Thermal analysis in matrix acidization

The present paper addresses the heat transfer that occurs during matrix acidization. The complete process is first approached by separately analyzing two problems: one aiming at the temperature profile down the wellbore and the other looking at the temperature distribution within the reservoir. The wellbore-problem is modeled to consider short-term effects, including energy accumulation during the heat exchange between the wellbore and the surrounding formations. The solution obtained shows the transient behavior in detail, until the consistent collapse to known profiles for the late time periods. The model proposed to the reservoir-problem includes heat generation by the chemical reactions, an essential feature for the proper accounting of the acid–rock interaction. The eventual temperature distribution after the acid penetration into the reservoir, for the complete problem, is then obtained by coupling the solution to the wellbore-problem and the solution to the reservoir-problem. The wellbore-problem and the reservoir-problem are both solved individually via Laplace transforms and the coupled solution is then rendered by convolution in Laplace space. Stehfest's algorithm is used to convert the results to the real domain. Results obtained for typical operational parameters show that the acid temperature is very sensitive to injection flow rate and to fluid volumes injected during the pre-flush operation. Heat accumulation effects are important for injection periods in the order of 10 h. High injection rates result in temperatures, at the formation entrance, yet close to the surface temperature. The effect of heat loss to neighboring formations is rather small. Also, temperatures of the acid in the near-wellbore regions stay at values that are significantly lower than the reservoir initial temperature. The temperature calculation procedures for both specific problems and for the coupled problem are simple to implement and straightforward to use.