Case01 Constant contact properties for fluid and thermal contact

Contents

Basic Set Up: Data File Description

The initial data file for the project is: Cont_002\Case01\Data\Cont_002_Case01a.dat. The basic data includes:

1Geometry_set data for all model boundaries and the two fault surfaces.

2Contact data (Contact_set, Contact_property and Contact_global) for defining contact between fault hanging wall and foot wall.

3A single Group_data with 2D triangular elements and Group_control_data defining the group active for geomechanical, fluid flow and thermal fields.

4Material_data and Fluid_properties defining elastic properties, constant isotropic permeability and constant isotropic thermal conductivity.

5Support_data to defining:

(a) Displacements constraints in the normal direction to bottom and side boundaries

(b) Pore pressure constraints in the top and bottom model boundaries.

6Geostatic_data to define an initial state with 0 MPa pore pressure.

7Load data defining:

(a) A stress load at the top surface of 10 MPa

(b) Pore pressure of 10 MPa at the bottom boundary

8Mesh control (Mesh_control) and Unstructured mesh generation data (Unstructured_mesh_data) defining a constant mesh size of 100 m.

9Damping data (Damping_global_data) defining velocity damping of 2%.

10Couple_control_data defining:

(a) Coupling for geomechanical, fluid flow and thermal fields

(b) Incremental solution algorithm

11Control data (Control_data) for two stages defining:

(a) Incremental transient solution algorithm (Type 4),

(b) Maximum number of time steps of 108 (very large)

(d) Termination time for each stage (1 Ma and 11 Ma respectively),

(e) Coupling step of 0.01 Ma (Initial_time_increment)

(f) Maximum number of iterations of 5000

(g) Factor of critical time step = 0.7,

(h) Plot file output at the end of each stage,

(i) Plot file output every 0.25 Ma,

(j)Screen message output every 10 coupling steps,

12Geometry data (nodal_data, Geometry_line and Geometry_surface) for definition of the 2D geometry.

This tutorial example focuses on definition of the contact data for the flow and thermal fields. Hence a detailed description of data structures not relevant to the topic will not be provided. However a summary of the data relevant to perform a coupled simulation is provided.

Data set up required to run a coupled simulation

The data required to run a coupled simulation comprises:

1.Couple_control_data with definition of the coupled fields. In this case all fields (geomechanical, fluid flow and thermal) are coupled.

2.Activation of the coupled fields for the domain groups in Group_control_data.

3.Set Porous_flow_type 4 in Group_data

4.Set Solution_algorithm 4 in Control_data

5.Definition of the coupling step size via Initial_time_increment in Control_data. In this case the coupling step size is set to 0.01 Ma.

6.Definition of the mechanical steps for each coupling step via Target_number_time_steps. In this case a target of 200 mechanical steps per flow step is defined. Hence for the flow step size of 0.01 Ma, the target mechanical step will be 5.0 · 10-5 Ma. This number will be later multiplied by the critical time step factor which in this case is 0.7 so the mechanical time step is expected to be 3.5 · 10-5 Ma.

In addition to the data listed above the relevant material and fluid properties for the flow and thermal fields need to be defined:

1.Grain stiffness for the coupling, Biot's constant and intrinsic permeability

2.Grain thermal conductivity and grain specific heat capacity

3.Fluid stiffness and fluid viscosity

4.Fluid thermal conductivity and fluid specific heat capacity

Contact Data

The contact data for defining contact relationships is specified using Contact_set, Contact_property and Contact_global data structures. In this case Contact_surface is not required as only two interacting contact surfaces are defined.

For more information about contact mechanics see Overview of Contact in ParaGeo and for contact data definition see Contact Data.

Contact_set

Data File

* Contact_set NUM=1

! ----------------------------------------

Name "All"

Geometry_sets IDM=2

"Fault_hgw"

"Fault_ftw"

Algorithm "Penalty"

Property_name "Sand_contact"

Global_update_frequency 1000

Field_factor 0.2

Buffer_factor 1.0

1Contact_set data is defined with the minimal data required for the current analysis.

2Considered geometry sets to establish contact are "Fault_hgw" and "Fault_ftw".

3The penalty algorithm is used for the contact set (only option currently available).

4The Contact_property named "Sand_contact" is assigned as the default property to the contact surfaces included in this contact set.

5The update frequency for the global contact list (list which stores the potential target facets within a buffer distance for each contact node at a given time of the simulation) is set every 1000 mechanical time steps.

6The field factor is set to 0.2 (a node and a facet are in contact if the distance between them is 0.2 · lfacet or less, where lfacet is the facet length).

7The buffer factor for defining the buffer box size is set to 1.0 (the candidate target facets that can potentially establish a contact relationship with a given contactor node are those within the buffer box during a global search update). In this case the buffer box for a given node is a circle centred at the node with radius R=1.0· lfacet where lfacet is the average length of the facets that terminate on the node. In this case a buffer factor of 1.0 is enough as no slip is expected. Generally, a default value of 5.0 is recommended.

