Case4 Usage of Spatial table (property dependencies)

Data File

* Include

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

 Filename "porosity_SpatVar_001_case4.spat"          

1The included file name should point to the edited .spat file (ending with suffix _case4).

Data File

* Spatial_grid    NUM=1

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

 Name        "Porosity_Spatial"

 Type                   "Grid1"

 Num_cells_x                 10

 Num_cells_y                  4

 Num_cells_z                  8

 Cell_division_X            800              

 Cell_division_Y           1000

 Cell_division_Z            500

 Grid_origin    IDM=3

   0.0   0.0  0.0  

 Nodal_variables   IDM=3

   "Porosity"  

  "P_strnv"

   "Poiss"

 Point_values   IDM=3   JDM=495

   0.05      -0.553652881   0.35

   0.049     -0.554013553   0.35

     .

     .

     .

   0.390672  -0.159889195   0.35

1The grid definition is identical to case 1 except that Poisson's ratio values are also input.

2Grid point_values can be copied from Case4 sheet in "SpatVar_001.xlsx" file.

3Poisson's ratio is set to 0.35 except for the "high porosity layer" near the base which is set to 0.22.

Data File

* Spatial_table   NUM=1

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

 Material_names        IDM=1

   "Shale_CF75"

 Variable_name

   "Young"

 Dependent_variables   IDM=2

   "Porosity"

  "Poiss"

 Dependent_grids       IDM=2

   "Porosity_Spatial"

  "Porosity_Spatial"

 Table_size            IDM=2

    10 2

 Table_values          IDM=3   JDM=20

   1.00E+05        0.00  0.25

   1.00E+05        0.05  0.25

   1.00E+05        0.10  0.25

   1.00E+05        0.15  0.25

   1.00E+05        0.20  0.25

   1.00E+05        0.25  0.25

   1.00E+05        0.30  0.25

   1.00E+05        0.35  0.25

   1.00E+05        0.40  0.25

   1.00E+05        0.45  0.25

   1.00E+04        0.00  0.35

   1.00E+04        0.05  0.35

   1.00E+04        0.10  0.35

   5.00E+03        0.15  0.35

   5.00E+03        0.20  0.35

   5.00E+03        0.25  0.35

   1.00E+03        0.30  0.35

   1.00E+03        0.35  0.35

   1.00E+03        0.40  0.35

   1.00E+03        0.45  0.35

1A spatial_table data structure to define Young's modulus as a function of both, porosity and Poisson's ratio is defined.

2Material_names is optional and can be used to apply the spatial table dependencies only to specified materials. If not specified the spatial table dependencies are applied to all materials. Here Material "Shale_CF75" is specified.

3In Variable_name the variable which are assigned values as a function of dependencies is specified. Here "Young" is selected.

4The dependencies are specified in a list in Dependent_variables. Here "Porosity" and "Poiss" are selected.

5In Dependent_grids the grids from which each dependency values are obtained are listed. Both "Porosity" and "Poiss" are obtained from the grid "Porosity_Spatial". If any dependency is not specified via a grid it must be set as "Internal".

6In Table_size the number of different values for each dependency variables to be input in the table must be defined. In this example 10 different values of Porosity and 2 different values of Poisson's ratio will be used to define the spatial table.

7In Table_values the spatial table is defined. The number of columns must be equal to the number of dependent variables + 1. The number of rows must be equal to the total table size (in this example 10x2=20). First column is for the spatial variable (Young's Modulus) and subsequent columns are for dependencies in the same order specified in Dependent_variables. Values for each dependency must be provided in ascending order. For an hipotetical Table_size of (3, 2) the table would be specified as follows:

        E1   Ø1   υ1

        E2   Ø2   υ1

        E3   Ø3   υ1

        E4   Ø1   υ2

        E5   Ø2   υ2

        E6   Ø3   υ2

    Where En, Øn and υn are the "n-th" values of Young's modulus, Porosity and Poisson's

    ratio respectively.