Permeability Parameterizations

Methods

A number of permeability parameterisations are implemented, which can be set with:

GeoParams.MaterialParameters.Permeability.ConstantPermeability Type

ConstantPermeability(k = 1e-12m^2)

Defines a constant permeability value for a given material.

Arguments

• k: The permeability value in square meters (m^2). Default is 1e-12 m^2.

Example

julia> rheology = SetMaterialParams(;
           Phase = 1,
           CreepLaws = (PowerlawViscous(), LinearViscous(; η = 1e21Pa * s)),
           Gravity = ConstantGravity(; g = 9.81m / s^2),
           Density = MeltDependent_Density(),
           Permeability = ConstantPermeability(; k = 1e-12m^2),
       );

julia> rheology.Permeability[1]
Constant permeability: k=1.0e-12 m²·⁰

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GeoParams.MaterialParameters.Permeability.HazenPermeability Type

HazenPermeability(C = 1.0 * NoUnits, D10 = 1e-4m)

Defines the Hazen permeability equation for a given material.

$$k=C\cdot D_{10}^2$$

Arguments

• C: The Hazen constant. Default is 1.0.

• D10: The effective grain size. Default is 1e-4 m.

Example

julia> rheology = SetMaterialParams(;
           Phase = 1,
           CreepLaws = (PowerlawViscous(), LinearViscous(; η = 1e21Pa * s)),
           Gravity = ConstantGravity(; g = 9.81m / s^2),
           Density = MeltDependent_Density(),
           Permeability = HazenPermeability(; C = 1.0, D10 = 1e-4m),
       );

julia> rheology.Permeability[1]
Hazen permeability: k = C * D10^2; C=1.0; D10=0.0001

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GeoParams.MaterialParameters.Permeability.PowerLawPermeability Type

PowerLawPermeability(c = 1.0, k0 = 1e-12m^2, ϕ = 1e-2, n = 3)

Defines the power-law permeability equation for a given material.

$$c\ast k_0\ast {\varphi }^n$$

Arguments

• c: The power-law constant. Default is 1.0.

• k0: The reference permeability. Default is 1e-12 m^2.

• ϕ: The reference porosity. Default is 1e-2.

• n: The exponent. Default is 3.

Example

julia> rheology = SetMaterialParams(;
           Phase = 1,
           CreepLaws = (PowerlawViscous(), LinearViscous(; η = 1e21Pa * s)),
           Gravity = ConstantGravity(; g = 9.81m / s^2),
           Density = MeltDependent_Density(),
           Permeability = PowerLawPermeability(; c = 1.0, k0 = 1e-12m^2, ϕ = 1e-2, n = 3),
       );

julia> rheology.Permeability[1]
Power-law permeability: k = c* k0 * ϕ^n; c = 1.0, k0=1.0e-12; n=3.0

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GeoParams.MaterialParameters.Permeability.CarmanKozenyPermeability Type

CarmanKozenyPermeability(c = 1.0m^2, ϕ0 = 0.01, n = 3)

Defines the Carman-Kozeny permeability equation for a given material.

$$k=c{\left(\frac{\varphi }{{\varphi }_0}\right)}^n$$

Arguments

• c: The Carman-Kozeny constant. Default is 1.0 m^2.

• ϕ0: The reference porosity. Default is 0.01.

• n: The exponent. Default is 3.

Example

julia> rheology = SetMaterialParams(;
           Phase = 1,
           CreepLaws = (PowerlawViscous(), LinearViscous(; η = 1e21Pa * s)),
           Gravity = ConstantGravity(; g = 9.81m / s^2),
           Density = MeltDependent_Density(),
           Permeability = CarmanKozenyPermeability(; c = 1.0m^2, ϕ0 = 0.01, n = 3),
       );

julia> rheology.Permeability[1]
Carman-Kozeny permeability: k = c * (ϕ / ϕ0)^n; c=1.0; ϕ0=0.01; n=3.0

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Computational routines

To compute the permeability, use:

GeoParams.MaterialParameters.Permeability.compute_permeability! Function

compute_permeability!(k::AbstractArray{_T, N}, MatParam::NTuple{K,AbstractMaterialParamsStruct}, PhaseRatios::AbstractArray{_T, M}, P=nothing, T=nothing)

In-place computation of permeability k for the whole domain and all phases, in case a vector with phase properties MatParam is provided, along with P and T arrays. This assumes that the PhaseRatio of every point is specified as an Integer in the PhaseRatios array, which has one dimension more than the data arrays (and has a phase fraction between 0-1)

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GeoParams.MaterialParameters.Permeability.compute_permeability Function

compute_permeability(k::AbstractPermeability, args)

Computation of permeability k for the whole domain and all phases, in case a vector with phase properties MatParam is provided.

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