Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
Journal of Porous Media
IF: 1.061 5-Year IF: 1.151 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

Volume 22, 2019 Volume 21, 2018 Volume 20, 2017 Volume 19, 2016 Volume 18, 2015 Volume 17, 2014 Volume 16, 2013 Volume 15, 2012 Volume 14, 2011 Volume 13, 2010 Volume 12, 2009 Volume 11, 2008 Volume 10, 2007 Volume 9, 2006 Volume 8, 2005 Volume 7, 2004 Volume 6, 2003 Volume 5, 2002 Volume 4, 2001 Volume 3, 2000 Volume 2, 1999 Volume 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.v20.i3.60
pages 263-285


J. Chang
Department of Civil and Environmental Engineering, University of Houston, Houston, Texas, TX 77204, USA
K. B. Nakshatrala
Department of Civil and Environmental Engineering, University of Houston, Houston, Texas, TX 77204, USA
J. N. Reddy
Department of Mechanical Engineering, Texas A&M University, College Station, Texas, TX 77843, USA


The standard Darcy model is based on a plethora of assumptions. One of the key assumptions is that the drag coefficient is constant. However, there is irrefutable experimental evidence that viscosities of organic liquids and carbon dioxide, for example, depend on the pressure. Experiments have also shown that the drag varies nonlinearly with respect to the velocity and its gradient at high flow rates. The flow characteristics and pressure variation under varying drag are both quantitatively and qualitatively different from that of a constant drag. Motivated by experimental evidence, we consider an application of the Darcy model where the drag coefficient depends on both the pressure and velocity. We focus on major modifications to the Darcy model based on the Barus formula and Forchheimer approximation in this paper. The proposed modifications to the Darcy model result in nonlinear partial differential equations that are not amenable to analytical solutions. To this end, we present a mixed finite element formulation based on the variational multiscale (VMS) formulation for the resulting governing equations. We also illustrate how to recover local mass conservation through a postprocessing technique based on convex optimization.With the proposed modifications to the Darcy model and the associated finite element framework, we study the competition between the nonlinear dependence of drag on the velocity and the dependence of viscosity on the pressure. To the best of the authors' knowledge such a systematic study has not been reported in the literature.