Fractal nature of acid-etched wormholes and the influence of acid type on wormholes

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 (1.60.1). 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.