Computationally Efficient 3D Fully Coupled Reactive Transport Model for Wormhole Propagation in Carbonate Formation

Matrix acidizing is one of carbonate reservoirs' most efficient and widely implemented stimulation techniques. It improves productivity and flow capacity by creating new conductive flow channels called wormholes. The propagation of these channels has been a topic of interest as many researchers tried to investigate this phenomenon experimentally, theoretically, and numerically. Among various models, the two-scale continuum (TSC) model is the most common and reliable model due to its ability to predict better results as it combines Darcy and pore scales to capture the phenomenon. However, the main disadvantage of using the TSC model is its high computational cost. This highlights the need for a computationally efficient model that reduces that cost while maintaining solution accuracy. Also, examining wormhole propagation in 3D perforation is untouched yet. In this paper, we developed a numerical model in-house using MATLAB® software to simulate the wormhole generation considering the perforation in three-dimensional space based on the two-scale continuum mathematical model. The model performance is optimized to be a time-efficient simulation model that considers thermal energy transfer beside flowing and reactive mass transfer. Computation efficiency is achieved using the Darcy equation, vectorizing code operations, and implementing a proposed iterative algorithm that is based on the GMRES method. The associated tuning parameters and a proper preconditioner are obtained, which improved the model efficiency by more than 90%. The model used typical data reported in experimental acidizing work.