Anna L. Herring, Ruotong Huang (黄若橦), Adrian Sheppard
{"title":"Directionality of gravitational and thermal diffusive transport in geologic fluid storage","authors":"Anna L. Herring, Ruotong Huang (黄若橦), Adrian Sheppard","doi":"10.1103/physreve.110.015106","DOIUrl":null,"url":null,"abstract":"Diffusive transport has implications for the long-term status of underground storage of hydrogen <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub><mo>)</mo></math> fuel and carbon dioxide <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi>CO</mi><mn>2</mn></msub><mo>)</mo></math>, technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport (“Ostwald ripening”). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math>, even geothermal gradients less than <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>10</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math> (far less than typical gradients of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>25</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math>) are sufficient to induce downwards diffusion at depths relevant to storage. Diffusive transport of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> is less affected but still reverses direction under typical gradients, e.g., <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>30</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math>, at a depth of 1000 m. This reversal occurs independent of the solute's thermophobicity or thermophilicity in aqueous solutions. The entropic contribution also modifies the magnitude of flux where geothermal gradients are present, with the largest diffusive fluxes estimated for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> with a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>30</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math> gradient, despite the higher diffusion coefficient of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math>. We find a maximum flux on the order of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>mol</mi><mo>/</mo><mo>(</mo><msup><mrow><mi>cm</mi></mrow><mn>2</mn></msup><mi mathvariant=\"normal\">s</mi><mo>)</mo></mrow></math> for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>30</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math> scenario; significantly lower than literature estimates for maximum convective fluxes in moderate to high permeability formations. Contrary to previous studies, we find that in diffusion and convection will likely work in concert—both driving <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> downwards, and both driving <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> upwards—for conditions representative of their respective storage reservoirs.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.015106","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Diffusive transport has implications for the long-term status of underground storage of hydrogen fuel and carbon dioxide , technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, and will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport (“Ostwald ripening”). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved and driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for and at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For , even geothermal gradients less than (far less than typical gradients of ) are sufficient to induce downwards diffusion at depths relevant to storage. Diffusive transport of is less affected but still reverses direction under typical gradients, e.g., , at a depth of 1000 m. This reversal occurs independent of the solute's thermophobicity or thermophilicity in aqueous solutions. The entropic contribution also modifies the magnitude of flux where geothermal gradients are present, with the largest diffusive fluxes estimated for with a gradient, despite the higher diffusion coefficient of . We find a maximum flux on the order of for in the scenario; significantly lower than literature estimates for maximum convective fluxes in moderate to high permeability formations. Contrary to previous studies, we find that in diffusion and convection will likely work in concert—both driving downwards, and both driving upwards—for conditions representative of their respective storage reservoirs.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.