Matrix acidizing is a common technique to stimulate wells for improving well inflow performance. In this treatment that is widely used in the oil industry, acid volution is injected into the formation to dissolve some minerals to increase permeability of carbonate near the wellbore. The aim of the treatment is to create empty channels called wormholes. Wormholing in carbonate rocks is a complex 3-D phenomenon. Matrix acidizing generally should be applied when a well has a high skin factor that cannot be attributed to partial penetration, perforation efficiency or other mechanical aspects of the completion. Obviously, it is of extreme importance to quantify the skin factor to evaluate the effectiveness of stimulation treatments. When wormholes extend beyond the damaged zone or connect with natural fissures in the formation, a negative skin effect is obtained. An ideal matrix treatment restores the permeability in the near wellbore region to a value at least as high as the original undamaged permeability; it accomplishes this over the entire completed interval and it leaves the formation in the treated region with high relative permeability to the oil and/or gas phase. Designing a treatment should strive to achieve this ideal at the lowest possible cost, which requires consideration of the many physical and chemical interactions taking place between the injected fluids and the reservoir minerals and fluids. In this work, a three-scale continuum model is used to model reactive dissolution of carbonate rocks in radial flow. Both the Darcy and pore scale physics such as mass transfer of acid molecules to the mineral surface and subsequent reaction at the surface, changing pore structure and variations in reservoir permeability are included in this model. Partial differential equations obtained from the model, have been solved by numerical method. The influence of reservoir temperature on optimum injection rate is investigated. Results show that optimum injection rate increases with temperature.
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