Pump And Pump Piping System Performance.pdf

Engineering Encyclopedia Saudi Aramco DeskTop Standards

PUMP AND PUMP/PIPING SYSTEM PERFORMANCE AS DEPICTED IN PERFORMANCE CURVES

Note: The source of the technical material in this volume is the Professional Engineering Development Program (PEDP) of Engineering Services. Warning: The material contained in this document was developed for Saudi Aramco and is intended for the exclusive use of Saudi Aramco’s employees. Any material contained in this document which is not already in the public domain may not be copied, reproduced, sold, given, or disclosed to third parties, or otherwise used in whole, or in part, without the written permission of the Vice President, Engineering Services, Saudi Aramco.

Chapter : Mechanical File Reference: MEX-211.02

For additional information on this subject, contact PEDD Coordinator on 874-6556

Engineering Encyclopedia

Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Section

Page

INFORMATION ............................................................................................................... 4 INTRODUCTION............................................................................................................. 4 PUMP PERFORMANCE CURVES ................................................................................. 5 Centrifugal Pump Performance Curves ................................................................ 6 Velocity Triangles....................................................................................... 8 Specific Speed......................................................................................... 17 Curve Variations ...................................................................................... 22 Positive-Displacement Pump Performance Curves ............................................ 39 Performance Relationships...................................................................... 42 Curve Variations ...................................................................................... 44 EFFECTS OF CHANGES IN SYSTEM HEAD CURVES ON PUMP PERFORMANCE .......................................................................... 45 Piping System Head ........................................................................................... 46 Static Head Component........................................................................... 47 Friction Head Component ........................................................................ 50 Pump Operating Point ........................................................................................ 54 Throttling Flow ......................................................................................... 54 Pump Speed ............................................................................................ 56 Pump Minimum Flow Arrangements ........................................................ 58 Typical System Curves for Refineries and Pipelines .......................................... 63 High Static, Low Friction .......................................................................... 63 Low Static, High Friction .......................................................................... 64 Parallel Pump Operation.......................................................................... 65 Series Pump Operation............................................................................ 66 GLOSSARY .................................................................................................................. 70

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LIST OF FIGURES Figure 1. Centrifugal Pump Performance Curve (not to scale)....................................... 6 Figure 2. Radial-Flow Impeller Velocity Triangles .......................................................... 8 Figure 3. Exit Velocity Triangles for a Centrifugal Pump for Changing Discharge Flow Conditions......................................................................... 13 Figure 4. Entrance Velocity Triangles for Changing Discharge Conditions .................. 14 Figure 5. Entrance Velocity Triangles for a Centrifugal Pump Taking Prewhirl Into Account ............................................................................................... 16 Figure 6. Impeller Types Compared to Specific Speed (English Units) (To convert specific speed to metric index, multiply by 0.6123)........................ 18 Figure 7. Drooping Head-Capacity Curve .................................................................... 20 Figure 8. Dip in Head-Capacity Curve.......................................................................... 21 Figure 9. Pump Curve (not to scale) ............................................................................ 25 Figure 10. Viscosity Correction Curve From Saudi Aramco Standard Drawing AE-36841 ................................................................................................... 28 Figure 11. Parallel Pump Configuration Performance Curves...................................... 34 Figure 12. Parallel Pump Operation with Different Pump Flow Rates .......................... 35 Figure 13. Series Pump Configuration Performance Curves........................................ 36 Figure 14. Change in Centrifugal Pump Performance Curves from Wear Ring Wear Positive-Displacement Pump Performance Curves .......................... 38 Figure 15. Rotary and Centrifugal Pump Performance Curve Comparison.................. 39 Figure 16. Rotary Pump Performance Curves at a Constant Speed............................ 40 Figure 17. Rotary Pump Performance Curves at a Constant Differential Pressure ..................................................................................................... 41 Figure 18. The Effect of Viscosity on a Screw Pump Performance Curve.................... 44 Figure 19. Basic System Curve.................................................................................... 46 Figure 20. Positive Static Head .................................................................................... 47 Figure 21. Negative Static Head .................................................................................. 48 Figure 22. Pressure Head ............................................................................................ 49 Figure 23. System Resistance Example....................................................................... 51 Figure 24. Fluid Velocity Profile.................................................................................... 52 Figure 25. Effect of Discharge Valve Throttling on a System Curve............................. 55 Figure 26. Effect of Changing Centrifugal Pump Speed on the Pump Operating Point .......................................................................................... 57

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Figure 27. Integral Minimum Flow Control.................................................................... 59 Figure 28. Pump Performance Characteristic Curve and System Head Curve for a System that uses a Constant Minimum Flow Orifice .......................... 61 Figure 29. Operating Point in Bypass System as System Flow Approaches Zero ............................................................................................................ 62 Figure 30. High Static Head, Low Friction Head System Curve ................................... 63 Figure 31. Low Static Head, High Friction Head System Curve ................................... 64 Figure 32. Parallel Pump Operation Head-Capacity and System-Head Curves ........................................................................................................ 65 Figure 33. Series Pump Operation Head-Capacity and System-Head Curves ............ 66 Figure 34. Pump Characteristics and System Head Curve Comparisons .................... 67 Figure 35. Steep Head-Capacity Curve........................................................................ 69

