diff --git a/Applications/ApplicationsLib/ProjectData.cpp b/Applications/ApplicationsLib/ProjectData.cpp
index 66691e128ec13ff9feeeeee529befa4b9431627e..19de02f073bc874920ba93f9303fe2f4f945fd1c 100644
--- a/Applications/ApplicationsLib/ProjectData.cpp
+++ b/Applications/ApplicationsLib/ProjectData.cpp
@@ -544,7 +544,7 @@ void ProjectData::parseProcesses(BaseLib::ConfigTree const& processes_config,
             process = ProcessLib::GroundwaterFlow::createGroundwaterFlowProcess(
                 name, *_mesh_vec[0], std::move(jacobian_assembler),
                 _process_variables, _parameters, integration_order,
-                process_config, _mesh_vec, output_directory);
+                process_config, _mesh_vec, output_directory, _media);
         }
         else
 #endif
diff --git a/Applications/FileIO/XmlIO/OpenGeoSysProject.xsd b/Applications/FileIO/XmlIO/OpenGeoSysProject.xsd
index 632db0d229867441db0e3d1409020e6307d26c89..f9f4d93c655df8db470d149292ac80b160c3a38a 100644
--- a/Applications/FileIO/XmlIO/OpenGeoSysProject.xsd
+++ b/Applications/FileIO/XmlIO/OpenGeoSysProject.xsd
@@ -95,6 +95,7 @@
           </xs:complexType>
         </xs:element>
         <xs:element name="processes" minOccurs="0"/> <!--ignore-->
+        <xs:element name="media" minOccurs="1" maxOccurs="1"/> <!--ignore-->
         <xs:element name="time_loop" minOccurs="0"/> <!--ignore-->
         <xs:element name="parameters" minOccurs="0">
           <xs:complexType>
diff --git a/Documentation/ProjectFile/prj/processes/process/GROUNDWATER_FLOW/t_hydraulic_conductivity.md b/Documentation/ProjectFile/prj/processes/process/GROUNDWATER_FLOW/t_hydraulic_conductivity.md
deleted file mode 100644
index 576add64edccf5d980a0ff86143dc43a7109a788..0000000000000000000000000000000000000000
--- a/Documentation/ProjectFile/prj/processes/process/GROUNDWATER_FLOW/t_hydraulic_conductivity.md
+++ /dev/null
@@ -1 +0,0 @@
-\ogs_missing_documentation
diff --git a/MaterialLib/MPL/PropertyType.h b/MaterialLib/MPL/PropertyType.h
index 6c36701d8c8eaa8d60090c5650847a6d136bcc43..227a5353ee2c98154c3186dbe5b521be745dde4a 100644
--- a/MaterialLib/MPL/PropertyType.h
+++ b/MaterialLib/MPL/PropertyType.h
@@ -46,6 +46,7 @@ enum PropertyType : int
     /// used to specify decay rate of a substance.
     decay_rate,
     density,
+    diffusion,
     drhodT,
     effective_stress,
     entry_pressure,
@@ -138,6 +139,10 @@ inline PropertyType convertStringToProperty(std::string const& inString)
     {
         return PropertyType::density;
     }
+    if (boost::iequals(inString, "diffusion"))
+    {
+        return PropertyType::diffusion;
+    }
     if (boost::iequals(inString, "drhodT"))
     {
         return PropertyType::drhodT;
@@ -280,6 +285,7 @@ static const std::array<std::string, PropertyType::number_of_properties>
                              "compressibility",
                              "decay_rate",
                              "density",
+                             "diffusion",
                              "drhodT",
                              "effective_stress",
                              "entry_pressure",
diff --git a/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.cpp b/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.cpp
index e62f319cb5457a3c0cdcc60d96ba271f1b091be0..204ec22ff7d8936b47a6ba1fa0def411314b6ab5 100644
--- a/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.cpp
+++ b/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.cpp
@@ -13,6 +13,8 @@
 #include "BaseLib/FileTools.h"
 #include "GroundwaterFlowProcess.h"
 #include "GroundwaterFlowProcessData.h"
+#include "MaterialLib/MPL/CreateMaterialSpatialDistributionMap.h"
+#include "MaterialLib/MPL/MaterialSpatialDistributionMap.h"
 #include "MeshLib/IO/readMeshFromFile.h"
 #include "ParameterLib/Utils.h"
 #include "ProcessLib/Output/CreateSecondaryVariables.h"
@@ -31,7 +33,8 @@ std::unique_ptr<Process> createGroundwaterFlowProcess(
     unsigned const integration_order,
     BaseLib::ConfigTree const& config,
     std::vector<std::unique_ptr<MeshLib::Mesh>> const& meshes,
-    std::string const& output_directory)
+    std::string const& output_directory,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media)
 {
     //! \ogs_file_param{prj__processes__process__type}
     config.checkConfigParameter("type", "GROUNDWATER_FLOW");
@@ -51,17 +54,10 @@ std::unique_ptr<Process> createGroundwaterFlowProcess(
          "process_variable"});
     process_variables.push_back(std::move(per_process_variables));
 
-    // Hydraulic conductivity parameter.
-    auto& hydraulic_conductivity = ParameterLib::findParameter<double>(
-        config,
-        //! \ogs_file_param_special{prj__processes__process__GROUNDWATER_FLOW__hydraulic_conductivity}
-        "hydraulic_conductivity", parameters, 0 /*arbitrary many components*/,
-        &mesh);
+    auto media_map =
+        MaterialPropertyLib::createMaterialSpatialDistributionMap(media, mesh);
 
