diff --git a/Applications/ApplicationsLib/ProjectData.cpp b/Applications/ApplicationsLib/ProjectData.cpp
index 95eece383956bcc27c23e692e1850f3feb30ab84..9aae20a6fa952f0b29783914d2ad15b022c7ebba 100644
--- a/Applications/ApplicationsLib/ProjectData.cpp
+++ b/Applications/ApplicationsLib/ProjectData.cpp
@@ -922,7 +922,7 @@ void ProjectData::parseProcesses(
                             name, *_mesh_vec[0], std::move(jacobian_assembler),
                             _process_variables, _parameters,
                             _local_coordinate_system, integration_order,
-                            process_config);
+                            process_config, _media);
                     break;
                 case 3:
                     process = ProcessLib::LIE::HydroMechanics::
@@ -930,7 +930,7 @@ void ProjectData::parseProcesses(
                             name, *_mesh_vec[0], std::move(jacobian_assembler),
                             _process_variables, _parameters,
                             _local_coordinate_system, integration_order,
-                            process_config);
+                            process_config, _media);
                     break;
                 default:
                     OGS_FATAL(
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_biot_coefficient.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_biot_coefficient.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_biot_coefficient.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_material_id.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_material_id.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_material_id.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_specific_storage.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_specific_storage.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/fracture_properties/t_specific_storage.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_biot_coefficient.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_biot_coefficient.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_biot_coefficient.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_density.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_density.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_density.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_viscosity.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_viscosity.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_fluid_viscosity.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_intrinsic_permeability.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_intrinsic_permeability.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_intrinsic_permeability.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_porosity.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_porosity.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_porosity.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_reference_temperature.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_reference_temperature.md
deleted file mode 100644
index ce255b04b7954788eb839b536e39a8f146dc9f1d..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_reference_temperature.md
+++ /dev/null
@@ -1 +0,0 @@
-Reference temperature, an optional input.
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_solid_density.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_solid_density.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_solid_density.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_specific_storage.md b/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_specific_storage.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/HYDRO_MECHANICS_WITH_LIE/t_specific_storage.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/Documentation/ProjectFile/properties/property/CubicLawPermeability/t_fracture_aperture.md b/Documentation/ProjectFile/properties/property/CubicLawPermeability/t_fracture_aperture.md
index 325bb3c6eed811c57e0d492aeaac38a670867400..738e2566f2f6791a8b6f9a25e4df0fe55b27c0a3 100644
--- a/Documentation/ProjectFile/properties/property/CubicLawPermeability/t_fracture_aperture.md
+++ b/Documentation/ProjectFile/properties/property/CubicLawPermeability/t_fracture_aperture.md
@@ -1 +1 @@
-Collection of fracture properties for a specific fracture given by material id.
+\copydoc MaterialPropertyLib::CubicLawPermeability::_b
diff --git a/MaterialLib/MPL/Properties/CreateCubicLawPermeability.cpp b/MaterialLib/MPL/Properties/CreateCubicLawPermeability.cpp
index d73c1519e942481348a2cf9c57a870046e84ba56..5191ac6895f1b9b4a142c5b752914ec0c4baf90e 100644
--- a/MaterialLib/MPL/Properties/CreateCubicLawPermeability.cpp
+++ b/MaterialLib/MPL/Properties/CreateCubicLawPermeability.cpp
@@ -9,6 +9,9 @@
 
 #include "CreateCubicLawPermeability.h"
 
+#include <limits>
+#include <string>
+
 #include "BaseLib/ConfigTree.h"
 #include "CubicLawPermeability.h"
 #include "ParameterLib/Utils.h"
@@ -27,10 +30,15 @@ std::unique_ptr<Property> createCubicLawPermeability(
     //! \ogs_file_param{properties__property__name}
     auto property_name = config.peekConfigParameter<std::string>("name");
 
-    auto const& b = ParameterLib::findParameter<double>(
+    auto const fracture_aperture_name =
         //! \ogs_file_param{properties__property__CubicLawPermeability__fracture_aperture}
-        config.getConfigParameter<std::string>("fracture_aperture"), parameters,
-        0, nullptr);
+        config.getConfigParameter<std::string>("fracture_aperture", "");
+
+    ParameterLib::Parameter<double>* b =
+        fracture_aperture_name == ""
+            ? nullptr
+            : &ParameterLib::findParameter<double>(
+                  fracture_aperture_name, parameters, 0, nullptr);
 
     return std::make_unique<CubicLawPermeability>(std::move(property_name), b);
 }
diff --git a/MaterialLib/MPL/Properties/CreateCubicLawPermeability.h b/MaterialLib/MPL/Properties/CreateCubicLawPermeability.h
index fee4541eb45f7b51bc74c9a714170397181f5467..97d02a32da3834d5f1e859550f8fa259266bb18e 100644
--- a/MaterialLib/MPL/Properties/CreateCubicLawPermeability.h
+++ b/MaterialLib/MPL/Properties/CreateCubicLawPermeability.h
@@ -17,14 +17,14 @@ namespace BaseLib
 class ConfigTree;
 }
 
-namespace MaterialPropertyLib
+namespace ParameterLib
 {
-class Property;
+struct ParameterBase;
 }
 
-namespace ParameterLib
+namespace MaterialPropertyLib
 {
-struct ParameterBase;
+class Property;
 }
 
 namespace MaterialPropertyLib
diff --git a/MaterialLib/MPL/Properties/CubicLawPermeability.cpp b/MaterialLib/MPL/Properties/CubicLawPermeability.cpp
index abb8ca587aa1f8b2b4319116d386a8d16f0e4bbc..8c609106dcf57344e30096be76f1d2b44cc8a5e7 100644
--- a/MaterialLib/MPL/Properties/CubicLawPermeability.cpp
+++ b/MaterialLib/MPL/Properties/CubicLawPermeability.cpp
@@ -11,20 +11,34 @@
 
 namespace MaterialPropertyLib
 {
+CubicLawPermeability::CubicLawPermeability(
+    std::string name, ParameterLib::Parameter<double> const* b)
+    : _b(b)
+{
+    name_ = std::move(name);
+}
+
 PropertyDataType CubicLawPermeability::value(
-    VariableArray const& /*variable_array*/,
+    VariableArray const& variable_array,
     ParameterLib::SpatialPosition const& pos, double const t,
     double const /*dt*/) const
 {
-    double const aperture_m = _b(t, pos)[0];
+    double const aperture_m =
+        _b ? (*_b)(t, pos)[0] : variable_array.fracture_aperture;
+
     return aperture_m * aperture_m / 12;
 }
 
 PropertyDataType CubicLawPermeability::dValue(
-    VariableArray const& /*variable_array*/, Variable const /*variable*/,
+    VariableArray const& variable_array, Variable const variable,
     ParameterLib::SpatialPosition const& /*pos*/, double const /*t*/,
     double const /*dt*/) const
 {
-    OGS_FATAL("CubicLawPermeability::dValue is not implemented.");
+    if (variable != Variable::fracture_aperture || _b)
+    {
+        return 0.0;
+    }
+
+    return variable_array.fracture_aperture / 6.0;
 }
 }  // namespace MaterialPropertyLib
diff --git a/MaterialLib/MPL/Properties/CubicLawPermeability.h b/MaterialLib/MPL/Properties/CubicLawPermeability.h
index 95aec8d192fac6c3adff641424fde84928200b7f..1bc9fffbb4928d75a19142dc8c294726043c362c 100644
--- a/MaterialLib/MPL/Properties/CubicLawPermeability.h
+++ b/MaterialLib/MPL/Properties/CubicLawPermeability.h
@@ -9,8 +9,12 @@
 
 #pragma once
 
+#include <limits>
+#include <string>
+
 #include "MaterialLib/MPL/Property.h"
 #include "MaterialLib/MPL/VariableType.h"
+#include "ParameterLib/ConstantParameter.h"
 #include "ParameterLib/Parameter.h"
 
 namespace MaterialPropertyLib
@@ -37,12 +41,8 @@ namespace MaterialPropertyLib
  */
 struct CubicLawPermeability final : public Property
 {
-    explicit CubicLawPermeability(std::string name,
-                                  ParameterLib::Parameter<double> const& b)
-        : _b(b)
-    {
-        name_ = std::move(name);
-    }
+    CubicLawPermeability(std::string name,
+                         ParameterLib::Parameter<double> const* b);
 
     void checkScale() const override
     {
@@ -50,7 +50,7 @@ struct CubicLawPermeability final : public Property
         {
             OGS_FATAL(
                 "The property 'CubicLawPermeability' is implemented on the "
-                "'media' scaleonly.");
+                "'media' scale only.");
         }
     }
 
