Herschel-Bulkley Shear Stress Calculator
Calculate Herschel-Bulkley drilling-fluid shear stress from fitted yield stress, consistency, exponent and positive shear rate on the flowing branch.
Calculate Herschel-Bulkley drilling-fluid shear stress from fitted yield stress, consistency, exponent and positive shear rate on the flowing branch.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate shear-stress magnitude on the flowing branch of the Herschel-Bulkley drilling-fluid model from yield stress, consistency factor, shear rate and flow exponent. This adds a yield-power-law relation rather than substituting a Newtonian viscosity for drilling mud.
Use fitted rheological parameters on a consistent SI basis to reproduce a positive-shear-rate point. Preserve the fitting conditions and shear-rate range before using the parameters in a separate hydraulics model; this calculator does not derive them from dial readings.
Solves for
tau (Pa)
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Formula, variables, and sourceReproduce a flowing-branch stress
For illustrative tau_y = 10 Pa, K = 0.2 Pa.s^0.6, n = 0.6 and shear rate = 100 per second, the power-law contribution is 3.169786 Pa. Adding yield stress gives 13.169786 Pa. The units of K change with n so that K times shear rate raised to n always has stress units.
With n = 1, the expression becomes the flowing branch of a Bingham model. With yield stress zero it becomes a power-law fluid. Combining n = 1 with zero yield stress gives a Newtonian relation, where the consistency factor has ordinary Pa.s viscosity units.
Do not turn a stress point into a hydraulics approval
A stress-versus-shear-rate relation is one input to a drilling hydraulics calculation, not a complete pressure-loss model. Geometry, flow regime, density and the appropriate pipe or annular treatment remain necessary. The Newtonian turbulent pipe assumptions in the linked Haaland page are not an interchangeable mud model.
At zero shear rate, an ideal yield-stress material can support a range of stresses in an unyielded state. This calculator therefore accepts only positive shear rates for its flowing branch. It does not silently interpret the algebraic intercept as the uniquely determined stress of a static mud column.
Compare compatible calculations
Herschel-Bulkley Annular Pressure Loss CalculatorHerschel-Bulkley Rheology Fitting CalculatorFormula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns tau = 13.169786 Pa. Defaults demonstrate the implementation; they are not recommended field values.
10
0.2
100
0.6
Input definitions
tau_y
PaFitted Yield Stress
K
Pa.s^nConsistency Factor (Units Depend on n)
gamma_dot
1/sPositive Shear Rate on the Flowing Branch
n
dimensionlessPositive Flow Behavior Exponent
Output definitions
tau
Shear Stress Magnitude on the Flowing Branch
Engineering use, assumptions, and limits
Use fitted rheological parameters on a consistent SI basis to reproduce a positive-shear-rate point. Preserve the fitting conditions and shear-rate range before using the parameters in a separate hydraulics model; this calculator does not derive them from dial readings.
Assumptions
- Positive shear rate describes the flowing branch of the fitted fluid model.
- Yield stress is nonnegative, consistency and exponent are positive, and the parameter units share an SI basis.
Limitations
- No rheometer fitting, unyielded-zone solution, apparent-viscosity curve or annular pressure-loss calculation is performed.
- A fitted parameter set does not automatically transfer to other temperature, pressure, fluid condition or shear-rate intervals.
Common mistakes
- Entering a rheometer dial reading directly as shear stress in Pa without the instrument conversion.
- Treating K as a Newtonian viscosity when n differs from one, or confusing fitted yield stress with gel strength.
Frequently asked questions
What inputs does the Herschel-Bulkley Drilling Fluid Shear Stress calculator need?
The calculation uses Fitted Yield Stress (tau_y), Consistency Factor (Units Depend on n) (K), Positive Shear Rate on the Flowing Branch (gamma_dot), Positive Flow Behavior Exponent (n). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is shear stress magnitude on the flowing branch in Pa. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. No rheometer fitting, unyielded-zone solution, apparent-viscosity curve or annular pressure-loss calculation is performed. Entering a rheometer dial reading directly as shear stress in Pa without the instrument conversion.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
SLB Energy Glossary, Herschel-Bulkley fluid: tau=tau_0+k*gamma^n. SI stress and shear-rate units used here; parameters must be fitted on the same basis.
Open source reference