Transport in Porous Media最新文献

{"title":"Decomposing Capillary Hysteresis: A Topology-Aware Dynamic Graphical Game for Multiphase Displacement in Pore Networks","authors":"Arman Mojoodi","doi":"10.1007/s11242-026-02362-w","DOIUrl":"10.1007/s11242-026-02362-w","url":null,"abstract":"<div><p>Conventional pore-network models (PNMs) typically rely on empirical rules—such as explicit snap-off criteria and contact angle hysteresis—to reproduce capillary hysteresis and residual trapping. In this study, we introduce a fundamentally different approach by formulating quasi-static multiphase displacement as a topology-aware dynamic graphical game, in which each pore is treated as an autonomous agent that locally minimizes its thermodynamic free energy. Within this game-theoretic framework, topological constraints are embedded directly into the local utility function of each pore agent, enabling trapping to emerge as a metastable state transition rather than an imposed geometric rule. A key result of the framework is a model-based characterization of the thermodynamic and topology-constrained mechanisms underlying the simulated hysteresis. Simulations reveal that even in the absence of topological barriers, path-dependent energy minimization within a disordered landscape generates inherent thermodynamic hysteresis. When topological constraints are activated, the model successfully prevents unphysical complete drainage and accurately predicts residual saturations. The framework is applied to six distinct micro-CT-derived pore networks obtained from the Imperial College London pore-network library (Bentheimer, Berea, Heletz, A1, F42B, and Lv60B). Quantitative validation of the primary drainage response, with semi-quantitative comparison of imbibition against experimental data for Berea and Bentheimer sandstones demonstrates reasonable agreement with measured capillary pressure hysteresis, scanning curves, and forced imbibition behavior. Without tuning artificial hysteresis parameters, the model reproduces complex displacement phenomena—including primary and secondary drainage, scanning curve closure, and forced imbibition. Furthermore, ensemble simulations (20 independent realizations per wettability state) reveal a consistent non-monotonic (U-shaped) dependence of displacement efficiency on wettability, with optimal recovery emerging near-neutral-wet conditions (<span>(theta sim mathcal{N}left({100}^{circ },{10}^{circ }right))</span>). Notably, this same wettability regime also maximizes the potential for forced imbibition recovery, identifying an optimal wettability regime for forced recovery with significant implications for wettability alteration strategies. These results show that, within the proposed framework, path-dependent displacement and residual trapping emerge naturally from quasi-static energy minimization subject to topology-dependent accessibility constraints.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revisiting the Solute Transport Equation Associated with Coupled Chemo-mechanical Consolidation Problems in Perfectly Semi-permeable Porous Media","authors":"Chongbin Zhao,&nbsp;Yao Liu,&nbsp;B. E. Hobbs,&nbsp;A. Ord,&nbsp;Xiangtao Zhang","doi":"10.1007/s11242-026-02358-6","DOIUrl":"10.1007/s11242-026-02358-6","url":null,"abstract":"<div><p>The fundamental characteristic of a semi-permeable porous medium, by which we mean a perfectly semi-permeable porous medium in this study, is that the solvent is allowed to move but the solute is not. Due to this fundamental characteristic, there should be no solute mass flux within a solution-saturated semi-permeable porous medium. Consequently, the solute is not allowed to be transported either by solute diffusion or by solvent advection in the semi-permeable porous medium. This means that the conventional form of solute transport equation, which involves both the solute diffusion and solvent advection transport terms, cannot be used to describe the mass conservation of the solute in the semi-permeable porous medium. However, in dealing with the coupled chemo-mechanical consolidation problem in a solution-saturated semi-permeable porous medium, the conventional form of solute transport equation was incorrectly used to describe the mass conservation of the solute in the semi-permeable porous medium. The main purpose of this study is to investigate how this conceptual error affects the numerical solutions for dealing with the coupled chemo-mechanical consolidation problem in a solution-saturated semi-permeable porous medium. This purpose has been achieved through using the following two different kinds of mass conservation equations of the solute in the semi-permeable porous medium. The first is the conventional form of solute transport equation, just like what was incorrectly used in the preceding study, while the second is a local mass conservation equation of the solute, which is presented in this study, in the semi-permeable porous medium. The related theoretical and numerical results have demonstrated that using the conventional form of solute transport equation can lead to the incorrect distributions of the solute concentration and porosity within the solution-saturated semi-permeable porous medium.