@@ -65,7 +65,7 @@ struct CubicLawPermeability final : public Property
                             double const t, double const dt) const override;
 
 private:
-    /// fracture aperture
-    ParameterLib::Parameter<double> const& _b;
+    /// Predefined fracture aperture.
+    ParameterLib::Parameter<double> const* _b = nullptr;
 };
 }  // namespace MaterialPropertyLib
diff --git a/MaterialLib/MPL/VariableType.cpp b/MaterialLib/MPL/VariableType.cpp
index 491f3759aaa5c64a982394c49961e10a43728edc..7a7b97083cfdc168b8e7ae2ce9357e9041e6860b 100644
--- a/MaterialLib/MPL/VariableType.cpp
+++ b/MaterialLib/MPL/VariableType.cpp
@@ -60,6 +60,8 @@ VariableArray::VariablePointerConst VariableArray::address_of(
             return &enthalpy_of_evaporation;
         case Variable::equivalent_plastic_strain:
             return &equivalent_plastic_strain;
+        case Variable::fracture_aperture:
+            return &fracture_aperture;
         case Variable::grain_compressibility:
             return &grain_compressibility;
         case Variable::liquid_phase_pressure:
diff --git a/MaterialLib/MPL/VariableType.h b/MaterialLib/MPL/VariableType.h
index f7351bd46901bd94f081e4db37cac38dcecf0221..2d4f3ea84af620df67765dcaa4baa8d1f4269ad2 100644
--- a/MaterialLib/MPL/VariableType.h
+++ b/MaterialLib/MPL/VariableType.h
@@ -36,6 +36,7 @@ enum class Variable : int
     enthalpy,
     enthalpy_of_evaporation,
     equivalent_plastic_strain,
+    fracture_aperture,
     grain_compressibility,
     liquid_phase_pressure,
     liquid_saturation,
@@ -66,6 +67,7 @@ static const std::array<std::string,
                              "enthalpy",
                              "enthalpy_of_evaporation",
                              "equivalent_plastic_strain",
+                             "fracture_aperture",
                              "grain_compressibility",
                              "liquid_phase_pressure",
                              "liquid_saturation",
@@ -174,6 +176,7 @@ public:
     double enthalpy = nan_;
     double enthalpy_of_evaporation = nan_;
     double equivalent_plastic_strain = nan_;
+    double fracture_aperture = nan_;
     double grain_compressibility = nan_;
     double liquid_phase_pressure = nan_;
     double liquid_saturation = nan_;
diff --git a/ProcessLib/LIE/Common/FractureProperty.h b/ProcessLib/LIE/Common/FractureProperty.h
index 0dbddebde3ba2e4a5cb8a380fc33ce7cab1842b3..883a5a4c9d91400cdd3da6f5317251ecfd7f6033 100644
--- a/ProcessLib/LIE/Common/FractureProperty.h
+++ b/ProcessLib/LIE/Common/FractureProperty.h
@@ -53,24 +53,6 @@ struct FractureProperty
     virtual ~FractureProperty() = default;
 };
 
-struct FracturePropertyHM : public FractureProperty
-{
-    FracturePropertyHM(int const fracture_id_, int const material_id,
-                       ParameterLib::Parameter<double> const& initial_aperture,
-                       ParameterLib::Parameter<double> const& specific_storage_,
-                       ParameterLib::Parameter<double> const& biot_coefficient_)
-        : FractureProperty(fracture_id_, material_id, initial_aperture),
-          specific_storage(specific_storage_),
-          biot_coefficient(biot_coefficient_)
-    {
-    }
-    ParameterLib::Parameter<double> const& specific_storage;
-    ParameterLib::Parameter<double> const& biot_coefficient;
-
-    std::unique_ptr<MaterialLib::Fracture::Permeability::Permeability>
-        permeability_model;
-};
-
 /// configure fracture property based on a fracture element assuming
 /// a fracture is a straight line/flat plane
 inline void setFractureProperty(int const dim, MeshLib::Element const& e,
diff --git a/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.cpp b/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.cpp
index ba887104e637b90ec1c99818edf360e319b29d17..268d9f20b234052a78b069f0221e747d4af1196c 100644
--- a/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.cpp
+++ b/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.cpp
@@ -18,7 +18,13 @@
 #include "MaterialLib/FractureModels/CreateCoulomb.h"
 #include "MaterialLib/FractureModels/CreateLinearElasticIsotropic.h"
 #include "MaterialLib/FractureModels/Permeability/CreatePermeabilityModel.h"
+#include "MaterialLib/MPL/CreateMaterialSpatialDistributionMap.h"
+#include "MaterialLib/MPL/MaterialSpatialDistributionMap.h"
+#include "MaterialLib/MPL/PropertyType.h"
+#include "MaterialLib/MPL/Utils/CheckMPLPhasesForSinglePhaseFlow.h"
+#include "MaterialLib/MPL/VariableType.h"
 #include "MaterialLib/SolidModels/CreateConstitutiveRelation.h"
+#include "ParameterLib/SpatialPosition.h"
 #include "ParameterLib/Utils.h"
 #include "ProcessLib/Output/CreateSecondaryVariables.h"
 
@@ -38,7 +44,8 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
     std::optional<ParameterLib::CoordinateSystem> const&
         local_coordinate_system,
     unsigned const integration_order,
-    BaseLib::ConfigTree const& config)
+    BaseLib::ConfigTree const& config,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media)
 {
     //! \ogs_file_param{prj__processes__process__type}
     config.checkConfigParameter("type", "HYDRO_MECHANICS_WITH_LIE");
@@ -137,58 +144,6 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
         MaterialLib::Solids::createConstitutiveRelations<GlobalDim>(
             parameters, local_coordinate_system, materialIDs(mesh), config);
 
-    // Intrinsic permeability
-    auto& intrinsic_permeability = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__intrinsic_permeability}
-        "intrinsic_permeability", parameters, 1, &mesh);
-
-    DBUG("Use '{:s}' as intrinsic permeability parameter.",
-         intrinsic_permeability.name);
-
-    // Storage coefficient
-    auto& specific_storage = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__specific_storage}
-        "specific_storage", parameters, 1, &mesh);
-
-    DBUG("Use '{:s}' as specific storage parameter.", specific_storage.name);
-
-    // Fluid viscosity
-    auto& fluid_viscosity = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fluid_viscosity}
-        "fluid_viscosity", parameters, 1, &mesh);
-    DBUG("Use '{:s}' as fluid viscosity parameter.", fluid_viscosity.name);
-
-    // Fluid density
-    auto& fluid_density = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fluid_density}
-        "fluid_density", parameters, 1, &mesh);
-    DBUG("Use '{:s}' as fluid density parameter.", fluid_density.name);
-
-    // Biot coefficient
-    auto& biot_coefficient = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__biot_coefficient}
-        "biot_coefficient", parameters, 1, &mesh);
-    DBUG("Use '{:s}' as Biot coefficient parameter.", biot_coefficient.name);
-
-    // Porosity
-    auto& porosity = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__porosity}
-        "porosity", parameters, 1, &mesh);
-    DBUG("Use '{:s}' as porosity parameter.", porosity.name);
-
-    // Solid density
-    auto& solid_density = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__solid_density}
-        "solid_density", parameters, 1, &mesh);
-    DBUG("Use '{:s}' as solid density parameter.", solid_density.name);
-
     // Specific body force
     Eigen::Matrix<double, GlobalDim, 1> specific_body_force;
     {
@@ -249,7 +204,7 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
     }
 
     // Fracture properties
-    std::unique_ptr<FracturePropertyHM> frac_prop = nullptr;
+    std::unique_ptr<FractureProperty> frac_prop = nullptr;
     auto opt_fracture_properties_config =
         //! \ogs_file_param{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties}
         config.getConfigSubtreeOptional("fracture_properties");
@@ -257,21 +212,11 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
     {
         auto& fracture_properties_config = *opt_fracture_properties_config;
 
-        frac_prop = std::make_unique<ProcessLib::LIE::FracturePropertyHM>(
-            0 /*fracture_id*/,
-            //! \ogs_file_param{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties__material_id}
-            fracture_properties_config.getConfigParameter<int>("material_id"),
+        frac_prop = std::make_unique<ProcessLib::LIE::FractureProperty>(
+            0 /*fracture_id*/, 0 /*material_id*/,
             ParameterLib::findParameter<double>(
                 //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties__initial_aperture}
                 fracture_properties_config, "initial_aperture", parameters, 1,
-                &mesh),
-            ParameterLib::findParameter<double>(
-                //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties__specific_storage}
-                fracture_properties_config, "specific_storage", parameters, 1,
-                &mesh),
-            ParameterLib::findParameter<double>(
-                //! \ogs_file_param_special{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties__biot_coefficient}
-                fracture_properties_config, "biot_coefficient", parameters, 1,
                 &mesh));
         if (frac_prop->aperture0.isTimeDependent())
         {
@@ -280,13 +225,6 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
                 "time-dependent.",
                 frac_prop->aperture0.name);
         }
-
-        auto permeability_model_config =
-            //! \ogs_file_param{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__fracture_properties__permeability_model}
-            fracture_properties_config.getConfigSubtree("permeability_model");
-        frac_prop->permeability_model =
-            MaterialLib::Fracture::Permeability::createPermeabilityModel(
-                permeability_model_config);
     }
 
