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Drilling fluids · rheology · field units
Mud rheology: plastic viscosity, yield point and gel strength from Fann readings
Plastic viscosity is the 600 rpm dial reading minus the 300 rpm reading: PV (cP) = θ600 − θ300. Yield point is the 300 rpm reading minus PV: YP (lbf/100 ft²) = θ300 − PV = 2 × θ300 − θ600. Gel strength is the peak 3 rpm reading after the mud has stood still for 10 seconds and 10 minutes. With readings of 56 and 34, PV is 22 cP and YP is 12 lbf/100 ft². This page explains each number, the low-shear yield point and power-law n and K that hydraulics models use, and what a change in each one usually tells the mud engineer.
Reference material only. Mud properties and treatments are set by the drilling fluids programme and the mud engineer. Test procedures are defined in API RP 13B-1 (water-based) and API RP 13B-2 (oil-based); follow the procedure in use on your rig.
1. The rheology formulas
Plastic viscosity
PV (cP) = θ600 − θ300
Yield point (Bingham)
YP (lbf/100 ft²) = θ300 − PV
Apparent viscosity
AV (cP) = θ600 ÷ 2
Low-shear yield point
LSYP (lbf/100 ft²) = 2 × θ3 − θ6
Power-law n and K (pipe)
np = 3.32 × log(θ600 ÷ θ300)
Kp = 1.066 × θ600 ÷ 1022^np
Power-law n and K (annulus)
na = 0.657 × log(θ100 ÷ θ3)
Ka = 1.066 × θ100 ÷ 170.2^na
θ is the dial reading of a six-speed rotational (Fann-type) viscometer at the stated rpm. With the standard R1-B1 rotor, bob and F1 spring, one dial degree equals 1.0678 lbf/100 ft² of shear stress, close enough to 1 that dial readings are used directly as lbf/100 ft² in the field. Shear rate in s⁻¹ is 1.703 × rpm, so 600 rpm is 1,022 s⁻¹, 300 rpm is 511 s⁻¹, 100 rpm is 170 s⁻¹ and 3 rpm is 5.1 s⁻¹. K comes out in lbf·sⁿ/100 ft². log is base 10; 3.32 is 1 ÷ log 2 and 0.657 is 1 ÷ log(170.2 ÷ 5.11). Some older field formulas use K = θ300 ÷ 511ⁿ without the 1.066 factor; the n value is the same, and K differs only by the dial-to-stress conversion and the reference reading, so keep to one convention within a hydraulics calculation.
2. What each number means
Plastic viscosity (PV)
The slope of the shear stress against shear rate line in the Bingham plastic model, i.e. the resistance to flow caused by mechanical friction. It rises with the viscosity of the base fluid and with the amount of solids, especially fine and colloidal solids. A low PV helps the bit drill fast; a rising PV at constant mud weight usually means drilled solids are building up.
Yield point (YP)
The Bingham-model stress at zero shear rate, caused mainly by electrochemical attraction between particles. It is the number most closely tied to the mud's ability to carry cuttings in the annulus. It is raised by bentonite, polymers or flocculation (for example from cement, salt or carbonate contamination) and lowered with thinners or deflocculants.
Gel strengths
The shear stress needed to break the mud's structure after it has stood still. Measured at 3 rpm after 10 seconds and 10 minutes at rest (30-minute or 16-hour gels may also be run). Gels suspend cuttings and barite when circulation stops, but high or rising gels increase the pressure needed to break circulation and the surge on trips.
Low-shear yield point (LSYP)
An estimate of the true yield stress from the two slowest readings. It is the parameter used for hole cleaning in deviated wells and for barite sag. The Bingham YP extrapolated from 600 and 300 rpm usually overstates the real stress at zero shear rate.