-    DBUG("Use '%s' as hydraulic conductivity parameter.",
-         hydraulic_conductivity.name.c_str());
-
-    GroundwaterFlowProcessData process_data{hydraulic_conductivity};
+    GroundwaterFlowProcessData process_data{std::move(media_map)};
 
     SecondaryVariableCollection secondary_variables;
 
diff --git a/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.h b/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.h
index fd28028d3bdaddaa1527a2ddbbcca8200c02a6e7..afb2fdc84d427fca733b92e3fc9d3400ea12008a 100644
--- a/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.h
+++ b/ProcessLib/GroundwaterFlow/CreateGroundwaterFlowProcess.h
@@ -13,6 +13,10 @@
 #include <memory>
 #include "ProcessLib/Process.h"
 
+namespace MaterialPropertyLib
+{
+class Medium;
+}
 
 namespace ProcessLib
 {
@@ -27,7 +31,8 @@ std::unique_ptr<Process> createGroundwaterFlowProcess(
     unsigned const integration_order,
     BaseLib::ConfigTree const& config,
     std::vector<std::unique_ptr<MeshLib::Mesh>> const& meshes,
-    std::string const& output_directory);
+    std::string const& output_directory,
+    std::map<int, std::shared_ptr<MaterialPropertyLib::Medium>> const& media);
 
 }   // namespace GroundwaterFlow
 }   // namespace ProcessLib
diff --git a/ProcessLib/GroundwaterFlow/GroundwaterFlowFEM.h b/ProcessLib/GroundwaterFlow/GroundwaterFlowFEM.h
index edc5f0dbbc4ba624b3bd42e383d4a73042a5af65..60f2466ca15dcfc480ec158d6140a0674ec9d15c 100644
--- a/ProcessLib/GroundwaterFlow/GroundwaterFlowFEM.h
+++ b/ProcessLib/GroundwaterFlow/GroundwaterFlowFEM.h
@@ -13,11 +13,15 @@
 #include <vector>
 
 #include "GroundwaterFlowProcessData.h"
+#include "MaterialLib/MPL/Medium.h"
+#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
+#include "MaterialLib/MPL/VariableType.h"
 #include "MathLib/LinAlg/Eigen/EigenMapTools.h"
 #include "NumLib/DOF/DOFTableUtil.h"
 #include "NumLib/Extrapolation/ExtrapolatableElement.h"
 #include "NumLib/Fem/FiniteElement/TemplateIsoparametric.h"
 #include "NumLib/Fem/ShapeMatrixPolicy.h"
+#include "NumLib/Function/Interpolation.h"
 #include "ParameterLib/Parameter.h"
 #include "ProcessLib/LocalAssemblerInterface.h"
 #include "ProcessLib/LocalAssemblerTraits.h"
@@ -29,34 +33,6 @@ namespace GroundwaterFlow
 {
 const unsigned NUM_NODAL_DOF = 1;
 
-template <int GlobalDim>
-Eigen::Matrix<double, GlobalDim, GlobalDim> hydraulicConductivity(
-    std::vector<double> const& values)
-{
-    auto const size{values.size()};
-    if (size == 1)  // This is a duplicate but preferred case for GlobalDim==1.
-    {
-        return Eigen::Matrix<double, GlobalDim, GlobalDim>::Identity() *
-               values[0];
-    }
-    if (size == GlobalDim)
-    {
-        return Eigen::Map<Eigen::Matrix<double, GlobalDim, 1> const>(
-                   values.data(), GlobalDim, 1)
-            .asDiagonal();
-    }
-    if (size == GlobalDim * GlobalDim)
-    {
-        return Eigen::Map<Eigen::Matrix<double, GlobalDim, GlobalDim> const>(
-            values.data(), GlobalDim, GlobalDim);
-    }
-
-    OGS_FATAL(
-        "Hydraulic conductivity parameter values size is neither one nor %d "
-        "nor %d squared, but %d.",
-        GlobalDim, GlobalDim, values.size());
-}
-
 class GroundwaterFlowLocalAssemblerInterface
     : public ProcessLib::LocalAssemblerInterface,
       public NumLib::ExtrapolatableElement
@@ -100,7 +76,7 @@ public:
     {
     }
 
-    void assemble(double const t, double const /*dt*/,
+    void assemble(double const t, double const dt,
                   std::vector<double> const& local_x,
                   std::vector<double> const& /*local_xdot*/,
                   std::vector<double>& /*local_M_data*/,
@@ -121,13 +97,28 @@ public:
         ParameterLib::SpatialPosition pos;
         pos.setElementID(_element.getID());
 
