Identification of Reservoir Heterogeneities Using Tracer Breakthrough Profiles and Genetic Algorithms
- J.N.C. Guerreiro (LNCC/CNPq) | H.J.C. Barbosa (LNCC/CNPq) | E.L.M. Garcia (LNCC/CNPq) | A.F.D. Loula (LNCC/CNPq) | S.M.C. Malta (LNCC/CNPq)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 1998
- Document Type
- Journal Paper
- 218 - 223
- 1998. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.1.1 Exploration, Development, Structural Geology, 5.3.1 Flow in Porous Media, 5.6.5 Tracers
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In this paper we describe a methodology to identify reservoir properties using numerical techniques which combine finite element methods, a streamline approach and genetic algorithms. As a model problem we consider the system of equations governing incompressible miscible displacement in two-dimensions whose solution furnishes tracer breakthrough profiles which are parametrized as function of the properties to be determined. Given a "population" of initial parameters, after the solution of the model problem and the comparison of each profile with a target one, we "evolve" to a new "population" following the concepts of genetic algorithms and according to the fitness of each member of the previous "population".
Tracer breakthrough profiles at production wells can be detected either experimentally or by solving the system of differential equations which describe the transport of a substance through a porous medium. In this paper we discuss the use of genetic algorithms in the identification of properties of heterogeneous reservoirs, through the matching of tracer breakthrough profiles.
As a model problem we consider the equations governing incompressible miscible displacement in twdimensions consisting of an elliptic subsystem for the pressure and Darcy velocity, and a convection dominated convection- diffusion equation for the tracer concentration. To obtain the tracer profiles, which are the basis of comparison, at high accuracy and low computational effort we combine finite element methods to solve the pressure and velocity system with the streamline approach to solve the concentration equation. Classical Galerkin finite element method is used to solve the Poisson problem associated with the pressure field. In this case, however, the velocity field obtained through the pressure gradients has very poor regularity and accuracy which will have a strongly negative influence on the concentration approximation. To calculate an accurate velocity approximation - a crucial point in tracer injection simulation - we adopt a post-processing technique consisting in after solving the Poisson problem associated with the pressure field compute the velocity approximation considering residual forms of both Darcy's law, with the known pressure, and balance of mass equation. For regular solutions, high order rates of convergence are obtained with this approach. Having accurate velocity approximation, a streamline technique based on Abbaszadeh-Dehghani and Brigham is used to integrate the concentration equation obtaining the breakthrough profiles at production wells at a very low computational cost.
|File Size||122 KB||Number of Pages||6|