Apparent Viscosity
Apparent viscosity (AV) is the viscosity of a non-Newtonian fluid calculated at a specific shear rate from a single point on the flow curve, expressed in millipascal-seconds (mPa·s) or centipoise (cP). Unlike a Newtonian fluid (such as water or light crude oil at reservoir temperature), which has a single constant viscosity independent of shear rate, drilling muds, cement slurries, fracturing fluids, and most completion fluids are non-Newtonian: their resistance to flow changes with how fast they are being sheared. The apparent viscosity at any given shear rate is the ratio of the shear stress to the shear rate at that point, measured in the same units as Newtonian viscosity but representing only a local tangent to the flow curve rather than an intrinsic material constant. For the Bingham plastic model commonly applied to water-based drilling fluids, the apparent viscosity at shear rate gamma (in reciprocal seconds) is AV = mu_p + tau_y / gamma, where mu_p is the plastic viscosity (the slope of the linear portion of the flow curve at high shear rates) and tau_y is the yield point (the stress intercept at zero shear rate extrapolated from the linear high-shear region). In the API field reporting convention, apparent viscosity is measured at 600 rpm on the Fann VG meter (a rotational viscometer) by reading the dial deflection and dividing by 2, giving AV in mPa·s at the 1,022 reciprocal-second shear rate that corresponds to 600 rpm with the standard B1 bob and R1 rotor geometry.
Key Takeaways
- The API method for measuring apparent viscosity uses the Fann VG meter at 600 rpm and divides the dial reading by 2 to obtain viscosity in mPa·s: The Fann VG meter (Model 35 or equivalent) is a coaxial cylinder viscometer with a fixed bob surrounded by a rotating outer cylinder (the rotor). At 600 rpm rotor speed, the shear rate at the bob surface is approximately 1,022 reciprocal seconds (the exact value depends on the bob-rotor geometry and is defined in API RP 13B-1 for the standard R1-B1 configuration). The torque on the bob is read from a calibrated spring deflection in degrees; at 600 rpm, the reading in dial units is equal to the apparent viscosity in mPa·s when divided by 2 (since 1 dial unit at 600 rpm corresponds to 0.5 mPa·s for the standard spring). At 300 rpm (corresponding to 511 reciprocal seconds), 1 dial unit corresponds to 1.0 mPa·s. From the 600 rpm and 300 rpm readings alone, the plastic viscosity (PV) is calculated as PV = theta_600 - theta_300 mPa·s, and the yield point (YP) is calculated as YP = theta_300 - PV in Pa (after unit conversion). These two readings are the most important rheological measurements taken on a drilling fluid at the wellsite and are the basis for all hydraulics calculations including equivalent circulating density (ECD) estimation.
- Apparent viscosity at low shear rates governs particle suspension, while apparent viscosity at high shear rates governs pressure loss during pumping: In the annulus of a well being drilled, the fluid shear rate varies from near zero at the center of the flow stream to its maximum value at the pipe and borehole walls. At low shear rates (less than 10 reciprocal seconds), the apparent viscosity determines whether drill cuttings and weighting material (barite) remain in suspension when the pump is off: a minimum gel strength and low-shear apparent viscosity of at least 5 to 10 mPa·s at 3 rpm is typically required for adequate suspension. At high shear rates (greater than 500 reciprocal seconds, corresponding to flow in the drillpipe), the apparent viscosity determines the friction pressure required to pump the fluid at a given flow rate and therefore controls the pump horsepower demand. A well-designed drilling fluid minimises its apparent viscosity at high shear rates to reduce ECD and pump pressure while maintaining adequate low-shear-rate apparent viscosity for cutting suspension. Polymer muds with shear-thinning character achieve this through high-molecular-weight polymers (such as xanthan gum) that create strong gel structures at low shear but align with the flow at high shear, reducing apparent viscosity by 80 to 95 percent between 3 rpm and 600 rpm on the Fann meter.
