Mathematical model of killing an oil horizontal well

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


Release:

2023. Vol. 9. № 2 (34)

Title: 
Mathematical model of killing an oil horizontal well


For citation: Korotchenko, A. N., & Kislitsin, A. A. (2023). Mathematical model of killing an oil horizontal well. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 9(2), 39–58. https://doi.org/10.21684/2411-7978-2023-9-2-39-58

About the authors:

Andrey N. Korotchenko,
Director of OOO InTech 

Anatoliy A. Kislitsin, Dr. Sci. (Phys.-Math.), Professor, Department of Applied and Technical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.a.kislicyn@utmn.ru, https://orcid.org/0000-0003-3863-0510

Abstract:

The physical picture of the killing fluid and the formation fluid movement in the process of killing a horizontal oil well has been described, a physical and mathematical model of the process has been developed and the limits of the model applicability have been indicated. It is recommended to conduct the killing process in two stages, separated by a technological break. During the first stage, the injected killing fluid fills the tubing, the annulus and the part of the horizontal wellbore. For the duration of the technological break, the denser tubing slowly displaces the formation fluid from the horizontal wellbore into the annulus where the formation fluid floats to the surface in the form of droplets. For the period of the second stage, the remaining amount of tubing is pumped into the well. The model is based on the well-known hydraulic equations for laminar flow of liquids, the solution of the flooded jet problem, as well as the model of one-dimensional vertical inertialess flow of a two-phase medium with incompressible phases. A closed system of equations has been formed taking into account the viscous friction losses on the walls of the horizontal pipe and at the interface between the formation fluid and the killing fluid flows. The solution of this system has been obtained and the values of the main process parameters have been found: velocities and flows of liquid gas and liquid coolant and time of complete replacement of liquid coolant by the killing fluid depending on the inclination angle of the horizontal pipe. It is shown that the character of the movement of the formation fluid drops in the pipe space depends on their volume fraction φ in the mixture with the killing fluid. With the value φ < 1/3 the jelly drops float up with a constant speed, while the jelly droplet radius and the speed of their floating up are unambiguously determined by the jelly stream size, density and viscosity of jelly and liquid hydrocarbon. The graphs of dependence of these parameters on the value of the formation fluid flow have been presented. On the basis of the research the recommendations for the process of killing horizontal oil wells have been formulated.

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