3. Worked example
A 10.5 ppg water-based mud gives these readings at 120 °F:
| rpm | 600 | 300 | 200 | 100 | 6 | 3 |
|---|---|---|---|---|---|---|
| Shear rate, s⁻¹ | 1,022 | 511 | 341 | 170 | 10.2 | 5.1 |
| Dial reading θ | 56 | 34 | 26 | 17 | 5 | 4 |
- PV = 56 − 34 = 22 cP
- YP = 34 − 22 = 12 lbf/100 ft² (about 5.7 Pa)
- AV = 56 ÷ 2 = 28 cP
- LSYP = 2 × 4 − 5 = 3 lbf/100 ft² (about 1.4 Pa), well below the Bingham YP of 12
- Pipe n and K: np = 3.32 × log(56 ÷ 34) = 3.32 × 0.217 = 0.719; Kp = 1.066 × 56 ÷ 1022^0.719 = 59.7 ÷ 146 = 0.408 lbf·sⁿ/100 ft²
- Annulus n and K: na = 0.657 × log(17 ÷ 4) = 0.657 × 0.628 = 0.413; Ka = 1.066 × 17 ÷ 170.2^0.413 = 18.1 ÷ 8.34 = 2.17 lbf·sⁿ/100 ft²
The annulus n is much lower than the pipe n because the mud is strongly shear-thinning at low shear rates, which is exactly the range in the annulus. That is why API RP 13D fits separate n and K values for the drill string and the annulus instead of using one pair for the whole well. These values feed the annular pressure loss and ECD calculations and the slip velocity in hole cleaning.
4. Why the Bingham YP overstates the yield stress
The Bingham model draws a straight line through the 600 and 300 rpm points and reads the stress where that line meets zero shear rate. Real drilling fluids curve downward at low shear rates, so the straight line hits the axis too high. A Drilling Contractor article on yield point in MPD wells gives an example where the two-reading method gave 29 lbf/100 ft² while a fit to all six readings gave 14.9, and points out that the true yield stress cannot be higher than the 3 rpm reading. In the example above the Bingham YP of 12 is three times the 3 rpm reading of 4, which is the same warning sign. The Herschel-Bulkley model, τ = τ0 + K × γⁿ, keeps a yield stress term τ0 and fits all six readings; LSYP is a quick field estimate of τ0. Use the Bingham numbers for daily trend tracking and the Herschel-Bulkley or power-law values for hydraulics and surge calculations.
5. Reading the trend
| What changes | Example readings (600/300) | PV / YP | Usual cause |
|---|---|---|---|
| Baseline | 56 / 34 | 22 / 12 | Mud in specification |
| PV up, YP about the same | 74 / 44 | 30 / 14 | Fine drilled solids building up; check solids control and dilution |
| YP and gels up, PV about the same | 70 / 48 | 22 / 26 | Flocculation, for example from cement, salt, anhydrite or carbonate contamination in water-based mud |
| Both down | 40 / 24 | 16 / 8 | Dilution with water or base fluid, or higher temperature |
These are illustrative patterns, not limits; the acceptable ranges for PV, YP and gels are set in the fluids programme for each hole section and mud weight. Readings are also temperature-dependent, so compare samples tested at the same temperature (120 °F and 150 °F are both common) and record it on the mud report.
6. Gel strength patterns
- Low, flat gels (10-second and 10-minute values close together and low): the mud breaks circulation easily, but may not suspend barite or cuttings well when the pumps are off.
- Progressive gels (10-minute much higher than 10-second, and still climbing at 30 minutes): structure keeps building with time, usually from high solids or contamination. Expect high pump pressure when breaking circulation and higher surge pressures when running pipe.
- Fragile gels (strong enough to hold solids but easy to break): the usual target.
A common field practice after a trip is to break circulation slowly and rotate the string first, so that a high gel does not add a pressure spike at the shoe, where the leak-off and MAASP limit applies.
7. Metric conversions
1 lbf/100 ft² = 0.479 Pa, so one dial degree with the standard spring is about 0.511 Pa. 1 cP = 1 mPa·s. The example mud above is PV 22 mPa·s, YP 5.7 Pa, LSYP 1.4 Pa. To convert K from lbf·sⁿ/100 ft² to Pa·sⁿ, multiply by 0.479.