LIST OF TABLES Table 1. Effect of Increasing Viscosity on the Performance Characteristics of a Typical Centrifugal Pump............................................................................. 27

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INFORMATION INTRODUCTION The selection and testing of centrifugal and positivedisplacement pumps for an application requires an evaluation of pump performance characteristics against the application requirements. Pump performance characteristics are typically provided by a vendor in a graphical format called a characteristic curve. Characteristic curves provide information about pump performance in terms of capacity, head, power, efficiency, and net positive suction head required (NPSHR). This module provides the Mechanical Engineer with the basis of centrifugal and positive-displacement pump characteristic curves and the effect of changes to piping systems on pump performance.

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PUMP PERFORMANCE CURVES Pump performance curves can be used to analyze an existing pump or to predict the performance of a new pump. The pump performance curves are provided by the pump manufacturer, and they are usually plotted as a “family” of curves that contains a graphical representation of the following: •

Head versus capacity

•

Efficiency versus capacity

•

Horsepower versus capacity

•

NPSHR versus capacity

Characteristic curves are available for both centrifugal and positive-displacement pumps.

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Centrifugal Pump Performance Curves An example of a centrifugal pump performance curve is shown in Figure 1.

Figure 1. Centrifugal Pump Performance Curve (not to scale) Each curve on Figure 1 illustrates different centrifugal pump performance characteristics. The head versus capacity curves are the most important pump performance curves. The head versus capacity curves are the four curves that are shown with diameter markings (8.88 min. dia.; 9.88 dia.; 10.50 dia.; 10.88 max. dia.). Most centrifugal pumps can be fitted with impellers that have different diameters while using the same size casing. This practice provides the flexibility to adapt the pump to a change in service. Because pumps are normally purchased with the impeller somewhere near the middle of the possible size range of impellers, a larger impeller can be installed if a head increase is required by changed operating conditions.

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The head versus capacity curves show the pump head (total dynamic head) at a known flow rate (U.S. gallons per minute) when the impeller diameter is known. The Mechanical Engineer reads this curve by referring to the flow rate (for example, 600 gpm) at the curve for the diameter of the installed impeller (for example, the 10.50 dia. curve) and by reading the value of head on the left side of the graph (example 475 ft.). The head versus capacity curve could also be affected by pump speed. Because most pumps are driven by a constant speed motor, the operating speed is designated in the information section of the plot (for the example that is shown in Figure 1, the pump speed is 3560 rpm). If a pump is to be driven by a variable speed driver (e.g., variable speed motor or turbine), the head versus capacity curves are shown for a range of speeds. As shown in Figure 1, efficiency versus capacity curves are superimposed on top of the head versus capacity curves and are marked by 73, 75, 77, 78, 79 in Figure 1. When the capacity and diameter of the impeller are known, the efficiency of the pump can be determined from these curves. The point of maximum efficiency is called the Best Efficiency Point (BEP). The BEP should be near the design operating point for the pump, but the design operating point should never be greater than 110% of the pump BEP. The horsepower versus capacity curves are shown at the bottom of the plot in Figure 1. The horsepower versus capacity curve is drawn for both the minimum impeller diameter (8.88 dia.) and the maximum impeller diameter (10.88 dia.) available for the pump. Note that this horsepower is valid only for the rated specific gravity. Typically, the pumped fluid is designated on the plot (not shown). If the liquid that is being pumped has a different specific gravity, the horsepower value must be corrected by multiplying the horsepower at the required flow and impeller diameter by the actual specific gravity. The net positive suction head required (NPSHR) versus capacity curve is shown in the upper right-hand corner of the plot. The NPSHR is independent of specific gravity, operating pressure, and impeller diameter. Impeller diameter changes do not affect the geometry on the suction side of the impeller. The NPSHR depends primarily on the suction eye area of the impeller and the impeller speed.

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Velocity Triangles Centrifugal pumps are designed to add energy to a fluid in the form of fluid velocity and then convert the fluid velocity to discharge head. The amount of discharge head generated by a centrifugal pump is related to the amount of change in fluid velocity that is generated by the impeller. The analysis of the fluid velocities at the impeller’s suction and at its discharge can be used to demonstrate the effect of impeller design on the pump discharge head. Vector diagrams, which are called velocity triangles, are used to determine the tangential velocity of the fluid at the impeller’s eye and at its discharge. Figure 2 shows an example of impeller entrance and exit (discharge) velocity triangles for a radial-flow impeller.

