Numerical simulation of wormhole propagation in fractured carbonate rocks during acidizing using a simplified Stokes–Brinkman model

Abstract

Abstract Most numerical simulations for modeling acid reactive fluid transport and wormhole propagation during matrix acidizing, waterflooding, and CO2 sequestration in carbonate formations are computationally expensive, limiting real-time reservoir management and deep learning training datasets generation for inverse modeling research. Therefore, there is a need for less computationally expensive acid-reactive fluid flow models with adequate accuracy. This study developed and validated a simplified acid reactive-transport model by integrating a simplified Stokes–Brinkman model (as opposed to Darcy’s law), an averaged continuum model, and a pseudo-fracture model. Using FEniCS, the model effectively simulates acid-reactive fluid transport and wormhole propagation in carbonate rocks, achieving a high R-square value of about 0.97 based on a quantitative comparison of the breakthrough volume with other models. The simplified model can also simulate wormhole propagation for the reciprocal of the Damköhler number (1/Da) ranging from 0.001 to 1 with adequate accuracy. Sensitivity studies on the natural fracture parameters such as orientation, length, width, and density showed that higher fracture density, wider fracture aperture, longer fracture length, and orientation aligned with the direction of acid injection contribute to lower pore volume to breakthrough ratio but may not increase long-term acid stimulation efficiency. Also, the presence or absence of fractures in the matrix does not alter the dissolving patterns and optimum injection rate. This simple acid reactive-transport model can generate large training datasets for developing surrogate models in deep learning research. Finally, the FEniCS code in this paper is shared so future researchers can reproduce the results or extend the research work.

Keywords

• Stokes–Brinkman
• Wormholes
• Fractures
• Matrix acidizing
• FEniCS