Characterizing Miscible Displacements in Heterogeneous Reservoirs Using the Karhunen–Loéve Decomposition

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Abstract
The article describes the application of the Karhunen–Loéve (K–L) decomposition in characterizing miscible displacements in geostatistically generated permeable media. A large number of simulation runs were performed in several heterogeneous reservoirs, each with different dimensionless scaling groups, and the spatial fluid concentrations were mapped at various times. The heterogeneous permeable media were generated geostatistically using the Matrix Decomposition Method with various degrees of permeability variations and correlation lengths. A finite difference numerical simulator (UTCHEM) has been used for this purpose. Results show that the correlation length and the permeability variation significantly affect the performance of miscible displacements and the transition between gravity-dominated and viscous-dominated displacements. The K–L decomposition was then used to determine an optimum set of eigenfunctions representing the coherent structure of all the simulated data. Results show that these complex patterns arising from a large number of simulation runs can be described by twenty dominant eigenfunctions. From these eigenfunctions and the eigenvalues associated with them, one can in principle predict the results of a simulation run without actually performing the run. These include the prediction of the fluid distribution in time and space as well as the production history curve.