Upscaling of Single- and Two-Phase Flow in Reservoir Engineering

This book describes fundamental upscaling aspects of single-phase/two-phase porous media flow for application in petroleum and environmental engineering. Many standard texts have been written about this subject. What distinguishes this work from other available books is that it covers fundamental issues that are frequently ignored but are relevant for developing new directions to extend the traditional approach, but with an eye on application. Our dependence on fossil energy is 80–90% and is only slowly decreasing. Of the estimated 37 (~40) Gton/year, anthropogenic emissions of about 13 Gton/year of carbon dioxide remain in the atmosphere. An Exergy Return on Exergy Invested analysis shows how to obtain an unbiased quantification of the exergy budget and the carbon footprint. Thus, the intended audience of the book learns to quantify his method of optimization of recovery efficiencies supported by spreadsheet calculations. As to single-phase-one component fluid transport, it is shown how to deal with inertia, anisotropy, heterogeneity and slip. Upscaling requires numerical methods. The main application of transient flow is to find the reasons for reservoir impairment. The analysis benefits from solving the porous media flow equations using (numerical) Laplace transforms. The multiphase flow requires the definition of capillary pressure and relative permeabilities. When capillary forces dominate, we have dispersed (Buckley-Leverett flow). When gravity forces dominate, we obtain segregated flow (interface models). Miscible flow is described by a convection-dispersion equation. We give a simple proof that the dispersion coefficient can be approximated by Gelhar's relation, i.e., the product of the interstitial velocity, the variance of the logarithm of the permeability field and a correlation length. The book will appeal mostly to students and researchers of porous media flow in connection with environmental engineering and petroleum engineering.