentially adsorb xenon. This leads to breakthrough trends that are strongly influenced by the degree of the rock saturation. Xenon is especially susceptible to this phenomenon, a finding that is crucial to incorporate in subsurface gas transport models used for nuclear event identification. We also find that the breakthrough of SF6 diverges significantly from that of noble gases within our system. When developing field scale models, it is important to understand how the behavior of xenon deviates from chemical tracers used in the field, such as SF6 (Carrigan et al., 1996). These new insights demonstrate the critical need to consider the interplay between rock saturation and fission product sorption during transport modeling, and the importance of evaluating specific interactions between geomedia and gases of interest, which may differ from geomedia interactions with chemical tracers.

Dynamics in Diffusive Emissions of Dissolved Gases from Groundwater Induced by Fluctuated Ground Surface Temperature.

During the lateral transport with subsurface flow, amounts of manufactured volatile organic chemicals and gases dissolved in groundwater are emitted into the atmosphere via upward diffusion through soils. Quantifying gas emissions is important for assessing environmental risk associated with these constituents (e.g., air pollution and global warming). It is widely recognized that the temperature would affect gas spreading in soils, which in turn regulates the gas emission from groundwater. However, the upward diffusive gas emission induced by the fluctuated ground surface temperature (GST) remains unexplored. A coupled heat transfer and gas transport model is developed to investigate emissions of tetrachloroethylene (PCE) and N2O, a typical manufactured volatile organic chemical and a natural gas, from groundwater with seasonally fluctuating GSTs. The results indicate that both PCE and N2O emissions vary significantly from month to month. Moreover, fluctuations of emissions lag obviously behind the fluctuation of GST due to the damping effects of both capillary fringe and soil sorption. The proposed model agrees with the observed data from a monolith lysimeter experiment well. The model is also applied to the estimations of N2O emissions from 12 aquifers in Walloon Region, Belgium. The estimated N2O emission is 12.6 μg N/m2/d that falls in the estimated range (9.0-21.5 μg N/m2/d) using the IPCC emission factor approach that commonly accounts for the N2O emission of groundwater discharge to surface water only. It suggests that the upward diffusion is non-negligible for estimations of N2O emission from groundwater.

Modeling of Anomalous Gas Transport in Heterogeneous Unconventional Reservoirs Using a Nonlinear Generalized Diffusivity Equation

Modeling of Anomalous Gas Transport in Heterogeneous Unconventional Reservoirs Using a Nonlinear Generalized Diffusivity Equation

Pore-Scale Hydro-Mechanical Modeling of Gas Transport in Coal Matrix

Pore-Scale Hydro-Mechanical Modeling of Gas Transport in Coal Matrix

A Microbial‐Explicit Soil Organic Carbon Decomposition Model (MESDM): Development and Testing at a Semiarid Grassland Site

AbstractExplicit representations of microbial processes in soil organic carbon (SOC) decomposition models have received increasing attention, because soil heterotrophic respiration remains one of the greatest uncertainties in climate‐carbon feedbacks projected by Earth system models (ESMs). Microbial‐explicit models have been developed and applied in site‐ and global‐scale studies. These models, however, lack the ability to represent microbial respiration responses to drying‐wetting cycles, and few of them have been incorporated in land surface models (LSMs) and validated against field observations. In this study, we developed a multi‐layer, microbial‐explicit soil organic carbon decomposition model (MESDM), based on two main assumptions that (a) extracellular enzymes remain active at dry reaction microsites, and (b) microbes at wet microsites are active or potentially active, while microbes at the dry microsites are dormant, by dividing the soil volume into wet and dry zones. MESDM with O2 and CO2 gas transport models was coupled with Noah‐MP LSM and tested against half‐hourly field observations at a semiarid grassland site in the southwest US characterized by pulsed precipitation. The results show MESDM can reproduce the observed soil respiration pulses of various sizes in response to discrete precipitation events (Birch effect) and thus improve the simulation of net ecosystem exchange. Here, both microbial accessibility to accumulated dissolved organic carbon and reactivation of dormant microbes at the dry microsites upon rewetting are critical to reproducing the Birch effect. This study improves our understanding of and ability to simulate complex soil carbon dynamics that experience drying‐wetting cycle in climate‐carbon feedbacks.

A Predictive Procedure to Model Gas Transport and Intrinsic Properties of Rubbery Polymeric Membranes Using Equilibrium Thermodynamics and Free Volume Theory

A Predictive Procedure to Model Gas Transport and Intrinsic Properties of Rubbery Polymeric Membranes Using Equilibrium Thermodynamics and Free Volume Theory

Solidarity measures: Assessment of strategic gas storage on EU regional risk groups natural gas supply resilience

This paper focuses on strategic storage as a solidarity measure in response to short-term “high-impact, low-probability” (HILP) disruptions in the European Union (EU) gas supply from major suppliers (i.e., Ukraine, Russia, Norway, and North Africa), assuming its implementation in selected Member States. A two-stage stochastic cost minimization gas transport model is used to evaluate the impact of HILP events on the level of demand curtailment, survival time, and the natural gas supply mix of EU regional risk group. Results show that geographic proximity alone, without solidarity measures, is inadequate in providing system resilience. In contrast, solidarity measures lead to a longer survival time for regional risk groups (14 days) and to a reduction in system (15%) and LNG (70%) costs relative to a base scenario with no strategic storage. The analysis stresses the value of the coordinated use of strategic storage in balancing the natural gas network during emergencies, and provides further evidence supporting the EU legislative path towards an Energy Union.

