Abstract:We describe experimental results on the extensional viscosity of mobile polymer solutions obtained from two instruments, the first being a commercial Spin Line Rheometer and the second a custom-built lubricated-die Converging Flow Rheometer. The interpretation of data in terms of Trouton ratios is facilitated by a simple analysis for the Generalized Newtonian Fluid model. Agreement between data from the two rheometers is satisfactory and we show that polymer solutions can be either tension stiffening or tension thinning. However, the Trouton ratios in both cases are greater than the Newtonian values and we anticipate that this will always be the case for polymer solutions.

Abstract:The rheometry and flow behaviour of aqueous solutions of polyacrylamide and xanthan gum are discussed, with the expectation that the results will be of use in Enhanced Oil Recovery (EOR). The rheometrical study gives particular prominence to the dramatically high values of extensional viscosity which are possible in aqueous solutions of flexible polymers such as polyacrylamide. The effect of such factors as polymer concentration, salt concentration and mechanical degradation on rheometrical properties is outlined. Reference is also made to the qualitatively-different rheometrical behaviour experienced by comparable solutions of xanthan gum.Further evidence is advanced that some dilute polymer solutions of potential use in EOR experience abnormally high resistance in flows which are dominated by extension. Since flow through a porous medium involves a substantial extensional component, it is argued that there is justification for studying the effect of this high extensional-viscosity behaviour in a number of idealized geometries of relevance to EOR conditions. The resulting experiments indicate that, at low flow rates, shear viscosity is the dominant influence, but that, after a critical set of conditions, extensional-viscosity considerations can become all important and the observed pressure losses are against any expectation based on conventional fluid mechanics.Flow visualization studies support the pressure-drop measurements in emphasising the strong influence of high extensional viscosities in flows through tortuous geometries.

The flow structure in a concentric annular geometry with a radius ratio of 0.506 has been investigated for inner cylinder (centrebody) rotation. Detailed velocity measurements made with a laser Doppler anemometer for an aqueous solution of glucose (Newtonian), at a Taylor number well above the critical value, reveal that the tangential velocity component has a periodic structure of the same wavelength as that for the axial component, but with the extrema corresponding to zero axial velocity. Higher values of the maximum axial velocity and velocity gradient are observed closer to the centrebody than at the outer wall, whilst the radial location of zero axial velocity in the vortex interior (i. e. the eye of the vortex) moves towards the outer wall with increasing Taylor number. Similar measurements for an aqueous solution of Xanthan gum, which is strongly shear thinning and slightly elastic, revealed that the asymmetry in the maximum axial velocities was more marked than for the Newtonian case with a significant radial shift in the location of the vortex eye towards the centrebody. It was also found that the vortices exhibit a slow axial drift in the direction opposite to the centrebody rotation vector, whereas there was zero drift in the Newtonian case. The vortex cell structure for the second non-Newtonian fluid, a Laponite/CMC aqueous blend, which is shear thinning and also thixotropic, was very similar to that for the Xanthan gum suggesting that the shear-thinning aspect of the fluid rheology for both non-Newtonian fluids was far more significant than either thixotropy or viscoelasticity. An axial drift was again apparent, but in the opposite direction to that for the Xanthan gum, indicating that this effect is associated with the differences in the rheological characteristics of the two fluids.

Distributions of mean axial velocity, axial and tangential turbulence intensities together with friction factor versus Reynolds number (f-Re) data are presented for three non-Newtonian liquids in fully developed laminar, transitional and turbulent flow in an annular geometry in the absence of centrebody rotation. Each of the non-Newtonian fluids was shear thinning and to some extent elastic and one was also thixotropic in character. For comparison purposes, measurements are also reported for a Newtonian fluid.In the case of the Newtonian fluid, a mixture of glucose syrup and water, the f-Re data in both laminar and turbulent flow follow the appropriate relationships for the annular geometry, with a clear demarcation at transition which is confirmed independently by a measured increase in the centre-channel axial turbulence intensities. The measured velocity profiles for laminar flow are in good agreement with those predicted theoretically, whilst the turbulent profiles obey the log-law relationship over much of the mid-channel region and tend to the u + =y + relationship in the immediate vicinity of both walls. For the first non-Newtonian fluid, an aqueous solution of sodium carboxymethylcellulose (CMC), good agreement with theoretical predictions for a power-law fluid was observed in the f-Re data in the laminar regime with evidence of drag reduction in turbulent flow. Velocity profiles, determined in two planes, indicate minor circumferential asymmetry in laminar flow. Law-of-the-wall plots for fully turbulent flow indicate an upward shift in the data in the log-law region of the annulus consistent with the drag-reduction behaviour, as also observed in pipe-flow experiments for this fluid (Escudier et al. 1992). In the near-surface regions of both the outer and inner tubes the data again tend towards the u § =y § relationship. Anomalous behaviour was observed in the f-Re curves for the second non-Newtonian fluid, o.125% and o.2% aqueous solutions of Xanthan gum, with data for both concentrations falling significantly below the appropriate f-Re relationship for a power-law fluid. The anomalies are attributed to the elastic character of Xanthan gum. In the near-surface region of the outer tube the velocity-profile data again tend towards the u § =y+ relationship but it proved impossible to obtain data in the near vicinity of the inner wall due to slight turbidity of the fluid.The third non-Newtonian fluid, a Laponite/CMC blend, again exhibits anomalous f-Re behaviour, attributed to the thixotropic nature of this fluid. Velocity profiles determined in two planes again indicate some circumferential asymmetry in the laminar regime. Law-of-the-wall plots for the transitional and turbulent profiles tend towards the u + =y § relationship in both near-wall regions, again with an upward shift in the core of the annulus, consistent with drag reduction. In general terms, the experimental results are consistent with previous work for non-Newtonian fluid flow in circular pipes and with limited data for an annular ge...

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