     // initial effective stress in matrix
@@ -317,33 +255,59 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
     if (deactivate_matrix_in_flow)
         INFO("Deactivate matrix elements in flow calculation.");
 
-    // Reference temperature
-    const auto& reference_temperature =
-        //! \ogs_file_param{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__reference_temperature}
-        config.getConfigParameter<double>(
-            "reference_temperature", std::numeric_limits<double>::quiet_NaN());
-
     //! \ogs_file_param{prj__processes__process__HYDRO_MECHANICS_WITH_LIE__use_b_bar}
     auto const use_b_bar = config.getConfigParameter<bool>("use_b_bar", false);
 
+    auto media_map =
+        MaterialPropertyLib::createMaterialSpatialDistributionMap(media, mesh);
+
+    std::array const requiredMediumProperties = {
+        MaterialPropertyLib::reference_temperature,
+        MaterialPropertyLib::permeability,
+        MaterialPropertyLib::biot_coefficient};
+    std::array const requiredFluidProperties = {MaterialPropertyLib::viscosity,
+                                                MaterialPropertyLib::density};
+    std::array const requiredSolidProperties = {MaterialPropertyLib::density};
+
+    MaterialPropertyLib::checkMPLPhasesForSinglePhaseFlow(mesh, media_map);
+
+    for (auto const& medium : media_map.media())
+    {
+        checkRequiredProperties(*medium, requiredMediumProperties);
+        checkRequiredProperties(fluidPhase(*medium), requiredFluidProperties);
+        checkRequiredProperties(medium->phase("Solid"),
+                                requiredSolidProperties);
+    }
+
+    // Check whether fracture permeability is given as a scalar value.
+    for (auto const& element_id : mesh.getElements() | MeshLib::views::ids)
+    {
+        media_map.checkElementHasMedium(element_id);
+        auto const& medium = *media_map.getMedium(element_id);
+
+        // For fracture element
+        if (mesh.getElement(element_id)->getDimension() != GlobalDim)
+        {
+            ParameterLib::SpatialPosition x_position;
+            MaterialPropertyLib::VariableArray variables;
+            auto const permeability =
+                medium.property(MaterialPropertyLib::PropertyType::permeability)
+                    .value(variables, x_position, 0.0 /*t*/, 0.0 /*dt*/);
+            if (!std::holds_alternative<double>(permeability))
+            {
+                OGS_FATAL(
+                    "The permeability model for the fracture must be "
+                    "isotropic, and it must return a scalar value.");
+            }
+        }
+    }
+
     HydroMechanicsProcessData<GlobalDim> process_data{
-        materialIDs(mesh),
-        std::move(solid_constitutive_relations),
-        intrinsic_permeability,
-        specific_storage,
-        fluid_viscosity,
-        fluid_density,
-        biot_coefficient,
-        porosity,
-        solid_density,
-        specific_body_force,
-        std::move(fracture_model),
-        std::move(frac_prop),
-        initial_effective_stress,
-        initial_fracture_effective_stress,
-        deactivate_matrix_in_flow,
-        reference_temperature,
-        use_b_bar};
+        materialIDs(mesh),         std::move(solid_constitutive_relations),
+        std::move(media_map),      specific_body_force,
+        std::move(fracture_model), std::move(frac_prop),
+        initial_effective_stress,  initial_fracture_effective_stress,
+        deactivate_matrix_in_flow, use_b_bar};
 
     SecondaryVariableCollection secondary_variables;
 
@@ -365,7 +329,9 @@ template std::unique_ptr<Process> createHydroMechanicsProcess<2>(
     std::optional<ParameterLib::CoordinateSystem> const&
         local_coordinate_system,
     unsigned const integration_order,
-    BaseLib::ConfigTree const& config);
+    BaseLib::ConfigTree const& config,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media);
+
 template std::unique_ptr<Process> createHydroMechanicsProcess<3>(
     std::string const& name,
     MeshLib::Mesh& mesh,
@@ -375,7 +341,8 @@ template std::unique_ptr<Process> createHydroMechanicsProcess<3>(
     std::optional<ParameterLib::CoordinateSystem> const&
         local_coordinate_system,
     unsigned const integration_order,
-    BaseLib::ConfigTree const& config);
+    BaseLib::ConfigTree const& config,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media);
 
 }  // namespace HydroMechanics
 }  // namespace LIE
diff --git a/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.h b/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.h
index c3795c43471d32ec4dd299f90368e7a4f732bf52..02ce3c87434fee179e43b9c97ac87523e3b12d82 100644
--- a/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.h
+++ b/ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.h
@@ -10,6 +10,7 @@
 
 #pragma once
 
+#include <map>
 #include <memory>
 #include <optional>
 #include <string>
@@ -19,6 +20,12 @@ namespace BaseLib
 {
 class ConfigTree;
 }
+
+namespace MaterialPropertyLib
+{
+class Medium;
+}
+
 namespace MeshLib
 {
 class Mesh;
@@ -51,8 +58,8 @@ std::unique_ptr<Process> createHydroMechanicsProcess(
     std::optional<ParameterLib::CoordinateSystem> const&
         local_coordinate_system,
     unsigned const integration_order,
-    BaseLib::ConfigTree const& config);
-
+    BaseLib::ConfigTree const& config,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media);
 }  // namespace HydroMechanics
 }  // namespace LIE
 }  // namespace ProcessLib
diff --git a/ProcessLib/LIE/HydroMechanics/HydroMechanicsProcessData.h b/ProcessLib/LIE/HydroMechanics/HydroMechanicsProcessData.h
index 09d0e506b27338f69a6b773def104ef32a435b6d..dfb508d267ab394874bdcb2b3f9e5cd31afbbb80 100644
--- a/ProcessLib/LIE/HydroMechanics/HydroMechanicsProcessData.h
+++ b/ProcessLib/LIE/HydroMechanics/HydroMechanicsProcessData.h
@@ -15,6 +15,7 @@
 #include <utility>
 
 #include "MaterialLib/FractureModels/FractureModelBase.h"
+#include "MaterialLib/MPL/MaterialSpatialDistributionMap.h"
 #include "MaterialLib/SolidModels/MechanicsBase.h"
 #include "MeshLib/ElementStatus.h"
 #include "MeshLib/PropertyVector.h"
@@ -38,24 +39,18 @@ struct HydroMechanicsProcessData
     std::map<int,
              std::shared_ptr<MaterialLib::Solids::MechanicsBase<GlobalDim>>>
         solid_materials;
-    ParameterLib::Parameter<double> const& intrinsic_permeability;
-    ParameterLib::Parameter<double> const& specific_storage;
-    ParameterLib::Parameter<double> const& fluid_viscosity;
-    ParameterLib::Parameter<double> const& fluid_density;
-    ParameterLib::Parameter<double> const& biot_coefficient;
-    ParameterLib::Parameter<double> const& porosity;
-    ParameterLib::Parameter<double> const& solid_density;
+
+    MaterialPropertyLib::MaterialSpatialDistributionMap media_map;
+
     Eigen::Matrix<double, GlobalDim, 1> const specific_body_force;
     std::unique_ptr<MaterialLib::Fracture::FractureModelBase<GlobalDim>>
         fracture_model;
-    std::unique_ptr<FracturePropertyHM> fracture_property;
+    std::unique_ptr<FractureProperty> fracture_property;
     ParameterLib::Parameter<double> const& initial_effective_stress;
     ParameterLib::Parameter<double> const& initial_fracture_effective_stress;
 
     bool const deactivate_matrix_in_flow;
 
-    double const reference_temperature;
-
     /// An indicator to use the B bar method \cite hughes1980generalization to
     /// tackle the  volumetric locking.
     const bool use_b_bar;
diff --git a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerFracture-impl.h b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerFracture-impl.h
index 1625f43f7b221f75b5d9743a360a45762ae2e6d5..a0e9b2eb0ac12f488a7e1fd1b89112ac8efa2e16 100644
--- a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerFracture-impl.h
+++ b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerFracture-impl.h
@@ -10,6 +10,8 @@
 
