Permeability Hysteresis Research Articles

Compositional simulation of coupled transport mechanisms in fractured-vuggy underground gas storage: A case study of LWC in the Sichuan Basin

Compositional models were built to simulate the underground gas storage (UGS) operation, which is characterized by multiple cycles of rapid injection and production. Based on the validated model of the fractured-vuggy underground gas storage Lao Weng-Chang (LWC), this study evaluated the individual and coupling effects of stress sensitivity, relative permeability hysteresis, and high-speed non-Darcy flow on UGS operation. It was found that stress sensitivity is the main controlling factor behind the reduced working gas volume, and it led to a 6.07% decline in working gas volume. Relative permeability hysteresis is the determining factor for the storage capacity, and it led to a 9.05% decline in storage capacity. The high-speed non-Darcy flow only led to a 0.16% reduction in storage capacity but led to a 4.19% decline in working gas volume. A higher stress sensitivity coefficient and increased residual gas saturation both lead to greater losses in both storage capacity and working gas volume. Coupling stress sensitivity and relative permeability hysteresis would have a more pronounced effect on working gas volume than when considered individually. Considering the high-speed non-Darcy flow further decreases working gas volume. The gas production per unit pressure drop will also decrease with the increasing Reynolds number, and there exists a critical value of Re where the decrease significantly accelerates.

Novel coupled hydromechanical model considering multiple flow mechanisms for simulating underground hydrogen storage in depleted low-permeability gas reservoir

Depleted low-permeability gas reservoirs are the primary storage media for underground hydrogen storage (UHS). An accurate assessment of the geomechanics and complex flow mechanisms in a depleted low-permeability gas reservoir is crucial for predicting the injection and production capabilities of UHS facilities. This paper proposes a novel hydromechanical multicomponent model that couples non-Darcy flow, relative permeability hysteresis (RPH), and geomechanics to evaluate the hydrogen storage capacity of UHS facilities in a depleted low-permeability gas reservoir. The coupled model was solved using a fully coupled strategy, employing the finite volume method to solve non-Darcy flow equations and the virtual element method to solve geomechanical problems. The results indicate that the high-velocity non-Darcy (hvnD) and geomechanical effects reduce the working gas volume by 12.82% and 10.56%, respectively. Additionally, the low-velocity non-Darcy (lvnD) effect causes the third stress/strain distribution to exhibit a “focusing” phenomenon, resulting in a 13.19% reduction in the working gas volume. This paper also describes a case where residual gas is captured by mechanisms such as “water lock” and “capillary capture” through the RPH effect. Considering the RPH effect, the gas-water transition zone expanded by 30%, and the peak volume of gas-containing pores in the water zone increased by 1.48 times. Ignoring the RPH effect led to a 19.73% overestimation of the utilization rate of the gas-containing pore space. Hence, this study achieves safe and successful seasonal hydrogen storage and provides theoretical support for designing multicycle operational plans.

Diffusion hysteresis in unsaturated porous media: A microfluidic study

In unsaturated flow studies, water saturation is commonly used as the sole descriptor for macroscale flow models. However, this approach often results in hydraulic hysteresis in capillary pressure and relative permeability during drainage and imbibition processes. Furthermore, the effects of these behaviors on solute diffusion remain unclear. To address this knowledge gap, we conducted microfluidic experiments to investigate these hysteresis relationships. We firstly implemented drainage and imbibition processes in the micromodel to establish pore-scale water configurations. Subsequently, we upscaled the capillary pressure and diffusion coefficients to the Representative-Elementary-Volume scale. Our results revealed that, at the same saturation levels, the unsaturated diffusion coefficients during drainage were at least 6.1 % higher than during imbibition, indicating the presence of diffusion hysteresis. We observed that this hysteresis was influenced by capillary number and residual water saturation. An increase in the capillary number reduced diffusion hysteresis, similar to the capillary pressure hysteresis. While a decrease in residual saturation rose diffusion hysteresis. We also proposed a quadratic polynomial model that effectively predicts the diffusion coefficient by incorporating both saturation and capillary pressure. This research emphasizes the importance of historical changes in unsaturated water flow, which hold significant implications for modeling solute transport processes.