Figure 2. Radial-Flow Impeller Velocity Triangles

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Velocity vectors are drawn at the entrance and at the exit, and they are labeled, respectively, with the subscripts 1 and 2. The symbol u2 represents the peripheral velocity of a point on the impeller’s exit and, because the speed of this point depends on the diameter of the impeller and its speed of rotation, the magnitude of u2 is determined through use of the following equation:

u2 =

πD2n 720

Where: u2

= The peripheral velocity of the impeller at the impeller’s exit, in feet per second

π

= Pi, 3.14

D2

= Outside diameter of the impeller vane in inches

n

= Speed of the impeller in revolutions per minute

720

= Conversion from inches per minute to feet per second

For example: If an impeller with an 18” outside diameter impeller is operating at 1150 rpm, the peripheral velocity of the impeller is: u2 =

3.14(18)(1150) 720

= 90.3 Feet Per Second The liquid flowing through the impeller must follow the shape of the vanes closely; therefore, the impeller’s peripheral velocity takes a direction fixed by the impeller’s vane angle. The vector sum of w2 (the relative velocity of the liquid leaving the impeller) and of u2 (the velocity of the impeller) is c2 (the absolute velocity of the liquid leaving the impeller). The meridional velocity, cm, is the component in the meridional plane of the absolute and the relative velocity. The meridional velocity is always perpendicular to the impeller’s velocity, u. The meridional velocity is the radial component of the absolute and relative velocities of the water leaving the impeller. The circumferential component of the absolute velocity is shown by the vector, cu2. The absolute

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velocity and direction of the water leaving the impeller is the vector sum of the meridional velocity and the radial component of the absolute velocity. The theory of moment of momentum is a principle of mechanics that states that the change of moment of momentum with respect to an axis is equal to the torque of the resultant force with respect to that axis. If energy losses as the fluid flows through the impeller are neglected, the torque (T) is equal to the change in moment of momentum, as shown in the following: T = change of moment of momentum Momentum is equal to the product of mass and velocity, and the moment of momentum will be this product times a moment arm, which is the radius (r1) at the impeller’s entrance and the radius at the impeller’s exit (r2). The torque is determined by the following formula: T=

Qγ ( cosθ 2 − r1c1 cos θ1 ) g r2 c2

Where:

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T

= Torque in foot pounds

Q

= Capacity in cubic feet per second

γ

= Weight of one cubic foot of the fluid

g

= The acceleration due to gravity, 32.2 feet per second

r1

= The radius of the impeller’s entrance in inches

r2

= The radius of the impeller’s exit in inches

c1

= The absolute velocity of the fluid at the entrance to the impeller in feet per second

c2

= The absolute velocity of the fluid at the exit of the impeller in feet per second

θ1

= Fluid angle at the entrance to the impeller

θ2

= Fluid angle at the exit from the impeller

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The power required to move the fluid through the pump can be determined by multiplying both sides of the torque equation by the angular velocity (ω), which is shown in the following formula: Tϖ =

(

Qγ r c cosθ − r c cosθ 2 1 1 1 g 2 2

)

P = Tω Where: P

= Power in foot pounds per second

ω

= Angular velocity in radians

Because Tω equals P, which is the power required, and r2ω equals u2 and r1ω equals u1, the equation can be written as follows: P=

(

Qγ u c cosθ − u c cosθ 2 1 1 1 g 2 2

)

Power is also equal to the weight of the fluid raised per second against the head, as shown in the following equation: P = QγHth Where: P

= Power in foot pounds per second

Q

= Capacity in cubic feet per second

γ

= Weight of one cubic foot of the fluid

Hth

= The theoretical head of the pump

Combining equations and solving for theoretical head provides the following equation, which is often referred to as Eulers equation: Qγ Hth =

Qγ ( cosα 2 − u1c1 cosα ) g u2 c 2

or Hth =

u2c 2cosθ2 − u1c1cosθ1 g

or

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Because c2 cosθ2 is equal to cu2 and c1 cosθ1 is equal to cu1, the equation can be written as: Hth =

u2c u2 − u1c u1 g

Where: Cu2 and Cu1

= Respectively, the liquid tangential velocities at the blade’s exit and at its inlet.

Eulers equation is the fundamental equation for the theoretical head of a centrifugal pump. Simply stated, the theoretical head produced by a pump is equal to the product of the tip speed and the fluid tangential velocity. The relationship between the impeller blade angles and the head provide the basis for impeller diameters and vane angles required to produce the required pump head for a given speed. The actual head, H, will be equal to the theoretical head, h′, minus the energy losses of the pump. Losses include fluid turbulence, friction, and hydraulic losses such as fluid leakage past wear rings. The actual head (H) produced by the impeller can be calculated by multiplying the theoretical head by the hydraulic efficiency (ηH), as shown in the following equation: H=η H

H th

Exit velocity triangles illustrate the change in pump head with changes in pump flow rate. When the rate of discharge of a constant speed pump changes, the following aspects of the velocity triangles remain constant: •

The peripheral velocity, u2, of the impeller at the impeller’s exit does not change because speed, n, is constant.

