In this paper a sequential coupling of mixed finite element and shock-capturing finite volume techniques is proposed, in order to numerically solve the system of partial differential equations arising from the Black-Oil model. The Brezzi-Douglas-Marini space of degree one (BDM 1 ) is used to approximate the Darcy's velocity in the parabolic-type pressure equation, while the system of mass conservation laws is solved by a higher order Godunov-type scheme, here extended to trianglebased unstructured grids. Numerical results on 1-D and 2-D test cases prove the effectiveness and the robustness of the coupling, which seems particularly suited to handling high heterogeneities and at the same time accurately resolving steep gradients without spurious oscillations.

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Summary A 3D elasto‐plastic rate‐dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium “Beyond 2000 in Computational Geotechnics,” pages 249‐261, 1999). An original strain‐driven algorithm with an Inexact Newton iterative scheme is used to compute the state variables for a given strain increment.The model is validated against laboratory measurements, checked on a simplified test case, and used to simulate land subsidence due to groundwater and hydrocarbon production. The numerical results prove computationally effective and robust, thus allowing for the use of the model on real complex geological settings.

SUMMARYCharacterization of reservoir properties like porosity and permeability in reservoir models typically relies on history matching of production data, well pressure data, and possibly other fluid-dynamical data. Calibrated (history-matched) reservoir models are then used for forecasting production and designing effective strategies for improved oil and gas recovery. Here, we perform assimilation of both flow and deformation data for joint inversion of reservoir properties. Given the coupled nature of subsurface flow and deformation processes, joint inversion requires efficient simulation tools of coupled reservoir flow and mechanical deformation. We apply our coupled simulation tool to a real underground gas storage field in Italy. We simulate the initial gas production period and several decades of seasonal natural gas storage and production. We perform a probabilistic estimation of rock properties by joint inversion of ground deformation data from geodetic measurements and fluid flow data from wells. Using an efficient implementation of the ensemble smoother as the estimator and our coupled multiphase flow and geomechanics simulator as the forward model, we show that incorporating deformation data leads to a significant reduction of uncertainty in the prior distributions of rock properties such as porosity, permeability, and pore compressibility.

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