Charms Jewelry Because the rheological properties of fluids often change with the geometry, it is important to measure those properties in a geometry as similar to the application as possible. Here we illustrate the case of flow in porous media, where converging and diverging channels bring out both the extensional and shear properties of the fluid. By using oscillatory flow, the Vilastic instruments have the unique ability to measure rheological properties in small spaces of porous media as well as in bulk, including the elasticity or storage modulus of the fluid.

Conventional rheological instruments strive to produce pure shear flow, but there is no useful way to predict the pressure-to-flow relations for porous media on the basis of bulk rheological properties measured in pure shear. Flow in porous media is of central importance in enhanced oil recovery methods (1-3) as well as in many other applications. The bulk properties measured in spaces that are large compared to the microstructure of the fluid may differ from those properties in small spaces.

The following shows the difference between the viscoelasticity in pores and in bulk for solutions of both rigid and flexible polymer molecules.



The pressure-to-flow relations for flow in the tube relate to the viscosity and elasticity of the fluid and the tube radius and length. For a fluid in a porous medium, the measured pressure-to-flow relation can be equated to that expected for a bundle of small, cylindrical tubes. A simple analysis(4) using Poiseuille’s law for tubes and Darcy’s law for flow of a Newtonian fluid through porous media relates the equivalent tubes radii “a” for the pores, their length “L”, and the number of parallel tubes “N” as

where “k” is the permeability, “Lp” is the thickness of porous sample, “A” is the radius of the sample, “t” is the tortuosity of the pore structure, and “phi” is the porosity.



To assess the effects of stiffness, two polymer solutions were tested. A solution of 1000 ppm xanthan gum (Mw=2x10E6) in distilled water was selected to represent the behavior of a stiff chain molecule. A solution of 1000 ppm of coagulant grade polyethylene oxide (Mw = 5x10E6) in distilled water was selected to represent the behavior of a flexible chain molecule.

The shear rate dependence of the viscosity and elasticity both in bulk and in pores was measured at a frequency of 2 Hz and at 22 °C. The bulk properties were measured in a cylindrical tube of 0.0508 cm radius and 6.0 cm length. The porous medium (sintered bronze beads) had a permeability of k = 2.64E-7 cm^2, t =1.4, phi = 0.31 and an equivalent pore radius of a=0.00373 cm.


At low shear rates the viscosity and elasticity are approximately the same in bulk and in pores; with increasing shear rate the viscosity and elasticity diminish. But in the porous medium, both the viscosity and elasticity of the xanthan gum become larger than in bulk (Figure 1).


Shear rate dependence of viscosity and elasticity of an aqueous solution of xanthan gum (a rigid polymer) in two confinements. The circles show the values in a porous medium with equivalent tube radius of 0.00373 cm. The squares are for a cylindrical tube of radius 0.0508 cm. Measurements are at 2 Hz and 22°C.








At shear rates less than ~2/sec the viscosity and elasticity are constant and are approximately the same in both bulk and in pores. As the shear rate increases, the viscosity and elasticity diminish in the large tube. In the porous medium, the viscosity and elasticity diminish with shear rate but above a shear rate of 70 /sec, the onset of dilatant behavior occurs and the viscosity and elasticity dramatically increase (Figure 2).


Viscosity and elasticity of polyethylene oxide in the same tube and porous medium used for figure 1. In the porous medium (circles), the flexible polymer becomes strongly dilatant above a shear rate of 70/s, whereas in the cylindrical tube (squares) there is no indication of dilatancy.

The viscoelasticity of both polymers tested in the porous medium differs from that in bulk. The inflexible xanthan gum molecules shows a sheer thinning character over the shear rate range of the test, while the flexible polyethylene oxide is strongly dilatant in the porous medium. This dilatancy could not be predicted from measurement of the bulk properties, pointing to the need to do measurements of viscoelasticity in porous media over a wide range of shear rates in order to show the effects of tortuous fluid movement on the rheological properties. These measurements of elasticity provide insight into the elastic energy storage mechanisms for the complex flow in porous media.



Porous media attachments are available to explore the effects of fluid flow in complex geometries. Samples are custom designed with effective pore diameters from 20 to 200 micrometers. In addition to the viscosity and elasticity, the Vilastic Software will automatically calculate 29 rheological parameters, including storage and loss moduli, sample impedance, pressure and volume flow. Measurements can be made as a function of shear rate, strain, frequency and time to produce a complete rheological profile.


(i) D’Onofrio, A., Paterson, A,, Allain, C., Hulin, J. P., Rosen, M., Flow of sheer thinning polymer solutions in heterogeneous porous media: tracer dispersion measurements, Revue de I’institut Francais du Petrole, 52, 219-221(1997).

(2) Al-Fariss, T. F., Flow of polymer solutions through porous media, Industrial & Engineering Chemistry Research, 29, 2159-2160 (1990).

(3) Sorbie, K. S., Parker, A., Clifford, P. J., Experimental and theoretical study of polymer flow in porous media, SPE Reservoir Engineering, 2, 281-304 (1987).

(4) Dullien, F. A. L. Porous media: Fluid transport and pore structure, Academic Press, New York, London (1979).

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