{"title":"多孔介质中的不溶两相流:连续极限中的有效流变学","authors":"Subhadeep Roy, Santanu Sinha, Alex Hansen","doi":"10.1007/s11242-024-02073-0","DOIUrl":null,"url":null,"abstract":"<div><p>We consider steady-state immiscible and incompressible two-phase flow in porous media. It is becoming increasingly clear that there is a flow regime where the volumetric flow rate depends on the pressure gradient as a power law with an exponent larger than one. This occurs when the capillary forces and viscous forces compete. At higher flow rates, where the viscous forces dominate, the volumetric flow rate depends linearly on the pressure gradient. This means that there is a crossover pressure gradient that separates these two flow regimes. At small enough pressure gradient, the capillary forces dominate. If one or both of the immiscible fluids percolate, the volumetric flow rate will then depend linearly on the pressure gradient as the interfaces will not move. If none of the fluids percolate, there will be a minimum pressure gradient threshold to mobilize the interfaces and thereby get the fluids moving. We now imagine a core sample of a given size. The question we pose is what happens to the crossover pressure gradient that separates the power-law regime from the high-flow rate linear regime and the threshold pressure gradient that blocks the flow at low pressure gradients when the size of the core sample is increased. Based on analytical calculations using the capillary bundle model and on numerical simulations using a dynamical pore-network model, we find that the crossover pressure gradient and the threshold pressure gradient decrease with two distinct power laws in the size. This means that the power-law regime disappears in the continuum limit where the pores are infinitely small compared to the sample size.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-024-02073-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Immiscible Two-Phase Flow in Porous Media: Effective Rheology in the Continuum Limit\",\"authors\":\"Subhadeep Roy, Santanu Sinha, Alex Hansen\",\"doi\":\"10.1007/s11242-024-02073-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider steady-state immiscible and incompressible two-phase flow in porous media. It is becoming increasingly clear that there is a flow regime where the volumetric flow rate depends on the pressure gradient as a power law with an exponent larger than one. This occurs when the capillary forces and viscous forces compete. At higher flow rates, where the viscous forces dominate, the volumetric flow rate depends linearly on the pressure gradient. This means that there is a crossover pressure gradient that separates these two flow regimes. At small enough pressure gradient, the capillary forces dominate. If one or both of the immiscible fluids percolate, the volumetric flow rate will then depend linearly on the pressure gradient as the interfaces will not move. If none of the fluids percolate, there will be a minimum pressure gradient threshold to mobilize the interfaces and thereby get the fluids moving. We now imagine a core sample of a given size. The question we pose is what happens to the crossover pressure gradient that separates the power-law regime from the high-flow rate linear regime and the threshold pressure gradient that blocks the flow at low pressure gradients when the size of the core sample is increased. Based on analytical calculations using the capillary bundle model and on numerical simulations using a dynamical pore-network model, we find that the crossover pressure gradient and the threshold pressure gradient decrease with two distinct power laws in the size. This means that the power-law regime disappears in the continuum limit where the pores are infinitely small compared to the sample size.</p></div>\",\"PeriodicalId\":804,\"journal\":{\"name\":\"Transport in Porous Media\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11242-024-02073-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transport in Porous Media\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11242-024-02073-0\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, CHEMICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport in Porous Media","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11242-024-02073-0","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
Immiscible Two-Phase Flow in Porous Media: Effective Rheology in the Continuum Limit
We consider steady-state immiscible and incompressible two-phase flow in porous media. It is becoming increasingly clear that there is a flow regime where the volumetric flow rate depends on the pressure gradient as a power law with an exponent larger than one. This occurs when the capillary forces and viscous forces compete. At higher flow rates, where the viscous forces dominate, the volumetric flow rate depends linearly on the pressure gradient. This means that there is a crossover pressure gradient that separates these two flow regimes. At small enough pressure gradient, the capillary forces dominate. If one or both of the immiscible fluids percolate, the volumetric flow rate will then depend linearly on the pressure gradient as the interfaces will not move. If none of the fluids percolate, there will be a minimum pressure gradient threshold to mobilize the interfaces and thereby get the fluids moving. We now imagine a core sample of a given size. The question we pose is what happens to the crossover pressure gradient that separates the power-law regime from the high-flow rate linear regime and the threshold pressure gradient that blocks the flow at low pressure gradients when the size of the core sample is increased. Based on analytical calculations using the capillary bundle model and on numerical simulations using a dynamical pore-network model, we find that the crossover pressure gradient and the threshold pressure gradient decrease with two distinct power laws in the size. This means that the power-law regime disappears in the continuum limit where the pores are infinitely small compared to the sample size.
期刊介绍:
-Publishes original research on physical, chemical, and biological aspects of transport in porous media-
Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)-
Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications-
Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes-
Expanded in 2007 from 12 to 15 issues per year.
Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).