Fronts.PorousModels module: unsaturated flow models

abstract type UnsaturatedFlowModel end

Abstract type for unsaturated flow models.

Implementation

To define a new model, make your model a subtype of UnsaturatedFlowModel and provide definitions for the relevant methods.

See also: θh, hθ, Ch, Cθ, Kh, Kθ, Dθ

BrooksAndCorey(; n, Ks=1, l=1, α=1, θr=0, θs=1) <: UnsaturatedFlowModel
BrooksAndCorey(; n, k, l=1, α=1, θr=0, θs=1, ρ=1e3, μ=1e-3, g=9.81) <: UnsaturatedFlowModel

Create a Brooks and Corey porous model.

Keyword arguments

• n: n parameter.
• Ks=1: saturated hydraulic conductivity.
• k: intrinsic permeability.
• l=1: l parameter.
• α=1 (\alpha<tab>): α parameter.
• θr=0 (\theta<tab>r): residual moisture content.
• θs=1 (\theta<tab>s): moisture content when saturated.
• ρ=1e3 (\rho<tab>): density of the fluid.
• μ=1e-3 (\mu<tab>): dynamic viscosity of the fluid.
• g=9.81: magnitude of the gravitational acceleration.

References

BROOKS, R.; COREY, T. Hydraulic properties of porous media. Hydrology Papers, Colorado State University, 1964, vol. 24, p. 37.

VanGenuchten(; n, Ks=1, l=0.5, α=1, θr=0, θs=1) <: UnsaturatedFlowModel
VanGenuchten(; m, Ks=1, l=0.5, α=1, θr=0, θs=1) <: UnsaturatedFlowModel
VanGenuchten(; n, k, l=0.5, α=1, θr=0, θs=1, ρ=1e3, μ=1e-3, g=9.81) <: UnsaturatedFlowModel
VanGenuchten(; m, k, l=0.5, α=1, θr=0, θs=1, ρ=1e3, μ=1e-3, g=9.81) <: UnsaturatedFlowModel

Create a Van Genuchten porous model.

Keyword arguments

• n, m: n or m parameter (the parameters are related by m = 1-1/n).
• Ks=1: saturated hydraulic conductivity.
• k: intrinsic permeability.
• l=0.5: l parameter.
• α=1 (\alpha<tab>): α parameter.
• θr=0 (\theta<tab>r): residual moisture content.
• θs=1 (\theta<tab>s): moisture content when saturated.
• ρ=1e3 (\rho<tab>): density of the fluid.
• μ=1e-3 (\mu<tab>): viscosity of the fluid.
• g=9.81: magnitude of the gravitational acceleration.

References

VAN GENUCHTEN, M. Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, vol. 44, no 5, p. 892-898.

LETxs(; Lw, Ew, Tw, Ls, Es, Ts, Ks=1, α=1, θr=0, θs=1) <: UnsaturatedFlowModel
LETxs(; Lw, Ew, Tw, Ls, Es, Ts, k, α=1, θr=0, θs=1, ρ=1e3, μ=1e-3, g=9.81) <: UnsaturatedFlowModel

Create a LETxs porous model.

Keyword arguments

• Lw, Ew, Tw: shape parameters for the LETx permeability correlation.
• Ls, Es, Ts: shape parameters for the LETs capillary pressure correlation.
• Ks=1: saturated hydraulic conductivity.
• k: intrinsic permeability.
• α=1 (\alpha<tab>): α parameter.
• θr=0 (\theta<tab>r): residual moisture content.
• θs=1 (\theta<tab>s): moisture content when saturated.
• ρ=1e3 (\rho<tab>): density of the fluid.
• μ=1e-3 (\mu<tab>): viscosity of the fluid.
• g=9.81: magnitude of the gravitational acceleration.

References

LOMELAND, F. Overview of the LET family of versatile correlations for flow functions. In: Proceedings of the International Symposium of the Society of Core Analysts, 2018, p. SCA2018-056.

GERLERO, G. S.; VALDEZ, A.; URTEAGA, R; KLER, P. A. Validity of capillary imbibition models in paper-based microfluidic applications. Transport in Porous Media, 2022, vol. 141, no. 7, p. 1-20.

LETd(; L, E, T, Dwt=1, θr=0, θs=1) <: UnsaturatedFlowModel

Create a LETd porous model.

Keyword arguments

• L, E, T: shape parameters for the LETd moisture diffusivity correlation.
• Dwt=1: constant diffusivity factor.
• θr=0 (\theta<tab>r): residual moisture content.
• θs=1 (\theta<tab>s): moisture content when saturated.

References

GERLERO, G. S.; VALDEZ, A.; URTEAGA, R; KLER, P. A. Validity of capillary imbibition models in paper-based microfluidic applications. Transport in Porous Media, 2022, vol. 141, no. 7, p. 1-20.

Fronts.DiffusionEquation(pm::UnsaturatedFlowModel)
Fronts.DiffusionEquation{m}(pm::UnsaturatedFlowModel)

Moisture diffusivity equation (with unknown θ) defined with the given unsaturated flow model.

Arguments

• pm: unsaturated flow model.

Type parameters

• m=1: number of spatial dimensions:
  • 1 for non-radial one-dimensional diffusion (default);
  • 2 for radial diffusion in polar or cylindrical coordinates;
  • 3 for radial diffusion in spherical coordinates.

RichardsEquation(pm::UnsaturatedFlowModel)
RichardsEquation{m}(pm::UnsaturatedFlowModel)

Richards equation (with unknown h) defined with the given unsaturated flow model.

Arguments

• pm: unsaturated flow model.

Type parameters

• m=1: number of spatial dimensions:
  • 1 for non-radial one-dimensional diffusion (default);
  • 2 for radial diffusion in polar or cylindrical coordinates;
  • 3 for radial diffusion in spherical coordinates.

θh(::UnsaturatedFlowModel, h)

Using the given model, evaluate the moisture content θ for the pressure head h.

Implementation

For this function to work with a custom model, the model needs to define a method.

hθ(::UnsaturatedFlowModel, θ)¡

Using the given model, evaluate the pressure head h for the moisture content θ.

Implementation

For this function to work with a custom model, the model needs to define a method.

Ch(::UnsaturatedFlowModel, h)

Using the given model, evaluate the capillary capacity C for the pressure head h.

Implementation

For this function to work with a custom model, the model needs to define a method, or alternatively a method of θh.

See also: θh

Cθ(::UnsaturatedFlowModel, θ)

Using the given model, evaluate the capillary capacity C for the moisture content θ.

Implementation

For this function to work with a custom model, the model needs to define a method of it or methods of hθ and Ch (or θh).

See also: hθ, Ch, θh

Kh(::UnsaturatedFlowModel, h)

Using the given model, evaluate the hydraulic conductivity K for the pressure head h.

Implementation

For this function to work with a custom model, the model needs to define a method of it or methods of Kθ and θh.

See also: Kθ, θh

Kθ(::UnsaturatedFlowModel, θ)

Using the given model, evaluate the hydraulic conductivity K for the moisture content θ.

Implementation

For this function to work with a custom model, the model needs to define a method of it or methods of Kh and hθ.

See also: Kh, hθ

Dθ(::UnsaturatedFlowModel, θ)

Obtain the moisture diffusivity D that corresponds to the volumetric water content θ with a given model.

Implementation

A default definition of this function exists for any custom UnsaturatedFlowModels that define methods of Kθ (or Kh and hθ) and Cθ (or one of Ch/θh).

See also: Kθ, Kh, hθ, Cθ, Ch, θh