Analytical solution of coupled stress-flow-transport processes in a single rock fracture
A closed-form solution is presented for modeling the coupled stress-flow-transport processes along a single fracture embedded in a porous rock matrix. Necessary assumptions were made to simplify the subject into a two-dimensional (2D) problem, considering the changes of fracture aperture and matrix...
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| Published in | Computers & geosciences Vol. 37; no. 9; pp. 1437 - 1449 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.09.2011
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0098-3004 1873-7803 1873-7803 |
| DOI | 10.1016/j.cageo.2011.02.015 |
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| Abstract | A closed-form solution is presented for modeling the coupled stress-flow-transport processes along a single fracture embedded in a porous rock matrix. Necessary assumptions were made to simplify the subject into a two-dimensional (2D) problem, considering the changes of fracture aperture and matrix porosity under various stress conditions. The cubic law was assumed to be valid for the fluid flow in the fracture, with an impermeable rock matrix. For transport mechanisms, advective transport along the fracture, longitudinal hydrodynamic dispersion in the flow direction, and the matrix diffusion were considered in three different transport models under constant concentration or constant flux (Danckwerts') inlet boundary conditions. This analytical solution can be used as a constitutive model, or as an example for validation of similar constitutive models, for modeling the coupled hydro-mechanical-chemical (HMC) processes in fracture networks of crystalline rocks. The influences of stress/deformation processes on different transport mechanisms in a single fracture under different inlet boundary conditions were studied for the first time. The results show that changes of fracture, as controlled by a combination of normal closure and shear dilatancy, have a significant influence on the solute concentration distribution both along the fracture and in the rock matrix, as well as on the solute residence/breakthrough time, especially when shear-induced dilatancy occurs. Under compressions, the decreasing matrix porosity slightly increases the solute concentration along the fracture and in the rock matrix. |
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| AbstractList | A closed-form solution is presented for modeling the coupled stress-flow-transport processes along a single fracture embedded in a porous rock matrix. Necessary assumptions were made to simplify the subject into a two-dimensional (2D) problem, considering the changes of fracture aperture and matrix porosity under various stress conditions. The cubic law was assumed to be valid for the fluid flow in the fracture, with an impermeable rock matrix. For transport mechanisms, advective transport along the fracture, longitudinal hydrodynamic dispersion in the flow direction, and the matrix diffusion were considered in three different transport models under constant concentration or constant flux (Danckwerts') inlet boundary conditions. This analytical solution can be used as a constitutive model, or as an example for validation of similar constitutive models, for modeling the coupled hydro-mechanical-chemical (HMC) processes in fracture networks of crystalline rocks. The influences of stress/deformation processes on different transport mechanisms in a single fracture under different inlet boundary conditions were studied for the first time. The results show that changes of fracture, as controlled by a combination of normal closure and shear dilatancy, have a significant influence on the solute concentration distribution both along the fracture and in the rock matrix, as well as on the solute residence/breakthrough time, especially when shear-induced dilatancy occurs. Under compressions, the decreasing matrix porosity slightly increases the solute concentration along the fracture and in the rock matrix. A closed-form solution is presented for modeling the coupled stress-flow-transport processes along a single fracture embedded in a porous rock matrix. Necessary assumptions were made to simplify the subject into a two-dimensional (2D) problem, considering the changes of fracture aperture and matrix porosity under various stress conditions. The cubic law was assumed to be valid for the fluid flow in the fracture, with an impermeable rock matrix. For transport mechanisms, advective transport along the fracture, longitudinal hydrodynamic dispersion in the flow direction, and the matrix diffusion were considered in three different transport models under constant concentration or constant flux (Danck- werts’) inlet boundary conditions. This analytical solution can be used as a constitutive model, or as an example for validation of similar constitutive models, for modeling the coupled hydro-mechanical- chemical (HMC) processes in fracture networks of crystalline rocks. The influences of stress/deformation processes on different transport mechanisms in a single fracture under different inlet boundary conditions were studied for the first time. The results show that changes of fracture, as controlled by a combination of normal closure and shear dilatancy, have a significant influence on the solute concentration distribution both along the fracture and in the rock matrix, as well as on the solute residence/breakthrough time, especially when shear-induced dilatancy occurs. Under compressions, the decreasing matrix porosity slightly increases the solute concentration along the fracture and in the rock matrix. |
| Author | Neretnieks, Ivars Moreno, Luis Jing, Lanru Zhao, Zhihong |
| Author_xml | – sequence: 1 givenname: Zhihong surname: Zhao fullname: Zhao, Zhihong email: zhzhao@kth.se organization: Department of Land and Water Resources Engineering, Royal Institute of Technology, Sweden – sequence: 2 givenname: Lanru surname: Jing fullname: Jing, Lanru organization: Department of Land and Water Resources Engineering, Royal Institute of Technology, Sweden – sequence: 3 givenname: Ivars surname: Neretnieks fullname: Neretnieks, Ivars organization: Department of Chemical Engineering and Technology, Royal Institute of Technology, Sweden – sequence: 4 givenname: Luis surname: Moreno fullname: Moreno, Luis organization: Department of Chemical Engineering and Technology, Royal Institute of Technology, Sweden |
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| Keywords | Single rock fractures Transport Analytical solution Stress Fluid flow diffusion rock matrix fracture networks dilatancy deformation boundary conditions flow fractures computers direction stress models solutes shear porosity crystalline rocks data processing concentration hydrodynamics transport compression dispersion |
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| SubjectTerms | Analytical solution computers Constitutive relationships Crystalline rocks deformation Earth sciences Earth, ocean, space Exact sciences and technology Fluid flow Fracture mechanics hydrodynamic dispersion Hydrology Hydrology. Hydrogeology Igneous and metamorphic rocks petrology, volcanic processes, magmas Mathematical analysis Mathematical models porosity Rock rocks Single rock fractures solutes Stress Stress concentration Transport |
| Title | Analytical solution of coupled stress-flow-transport processes in a single rock fracture |
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