A pore-network modeling perspective on the dynamics of residual trapping in geological carbon storage

This study presents the application of an efficient and robust Dynamic Pore-Network Modeling (DPNM) framework for accurate prediction of carbon dioxide (CO2) trapping behavior under the dynamic flow conditions prevalent in subsurface applications. Residual trapping of CO2 is crucial in the context of geological sequestration, serving as a constitutive relationship that controls relative permeability hysteresis and thereby determining the magnitude of CO2 trapping within formations over varying timescales. Utilizing our DPNM framework, we study the complexities of residual trapping in miniature-core-sized digital replicate of a sandstone. We systematically conduct series of two-phase flow simulations to examine the relationships between total residual CO2 amount, trapping efficiency, and initial saturations across a spectrum of capillary numbers and wettability states. Dynamic simulation results lead to a simple power-law scaling equation correlating CO2 trapping efficiency with initial saturation across various capillary numbers. Further analysis explores the morphological and topological characteristics of fluids during primary drainage and various imbibition displacements within the pore network. This work contributes an essential tool and deepens our understanding of CO2 trapping dynamics, driving progress towards more effective and safer strategies for carbon capture and storage.

Enhancing Hydrogen Recovery from Saline Aquifers: Quantifying Wettability and Hysteresis Influence and Minimizing Losses with a Cushion Gas

This study aims to numerically assess the impact of wettability and relative permeability hysteresis on hydrogen losses during underground hydrogen storage (UHS) and explore strategies to minimize them by using an appropriate cushion gas. The research utilizes the Carlson model to calculate the saturation of trapped gas and the Killough model to account for water hysteresis. By incorporating the Land coefficient based on laboratory-measured data for a hydrogen/brine system, our findings demonstrate a significant influence of gas hysteresis on the hydrogen recovery factor when H2 is used as a cushion gas. The base model, which neglects the hysteresis effect, indicates a recovery factor of 78% by the fourth cycle, which can be improved. In contrast, the modified model, which considers hysteresis and results in a trapped gas saturation of approximately 17%, shows a hydrogen recovery factor of 45% by the fourth cycle. Additionally, gas hysteresis has a notable impact on water production, with an observed 12.5% increase in volume in the model that incorporates gas hysteresis. Furthermore, optimization of the recovery process was conducted by evaluating different cushion gases such as CO2, N2, and CH4, with the latter proving to be the optimal choice. These findings enhance the accuracy of estimating the H2 recovery factor, which is crucial for assessing the feasibility of storage projects.

State of the Art on Relative Permeability Hysteresis in Porous Media: Petroleum Engineering Application

This paper delivers an examination of relative permeability hysteresis in porous media in the field of petroleum engineering, encompassing mathematical modeling, experimental studies, and their practical implications. It explores two-phase and three-phase models, elucidating the generation of scanning curves and their applications in various porous materials. Building on the research of traditional relative permeability hysteresis models, we have incorporated literature on forward calculations of relative permeability based on digital rock core models. This offers a new perspective for studying the hysteresis effect in relative permeability. Additionally, it compiles insights from direct relative permeability and flow-through experiments, accentuating the methodologies and key findings. With a focus on enhanced oil recovery (EOR), carbon capture, utilization and sequestration (CCUS), and hydrogen storage applications, the paper identifies existing research voids and proposes avenues for future inquiry, laying the groundwork for advancing recovery techniques in oil and gas sectors.

