## March 2023

## Valves, Pumps and Turbomachinery

# The effect of viscosity on centrifugal pumps and predicting performance for different fluids

Centrifugal pumps are used for a wide range of applications and services in the refining industry. In today’s dynamic scenario, changes in pumped fluid characteristics are common, especially for transfer/loading pumps.

Centrifugal pumps are used for a wide range of applications and services in the refining industry. In today’s dynamic scenario, changes in pumped fluid characteristics are common, especially for transfer/loading pumps. For the changing process fluid parameter, pump performance should be predicted to analyze the suitability of the pumping system for the proposed service conditions. A pump originally in service for the bulk loading of fuel oil was assessed for its suitability in use with higher viscosity vacuum residue. Using the existing pump for a new product opened a new business opportunity without any major investment. The original pump was installed in the early 1980s and has been in service since.

Centrifugal pump performance curves are provided by the original equipment manufacturer (OEM) for specific fluids with characteristics like density and viscosity at a defined pumping temperature. Pumps are performance tested using water, and the test data is utilized to predict the performance with the service fluid. When handling viscous fluid, the performance of the pump will differ from the water performance—this change will be more pronounced when handling fluids of higher viscosities. As the viscosity increases, the hydraulic losses within the pump increase, leading to a reduction in the head, flow and efficiency, and an increase in the power and NPSH3 (net positive suction head required resulting in a 3% loss of total head at the first-stage impeller due to cavitation).

The effects of viscosity on performance are well explained in the ANSI/Hydraulic Institute Standard 9.6.7.^{1} The standard clearly explains how performance parameters like flow, head, efficiency and power can be predicted with the viscous fluid when water performance values are known. The standard also captures the process to be adopted for preliminary selection of a new pump for given head, rate of flow and viscosity conditions.

Simply, viscosity is the property of a fluid indicating its resistance to flow when an external force acts on it. The resistance also varies with the temperature. For pumps, the viscosity of the fluid handled at pumping temperature is the important measurement. When considering viscosity, two terms—dynamic viscosity and kinematic viscosity—are prevalent.

Dynamic viscosity (absolute viscosity) is a measure of the fluid’s resistance to shear. The SI unit is pascal-second (*Pa·s*) and the centimeter/gram/sec (CGS) unit is poise (*P*); a commonly used unit is centipoise (*cP*) (1 *P* = 100 *cP*) (Eq. 1):

*1 Pa·s = 1 Ns/m ^{2} = 1 Kg/(m/sec) = 10^{3} cP* (1)

Kinematic viscosity of the fluid is the ratio of dynamic viscosity to its density. The SI unit of kinematic viscosity is m^{2}/sec and the CGS unit is Stokes. The most commonly used unit for petroleum products is centistokes (*cSt*) (Eq. 2):

*1 m ^{2}/sec = 10^{4} cSt* (2)

Kinematic viscosity (*cSt*) = centipoise/grams per cc

The temperature of the pumped fluid also has an impact on the kinematic viscosity. For petroleum liquids, the kinematic viscosity reduces with an increase in temperature.

For a centrifugal pump, the change in viscosity of the pumped fluid has an impact on the predicted performance of the pump (**FIG. 1**). Each centrifugal pump has a head-to-flow performance curve rather than a straight line. The curve is due to the varying losses in the pump at different flows. The losses are a sum of disc friction, mechanical, leakage and hydraulic losses, among which disc friction is the major component. Disc friction is directly influenced by the viscosity of the pumped media.

The maximum viscosity a centrifugal pump can handle is a bit subjective. Many references limit the use of centrifugal pumps to a maximum of 330 cSt. The impeller geometry and pump size play a role on the maximum viscosity that can be handled, also considering the torque and power limits of the pump shaft. The negative impact on efficiency and head may make the use of a suitable positive displacement pump beneficial to lifecycle cost. Depending on the pump size and geometry, centrifugal pumps’ viscosity limits can vary from 25 cP–700 cP normally. Another major consideration is the effect on the system curve from the increased viscosity. As the viscosity of the pumped fluid rises, more pipe friction will occur, and the system resistance curve also rises. This must be considered along with the revised pump curve to ensure suitability of the application.

**Background**

A pump’s performance should be predicted for a different service fluid (higher viscosity hydrocarbon). Performance data is available for the originally selected hydrocarbon but the water test data is unavailable. Utilizing the available instructions in HI Standard 9.6.7-2021, a reasonable estimate of pump performance has been developed and is captured in this article. The HI Standard does not offer a direct procedure for this extrapolation. However, the principles described for selecting a new pump for the fluid and the conversion of water performance to fluid performance are utilized to arrive at the revised performance.

This method is used to evaluate a pump used to transfer hydrocarbons from a tank to a ship; the loading originally selected was to handle fuel oil at a maximum viscosity of 125 cSt for an application to handle vacuum residue at 600 cSt. A new product with significantly different properties was required to be transferred using the same pump and existing line up. The performance curve available for the original 125-cSt fluid and water test data is unavailable. The expected performance with the 600-cSt VR is developed using the curves available for 125-cSt fuel oil.

The existing pump curve is taken as the starting point. Parameters are tabulated from the curve, as shown in **TABLE 1**, for the originally rated fluid. The pump is used to transfer fuel oil with a viscosity of 125 cSt and a specific gravity of 0.92 at 80°C.

**Pump curve**

The best efficiency point (BEP) flow is first identified from the curve as 1,700 m^{3}/hr, then the corresponding values of head and efficiencies from the curve are noted (**FIG. 2**). The values are also tabulated for 0.6, 0.8 and 1.2 times the BEP flow.

