Bugfix: Corrected computation of l_dry as geometric mean of the thermal...

Bugfix: Corrected computation of l_dry as geometric mean of the thermal conductivity of the solid and the fluid phase, as it is done for l_sat. Adapted documentation.

git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@10328 2fb0f335-1f38-0410-981e-8018bf24f1b0

dumux/material/fluidmatrixinteractions/2p/thermalconductivitysomerton.hh

@@ -35,9 +35,25 @@ namespace Dumux
  *
  *  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. It is assumed, that the
- *  non-wetting phase does not contribute to the conduction due to a large contrast
- *  in the fluid conductivities.
+ *  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:
+ * \f[
+ \lambda_\text{eff} = \lambda_{\text{dry}} + \sqrt{(S_w)} \left(\lambda_\text{wet} - \lambda_\text{dry}\right)
+ \f]
+ *
+ * with
+ * \f[
+ \lambda_\text{wet} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi
+ \f]
+ * and
+ *
+ * \f[
+ \lambda_\text{dry} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_n^\phi.
+ \f]
+ *
  */
 template<class Scalar>
 class ThermalConductivitySomerton
@@ -46,11 +62,6 @@ public:
     /*!
      * \brief Returns the effective thermal conductivity \f$[W/(m K)]\f$ after Somerton (1974).
      *
-     * The material law is:
-     * \f[
-     l_eff = l_solid + \sqrt(S_w)(l_wet - l_solid)
-     \f]
-     *
      * \param Sw The saturation of the wetting phase
      * \param lambdaW the thermal conductivity of the wetting phase
      * \param lambdaN the thermal conductivity of the non-wetting phase
@@ -58,6 +69,12 @@ public:
      * \param porosity The porosity
      *
      * \return Effective thermal conductivity \f$[W/(m K)]\f$ after Somerton (1974)
+     *
+     * This gives an interpolation of the effective thermal conductivities of a porous medium
+     * filled with the non-wetting 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.
      */
     static Scalar effectiveThermalConductivity(const Scalar Sw,
                                                const Scalar lambdaW,
@@ -66,8 +83,9 @@ public:
                                                const Scalar porosity)
     {
         const Scalar satW = std::max<Scalar>(0.0, Sw);
+        // geometric means
         const Scalar lSat = std::pow(lambdaSolid, (1.0 - porosity)) * std::pow(lambdaW, porosity);
-        const Scalar lDry = std::pow(lambdaSolid, (1.0 - porosity));
+        const Scalar lDry = std::pow(lambdaSolid, (1.0 - porosity)) * std::pow(lambdaN, porosity);
 
         return lDry + std::sqrt(satW) * (lSat - lDry);
     }