+        auto const& medium =
+            *_process_data.media_map->getMedium(_element.getID());
+        MaterialPropertyLib::VariableArray vars;
+        vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
+            medium
+                .property(
+                    MaterialPropertyLib::PropertyType::reference_temperature)
+                .template value<double>(vars, pos, t, dt);
+
         for (unsigned ip = 0; ip < n_integration_points; ip++)
         {
             pos.setIntegrationPoint(ip);
             auto const& sm = _shape_matrices[ip];
             auto const& wp = _integration_method.getWeightedPoint(ip);
-            auto const k = hydraulicConductivity<GlobalDim>(
-                _process_data.hydraulic_conductivity(t, pos));
+
+            double p_int_pt = 0.0;
+            NumLib::shapeFunctionInterpolate(local_x, sm.N, p_int_pt);
+            vars[static_cast<int>(
+                MaterialPropertyLib::Variable::phase_pressure)] = p_int_pt;
+            auto const k = MaterialPropertyLib::formEigenTensor<GlobalDim>(
+                medium.property(MaterialPropertyLib::PropertyType::diffusion)
+                    .value(vars, pos, t, dt));
 
             local_K.noalias() += sm.dNdx.transpose() * k * sm.dNdx * sm.detJ *
                                  sm.integralMeasure * wp.getWeight();
@@ -140,6 +131,10 @@ public:
                             double const t,
                             std::vector<double> const& local_x) const override
     {
+        // TODO (tf) Temporary value not used by current material models. Need
+        // extension of getFlux interface
+        double const dt = std::numeric_limits<double>::quiet_NaN();
+
         // eval dNdx and invJ at p
         auto const fe = NumLib::createIsoparametricFiniteElement<
             ShapeFunction, ShapeMatricesType>(_element);
@@ -155,10 +150,25 @@ public:
         // fetch hydraulic conductivity
         ParameterLib::SpatialPosition pos;
         pos.setElementID(_element.getID());
-        auto const k = hydraulicConductivity<GlobalDim>(
-            _process_data.hydraulic_conductivity(t, pos));
-
-        Eigen::Vector3d flux;
+        auto const& medium =
+            *_process_data.media_map->getMedium(_element.getID());
+
+        MaterialPropertyLib::VariableArray vars;
+        vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
+            medium
+                .property(
+                    MaterialPropertyLib::PropertyType::reference_temperature)
+                .template value<double>(vars, pos, t, dt);
+        double pressure = 0.0;
+        NumLib::shapeFunctionInterpolate(local_x, shape_matrices.N, pressure);
+        vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
+            pressure;
+
+        auto const k = MaterialPropertyLib::formEigenTensor<GlobalDim>(
+            medium.property(MaterialPropertyLib::PropertyType::diffusion)
+                .value(vars, pos, t, dt));
+
+        Eigen::Vector3d flux(0.0, 0.0, 0.0);
         flux.head<GlobalDim>() =
             -k * shape_matrices.dNdx *
             Eigen::Map<const NodalVectorType>(local_x.data(), local_x.size());
@@ -181,6 +191,10 @@ public:
         std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table,
         std::vector<double>& cache) const override
     {
+        // TODO (tf) Temporary value not used by current material models. Need
+        // extension of secondary variable interface.
+        double const dt = std::numeric_limits<double>::quiet_NaN();
+
         auto const n_integration_points =
             _integration_method.getNumberOfPoints();
 
@@ -201,11 +215,27 @@ public:
         ParameterLib::SpatialPosition pos;
         pos.setElementID(_element.getID());
 
+        auto const& medium =
+            *_process_data.media_map->getMedium(_element.getID());
+
+        MaterialPropertyLib::VariableArray vars;
+        vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
+            medium
+                .property(
+                    MaterialPropertyLib::PropertyType::reference_temperature)
+                .template value<double>(vars, pos, t, dt);
+        double pressure = 0.0;
         for (unsigned i = 0; i < n_integration_points; ++i)
         {
             pos.setIntegrationPoint(i);
-            auto const k = hydraulicConductivity<GlobalDim>(
-                _process_data.hydraulic_conductivity(t, pos));
+            NumLib::shapeFunctionInterpolate(local_x, _shape_matrices[i].N,
+                                             pressure);
+            vars[static_cast<int>(
+                MaterialPropertyLib::Variable::phase_pressure)] = pressure;
+
+            auto const k = MaterialPropertyLib::formEigenTensor<GlobalDim>(
+                medium.property(MaterialPropertyLib::PropertyType::diffusion)
+                    .value(vars, pos, t, dt));
             // dimensions: (d x 1) = (d x n) * (n x 1)
             cache_mat.col(i).noalias() =
                 -k * _shape_matrices[i].dNdx * local_x_vec;
diff --git a/ProcessLib/GroundwaterFlow/GroundwaterFlowProcess.cpp b/ProcessLib/GroundwaterFlow/GroundwaterFlowProcess.cpp
index 7a566705d8a8cedda001e1671ba7b7b4da3723ac..5e955ce8abeca6ae629115ee4e9dbc34f80d0afd 100644
--- a/ProcessLib/GroundwaterFlow/GroundwaterFlowProcess.cpp
+++ b/ProcessLib/GroundwaterFlow/GroundwaterFlowProcess.cpp
@@ -18,6 +18,27 @@ namespace ProcessLib
 {
 namespace GroundwaterFlow
 {
+
+void checkMPLProperties(MeshLib::Mesh const& mesh,
+                        GroundwaterFlowProcessData const& process_data)
+{
+    DBUG("Check the media properties of HT process ...");
+
+    std::array const requiredPropertyMedium = {
+        MaterialPropertyLib::PropertyType::reference_temperature,
+        MaterialPropertyLib::PropertyType::diffusion};
+
+    for (auto const& element : mesh.getElements())
+    {
+        auto const element_id = element->getID();
+
+        auto const& medium = *process_data.media_map->getMedium(element_id);
+        MaterialPropertyLib::checkRequiredProperties(
+            medium, requiredPropertyMedium);
+    }
+    DBUG("Media properties verified.");
+}
+
 GroundwaterFlowProcess::GroundwaterFlowProcess(
     std::string name,
     MeshLib::Mesh& mesh,
@@ -42,6 +63,7 @@ void GroundwaterFlowProcess::initializeConcreteProcess(
     MeshLib::Mesh const& mesh,
     unsigned const integration_order)
 {
+    checkMPLProperties(mesh, _process_data);
     const int process_id = 0;
     ProcessLib::ProcessVariable const& pv = getProcessVariables(process_id)[0];
     ProcessLib::createLocalAssemblers<LocalAssemblerData>(
diff --git a/ProcessLib/GroundwaterFlow/GroundwaterFlowProcessData.h b/ProcessLib/GroundwaterFlow/GroundwaterFlowProcessData.h
index d1d53d46307e59f946ac9066d0d109ebf2eeac20..b077da15b3cd08e632127ebf9ab572c9e0a207f9 100644
--- a/ProcessLib/GroundwaterFlow/GroundwaterFlowProcessData.h
+++ b/ProcessLib/GroundwaterFlow/GroundwaterFlowProcessData.h
@@ -10,6 +10,9 @@
 
