Ex_002_Case01 Base case

 

In this base case a drop in 6 MPa in reservoir pore pressure will be imposed during depletion. Pore pressure is defined at mesh nodes in Spatial_grid data and assigned using Spatial_boundary. The data files for the examples is found in: ParaGeo Examples\General Examples\Ex_002\Case01\Data. Note that only key data will be discussed.

 

 

 

Geostatic_data

 

Data File

 

 

* Geostatic_data            NUM=1

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

 Groups                   IDM=3

  "Underburden"

 "Reservoir"

 "Overburden"

 K_value_x                    0.7

 K_value_y                    0.7  

 Porosity_spatial               1

 Time_curve          "Step_scurve"

 

 

* Spatial_variation_definition NUM=1

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

 Description     "Porosity vs. Depth"

 Type                      "Absolute"

 Distribution       "Depth_dependent"

 Variation_assignment               1

 

 

* Spatial_variation_values   NUM=1

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

 Description  "NCT"

 Time                        0.0

 Values_vs_depth     IDM=35 JDM=2

/Depth/    0         179.3     358.6     ...   6097.4

/Porosity/ 0.48834   0.44717   0.40294   ...   0.039523

 

1.In first stage Geostatic_data is specified. This data may be used to prescribe an initial porosity depth curve, initial pore pressure distribution, horizontal stress ratios, etc.

2.In this case the same geostatic data is applied to all groups.

3.A horizontal to vertical effective stress ratio of 0.7 is applied in X and Y directions.

4.Porosity_spatial = 1 indicates that for porosity initialization, data specified in Spatial_variation_definition NUM=1 will be used.

5.The time curve assigned for geostatic initialization is an s-curve function over the duration of the stage

6.In Spatial_variation_definition the type of data for the spatial variation is defined (Absolute values, values are depth dependent, etc).

7.Variation_assignment = 1 indicates that the Spatial_variation_values NUM=1 is assigned.

8.In Spatial_variation_values the depth porosity curve is defined. Note that those porosity values correspond to a slightly overconsolidated state for the material properties considered.

 

 

 

Geostatic_control_data

 

Data File

 

 

* Geostatic_control_data

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

 Description              "Elastic_initialization"

 Stress_constitutive_model               "Elastic"

 Stress_initialisation_type             "Standard"

 Displacement_reinit_flag                        0

 State_reinit_flag                               0

 Porosity_reinit_flag                           -1

 Time_curve                          "Step_scurve"

 

 

* Geostatic_control_data

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

 Description           "Nonlinear Initialisation"

 Stress_constitutive_model             "Standard"

 Stress_initialisation_type            "Standard"

 Displacement_reinit_flag                       0

 State_reinit_flag                              0

 Poroelastic_init_flag                          1

 Porosity_reinit_flag                           1

 Time_curve                         "Step_scurve"

 

 

* Geostatic_control_data

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

 Description      "Displacement Reinitialisation"

 Stress_constitutive_model             "Standard"

 Stress_initialisation_type            "Standard"

 Displacement_reinit_flag                       1

 State_reinit_flag                              0

 Poroelastic_init_flag                          1

 Porosity_reinit_flag                           1

 Time_curve                         "Step_scurve"

 

1.A Geostatic_control_data structure is defined for each initialization stage. In such data structure the options for initialization during each stage can be selected.

2.During first stage the Stress_constitutive_model is set to "Elastic", so initialization will be performed using the elastic properties defined in Material_data. In subsequent stages this option is set to "Standard" so the constitutive model as defined in Material_data will be used.

3.Displacement_reinit_flag is set to 1 on the last initialization stage in order to reinitialize displacements and recover the initial geometry configuration.

4.State_reinit_flag is set to 0 for all stages (no state variable reinitialization). If set to 1 the state variables which do not control the Yield surface would be initialized.

