60th Annual Report on Research 2015

The goal of this project is to explore high Deborah (De) number elastic instabilities discovered by the PI,¹ that occur upstream of a confined cylinder and characterize their effect on porous flow. The phase space, pressure drop, and effect on oil displacement are all evaluated. A description of current efforts is given.  

1) Role of Geometry and Fluid Properties on Instability Phase Space and Excess Pressure Drop

The instability first occurs as a temporal and spatial varying flow behind a highly confined cylinder. As flow speed increases, upstream streamlines diverge and eventually an upstream vortex forms that is both spatially and temporally varying. In recently published work,² an examination of the viscoelastic Mach number (Ma), the ratio of local flow velocity to the speed of the viscoelastic shear wave, and Elasticity number (El) phase space has been used to identify the mechanisms that cause these instabilities  When Ma exceeds 1, the speed of the local flow exceeds that of the viscoelastic shear waves and hence dispersed components are highly strained.  When this is coupled with curved streamlines around the cylinder, the flow becomes unstable.  In our results, we see the downstream instability first occur at this point (Ma =1). The upstream instabilities’ onset occurs at a range of Ma (5< Ma <30) that are dependent on the geometry of the channels with more highly confined channels showing earlier occurrence of the instability. We believe the upstream instability occurs due to the downstream instability perturbing the base flow, and the critical onset depends on the size of the perturbation and a critical Ma. As geometry becomes more confined, flow is more perturbed and hence the variation in critical Ma.

Instabilities such as these are well known to cause excess pressure drop, which is likely why viscoelastic fluid are useful in enhanced oil recovery. When dimensional pressure drop is plotted against Ma, we observe that both Newtonian and Viscoelastic fluids initially demonstrate similar behavior. At Ma>1, all viscoelastic fluids show increased pressure drop due to the onset of the instability.  We see no significant change for larger Ma, indicating that the upstream instability does not greatly affect the excess pressure drop.  For Ma>1, the dimensionless pressure drop of viscoelastic fluids is larger than Newtonian fluids due to the instabilities; this value appears to be constant over all Ma.

2)  Phase Space, Excess Pressure and Oil displacement around Cylinder Arrays

We are currently examining how cylinder arrays with a range of porosities, spacing, and layout affect the onset of the instability and excess pressure in comparison to single cylinder. Initial results show that the instability, similar to the single cylinder instability, first forms downstream on the last cylinders in an array, and then progresses upstream. Depending on both spacing and cylinder arrangement, lateral instabilities may occur between rows of cylinders. Initial results show that pressure drop is not dependent on spacing, cylinder size, and structure; tt appears to depend on overall porosity of the array. We are currently analyzing data to determine the best way to represent these results for publication/analysis. We are also extrapolating these results to porous flows by extracting mobilities and friction factors from pressure measurements.³

Using the same systems as above, we are examining oil displacement by first filling channels with oil and letting them rest for 24 hours, and then using viscoelastic fluids to displace oil at Ma both above and below the critical Ma for instability onset.  Initial results indicate the instabilities play a major role in enhancing the ability of the viscoelastic fluid to displace residual oil.

3) Final Work and Outcome

We are currently finishing our work on arrays and oil displacement.  We need to examine a wider phase space of results for both and in particular expand upon the displacement experiments.  Once finished, we will turn this work into one if not two more papers.

4) Impact of Research

The current results on phase space and pressure drop have been published² and presented (at the 2014 annual meeting of the Society of Rheology). The work on cylinder arrays is being prepared for publication and preliminary results will be presented tat the 2015 annual meeting of the Society of Rheology.

1. Kenney, S., K. Poper, G. Chapagain, and G. Christopher, Large Deborah number flows around confined microfluidic cylinders. Rheologica Acta, 2013. 52(5): p. 485-497.

2. Shi, X., Kenney, S., G. Chapagain, and G. Christopher, Mechanisms of onset for moderate Mach number instabilities of visoelastic flows around confined cylinders. Rheologica Acta, 2015. Online.

3. Galindo-Rosales, F.J., L. Campo-Deano, F.T. Pinho, E. van Bokhorst, P.J. Hamersma, M.S.N. Oliveira, and M.A. Alves, Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media. Microfluidics and Nanofluidics, 2012. 12(1-4): p. 485-498.