Numerical simulation of matrix acidizing in carbonate formations using method of lines

In this study, a novel numerical approach is proposed to characterize the dissolution of rock minerals and wormhole propagation in carbonate rocks using the Darcy scale model. Accordingly, only the spatial variables of the governing partial differential equations are discretized, while the time variable remains continuous. Consequently, the partial differential equations are turned into ordinary ones, which are then numerically solved by high-order Runge-Kutta methods. The proposed approach is verified against the analytical solution in a 1D core model. Afterwards, it will be utilized to investigate the effect of multiple transport and reaction phenomena on the matrix acidizing in 2D carbonate formations. Also, the staggered grid technique is employed to accurately predict the wormhole patterns during several injection regimes. Compared to the previous studies, the proposed numerical approach is less complicated and straightforward. Furthermore, the computational cost is more affordable.