The BEP point is taken as the starting point for sizing an equivalent water pump using HI instruction 9.6.7.4.6. This instruction is used for the preliminary selection of a pump for given head, flowrate and viscosity conditions when the water performance is known. In the following case, the pump is already in service and so the curve BEP flow is considered rather than the pump rated flow to arrive at the water BEP conditions, as both are corresponding values. The BEP flow can be seen to be 1,700 m^{3}/hr at a differential head of 135 m. Viscosity and specific gravity at a pumping temperature of 80°C are 125 cSt and 0.92, respectively. The approximate water BEP performance can be calculated with this data. Use the values to calculate parameter *B* by applying Equation 10 of the HI Standard, shown here as Eq. 3:

(3)

*B = 2.8 x 125 ^{0.5}/(1,700^{0.25} x 135^{0.125 }) = 2.64064*

If 1.0 < *B* < 40, go to the next step. As the value of *B* is falling in range, continue to the next step of calculating *C _{Q}* and

*C*.

_{H}The flow correction factor (*C _{Q}*) and head correction factor (

*C*) must be calculated for the water BEP flow condition using Equation 4 of the HI Standard, shown here as Eq. 4:

_{H}*C _{Q }= C_{H} = (2.71)^{A } = *

*0.989221*

*A = -0.165 x (log _{10}2.64064)^{3.15} * (4)

Using this correction factor, calculate the water BEP flow and head (Eqs. 5 and 6):

*Water BEP flow Q _{W-BEP }= Liq BEP flow/C_{Q} = 1,700/*

*0.989221 = 1,718.5 m*(5)

^{3}/hr*Water BEP head H _{W-BEP }= Liq BEP head/C_{H} = 135/*

*0.989221 = 136.47 m*(6)

For sizing a brand new pump, the above values of water head and flow can be used to select a suitable pump. As the effort here is to predict the performance of an existing pump, the following approach is used. Calculate an efficiency correction factor using Equation 7 of the HI Standard, shown here as Eq. 7:

*C _{ƞ} = *

*2.64064^-(0.0547 x 2.64064*

^{0.69}) =*0.901406*(7)

The correction factor for efficiency and flow remains the same for all flows. The *C _{H}* varies with flow and must be calculated for each case using Equation 6 of the HI Standard, shown here as Eq. 8:

Calculating for 80% of BEP (Eq. 8):

*C _{H} = 1 – (1 – 0.98922)(0.8^{0.75}) = 0.991* (8)

Where,

Water head at 80 % = liquid head at 80% BEP/*C _{H}* at 80% BEP = 144/0.991 = 145.325 m

Water flow at 80% = liquid flow at 80% BEP/*C _{Q}* at 80% BEP = 1,360/0.98922 = 1,374.82 m

^{3}/hr.

The calculation is extended for other flows—namely 120%, 60%, 40% and 20% of the BEP flow. The calculated correction factors are applied to the entire range of operations.

For this case, the water efficiencies were already available in the performance curve but not for the service medium, so the same was used for the water case. If liquid corrected values are available in the curve, the water efficiency can be calculated with the same approach (**TABLE 2**).

Now that the water performance of the pump is established with a combination of a 9.6.7.4.6 reverse iteration of the process defined in 9.6.7.4.5, the pump performance for the new conditions can be established applying 9.6.7.4.5 straight away. The conditions for the new proposed liquid and the water performance of the pump are the starting point for this step, as shown in **TABLE 3.**

Parameter *B* is calculated, taking into consideration the water performance as per Equation 2 of the HI Standard, shown here as Eq. 9:

*B = 16.5 x (600 ^{0.5 }x 136.5^{0.0625})/(1,718.5^{0.375 }x 1,500^{0.25}) = 5.4186* (9)

The 1.0 < 5.4186 < 40 calculates *C _{Q}* as per Eq. 4 of the HI Standard (shown here as Eq. 10) as valid for all flows. Once

*C*is known, the viscous flow can be calculated as

_{Q}*Q*=

_{vis}*C*x

_{Q}*Q*(Eq. 11):

_{W }_{ }(10)

where:

*C _{Q}*

_{ }= (2.71)^(-0.165 x (log

_{10}5.4186)

^{3.15}) = 0.93982

*Q _{vis}*

_{ }= 0.93982 x 1,718.5 = 1,615.1 (11)

At BEP flow, use the same value for *C _{H}*.

_{ }At other flows, calculate

*C*using Equation 6 of the HI Standard, shown here as Eq. 12:

_{H}(12)

*C _{ƞ}*

_{ }can be calculated with Equation 7 of the HI Standard (shown above as Eq. 7) and remains same for all flows. The calculated values for the new conditions are tabulated in

**TABLE 4**using the derived water performance values.

Note: The standard also gives charts for correction factors for different B values and can also be used in place of the calculations. The predicted HQ curve vs. the original service is shown in **FIG. 3.**

**Takeaway**

Though the method may not predict the exact performance as in a performance test, it provides a fairly accurate estimate and can be of great value. In an agile business intent on maximizing revenue with minimum capital expenditure, a quick assessment of utilizing existing assets can be of significance. The derived curve for the new conditions can be used to evaluate potential limitations in pump discharge pressure, NPSH margin and prime mover limitation while handling the proposed fluid. The values are comparable with a predicted curve sourced from the OEM and can assist in preliminary system assessments with reasonable accuracy. Field observations of the available margins in the pumping system would be used to evaluate the suitability of the pump for the revised case. **HP**

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