Get To Know Me: Geek Edition®

Okay, if you've been reading this blog for any amount of time, you will likely have discovered that I am a certifiable nerd. I've played the get to know me game a few times, here and here. I've been asked to refrain from quizzing people based on my particular brand of nerdlyness, and I fear I have not contributed enough to people's understanding of anything ending in "ology". But I press on!

I am a rheologist, by profession. I study fluid flow, how it behaves under different conditions, for materials that can alternately seem like water or solid rock - what is called viscoelasticity. Here, for your reading pleasure, is a small excerpt from a paper I have been writing for an upcoming conference. This has kept me fairly busy at work, between trying to write and working on getting the little things done that kept popping up.

It has been noted that, despite the flexibility of some of these models, no single model does a sufficiently good job of predicting the behavior of all types of drilling fluids. Modeling of fluid behavior is of extreme importance to predicting downhole performance, and the lack of a single model that can be consistently applied detracts from the ability to do so accurately. Recently, several models have been developed which attempt to better model the yield stress behavior of fluids and even incorporate structural terms to account for thixotropic behavior. Good use of these models, as with other models, requires more data points than are available from a 6-speed viscometer. However, the increasing use of field-usable viscometers with an extended range of strain rates makes the use of such models more viable. One model, proposed by Mendes and Dutra , provides more accurate modeling of experimental data and relative ease of calculating parameters. Their viscosity function (Equation 1) predicts an upper shear-thinning region, a yield stress plateau, and a Newtonian behavior at low shear rates. The type of shear stress and viscosity response to strain rate is shown in Figure 1. From these curves it is easy to estimate the yield stress, s_y, the zero-shear viscosity, h₀, and the shear-thinning index, n. Using the estimated value for n, K can be quickly calculated as the stress at g'=1 s^-1.

(1)

Figure 1 Shear stress and viscosity as a function of strain rate as predicted by Equation 1, the Mendes-Dutra viscosity function.

Another recent model, proposed by Møller, Mewis, and Bonn, provides a more interesting method for predicting fluid behavior. In their model, they take into account both traditional shear-thinning and yield behavior and add a component that models structural connectivity in the fluid. They begin with three basic assumptions:

1. There exists a structural parameter, l, that describes the local degree of interconnection of the microstructure.


2. Viscosity increases with increasing l.


3. For an aging (thixotropic) system at low or zero shear rate, l increases while the flow breaks down the structure, l decreases and reaches a steady state value at sufficiently high shear rates.

Based on these assumptions, they developed the following structural evolution equation and viscosity equations.

(2)
(Model I) (3a)
(Model II) (3b)

Here t is the characteristic time of microstructural build-up at rest, h_¥ the limiting viscosity at high shear rates, and a, b and n are material-specific parameters. Under steady state conditions, using Equation 3b, the stress behavior of a fluid may be modeled as

(4)

which, at high shear rates, yields Newtonian behavior. When 0 < n < 1, a yield stress appears in the model; additionally, a critical stress is predicted below which no steady state shear rate can be achieved and flow is unstable (see Figure 2). It is therefore possible to have a sample of the same thixotropic fluid exhibiting the same viscosity at a given strain rate, but with very different structures.

Figure 2 Shear stress and viscosity as a function of strain rate as predicted by Equation 4, for n=2. Illustrated is the critical stress below which flow is unstable.

Tags: Rheology, Euphrony, Nerd, Geek, Thixotropy, Yield Stress