Steady-state two-phase relative permeability measurements in proppant-packed rough-walled fractures

Understanding multiphase flow in fractures filled with minerals and proppants is vital in various subsurface applications. Limited experimental data have led to reliance on correlations lacking physical basis. We conducted experiments to characterize relative permeability in rough-walled fractures packed with unconsolidated porous media. We tested fractures packed with water-wet 40/70 sand (silica) and surface-coated ceramic proppants. Brine and mineral oil were used as the wetting and non-wetting fluid phases, respectively. Steady-state (SS) drainage (non-wetting-phase displacing wetting-phase) and imbibition (wetting-phase displacing non-wetting-phase) tests were performed under a wide range of saturation histories (full-cycle and scanning-curves) to study relative permeability hysteresis of the propped fractures. Every SS drainage or imbibition test consisted of several discrete points at which fluid saturations and the corresponding relative permeability were measured by varying the fractional flow rates of fluids whilst maintaining a constant total flow rate. We analyzed residual non-wetting phase saturations and relative permeability trends to understand two-phase flow behavior in each proppant pack. High-resolution x-ray microtomography was used to understand the pore-scale topology, wettability, and to provide insights about the pore-scale displacement mechanisms involved in this study. The results showed that commonly used models to estimate relative permeabilities of fractures significantly overestimated the SS brine and oil relative permeabilities (denoted as krw and kro) measured in this study. Further analysis unveiled that the kro values during imbibition exceeded their drainage counterparts in both proppants, the ceramic proppant exhibited a lower initial water saturation and a higher end-point kro permeability at the end of the drainage displacement, as well as higher krw across all flooding processes. Updated fitting parameters for a Brooks-Corey-type relative permeability correlation are introduced. This study presents improved insights, extensive experimentally generated relative permeability data, and an updated relative permeability correlation, which can be collectively utilized to reduce uncertainties associated with continuum-scale forecasts of multiphase flow behavior in fractured subsurface formations.

Comprehensive parametric study of CO2 sequestration in deep saline aquifers

Carbon dioxide injection in deep saline aquifers is a key method for permanently sequestering anthropogenic CO2. This study employs a reactive transport model to explore mineral precipitation/dissolution and its impact on reservoir properties in deep saline aquifers. We also assess capillary pressure and relative permeability hysteresis on various CO2 trapping mechanisms. Results from this study reveal the significant influence of initial brine composition on mineral precipitation/dissolution. The dissolution and precipitation of minerals have different effects around the wellbores compared to the overall reservoir. Additionally, salt concentration (Ca++ and Mg++) and quartz surface area affect CO2 mineralization, while Na+ impacts halite precipitation, altering reservoir flow properties. The effect of capillary pressure is significant, as including the capillary pressure in the simulation case resulted in significantly improved CO2 trapping, achieving almost total dissolution of the injected CO2 in around 300 years. This study offers novel insights into the interactions of reservoir minerals, brine properties, and the injected CO2.

Theoretical quantification of pH-responsiveness of blend membrane

In this work, a simple predictive mathematical model has been presented that quantifies the membrane parameters, e.g., permeability, effective pore diameter and number of charged units in a polymer chain in a pH-varying environment devoid of added salt. This has been validated experimentally for the case of poly(vinylidene fluoride) (PVDF) membranes blended with poly(methyl methacrylate)-co-poly(acrylic acid) (PMMA-co-PAA) additive copolymer. The effect of Donnan potential was incorporated into the model and estimated using electrokinetic characterizations. It varied considerably from 0.25 to −1.93 units (dimensionless) from pH 2 to 11. Variations of surface morphology and the electronic structure of the blend membrane with pH were studied in detail. Molecular simulations were performed to estimate the effective distance between the neighboring units in the charged/uncharged states and for confirming the copolymer chain behavior in different pH environments. Adsorption experiments were conducted to compare the variation of the number of uncharged units with pH with those estimated using the model. A pH-dependent permeability hysteresis behavior was observed which was explained using an intermolecular hydrogen bonding mechanism. About 80 % variation in the permeability of the blend membrane was observed between the pH limits which was in close agreement with the model results.

