The parameter inversion in coupled geomechanics and flow simulations using Bayesian inference

In many situations, uncertainty about the mechanical properties of surrounding soils due to the lack of data and spatial variations requires tools that involve the study of parameters by means of random variables or random functions. Usually only a few measurements of parameters, such as permeability or porosity, are available to build a model, and some measurements of the geomechanical behavior, such as displacements, stresses, and strains are needed to check/calibrate the model. In order to introduce this type of modeling in geomechanical analysis, taking into account the random nature of soil parameters, Bayesian inference techniques are implemented in highly heterogeneous porous media. Within the framework of a coupling algorithm, these are incorporated into the inverse poroelasticity problem, with porosity, permeability and Young modulus treated as stationary random fields obtained by the moving average (MA) method. To this end, the Metropolis–Hasting (MH) algorithm was chosen to seek the geomechanical parameters that yield the lowest misfit. Numerical simulations related to injection problems and fluid withdrawal in a $3D$ domain are performed to compare the performance of this methodology. We conclude with some remarks about numerical experiments.