ParaGeoInv is a generic tool developed for performing inverse analysis and optimisation of material properties (including geomechanical and porous flow applications) and boundary conditions according to expected known target results. The implemented inversion method is based on the Nearest Neighbour Algorithm, thus allowing inversion of arbitrary sets of parameters from one or several arbitrary experimental / model set-ups. Given a selection of optimisation variables (e.g. permeability and Klinkenberg slippage factor), the algorithm is designed to minimise the misfit value (i.e. difference between the target and model solutions) during the inverse analysis and find the optimal values for the variables. In addition to the default application platform (i.e. ParaGeo), ParaGeoInv can be tailored to work with a variety of simulation tools, such as Eclipse, Abaqus, ELFEN, etc. Such flexibility renders it an analysis-independent tool.

 

This is a useful numerical tool, especially for experimentalists seeking to invert mechanical and/or flow properties of geomaterial under study. In addition to laboratory applications (inversion of material properties), users interested in large-scale geomechanical modelling may benefit from ParaGeoInv, which can conveniently homogenise properties contributed by some geological entities from a much smaller length scale (e.g. fractures) that are populated across the model. Also ParaGeoInv is used for boundary condition optimisation in large scale models as demonstrated in the tutorial example MEM_003.

 

A number ParaGeoInv applications focused on material property inversion are demonstrated in ParaGeoInv Tutorial Examples, but the expectation is that the list will grow as ParaGeo solver is enhanced over time. One example is the characterisation of flow properties in a pulse-decay experiment.

 

 

Pulse decay experiments are routinely used to measure petrophysical properties of tight cores by flowing helium. This shows, as part of tutorial example, the finding of optimal permeability and Klinkenberg slippage factor corresponding to core sample, while maintaining low misfit value, i.e. small difference against target solutions which, in this case, are the pore pressure evolution at both inlet and outlet.

 

 

The main workflow of ParaGeoInv is illustrated below. An inverse analysis is performed by running the executable ParaGeoInv on an inverse analysis .inp data file, e.g. "parageoinv_filename.inp". A template ParaGeo data file must be set up defining the modelling scenario (geometry, boundary conditions, etc) with dummy values for the variables to be optimised. Such template data file will be used to generate the models to be simulated during the inversion analysis as modified copies of the template data file by varying the input values for the variables to be optimised within user-established bounds. Initially the code generates an initial Sample of "n" models (with "n" defined by the user) with the optimization variables values populated using the user established bounds. That sample of models is then run with ParaGeo. The solution of each of the models is compared to the target (also refereed as experimental) solution results and the misfit value is calculated. Based on the misfit information, all models in the sample are ranked, and the "m" best models (the "m" models with lower misfit value with "m" defined by the user) will be used to generate a new sample of models with updated bounds for the optimisation variables via the nearest neighbour algorithm. Such procedure of generating a new sample of models with improved variable bounds is refereed here as resample. The inversion algorithm will continue performing resamples until either a model satisfies the convergence criteria or the maximum number of samples is performed without reaching convergence.

 

 

 

 

General workflow of ParaGeoInv

 

 

Currently there are two main inversion types / applications supported: "Material" and "Boundary". For the material inversion type any properties listed under Material_data, Fracture_data, and Fluid_properties data structures are supported. Some examples are given below.