Contact_property

Data File

* Contact_property NUM=1

! ----------------------------------------

Name "Sand_contact"

Compression_model 1

Compression_properties IDM=1

/Normal Penalty/ 5000

Tangential_model 2

Tangential_properties IDM=2

/Tangential Penalty/ 10

/Friction coefficient/ 0.1

Flow_model_normal 11

Flow_properties_normal IDM=2

/Penalty Perm./ 1E-21

/Filt. Cake Perm.)/ 1E-27

Flow_model_tangential 11

Flow_properties_tangential IDM=1

/Perm./ 1E-23

Thermal_model_normal 1

Thermal_properties_normal IDM=2

/Therm. Cond. (Penalty)/ 12.6144E+13

/Therm. Cond. (Filter Cake)/ 12.6144E+13

Contact_width 0.001

1The contact property is named "Sand_contact".

2The mechanical contact properties consider:

a.Linear elastic compression model with a penalty stiffness of 5000 MPa.

b.Coulomb friction model in the tangential direction with a penalty stiffness of 10 MPa and a friction coefficient of 0.1.

3The Flow_model_normal is set to 11 (constant intrinsic permeability).

4In Flow_properties_normal the penalty and the filter cake (fault gouge) permeabilities are defined as 10-21 and 10-27 m2 respectively.

5The Flow_model_tangential is set to 11 (constant permeability).

6In Flow_properties_tangential the tangential permeability is set to 10-23 m2.

7The Thermal_model_normal is set to 1 (constant thermal conductivity).

8In Thermal_properties_normal the thermal conductivities for the fracture and the filter cake (fault gouge) both are defined 12.6144·1013 J · Ma-1· m-1 · K-1.(which corresponds to 4.0 W · m-1 · K-1).

9The contact width is used to define the storativity of the fault and is defined as 0.001 m (1 mm).

10For more information on the contact flow and thermal models and their properties see Overview of Contact in ParaGeo.

Contact_global

Data File

* Contact_global NUM=1

! ----------------------------------------

Included_contact_sets IDM=1

"All"

Contact_flow_flag 1

Contact_thermal_flag 1

1The contact set named "All" is active in the simulation.

2It is compulsory to specify Contact_flow_flag = 1 and Contact_thermal_flag = 1 in order to consider flow and thermal contact in the simulation. Otherwise even though flow and thermal contact properties are specified the fault would be considered impervious (no flow nor temperature transfer).

Notes on Contact Property Interpretation

1.The Filter Cake properties may be interpreted as a physical parameters characterising the properties of the damaged zone (with a size defined by the Contact_width)

2.The penalty properties on the other hand are parameters required for the model formulation. Generally we would set the penalty term to be relatively high to ensure that both sides of the contact fracture are in equilibrium (i.e. we have the same pore pressure and temperature values at both sides of the contact)

3.The values chosen in the tutorial were selected for demonstration of the functionality only.

4.The contact flow models used in the present tutorial define the properties by means of permeability as opposed to conductivity, as comparisons with the matrix values become more straight forward. It should be noted that conductivity is related to permeability as: C=k / µ

Results

The results for the project are in: Cont_002\Case01\Results. In addition to the base case Cont_002_Case01a.dat additional data files and results are provided with variation on some contact parameters to show how they influence the results.

In the results below it can be seen that for the chosen conditions and properties some pore pressure has been transferred from the footwall to the hanging wall but provided the relatively low contact conductivity of the fault gouge the fault has behaved as a fluid flow barrier. In the plot on the right it can be seen that, as the contact thermal conductivity was input to be the same as the matrix grain thermal conductivity, the fault has no effect in the temperature distribution (so essentially horizontal contours without discontinuities / jumps are predicted).

Cont_002_02

Pore pressure and temperature distributed in the domain and fault.

In Case01b the filter cake perm has been increased by a factor of 104 . Such permeability for a fracture of 1 mm width is high enough to ensure that the fault does not act as a barrier for the flow and horizontal pore pressure contours are predicted.

Cont_002_04

Demonstration of the effect of contact normal conductivity

In Case01c the contact width is increased by a factor of 106 resulting in a contact width of 1000 m. It should be noted that such a value is unrealistic as no fault is expected to have 1 Km of fracture width. However it has been chosen for demonstration purposes to view the effect of contact width in the present conditions and properties. It can be seen that given the width is increased by a large amount, the storativity of the fault has also increased. Hence the fault can accommodate large amounts of fluid volume before experiencing any pore pressure increase. This resulted in no pore pressure transfer from the footwall to the hanging wall block.

Cont_002_03

Demonstration of the effect of contact width

In Case01d the contact thermal conductivity (filter cake) has been decreased by a factor of 106. Hence the thermal conductivity of the fault is 106 lower than the conductivity of the matrix. Even for a 1mm fault this resulted in larger temperatures in the footwal than in Case01a, due to the larger resistance to transfer heat.

Cont_002_05

Demonstration of the effect of contact thermal conductivities