Plastic Fluid: Bingham Model, Yield Point, and Drilling Mud Rheology in WCSB Wells
A plastic fluid is a non-Newtonian fluid that requires a finite minimum shear stress before it begins to flow, and once flowing, exhibits a shear stress to shear rate relationship that is not directly proportional. The defining property is the yield stress, the threshold below which the fluid behaves as a semi-rigid solid and above which it flows with a measurable apparent viscosity. This contrasts sharply with Newtonian fluids such as water or refined kerosene, where flow begins instantly with any applied shear and where viscosity stays constant regardless of shear rate. In the oilfield, plastic fluids dominate drilling mud rheology because suspended bentonite clay platelets, polymer chains, and weighting material like barite create internal structures that resist initial motion but break down progressively as shear increases. The most common rheological description for plastic drilling fluids is the Bingham plastic model, expressed as the shear stress equals yield point plus plastic viscosity multiplied by shear rate, where shear stress carries units of lbf per 100 square feet (or Pascal), yield point represents the initial flow resistance, plastic viscosity captures flow behaviour above yield, and shear rate is measured in reciprocal seconds. Field measurement happens on a six-speed rotational viscometer, usually a Fann Model 35 or equivalent, where the mud engineer records dial readings at 600 rpm and 300 rpm. Plastic viscosity equals the 600 rpm reading minus the 300 rpm reading in centipoise (1 cP equals 0.001 Pa·s), and yield point equals the 300 rpm reading minus plastic viscosity, reported in lbf/100 ft² (1 lbf/100 ft² equals 0.479 Pa). In Western Canadian Sedimentary Basin operations, mud engineers running water-based muds in Montney horizontals or Cardium directional sidetracks tune yield point upward (typically 18 to 35 lbf/100 ft²) to lift drilled cuttings up the annulus, while keeping plastic viscosity moderate (15 to 25 cP) to limit pump pressure and equivalent circulating density inside narrow downhole pressure windows. AER Directive 050 references mud properties in the well control context, and Directive 008 governs casing and cement programs where rheology drives displacement efficiency. Beyond drilling muds, cement slurries, crosslinked guar fracturing fluids, foam cements, and certain produced emulsions in the Clearwater heavy oil play all behave as plastic fluids across some shear regime, making the concept foundational to Yield Point calculations, hole cleaning analysis, and surge or swab pressure prediction during tripping.
Key Takeaways
- Bingham Plastic Equation: The Bingham plastic model assumes a linear shear stress versus shear rate relationship above the yield point, providing the simplest two-parameter description for drilling fluid hydraulics. Yield point is typically reported in lbf/100 ft² (1 lbf/100 ft² equals 0.479 Pa), and plastic viscosity in centipoise (1 cP equals 0.001 Pa·s). For better accuracy in low-shear annular flow common in horizontal wells, mud engineers in the Montney often switch to the Herschel-Bulkley three-parameter model for ECD modelling.
- Field Measurement Protocol: Plastic viscosity equals the 600 rpm dial reading minus the 300 rpm dial reading on a Fann Model 35 viscometer, expressed in centipoise. Yield point equals the 300 rpm reading minus plastic viscosity. A typical Montney water-based mud reports PV of 18 cP and YP of 22 lbf/100 ft² when freshly formulated. API RP 13B-1 governs testing procedures for water-based muds and 13B-2 covers oil-based and synthetic muds, with checks performed every tour.
- WCSB Tuning Standards: Mud engineers in the Duvernay (3,000 to 3,500 m TVD) maintain yield point between 25 and 35 lbf/100 ft² to lift cuttings in horizontal sections where ROP exceeds 30 m/hr. In Cardium directional wells around Pembina (1,500 to 1,800 m TVD), softer YP near 18 to 22 is acceptable because annular velocities are higher relative to hole size. Plastic viscosity is typically held under 25 cP regardless of formation to limit ECD spikes during connections.
- Hole Cleaning and ECD Trade-off: Higher yield point improves cuttings transport in deviated and horizontal wells because the gel-like behaviour suspends solids at low annular velocities. However, excessive YP increases equivalent circulating density and can exceed the fracture gradient in tight-pressure-window plays. The balance between lift capacity and ECD margin sits at the centre of WCSB hydraulics design, and a 5 lbf/100 ft² mis-tune can shift downhole pressure by 50 to 80 kPa in a 3,500 m horizontal.
