An upscaling technique for heterogeneous porous media based on a finite difference solution for the diffusivity equation
Andrea Failla1; Luiz A., Jr. Hegele2; Lindaura M. Steffens2
1 Polytechnic University of Milan; 2 Univeridade do Estado de Santa Catarina
doi:10.20906/CPS/CILAMCE2015-0864
Resumo
The objective of reservoir simulations is to predict how pressure distribution and production rates vary with the time. Geological models may consist up to ten million active grid blocks and it is impossible to run fluid flow simulations directly on it because a realistic simulation may require too much time, and often is out of practical limits. That is why upscaling techniques are nowadays fundamental for reservoir engineers. The use of upscaling techniques allows the substitution of a heterogeneous property region made up of fine grid cells by an equivalent homogeneous region made up of a coarse single cell. Therefore, upscaling is essentially an averaging procedure in which one or more properties of a fine scale model are approximated by that of a coarse scale model. In this paper, we propose a method developed for heterogeneous porous media with the purpose to calculate equivalent (or effective) permeability. The approach consists to solve the diffusion equation for a single incompressible phase by means of a finite difference scheme. Dirichlet-type boundary conditions are imposed at the faces of the set of fine cells in the main direction of the flow, while no-flow conditions are imposed at side cells. Three different experiments are carried out, for the three main directions. For each experiment, the main flow is forced to go along the principal direction, obtaining three main rates. The flow rate for the fine grid is calculated, and it is kept constant while solving the equivalent permeability for the coarse grid. It is sufficient to substitute equivalent permeability in place of the real permeability values in the region of interest. When equivalent permeability takes the place of real permeability values, the consequence is that pressure values have to change as well. In this way, a non-linear system has to be solved. To do that, is necessary to implement an iterative process, using the equivalent permeability value is possible to find new pressure values. With these values, a new value of equivalent pe
Palavras-chave: upscaling; heterogeneous reservoir; reservoir engineering