•

The blade outlet angle, β2, is contained between the direction of the relative velocity, w2, and the vector u2.

The change in pump discharge flow rate does affect the relative velocity, w2. The relative velocity through the impeller passages will increase or decrease according to changes in the rate of discharge. As a result, the shape of the velocity triangles will change, with the resulting changes in the absolute fluid velocity, cu2, producing a change in total head.

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Figure 3 illustrates the effect on pump head that results from changing the pump’s discharge flow rate on velocity triangles. Figure 3A shows the velocity triangle for pump operation below the BEP flow rate. Figure 3B illustrates the velocity triangle for operation at the BEP flow rate. Figure 3C shows the velocity triangle for pump operation above the BEP flow rate.

Figure 3. Exit Velocity Triangles for a Centrifugal Pump for Changing Discharge Flow Conditions

The comparison of the exit velocity triangles shown in Figure 3 illustrates the effect on pump head by changing pump discharge rate. A reduction in the discharge rate will increase the circumferential component of the absolute velocity, cu2, and it will decrease the meridional component, cm2, which causes pump head to increase. An increase in the discharge rate will decrease the circumferential component of the absolute velocity, and it will increase the meridional component, which results in a decrease in pump head. Because the power absorbed by the fluid is directly proportional to the product of HγQ, the changes in the pump’s flow rate determine the power of self-regulation of impeller pumps. If the total head of a pump increases during operation, the pump automatically reacts by reducing the discharge flow rate so that the impeller can overcome the increased resistance. Conversely, a reduction in the discharge head of a pump results in an increase in the pump’s discharge rate.

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When a change in the pump’s discharge rate occurs, the entrance velocity triangles also change. As shown in Figure 4, there is a change in the angle of entry (θ1). Figure 4A shows the reduction of the angle of entry when the pump’s flow rate is reduced below the BEP. Figure 4B shows the entrance velocity triangle during BEP flow rate. Figure 4C shows the increase in the angle of entry when the pump’s flow rate is increased above the BEP.

Figure 4. Entrance Velocity Triangles for Changing Discharge Conditions

The normal angle of entry is equal to the angle between the inlet element of the impeller vane and the tangent to the circumference of the inside diameter of the impeller. When pump flow rate is reduced below the BEP flow rate value, flow eddies form on the back face of the impeller vane and on the working (front) side of the impeller vane. Flow eddies are areas in which the pumped fluid travels in orbital recirculating patterns or reduced velocity instead of traveling through the passage to the impeller exit. The flow eddies reduce the hydraulic efficiency of the pump. A reduction in the hydraulic efficiency will lower the actual head produced by the impeller.

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When a pump is operated above or below the BEP flow rate, a prewhirl (also called prerotation) develops at the impeller’s inlet. This prewhirl produces a reduction in the difference between the angle of entry of the pumped fluid and the blade inlet angle. The change in the entrance velocity triangle is caused by the absolute velocity of the fluid that enters the impeller, cu1. As previously stated, cu1 is equivalent to u1c1 cos θ1. The effect of prewhirl on pump head can be shown by the inlet component of Eulers equation: Hth =

u2c 2cosθ2 − u1c1cosθ1 g

As prewhirl increases the fluid angle at the entrance of the impeller, the cosine of angle θ1 approaches zero. Analysis of impeller designs indicates that all centrifugal pump impellers cause a slight amount of prewhirl, even if guide vanes are installed in the pump suction. When there is a minimum amount of prewhirl, the inlet component of Eulers equation approaches zero (cosine of 90° = 0); therefore, Eulers equation can be written as follows: Hth =

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u2 c 2cosθ2 g

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Figure 5 shows the effect of prewhirl on entrance velocity triangles. Figure 5A shows the effect of prewhirl on an entrance velocity triangle when a pump is operated at a flow rate less than the BEP. Prewhirl occurs in the direction of impeller rotation (commonly called positive prewhirl), and the direction of the absolute velocity of the fluid at the entrance to the impeller (θ1) decreases, which results in a net decrease in pump discharge rate. Figure 5B shows the effect of prewhirl on an entrance velocity triangle when a pump is operated at a flow rate above the BEP. The prewhirl occurs in the direction opposite of impeller rotation (commonly called negative prewhirl). There is an increase in pump discharge rate, but the effect is less marked.

Figure 5. Entrance Velocity Triangles for a Centrifugal Pump Taking Prewhirl Into Account

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Specific Speed

The term “specific speed” is used to classify the overall geometry and performance characteristics of pump impellers by correlating the pump capacity, head, and most efficient operating speed. The specific speed of an impeller is defined as the revolutions per minute at which a geometrically similar impeller would run if it were of such a size as to discharge one gallon per minute against one foot head. An understanding of how to calculate and interpret specific speed for a particular pump provides a greater insight into the reasons why pump impellers are shaped differently, why the shape of performance curves changes for different pumps, and why there is a wide variation in the value of efficiency at the BEP for different pumps. Specific speed is a dimensionless number that can be calculated from the following equation: Ns =

N Q H0.75

Where: Ns

= Specific speed (nq for metric)

N

= Rotative speed in revolutions per minute (rpm)

Q

= Flow at optimum efficiency (BEP) in gallons per minute (gpm) or cubic meters per second (m3/sec)

H

= Total head per stage at BEP in feet or meters

A unit analysis of specific speed indicates that the value of specific speed is not truly dimensionless unless the value of the acceleration due to gravity (g) is placed in the equation denominator. By convention, the centrifugal pump industry omits the value of the acceleration due to gravity. Note that for double flow impellers, Q = Q/2.

