ESP Viscosity Corrections - Turpin and Stepanoff Methods

Overview

ESP pump performance curves are published based on tests with water (viscosity approximately 1 cP). When pumping viscous fluids -- common in heavy oil production, cold wells, and high-viscosity crude reservoirs -- the actual pump performance is significantly degraded compared to the catalog curves.

Viscosity affects three key performance parameters:

The magnitude of degradation depends on fluid viscosity, pump size, operating speed, and flow rate relative to BEP.

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Physics of Viscous Effects

Why Viscosity Degrades Performance

In a centrifugal pump, energy is transferred from the rotating impeller to the fluid through momentum exchange. Viscous fluids resist this process in several ways:

1. Disc friction losses -- viscous drag on the impeller shrouds and hub increases power consumption without useful work
2. Hydraulic friction -- thicker boundary layers in impeller channels reduce the effective flow area
3. Recirculation losses -- viscous fluids have difficulty following the designed flow path, increasing secondary flows
4. Leakage effects -- viscosity changes the leakage flow through wear ring clearances (can be beneficial at moderate viscosity)

Reynolds Number Analogy

The severity of viscous effects correlates with the pump Reynolds number:

$$Re_{pump} = \frac{N \cdot D^2}{\nu}$$

Where:

• $N$ = rotational speed (rev/s)
• $D$ = impeller diameter (ft)
• $\nu$ = kinematic viscosity (ft^2/s)

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Correction Factor Approach

General Method

Both the Turpin and Stepanoff methods use multiplicative correction factors applied to the water-based performance curves:

$$Q_{vis} = C_Q \times Q_{water}$$$$H_{vis} = C_H \times H_{water}$$$$\eta_{vis} = C_\eta \times \eta_{water}$$

Where:

• $C_Q$ = capacity (flow rate) correction factor
• $C_H$ = head correction factor
• $C_\eta$ = efficiency correction factor
• Subscript $vis$ = viscous fluid performance
• Subscript $water$ = catalog (water) performance

The corrected brake horsepower is then:

$$BHP_{vis} = \frac{Q_{vis} \times H_{vis} \times SG_{vis}}{3960 \times \eta_{vis}}$$

Correction Factor Ranges

Note: Exact correction factors depend on pump size and specific speed. Larger pumps are less affected by viscosity than smaller pumps.

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Turpin Method

Background

Turpin et al. (1986) developed viscosity correction charts specifically for ESP centrifugal pumps based on extensive laboratory testing with fluids of varying viscosity. The Turpin method is widely used in the ESP industry and is the basis for most manufacturer correction procedures.

Method

The Turpin correction uses the equivalent viscosity parameter $B$:

$$B = 26.6 \times \frac{(H_{BEP})^{0.0547} \times \nu^{0.2669}}{(Q_{BEP})^{0.1065} \times N_{speed}^{0.1065}}$$

Where:

• $H_{BEP}$ = head per stage at BEP on water (ft)
• $Q_{BEP}$ = capacity at BEP on water (GPM)
• $\nu$ = kinematic viscosity (centistokes)
• $N_{speed}$ = rotational speed (RPM)

The correction factors are then read from the Turpin charts or calculated from curve-fit equations as functions of $B$.

Correction Factors from Turpin

The correction factors can be approximated by the following relationships:

Capacity correction:

$$C_Q = 1.0 - 0.00000612 \times \nu^{1.072}$$

Head correction (at BEP):

$$C_H = 1.0 - 0.00000685 \times \nu^{1.062}$$

Efficiency correction:

$$C_\eta = 1.0 - 0.0000378 \times \nu^{0.963}$$

Where $\nu$ is kinematic viscosity in centistokes.

Important: These simplified equations are approximate fits to the Turpin charts and are valid for a typical mid-range ESP pump. For precise design, use the full chart-based procedure or manufacturer-specific correction data.

Head Correction at Off-BEP Rates

The head correction factor varies with the ratio of operating rate to BEP rate:

This variation means the viscous head-capacity curve is flatter than the water curve.