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local Thermal Non-equilibrium Models in Porous Media: A Comparative Study Under Forced Convection","authors":"Anna Mareike Kostelecky,&nbsp;Ivar Stefansson,&nbsp;Carina Bringedal,&nbsp;Tufan Ghosh,&nbsp;Helge K. Dahle,&nbsp;Rainer Helmig","doi":"10.1007/s11242-026-02347-9","DOIUrl":"10.1007/s11242-026-02347-9","url":null,"abstract":"<p>Heat transfer in saturated porous media plays a key role in many applications. Under certain conditions, the classical assumption of instantaneous heat transfer between phases may no longer hold, leading to local thermal non-equilibrium (LTNE). Even though many continuum-scale LTNE models exist, systematic comparisons between different models remain limited. In this study, we compare a dual-network model and different LTNE-REV-scale formulations under forced convection to evaluate their consistency in predicting LTNE behavior and to assess the influence of different model formulations. Simulations are performed for both steady-state and transient setups. For each setup and model, temperature profiles and non-dimensional temperature differences are analyzed for varying non-dimensional numbers, including Reynolds number, thermal conductivity ratio and Biot number. Across the investigated regimes, all empirical models predict an increase in LTNE with increasing Reynolds number and decreasing Biot number. However, no consistent trend is observed for varying thermal conductivity ratios. Differences between the models can be addressed to the different formulations of effective thermal properties. For idealized systems under natural porous-media conditions, in particular small Reynolds numbers, similar bulk conductivities and high Biot numbers, all models predict near-zero local fluid–solid temperature differences (LTE behavior). Under other conditions, however, the models differ in the magnitude of local temperature difference they predict, i.e., in the degree of LTNE. This highlights the importance of comparisons against detailed experimental data or simulations, for example, within the framework of a benchmark study.</p>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-026-02347-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Measuring Fluid Flow and Tracking Bio-Mediated Precipitation in Propped Shale Fractures","authors":"Matthew R. Willett,&nbsp;Adrienne J. Phillips,&nbsp;Dustin Crandall,&nbsp;Sarah L. Codd,&nbsp;Joseph D. Seymour,&nbsp;Catherine M. Kirkland","doi":"10.1007/s11242-026-02360-y","DOIUrl":"10.1007/s11242-026-02360-y","url":null,"abstract":"<p>Hydraulic fracturing has enabled the extraction of oil and gas from ultra-low permeability shale formations by creating propped fractures that serve as primary fluid flow conduits. While numerical models have advanced understanding of fluid flow through these fractures, experimental analyses remain limited. In this study, pulsed field gradient nuclear magnetic resonance (PFG NMR) velocimetry was used to characterize fluid transport through propped shale fractures and evaluate flow behavior before and after biologically driven mineral precipitation. Phase-shift velocimetry was used to generate high-resolution 2D velocity maps, which were validated with propagator measurements. Results demonstrated strong velocity heterogeneity, flow channeling, and fracture roughness effects. Following microbially induced calcium carbonate precipitation, velocity maps revealed more tortuous and disrupted flow paths, while bulk propagators failed to resolve the full velocity distribution. This study highlights the potential of PFG NMR as a unique, noninvasive experimental tool for investigating complex, reactive flow in rock fractures.</p>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-026-02360-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Closed-Form Model for Relative Permeability Hysteresis Using Saturation and Connectivity","authors":"Russell T. Johns,&nbsp;Osaro Egharevba,&nbsp;Sanchay Mukherjee,&nbsp;Hanif F. Yoga,&nbsp;Hamid Emami-Meybodi","doi":"10.1007/s11242-026-02355-9","DOIUrl":"10.1007/s11242-026-02355-9","url":null,"abstract":"<div><p>This paper presents a closed-form analytical function for the relative permeability of the nonwetting phase that captures nonlinear variations with saturation and phase connectivity (normalized Euler characteristic) via the state function approach. The developed physical state function for relative permeability is unique among prior models in that both imbibition and drainage experimental data, as well as subsequent scans, can be matched simultaneously, while maintaining continuous, single-valued relative permeability and residual saturation predictions. The closed-form model is the first completely robust hysteretic model, ensuring that relative permeability remains within its physical bounds for any scan. The results show that the new function can easily match experimental scanning data with significant hysteresis using only one imbibition and drainage curve and predict subsequent two-phase experimental scanning data with high accuracy. Predicted scans are physically consistent in relative magnitude and degree of hysteresis with the tuned experimental data. Residual saturations, which are a natural output of our model, are defined as the remaining saturations at very low relative permeability, e.g., as <i>k</i>_<i>r</i> approaches 0.01. The model matches and accurately predicts residual saturation for other scanning curves, yielding the expected Land-type shape of the initial-residual curve. Unlike all prior models, relative permeabilities are exactly zero only when connectivity or saturation is zero, thereby allowing relative permeability continuity during vaporization or condensation of the residual phase, or other complex processes such as film drainage of a spreading intermediate wetting phase in a three-phase system. Although having at least one drainage and imbibition scan is desired for model tuning, the model can generate hysteresis curves from a single drainage or imbibition curve, provided that the degree of hysteresis is specified.