Abstract
This paper examines the process of wormholes formation during hydrochloric acid treatment of well bottom-hole zone in carbonate formations. An algorithm for solving the problem of wormhole formation in a porous medium for a two-dimensional case was developed. Two-scale model (porescale and Darcy’s scale) taking into account convection, diffusion, and chemical reaction were used in this work in order to describe the dissolution of carbonates with hydrochloric acid (hydrochloric acid treatment). The initial distribution of the porosity field was generated as a distribution of random numbers around some mean value. Based on the distribution of the initial porosity field, the initial permeability field of the rock was calculated. The random distribution was used to describe the heterogeneity of the actual rock. The rest of the study parameters were taken from known experiments on the dissolution of carbonate cores. The numerical model was built for solving the system of equations for acid dissolution, and carbonate dissolution modes with hydrochloric acidwere obtained depending on the Damkohler number, Thiele modulus on the pore-scale and Darcy’s scale as a result of this research. Also, the optimal Damkohler numbers (injection rates) were found. The computer code for the problem of the development/growth of wormholes in a porous medium based on the developed algorithm was built using the C++ programming language.