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Stepanoff Method

Background

Stepanoff (1957) developed one of the earliest comprehensive methods for predicting centrifugal pump performance with viscous liquids. While originally developed for industrial pumps, the Stepanoff method has been adapted for ESP applications and provides an independent verification of viscosity corrections.

Method

Stepanoff uses a dimensionless viscosity parameter based on specific speed:

$$N_s = \frac{N \sqrt{Q_{BEP}}}{H_{BEP}^{0.75}}$$

Where:

• $N$ = rotational speed (RPM)
• $Q_{BEP}$ = capacity at BEP (GPM)
• $H_{BEP}$ = head per stage at BEP (ft)

Stepanoff Correction Factors

The Stepanoff method expresses correction factors as functions of a Reynolds number parameter:

$$Re_s = \frac{Q_{BEP}}{(H_{BEP})^{0.5} \times \nu}$$

The correction factors are then:

$$C_H = f_1(Re_s, N_s)$$$$C_Q = f_2(Re_s, N_s)$$$$C_\eta = f_3(Re_s, N_s)$$

These functions are typically provided as charts or lookup tables. A practical approximation:

$$C_\eta \approx \left(\frac{1}{Re_s}\right)^{0.1} \quad \text{for } Re_s > 100$$

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Comparison of Methods

Turpin vs. Stepanoff

When to Use Each Method

• Turpin: Primary method for ESP viscosity corrections. Use for all ESP design work.
• Stepanoff: Cross-check against Turpin. Also useful when pump-specific data matches industrial centrifugal pump parameters.
• Manufacturer data: Always preferred when available. Use Turpin/Stepanoff when manufacturer-specific viscous test data does not exist.

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Application Workflow

Step-by-Step Viscosity Correction

Example Viscosity Impact

Consider a pump with BEP at 2,500 GPM and 30 ft head/stage on water:

This example illustrates why ESP application in viscous fluids requires careful analysis. At 200 cP, the pump requires 33% more stages and 2.5 times the brake horsepower compared to water.

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Practical Considerations

Viscosity at Intake Conditions

The viscosity that matters is at pump intake conditions (pressure and temperature), not at surface or stock-tank conditions. Key considerations:

• Temperature: Viscosity decreases sharply with increasing temperature. Deep wells with high BHT may have acceptable viscosity even with heavy crude.
• Pressure: Above the bubble point, viscosity increases slightly with pressure. Below the bubble point, dissolved gas reduces viscosity.
• Water cut: High water cut reduces the effective mixture viscosity, improving pump performance.

Mixture Viscosity Estimation

For oil-water mixtures, the effective viscosity depends on which phase is continuous:

• Oil-continuous (water cut < 40-60%): mixture viscosity approximates oil viscosity
• Inversion point (water cut 40-70%): abrupt viscosity change
• Water-continuous (water cut > 60-70%): mixture viscosity much lower

Practical Viscosity Limits

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Related Topics

• ESP System Design Overview -- Complete design workflow with viscosity correction step
• ESP Pump Performance -- Base pump curves that get corrected
• ESP Gas Handling -- Combined gas and viscosity effects
• ESP Motor and Cable Sizing -- Motor sizing for viscous BHP
• PVT Overview -- Oil viscosity correlations at intake conditions

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References

1. Turpin, J.L., Lea, J.F., and Bearden, J.L. (1986). "Gas-Liquid Flow Through Centrifugal Pumps -- Correlation of Data." Proceedings of the Third International Pump Symposium, Texas A&M University, pp. 13-20.

2. Stepanoff, A.J. (1957). Centrifugal and Axial Flow Pumps: Theory, Design, and Application, 2nd Edition. John Wiley & Sons.

3. Hydraulic Institute. (2012). Rotodynamic Pumps -- Guideline for Effects of Liquid Viscosity on Performance. ANSI/HI 9.6.7.

4. Solano, E.A. (2009). "Viscous Effects on the Performance of Electro Submersible Pumps." M.S. Thesis, The University of Tulsa.

5. Barrios, L. and Prado, M.G. (2011). "Modeling Two-Phase Flow Inside an Electrical Submersible Pump Stage." Journal of Energy Resources Technology, 133(4), pp. 042902. ASME.