A study of non-equilibrium wave groups in two-phase flow in high-contrast porous media with relative permeability hysteresis

Non-equilibrium models are applicable in various physical situations, including phase transitions, hysteresis, and chemical reactions, among others. To model the dynamics of such phenomena, partial differential equations are employed with source terms, as seen in Eq. (1.1). This work focuses on situations where we connect states in equilibrium while allowing for non-equilibrium times. In our model, we model non-equilibrium through relaxation. The source term, in this case, acts as an attractor, and the model’s dynamics allow only a small-time far from equilibrium. We use this theory to model a two-equation system in a two-phase fluid in porous media, where different permeabilities of the flow lead to hysteresis phenomena. We show several examples and study the Riemann solution to gain a better understanding of the solution. We investigate the interplay between nonlinear wave groups of water–oil saturation with different permeabilities in the non-wetting phase and the high-contrast heterogeneity of the porous medium in two-space dimensions. This phenomenon is described by a coupled set of time-dependent partial differential equations of hyperbolic–parabolic–elliptic mixed type. We present and discuss a new projection method with relaxation to obtain 1D-analytical Riemann solutions in an idealized homogenized medium, and we use this solution to validate our numerical method. The primary components of obtaining these solutions are shocks, rarefactions, and bifurcations. We obtain 2D-numerical solutions using an operator splitting approach based on physics, highlighting the discretization methods used. We provide robust analytical–numerical examples to verify the theory and illustrate the approach’s capabilities. In particular, we discuss the 1D-2D behavior of wave groups in situations driven by water–oil infiltration problems of permeable reservoir rocks.

Direct measurement of hydrogen relative permeability hysteresis for underground hydrogen storage

Underground Hydrogen Storage (UHS) is a long-term storage solution which utilises hydrogen as an energy carrier to store large-scale excess renewable energy in the subsurface. Key petrophysical properties, such as wettability and interfacial tension of hydrogen and water have been discovered which provide a practical basis for simulation models. Our work directly measures relative permeability hysteresis during co-injection core floods of hydrogen and water with a capillary number of Nc=2.92×10−7. Segmented micro-CT images are used to determine saturation in the Bentheimer sandstone. Our results demonstrate that hydrogen relative permeability in sandstones is very low, with an end-point relative permeability of krg0=0.049 at Swi= 0.24. Capillary trapping results in residual gas saturation of Sgr= 0.4. Wettability analysis confirms the system is water-wet, with contact angles of 57° at Sgr and 44° at Swi. These results improve the reliability of numerical simulations and demonstrate the possible challenges involved with the commercial application of UHS.

Numerical study of the efficiency of underground hydrogen storage in deep saline aquifers, rock springs uplift, Wyoming

Underground hydrogen storage (UHS) is able to store a large amount of energy with efficiency, thus meeting the high demand for energy in winter. This study aims at investigating the feasibility and efficiency of UHS in the Nugget Sandstone, Rock Springs Uplift, Wyoming. The representative geological model is first constructed with the control of well logs and seismic data. Then the multiphase flow functions are well coupled into the subsurface reservoir model. Following that, based on the uncertainty of reservoir parameters, gas source accessibility, and production cost, the effects of key parameters on H2 fate within the reservoir and H2 recovery efficiency are researched. Simulation outcomes reveal that H2 dissolution into formation brine gives rise to a lower amount of trapped H2 within the reservoir but the recovery ratio is reduced by the H2 dissolution at the end. Relative permeability hysteresis can not only relieve the H2 vertical migration, but also give a wider H2 radial distribution. As the cycle proceeds, relative permeability hysteresis results in the notable enhancement in the trapped H2, leading to a reduction of the final recovery ratio from 0.86 to 0.76 when the residual gas saturation, Sgmax, ranges from 0.2 to 0.4. A slower cushion gas (CG) injection rate gives rise to a smaller final trapped H2, which accordingly results in an increase of recovery ratio. Further, the final recovery ratio changes from 0.835 to 0.846 due to an increase in working gas components from H2:CH4 = 1:1 to H2:CH4 = 3:1. The insights obtained in this study shed a light on accelerating the achievements of decarbonisation goals through the commercial-scale energy conversion and transition from conventional fossil energy and renewable energy to hydrogen.

