Case02 Spatial Embedded Fracture (SEF)
Contents
In this example, the discrete fractures in the reference model are represented in the homogenised model using continuum approach, as illustrated below. The optimisation variable is the fracture permeability multiplier, which is multiplied by the algorithm with the matrix permeability to obtain fracture permeability. Note that the homogenised model inherits the boundary conditions from the reference model.
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Fig. 1 Continuum representation of discrete fracture distribution |
The starting folder structure with the data required for the inverse analysis is provided in Fract_004\Case02\Data and is as follows:
•Fract_004_case02.inp: Data file defining the inverse analysis to be run with the ParaGeoInv executable. •Target: folder containing the target results file(s) from Fract_002 to be used for optimisation. ▪fract_002_001.hdh ▪fract_002_002.hdh •Template: folder containing the template data file that will be used to define all model simulation data files. ▪Fract_004_case02.dat ▪Fract_004_case02.fab •Test: folder to which the simulations will be run to.
The optimisation variable for this inverse problem is the fracture permeability multiplier. In the ParaGeo template data file, we create the placeholder denoted by <p>FracPermMult<p> under the Fracture_data data structure after the keyword Permeability_multiplier.
In the following, we describe the setup of ParaGeoInv data file (Fract_004_case02.inp), which includes: 1Parameter_data defines the minimum and maximum, as well as the initial values of selected optimisation variables. 2NA_options tunes the parameters of optimisation algorithm, including tolerance, number of iterations, etc. 3Misfit_data_set sets the file name(s) of target solution and the variable name(s) to be compared with.
Note that only key data structures are shown below. |
Parameter_data defines the minimum and maximum, as well as the initial values of selected optimisation variables.
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NA_options tunes the parameters of optimisation algorithm, including tolerance, number of iterations, etc.
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Misfit_data_set sets the file name(s) of target solution and the variable name(s) to be compared with.
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The result files for this example is available in directory: Fract_004\Case02\Results.
The optimal homogenised model achieved through inverse analysis corresponds to model number 303 (see fract_004_case02.ParOpt). Comparing against the reference discrete model whose matrix permeability is 1E-23m2, the fracture permeability in the homogenised model is 68.01E-23m2.
The following table shows the comparison of fluid volume and flow rate on the outlet surfaces between optimal values achieved through the ParaGeoInv algorithm and target values, with outcome of low error.
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