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**Hershel-Bulkley rheology model, release 2a, issued 3 July 2013.**

*Description*

This worksheet takes Fann viscometer readings at 3, 6, 300rpm and 600 rpm. It outputs values of τ_{0} (the shear stress at zero shear rate), n and K for the Herschel-Buckley model and plots the consistency curve of Shear Stress against Shear Rate.

For a given shear rate of interest, the shear stress and viscosity are also calculated.

12 |

13 |

Θ_{3} dial reading, Pστ_{5} =

Θ_{6} dial reading, Pστ_{10} =

43 |

67 |

Θ_{300} dial reading, Pστ_{511} =

Θ_{600} dial reading, Pστ_{1022} =

50 |

Shear rate of interest, Γ_{i} sec^{-1} =

*(You can enter a shear rate of interest to calculate the shear stress and viscosity)*

Shear stress at zero shear rate;

(metric units)

**Calculate n and K**. Note that the Herschel-Bulkley value for K is not represented by K as a variable name here. This conflicts with the Drillers.com Standard Variable Names standard, also the variable name K is a standard Mathcad variable, used for chemical concentration. The variable P_K is used instead as the units for K are the same as the units for stress, psi or kgf/m^{2}. K is also called the Consistency Index and equals the shear stress at a shear rate of 1 sec^{-1}.

(metric units)

Shear stress at sec^{-1 }=

(metric units)

Viscosity η at

(metric units)

If n = 1, the fluid is Newtonian.

If n > 1, the fluid is Dilatent.

If n < 1, the fluid is non-Newtonian (most muds).

Shear stress Pστ = KΓ^{n}

Plot shear stress (Pστ) vs shear rate (Γ)

**Click here when any values are modified to update the result.**

*Worksheet references*

Version 1 of this worksheet was released on 7 October 2008 by Steve Devereux.

Version 2 refined the results, added units, added a calculation for shear stress and viscosity at a shear rate of interest. 2a added some further small refinements. This was released on 3 July 2013 by Steve Devereux.

Formulae from the Dowell Fluids Handbook.