 #pragma once
 
+#include <variant>
+
 #include "HydroMechanicsLocalAssemblerFracture.h"
 #include "MaterialLib/FractureModels/FractureIdentity2.h"
 #include "MathLib/KelvinVector.h"
@@ -24,6 +26,8 @@ namespace LIE
 {
 namespace HydroMechanics
 {
+namespace MPL = MaterialPropertyLib;
+
 template <int GlobalDim, typename RotationMatrix>
 Eigen::Matrix<double, GlobalDim, GlobalDim> createRotatedTensor(
     RotationMatrix const& R, double const value)
@@ -116,9 +120,6 @@ HydroMechanicsLocalAssemblerFracture<ShapeFunctionDisplacement,
         ip_data.aperture0 = aperture0_node_values.dot(sm_u.N);
         ip_data.aperture = ip_data.aperture0;
 
-        ip_data.permeability_state =
-            frac_prop.permeability_model->getNewState();
-
         auto const initial_effective_stress =
             _process_data.initial_fracture_effective_stress(0, x_position);
         for (int i = 0; i < GlobalDim; i++)
@@ -206,6 +207,14 @@ void HydroMechanicsLocalAssemblerFracture<ShapeFunctionDisplacement,
     ParameterLib::SpatialPosition x_position;
     x_position.setElementID(_element.getID());
 
+    MPL::VariableArray variables;
+    auto const& medium = _process_data.media_map.getMedium(_element.getID());
+    auto const& liquid_phase = medium->phase("AqueousLiquid");
+    auto const T_ref =
+        medium->property(MPL::PropertyType::reference_temperature)
+            .template value<double>(variables, x_position, t, dt);
+    variables.temperature = T_ref;
+
     unsigned const n_integration_points = _ip_data.size();
     for (unsigned ip = 0; ip < n_integration_points; ip++)
     {
@@ -228,10 +237,22 @@ void HydroMechanicsLocalAssemblerFracture<ShapeFunctionDisplacement,
         auto& state = *ip_data.material_state_variables;
         auto& b_m = ip_data.aperture;
 
-        double const S = frac_prop.specific_storage(t, x_position)[0];
-        double const mu = _process_data.fluid_viscosity(t, x_position)[0];
-        auto const alpha = frac_prop.biot_coefficient(t, x_position)[0];
-        auto const rho_fr = _process_data.fluid_density(t, x_position)[0];
+        auto const rho_fr =
+            liquid_phase.property(MPL::PropertyType::density)
+                .template value<double>(variables, x_position, t, dt);
+        variables.density = rho_fr;
+
+        auto const alpha =
+            medium->property(MPL::PropertyType::biot_coefficient)
+                .template value<double>(variables, x_position, t, dt);
+
+        double const S =
+            medium->property(MPL::PropertyType::storage)
+                .template value<double>(variables, x_position, t, dt);
+
+        auto const mu =
+            liquid_phase.property(MPL::PropertyType::viscosity)
+                .template value<double>(variables, x_position, t, dt);
 
         // displacement jumps in local coordinates
         w.noalias() = R * H_g * g;
@@ -259,15 +280,6 @@ void HydroMechanicsLocalAssemblerFracture<ShapeFunctionDisplacement,
             t, x_position, ip_data.aperture0, stress0, w_prev, w,
             effective_stress_prev, effective_stress, C, state);
 
-        auto& k = ip_data.permeability;
-        k = frac_prop.permeability_model->permeability(
-            ip_data.permeability_state.get(), ip_data.aperture0, b_m);
-
-        // derivative of permeability respect to aperture
-        double const dk_db =
-            frac_prop.permeability_model->dpermeability_daperture(
-                ip_data.permeability_state.get(), ip_data.aperture0, b_m);
-
         //
         // displacement equation, displacement jump part
         //
@@ -284,26 +296,43 @@ void HydroMechanicsLocalAssemblerFracture<ShapeFunctionDisplacement,
         //
         // pressure equation, pressure part.
         //
+
+        variables.fracture_aperture = b_m;
+        // Assume that the fracture permeability is isotropic
+        auto const permeability =
+            medium->property(MPL::PropertyType::permeability)
+                .value(variables, x_position, t, dt);
+
+        auto& k = ip_data.permeability;
+        k = std::get<double>(permeability);
+        double const k_over_mu = k / mu;
         storage_p.noalias() += N_p.transpose() * b_m * S * N_p * ip_w;
         laplace_p.noalias() +=
-            dNdx_p.transpose() * b_m * k / mu * dNdx_p * ip_w;
+            dNdx_p.transpose() * b_m * k_over_mu * dNdx_p * ip_w;
         rhs_p.noalias() +=
-            dNdx_p.transpose() * b_m * k / mu * rho_fr * gravity_vec * ip_w;
+            dNdx_p.transpose() * b_m * k_over_mu * rho_fr * gravity_vec * ip_w;
 
         //
         // pressure equation, displacement jump part.
         //
-        GlobalDimVectorType const grad_head_over_mu =
-            (dNdx_p * p + rho_fr * gravity_vec) / mu;
+        GlobalDimVectorType const grad_head = dNdx_p * p + rho_fr * gravity_vec;
         Eigen::Matrix<double, 1, displacement_size> const mT_R_Hg =
             identity2.transpose() * R * H_g;
         // velocity in global coordinates
-        ip_data.darcy_velocity = -k * grad_head_over_mu;
+        ip_data.darcy_velocity = -k_over_mu * grad_head;
         J_pg.noalias() +=
             N_p.transpose() * S * N_p * (p - p_prev) / dt * mT_R_Hg * ip_w;
+
+        // derivative of permeability with respect to aperture
+        double const dk_db_over_mu =
+            medium->property(MPL::PropertyType::permeability)
+                .template dValue<double>(variables,
+                                         MPL::Variable::fracture_aperture,
+                                         x_position, t, dt) /
+            mu;
         J_pg.noalias() +=
-            dNdx_p.transpose() * k * grad_head_over_mu * mT_R_Hg * ip_w;
-        J_pg.noalias() += dNdx_p.transpose() * b_m * dk_db * grad_head_over_mu *
+            dNdx_p.transpose() * k_over_mu * grad_head * mT_R_Hg * ip_w;
+        J_pg.noalias() += dNdx_p.transpose() * b_m * dk_db_over_mu * grad_head *
                           mT_R_Hg * ip_w;
     }
 
diff --git a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix-impl.h b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix-impl.h
index 220a524ab851c93578f1f74e2ca3ac5f2dd2f803..8d977b1d6b1e834f9563204e9cfdf0606c6706cd 100644
--- a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix-impl.h
+++ b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix-impl.h
@@ -10,7 +10,12 @@
 
 #pragma once
 
+#include <limits>
+
 #include "HydroMechanicsLocalAssemblerMatrix.h"
+#include "MaterialLib/MPL/Medium.h"
+#include "MaterialLib/MPL/Property.h"
+#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
 #include "MaterialLib/PhysicalConstant.h"
 #include "MaterialLib/SolidModels/SelectSolidConstitutiveRelation.h"
 #include "MathLib/KelvinVector.h"
@@ -26,6 +31,8 @@ namespace LIE
 {
 namespace HydroMechanics
 {
+namespace MPL = MaterialPropertyLib;
+
 template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
           int GlobalDim>
 HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
@@ -125,8 +132,7 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
 {
     auto p = const_cast<Eigen::VectorXd&>(local_x).segment(pressure_index,
                                                            pressure_size);
-    auto p_prev = const_cast<Eigen::VectorXd&>(local_x_prev)
-                      .segment(pressure_index, pressure_size);
+    auto const p_prev = local_x_prev.segment(pressure_index, pressure_size);
 
     if (_process_data.deactivate_matrix_in_flow)
     {
@@ -190,6 +196,19 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
     ParameterLib::SpatialPosition x_position;
     x_position.setElementID(_element.getID());
 
+    auto const& medium = _process_data.media_map.getMedium(_element.getID());
+    auto const& liquid_phase = medium->phase("AqueousLiquid");
+    auto const& solid_phase = medium->phase("Solid");
+
+    auto const T_ref =
+        medium->property(MPL::PropertyType::reference_temperature)
+            .template value<double>(variables, x_position, t, dt);
+    variables.temperature = T_ref;
+    variables_prev.temperature = T_ref;
+
+    bool const has_storage_property =
+        medium->hasProperty(MPL::PropertyType::storage);
+
     auto const B_dil_bar = getDilatationalBBarMatrix();
 
     unsigned const n_integration_points = _ip_data.size();
@@ -205,14 +224,18 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         auto const& dNdx_p = ip_data.dNdx_p;
         auto const& H_u = ip_data.H_u;
 