Mechanistic evaluation of the reservoir engineering performance for the underground hydrogen storage in a deep North Sea aquifer

Underground hydrogen storage (UHS) in aquifers, salt caverns and depleted hydrocarbon reservoirs allows for the storage of larger volumes of H2 compared to surface storage in vessels. In this work, we investigate the impact of aquifer-related mechanisms and parameters on the performance of UHS in an associated North Sea aquifer using 3D numerical compositional simulations.Simulation results revealed that the aquifer's permeability heterogeneity has a significant impact on the H2 recovery efficiency where a more homogenous rock would lead to improved H2 productivity. The inclusion of relative permeability hysteresis resulted in a drop in the H2 injectivity and recovery due to H2 discontinuity inside the aquifer which leads to residual H2 during the withdrawal periods. In contrast, the effects of hydrogen solubility and hydrogen diffusion were negligible when studied each in isolation from other factors. Hence, it is essential to properly account for hysteresis and heterogeneity when evaluating UHS in aquifers.

The Impact of Relative Permeability Hysteresis on CO2 Sequestration in Saline Aquifer

This work analyzed the amount of capillary-trapped CO2 for maximum residual gas saturation due to relative permeability hysteresis. Upward migration of CO2 is unwanted because it increases the risk of CO2 migration from storage sites to the surface. One way to mitigate CO2 leakage risk is to reduce the vertical CO2 migration to improved storage capacity and containment security. A compositional simulator (CMG-GEM) was used to simulate the flow of two components (CO2 and H2 O). A fluid model was built with the PR 78 EOS using WINPROP. A base case model without relative permeability hysteresis was simulated and compared with the case with relative permeability hysteresis. The amount of CO2 trapped, and CO2 saturation distribution were analyzed for maximum trapped gas saturation of 0.3, 0.4 and 0.5. Results shows an increase in the amount of CO2 trapped as the maximum residual gas saturation was increased from 0.3 to 0.4 and 0.5 with a value of 16560128mol for the base case study, 49041744mol, 59502924mol and 67286728mol respectively for maximum residual gas saturation due to relative permeability hysteresis of 0.3, 0.4 and 0.5 respectively. Very little accumulation of CO2 occurs when the maximum trapped gas saturation due to relative permeability hysteresis was set at 0.5. Result reveals that after 200 years, almost all the CO2 was trapped in the formation. Therefore, the imbibition cycle at the trailing end of the CO2 plume should be considered as accounting for hysteresis effects has led to a spread-out distrib

Experimental determination of gas-water relative permeability for ultra-low-permeability reservoirs using crushed-rock samples: Implications for drill cuttings characterization