 #pragma once
 
+#include <memory>
+#include "MaterialLib/MPL/MaterialSpatialDistributionMap.h"
+
 namespace ProcessLib
 {
 
@@ -20,7 +23,8 @@ namespace GroundwaterFlow
 {
 struct GroundwaterFlowProcessData final
 {
-    ParameterLib::Parameter<double> const& hydraulic_conductivity;
+    std::unique_ptr<MaterialPropertyLib::MaterialSpatialDistributionMap>
+        media_map;
 };
 
 } // namespace GroundwaterFlow
diff --git a/ProcessLib/LiquidFlow/LiquidFlowLocalAssembler-impl.h b/ProcessLib/LiquidFlow/LiquidFlowLocalAssembler-impl.h
index cf5131192350b1478ed6839515223ffadb0bc99f..da90cbdc39ed2c1c2f197319959cce67ae1814dd 100644
--- a/ProcessLib/LiquidFlow/LiquidFlowLocalAssembler-impl.h
+++ b/ProcessLib/LiquidFlow/LiquidFlowLocalAssembler-impl.h
@@ -233,8 +233,6 @@ LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
 
     ParameterLib::SpatialPosition pos;
     pos.setElementID(_element.getID());
-    // evaluate the permeability to distinguish which computeDarcyVelocity
-    // method should be used
 
     auto const& medium = _process_data.media_map->getMedium(_element.getID());
     MaterialPropertyLib::VariableArray vars;
@@ -252,6 +250,8 @@ LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
     //  the assert must be changed to perm.rows() == _element->getDimension()
     assert(permeability.rows() == GlobalDim || permeability.rows() == 1);
 
