Drilling Fluid Analyzer
Enter your Fann viscometer readings to instantly fit six rheology models — Bingham Plastic, Power Law, Herschel-Bulkley, Casson, Carreau, and Cross. Compare model accuracy and calculate key mud properties.
Fann Viscometer Readings
Enter your 6-speed Fann 35 dial readings (standard R1B1 rotor-bob configuration).
Mud Properties
Derived Properties
Plastic Viscosity (PV)
--
cp
Yield Point (YP)
--
lb/100ft²
Flow Behavior Index (n)
--
dimensionless
Consistency Index (K)
--
eq.cp
Apparent Viscosity
--
cp
Low-Shear Yield Point
--
lb/100ft²
Rheology Model Comparison
Six models fitted to your data. The best fit (highest R²) is highlighted.
Bingham Plastic
τ = YP + PV × γ̇
--
R²
PV = -- cp
YP = -- lb/100ft²
Power Law
τ = K × γ̇n
--
R²
K = --
n = --
Herschel-Bulkley
τ = τ0 + K × γ̇m
--
R²
τ0 = -- lb/100ft²
K = --
m = --
Casson
√τ = √τ0 + √(μ∞γ̇)
--
R²
τ0 = -- lb/100ft²
μ∞ = -- cp
Best for OBM
Carreau
η = η∞ + (η0−η∞) / (1+(λγ̇)2)(1−n)/2
--
R²
η0 = -- cp
η∞ = -- cp
λ = -- s
n = --
Cross
η = η∞ + (η0−η∞) / (1+(Kcγ̇)m)
--
R²
η0 = -- cp
η∞ = -- cp
Kc = -- s
m = --
How this was calculated
Fann viscometer conversion: Shear rate (s-1) = RPM × 1.7023. Shear stress (lb/100ft²) = 1.0678 × dial reading. Standard R1B1 rotor-bob geometry per Fann Instrument Company specifications.
Bingham Plastic: τ = YP + PV × γ̇. Fitted via least-squares linear regression on all 6 data points. API standard PV = θ600 - θ300 and YP = θ300 - PV shown separately as derived properties.
Power Law: τ = K × γ̇n. Fitted via log-log linear regression: log(τ) = log(K) + n × log(γ̇).
Herschel-Bulkley: τ = τ0 + K × γ̇m. Fitted via Levenberg-Marquardt nonlinear least squares with analytical Jacobian. Constraints: τ0 ≥ 0, K > 0, 0 < m < 2.
Casson: √τ = √τ0 + √(μ∞ × γ̇). Linearized regression on √τ vs √γ̇: slope² = μ∞, intercept² = τ0. Particularly suited for oil-based muds (OBM).
Carreau: η(γ̇) = η∞ + (η0 − η∞) / (1 + (λγ̇)2)(1−n)/2. Four-parameter viscosity model capturing the full shear-thinning curve from zero-shear plateau to infinite-shear viscosity. Fitted by nonlinear least squares on apparent viscosity η = τ/γ̇. Best for polymer-based fluids.
Cross: η(γ̇) = η∞ + (η0 − η∞) / (1 + (Kcγ̇)m). Four-parameter model similar to Carreau but with a simpler power-law transition. Fitted by nonlinear least squares. Suitable for polymer-based and synthetic-based muds.
R²: Coefficient of determination. R² = 1 - SSres/SStot. Higher is better (1.0 = perfect fit).
References: API RP 13D (Rheology and Hydraulics of Oil-Well Drilling Fluids). Bourgoyne et al., Applied Drilling Engineering, SPE Textbook Series. Casson (1959), Rheology of Disperse Systems. Carreau (1972), Trans. Soc. Rheol. Cross (1965), J. Colloid Sci.
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Open LAS Viewer →Understanding Drilling Fluid Rheology
Drilling fluid rheology describes how mud flows under different shear conditions. The Fann 35 viscometer is the industry-standard instrument for measuring these properties, providing dial readings at six rotational speeds (600, 300, 200, 100, 6, and 3 RPM) that correspond to specific shear rates.
Why Model Selection Matters
The Bingham Plastic model is the most commonly used in the field because it gives the familiar PV and YP values that drilling engineers use daily. However, it assumes a linear relationship between shear stress and shear rate, which most drilling fluids don't follow exactly.
The Power Law model captures the shear-thinning behavior of most drilling fluids (where viscosity decreases at higher shear rates) but doesn't account for yield stress — the minimum force needed to initiate flow.
The Herschel-Bulkley model combines both: it includes a yield stress term and allows for nonlinear shear-thinning. It typically provides the best fit for drilling fluids, especially at low shear rates where hole cleaning and barite sag behavior are critical.
Key Properties Explained
Plastic Viscosity (PV) reflects the mechanical friction between solids, between solids and liquid, and within the liquid phase itself. High PV usually indicates excessive fine solids. Yield Point (YP) indicates the electrochemical attractive forces between particles and is a primary indicator of hole cleaning ability in vertical wells.
The flow behavior index (n) indicates how much the fluid deviates from Newtonian behavior. A value of 1.0 is Newtonian; most drilling fluids fall between 0.4 and 0.8. The Low-Shear Yield Point (LSYP) is particularly important for evaluating barite sag potential and hole cleaning in deviated wells.
Advanced Rheology Models
The Casson model was originally developed for pigment-oil suspensions and has been widely adopted for oil-based muds (OBM). Its linearized form — plotting √τ vs √γ̇ — makes parameter extraction straightforward. The Casson yield stress (τ0) is often closer to the true dynamic yield stress than the Bingham yield point.
The Carreau model captures the complete viscosity profile: a zero-shear-rate plateau (η0), an infinite-shear-rate plateau (η∞), and a power-law transition region controlled by the relaxation time (λ) and power index (n). It excels at characterizing synthetic-based muds and high-performance polymer systems across the full shear rate range encountered in drilling.
The Cross model offers a similar four-parameter viscosity description with a simpler power-law transition term. It is commonly used for polymer solutions and biopolymer-based drilling fluids where the transition from Newtonian to shear-thinning behavior is gradual. A lower rate index (m) corresponds to a broader transition region.