Matrix stimulation of carbonates involves injecting acid into the wellbore where it reacts with the formation and bypasses the damage. Different types of patterns, like face dissolution, wormhole, and uniform dissolution, are created as a result of the dissolution process. During acid injection, the fluid temperature is typically lower than the formation temperature. As a result, thermal interactions between the fluid and formation occur and lead to retardation of surface reaction rate, decrease in fluid viscosity, and density and increase in diffusivity. Experimental studies of the effect of temperature on wormholing conducted in the past indicated that, depending on the type of acid being injected, a high formation temperature can either aid or impede stimulation. This implies that either a higher or lower total volume of acid might be required to increase the medium permeability. In addition to the temperature difference between the fluid and formation, the fluid-injection rate is also often varied during a single acid job. Therefore, the type of patterns created under lab conditions might not be representative of those formed in the field. Hence, it is not straightforward to design a treatment based on experimental data when flow rate and temperature variations are involved.

In this work, a two-scale continuum model is developed to understand the coupling between flow, reaction, and transport under transient temperature and flow-rate conditions. The effect of fluid temperature on wormholing has been investigated. Specifically, it is shown that injecting a colder fluid in a high-temperature formation leads to a higher wormhole density under laboratory conditions. In addition, it is shown that the acid volume required to achieve a given increase in permeability also depends on the temperature of the injected fluid.

It is important to investigate techniques that enhance hydrocarbon recovery from carbonate reservoirs as more than 50% of the world's current hydrocarbon reserves are present in these formations. The modeling study in this work attempts to answer critical questions pertaining to the effect of temperature variations on stimulation design. In particular, the results from this work can be used to optimize acid volume, flow rates, and acid types in a matrix-acid design.

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