The pore space near the wellbore damaged with a time due to fine particles, chemical reactions, reservoir pressure difference, etc. As a result of the above mentioned factors reservoir properties of near-wellbore zone are altered, which negatively affects the productivity/injectivity of wells. One way to restore the reservoir properties of near-wellbore zone is matrix acidizing. An analysis of the literature review shows that there is a definite law of permeability reduction of the near-wellbore zone due to formation damage with the maximum reduction observed at the wellbore, and with the distance from the wellbore it restores to the original value. The influence of reservoir properties reduction due to damage on the effectiveness of the matrix acidizing is the subject of these studies, which based on numerical simulation of the dissolution of carbonate rock with hydrochloric acid.

Numerical simulation of the dissolution of carbonate rock with hydrochloric acid is carried out using two-scale model in the polar coordinate system. To account the reduced reservoir properties due to formation damage of near-wellbore zone in numerical calculations special function fd is introduced. In this paper, a comparative analysis of results of dissolution modeling with the damage (fd ≠ 0) and without damage (fd = 0) function is shown.

As a result of numerical simulations it was revealed that the dominant wormholes grows faster than non-dominant wormholes in the case with fd ≠ 0, which leads to a quick acid breakthrough. On the contrary, in the base case (fd = 0), non-dominant wormholes become relatively developed. Optimal Damköhler number for the base case is Daopt = 330, while fd ≠ 0 for the number is varying from 210 to 310 depending on the damage ratio Δεd and parameter λ.

It was also shown that in the case of fd ≠ 0 wormhole grows faster than in the case of fd = 0. In the first case, the final skin factor is achieved when a volume of the injected acid is 75% less than amount required for the base case.

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