+        variables.liquid_phase_pressure = N_p.dot(p);
+
         auto const x_coord =
             NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                            ShapeMatricesTypeDisplacement>(
                 _element, N_u);
-        auto const B = LinearBMatrix::computeBMatrixPossiblyWithBbar<
-            GlobalDim, ShapeFunctionDisplacement::NPOINTS, BBarMatrixType,
-            typename BMatricesType::BMatrixType>(
-            dNdx_u, N_u, B_dil_bar, x_coord, this->_is_axially_symmetric);
+        auto const B =
+            LinearBMatrix::computeBMatrixPossiblyWithBbar<
+                GlobalDim, ShapeFunctionDisplacement::NPOINTS, BBarMatrixType,
+                typename BMatricesType::BMatrixType>(
+                dNdx_u, N_u, B_dil_bar, x_coord, this->_is_axially_symmetric)
+                .eval();
 
         auto const& eps_prev = ip_data.eps_prev;
         auto const& sigma_eff_prev = ip_data.sigma_eff_prev;
@@ -221,10 +244,19 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         auto& eps = ip_data.eps;
         auto& state = ip_data.material_state_variables;
 
-        auto const alpha = _process_data.biot_coefficient(t, x_position)[0];
-        auto const rho_sr = _process_data.solid_density(t, x_position)[0];
-        auto const rho_fr = _process_data.fluid_density(t, x_position)[0];
-        auto const porosity = _process_data.porosity(t, x_position)[0];
+        auto const rho_sr =
+            solid_phase.property(MPL::PropertyType::density)
+                .template value<double>(variables, x_position, t, dt);
+        auto const rho_fr =
+            liquid_phase.property(MPL::PropertyType::density)
+                .template value<double>(variables, x_position, t, dt);
+
+        auto const alpha =
+            medium->property(MPL::PropertyType::biot_coefficient)
+                .template value<double>(variables, x_position, t, dt);
+        auto const porosity =
+            medium->property(MPL::PropertyType::porosity)
+                .template value<double>(variables, x_position, t, dt);
 
         double const rho = rho_sr * (1 - porosity) + porosity * rho_fr;
         auto const& identity2 =
@@ -241,7 +273,7 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         variables_prev.mechanical_strain
             .emplace<MathLib::KelvinVector::KelvinVectorType<GlobalDim>>(
                 eps_prev);
-        variables_prev.temperature = _process_data.reference_temperature;
+        variables_prev.temperature = T_ref;
 
         auto&& solution = _ip_data[ip].solid_material.integrateStress(
             variables_prev, variables, t, x_position, dt, *state);
@@ -268,10 +300,32 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         {
             Kup.noalias() += B.transpose() * alpha * identity2 * N_p * ip_w;
 
-            double const k_over_mu =
-                _process_data.intrinsic_permeability(t, x_position)[0] /
-                _process_data.fluid_viscosity(t, x_position)[0];
-            double const S = _process_data.specific_storage(t, x_position)[0];
+            variables.density = rho_fr;
+            auto const mu =
+                liquid_phase.property(MPL::PropertyType::viscosity)
+                    .template value<double>(variables, x_position, t, dt);
+
+            auto const k_over_mu =
+                (MPL::formEigenTensor<GlobalDim>(
+                     medium->property(MPL::PropertyType::permeability)
+                         .value(variables, x_position, t, dt)) /
+                 mu)
+                    .eval();
+
+            double const S =
+                has_storage_property
+                    ? medium->property(MPL::PropertyType::storage)
+                          .template value<double>(variables, x_position, t, dt)
+                    : porosity *
+                              (liquid_phase.property(MPL::PropertyType::density)
+                                   .template dValue<double>(
+                                       variables,
+                                       MPL::Variable::liquid_phase_pressure,
+                                       x_position, t, dt) /
+                               rho_fr) +
+                          (porosity - alpha) * (1.0 - alpha) /
+                              _ip_data[ip].solid_material.getBulkModulus(
+                                  t, x_position, &C);
 
             auto q = ip_data.darcy_velocity.head(GlobalDim);
             q.noalias() = -k_over_mu * (dNdx_p * p + rho_fr * gravity_vec);
@@ -342,6 +396,15 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
     velocity_avg.setZero();
 
     unsigned const n_integration_points = _ip_data.size();
+
+    auto const& medium = _process_data.media_map.getMedium(_element.getID());
+    auto const& liquid_phase = medium->phase("AqueousLiquid");
+    auto const T_ref =
+        medium->property(MPL::PropertyType::reference_temperature)
+            .template value<double>(variables, x_position, t, dt);
+    variables.temperature = T_ref;
+    variables_prev.temperature = T_ref;
+
     auto const B_dil_bar = getDilatationalBBarMatrix();
 
     for (unsigned ip = 0; ip < n_integration_points; ip++)
@@ -358,16 +421,21 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         auto& state = ip_data.material_state_variables;
 
         auto const& N_u = ip_data.N_u;
+        auto const& N_p = ip_data.N_p;
         auto const& dNdx_u = ip_data.dNdx_u;
 
+        variables.liquid_phase_pressure = N_p.dot(p);
+
         auto const x_coord =
             NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                            ShapeMatricesTypeDisplacement>(
                 _element, N_u);
-        auto const B = LinearBMatrix::computeBMatrixPossiblyWithBbar<
-            GlobalDim, ShapeFunctionDisplacement::NPOINTS, BBarMatrixType,
-            typename BMatricesType::BMatrixType>(
-            dNdx_u, N_u, B_dil_bar, x_coord, this->_is_axially_symmetric);
+        auto const B =
+            LinearBMatrix::computeBMatrixPossiblyWithBbar<
+                GlobalDim, ShapeFunctionDisplacement::NPOINTS, BBarMatrixType,
+                typename BMatricesType::BMatrixType>(
+                dNdx_u, N_u, B_dil_bar, x_coord, this->_is_axially_symmetric)
+                .eval();
 
         eps.noalias() = B * u;
 
@@ -380,7 +448,6 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         variables_prev.mechanical_strain
             .emplace<MathLib::KelvinVector::KelvinVectorType<GlobalDim>>(
                 eps_prev);
-        variables_prev.temperature = _process_data.reference_temperature;
 
         auto&& solution = _ip_data[ip].solid_material.integrateStress(
             variables_prev, variables, t, x_position, dt, *state);
@@ -398,16 +465,27 @@ void HydroMechanicsLocalAssemblerMatrix<ShapeFunctionDisplacement,
         if (!_process_data.deactivate_matrix_in_flow)  // Only for hydraulically
                                                        // active matrix
         {
-            double const k_over_mu =
-                _process_data.intrinsic_permeability(t, x_position)[0] /
-                _process_data.fluid_viscosity(t, x_position)[0];
-            auto const rho_fr = _process_data.fluid_density(t, x_position)[0];
+            auto const rho_fr =
+                liquid_phase.property(MPL::PropertyType::density)
+                    .template value<double>(variables, x_position, t, dt);
+            variables.density = rho_fr;
+            auto const mu =
+                liquid_phase.property(MPL::PropertyType::viscosity)
+                    .template value<double>(variables, x_position, t, dt);
+
+            auto const k = MPL::formEigenTensor<GlobalDim>(
+                               medium->property(MPL::PropertyType::permeability)
+                                   .value(variables, x_position, t, dt))
+                               .eval();
+
+            GlobalDimMatrixType const k_over_mu = k / mu;
+
             auto const& gravity_vec = _process_data.specific_body_force;
             auto const& dNdx_p = ip_data.dNdx_p;
 
             ip_data.darcy_velocity.head(GlobalDim).noalias() =
                 -k_over_mu * (dNdx_p * p + rho_fr * gravity_vec);
-            velocity_avg += ip_data.darcy_velocity.head(GlobalDim);
+            velocity_avg.noalias() += ip_data.darcy_velocity.head(GlobalDim);
         }
     }
 
diff --git a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix.h b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix.h
index ce522b8db72a5606023c5a813cc5f8d0199366c6..a77947978a70165a9756c91e4805b58fe18827e4 100644
--- a/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix.h
+++ b/ProcessLib/LIE/HydroMechanics/LocalAssembler/HydroMechanicsLocalAssemblerMatrix.h
@@ -171,6 +171,8 @@ protected:
         IntegrationPointDataMatrix<BMatricesType, ShapeMatricesTypeDisplacement,
                                    ShapeMatricesTypePressure, GlobalDim,
                                    ShapeFunctionDisplacement::NPOINTS>;
+    using GlobalDimMatrixType =
+        typename ShapeMatricesTypePressure::GlobalDimMatrixType;
 
     using GlobalDimVector = Eigen::Matrix<double, GlobalDim, 1>;
 
diff --git a/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataFracture.h b/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataFracture.h
index 5234a9538c3b7c953b217dedeb7188fecfb923fe..9c24fa8760b2291df6374880d2763205e6fcb7e6 100644
--- a/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataFracture.h
+++ b/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataFracture.h
@@ -51,10 +51,6 @@ struct IntegrationPointDataFracture final
         GlobalDim>::MaterialStateVariables>
         material_state_variables;
 
