Matrix acidizing of carbonates is routinely carried out to increase hydrocarbon production rates from a reservoir. This involves pumping acid through the wellbore into the formation where it reacts with the rock and results in an increase in permeability. As a result of the dissolution reaction, different types of dissolution patterns are created. These patterns depend on the injection rate, type of fluid, rock mineralogy, temperature, flow geometry, etc. The effect of these factors on dissolution patterns has been studied extensively in the past. However, most of the reported experimental and theoretical work presents wormholing under openhole conditions. When the well completion includes perforated casing, fluid-flow through the perforations is markedly different from that in an openhole completion. The degree of success of an acid job in a perforated completion is limited by the proximity of the damage to the perforation tunnel. The wormhole pattern structure, penetration distance, and acid volume required to achieve a given permeability increase in such a completion is still not clearly understood. In this paper, the effect of injecting acid into a rock sample through perforations is studied by using a two-scale continuum model. The model represents the complex coupling between flow, transport, and reaction of acid in a carbonate rock. Two-dimensional simulations of the model show the flow redistribution inside a rock sample when acid is injected through a constriction. It is shown that the amount of acid required to achieve a given permeability (or, wormhole-penetration distance for a given volume of acid) depends on both perforation and sample dimensions. Conditions under which maximum skin decrease is observed are also identified. In addition, the main differences in predictions from perforated and openhole completions are highlighted. Because a substantial number of current carbonate well completions are cased and perforated, it is important to understand matrix acidizing under such conditions. Particular application from this work includes better matrix-acid treatment designs with optimum acid volumes and rates.
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