Abstract: Carbonate matrix acidizing mainly features acid wormholes that are deemed to be unordered and disorganized in Euclidean space. It is difficult to conduct experimental simulations and mathematically describe wormholes using classic mathematical methods; however, an accurate description of the penetration depth of acid wormholes is of significance for construction parameter optimization and acidizing effect improvement. To this end, multiple groups of core acidification flow simulation tests were carried out first in this study, using CT scanning to determine the true forms of the wormholes. The term "box dimension" was introduced to verify the wormhole fractal properties and to calculate the Hausdorff fractal dimensions of different wormhole forms. Test results indicate that the wormholes in this test featured favorable fractal properties; fractal dimensions varied from 1.19-1.98 as solution features changed; and the dimension corresponding to the optimum capacity was approximately 1.6. Moreover, a combined method of laboratory testing and fractal geometry was employed to establish a fractal calculation model for the equivalent length of acidized wormholes, and to conduct a sensitivity analysis of factors affecting the wormhole's equivalent length.

Key words: carbonate, acidizing, wormhole, fractal, fractal dimension