Carbonate Acidising Calculation Model Coupled with Dual-Fractal Wormhole
Authors: Zhang Hewen , Zou Honglan , Yan Xuemei , Cui Mingyue , Liang Chong , Sun Yuping , Li Haibo , Wang Xuewu 
Published: March 2021

Abstract
As recognized as the most economical and effective measure to increase carbonate oil and gas well production, matrix acidising is widely used. The main feature of acidising and the key influence factor of increasing production is what kind of acid etched wormholes can be formed. The actual etched wormholes grow in disorder and randomly, that's why it is extremely difficult to describe by classical mathematical methods. Due to the lack of a quantitative calculation model for the growth law of acid-etched wormholes, penetration depth, competition and distribution patterns among different etched wormholes, an effective method for acidising parameters optimization cannot be formed. The stimulated production of different wells vary greatly.
In order to establish the corresponding quantitative calculation model for geometric size of acid etched wormholes, three-dimensional competitive distribution of different wormholes, and production prediction, also to achieve the quantitative optimization of treatment parameters for different wells and improve oil and gas production, firstly, we designed and completed indoor core etched experiments and CT scanning technology to obtain the true three-dimensional morphology of linear acid etched wormholes. Besides, the radial wormholes in 14 cubic feet of super large cores were proven to meet the requirement of fractal. The fractal dimensions of these two wormhole types were also obtained. Furthermore, a quantitative calculation model for the wormhole length expansion was established. Secondly, according to the mathematical model of extending competition among different acid etched wormholes, the fractal distribution law of the length of wormholes in the vertical direction is obtained. Combined with the fractal wormhole length calculation model, a method to solve the dual fractal model by calculating the maximum wormhole length is given. Finally, the classic acidised production rate calculation model was revised. The influence of the three-dimensional expansion length and distribution of wormholes on the skin factor was considered in detail. The sensitivity of key acidising parameters, such as acid strength and pumping rate, was also analyzed.
The results show that both the linear wormholes obtained from conventional cores and the radial wormholes obtained from super-large cores can be described by fractal geometry. The fractal dimension corresponding to the optimal pumping rate is 1.46-1.63. Considering the dual-fractal distribution of acid-etched wormholes, the skin factor is larger than that of the conventional equalization model. This is mainly due to the fact that the equalization model only uses the maximum length of the wormholes. This also explains why wells or layers with negative skin factors can still increase production rate after uniform acidising. At the same time, for a specific layer, there is a better acid strength and pumping rate. With these parameters, the acid consumption and predicted production rate are better, which provides a theoretical basis for the quantitative optimization of acidising treatment parameters.