Upscaling of Flow in Porous Media
from a Tracer Perspective

By Cas Berentsen
December 2003
Delft University Press
ISBN: 90-407-2450-4
315 pages, Illustrated, 6 " x 9 "
$79.50 Paper Original


This is a Ph.D. dissertation. Most of our knowledge of flow in porous media is obtained at the pore and macro scale. For reservoir scale modeling it is not practical to model the flow at these fine scales. Considering the usual objectives (e.g. large scale flow pattern and production forecast) it is undesirable to have to gather the tremendous amount of fine scale data that is required to model an entire reservoir. Moreover, present computational resources are simply not able to handle flow simulations of this size.

Hence we resort to models that describe the essential physical behavior in an averaged sense at the mega scale without modeling all finer scale details. Unfortunately, fine scale details are often correlated over large distances and appear to be part of the essential behavior at a larger scale. As a consequence the reservoir scale flow is not just a function of some average properties of the finer scale structures. For these cases the scales in the problem are non-separable. The major challenge in upscaling is to account for this non-separability of scales. Going from single phase single component, via single phase multi component to multi phase fluid flow, upscaling becomes progressively more complex. In this thesis we treat several aspects of upscaling of single and multi phase flow in porous media approached from a single phase context.

Content includes: Upscaling of flow in heterogeneous porous media, Upscaling of Absolute Permeability: Upscaling of permeability from the macro to the mega scale, Upscaling of permeability and the effects of boundary conditions; Upscaling of Tracer Dispersion: Review dispersion in porous media, Taylor dispersion induced by molecular diffusion, Taylor dispersion induced by macroscopic transverse dispersion, Analysis of the modal interaction term and the 3rd spatial moment, Taylor dispersion from a Markovian-Lagrangian point of view, Taylor dispersion for non-uniform initial tracer distributions, Extension to arbitrary velocity fields - Ansatz, Discussion; Upscaling of Two Phase Flow: Review upscaling of two phase flow, Two phase flow from a tracer perspective, Bibliography.


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