- The Power Law model expresses apparent viscosity as a function of shear rate using the flow behaviour index n and consistency index K: For fluids better characterised by a power law than a Bingham plastic (particularly polymer-based and synthetic drilling fluids), the relationship between shear stress tau and shear rate gamma is tau = K times gamma^n. The apparent viscosity is then AV = tau / gamma = K times gamma^(n-1). For shear-thinning fluids (n less than 1, which includes nearly all drilling muds), AV decreases as shear rate increases, which is the desired rheological behaviour for drilling. At the high shear rate of 1,022 reciprocal seconds (600 rpm), AV = K times 1022^(n-1); at the low annular shear rate of 10 reciprocal seconds, AV = K times 10^(n-1). For a typical xanthan-based WCSB horizontal drilling fluid with n = 0.45 and K = 1.8 Pa·s^n, the apparent viscosity at 1,022 reciprocal seconds is approximately 0.025 Pa·s (25 mPa·s) and at 10 reciprocal seconds is approximately 0.60 Pa·s (600 mPa·s), a 24-fold reduction from annular conditions to drillpipe conditions that demonstrates the extreme shear-thinning behaviour engineered into modern polymer drilling fluids to simultaneously achieve good cutting transport and low ECD.
- ECD calculations for HPHT wells use apparent viscosity profiles to estimate annular friction pressure at each depth increment: The equivalent circulating density is the effective downhole pressure gradient during active pumping, expressed as a density equivalent: ECD = (static mud weight in kg/m³) + (annular friction pressure in kPa) / (9.81 × depth in m). The annular friction pressure is calculated from the Bingham plastic or power law apparent viscosity at the local shear rate (which varies with annular velocity, annular dimensions, and the fluid rheology model). In a deep Duvernay horizontal well at Kaybob South with a 9.5-inch casing shoe at 3,600 m and a 6.125-inch open-hole section drilled to 4,500 m TVD at 80-degree inclination, the ECD at the shoe while drilling ahead can be 40 to 80 kg/m³ above the static mud weight if the mud apparent viscosity is too high. For a pore pressure gradient of 1,650 kg/m³ and a fracture gradient of 1,720 kg/m³ at the shoe, the allowable ECD window is only 70 kg/m³, meaning the annular friction contribution cannot exceed 70 kg/m³ while drilling ahead at the full optimum rate of penetration of 15 m/h. This tight ECD window drives the fluid design toward low apparent viscosity at annular shear rates (typically 30 to 60 reciprocal seconds in the 6-inch open hole) while maintaining adequate gel strength for cutting suspension during connection stops.
- Cement slurry apparent viscosity is measured before and after mixing to verify the slurry will be pumpable and placeable within the designed thickening time: Cement slurries follow the Bingham plastic model at low to moderate shear rates, with a yield stress that must be overcome before the slurry begins to flow and a plastic viscosity that governs the friction pressure during pumping. The apparent viscosity of a freshly mixed Class G cement slurry at API water (44 percent) at the 600 rpm Fann reading is typically 60 to 90 mPa·s, corresponding to a PV of 35 to 55 mPa·s and a YP of 10 to 20 Pa. For a long cement job (more than 2 hours pump time), the apparent viscosity must remain below 150 mPa·s at 600 rpm throughout the job to ensure the friction pressure stays within the pump rating and does not exceed the formation fracture gradient. Field viscometers at the wellsite measure the apparent viscosity of the slurry as it is being mixed (from a sample taken at the mixing unit discharge) and at intervals during the job to confirm that slurry quality is consistent with the lab design. If the 600 rpm reading exceeds 200 mPa·s, the job may be at risk of developing unacceptably high pump pressures before cement reaches the designed placement depth, and the cementing supervisor may call for a reduction in pump rate or a check of the mixing water ratio.
Apparent Viscosity in Drilling Fluid Design, Hydraulics, and Wellbore Quality
The design of a drilling fluid for a specific well section begins with defining the target apparent viscosity at two critical shear rates: the high-shear apparent viscosity (at 600 rpm, representing flow in drillpipe and through the bit nozzles) and the low-shear apparent viscosity (at 3 to 6 rpm, representing near-static conditions in the annulus during connections). For a typical Cardium horizontal well in the Pembina area with a 7.875-inch open-hole section drilled with a 5-inch drillstring at 1 m/s average annular velocity, the annular shear rate is approximately 150 to 200 reciprocal seconds. At this shear rate, the target apparent viscosity for an oil-based mud is 30 to 50 mPa·s, sufficient to transport drill cuttings (typically 8 to 20 mm diameter Cardium sandstone chips) at transport ratios above 50 percent while keeping annular ECD below the fracture gradient. If the apparent viscosity exceeds 80 mPa·s at 150 reciprocal seconds (an intermediate shear rate not directly measured by the Fann meter but interpolated from the 100 rpm and 200 rpm readings), the increased ECD may exceed the fracture gradient during surge events (when the drillstring is run in quickly after a connection), causing lost circulation in the weakest zone of the section.
