Efficient Sparse Quasi-Newton Algorithm for Multi-Physics Coupled Acid Fracturing Model in Carbonate Reservoirs

Acid stimulation is a widely used technique for enhancing hydrocarbon recovery from carbonate reservoir formations. In this study, a mathematical model is developed to describe acidizing-induced pressure behavior in carbonate rocks, based on fluid dynamics and acid transport equations. The model is discretized using the finite volume method, resulting in a numerical framework suitable for simulating acidizing processes in carbonate reservoirs. Due to the model’s inherent characteristics—strong nonlinearity and the presence of high-dimensional sparse systems of equations—a sparse quasi-Newton method is proposed to efficiently solve the resulting system. Numerical experiments confirm the practicality and effectiveness of the proposed approach.