Numerical Simulation of the Filtration of a Steam–Water–Oil Mixture during the Thermal-Steam Treatment of a Reservoir

Bublik, S. A.; Семин, М. А.

doi:10.1134/s2070048222020041

Math Models Comput Simul

2022

DOI: 10.1134/s2070048222020041

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Numerical Simulation of the Filtration of a Steam–Water–Oil Mixture during the Thermal-Steam Treatment of a Reservoir

S. A. Bublik

М. А. Семин

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Cited by 2 publications

References 17 publications

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Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir

Bublik

Семин

2022

Computation

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This study focuses on the analysis of an approach to the simulation of the phase transition in porous media when hot steam is injected into the oil reservoir. The reservoir is assumed to consist of a porous medium with homogeneous thermal properties. Its porous space is filled with a three-phase mixture of steam, water, and oil. The problem is considered in a non-stationary and non-isothermal formulation. Each phase is considered to be incompressible, with constant thermal properties, except for the dynamic viscosity of oil, which depends on the temperature. The 1D mathematical model of filtration, taking into account the phase transition, consists of continuity, Darcy, and energy equations. Steam injection and oil production in the model are conducted via vertical or horizontal wells. In the case of horizontal wells, the influence of gravity is also taken into account. The Lee model is used to simulate the phase transition between steam and water. The convective terms in the balance equations are calculated without accounting for artificial diffusion. Spatial discretization of the 1D domain is carried out using the finite volume method, and time discretization is implemented using the inverse (implicit) Euler scheme. The proposed model is analyzed in terms of the accuracy of the phase transition simulation for various sets of independent phases and combinations of continuity equations. In addition, we study the sensitivity of the model to the selected independent phases, to the time step and spatial mesh parameters, and to the intensity of the phase transition. The obtained results allow us to formulate recommendations for simulations of the phase transition using the Lee model.

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Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir

Bublik

Семин

2022

Computation

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Linear Stability of Filtration Flow of a Gas and Two Immiscible Liquids with Interfaces

Shargatov,

Tsypkin,

Kozhurina

2023

Mathematics

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The stability of the vertical flow that occurs when gas displaces oil from a reservoir is investigated. It is assumed that the oil and gas areas are separated by a layer saturated with water. This method of oil displacement, called water-alternating-gas injection, improves the oil recovery process. We consider the linear stability of two boundaries that are flat at the initial moment, separating, respectively, the areas of gas and water, as well as water and oil. The instability of the interfaces can result in gas and water fingers penetrating into the oil-saturated area and causing residual oil. Two cases of perturbation evolution are considered. In the first case, only the gas–water interface is perturbed at the initial moment, and in the second case, small perturbations of the same amplitude are present on both surfaces. It is shown that the interaction of perturbations at interfaces depends on the thickness of the water-saturated layer, perturbation wavelength, oil viscosity, pressure gradient and formation thickness. Calculations show that perturbations at the oil–water boundary grow much slower than perturbations at the gas–water boundary. It was found that, with other parameters fixed, there is a critical (or threshold) value of the thickness of the water-saturated layer, above which the development of perturbations at the gas–water boundary does not affect the development of perturbations at the water–oil boundary.

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Numerical Simulation of the Filtration of a Steam–Water–Oil Mixture during the Thermal-Steam Treatment of a Reservoir

Cited by 2 publications

References 17 publications

Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir

Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir

Linear Stability of Filtration Flow of a Gas and Two Immiscible Liquids with Interfaces

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