Effect of normally distributed porosities on dissolution pattern in carbonate acidizing

In carbonate acidizing, acid dissolves rock to create a high permeability channel called wormhole. One of the main factors to influence the formation of wormhole is the heterogeneity of porous medium. In former literature, uniformly distributed porosity fields were considered which are not in accord with the real distribution of porosities in rocks. In this paper, we use a normal distribution method to generate porosities. The comparison of the two methods shows that the pore volume to breakthrough for the normal distribution method is less than that for the uniform distribution method. Due to the characteristics of normal law, correlation length and standard deviation which characterize heterogeneity are introduced. The correlation in the radial or circumferential direction among girds has an effect on wormholing. Wormhole tends to propagate away from the radial direction to make itself thicker due to the big correlation length in the circumferential direction. The number of wormholes is increased and the wormholes become thinner because of big correlation length in the radial direction. The total acid injection volume decreases with the increase of initial porosity. A critical value for standard deviation exists, below which the pore volume to breakthrough is insensitive, above which the pore volume to breakthrough decreases sharply. The increase of perforation length decreases the pore volume to breakthrough whether there is acid leakoff along the perforation or not. The sharp decline of pressure at the end for the face dissolution pattern is due to the faster propagation velocity for the spent acid front than that for the reaction front and the short distance between them. Continuous vugs change the wormhole propagation path and decrease the injection volume. Finally, an apparent skin factor model is developed to study the performance of wormholing. Before the breakthrough of the damage zone, the sharply decreased skin factor indicates huge improvement, after the breakthrough, the skin factor decreases slowly. Wormhole length and time follow a power–law relationship.