Two-dimcnsional flow of polymer solutions through porous media

P. Gestoso, A. J. Müller, A. E. Sáez

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this work we develop a mathematical model to predict velocity and pressure profiles for two-dimensional flow of polymer solutions through porous media. The model is based on a modification of the differential form of Darcy's law in which the apparent viscosity of the polymer solution is expressed as a function of the local (pore-scale) deformation rate. The relationship between apparent viscosity and deformation rate was obtained from experimental results corresponding to one-dimensional flow. Once this relationship is available, the model is completely predictive, i.e., it has no adjustable parameters. Experiments were conducted to characterize the relationship between total pressure drop and fluid flow rate in a two-dimensional porous medium. The fluids used in the experiments were aqueous solutions of high molecular weight polymers: (1) a flexible polymer, polyfethylene oxide), which exhibits extension thickening in one-dimensional flows through porous media, and (2) a semirigid polymer, hydroxypropyl guar, whose behavior in porous media is shear thinning. For the flexible polymer, the model predicts an extension thickening behavior that is less critical in terms of deformation rate variations than what is observed experimentally. We present arguments that suggest that the absence of elasticity in the constitutive relationship used in the model formulation is the reason for this inaccuracy. This indicates that elastic behavioral the pore level plays an important role in the macroscopic pressure drops of solutions of flexible polymer in porous media flows.

Original languageEnglish (US)
Pages (from-to)251-262
Number of pages12
JournalJournal of Porous Media
Issue number3
StatePublished - 1999

ASJC Scopus subject areas

  • Modeling and Simulation
  • Biomedical Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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