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The specific speed of any centrifugal pump can be determined by using the pump speed and the head in flow rate at the BEP and the specific speed equation. The value for specific speed for the pump designated by the characteristic curve will never change, even if the pump speed changes. If the pump is run at a different speed, the pump head and flow rate will change, but the specific speed will not change because the values are defined in the specific speed equation at the BEP. Specific speed is relative to the shape and characteristics of the impeller. As shown in Figure 6, specific speed varies with impeller form and proportions.

Figure 6. Impeller Types Compared to Specific Speed (English Units) (To convert specific speed to metric index, multiply by 0.6123)

The effect of specific speed on pump performance characteristics is generally associated with the types of impellers for a specific speed range, radial flow impellers, Francis-vane impellers, mixed flow impellers, and axial flow impellers. The effect of specific speed on pump performance characteristics is described in terms of the impeller type for the specific speed range.

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Specific speed has a direct effect on the shape and slope of a centrifugal pump head-capacity curve and the horsepower curves. The lower the specific speed of an impeller, the flatter the head-capacity curve. As shown in Figure 6, radial flow impellers have the lowest specific speed. A low specific speed results in flat head capacity curves in which the head at zero flow (shutoff head) is typically less than 110% of the head at BEP. Low specific speed pumps commonly have a drooping characteristic curve at shutoff head. Figure 7 shows an example of a drooping characteristic curve. Unstable pump operation can occur if a pump is operated at the flow rates and head between the dashed lines labeled A and B. A pump that exhibits a drooping characteristic curve may be acceptable in applications in which the pump is not operated in the region between lines A and B. For instance, if a pump with a drooping characteristic curve is installed with another pump in a parallel configuration (both pumps taking suction from the same source and discharging to a common header), the pump may be acceptable for use as long as the pump is operated outside of the range defined by the lines labeled A and B and the parallel pump is not operated simultaneously. If the two pumps are operated in parallel, one of the pumps may carry the majority of the pumping load and the second pump may carry a lesser pump load; both pumps will be operating at the same head but with different capacities. The points labeled 1 and 2 on Figure 7 illustrate the point of a pump capable of operating at the same head but with two different flow rates. In the example of the operation of the two parallel pumps, one pump may be operating at point 1 while the second pump is operating at point 2. If the parallel pump system discharge is throttled or if system flow demand is lowered, the pump operating at point 2 will start to increase head, which shifts the operating point toward point 3. The increase in head developed by the pump now operating at point 3 will result in the other parallel pump (operating at point 1) operating at shutoff head. If no provision is available to protect the pumps against operation at shutoff head (through the use of a recirculation bypass), the pump operating at point 1 will overheat and become damaged.

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Another problem situation may occur if two pumps are installed in parallel and only one pump is operating. In this situation, it may be impossible to start the second pump because the pressure developed by the second pump may be less than shutoff head, which results in overheating the second pump. This situation may occur if the first pump is operating at a capacity less than point 4, below the unstable region of the curve.

Figure 7. Drooping Head-Capacity Curve

In some applications, a drooping characteristic curve can present problems even if a parallel pump is not installed. Operation of a single pump in the unstable region of the curve may cause the pump to operate with pressure and flow swings. Operation of the pump in the unstable region results in a tendency for backflow through the pump, which increases the magnitude of the flow and pressure swings.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Mixed flow impeller pumps have a steeper head-capacity curve with the shutoff head typically at 160% of the pump head at BEP. Mixed flow impellers may exhibit a dip in the headcapacity curve that indicates an area of unstable operation. An example of a dip in a mixed flow impeller pump head-capacity curve is shown in Figure 8. The dip in the head-capacity curve may not be considered a problem if the pump is operated outside of the dip region. Many pump manufacturers do not show the dip on the pump curves but stop the head-capacity curve before the dip region and note that the pump should not be operated in the unstable region.