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-026-02355-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow-Induced Compaction and Elastic Rebound in Saturated Deformable Fibre Networks","authors":"Samuel N. M. Brown,&nbsp;Axel Drotz,&nbsp;Matheus Ferreira,&nbsp;James Drummond,&nbsp;D. Mark Martinez","doi":"10.1007/s11242-026-02357-7","DOIUrl":"10.1007/s11242-026-02357-7","url":null,"abstract":"<p>During the flow-induced compaction of saturated deformable fibrous media, local nonuniformity in solid volume fraction can develop, persist after compression, and partially relax through elastic rebound. Using an experimental approach that spatially resolves the local volume fraction in situ, we characterize the formation and elastic relaxation of this nonuniformity, which manifests as a solid-fraction gradient, in two distinct lignocellulosic fibre networks and over a range of compression rates and bulk solid fractions. Gradient severity increases with compression rate and is more pronounced in the less permeable, less compressible network, consistent with the competition between mechanical loading and hydraulic drainage. Following compression, these gradients relax partially but arrest irreversibly in a nonuniform state, a behaviour indicative of elasto-(visco)plastic network deformation. Across the two materials and various bulk solid fractions studied, the recoverable component of the nonuniformity shows a primary dependence on compression rate, with comparatively weak sensitivity to material type over the range studied; this trend is consistent with an approximately material-insensitive ratio of elastic modulus to compressive yield stress. At high compression rates, the normalized relaxation curves collapse onto a common functional form consistent with a poroelastic diffusion framework, suggesting that, at least for the media studied here, the relaxation kinetics may depend more on structural network properties than on constituent-specific chemistry. Overall, compression rate emerges as a key governing variable controlling both the amplitude of elastic rebound and the transition to a regime in which appreciable rebound occurs.</p>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling Coupled Dissolution–Precipitation and Flow in Fractured Media: Sensitivity of Carbon Mineralization to Subsurface Heterogeneity","authors":"Jeffrey D. Hyman,&nbsp;Aronne Dell’Oca,&nbsp;Alexis Navarre-Sitchler,&nbsp;Hari S. Viswanathan","doi":"10.1007/s11242-026-02352-y","DOIUrl":"10.1007/s11242-026-02352-y","url":null,"abstract":"<div><p>Geologic carbon storage in mafic and ultramafic formations offers a promising strategy for long-term <span>(hbox {CO}_2)</span> sequestration through <i>in situ</i> mineralization. Although this process can permanently immobilize carbon, the efficiency of mineral trapping depends on the interplay between fluid flow, solute transport, and geochemical reactions occurring within complex fracture networks. In this study, we develop a two-dimensional coupled fracture-matrix model that explicitly resolves fracture geometry to simulate coupled flow, solute transport, and dissolution/precipitation reactions using <span>dfnWorks</span> and <span>PFLOTRAN</span>. Global sensitivity analysis using multiple complementary approaches is performed to quantify the influence of key parameters on <i>in situ</i> mineralization in heterogeneous fractured formations, covering structural parameters (fracture density), hydraulic parameters (fracture and matrix permeability), and geochemical parameters (mineral reaction rates). Our results indicate that hydraulic heterogeneity between fracture and matrix permeability along with the intensity of solute diffusion jointly control the mineralization response. As the fracture–matrix permeability contrast increases, flow becomes progressively channelized, limiting the portions of the formation that come into contact with the injected fluid. Under strong flow channelization driven by high fracture–matrix permeability contrasts, mineralization becomes sensitive to the strength of solute diffusion. Variations in geochemical parameters, such as reaction rates and surface areas, exert negligible influence. These findings demonstrate that the interplay between fracture-matrix permeability contrast, fracture hydraulic resistance, and the intensity of solute diffusion govern carbon trapping efficiency, providing new mechanistic insight for optimizing mineralization-based carbon storage in fractured mafic and ultramafic rocks.\u0000</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Physics of Water Retention in Very Dry Porous Media","authors":"John R. Nimmo","doi":"10.1007/s11242-026-02359-5","DOIUrl":"10.1007/s11242-026-02359-5","url":null,"abstract":"<div><p>Very low water contents in porous media are receiving increasing attention as research expands into previously neglected dry environments. Examples include Mars, Antarctica, extreme deserts, and soils exposed to wildfire. Working with very low water contents requires recognition that the generally accepted oven-dryness-based water content scale is a relative scale, analogous to the Celsius scale for temperature, and that oven-dryness is not an absence of water but rather a definable point on a retention curve. The usual definition has ambiguity in that the water content of the oven-dry sample does not depend solely on the oven temperature, but also on unspecified atmospheric conditions outside the oven. An unambiguous definition of zero water content would set it at a specified matric potential, determined by application