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, sTags: Rheology, Euphrony, Nerd, Geek, Thixotropy, Yield Stress_{y}, the zero-shear viscosity, h_{0}, 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 1Shear 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:Based on these assumptions, they developed the following structural evolution equation and viscosity equations.

- There exists a structural parameter, l, that describes the local degree of interconnection of the microstructure.
- Viscosity increases with increasing l.
- 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.

(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 2Shear 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.

## 8 comments:

You lost me at hello.

I have a survival instinct that kicks in when I see graphs, charts or anything that resembles math. My eyes glaze over and I descend into a hibernation like state.

I just hope you're using your brain for good.

:-)

Hmmm.

I bet you're pretty conscientious about regular oil changes in your automobiles, aren't you?

Do you prefer synthetic or dino oil?

I'm feeling a little queasy. Help, I'm slippin' into a catatonic zone.

Does all that mean I can still drink my orange juice?

It's fluid?????

That's all pretty cool but watch this....

5 x 5 = 25. Oh yeah. check that out. More?? If you insist.

347394234 x 3948302834098 x923849283703945 - 7 x 934598 x 1.2 -3948 x 23498739458709 x 0

= 0

Pretty nifty huh? See, anything times zero, = you got it, zero. Cuz zero is like, zero. And anything times it... well, it's a big zero too. It's called, the ... .... zero... rule. Yeah the zero rule.

Top that braino.

Okay, hope I didn't send anyone into shock with this.

Kat, Mrs. E agrees - I lost her at hello, too.

Anne, take deep breaths and put on some AKUS. If queasiness persists, repeat as necessary.

C-Hammer, I'm actually as lazy about getting the car in for an oil change as anyone else. I tend to be flexible in choosing synthetic or "black gold". In the end, many of the synthetics are made using natural gas, which we drill for as well. :)

Seth, quit showing off! I figured most of the blogs I've been reading were sinking into a deep music theory coma, so I wanted to try and wake everyone up with a does of practicality.

Hey -

Thanks for dropping by my blog. Back at ya! I've added you to my Google reader...but I don't know, too many posts about viscosity and I might delete you!

God bless -

Paul J.

Paul, thanks for dropping by. I hope you enjoy the reading that comes along - some is thoughtful on my Christian walk, some is random, some is just plain silly, and some (like this post) is simply intended to go over the heads of most people who might read it. But is all rambles. And while I cannot promise that I will never blog on rheology and viscosity again, I can promise that it will not be an daily practice. However, it you don't want to read about babies, you may want to change the channel, as I am about to have a new one any day now and have a few things to say (because I can).

"and some (like this post) is simply intended to go over the heads of most people who might read it."

So, what are you trying to say here? :)

P.S. Will be thinking about your family and praying for a safe delivery. I'm expecting to see lots of pictures once the dust settles.

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