Heat Transfer during the Extraction of a Chemically Active or Radioactive Fluid from a Reservoir

About the authors:

Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, filippovai@rambler.ru

Oksana V. Akhmetova, Dr. Sci. (Phys.-Math.), Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, ahoksana@yandex.ru

Aleksei A. Kovalsky, Cand. Sci. (Phys.-Math.), Director, Sterlitamak Branch of the Bashkir State University; eLibrary AuthorID, aakov68@mail.ru

Ilshat F. Kabirov, Junior Researcher, Institute for Strategic Studies of the Republic of Bashkortostan (Ufa); kabirov.ilshat@bk.ru

Abstract:

The aim of the study is to develop the physical-mathematical model of the temperature field at the extraction of a chemically active fluid from the productive carbonate-bearing reservoir taking into account temperature perturbations caused by previous technological processes. The first source of these temperature perturbations is the fluid containing hydrochloric acid or radioactive impurities in the dissolved state, and the second source is the accompanying thermophysical processes.

The method for constructing the solution of the conjugation problem about the temperature field at the extraction of a chemically active fluid from a productive formation is developed. This method is the development of the "the average exact" asymptotic method with regard to the conjugation problems with nonzero initial conditions, which is an important achievement in the actual trend of mathematical physics and hydrodynamics. The method implemented in the article includes a specially developed procedure for finding the nonlocal average integral condition at the initial time, which is determined from the requirement that the solution of the integrally averaged problem for the remainder term must be trivial after the zero coefficient of asymptotic expansion.

The asymptotic solution of the conjugation problems about the temperature field during the extraction of a chemically active fluid from a reservoir is constructed for the zero and first coefficients of the asymptotic expansion. It is shown that the solution in the zero asymptotic approximation represents the temperature value averaged over the central bounded region, and the first approximation implies the value for the steady-state temperature field. The analytical formulas can be used for calculations under conditions of multiple cyclic hydrochloric acid impact on the oil and gas reservoirs. Space-time dependences of the temperature field complicated by initial perturbations when selecting a chemically active fluid from a productive formation are presented.

References:

1. Glushchenko V. N., Silin M. A. 2010. Neftepromyslovaya khimiya. Izd. v 5-ti tomakh. T. 4. Kislotnaya obrabotka skvazhin [Oilfield Chemistry. Ed. in 5 Volumes. Vol. 4. Acid treatment of wells], edited by Mishchenko I. T. Moscow: Interkontakt, Nauka.
2. Ditkin V. A., Prudnikov A. P. 1963. Spravochnik po operatsionnomu ischisleniyu [Operational Calculus Handbook]. Moscow: Vysshaya shkola.
3. Zakirov T. R., Nikiforov A. I. 2012. “Modelirovanie kislotnogo vozdeystviya na neftyanye plasty pri zavodnenii” [Modeling Acid Impact in Water Flooding Oil Reservoir]. Oil Industry, no 6, pp. 62-65.
4. Kremleva T. A., Smirnov A. S., Fedrov K. M. 2011. “Modelirovanie protsessov kislotnoy obrabotki karbonatnykh plastov s uchetom effekta obrazovaniya kanalov chervotochin” [Modeling of the Processes of the Acid Treatment of Carbonate Layers Taking into Account the Effect of the Formation of Wormhole Channels]. Fluid Dynamics, no 5, pp. 76-84.
5. Filippov A. I., Mikhailov P. N., Pestova N. V., Krupinov A. G. 2008. “Temperature Fields in the Oil Reservoir Rocks Being Treated with an Acid”. Theoretical Foundations of Chemical Engineering, vol. 42, no 5, pp. 556-564. DOI: 10.1134/S0040579508050126
6. Filippov A. I., Akhmetova O. V., Kabirov I. F. 2013. “Temperature Field of Heat Sources during Fluid Injection in an Anisotropic Inhomogeneous Reservoir”. Journal of Applied Mechanics and Technical Physics, vol. 54, no 6, pр. 945-951. DOI: 10.1134/S0021894413060102