Water-based muds used in shallow surface hole sections of WCSB wells typically contain bentonite (a smectite clay) as the primary viscosifier. Bentonite creates apparent viscosity through the formation of a card-house gel structure from the charged clay platelets. The 600 rpm apparent viscosity of a 40 kg/m³ bentonite mud is approximately 15 to 25 mPa·s, adequate for carrying 311-mm-hole cuttings at low penetration rates but often insufficient for maintaining cuttings transport during fast drilling in soft formations. Addition of high-viscosity carboxymethylcellulose (HV-CMC) or xanthan gum at 1 to 2 kg/m³ raises the 600 rpm apparent viscosity to 30 to 45 mPa·s while simultaneously increasing the 3-rpm gel strength from 3 to 5 Pa to 8 to 15 Pa, dramatically improving cuttings suspension during connections without proportionally increasing the high-shear apparent viscosity and ECD. The ratio of low-shear apparent viscosity (at 3 rpm) to high-shear apparent viscosity (at 300 rpm) is a direct measure of the shear-thinning character of the fluid and is used as a quality control parameter in drilling fluid engineering: a ratio greater than 8 to 1 indicates good suspension capability with acceptable pumping pressure, while a ratio below 4 to 1 suggests the fluid is too Newtonian and may have poor suspension during connections.
In hydraulic fracturing operations, the apparent viscosity of the fracturing fluid determines the fracture width achieved at a given pump rate and the proppant transport capacity of the fluid inside the fracture. Crosslinked borate gels (the dominant fracturing fluid type for Cardium and Viking treatments in Alberta) develop very high apparent viscosities at low shear rates (apparent viscosity greater than 500 mPa·s at 10 reciprocal seconds) through the formation of a three-dimensional polymer network, which provides excellent proppant suspension and allows tight proppant packs to be placed at the fracture tip. At the high shear rates encountered as the gel passes through the perforations (thousands to tens of thousands of reciprocal seconds), the crosslinked gel temporarily delumps and the apparent viscosity drops to 30 to 80 mPa·s, reducing the perforation friction pressure. The fracturing engineer specifies a minimum fluid apparent viscosity at the bottom-hole temperature condition (typically measured at 100 reciprocal seconds using a high-pressure, high-temperature viscometer at 70 to 90 degrees Celsius for Cardium wells) to ensure the fluid maintains adequate proppant-carrying capacity throughout the fracture at reservoir conditions, accounting for thermal degradation of the polymer during the 2 to 4-hour fracture operation.
The relationship between apparent viscosity and temperature is critical for deep HPHT well applications. All petroleum fluids show decreasing apparent viscosity with increasing temperature (viscosity of crude oil may drop from 5,000 mPa·s at 15 degrees Celsius to 3 mPa·s at 150 degrees Celsius), and drilling muds behave similarly. For oil-based muds used in HPHT wells such as the Duvernay at temperatures exceeding 130 degrees Celsius, the base oil viscosity at bottomhole conditions may be only 1 to 3 mPa·s, and the overall apparent viscosity of the mud at bottomhole temperature and 150 reciprocal seconds may be 30 to 50 percent lower than at the surface measurement temperature of 65 degrees Celsius (the standard API mud check temperature). The surface apparent viscosity measurement alone is therefore not sufficient for ECD calculations in HPHT wells; the mud supplier provides a viscosity-temperature profile measured with a high-pressure viscometer at pressures matching bottomhole conditions, and the hydraulics model uses this profile to predict the apparent viscosity at each depth point along the wellbore for accurate ECD computation.