5.For initialization stages 2 and 3 Poroelastic_init_flag is set to 1 in order to use poroelastic constant values evaluated with the end of step stresses (calculated during first initialization stage).

6.Porosity_reinit_flag may be used to re-initialize porosity at the end of the displacement reinitialization.

7.Time_curve assigns a Time_curve in order to preform the initialization procedures (e.g. ramp up of stresses calculated during stage 1, displacement reinitialization, etc). In the present case an internally generated time curve following an s-curve over the duration of each stage is assigned.

 

 

 

 

 

Spatial_grid

 

Data File

 

 

 

* Spatial_grid                     NUM=1

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

 Name                     "Pore_pressure"

 Type                     "Nodal"

 Nodal_variables                  IDM=1

   "Pore_nod"

 Node_numbers                     IDM=244

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

.









.









.









241

242

243

244





 Point_values              IDM=1  JDM=244

 4.91

 4.91

   .

   .

   .

 21.21

 

 

1.Two Spatial_grid with pore pressure values at nodes are defined in files Ex_002_PP_initial.spat and Ex_002_Case01_PP_depletion.spat for initialization and pore pressure depletion stages respectively.

2.Spatial_grid name is "Pore_pressure".

 

 

 

 

Spatial_boundary

 

Data File

 

 

* Include ! Include spatial grid with PP values

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

 Filename  Ex_002_PP_initial.spat        

 

 

* Spatial_boundary                NUM=1

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

 Name                     "Pore Pressure"

 Boundary_type            "Spatial_grid"

 Value_type               "Absolute"

 Mapping_entity_flag                 0

 Spatial_grids                    IDM=1

   "Pore_pressure"

 Time_curve              "Step_scurve"

 Relative_time_curve                 1

 Prescribed_components            IDM=1   JDM=1

   4

 

 

1.Include is used to read the Spatial_grid files at every stage (when it requires to be updated). Because the spatial grids in both files have the same number and name, data will be overwritten in the depletion stage.

2.Spatial_boundary is used to deploy the values read from the spatial grid to prescribe pore pressure:

a.Assigned spatial grid is "Pore_pressure"

b.Prescribed_components is assigned component 4 (pore pressure).

3.In stage 4 the spatial grid is overwritten (same values in shale nodes, 6 MPa less pore pressure in reservoir nodes). Then the change will occur gradually during stage 4 following an s-curve function over the duration of the stage.

 

 

 

 

Top surface load

 

Data File

 

* Stratigraphy_surface_load

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

 Applied_stress                   5.0  

 Time_curve_stress                "Step_scurve"

 Pore_pressure_flag               0

 

 

1.The pore pressure defined in the spatial grid is representative of a water level of 500 m measured from the top surface. Consequently a stress load must be applied to the top surface to compensate for the pore pressure and avoid upward expansion of the model. The load is applied slightly larger than the top surface nodes pore pressure value (which are assigned a pore pressure of 4.91 MPa)

 

 

 

Results

The result files for the project are in directory: ParaGeo Examples\General Examples\Ex_002\Case01\Results.

 

The plots below show that the pore pressure in the reservoir has dropped after depletion.

History results show:

 

1.Elastic initialization phase from time 0 to time 1, Non-linear initialization from time 1 to 2, displacement re-initialization from time 2 to 3 and  and reservoir depletion from time 3 to time 4. Note that displacements during initialisation have been negligible at the history point location. Consequently the effects of displacement reinitialisation are not observable.

 

2.The drop in pore pressure is performed gradually following an s-shaped function. The decrease in pore pressure lead to a stress increase. This results in porosity decrease, initially following an elastic path, and then developing plastic strains (see the increase in pre-consolidation pressure magnitude).

 

 

 

Ex_002_Case01_02

Pore pressure after initialization (left) and after depletion (right) stages

 

 

 

Ex_002_Case01_03

History results in a point located in the centre of the reservoir. The grey discontinuous line indicates the end of initialization and the onset of the depletion stage.