+    // evaluate the permeability to distinguish which computeDarcyVelocity
+    // method should be used
     if (permeability.size() == 1)
     {  // isotropic or 1D problem.
         computeDarcyVelocityLocal<IsotropicCalculator>(t, dt, local_x, pos,
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e1_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e1_axi.prj
index f6a2578f46a6f9b8114f4aeb58443fcbdc7fe9ce..8df58bc5e03279d1bdcaab928cf033e596017c41 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e1_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e1_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e2_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e2_axi.prj
index 184c22e47c71a0ff4597b2345154f69ca7dfb16d..5fe1e967e09f7f327574a6af2575f6396fd47aba 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e2_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e2_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e3_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e3_axi.prj
index e871bafa8096ca2fa37a66c170333c3a1c905daa..d3294a8027f55e3f574ed3d3ec3385fc01492808 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e3_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e3_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e4_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e4_axi.prj
index 434e0fc982397e59879d9317b7513c611aa6866e..86508cfd095f52f5503fd7fa4266b7a69bda83f7 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e4_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e4_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e5_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e5_axi.prj
index c62df8ea448060c75079d73b5b7b5354b3527a7f..8b0c584ce53bb684f2754faf744ca2b259f7a1f7 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e5_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e5_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/circle_radius_1/circle_1e6_axi.prj b/Tests/Data/Elliptic/circle_radius_1/circle_1e6_axi.prj
index 164171bbd169f1bd0106b05bd1043bf846e92258..3beff0d3a22e0cfbbb7a14a60588f604925bd1f2 100644
--- a/Tests/Data/Elliptic/circle_radius_1/circle_1e6_axi.prj
+++ b/Tests/Data/Elliptic/circle_radius_1/circle_1e6_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>kappa</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -64,11 +80,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>kappa</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0.prj
index c309829114cb06ad01539f07b0b022ade1644a41..95d8326904b9f028f17f5a30e2d8b748a84d7e10 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,22 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1.0</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_neumann.prj
index 9fd4b526b60a034dbcf27f30c269287fed4f8af2..e99d60e9128ef6ae30d0a7155fc9701c8fc71994 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_newton.prj
index aa6e07e5bb4d88a3853908c59b50a185c4f05c49..8198f350da50c029832b831f9e4ac3078a507263 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_quadratic_hex.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_quadratic_hex.prj
index 4edd8550694f54423d0114afb654735f80fe0633..ec2d0ae578c684cc4c75a205ceb9cc91996f0519 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_quadratic_hex.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e0_quadratic_hex.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>3</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1.prj
index 2e8b45969e1930ac5cb426030934e12f6eb6a42a..2eb1df2fe92c4a39e2e1e5590856c4e5c0e03df6 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_neumann.prj
index de178a40b0894405ea315c4efe6025573164cb47..d194b4ec6bdb5ad268c9d0176a674df5f2265154 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_newton.prj
index 60d99876454d853d73582b0cdd3b0b3fd5688cba..4ff5a14ecf53595e8f5a6bb8023dd94c5d834ef1 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e1_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2.prj
index afd6f7a3fb6a634653e339b19264053a47db1cc5..753497c0ed5fbb277abb9c11d3ad95bdd151d9b5 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_neumann.prj
index cffead857083eaed0314bacc0193fadebae93545..ec15554f7106f9e46d9eb6bb63a5f0e15ea05cc7 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_newton.prj
index 2af8e9def81e589974004b6fd4e95b2d82acbbdd..aea7d9ecf395ccc6c710b4e0721309211fd711f1 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e2_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3.prj
index c0ee1e5e7dc5973b455c7cefc184881f7ceaf80a..0ca2ea6b52af33a99cb98dc9d774fdb3f0913207 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann.prj
index 5991272041659ce9a6e7dde736cb54582e0de631..55a9a3dff2069a7858cb995ac6c1c159fc039f74 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann_newton.prj
index f7ea01441e713ef3da607a716b1e376619a2e4a3..875dca47786191b3eb60341ea3ce3ad7f6e771af 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_bottom_neumann_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_calculatesurfaceflux.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_calculatesurfaceflux.prj
index ec9a1b6ea1a7ea8404c5b22a3b68408d63cce3fc..6f40705d6dcab3d07ba42a4e16afca6aa2ff0a40 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_calculatesurfaceflux.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_calculatesurfaceflux.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -51,12 +50,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann.prj
index 4da682e0255a6071793587b827ea3bdd4e62444b..608755d4bc2dfad48c938589d951facd8b8ed52b 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann_calculatesurfaceflux.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann_calculatesurfaceflux.prj
index 69a8794d7fc857a5a58b9ff1f023b5a0517855cf..08484cfbfe4d1b78c5f73ed7fe45c82c2753a5cd 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann_calculatesurfaceflux.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_neumann_calculatesurfaceflux.prj
@@ -12,7 +12,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -52,12 +51,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_newton.prj
index ddef55c40e682d7e8a765a6ebd23f6997e06de08..0065590188ff17f9619df2c01a22f8f581bcfa30 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann.prj
index d74457c5f9d13bf74d63c3b4ae9b98899c116c00..ea34bfcaf7d83a2ec4b8375262e66dad0065076c 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann_newton.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann_newton.prj
index 1846d5608d98a43d3c34accb87e38c251a96d215..7e039e8458dc19979e167e8818248f4e4853648e 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann_newton.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e3_top_neumann_newton.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <jacobian_assembler>
                 <type>CentralDifferences</type>
             </jacobian_assembler>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4.prj
index 1bde58382a00e7dd937514802a791f2fcafacdb5..34fa47cc690380fd680055a23388ed8a9e046db8 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj
index aa861751cdefed09c73ce5004e358ab331a8e0a6..ccdff219b9df5801bace69ca66d25011ccb062a5 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,22 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0,1,2">
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Parameter</type>
+                    <parameter_name>K</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_neumann.prj
