Analytical model for estimation of pore volume to breakthrough in carbonate acidizing with organic and mineral acids

Abstract

Acidizing treatment is one of the most useful methods in oil well stimulations to form wormholes in carbonate formations in order to enhance reservoir fluid production. Obtaining the number of pore volumes to breakthrough is an important objective in carbonate acidizing to determine the wormhole properties such as type, shape, and size. Finding this number in experimental works requires a considerable amount of time, energy, and cost. Therefore, this study aimed to establish an analytical model in which a reasonable result would be achieved for the number of pore volumes to breakthrough. This purpose was accomplished by only using acid and formation properties without performing any experimental works. The process of wormhole modelling is simulated by developing an analytical model which uses the conservation of mass law. The carbonate core is treated as a closed system and the overall mass in the system as constant during the acid injection process. Furthermore, a constant number is added to the mathematical part of the model in order to eliminate the dimensionless Damköhler number which is supposed to be calculated experimentally. The results of the analytical procedure of the developed model are further compared to six other experimental and numerical works, which led to the computation of average accuracy and coefficient of determination of this model. Evaluation of the developed model with other experimental and numerical results gives an excellent assessment of 95.45% for the average accuracy and 0.9938 for the average coefficient of determination. This study establishes a comprehensive analytical model to estimate the number of pore volumes to breakthrough with an acceptable accuracy rate merely through implementing known acid and core properties.