- Regulatory and Documentation Context: AER Directive 008 and Directive 050 govern drilling fluid properties in the well control context, requiring documented mud reports and the ability to weight up rapidly if a kick is detected. Rheology data is recorded on the daily IADC drilling report and submitted with well files at total depth. Improper rheology has been cited in influx events at deep WCSB wells, reinforcing the need for systematic mud checks every tour and the role of the rig-site mud engineer.
Bingham, Power Law, and Herschel-Bulkley Model Selection
Mud engineers choose among three rheological models depending on hole geometry and the dominant flow regime. The Bingham plastic model fits well at the high shear rates inside the drill pipe and at the bit (300 to 1,000 reciprocal seconds), but it overpredicts shear stress in low-shear annular flow because real muds do not respond linearly there. The Power Law model uses two parameters, consistency index K and flow behaviour index n, and matches annular flow in Montney laterals more accurately. The Herschel-Bulkley model combines yield stress with a power-law term, requiring three parameters but capturing both regimes well. WCSB wells with extended-reach horizontals over 2,500 m typically use Herschel-Bulkley in hydraulics simulators like Drillbench or Maurer software.
Plastic Behaviour in Cement Slurries and Frac Fluids
Cement slurries pumped through casing in the Duvernay production string display plastic-fluid behaviour, with yield stresses ranging from 5 to 25 Pa depending on additive load. Designers running 1,900 kg/m³ slurries (about 15.9 ppg) must control yield to avoid channelling during displacement, per API RP 10B-2. Crosslinked guar fracturing fluids loaded at 30 to 50 kg/m³ guar with borate or zirconate crosslinkers behave as plastic fluids, with yield stresses high enough to transport 40/70 mesh proppant at low velocities. Foam cements pumped in shallow Mannville wells also follow plastic-fluid mechanics, with yield supporting bubble structure and reducing density.
Fast Facts
The Bingham plastic model is named after American chemist Eugene Cook Bingham, who proposed it in 1916 while studying paints and pastes at the United States Bureau of Standards. Bingham coined the term "rheology" in 1920 from the Greek "rheos" meaning current or flow, and founded the Society of Rheology in 1929. His two-parameter equation remains the dominant field-level description of drilling muds nearly 110 years later, despite the rise of more accurate three-parameter models, because mud engineers can compute PV and YP with two dial readings in under 30 seconds at the rig.
Related Terms
Plastic fluid behaviour is foundational to several closely related glossary entries. The Yield Point is the specific parameter that quantifies the minimum shear stress for flow, while Plastic Viscosity captures the linear flow region above yield. The Bingham Plastic model is the two-parameter equation describing this behaviour, and Non-Newtonian Fluid is the broader category that includes plastic, pseudoplastic, dilatant, and thixotropic fluids. Together they form the rheological framework used in every WCSB drilling fluid program from Cardium verticals to deep Duvernay horizontals.
Real-World WCSB Scenario: Montney Lateral Hole Cleaning
An operator drilling a 3,200 m vertical, 2,800 m lateral Montney well in the Karr field near Grande Prairie encountered cuttings beds in the horizontal at the 1,800 m measured depth in the lateral. The mud system, a 1,180 kg/m³ KCl-polymer water-based fluid from a regional service provider, showed PV of 14 cP and YP of 14 lbf/100 ft² on the morning report. Drilling parameters had been pushed aggressively at 40 m/hr ROP, generating more cuttings than the mud could lift. The mud engineer added 12 kg/m³ of xanthan gum supplement at CAD 4.20/kg, raising YP to 28 lbf/100 ft² over two circulations while keeping PV at 17 cP. Total mud rebuild cost was approximately CAD 14,500 for the supplement plus 8 hours of circulation time.
After the rheology adjustment, ECD dropped marginally and cuttings returns at the shaker normalised within four hours. The well reached TD without a stuck-pipe event, saving an estimated CAD 250,000 in non-productive time that a wash-and-ream remediation would have cost. The case underscores why mud engineers monitor plastic-fluid parameters every tour and why YP tuning is the first lever pulled when cuttings transport degrades.