index a7c4ce970b8ef54f724c40b39c27d3fd2f1f63de..36967f535fff2957517a4f40b23a5f253afa949a 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5.prj
index 37372ec3b5bee76e48bf5abf55d8b264c6840ff2..52a9b0fb763e903df797d224af956484de9d95b0 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5_neumann.prj
index 931bd42dfef12479039cde38bd2670bda99d0879..dd5eb314e53bc9137bebcf193ebe05d0817eaf42 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e5_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6.prj
index 4ee3ca943442b4f8491617e538b9c580ceba2c91..cddccfe8715670b6a376262b767ebb83166cad27 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6_neumann.prj
index bba20ef0c6684847455497fae30f5c767246233e..7b6a62a38815ff53bf02647eee1dde2ceea50406 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e6_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_front_back.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_front_back.prj
index bfbf38cf3688d3663645c499c8ed7e650ea29e12..2a31d7c0ea67aec5eb3a6f6b8106845de3caf206 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_front_back.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_front_back.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -51,12 +50,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_left_right.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_left_right.prj
index 51f9eda2d21f74915ccb8d75fa53425d6a6c74ff..d23f3d306690017ff18ca192480937f89edb6e01 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_left_right.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_left_right.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -51,12 +50,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_top_bottom.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_top_bottom.prj
index 4354d87bc67c6ea7e6e21aa127fd176ed79da3bb..c0aa43205d12729cd53c28f310f3bcaa49ec2af5 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_top_bottom.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e3_prism_surfaceflux_top_bottom.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -51,12 +50,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4.prj
index dac304cddba9b8b63e19a0868cc1f9e71516416e..737726e79fa386737aa1a6f31e66f7ee14ade4b2 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4_neumann.prj
index 4db9b7517b61b64d5b3a84e3a8e7069ca577f8e9..857e48f0c8f638c8a8e00d6261e2b02d62e55f82 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_2e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4.prj
index bd79b4cb102466419c2939b9e8427d6f22cda928..fbcca06b49dcb0d1b380f561468f241bcc11255e 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4_neumann.prj
index c185a39eba528a394f4038571b920cceebc06b33..98142b262a51cd140f30672d6f0f79832c4b2f9f 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_3e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4.prj
index 68dcb4e968c1d08b182a5bcceb430175a5971777..6c23a97a11a3659b0c98d5f4f04ffd3db0b65764 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4_neumann.prj
index 860aa3097391cda95797c733ed17921d5a4b6241..c6e44a5742e2672d9ee5e0960510247481f64796 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_4e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4.prj
index b81c0d15f94a35d57c3edeff085a0578d0dd9fb9..0a3f4ad3a297cf65f3b11cd454619535fbc95f02 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4_neumann.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4_neumann.prj
index 6fde1a8c3f2a36334f6f8d4b031c5f42ea68abb6..86704e486570df785b309d46b0c44d6fe217e0db 100644
--- a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4_neumann.prj
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_5e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1.prj
index e8c97392e4079db6ec9b17ef4e3b69b3220ec45c..8f001482a366441e2f24f31056fea2efbe2763de 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_neumann.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_neumann.prj
index 1d7e812c93419890d333f3c29de401a55ff71cd5..204e420e5f4bc3fad3dcae4c57445769bd22dae3 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_neumann.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_left_picard.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_left_picard.prj
index ff24721ab0f0adcccc41b5e621038911df98e4d0..deaf95397295ea8056ba4316221df5e888e3ce7a 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_left_picard.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_left_picard.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_right_picard.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_right_picard.prj
index 98695821e58ecbcbab4777ff2fdc8f047ed97fba..694ea40d8733553e153b2cbe0762644538b9dc43 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_right_picard.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_robin_right_picard.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_dirichlet.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_dirichlet.prj
index ce774933a8bd7b93659095cbeb999fc1b2b8f1bf..8f25c81e8d50f9c79499687431ab2d7303a37fcb 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_dirichlet.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_dirichlet.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -51,11 +67,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_neumann.prj b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_neumann.prj
index 3509ce978f8ff3957b489a1dd671fbb541cf7fad..cf35554f4f48912223d0c815f377b8575beef6f6 100644
--- a/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_neumann.prj
+++ b/Tests/Data/Elliptic/line_1_GroundWaterFlow/line_1e1_time_dep_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -51,11 +67,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/dirichlet_nonuniform.prj b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/dirichlet_nonuniform.prj
index 7518b9483bbb621aee9d51739beebd26cb73eab1..4120c704cf22b57d6953e3dc9baee94d26cdaadc 100644
--- a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/dirichlet_nonuniform.prj
+++ b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/dirichlet_nonuniform.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -43,12 +42,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/inhomogeneous_permeability.prj b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/inhomogeneous_permeability.prj
index 612a2cc0036f9b07436f9f9f36e9574b734801aa..c91f2aa83d1e59ab9730f74286e388c989c94feb 100644
--- a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/inhomogeneous_permeability.prj
+++ b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/inhomogeneous_permeability.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K_rho_over_mu__eff</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -45,6 +44,23 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Parameter</type>
+                    <parameter_name>K_rho_over_mu__eff</parameter_name>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
         <parameter>
             <name>K_rho_over_mu__eff</name>
diff --git a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/neumann_nonuniform.prj b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/neumann_nonuniform.prj
index b0f4fdccd2153276cc13bf7cf95f8f78961551eb..b15d347c7673c8fec90209984922189468d893ae 100644
--- a/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/neumann_nonuniform.prj
