# Mathematical modeling heat and mass transfer in a vertical hydraulic fracture crack during inflation and cleaning

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy

Release:

2020. Vol. 6. № 2 (22)

Title:
Mathematical modeling heat and mass transfer in a vertical hydraulic fracture crack during inflation and cleaning

For citation: Bulgakova G. T., Sharifullin A. R., Sitdikov M. R. 2020. “Mathematical modeling heat and mass transfer in a vertical hydraulic fracture crack during inflation and cleaning”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 6, no. 2 (22), pp. 41-62. DOI: 10.21684/2411-7978-2020-6-2-41-62

Guzel T. Bulgakova, Dr. Sci. (Phys.-Math.), Professor, Department of Mathematics, Ufa State Aviation Technical University; bulgakova.guzel@mail.ru; ORCID: 0000-0001-8030-1791

Andrey R. Sharifullin, Cand. Sci. (Tech.), Senior Researcher, Department of Mathematics, Ufa State Aviation Technical University; sharifullinar@mail.ru; ORCID: 0000-0002-0958-778X

Marat R. Sitdikov, Cand. Sci. (Tech.), Chief Specialist, Tetakom LLC (Ufa); maratsitdikov@mail.ru; ORCID: 0000-0002-5051-3213

Abstract:

When designing hydraulic fracturing for high-temperature formations, it is important to know the temperature change in the fracture during the injection of fracturing fluid. The temperature profile in the hydraulic fracture is necessary to calculate the optimal composition of the fracturing fluid, which necessarily includes a crosslinker (crosslinker) and a breaker (breaker), the concentration of which is calculated by the temperature at the end of the crack. Currently, this concentration is calculated based on the maximum temperature of the formation, which can lead to a decrease in the efficiency of hydraulic fracturing, since a breaker will not completely destroy the crosslinked gel. Therefore, when a well is brought into operation after the stimulation, proppant removal may occur, reducing the effectiveness of stimulation to zero. In this regard, the optimization of the decision-making process in the design of hydraulic fracturing in terrigenous and carbonate reservoirs by calculating the optimal parameters of process fluids based on predicting heat and mass transfer processes occurring during processing is a very urgent task. A tool has been developed to improve the design efficiency of hydraulic fracturing based on mathematical modeling of temperature fields in a hydraulic fracture during its development and during the period of technological sludge.

A mathematical model that describes the temperature dynamics in a hydraulic fracture taking into account fluid leakage into the formation represents the evolutionary equation of convective heat transfer with a source, which is defined as the density of the heat flux from the formation. To check the adequacy of the model of temperature dynamics in a hydraulic fracture, a model of temperature recovery in a fracture is presented with the subsequent adaptation of simulation results to actual data. Developed mathematical models can be used in hydraulic fracturing simulators.

Keywords:

References:

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