Figure 8. Dip in Head-Capacity Curve

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The bhp curve is also affected by specific speed. Radial flow impeller pumps typically have a rising bhp curve with an increase in pump flow. The maximum bhp commonly occurs at the maximum flow at which the pump can operate in the system. Mixed flow impellers have a flatter bhp curve, with the maximum bhp at the maximum flow at which the pump can operate in the system. Axial flow impellers have a bhp curve that is the opposite of a radial flow impeller, with the highest bhp at the lowest flow rate. Because the highest bhp for an axial impeller pump is at the lowest flow rate, axial flow pumps are typically started with the pump discharge valve open. Starting an axial flow pump with the little or no discharge flow can result in overloading the pump motor. Curve Variations

The following section provides an explanation of the different curve variations for centrifugal pumps. Centrifugal pump performance curves will vary based on the following: •

Affinity laws

•

Viscosity corrections

•

Parallel and series pump operation

•

Reduction in pump efficiency from operational wear

Affinity Laws - Performance curves for centrifugal pumps vary

with changes in pump speed, head, flow, and power. The rules that govern the effect of the changes in the performance curve are called the Affinity Laws. The basis for the derivation of the Affinity Laws is specific speed, which does not change for a given impeller diameter. If the performance of a pump is known at one speed and impeller diameter, the performance of the pump can be calculated if the pump speed or the impeller diameter are changed. There are two sets of Affinity Laws; one set of Affinity Laws is used when the impeller diameter is held constant and speed is changed, the other set of Affinity Laws is used when the pump speed is constant and the pump impeller diameter is changed.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The following equations express the pump Affinity Laws for a constant diameter impeller:

Q1 N1 = Q 2 N2 H1  N1  =  H2  N2 

2

bhp1  N1  =  bhp 2  N2 

3

Where: Q

= Flow rate in gallons per minute or cubic meters per hour

H

= Total head in feet or meters

N

= Pump speed in revolutions per minute

bhp

= Brake horse power

Subscript 1 = Initial condition Subscript 2 = Final condition

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The following equations express the pump Affinity Laws for a constant speed impeller: Qq

1

D = 1 Q 2 D2

H1  D1  =  H2  D2 

2

bhp1  D1  =  bhp 2  D2 

3

Where: Q

= Flow rate in gallons per minute or cubic meters per hour

H

= Total head in feet or meters

D

= Impeller diameter in feet or meters

bhp

= Brake horse power

Subscript 1 = Initial condition Subscript 2 = Final condition The two sets of Affinity Laws are sometimes combined into the following equations: Q1 N1D1 = Q 2 N2D2 H1 N12D12 = H2 N22D22 bhp1 N13D13 = bhp 2 N32D32

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The use of the Affinity Laws to determine pump characteristics can be shown in the following example using the pump curves shown in Figure 9.

Figure 9. Pump Curve (not to scale)

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The following example assumes that the pump is at a constant speed, 3560 rpm, with a 9.88 inch diameter impeller. A pump is operating at 400 gpm with a discharge head of 410 feet and 80 bhp. If a 10.50 inch impeller is installed in the pump, the pump characteristics for specific flow, head, and bhp will change as follows: Initial flow rate

= 400 gpm

400 9.88 = Q 2 10.50 Q2 = 425gpm Initial head at 400 gpm 410  9.88 = H2  10.50

= 410 feet   

2

H2 = 463 Ft. Initial brake horsepower 80  9.88 = bhp 2  10.50

= 80 bhp   

3

bhp2 = 96bhp The results of the calculations can be shown by plotting the new flow, head, and bhp points and comparing those plots to the actual 10.50 inch diameter characteristic curve.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Viscosity Corrections - The viscosity of the pumped fluid will also affect pump performance characteristics. As the viscosity of a pumped fluid increases, the pump will expend more power moving the fluid; therefore, less energy will be available for flow and head. As a result, an increase in kinematics viscosity of a pumped fluid will result in a large reduction in pump capacity, head, and efficiency. Table 1 illustrates the impact on a typical centrifugal pump performance characteristics by changes in the pumped fluid kinematics viscosity.

Viscosity, SSU (cSt)

Capacity gpm (m3/h)

Total Head ft (m)

Efficiency %

Power bhp (kW)

0

3000 (681)

300 (91)

85

241 (180)

500 (110)

3000 (681)

291 (89)

71

279 (208)

2,000 (440

2900 (658)

279 (85)

59

312 (233)

5,000 (1110)

2670 (606)

264 (80)

43

373 (278)

10,000 (2200)

2340 (531)

243 (74)

31

417 (311)

15,000 (3300)

2100 (477)

228 (69)

23

473 (353)

Table 1. Effect of Increasing Viscosity on the Performance Characteristics of a Typical Centrifugal Pump

The effect of viscosity on pump performance characteristics can be determined using viscosity correction curves. In accordance with SAES-G-005, viscosity correction curves issued by Hydraulic Institute Standards can be used for conventional units; for SI units, Standard Drawing AE-036841 may be used. Figure 10 shows Standard Drawing AE-36841.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

SAU

AP PD.

CE RT.

OI

COMPA

1OO

HEAD.

CH

9O

CH KD.

8O

O.6XQ O.8XQ 1.OXQ 1.2XQ

7O 6O

N N N N

1OO

DE SC RIP TIO N

RE VIS ED AN D CH AN GE D TO NE W BO RD ER.