+++ b/Tests/Data/Elliptic/nonuniform_bc_Groundwaterflow/neumann_nonuniform.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -19,6 +18,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -46,11 +62,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/quarter_circle/quarter_circle_neumann.prj b/Tests/Data/Elliptic/quarter_circle/quarter_circle_neumann.prj
index a777723bac1cde8b2c095640091b22be0c86030b..bbfb3f3769d3f8668815096859a6ff559d734de8 100644
--- a/Tests/Data/Elliptic/quarter_circle/quarter_circle_neumann.prj
+++ b/Tests/Data/Elliptic/quarter_circle/quarter_circle_neumann.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -45,12 +44,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/quarter_circle/quarter_circle_nodal_source_term.prj b/Tests/Data/Elliptic/quarter_circle/quarter_circle_nodal_source_term.prj
index 9f14e245fd26d8ad2285946c2f649a79780c9c14..180814fd4fffc203473c544fdfb93e3b4902f660 100644
--- a/Tests/Data/Elliptic/quarter_circle/quarter_circle_nodal_source_term.prj
+++ b/Tests/Data/Elliptic/quarter_circle/quarter_circle_nodal_source_term.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -45,12 +44,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/quarter_disc/quarter_disc_neumann.prj b/Tests/Data/Elliptic/quarter_disc/quarter_disc_neumann.prj
index 79fcd1c3af86cb920d7f67869c08bb072eaf1a0d..74e71c44594a6e8057484def287f340889b8f05a 100644
--- a/Tests/Data/Elliptic/quarter_disc/quarter_disc_neumann.prj
+++ b/Tests/Data/Elliptic/quarter_disc/quarter_disc_neumann.prj
@@ -10,7 +10,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -45,12 +44,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0.prj
index 53626ae68ef3d298585a558487327327dfe628f8..48ad673ffa8fad09e9fbf7108cb0a8b14a5f5963 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0_neumann.prj
index 35fe277fd30957048d0f688f3687283d9a9df592..16169c7fb2137a9ee453719c8ccec4342e656d9d 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e0_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1.prj
index cb2c9f282fd352521a4b3fa1d5c63528ad87892f..b213ed82dd3292a652fc2d2ca6476f7ccec5cb9b 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1_neumann.prj
index 3c18b6e6a804fd24029710dc7d030d66d14a4b49..2339212bdd2c23f59fdd235e99651aab3762ddc1 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e1_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2.prj
index 87166a70ba2371389cbd795c2128e75ba790002b..e07d1018a89151bc9f0ef54d83900ad2395570bf 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_axi.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_axi.prj
index f35ae347aa172f3b881fb372c4da00f4f0e121e3..80cfc38bd2f699b4dae9552ac98a1fd253f90767 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_axi.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>lambda</hydraulic_conductivity>
             <process_variables>
                 <process_variable>temperature</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>lambda</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>T0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann.prj
index a4cbfb8ee3ac3c83ebf19b29d0561ce8fff9d92c..2a16e6d38e6ed87b259e494312a43a61f417cbba 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj
index d8021955422eabfe3554b423eef45fba61f3ccaf..dae05500bfc4cade87d408384e8d6f333a77a4ac 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -46,6 +45,23 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <nonlinear_solvers>
         <nonlinear_solver>
             <name>basic_picard</name>
@@ -71,11 +87,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3.prj
index 3fd2835e4164b1cd85ef1e0058c993558e861901..cdce472e308e23a774dec35a043da54eb3db7f0f 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3.prj
@@ -3,6 +3,23 @@
     <mesh>square_1x1_quad_1e3.vtu</mesh>
     <geometry>square_1x1.gml</geometry>
     <!-- Just for testing the search length algorithm -->
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <search_length_algorithm>
         <type>fixed</type>
         <value>1e-16</value>
@@ -12,7 +29,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -48,11 +64,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_neumann.prj
index 2e24501732dcedf0abc679142403cd6e67f56d76..459fefd5f8433422b5d93f6a35a19c9cea2eecde 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_neumann.prj
@@ -3,6 +3,23 @@
     <mesh>square_1x1_quad_1e3.vtu</mesh>
     <geometry>square_1x1.gml</geometry>
     <!-- Just for testing the search length algorithm -->
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <search_length_algorithm>
         <type>heuristic</type>
     </search_length_algorithm>
@@ -11,7 +28,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -47,11 +63,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourceterm.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourceterm.prj
index 1cbaaf46fa623a3343c42a05f284409a4fc03eea..8c0369b3103aedc10d90266748e6b83819462ca6 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourceterm.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourceterm.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -46,6 +45,23 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <nonlinear_solvers>
         <nonlinear_solver>
             <name>basic_picard</name>
@@ -71,11 +87,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourcetermdataarray.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourcetermdataarray.prj
index c00549d22e03024be0b92f15894e775c035e29f9..cae7e56b40af92b26b94a2aefd9e612b9729ccd6 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourcetermdataarray.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e3_volumetricsourcetermdataarray.prj
@@ -13,7 +13,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -48,6 +47,23 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <nonlinear_solvers>
         <nonlinear_solver>
             <name>basic_picard</name>
@@ -73,11 +89,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4.prj
index 650b394cce2aaf7616fa2ab29908be7e39645e84..8ff290334164cfc7799e9e2b14f19b8973746f6a 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_axi.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_axi.prj
index e8bfbd73ec4f9012098071ebe02387822b871f66..0d8d0e80e6b3889f25525deede6bc4deca805bb5 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_axi.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_axi.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>lambda</hydraulic_conductivity>
             <process_variables>
                 <process_variable>temperature</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>lambda</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>T0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_neumann.prj
index d4c9c92a0eaf0d7411e6881b841699d947288504..0364a7cab58bcaeb3a9423bf6fd0c3dce72facd8 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e4_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5.prj
index fb71d9ba40f6a55dc7609c00a64e26548f70c0f5..b505f9f61ac1e2ba0ce14535304e30d2c1e9e991 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5_neumann.prj
index a3e454b77f582b49463d2ccd6c6b8e6a88b19cec..7b1afd293d5bc70a55f84ab848786fad2882d11a 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e5_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6.prj
index b40597d22196d5035f390709633a806e716cd390..c7e2fcb966ed0bbec1788640ff870941e1256cc1 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_neumann.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_neumann.prj
