Two-scale (Darcy scale and pore scale) continuum wormholing models are built to study the fractal nature of the acid-etched wormholes in acidizing carbonate reservoirs and the influence of acid type on the conditions for wormholes to form. This model considers convection-diffusion mass transfer and reaction on the acid-rock interface, and the fractal dimension of dissolution patterns is calculated using box-counting method. The results show that wormholes are formed when convection and diffusion are equivalent in strength; when convection dominates, uniform dissolution is formed; when diffusion dominates, surface dissolution is generated. For the zones where the porosity is greater than 0.7, the fractal dimensions of the surface dissolution, wormholes and uniform dissolution are 1.46, 1 50 and 1.44, respectively, among which, the fractal dimension of the wormholes is approximate to the experimental results obtained by Daccord and Lenormand (1.6±0.1). The reaction between weak acid and rocks is controlled by reaction kinetics, the acid-etched wormholes are wide, and more acid is consumed. The reaction between strong acid and rocks is controlled by mass transfer, the acid-etched wormholes are narrow, and less acid is consumed. According to an example calculation, it is found that acidizing treatments should be performed in an isolated short section each time when the horizontal well is long.%建立双尺度(达西尺度和孔隙尺度)蚓孔扩展模型,研究碳酸盐岩油藏酸化酸蚀蚓孔的分形性及酸液类型对酸蚀蚓孔形成条件的影响.模型考虑了孔隙中的对流传质和液固表面的酸岩反应,并用盒维数法计算了酸蚀溶解形态的分形维数.结果表明,蚓孔是对流作用与扩散作用相当时形成的,对流作用占主导作用时形成均一溶蚀,扩散作用占主导作用时形成面溶蚀;对于孔隙度大于0.7的区域,面溶蚀、蚓孔和均一溶蚀的分形维数分别为1.46、1.50和1.44,其中蚓孔的分形维数与Daccord和Lenormand得到的实验结果(1.6士0.1)相近;弱酸与岩石反应受反应动力控制,酸蚀蚓孔较粗,消耗酸液量较多;强酸与岩石反应受传质作用控制,酸蚀蚓孔较细,消耗酸液量较少.通过算例模拟发现,水平井段较长时,产生蚓孔所需的排量大,不可对其笼统酸化,宜采用分段酸化方式.
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