9O

CORRECTION FACTORS

CQ

8O 7O

CAPACITY AND EFFICIENCY

6O 5O

C

E

4O 3O

JO/ EW O

2O

BY

ESRL SDO

DA TE

01

NO.

VISCOSITY mm2/S

22 33 44 66 88 1317 O 1O 15 2O32 43 6588 131722 33 2 6 O 26OO O O OO O O O

JU NE' 95

185 9O 45 25 12

01

REVISION S DRAW N BY

4.3

12O 6O 3O 2O 1O

6 4

DATE CHKD. BY

OPRG.

HEAD IN METERS (FIRST STAGE)

BY DATE

ENG. 185 12O 9O 6O 45 3O 2O 25 12 1O O.O5 O.1O O.2O O.3O O.5O 5 O.25 O.4O O.65

BY DATE

APP'D. O CONST R BY

DATE

CERTIFI

O.95

1.25 1.9O

6.5O 2.5O 3.8O 5.OO 3.15

CAPACITY IN 1OO L/S

BY

MANDATORY DRAWING

DATE THIS DRAWING IS NOT TO BE USED FOR CONSTRUCTION OR FOR ORDERING MATERIAL UNTIL CERTIFIED AND DATED

DRAWING TITLE

SI METRIC UNITS

PLANT NO.

99O

INDEX

DRAWING NO.

AE-O36841

SHT. NO.

001

REV. NO.

01

JO/EWO Saudi Aramco 2616 ENG. (3/91)

CADD-

Figure 10. Viscosity Correction Curve From Saudi Aramco Standard Drawing AE-36841

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

If the desired capacity and head for pumping a viscous fluid is known, and if the fluid viscosity and specific gravity at the pumping temperature is known, a viscosity correction curve can be used to find the approximate equivalent capacity and head when pumping water. The following symbols and definitions are used on the correction curve shown in Figure 10 and to perform the required calculations: •

Qvis

-

The viscous capacity in gallons per minute or liters per second. Qvis is the capacity when pumping a viscous fluid.

•

Hvis0

-

Viscous head in feet or meters. Hvis is the head when pumping a viscous fluid.

•

ηvis

-

Viscous efficiency in percent. ηvis is the pump efficiency when pumping a viscous fluid.

•

bhpvis -

Viscous brake horsepower. The horsepower required by the pump for the viscous conditions.

•

Qw

-

Water capacity in gallons per minute or liters. Qw is the capacity when a pump is pumping water.

•

Hw

-

Water head in feet or meters. Hw is the pump head when pumping water.

•

ηw

-

Water efficiency in percent. ηw is the pump efficiency when pumping water.

•

S

-

Specific gravity.

•

CQ

-

Capacity correction factor.

•

CH

-

Head correction factor.

•

Cη

-

Efficiency correction factor.

•

QNW

-

Water capacity at which the maximum efficiency is obtained.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The information from the viscosity correction curve is used in the following equations:

Q vis = CQ × Q W Hvis = CH × HW ηvis = Cη × ηW For English units: bhp vis =

Q vis × Hvis × S 3960 × ηvis

For Metric units: bhp vis =

Q vis × Hvis × S 376.5 × ηvis

(Note: Qvis is in m3/hr, Hvis is in meters) The viscosity correction curve is used by finding the required viscous capacity at the bottom of the chart and moving upward to the required viscous head in feet or meters of fluid. For multistage pumps, the value for the viscous head should be the viscous head per stage. From the point of viscous head, a horizontal line is drawn (left or right) to the fluid viscosity line. At the point at which the line intersects the fluid viscosity line, a line is drawn straight up to the correction curves at the top of the plot. The line will intersect with the curves for Cη, CQ, and the 1.0 × QNW curve. Each correction factor value is read by drawing a line from the point of intersection with the applicable curve to the scale on the left side of the plot. The correction factors can then be used in the equations for calculating the equivalent water capacity and head for a pump. The following example uses the viscosity correction curve shown in Figure 10. The specific plot used to determine the correction factors are shown as a dotted line.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

As the pump is required to deliver 35 liters per second at 28 meters total head of a fluid with a viscosity of 132 centistokes, the fluid specific gravity is 0.90 at the pumping temperature. To determine the equivalent characteristics for a pump that pumps water, the starting point is at the viscous capacity at the base of the plot. Moving up to the viscous head, a line can be drawn to the right to intersect with the fluid viscosity. From the intersection at the fluid viscosity line, a vertical line can be drawn up to intersect the correction factor curves. The values for each correction factor can be read from the scale on the left side of the plot. For the example discussed, the correction factors are as follows: Cη

= Approximately .68

CQ

= Approximately .97

CH

= Approximately .93 (as read from the 1.0 × QNW curve)

The values for an equivalent pump using water can be determined by the calculations as follows: QW =