Relative permeability controls fluid flow through rocks, with applications to hydrocarbon production, geologic carbon and energy storage. However, significant challenges are associated with the measurement of relative permeability for rocks with matrix permeability in the microdarcy to nanodarcy range. The primary objectives of this study are therefore to 1) propose an integrated experimental and modeling approach for gas relative permeability (krg) evaluation using crushed-rock samples and 2) perform a proof-of-concept study to demonstrate that gas–liquid relative permeability can be determined for ultra-low-permeability (unconventional) reservoir samples that have been crushed to certain grain sizes (20–35 mesh size).In this study, the water vapor ad-/desorption technique was employed to provide a wide range of water saturations (Sw). The evolution of water distribution in the shale matrix with a change in Sw was investigated by using a modified low-pressure adsorption (LPA) technique. A recently-developed numerical model was modified to estimate effective permeability to gas at each saturation level. Four clay-rich shales from the Duvernay (Canadian) and Kyalla (Australian) formations were analyzed.The vapor ad-/desorption technique provided an efficient approach to saturate the studied samples. By changing relative humidity in sealed desiccators using different salt solutions, a maximum Sw of 83% was obtained for organic-matter rich samples, and 99% for organic-matter lean shales. As interpreted using the modified LPA technique applied at different saturation levels, water is held in films in mineral-associated macro-/mesopores, and can block access to organic-matter pores through the formation of water clusters, significantly reducing the accessible organic-matter porosity and gas effective permeability. Imbibition krg decreases rapidly and significantly (over 90%) when Sw reaches approximately 0.3–0.4 for samples containing significant amounts of water-sensitive clay minerals (Kyalla #2) and TOC (Duvernay #2). Relative permeability hysteresis occurs for Duvernay #2 and Kyalla #1. Overall, the use of crushed-rock samples (non-matrix/fracture system), and application of the vapor sorption technique, results in a small amount of hysteresis.A laboratory-based method for measuring gas relative permeability of ultra-low-permeability reservoirs using crushed-rock samples is provided for the first time, with important applications to the energy and carbon capture industries.

“Extreme utilization” theory and practice in gas storages with complex geological conditions

Based on more than 20-year operation of gas storages with complex geological conditions and a series of research findings, the pressure-bearing dynamics mechanism of geological body is revealed. With the discovery of gas-water flowing law of multi-cycle relative permeability hysteresis and differential utilization in zones, the extreme utilization theory targeting at the maximum amount of stored gas, maximum injection-production capacity and maximum efficiency in space utilization is proposed to support the three-in-one evaluation method of the maximum pressure-bearing capacity of geological body, maximum well production capacity and maximum peak shaving capacity of storage space. This study realizes the full potential of gas storage (storage capacity) at maximum pressure, maximum formation-wellbore coordinate production, optimum well spacing density match with finite-time unsteady flow, and peaking shaving capacity at minimum pressure, achieving perfect balance between security and capacity. Operation in gas storages, such as Hutubi in Xinjiang, Xiangguosi in Xinan, and Shuang6 in Liaohe, proves that extreme utilization theory has promoted high quality development of gas storages in China.

Effect of relative permeability hysteresis on reservoir simulation of underground hydrogen storage in an offshore aquifer

Underground hydrogen storage (UHS) in porous media is proposed to balance seasonal fluctuations between demand and supply in an emerging hydrogen economy. Despite increasing focus on the topic worldwide, the understanding of hydrogen flow in porous media is still not adequate. In particular, relative permeability hysteresis and its impact on the storage performance require detailed investigations due to the cyclic nature of H2 injection and withdrawal. We focus our analysis on reservoir simulation of an offshore aquifer setting, where we use history matched relative permeability to study the effect of hysteresis and gas type on the storage efficiency. We find that omission of relative permeability hysteresis overestimates the annual working gas capacity by 34 % and the recovered hydrogen volume by 85 %. The UHS performance is similar to natural gas storage when using hysteretic hydrogen relative permeability. Nitrogen relative permeability can be used to model the UHS when hysteresis is ignored, but at the cost of the accuracy of the bottom-hole pressure predictions. Our results advance the understanding of the UHS reservoir modeling approaches.

Relative permeability hysteresis analysis in a reservoir with characteristics of the Brazilian pre-salt

The hysteresis of relative permeability and capillary pressure need to be more widespread in academic studies, in order to understand how they can influence reservoirs with light oil and high pressure. These phenomena become extremely important to have a good prediction of oil production, considering that in many cases, the use of hysteresis in calculations can lead to a better prediction of oil recovery, allowing the exploration of certain fields. Thus, this study had as main objective the analysis of two hysteresis models (Killough and Larsen and Skauge) widely used in commercial software, in order to investigate the behavior of a light oil reservoir using a miscible WAG-CO2 process. Thus, to achieve this goal, a semi-synthetic reservoir, with characteristics similar to those found in the Brazilian pre-salt, was considered and was modeled using commercial software from CMG. Hysteresis reduces fluid permeability, which can generate two effects: increased local sweep efficiency of the oil and loss of injectivity. The former effect contributes to increased oil recovery, while injectivity loss can decrease oil sweep, reducing oil recovery. Furthermore, this work found that hysteresis can cause loss of gas and water injectivity, however this did not prevent hysteresis from increasing oil recovery compared to the case without hysteresis.