8. In DrillX
DrillX brings daily drilling reports with IADC-style time logs, a rig fleet view, NPT insights and engineering calculators into one tool. The calculators cover hydrostatic pressure, ECD, annular pressure loss, triplex pump output, annular capacity and velocity, buoyancy and the kill sheet. This page explains how rheology numbers are derived from viscometer readings; it does not describe a DrillX rheology calculator. For changing the mud weight itself see mud weight up and dilution. DrillX is in final testing; email info@drillx.app for a demo or early access.
Questions
How do you calculate plastic viscosity and yield point?
Plastic viscosity in centipoise is the 600 rpm dial reading minus the 300 rpm reading, PV = θ600 − θ300. Yield point in lbf/100 ft² is the 300 rpm reading minus the plastic viscosity, YP = θ300 − PV, which is the same as 2 × θ300 − θ600. With readings of 56 and 34, PV is 22 cP and YP is 12 lbf/100 ft².
What is the difference between yield point and gel strength?
Yield point is calculated from the 600 and 300 rpm readings while the mud is flowing and indicates its cuttings-carrying ability during circulation. Gel strength is measured at 3 rpm after the mud has stood still for 10 seconds and 10 minutes and shows how much structure builds when circulation stops, which affects suspension of solids and the pressure needed to break circulation.
What is low-shear yield point?
Low-shear yield point is an estimate of the mud's true yield stress from the two slowest viscometer readings: LSYP = 2 × θ3 − θ6 in lbf/100 ft². It is usually much lower than the Bingham yield point and is the better indicator for hole cleaning in deviated wells and for barite sag.
What does a high plastic viscosity mean?
A high or rising plastic viscosity at constant mud weight usually means fine drilled or colloidal solids are building up in the mud, or the base fluid is more viscous. It slows the rate of penetration and raises circulating pressures; the usual remedies are better solids control and dilution.
What causes the yield point to increase?
Yield point rises when the attractive forces between particles increase, for example when bentonite or polymer is added, or when a water-based mud is flocculated by contamination from cement, salt, anhydrite or carbonates. A jump in yield point and gels without a matching rise in plastic viscosity is a classic sign of contamination.
How do you calculate n and K from Fann readings?
For the drill string, API RP 13D uses n = 3.32 × log(θ600 ÷ θ300) and K = 1.066 × θ600 ÷ 1022^n. For the annulus it uses n = 0.657 × log(θ100 ÷ θ3) and K = 1.066 × θ100 ÷ 170.2^n, with K in lbf·sⁿ/100 ft². For readings of 56, 34, 17 and 4 this gives a pipe n of 0.72 and an annulus n of 0.41.
Sources and further reading
- SLB Energy Glossary, PV (plastic viscosity): PV as the slope of the shear stress/shear rate line above the yield point; caused by a viscous base fluid and excess colloidal solids; lowered by dilution.
- SLB Energy Glossary, gel strength: shear stress at low shear rate after the mud has stood quiescently; API procedure at 10 seconds and 10 minutes, with 30-minute or 16-hour gels optional.
- SLB, The Defining Series: Rheology, Oilfield Review: Bingham plastic, power-law and yield stress concepts.
- Drilling Contractor, Understanding yield point: effect on pressure surges critical to managing deep, difficult MPD wells (2009): PV = θ600 − θ300, YP = θ300 − PV, and why YP should be estimated from low-rpm readings.
- API Recommended Practice 13D, Rheology and Hydraulics of Oil-well Drilling Fluids: separate pipe and annulus power-law n and K, and the Herschel-Bulkley model.
- API RP 13B-1 and RP 13B-2: field testing of water-based and oil-based drilling fluids, including viscometer and gel strength procedures.
- A. T. Bourgoyne Jr. et al., Applied Drilling Engineering, SPE Textbook Series Vol. 2 (1986), chapter 4: rotational viscometer, Bingham plastic and power-law models.
Reference summary only. Worked examples are illustrative arithmetic, not property limits. Acceptable PV, YP and gel ranges depend on the mud system, hole section and mud weight.