Case02 Calibration Exercise
Contents
In this case an exercise to perform a calibration of the SR4 hardening and poroelastic parameters is suggested. The exercise considers a hydrostatic column burial model. The initial datafile and data for calibration is provided in Mat_001b\Case2\Data. Look for ! TODO text in the material data file and follow the instructions.
Data for calibration overview
The data used to perform the calibration comprises:
1.Stratigraphy data consisting in 10 layers from which 8 are shale and 2 are sandstones.
2.Average porosities for all stratigraphic layers.
3.Average Young's Modulus for the two sandstone layers
4.Decompacted thickness calculated from the present day thickness, the average present day porosity and the depositional porosity.
Average porosity with depth and average Young's modulus data to be used for calibration
Stratigraphy formations table with calculation of the decompacted thickness
Model overview
The model considers an initial shale layer layer (Shale01) and the deposition of 9 additional formations as specified in the previous table. Every formation is discretized into 10 quadrilateral elements over the vertical axis with no divisions on the horizontal axis. The deposition is performed using the "Drape" algorithm so that the code will use the specified reference thickness and the location of the current top surface to position the sedimentation horizon. The simulation considers hydrostatic conditions using Porous_flow_type 5 (hydrostatic conditions based on the effective density).
Schematic of initial model geometry and boundary conditions
Exercise objectives and guidelines
The aim of this exercise is to calibrate kappa and lambda for the two sandstone layers in the stratigraphic column. Note that the datafile provided is already set up with the appropriate sedimentation thicknesses as calculated in the previous table. The only data that should be defined are the hardening and poroelastic material parameters to be calibrated. Note that:
1.The material characterisation for the shale formations is provided. It considers the same material parameters shown in Case01 which describe a compaction trend calibrated according to Hudec et al. (2009) data for Gulf of Mexico sediments (see the plot below with the analytical hardening curve fitting the data).
2.The material parameters for the two sandstone layers may be different so two Material_data structures are defined in the provided .mat file.
3.Usage of the spreadsheet provided for a quick view to the expected compaction trend and expected Young's modulus is recommended. The material parameters already provided should not be changed for this case.
4.It is recommended to start calibrating value for Kappa first followed by lambda and readjust as required.
Comparison of target average porosities and the shale compaction curve
| Basic set up file description |
The basic data includes:
1Geometry_set data for all model boundaries. 2A single pre-existing group for the Shale01 formation which is assigned "GoM_Shale" properties defined using Group_control_data and Group_data data structures. The Porous_flow_type = 5 (i.e. hydrostatic pore pressure based on effective density to calculate the vertical effective stress). 3Material_data to read the material properties for "GoM_Shale", "Sandstone01" and "Sandstone02" materials. Note that there is data to be set by the user in the .mat file. 4Stratigraphy_definition and Stratigraphy_horizon defining the initial stratigraphy for the model. 5Support_data defining perpendicular displacement fixities for "Base", "East" and "West" boundaries . 6Gravity_data to apply the gravity load following an S-curve function. 7Mesh_control_data, Structured_mesh_data and Structured_line_set defining 10 divisions along the vertical axis with a single division on the horizontal axis. 8Adaptivity_control_data and Adaptivity_set_data set so that remesh is only performed when a new formation is deposited (adaptivity data is only incorporated to enable sedimentation). 9Global damping (Damping_global_data) for the geomechanical field using Bulk damping model. 10A Sedimentation_horizon and Sedimentation_data for every depositional stage. 11A Control_data for each formation (including the initial pre-existing formation). Note that the mechanical time step is set using Target_number_time_steps which is set to 10000.
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The relevant material parameters for the three formations are shown in the table below. Cells with green background indicate the calibrated parameters.
Table with material parameters relevant to the present exercise for the three considered lithologies
As can be seen in the plots below the chosen parameters provide a reasonable good fit of the simulation results to the data. Nonetheless it can be noted that the predicted compaction curve provides an exact fit to the two shallower shale formations (the curve intersects the center of the target average porosity data) but is slightly less accurate onwards. This is because the chosen parameters were determined using the analytical hardening spreadsheet which considers a single lithology and hence it provides an approximation of the optimal hardening values. In this case for example the predicted average porosity for Sandstone02 is slightly lower than the target value because the shale porosities above such layer are higher than the ones considered in the spreadsheet and hence the actual simulated vertical effective stress will be lower than the one considered in the spreadsheet. The predicted porosities for the shales below are slightly lower than the target values because the Sandstone02 has lower porosity that the shale curve at the same depth and hence the vertical effective stress at the base of Sandstone02 will be higher than the one considered in the spreadsheet.
Comparison of simulated results and data
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| References |
Hudec, M.R., Jackson, M.P.A. & Schultz-Ela, D.D. (2009). The paradox of minibasin subsidence into salt: Clues to the evolution of crustal basins. Geological Society of America Bulletin. 121, pp. 201-221.
Wong, T.-F., Christian, D., & Wenlu, Z. (1997). The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation. Journal of Geophysical Research, 102(B2), 3009–3025.
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