Impact of mesh adaptivity on the interpretation of transport processes in porous media

An accurate modeling of solute transport processes in the subsurface is a crucial issue with a view to several engineering applications. These include groundwater vulnerability assessment and modeling of hydrocarbon reservoirs. All the available modeling options encompass the definition of effective transport parameters, which are essentially representative of the porous medium and of the geometry at hand. The estimation of these parameters is typically performed within model calibration schemes, which require an iterated numerical approximation of the selected model with a consequent computational burden. In this contribution, we provide a space-time grid adaptation procedure to improve the accuracy of the numerical simulation of solute transport in porous media, while containing the computational costs. We rely on a simple model for transport processes, based on the standard Advection Dispersion Equation (ADE). In particular, we focus on the interpretation of non-reactive transport experiments in homogeneous and heterogeneous porous media through model calibration. In contrast to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and of the time step to capture the main space-time system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator [1,2], which enables us to properly select the size, shape and orientation of the mesh elements. The adaptation of the time step is performed through an ad-hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach [3]. The impact of the proposed adaptation strategy on the capability to provide reliable estimates of the key parameters of an ADE model is assessed with reference to experimental solute breakthrough data measured after the injection of a non reactive tracer in a porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). The results obtained show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization