Efficient Simulation of Tracer Transport in Fractured Porous Media and Data-Driven Aperture Estimation

Abstract

Subsurface applications such as geothermal heat extraction or CO2 sequestration are vital for solving today's energy and climate challenges. Their reservoir rock typically consists of fractured porous media, whose fractures can greatly affect flow, transport, and mechanics. Accurate and efficient modelling of the relevant physical processes and characterising the related parameters are crucial for performance estimation and risk assessment. This simulation-based thesis aims to enhance these aspects. Time-dependent hyperbolic partial differential equations (PDEs) are commonly used for modelling transport phenomena and seismic activity. Adaptive time stepping methods, like the adaptive conservative time integration (ACTI) scheme, improve the efficiency of explicit time integration by allowing variable local time steps. We extend ACTI to tracer transport in fractured porous media, achieving accurate results while reducing computational costs by orders of magnitude compared to global time stepping. Limited observability of subsurface reservoirs and substantial uncertainties, particularly concerning fractures and their apertures, pose challenges to accurate modelling. Ensemble-based data assimilation (DA) methods, like the ensemble smoother with multiple data assimilation (ESMDA), are established tools for reducing uncertainty in model parameters and improving simulation results. We demonstrate the significant impact of measurement strategies and matrix permeability on DA results, highlighting the utility of intermediate measurements during reservoir stimulation and the influence of matrix permeability on fracture parameter estimation. Constructing a prior ensemble that accurately reflects available knowledge is crucial for ensemble-based DA methods. We introduce the far-field stress approximation (FFSA), a proxy model which projects the far-field stresses onto the fracture planes and approximates shear displacement with linear elastic theory. The FFSA efficiently generates reasonable prior realisations of fracture apertures in a realistic two-dimensional fracture network. The resulting posterior ensemble matches the flow and transport behaviour of the synthetic reference at measurement locations. It improves the estimation of the fracture apertures, markedly outperforming results from prior ensembles based on naïve stochastic approaches. In conclusion, this thesis contributes to a more efficient and accurate simulation of fractured porous media, paving the way for improved reservoir management and decision-making in various subsurface applications.