Mathematical Model of Water Alternated Polymer Injection
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Mathematical Model of Water Alternated Polymer Injection Bruno J. Vicente1 · Viatcheslav I. Priimenko2 · Adolfo P. Pires2 Received: 31 March 2019 / Accepted: 15 September 2020 / Published online: 1 October 2020 © Springer Nature B.V. 2020
Abstract Chemical enhanced oil recovery (EOR) methods include the injection of aqueous polymer solutions slugs driven by water. Polymer solutions increase water viscosity, decreasing the water phase mobility and improving oil recovery through better sweep efficiency. In this paper, we present the water alternated polymer EOR technique, which is based on the injection of successive polymer slugs alternated by water slugs. The mathematical problem is composed by two conservation equations: one of them is related to the water volume and the other one to the polymer mass. We assume that the polymer may be adsorbed by the rock, and the relation between the concentration in the aqueous solution and the solid is governed by a Langmuir type adsorption isotherm. The water viscosity is a function of the polymer concentration in water. The 2 × 2 system of hyperbolic equations was decoupled by introducing a potential function instead of time as an independent variable. The water alternated polymer injection is represented by a varying boundary condition. The analytical solution presents interactions between waves of different families. It is shown that the polymer slugs always catch up each other along the porous media generating a single slug. As a consequence, the water slugs will disappear. This solution is new and was compared to numerical results with close agreement. It also can be used for the selection of the most suitable enhanced oil recovery technique for a particular oil field. Keywords Conservation laws · Enhanced oil recovery · Polymer flooding · Flow in porous media
1 Introduction Polymer flooding is a method of enhanced oil recovery (EOR) appropriate to highly heterogeneous reservoirs, and for cases where oil is displaced by water at unfavorable mobility ratio. Adsorption and the relation between the polymer concentration in water phase and its viscosity are the main phenomena that govern the hydrodynamics of oil displacement by a polymeric solution (Littmann 1988; Sorbie 1991). At equilibrium conditions, the polymer concentration adsorbed on the pore surface can be modeled by * Adolfo P. Pires [email protected] 1
Universidade Federal do Pará, Salinópolis, Brazil
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Universidade Estadual do Norte Fluminense, Macaé, Brazil
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an adsorption isotherm, for example, the Langmuir isotherm. To overcome the problem of high cost of the continuous injection of polymer solutions, a finite volume of water containing this chemical product (slug) is injected (Thiele et al. 2010). Two-phase flow of a polymer solution in porous media (Hatzignatiou et al. 2013, 2015; Zhao et al. 2019) is governed by a 2 × 2 hyperbolic system of conservation laws (Fayers and Perrine 1958) obtained from the mass balance of the water phase and polymer
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