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This study develops a mathematical model for pressure behavior in carbonate reservoirs, suggesting that a sparse quasi-Newton method improves simulation efficiency.
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.
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Li et al. (2025) studied this question.
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