of the Kelvin equation to pertinent conditions of the method of drying. An absolute, rather than relative, scale is conceivable but is impractical to establish universally. Mathematical representation of dry-range water retention is often done with a two-parameter logarithmic relation interpretable in terms of the energy per unit volume required to remove a particle of water being proportional to the matric potential. Its parameters have strong physical interpretations, related to the specific surface area of the medium’s solid material and the zero point of the relative water content scale. Application of this formula requires attention to the limits of its validity and the means of combining it with formulas for other portions of the water retention curve. These new methods and refined concepts do not constitute a new theory of water retention in porous media, but rather an improved framework for conceptualizing and working with measurements of water retention in the very dry range.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structure-Flow Correlations in Deformable Porous Media Probed by Magnetic Resonance Velocimetry","authors":"Nikolaos Avrantinis,&nbsp;Andrew J. Sederman,&nbsp;Michael D. Mantle,&nbsp;Matthias Appel,&nbsp;Lynn F. Gladden","doi":"10.1007/s11242-026-02350-0","DOIUrl":"10.1007/s11242-026-02350-0","url":null,"abstract":"<p>Although the influence of an applied stress across a deformable porous medium has been well studied theoretically and using numerical simulations, direct experimental studies of how applied stress influences both the microstructure of the pore space and the fluid flow through the porous medium remain challenging due to the optically opaque nature of porous media. Of particular interest has been the observation that the rate of permeability decrease reduces with increasing applied effective stress, and that this rate of permeability decrease is associated with a critical stress state at which substantial flow redistribution occurs. In this work, a randomly packed bed of monodisperse elastic spheres is used to study the effect of matrix deformation on fluid flow under conditions of confined uniaxial compression. Changes in the local hydrodynamics have been identified and are associated with structural changes such as pore expansion and closing, and generation of new pores. Evidence is reported for a change in the morphology of the pore space at the highest applied effective stress studied and that this is associated with a substantial redistribution of the flow.</p>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-026-02350-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear Stability Analysis of Buoyancy-Driven Convection of Two-Phase Fluid in a Porous Medium","authors":"Xin Du,&nbsp;Detang Lu,&nbsp;Haoran Liu","doi":"10.1007/s11242-026-02353-x","DOIUrl":"10.1007/s11242-026-02353-x","url":null,"abstract":"<div><p>Understanding the onset and stability conditions of buoyancy-driven convection in two-phase immiscible flows through the porous medium is paramount for a wide range of subsurface engineering applications, such as density-driven <span>(textrm{CO}_2)</span> convective dissolution in saline aquifers and water flooding for enhanced oil recovery. Motivated by these imperative processes, we present a rigorous linear stability analysis of buoyancy-driven multiphase immiscible thermal convection in a porous medium. Starting from the extended Darcy’s law, the local thermal equilibrium assumption and the Oberbeck–Boussinesq approximation, and incorporating appropriate relative permeability and capillary pressure models, we derive the mathematical equations governing two-phase Rayleigh–Darcy convection. Steady-state profiles for saturation and temperature are established, and small perturbations are introduced to formulate the linearized perturbation equations, which are solved as a generalized eigenvalue problem. A dedicated numerical solver is developed to map the neutral stability curves, critical wavenumbers, and critical Rayleigh–Darcy numbers <span>(Ra_c)</span> governing convective onset. We systematically evaluate the influence of key dimensionless parameters, including the gravity number <i>G</i>, the non-wetting to wetting phase ratios of volumetric thermal expansion coefficient <span>(B_n)</span>, viscosity <span>(M_n)</span>, heat conductivity <span>(Lambda _n)</span>, and volumetric heat capacity <span>(C_n)</span>, the porous medium ratios (<span>(Lambda _s)</span>, <span>(C_s)</span>), as well as capillary pressure parameters and boundary conditions. The results demonstrate that <i>G</i> exerts a modest stabilizing effect, elevating the threshold for convective onset. Furthermore, the stability threshold increases with decreasing <span>(B_n)</span> and <span>(C_n)</span>, and with increasing <span>(M_n)</span>, <span>(Lambda _n)</span>, and <span>(Lambda _s)</span>, whereas <span>(C_s)</span> has negligible impact. Additionally, stronger capillary pressure further stabilizes the system, thereby raising the threshold for convective initiation. Finally, by combining the individual power-law dependencies obtained from the single-parameter sensitivity analyses, we establish an empirical scaling relation between the critical Rayleigh–Darcy number and the dominant governing parameters, <span>(Ra_c propto B_n^{-1} M_n Lambda _n C_n^{-1} Lambda _s)</span>, providing a practical predictive compass for the onset of buoyancy-driven multiphase convection in subsurface storage and geo-energy systems.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"153 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}