-    std::unique_ptr<
-        typename MaterialLib::Fracture::Permeability::PermeabilityState>
-        permeability_state;
-
     Eigen::MatrixXd C;
     double integration_weight;
 
diff --git a/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataMatrix.h b/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataMatrix.h
index 083da8852747f098d43229df07b4757b8d5ea44b..395d7d86259d5ca792bb4b5dcd3d6f71b819b7c7 100644
--- a/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataMatrix.h
+++ b/ProcessLib/LIE/HydroMechanics/LocalAssembler/IntegrationPointDataMatrix.h
@@ -47,6 +47,9 @@ struct IntegrationPointDataMatrix final
     typename ShapeMatrixTypePressure::NodalRowVectorType N_p;
     typename ShapeMatrixTypePressure::GlobalDimNodalMatrixType dNdx_p;
 
+    using GlobalDimVectorType =
+        typename ShapeMatrixTypePressure::GlobalDimVectorType;
+
     MaterialLib::Solids::MechanicsBase<GlobalDim>& solid_material;
     std::unique_ptr<typename MaterialLib::Solids::MechanicsBase<
         GlobalDim>::MaterialStateVariables>
@@ -55,7 +58,7 @@ struct IntegrationPointDataMatrix final
     typename BMatricesType::KelvinMatrixType C;
     double integration_weight;
 
-    GlobalDimVector darcy_velocity;
+    GlobalDimVectorType darcy_velocity;
 
