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Simulation of Acidizing Dissolution Front Instability in Carbonate Rocks

Abstract

Matrix acidizing is a technique to improve permeability and enhance production especially for carbonate reservoirs, which involves injecting acid to dissolve minerals to create highly conductive channels known as wormholes. Since acidizing is a self-feeding process, dissolution fronts may become unstable under certain conditions, which leads to formation of wormholes. Designing acidizing operations require accurate modeling of acidizing dissolution front instability. Most of previous simulation work is based on the standard finite volume method (FVM), which smears dissolution fronts and needs very fine mesh to resolve fine-scale wormholes.

A new 3D acidizing simulator is developed using enriched Galerkin finite element methods (EG). EG is formulated by enriching standard finite element methods with piecewise constant functions. A two-scale continuum model is adopted to describe the process of acidizing dissolution. To model naturally fractured carbonate reservoirs, a diffusive fracture network model is developed with a phase-field variable as an indicator to distinguish fractures and un-fractured rock matrix. The technique of adaptive mesh refinement (AMR) is implemented and allows the simulator to refine the mesh around dissolution fronts dynamically, which saves substantial computational cost when compared with global mesh refinement on the whole computational domain.

The simulator has been benchmarked with laboratory core flooding experiments. The simulation results can reproduce dissolution patterns under different injection rates, including uniform dissolution, wormhole and face dissolution. The realistic radial acidizing around the wellbore has been simulated. It is found that the unstable acidizing dissolution fronts can be resolved only when the mesh size is fine enough. The simulation using AMR can be about four times faster than that without AMR in terms of run time based on our numerical experiments. For the fractured carbonate reservoir, simulation results show that the fracture system controls the dissolution patterns since fractures are preferential flow paths for acids. The simulator can get sharper dissolution fronts and is flexible to model complicated geometry of geologic models since EG has less numerical dispersion and grid orientation effects than FVM. Our simulator is efficient and accurate to model the acidizing process and can be invaluable in optimizing acidizing designs.