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- Shestopalov, Yury, 1953-, et al.
(författare)
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Alternative conception of the monitoring and optimization of water flooding of oil reservoirs under instability of displacement front
- 2019
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Ingår i: Oil industry (Neftyanoye khozyaystvo). - Moscow. - 0028-2448. ; :12, s. 118-123
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Tidskriftsartikel (refereegranskat)abstract
- The theory of Buckley and Leverett does not take into account the loss of stability of the displacement front whch provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed: a differentiable approximation to eliminate the ' jump' in water saturation. Such a simplified solution led to negative consequences well-know from the water flooding practice, recognized by experts as 'viscous instability of the displacement front' and 'fractal geometry of the displacement front'.The core of the issue is to attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative effect on the water flooding process under difficult conditions of interaction of hydro-thermodynamic, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be determined using this model. A unified control parameter has been selected which enables one to propose and validate a discriminant criterion for oil and water growth models for monitoring and optimization.
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| 2. |
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| 3. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields
- 2019
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Ingår i: Lobachevskii Journal of Mathematics. - : Pleiades Publishing. - 1995-0802 .- 1818-9962. ; 40:10, s. 1695-1710
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Tidskriftsartikel (refereegranskat)abstract
- The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, with the discriminant criteria created on the basis of the growth model constructed in the present study, it is possible to formulate practical recommendations for regulating and monitoring the process of waterflooding and the development of an oil field.
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| 4. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Qualitative theory of two-dimensional polynomial dynamical systems
- 2021
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Ingår i: Symmetry. - : MDPI. - 2073-8994. ; 13:10
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Tidskriftsartikel (refereegranskat)abstract
- A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.
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