     void pushBackState()
     {
diff --git a/Tests/Data/LIE/HydroMechanics/GreatCellWithBBar/point_injection_embedded_fracture_F.prj b/Tests/Data/LIE/HydroMechanics/GreatCellWithBBar/point_injection_embedded_fracture_F.prj
index 6af1546001cb5b05dbc85a617fc8d0f9a2733956..7147657cecf18104b6d615d59cea2f3546a9f16b 100644
--- a/Tests/Data/LIE/HydroMechanics/GreatCellWithBBar/point_injection_embedded_fracture_F.prj
+++ b/Tests/Data/LIE/HydroMechanics/GreatCellWithBBar/point_injection_embedded_fracture_F.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <meshes>
         <mesh>2d_mesh.vtu</mesh>
@@ -70,13 +70,6 @@
                 <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
                 <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
             </secondary_variables>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
                 <type>LinearElasticIsotropic</type>
@@ -86,13 +79,7 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>2</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
@@ -149,6 +136,170 @@
             </timesteps>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="2">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <parameter>
             <name>E1</name>
diff --git a/Tests/Data/LIE/HydroMechanics/GreatCellWithTrianglularMesh/great_cell_2d_HM_LIE_embedded_fracture.prj b/Tests/Data/LIE/HydroMechanics/GreatCellWithTrianglularMesh/great_cell_2d_HM_LIE_embedded_fracture.prj
index 7f7da5c14d89e6fa6089d36270882b7531b46800..c963d0fc49339ea9911b0968aa683f5d89c1bcfe 100644
--- a/Tests/Data/LIE/HydroMechanics/GreatCellWithTrianglularMesh/great_cell_2d_HM_LIE_embedded_fracture.prj
+++ b/Tests/Data/LIE/HydroMechanics/GreatCellWithTrianglularMesh/great_cell_2d_HM_LIE_embedded_fracture.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <meshes>
         <mesh>2d_mesh.vtu</mesh>
@@ -39,7 +39,7 @@
         <mesh>2D_p_top.vtu</mesh>
         <mesh>2D_p_bottom.vtu</mesh>
         <mesh>2D_injection_position.vtu</mesh>
-        <mesh>2D_outflow_position.vtu</mesh>        
+        <mesh>2D_outflow_position.vtu</mesh>
     </meshes>
     <processes>
         <process>
@@ -71,13 +71,6 @@
                 <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
                 <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
             </secondary_variables>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
                 <type>LinearElasticIsotropic</type>
@@ -87,13 +80,7 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>2</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
@@ -150,6 +137,170 @@
             </timesteps>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="2">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <parameter>
             <name>E1</name>
@@ -205,7 +356,7 @@
         <parameter>
             <name>biot_m</name>
             <type>Constant</type>
-            <value>0.005</value>            
+            <value>0.005</value>
         </parameter>
         <!-- Fracture properties -->
         <parameter>
@@ -220,7 +371,7 @@
         </parameter>
         <parameter>
             <name>S_f</name>
-            <type>Constant</type> 	
+            <type>Constant</type>
             <value>1e-11</value>
         </parameter>
         <parameter>
@@ -253,7 +404,7 @@
             <name>p0</name>
             <type>Constant</type>
             <value>2.0e6</value>
-        </parameter>        
+        </parameter>
         <!-- BC -->
         <parameter>
             <name>p_down_stream</name>
@@ -265,14 +416,12 @@
             <type>Constant</type>
             <value>4.167e-7</value>
         </parameter>
-
         <parameter>
             <name>p_injection_ramp</name>
             <type>CurveScaled</type>
             <curve>timeRamp</curve>
             <parameter>p_injection_rate</parameter>
         </parameter>
-
         <parameter>
             <name>u0</name>
             <type>Constant</type>
diff --git a/Tests/Data/LIE/HydroMechanics/TaskB.prj b/Tests/Data/LIE/HydroMechanics/TaskB.prj
index 00327e78cf2ee879143c481c65cbc7021a2e5a8b..bd8766965a4bdeba12d0acf71faac0b95e383adf 100644
--- a/Tests/Data/LIE/HydroMechanics/TaskB.prj
+++ b/Tests/Data/LIE/HydroMechanics/TaskB.prj
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
@@ -36,13 +29,7 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>1</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <secondary_variables>
                 <secondary_variable internal_name="sigma" output_name="sigma" />
@@ -120,6 +107,119 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Constant</type>
+                    <value>0.0</value>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/convert_LIE_HM2MPL.py b/Tests/Data/LIE/HydroMechanics/convert_LIE_HM2MPL.py
new file mode 100644
index 0000000000000000000000000000000000000000..47b9674120af51ae8e2d1b359d227d3be40ceb02
--- /dev/null
+++ b/Tests/Data/LIE/HydroMechanics/convert_LIE_HM2MPL.py
@@ -0,0 +1,271 @@
+import sys
+import xml.etree.ElementTree as ET
+from pathlib import Path
+from xml.dom import minidom
+
+
+def add_parameter_property(properties, name_, parameter_name):
+    new_property = ET.SubElement(properties, "property")
+    ET.SubElement(new_property, "name").text = name_
+    ET.SubElement(new_property, "type").text = "Parameter"
+    ET.SubElement(new_property, "parameter_name").text = parameter_name
+
+
+def add_liquid_phase(phases, parameter_name_viscosity, parameter_name_density):
+    phase = ET.SubElement(phases, "phase")
+    ET.SubElement(phase, "type").text = "AqueousLiquid"
+    properties = ET.SubElement(phase, "properties")
+
+    add_parameter_property(properties, "viscosity", parameter_name_viscosity)
+    add_parameter_property(properties, "density", parameter_name_density)
+
+
+def add_solid_phase(phases, parameter_name_density):
+    phase = ET.SubElement(phases, "phase")
+    ET.SubElement(phase, "type").text = "Solid"
+    properties = ET.SubElement(phase, "properties")
+
+    add_parameter_property(properties, "density", parameter_name_density)
+
+
+def add_medium_properties_common(properties, storage_parameter, biot_parameter):
+    add_parameter_property(properties, "storage", storage_parameter)
+    add_parameter_property(properties, "biot_coefficient", biot_parameter)
+
+    property_T = ET.SubElement(properties, "property")
+    ET.SubElement(property_T, "name").text = "reference_temperature"
+    ET.SubElement(property_T, "type").text = "Constant"
+    ET.SubElement(property_T, "value").text = "293.15"
+
+
+def add_medium_properties_matrix(
+    medium,
+    storage_parameter,
+    biot_parameter,
+    permeability_parameter,
+    porosity_parameter,
+):
+    properties = ET.SubElement(medium, "properties")
+    add_parameter_property(properties, "permeability", permeability_parameter)
+    add_parameter_property(properties, "porosity", porosity_parameter)
+
+    add_medium_properties_common(properties, storage_parameter, biot_parameter)
+
+
+def add_medium_properties_fracture(
+    medium, storage_parameter, biot_parameter, permeability_parameter
+):
+    properties = ET.SubElement(medium, "properties")
+    property_kf = ET.SubElement(properties, "property")
+    ET.SubElement(property_kf, "name").text = "permeability"
+    if permeability_parameter == "0.0":
+        ET.SubElement(property_kf, "type").text = "CubicLawPermeability"
+    else:
+        ET.SubElement(property_kf, "type").text = "Constant"
+        ET.SubElement(property_kf, "value").text = permeability_parameter
+
+    add_medium_properties_common(properties, storage_parameter, biot_parameter)
+
+
+def add_matrix_medium(
+    media,
+    mat_id,
+    k_m_tag,
+    S_m_tag,
+    biot_m_tag,
+    phi_m_tag,
+    mu_tag,
+    rho_fr_tag,
+    rho_sr_tag,
+):
+    medium = ET.SubElement(media, "medium", id=mat_id)
+    phases = ET.SubElement(medium, "phases")
+
+    add_liquid_phase(phases, mu_tag.text, rho_fr_tag.text)
+
+    add_solid_phase(phases, rho_sr_tag.text)
+
+    add_medium_properties_matrix(
+        medium,
+        storage_parameter=S_m_tag.text,
+        biot_parameter=biot_m_tag.text,
+        permeability_parameter=k_m_tag.text,
+        porosity_parameter=phi_m_tag.text,
+    )
+
+
+def add_fracture_medium(
+    media,
+    mat_id,
+    if_constant_permeability,
+    fracture_props_tag,
+    mu_tag,
+    rho_fr_tag,
+    rho_sr_tag,
+):
+    medium = ET.SubElement(media, "medium", id=mat_id)
+    phases = ET.SubElement(medium, "phases")
+
+    add_liquid_phase(phases, mu_tag.text, rho_fr_tag.text)
+    add_solid_phase(phases, rho_sr_tag.text)
+
+    S_f_tag = fracture_props_tag.find("specific_storage")
+    fracture_props_tag.remove(S_f_tag)
+    b_f_tag = fracture_props_tag.find("biot_coefficient")
+    fracture_props_tag.remove(b_f_tag)
+    k_f_tag = fracture_props_tag.find("permeability_model")
+    fracture_props_tag.remove(k_f_tag)
+
+    add_medium_properties_fracture(
+        medium,
+        storage_parameter=S_f_tag.text,
+        biot_parameter=b_f_tag.text,
+        permeability_parameter=if_constant_permeability,
+    )
+
+
+def prettify(elem):
+    """Return a pretty-printed XML string for the Element without extra blank lines."""
+    encoding = "ISO-8859-1"
+    rough_string = ET.tostring(elem, encoding=encoding)
+    reparsed = minidom.parseString(rough_string)
+    pretty_xml = reparsed.toprettyxml(indent="    ", encoding=encoding)
+
+    pretty_xml_decode = pretty_xml.decode(encoding)
+    # Remove extra blank lines
+    return "\n".join([line for line in pretty_xml_decode.splitlines() if line.strip()])
+
+
+def insert_media_tags_after_time_loop(input_file, output_file):
+    parser = ET.XMLParser(target=ET.TreeBuilder(insert_comments=True))
+    tree = ET.parse(input_file, parser=parser)
+    root = tree.getroot()
+
+    if root.find(".//media") is not None:
+        print(f"The project file {input_file} has already been processed")
+        return False
+
+    process_tag = root.find(".//processes/process")
+    mu_tag = process_tag.find("fluid_viscosity")
+    process_tag.remove(mu_tag)
+    rho_fr_tag = process_tag.find("fluid_density")
+    process_tag.remove(rho_fr_tag)
+    rho_sr_tag = process_tag.find("solid_density")
+    process_tag.remove(rho_sr_tag)
+
+    k_m_tag = process_tag.find("intrinsic_permeability")
+    process_tag.remove(k_m_tag)
+    S_m_tag = process_tag.find("specific_storage")
+    process_tag.remove(S_m_tag)
+    biot_m_tag = process_tag.find("biot_coefficient")
+    process_tag.remove(biot_m_tag)
+    phi_m_tag = process_tag.find("porosity")
+    process_tag.remove(phi_m_tag)
+
+    constitutive_relation_tags = process_tag.findall("constitutive_relation")
+
+    matrix_ids = []
+    if len(constitutive_relation_tags) > 1:
+        for tag in constitutive_relation_tags:
+            matrix_ids.append(tag.attrib["id"])
+    else:
+        matrix_ids.append("0")
+
+    fracture_props_tag = process_tag.find("fracture_properties")
+    fracture_id_tag = fracture_props_tag.find("material_id")
+    fracture_id = fracture_id_tag.text
+    if len(matrix_ids) > 1:
+        if fracture_id in matrix_ids:
+            print(
+                f"The fracture material id {fracture_id} is  the same as one"
+                "of one matrix material IDs."
+            )
+    else:
+        if int(fracture_id) == 0:
+            matrix_ids[0] = "1"
+            fracture_id = "0"
+    fracture_props_tag.remove(fracture_id_tag)
+
+    time_loop = root.find(".//time_loop")
+
+    if time_loop is None:
+        print("<time_loop> tag not found in the project file.")
+        return False
+
+    # Create the new <media> structure
+    media = ET.Element("media")
+
+    # Matrix medium
+    for matrix_id in matrix_ids:
+        add_matrix_medium(
+            media,
+            matrix_id,
+            k_m_tag,
+            S_m_tag,
+            biot_m_tag,
+            phi_m_tag,
+            mu_tag,
+            rho_fr_tag,
+            rho_sr_tag,
+        )
+
+    # Fracture medium
+    fracture_permeability_tag = fracture_props_tag.find("permeability_model")
+    fracture_permeability_type = fracture_permeability_tag.find("type").text
+    const_k_f = (
+        fracture_permeability_tag.find("value").text
+        if fracture_permeability_type == "ConstantPermeability"
+        else "0.0"
+    )
+
+    add_fracture_medium(
+        media,
+        fracture_id,
+        const_k_f,
+        fracture_props_tag,
+        mu_tag,
+        rho_fr_tag,
+        rho_sr_tag,
+    )
+
+    # Insert the <media> element after <time_loop>
+    parent = root
+    index = list(parent).index(time_loop)
+    parent.insert(index + 1, media)
+
+    with Path(output_file).open("w") as f:
+        f.write(prettify(root))
+        f.write("\n")
+
+    return True
+
+
+def main():
+    if "--help" in sys.argv:
+        print(
+            "This script converts the LIE_HM project file to the new "
+            "output syntax for MPL properties."
+        )
+        print("Usage: convert_LIE_HM2MPL.py <input_file> <output_file>")
+        return
+
+    if len(sys.argv) != 3:
+        print("Usage: convert_LIE_HM2MPL <input_file> <output_file>")
+        return
+
+    input_file = sys.argv[1]
+    output_file = sys.argv[2]
+
+    try:
+        status = insert_media_tags_after_time_loop(input_file, output_file)
+        if status:
+            print("The conversion succeeds!")
+
+    except FileNotFoundError:
+        print(f"Error: The file {input_file} is not found")
+    except Exception as e:
+        print(f"An error occurred: {e}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture.prj b/Tests/Data/LIE/HydroMechanics/single_fracture.prj
index 8a32d24596216fc54d16033e0a9ab0200515780b..2bc05171821e6ad2c9c9a66c062502149fb2df03 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture.vtu</mesh>
     <geometry>single_fracture.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,23 +27,17 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -114,6 +101,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3D.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3D.prj
index 5836e3f7c063fb3d804bb12c7203bacee6a4e4c2..f0ed314c71c65e3f7b52df73ebc1dd3a0f4cbc05 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3D.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3D.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_3D.vtu</mesh>
     <geometry>single_fracture_3D.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,23 +27,17 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -114,6 +101,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow.prj
index 1a580e72d5ebaf24ddc2729009e62382d13bbbbc..347b0791a7481a9b9a10465d65086fd48c19eb19 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,24 +27,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>1</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -120,6 +107,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ.prj
index 7a0e944784f7bba59ee264db4e81a70b289c8fa5..fb71cacdd2f35e32ae4b8116af5a352ab195ace1 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <!--fracture_model>
@@ -43,24 +36,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -129,6 +116,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ_sigma0.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ_sigma0.prj
index 81b613da30015092a0178f9d5505d118c792b1ec..fc310e67d1d31dc9a7cef99fd1fa516210b55776 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ_sigma0.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_CHZ_sigma0.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <!--fracture_model>
@@ -43,24 +36,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -129,6 +116,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0.prj
index 0d6400773a667410780bc67c6cd408fc9c40d6f4..0a73011541e05e7b66187c0e984ef3e87ab9765d 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_linear_aperture.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,24 +27,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>1</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -120,6 +107,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0_e.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0_e.prj
index 96e1ed516e48b2f945f84af79fc30f38031679f6..629446cecb6f1e7f815f658794862bb3ace42913 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0_e.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_3compartments_flow_linear_aperture0_e.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_linear_aperture_e.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,24 +27,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>1</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -120,6 +107,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_const.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_const.prj
index 0e260300f8a43f3a39a1a80393b68394acc3214a..8eff034510861967afc4d8240fd4c844485c5362 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_const.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_const.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2_mesh2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -36,25 +29,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>ConstantPermeability</type>
-                    <value>8.33333E-12</value>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -127,6 +113,115 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Constant</type>
+                    <value>8.33333E-12</value>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_cubic.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_cubic.prj
index bd0ed802345372c537f822d40ba2e634a0194bcc..44dc72694e5283dc2043bb1d2e167eaf8f1a8add 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_cubic.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_CZ_kf_cubic.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2_mesh2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -36,24 +29,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -126,6 +113,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_const.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_const.prj
index 641924e6d783656b850e6d0aa54927b39e738869..eb38ad71563673270ea858af7a044f7f6ad99efb 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_const.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_const.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2_mesh2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,25 +27,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>ConstantPermeability</type>
-                    <value>8.33333E-12</value>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -125,6 +111,115 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Constant</type>
+                    <value>8.33333E-12</value>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_cubic.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_cubic.prj
index ce62abac908b29eb5efcb66b580fa52c2c7b0735..b0c3bd7bc5d7be012a00c2a150be628fe0fb43c2 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_cubic.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_LE_kf_cubic.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture_2x2_mesh2.vtu</mesh>
     <geometry>single_fracture_2x2.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,24 +27,18 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>CubicLaw</type>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <deactivate_matrix_in_flow>true</deactivate_matrix_in_flow>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -124,6 +111,114 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>CubicLawPermeability</type>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/Data/LIE/HydroMechanics/single_fracture_constK.prj b/Tests/Data/LIE/HydroMechanics/single_fracture_constK.prj
index 8cea18e4d43b170a55c8daa814b335019468edc8..7090706538bc805617610fdc21155dde981fc3d7 100644
--- a/Tests/Data/LIE/HydroMechanics/single_fracture_constK.prj
+++ b/Tests/Data/LIE/HydroMechanics/single_fracture_constK.prj
@@ -1,4 +1,4 @@
-<?xml version='1.0' encoding='ISO-8859-1'?>
+<?xml version="1.0" encoding="ISO-8859-1"?>
 <OpenGeoSysProject>
     <mesh>single_fracture.vtu</mesh>
     <geometry>single_fracture.gml</geometry>
@@ -17,13 +17,6 @@
                 <youngs_modulus>E</youngs_modulus>
                 <poissons_ratio>nu</poissons_ratio>
             </constitutive_relation>
-            <intrinsic_permeability>k</intrinsic_permeability>
-            <specific_storage>S</specific_storage>
-            <fluid_viscosity>mu</fluid_viscosity>
-            <biot_coefficient>biot_m</biot_coefficient>
-            <porosity>phi</porosity>
-            <solid_density>rho_sr</solid_density>
-            <fluid_density>rho_fr</fluid_density>
             <specific_body_force>0 0</specific_body_force>
             <initial_effective_stress>effective_stress0</initial_effective_stress>
             <fracture_model>
@@ -34,24 +27,17 @@
                 <tension_cutoff>1</tension_cutoff>
             </fracture_model>
             <fracture_properties>
-                <material_id>0</material_id>
                 <initial_aperture>aperture0</initial_aperture>
-                <specific_storage>S_f</specific_storage>
-                <biot_coefficient>biot_f</biot_coefficient>
-                <permeability_model>
-                    <type>ConstantPermeability</type>
-                    <value>1e-11</value>
-                </permeability_model>
             </fracture_properties>
             <initial_fracture_effective_stress>fracture_effective_stress0</initial_fracture_effective_stress>
             <secondary_variables>
-                <secondary_variable internal_name="sigma" output_name="sigma" />
-                <secondary_variable internal_name="epsilon" output_name="epsilon" />
-                <secondary_variable internal_name="velocity" output_name="velocity" />
-                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity" />
-                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability" />
-                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress" />
-                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture" />
+                <secondary_variable internal_name="sigma" output_name="sigma"/>
+                <secondary_variable internal_name="epsilon" output_name="epsilon"/>
+                <secondary_variable internal_name="velocity" output_name="velocity"/>
+                <secondary_variable internal_name="fracture_velocity" output_name="fracture_velocity"/>
+                <secondary_variable internal_name="fracture_permeability" output_name="fracture_permeability"/>
+                <secondary_variable internal_name="fracture_stress" output_name="fracture_stress"/>
+                <secondary_variable internal_name="fracture_aperture" output_name="fracture_aperture"/>
             </secondary_variables>
         </process>
     </processes>
@@ -112,6 +98,115 @@
             <suffix>_ts_{:timestep}_t_{:time}</suffix>
         </output>
     </time_loop>
+    <media>
+        <medium id="1">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Parameter</type>
+                    <parameter_name>k</parameter_name>
+                </property>
+                <property>
+                    <name>porosity</name>
+                    <type>Parameter</type>
+                    <parameter_name>phi</parameter_name>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_m</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+        <medium id="0">
+            <phases>
+                <phase>
+                    <type>AqueousLiquid</type>
+                    <properties>
+                        <property>
+                            <name>viscosity</name>
+                            <type>Parameter</type>
+                            <parameter_name>mu</parameter_name>
+                        </property>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_fr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+                <phase>
+                    <type>Solid</type>
+                    <properties>
+                        <property>
+                            <name>density</name>
+                            <type>Parameter</type>
+                            <parameter_name>rho_sr</parameter_name>
+                        </property>
+                    </properties>
+                </phase>
+            </phases>
+            <properties>
+                <property>
+                    <name>permeability</name>
+                    <type>Constant</type>
+                    <value>1e-11</value>
+                </property>
+                <property>
+                    <name>storage</name>
+                    <type>Parameter</type>
+                    <parameter_name>S_f</parameter_name>
+                </property>
+                <property>
+                    <name>biot_coefficient</name>
+                    <type>Parameter</type>
+                    <parameter_name>biot_f</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <!-- Fluid phase properties -->
         <parameter>
diff --git a/Tests/MaterialLib/TestMPLCubicLawPermeability.cpp b/Tests/MaterialLib/TestMPLCubicLawPermeability.cpp
index 4aa8dd7271afd9a66a0f797c57a1adb835b3c646..7c1d00a5ef931cc0b830861f450f2cae3c624baf 100644
--- a/Tests/MaterialLib/TestMPLCubicLawPermeability.cpp
+++ b/Tests/MaterialLib/TestMPLCubicLawPermeability.cpp
@@ -7,30 +7,55 @@
                Distributed under a Modified BSD License.
                See accompanying file LICENSE.txt or
                http://www.opengeosys.org/project/license
-*/
+ */
 #include <gtest/gtest.h>
 
