Experimental Simulation And Fractal Model Study Of Carbonate Acidized Wormhole

Carbonate oil and gas reservoir, from the view of either reserves or production, all plays an important role in the global oil pattern. For such reservoir, acidizing treatment is one of the most commonly used measures, because of its effectiveness in increasing production and its economy. The key feature of carbonate acidizing is forming wormholes, which are deemed as disordered and unsystematic. Competitive mechanism between wormholes is complex, so it’s difficult to describe wormholes by experiment and classical mathematic methods. In order to get better production after acidized and optimize construction parameters, it’s need to accurately describe wormhole penetration depth and its distribution pattern along wellbore direction.Based on this purpose, this paper first completed indoor experiments of core acidification. Using CT scan, the acid corrosion wormhole shape and its fractal dimension were described. Combined with the material balance equation, the model of calculating equivalent acid erosion wormhole length was given. Then according to the fractal distribution of acid corrosion wormholes along wellbore direction, wormhole fractal distribution model was established, and skin factor model was corrected under different conditions, which is the theoretical basis of acidizing optimization. The main understandings and conclusions are as follows:(1) The wormholes gotten by indoor experimental methods have fractal characteristic. Wormhole equivalent length model was established, also it can be extrapolated into two dimension Euclidean space to represent face dissolution.(2) Actual wormhole distribution was gotten by core experiments and three dimension Computer Tomography. The fractal box dimension was also obtained. All results showed that wormholes formed by experiment followed fractal law and its value changed with wormhole shape. Fractal dimension ranged from 1.19 to 1.98, and it is 1.6-1.7 under optimized pumping rate.(3) Competitive distribution mathematic model between wormholes was solved, and it concluded that wormhole longitudinal distribution obeyed fractal feature. Besides, its fractal dimension was calculated, which is between 1.35 and 1.73.(4) Double fractal model of maximum wormhole length was established considering wormholes competition. On this basis, the skin factor correction mathematical model was given under two cases:all the wormholes equivalent length are the same or are assumed as fractal distribution. The latter one considered two fractal features of wormhole length and its distribution.Innovations are as follows:the laboratory and fractal geometry mathematical methods are combined to create a fractal model for etching wormhole equivalent length calculation; wormhole validated scale invariance was proven, and its Hausdroff fractal dimension was gotten by using real experiments data (linear flow and radial flow), which also expanded the past awareness of fractal dimension about 1.6; A dual fractal new model describing wormhole length and competition was established, and skin factor correction mathematical model considering wormholes competition was also given.