Impact of experimentally measured relative permeability hysteresis on reservoir-scale performance of underground hydrogen storage (UHS)

Underground Hydrogen Storage (UHS) is an emerging large-scale energy storage technology. Researchers are investigating its feasibility and performance, including its injectivity, productivity, and storage capacity through numerical simulations. However, several ad-hoc relative permeability and capillary pressure functions have been used in the literature, with no direct link to the underlying physics of the hydrogen storage and production process. Recent relative permeability measurements for the hydrogen-brine system show very low hydrogen relative permeability and strong liquid phase hysteresis, very different to what has been observed for other fluid systems for the same rock type. This raises the concern as to what extend the existing studies in the literature are able to reliably quantify the feasibility of the potential storage projects. In this study, we investigate how experimentally measured hydrogen-brine relative permeability hysteresis affects the performance of UHS projects through numerical reservoir simulations. Relative permeability data measured during a hydrogen-water core-flooding experiment within ADMIRE project is used to design a relative permeability hysteresis model. Next, numerical simulation for a UHS project in a generic braided-fluvial water-gas reservoir is performed using this hysteresis model. A performance assessment is carried out for several UHS scenarios with different drainage relative permeability curves, hysteresis model coefficients, and injection/production rates. Our results show that both gas and liquid relative permeability hysteresis play an important role in UHS irrespective of injection/production rate. Ignoring gas hysteresis may cause up to 338% of uncertainty on cumulative hydrogen production, as it has negative effects on injectivity and productivity due to the resulting limited variation range of gas saturation and pressure during cyclic operations. In contrast, hysteresis in the liquid phase relative permeability resolves this issue to some extent by improving the displacement of the liquid phase. Finally, implementing relative permeability curves from other fluid systems during UHS performance assessment will cause uncertainty in terms of gas saturation and up to 141% underestimation on cumulative hydrogen production. These observations illustrate the importance of using relative permeability curves characteristic of hydrogen-brine system for assessing the UHS performances.

A PERMEABILITY HYSTERESIS MODEL FOR FRACTAL POROUS MEDIA BASED ON ELASTIC-STRUCTURAL DEFORMATION OF CAPILLARY CROSS SECTION

Permeability hysteresis under cyclic pressure loading and unloading has received a lot of attention in both science and engineering. But most of the existing model is only for a one-time pressure cycle. Therefore, a permeability hysteresis model is established based on the theory of elastic-structural deformation of capillary cross section and the fractal theory of porous media. Both the triangular and quadrilateral structures are considered. The stress sensitivity of structural deformation decreases with the increase in the cycle. The porosity hysteresis can also be predicted by the proposed model. Compared with experimental data with different permeability hysteresis, the prediction of the proposed model is consistent with the experimental results. Compared with other models, the proposed model has a smaller average error and a better agreement with experimental data. The proposed model can predict the permeability hysteresis under not only a one-time pressure cycle like the existing model but also multiple pressure cycles. The influence of parameters shows that the decrease in Young’s modulus and Poisson’s ratio of the solid cluster increases the permeability stress sensitivity but does not influence the permeability hysteresis. The increase in the proportion of quadrilateral structure and stress sensitivity of structural deformation increases the permeability hysteresis and stress sensitivity at the same time, while the capillary fractal dimension, tortuosity fractal dimension, and the decay rate of stress sensitivity of structural deformation during the cycles show the opposite. The proposed model has a significant meaning in underground resource mining and the study of permeability hysteresis mechanism.