 #include <memory>
+#include <vector>
 
 #include "MaterialLib/MPL/Properties/CubicLawPermeability.h"
 #include "ParameterLib/ConstantParameter.h"
 #include "TestMPL.h"
 
-TEST(MaterialPropertyLib, checkCubicLawPermeability)
+void testCubicLawPermeability(MPL::Property const& k_model,
+                              double const aperture, bool const is_predefined_b)
 {
-    ParameterLib::ConstantParameter<double> const b("b", 1.e-4);
-
-    MPL::Property const& k_model =
-        MPL::CubicLawPermeability{"CubicLawPermeability", b};
-
-    double const expected_k = 8.3333e-10;
-
     ParameterLib::SpatialPosition const pos;
     double const t = std::numeric_limits<double>::quiet_NaN();
     double const dt = std::numeric_limits<double>::quiet_NaN();
     MPL::VariableArray vars;
+    vars.fracture_aperture = aperture;
 
+    double const expected_k = aperture * aperture / 12.0;
     double const k = k_model.template value<double>(vars, pos, t, dt);
-
     ASSERT_NEAR(expected_k, k, 3.4e-15);
+
+    double const expected_dk = is_predefined_b ? 0.0 : aperture / 6.0;
+    double const dk = k_model.template dValue<double>(
+        vars, MPL::Variable::fracture_aperture, pos, t, dt);
+    ASSERT_NEAR(expected_dk, dk, 3.4e-15)
+        << "\nExpected dk " << expected_dk << "\nCalculated dk " << dk;
+}
+
+TEST(MaterialPropertyLib, checkCubicLawPermeability)
+{
+    std::vector<double> const apertures = {1.0e-4, 2.e-5, 3.0e-6};
+    for (double const aperture : apertures)
+    {
+        {  // Aperture as a variable:
+            MPL::Property const& k_model = MPL::CubicLawPermeability{
+                "CubicLawPermeability", nullptr /*predefined b*/};
+            testCubicLawPermeability(k_model, aperture,
+                                     false /*is_predefined_b*/);
+        }
+
+        {  // Aperture being pre-defined:
+            ParameterLib::ConstantParameter<double> const b("b", aperture);
+
+            MPL::Property const& k_model =
+                MPL::CubicLawPermeability{"CubicLawPermeability", &b};
+            testCubicLawPermeability(k_model, aperture,
+                                     true /*is_predefined_b*/);
+        }
+    }
 }