This paper presents an improved practical model including the non-isothermal effects involved in the acid stimulation of hydraulically fractured wells. The mathematical model presented here considers a transient-state invasion of acid solution into fractured reservoir formations, dilution of acid by mixing with the reservoir brines, and reaction of acid with the carbonate formation under the effect of the local temperature increase due to the release of the heat of reaction, coupled with the well heat transfer problem. The dissipation of the reaction heat occurs rapidly and increases the acidizing reaction rate according to the Arrhenius law. This is considered in the differential heat balance. The fluid flow is described by means of the material and momentum balance equations in the formation around the fractured well. The model developed here can be facilitated for convenient description of the effect of non-isothermal conditions in acidizing hydraulically fractured wells completed in carbonate reservoirs.

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