International Journal of Engineering and Advanced Technology Studies (IJEATS)

# Finite Difference Method

## Design of a Simulator of a Reservoir Investigating the Effect of Surfactant Mixture in an Enhanced Oil Recovery Process (Published)

In this paper, we present development of a simulator for multidimensional, multiphase and multicomponent surfactant flooding concerned with the characteristics of the chemical slugs for an enhanced oil recovery process. The development starts with the description of the fluid flow in permeable media from the basic conservation laws and with linear constitutive theory. From this physical basis a mathematical formulation of the flow problem may be posed in the form of an initial-boundary value system of partial differential equations. The form is presented in detail for the general multicomponent, multiphase system and several special cases. A surfactant flood model for a two or three dimensions, two fluid phases (aqueous, oleic) and one adsorbent phase and four components (oil, water, surfactants 1 and 2) system is presented and analyzed. It is ruled by a system of non-linear, partial, differential equations; the continuity equation for the transport of each component, Darcy’s equation for the flow of each phase and algebraic equations. This system is numerically solved in the one-dimensional case. The orthogonal collocation and finite difference techniques were used in solving the equations that characterized the multidimensional, multiphase and multicomponent flow problem. The simulator is fed with the physical properties that are concentration dependent functions. The material transport equations are decoupled from the momentum transport equations and the complex, time changing flow-field requires a numerical solution. Matlab computer programs were used for the numerical solution of the model equations. The results of the orthogonal collocation solution were compared with those of finite difference solutions. The results indicate that the concentration of surfactants for orthogonal collocation show more features than the predictions of the finite difference, offering more opportunities for further understanding of the physical nature of the complex problem and chemical effectiveness. Also, comparison of the orthogonal collocation solution with computations based on finite difference method offers possible explanation for the observed differences especially between the methods and the two reservoirs.

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