Permeability

A porous material's insitu permeability tensor can take one of several forms. It can be constant, spatially varying, or depend on porosity.

Constant: PorousFlowPermeabilityConst

The simplest case where the permeability tensor is a constant tensor.

Spatially-varying: PorousFlowPermeabilityConstFromVar

To implement a heterogeneous permeability distribution, PorousFlow also provides a permeability formulation where the elements of the permeability tensor can be AuxVariables, enabling permeability to vary spatially.

Exponential: PorousFlowPermeabilityExponential

A simple porosity-permeability model where $var element = document.getElementById("moose-equation-382f0fc4-5e61-448d-a396-527684ee11d3");katex.render("k_{ij} = k_{ij}^{0} e^{a\\phi} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-eb7798f4-b7e1-4ad0-8cf8-71d692d9930e");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porosity, and $var element = document.getElementById("moose-equation-ea752230-e1f7-4339-91b4-8c66dea75393");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a user-defined constant.

Kozeny-Carman: PorousFlowPermeabilityKozenyCarman

Permeability is calculated from porosity using the Kozeny-Carman relationship (Oelkers, 1996) $var element = document.getElementById("moose-equation-58116ea1-a351-4edb-8b8e-4dc06f8ef795");katex.render("k_{ij} = k_{ij}^{0} \\frac{\\phi^{n}}{(1 - \\phi)^{m}},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-2c1f043e-bc97-48fe-84d8-803d60ecbacf");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-111c9dac-a02f-4901-8412-a59446cdab42");katex.render("m", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are user-defined constants.

Permeability with a solid phase

A solid phase (from chemical precipitation, for instance) can be included in the framework described herein simply by setting its relative permeability to zero. However, in this case, the absolute permeability of the porous material should be $var element = document.getElementById("moose-equation-de40d794-e6c3-4bbc-85e8-6b4f4f08f5f6");katex.render("k = k^{\\mathrm{without\\ solid\\ phase}}(1 - S_{\\mathrm{s}})^{2} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-7b2bdadf-0bf3-4e17-bcf4-db8ad4e95f4a");katex.render("S_{\\mathrm{s}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the solid-phase saturation.

References

E. H. Oelkers. Physical and chemical properties of rocks and fluids for chemical mass transport calculations. Reviews in Mineralogy and Geochemistry, 34:131–191, 1996.

@article{oelkers1996,
    author = "Oelkers, E. H.",
    title = "Physical and chemical properties of rocks and fluids for chemical mass transport calculations",
    journal = "Reviews in Mineralogy and Geochemistry",
    volume = "34",
    pages = "131--191",
    year = "1996"
}

Constant : PorousFlowPermeabilityConst
Spatially - varying : PorousFlowPermeabilityConstFromVar
Exponential : PorousFlowPermeabilityExponential
Kozeny - Carman : PorousFlowPermeabilityKozenyCarman
Permeability with a solid phase
References