Bingham Plastic Law

When drilling engineers talk about mud rheology, one model always comes up: the Bingham Plastic Model. It’s simple, useful, and has guided hydraulics calculations for decades. But there are two ways to determine its key parameters — and depending on which way you choose, you may get different answers. Let’s unpack this.

The Bingham model says that mud flow requires a minimum stress to start moving (the yield point, YP), and after that, stress increases linearly with shear rate, with slope equal to the plastic viscosity, PV:

• τ = Shear Stress
• τy​ = Yield Point
• μp​ = Plastic Viscosity
• γ = Shear Rate

So to use this model, we need two numbers: PV and YP.

Back in the day, drilling engineers needed something quick and practical. The Fann viscometer gave readings at 600 RPM and 300 RPM. API defined a neat shortcut:

That’s it! Two readings → two numbers. Fast enough for a rig hand to do in their head.

But here’s the catch: this assumes the line connecting the 600 and 300 RPM points represents the entire mud behavior. If the mud doesn’t perfectly follow a straight Bingham line, these estimates can be off.

Now imagine plotting all viscometer data points (e.g. 600, 300, 200, 100, 6, 3 RPM) on a shear stress vs. shear rate graph. If you draw the best-fit straight line through them (using regression), you get another pair of PV and YP.

• This method uses all available data, not just two points.
• It gives a more statistically reliable slope (viscosity) and intercept (yield point).
• But it’s also a bit more work (you can’t do it in your head — you need a calculator or spreadsheet).

• or routine field checks, the API shortcut is good enough.
• For detailed hydraulics modeling, pressure drop, and hole cleaning analysis, the regression method is more accurate because it captures how mud behaves across the entire shear-rate range.

let’s look at rheology data as shown in the following table.