Simultaneous characterization of geological shapes and permeability distributions in reservoirs using the level set method

An important technique in modern reservoir management is the use of production data for the characterization of permeability distributions with more than one lithology from production data. A major difficulty which arises in these situations is that sharp discontinuities of permeabilities between these lithofacies need to be reconstructed at the same time with more smoothly varying profiles inside of them. So far, techniques have been developed which recover either the interfaces or a smoothly varying profile, but not both of them. Our group has developed recently a novel method for modelling and reconstructing geological shapes in reservoirs from production data. This method is based on a level set representation of the shapes. In our previous work[1,2] we have assumed that the permeability distribution in the different regions of the reservoirs do not vary significantly such that they can be approximated by a constant value which was approximately known from prior information. In this paper we will present an extension of this new method which is able to recover at the same time the shapes of the different geological regions and variations of the permeability distribution in each of these regions. In each step of our new reconstruction technique the production data are used in order to calculate an update for the shape of the two lithofacies and at the same time a pixel-based correction of the parameter profiles inside of these regions. Only one simulation of a two-phase flow simulator and a corresponding adjoint simulator are necessary for calculating both updates. In our paper we will present numerical results in 2D for realistic situations of a water flooding process. We show that our method is able to reconstruct two lithofacies of complicated shape and the corresponding permeability distributions simultaneously from these production data.