Using K-L Decomposition in Characterizing Miscible Fluid Displacements in Porous Media
by
Ridha Gharbi
Kuwait University

The paper describes the application of the Karhunen-Loéve (K-L) decomposition in characterizing miscible displacements in statistically generated permeable media. A large number of simulation runs were performed in several heterogeneous reservoirs, each with different statistical properties, and the spatial fluid concentrations were mapped at various times. The heterogeneous permeable media were generated statistically 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 statistical parameters (i.e. permeability variation and correlation length) significantly affect the performance of miscible fluid displacements and the transition between gravity-dominated and viscous-dominated displacements. The K-L decomposition tools 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.

Date received: September 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caid-34.