Abstract
Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest. The prediction reliability depends on different sources of uncertainty, such as the parameterization of the constitutive model characterizing the deep rock behaviour. In this study, we focus on a Sobol’-based sensitivity analysis and uncertainty reduction via assimilation of land deformations. A synthetic test case application on a deep hydrocarbon reservoir is considered, where land settlements are predicted with the aid of a 3-D Finite Element (FE) model. Data assimilation is performed via the Ensemble Smoother (ES) technique and its variation in the form of Multiple Data Assimilation (ES-MDA). However, the ES convergence is guaranteed with a large number of Monte Carlo (MC) simulations, that may be computationally infeasible in large scale and complex systems. For this reason, a surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem. This approach allows to efficiently compute the Sobol’ indices for the sensitivity analysis and greatly reduce the computational cost of the original ES and MDA formulations, also enhancing the accuracy of the overall prediction process.
Highlights
Geomechanical modelling is a scientific and engineering activity of paramount importance to evaluate the safety and predict possible environmental impacts related to the exploitation of subsurface resources
Once the surrogate model is available, the uncertainty quantification step can be completed by means of the classical Ensemble Smoother (ES) or ES-MDA algorithms, where a very large number of Monte Carlo (MC) realizations can be computed at a low computational cost
Due to the high computational cost of the forward model runs required by the ensemble approaches, the proposed generalized Polynomial Chaos Expansion (gPCE)-ES and gPCE-MDA algorithms, if able to effectively approximate the full model behaviour, can allow for the use of large ensembles and successive assimilations at an affordable cost
Summary
Geomechanical modelling is a scientific and engineering activity of paramount importance to evaluate the safety and predict possible environmental impacts related to the exploitation of subsurface resources. The reliability of the predictions depends on different sources of uncertainty, which are somewhat intrinsically introduced in any modelling process. Uncertainty typically affects the knowledge of the constitutive rock behaviour, the geometry of the depleted formations, the diffusion of the pressure perturbation, just to mention a few important occurrences. We focus on the reduction of uncertainty affecting the constitutive model parameters and the land subsidence prediction via assimilation of ground surface displacements. The focus is on the calibration of the rock constitutive parameters that mainly control the compaction of the rock formation caused by the hydrocarbon production. Assuming the use of some well-established constitutive models, such as Mohr-Coulomb, Modified Cam-Clay, hypo-elastic, hypo-plastic or visco-elasto-plastic laws [4,5,6,7], different approaches can be used to estimate the governing parameters.
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