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version 3.8
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Relation for the saturation-dependent effective thermal conductivity. More...
#include <dumux/material/fluidmatrixinteractions/2p/thermalconductivity/somerton.hh>
The Somerton method computes the thermal conductivity of dry and the wet soil material and uses a root function of the wetting saturation to compute the effective thermal conductivity for a two-phase fluidsystem. The individual thermal conductivities are calculated as geometric mean of the thermal conductivity of the porous material and of the respective fluid phase.
The material law is: \(\mathrm{ \lambda_\text{eff} = \lambda_{\text{dry}} + \sqrt{(S_w)} \left(\lambda_\text{wet} - \lambda_\text{dry}\right) }\)
with \(\mathrm{ \lambda_\text{wet} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi }\) and
\(\mathrm{ \lambda_\text{dry} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_n^\phi. }\)
The Somerton method computes the thermal conductivity of dry and the wet soil material. It is extended here to a three phase system of water (w), NAPL (n) and gas (g). It uses a root function of the water and NAPL saturation to compute the effective thermal conductivity for a three-phase fluidsystem. The individual thermal conductivities are calculated as geometric mean of the thermal conductivity of the porous material and of the respective fluid phase.
The material law is:
\[ \lambda_\text{eff} = \lambda_\text{g,eff} + \sqrt{(S_w)} \left(\lambda_\text{w,eff} - \lambda_\text{g,eff}\right) + \sqrt{(S_n)} \left(\lambda0_\text{n,eff} - \lambda_\text{g,eff}\right) \]
with
\[ \lambda_\text{w,eff} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi \]
and
\[ \lambda0_\text{n,eff} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_n^\phi. \]
\[ \lambda_\text{g,eff} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_g^\phi. \]
Static Public Member Functions | |
| template<class VolumeVariables > | |
| static Scalar | effectiveThermalConductivity (const VolumeVariables &volVars) |
| effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Somerton (1974) [73] More... | |
| template<class VolumeVariables > | |
| static Scalar | effectiveThermalConductivity (const VolumeVariables &volVars) |
| effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Somerton (1974) extended for a three phase system More... | |
| static Scalar | effectiveThermalConductivity (const Scalar sw, const Scalar sn, const Scalar lambdaW, const Scalar lambdaN, const Scalar lambdaG, const Scalar lambdaSolid, const Scalar porosity) |
| effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Somerton (1974) More... | |
|
inlinestatic |
| sw | The saturation of the wetting phase |
| sn | The saturation of the nonwetting phase |
| lambdaW | The thermal conductivity of the water phase in \(\mathrm{[W/(m K)]}\) |
| lambdaN | The thermal conductivity of the NAPL phase in \(\mathrm{[W/(m K)]}\) |
| lambdaG | The thermal conductivity of the gas phase in \(\mathrm{[W/(m K)]}\) |
| lambdaSolid | The thermal conductivity of the solid phase in \(\mathrm{[W/(m K)]}\) |
| porosity | The porosity |
|
inlinestatic |
| volVars | volume variables |
This gives an interpolation of the effective thermal conductivities of a porous medium filled with the nonwetting phase and a porous medium filled with the wetting phase. These two effective conductivities are computed as geometric mean of the solid and the fluid conductivities and interpolated with the square root of the wetting saturation. See f.e. Ebigbo, A.: Thermal Effects of Carbon Dioxide Sequestration in the Subsurface, Diploma thesis [26] .
|
inlinestatic |
| volVars | volume variables |
This gives an interpolation of the effective thermal conductivities of a porous medium filled with the water phase (w), a NAPL phase (n) and a gas phase (g). These two effective conductivities are computed as geometric mean of the solid and the fluid conductivities and interpolated with the square root of the wetting saturation.
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