index e383b2ef5c93bcd4a822892d18385c3546482e44..4c51332fb8ac4c5dc133381d9cba9127635ac222 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_neumann.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_neumann.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_with_nodal_sources.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_with_nodal_sources.prj
index c3903948740320deb5ab6fb2b05a97d3f0fcbb45..ec4a93b62db2d95c0d1691e8f43fac8dd5a4a44a 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_with_nodal_sources.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e6_with_nodal_sources.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -46,12 +45,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.02.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.02.prj
index 92f9a49376c79beb0168edc3ea178c2338698e01..dea3c954e83971236eae55a5acc57a3b835c65ed 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.02.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.02.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>lambda</hydraulic_conductivity>
             <process_variables>
                 <process_variable>temperature</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>lambda</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>T0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.2.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.2.prj
index 89983c2455f5dccdc79fc51f0ce1480d2cd983d1..967ae756d50c227b4ddf732691b8ef8e061c93d1 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.2.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e2_axi_ang_0.2.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>lambda</hydraulic_conductivity>
             <process_variables>
                 <process_variable>temperature</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>lambda</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>T0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e4_axi_ang_0.02.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e4_axi_ang_0.02.prj
index fc176992031f9a6b6cb7b37eecc8c714cff88a36..ff53423bb32f36e9cb5f5e500731c9907520921b 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e4_axi_ang_0.02.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/wedge_1e4_axi_ang_0.02.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>lambda</hydraulic_conductivity>
             <process_variables>
                 <process_variable>temperature</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -67,11 +83,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>lambda</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>T0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_laplace_eq.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_laplace_eq.prj
index d8b1b22508d1d3dae016f0ae733d059bf4c327ab..3f70304f582694913afcfad0f35648604fa4c7f7 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_laplace_eq.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_laplace_eq.prj
@@ -3,12 +3,28 @@
     <mesh>square_1x1_quad_1e3.vtu</mesh>
     <geometry>square_1x1.gml</geometry>
     <python_script>bcs_laplace_eq.py</python_script>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <processes>
         <process>
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -47,11 +63,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>zero</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_poisson_sin_x_sin_y.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_poisson_sin_x_sin_y.prj
index c7f95d4901d9b08396435b33e3d953acabc2c102..d95416989bb222284808a27ead2b5558d6d342df 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_poisson_sin_x_sin_y.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e3_poisson_sin_x_sin_y.prj
@@ -14,7 +14,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -23,6 +22,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -74,11 +90,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e5_poisson_sin_x_sin_y.prj b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e5_poisson_sin_x_sin_y.prj
index b02c9167683969e51ec13656ffccacd6926fc2df..29708886a1dc5b6a2463458c6d2d29bec86ee91f 100644
--- a/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e5_poisson_sin_x_sin_y.prj
+++ b/Tests/Data/Elliptic/square_1x1_GroundWaterFlow_Python/square_1e5_poisson_sin_x_sin_y.prj
@@ -14,7 +14,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -23,6 +22,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -74,11 +90,6 @@
         </linear_solver>
     </linear_solvers>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/Elliptic/wedge_1x1x1_GroundWaterFlow/wedge_1e3_prism_surfaceflux_diagonal.prj b/Tests/Data/Elliptic/wedge_1x1x1_GroundWaterFlow/wedge_1e3_prism_surfaceflux_diagonal.prj
index f4d72987e19b38f40e05c40890018a7cdb88d1b4..fb8a562995621c9c28541c6277d013533cb5cd74 100644
--- a/Tests/Data/Elliptic/wedge_1x1x1_GroundWaterFlow/wedge_1e3_prism_surfaceflux_diagonal.prj
+++ b/Tests/Data/Elliptic/wedge_1x1x1_GroundWaterFlow/wedge_1e3_prism_surfaceflux_diagonal.prj
@@ -11,7 +11,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -51,12 +50,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/EllipticPETSc/cube_1e3.prj b/Tests/Data/EllipticPETSc/cube_1e3.prj
index a26ccc75609282060566c9da5265943f0f4d60c8..467c177dc7326d4679b12e104bf185295eb6a0f2 100644
--- a/Tests/Data/EllipticPETSc/cube_1e3.prj
+++ b/Tests/Data/EllipticPETSc/cube_1e3.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/EllipticPETSc/cube_1e3_neumann.prj b/Tests/Data/EllipticPETSc/cube_1e3_neumann.prj
index 45b58ebeb7ad031a568386a4a891e22231a3ab08..cb465ee5811ccd4a82faee741d5b2e19a1be6555 100644
--- a/Tests/Data/EllipticPETSc/cube_1e3_neumann.prj
+++ b/Tests/Data/EllipticPETSc/cube_1e3_neumann.prj
@@ -14,7 +14,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -49,12 +48,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/EllipticPETSc/quad_20x10_GroundWaterFlow.prj b/Tests/Data/EllipticPETSc/quad_20x10_GroundWaterFlow.prj
index b14f6d2a545ad78acd9662478ad868f6ad42fe83..d3dd5bc7b1e4846007f9d3c83862e5d63395487b 100644
--- a/Tests/Data/EllipticPETSc/quad_20x10_GroundWaterFlow.prj
+++ b/Tests/Data/EllipticPETSc/quad_20x10_GroundWaterFlow.prj
@@ -7,7 +7,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -16,6 +15,23 @@
             </secondary_variables>
         </process>
     </processes>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <time_loop>
         <processes>
             <process ref="GW23">
@@ -43,11 +59,6 @@
         </output>
     </time_loop>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>
diff --git a/Tests/Data/EllipticPETSc/square_1e1_neumann.prj b/Tests/Data/EllipticPETSc/square_1e1_neumann.prj
index 0dfd75a83faf40cb3f8e9986b9effaff0554733d..6f5742a1ce6c99b257878554249c16163e69ede0 100644
--- a/Tests/Data/EllipticPETSc/square_1e1_neumann.prj
+++ b/Tests/Data/EllipticPETSc/square_1e1_neumann.prj
@@ -12,7 +12,6 @@
             <name>GW23</name>
             <type>GROUNDWATER_FLOW</type>
             <integration_order>2</integration_order>
-            <hydraulic_conductivity>K</hydraulic_conductivity>
             <process_variables>
                 <process_variable>pressure</process_variable>
             </process_variables>
@@ -47,12 +46,24 @@
             </variables>
         </output>
     </time_loop>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
     <parameters>
-        <parameter>
-            <name>K</name>
-            <type>Constant</type>
-            <value>1</value>
-        </parameter>
         <parameter>
             <name>p0</name>
             <type>Constant</type>