Hydro-mechanical modelling of gas transport in clayey host rocks for nuclear waste repositories

Host rocks, as the final impediment to waste migration, play a significant role in the nuclear waste repositories. Modelling of gas migration in saturated host rocks as well as its coupled hydro-mechanical (HM) behaviors is of importance to the assessment of geological disposal facilities. A comprehensive literature review is carried out on the models for simulating gas migration in saturated rock materials. Several aspects have been provided and discussed, including the material properties and experimental interpretations, governing equations, constitutive models for hydraulic and mechanical processes, fracture propagation models. Specifically, these models are discussed in detail with respect to their performance in describing the recorded experimental behaviors. It is found that the visco-capillary two phase flow model with enriched intrinsic permeability is commonly used to describe the advective gas transport in saturated host rocks. The embedded fracture model (EFM) or enriched EFM seems to be the most favored model as it accounts for the fracturing mechanism which is more representative to implicitly simulate the preferential gas pathways. To describe the mechanical behavior of rocks during the gas migration process, linear/nonlinear elastic, elastoplastic and damage models have been included in the mechanical processes. The HM models incorporating plasticity or damage may not be applicable in most experimental studies, which are not competent to simulate the key experimental behavior associated with the development of gas preferential pathways. Current models that can explicitly describe the gas induced micro-fracturing are seldomly reported, the existed ones are not able to represent all the key experimental behaviors related to preferential gas flow. Advanced approaches, i.e., phase field (PF) method, extended finite element method (XFEM), discrete element method (DEM), hybrid finite discrete element method (FDEM) can be integrated with cohesive zone model (CZM) to provide some promising aspects in representing the development of preferential gas pathways. Lastly, the conclusions and recommendations for future modelling are given.

Rarefied gas transport in heterogeneous shale matrix using a practical apparent permeability model and fuzzy statistical method

A new shale gas transport model is derived to characterize the matrix structural heterogeneity impact on the gas apparent permeability (AP). The developed analytical model is built upon two steps: first, the homogeneous AP model is formulated by assigning the Knudsen-number-parameterized weight coefficients to flow mechanisms based on the analyses of representative rarefied gas transport models; then, the homogeneous model is improved to the heterogeneous model with the help of fuzzy statistical method to assess the structural heterogeneity influences. More specifically, the homogeneous AP model incorporates the multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The physical terms in the apparent permeability including the rarefaction coefficient and multilayer adsorption model are simplified to facilitate the large-scale simulation. Meanwhile, the heterogeneous AP model is quantified by the distribution of porosity, tortuosity, and pore size. It is demonstrated that the developed AP model can reproduce the experimental and numerical experiments for five types of gases. It is concluded that the rarefaction in nanopores could be reasonably characterized by the weighted Knudsen diffusion and viscous flow mechanisms. Moreover, it is noticed that the surface diffusion and Knudsen diffusion cannot be ignored in nanopores with radius smaller than 3 nm at low reservoir pressures. In contrast, the viscous flow plays a significant role in shale gas transport in nanopores with radius larger than 75 nm. In addition, the fuzzy statistical method in the proposed heterogenous model provides the indicators to evaluate the impact of structural heterogeneity on the AP. It is observed that the heterogeneous model can accurately predict the realistic apparent permeability as the heterogeneity increases to σ = 0.15. However, the accuracy decreases when the matrix heterogeneity increases.

A Fractal Permeability Model for Gas Transport in the Dual-Porosity Media of the Coalbed Methane Reservoir

A Fractal Permeability Model for Gas Transport in the Dual-Porosity Media of the Coalbed Methane Reservoir

Chemical Potential-Based Modeling of Shale Gas Transport

Shale gas plays an increasingly important role in the current energy industry. Modeling of gas flow in shale media has become a crucial and useful tool to estimate shale gas production accurately. The second law of thermodynamics provides a theoretical criterion to justify any promising model, but it has been never fully considered in the existing models of shale gas. In this paper, a new mathematical model of gas flow in shale formations is proposed, which uses gas density instead of pressure as the primary variable. A distinctive feature of the model is to employ chemical potential gradient rather than pressure gradient as the primary driving force. This allows to prove that the proposed model obeys an energy dissipation law, and thus, the second law of thermodynamics is satisfied. Moreover, on the basis of energy factorization approach for the Helmholtz free energy density, an efficient, linear, energy stable semi-implicit numerical scheme is proposed for the proposed model. Numerical experiments are also performed to validate the model and numerical method.

A Novel Multiphysics Multiscale Multiporosity Shale Gas Transport Model for Geomechanics/Flow Coupling in Steady and Transient States

Summary A novel multiphysics multiscale multiporosity shale gas transport (M3ST) model was developed to investigate shale gas transport in both transient and steady states. The microscale model component contains a kerogen domain and an inorganic matrix domain, and each domain has its own geomechanical and gas transport properties. Permeabilities of various shale cores were measured in the laboratory using a pulse decay permeameter (PDP) with different pore pressure and confining stress combinations. The PDP-measured apparent permeability as a function of pore pressure under two effective stresses was fitted using the microscale M3ST model component based on nonlinear least squares fitting (NLSF), and the fitted model parameters were able to provide accurate model predictions for another effective stress. The parameters and petrophysical properties determined in the steady state were then used in the transient-state, continuum-scale M3ST model component, which performed history matching of the evolutions of the upstream and downstream gas pressures. In addition, a double-exponential empirical model was developed as a powerful alternative to the M3ST model to fit laboratory-measured apparent permeability under various effective stresses and pore pressures. The developed M3ST model and the research findings in this study provided critical insights into the role of the multiphysics mechanisms, including geomechanics, fluid dynamics and transport, and the Klinkenberg effect on shale gas transport across different spatial scales in both steady and transient states.