Q vis CQ

35 0.97 = 36 liters per second (130 cubic meters per hour ) =

HW =

Hvis CH

28 0.93 = 30 meters =

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

A pump would be selected with a water capacity of 36 liters per second at 30 meters total head. The selection of the pump should be at or close to the most efficient point for water performance. To determine the performance while pumping the viscous fluid, the water efficiency is multiplied by the efficiency correction factor. For example, if the water efficiency of the pump selected in the previous example was 81%, the efficiency of the pump while pumping the viscous fluid can be calculated by the following: ηvis = Cη × ηW =0.68 × 81 = 55%

The brake horsepower required for pumping the viscous fluid can be determined by using the following equation:

bhp vis =

Q vis × Hvis × S 376.5 × ηvis

130 × 28 × 0.9 376.5 × 0.55 = 16 KW =

The viscosity correction curves can also be used to determine the performance characteristics of a pump that handles a viscous fluid from a set of performance characteristics of the pump that handles water. Using the performance curve for water, the capacity of the pump at the BEP can be obtained. Using the capacity at BEP for QNW, the capacities for 0.6 × QNW, 0.8 × QNW, and 1.2 × QNW can be determined. Using the capacity at BEP and the capacity scale on the bottom of the performance curve, a horizontal line can be drawn to obtain the head at BEP for water. From the head at BEP for water, a line can be drawn horizontally left or right to the viscosity line of the pumped fluid on Figure 10; the line should then be drawn vertically through the correction curves. The values for each correction factor can be read from the scale on the left side of the plot. The correction factors are then determined for the other values of capacity (0.6 × QNW, 0.8 × QNW, and 1.2 × QNW). The corrected head value is determined using each of the correction factors. The efficiency with water at each of the corrected water capacities is multiplied by the

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

efficiency correction factor determined for the corrected water capacity. The values of head and efficiency can then be plotted against the corrected water capacities, with the points connected by a curved line. The resultant plots provide the performance curves of efficiency versus capacity and head versus capacity for the viscous fluid. The brake horsepower can be calculated and plotted using several of the capacity efficiency and head points for the viscous fluid. Saudi Aramco Standard SAES-G-005 provides the following guidance and limitations for calculating head, capacity, and efficiency for viscous fluids using viscosity correction curves: •

Extrapolation of points not on the plot is not recommended.

•

Correction factors for water are 1:1:1.

•

The viscosity correction curves can only be used for pumps of conventional hydraulic design, in the normal operating range, with open or closed impellers. The viscosity correction curves are not used for mixed flow or axial flow pumps or for pumps of special hydraulic design for either viscous or nonuniform liquids.

•

Only Newtonian (uniform) liquids should be used. Gels, slurries, and other nonuniform liquids may produce widely varying results, depending on the particular characteristics of the liquids.

Parallel and Series Pump Operation - Two or more pumps can

be configured in a system to increase the range of head and capacity demand. There are two configurations for installing multiple pumps in a system: parallel and series. For proper specification of the pumps and the evaluation of their performance under various conditions, a system load curve (discussed later in this module) must be used in conjunction with composite pump performance curves. Pumps installed in parallel discharge to a common source or header, as shown in Figure 11. When the two pumps are installed in parallel, the head that is produced is the same as for a single pump. However, at any given value of head, the capacity for the two pumps is double the capacity for the single pump provided that each pump is identical. Thus, a new

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

head/capacity curve can be drawn for the two pumps in parallel by adding the capacity of points of equal head from each head versus capacity curve. The new pump curve and the system head curve can be used to determine the maximum capacity. The operation of identical pumps in parallel pumps does not increase the system capacity in increments of the capacity for each operating pump. Because the system head curve rises with an increase in flow, the operation of two identical pumps in parallel will not produce a discharge equal to twice the capacity of one pump. If more parallel pumps are placed in service on the same system, the incremental increase in pumping capacity becomes smaller.

Figure 11. Parallel Pump Configuration Performance Curves

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

A problem that can occur with pumps that are operating in parallel is shown in Figure 12. If two pumps are installed in parallel, one pump (pump A) may take more than half of the total flow, and the other pump (pump B) may take less than half of the total flow. The pump with the lower flow rate may be operating below its minimum acceptable flow rate. When this situation occurs, the head that is produced by the two pumps will be identical because they are connected to the same process. The actual head that is produced by pump B at the target flow rate is lower than the head that is produced by pump A at the target flow rate. Pump B will decrease its flow rate until it can produce the same head as pump A, and it is possible that the pump B flow rate may drop below pump B's minimum acceptable flow rate. As mentioned previously in the discussion on drooping and dips of performance curves, the simultaneous operation of parallel pumps can become a problem if the unstable region of the head versus capacity curve falls into the operating range of pump operation.

Figure 12. Parallel Pump Operation with Different Pump Flow Rates

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Pumps are frequently connected in series to supply heads greater than those of an individual pump.The head/capacity curve for two pumps operating in series are shown in Figure 13. The head/capacity curve for a single pump is also shown for a comparison. When the two pumps operate in series, the heads that are produced by each pump are added together and, at any given capacity, the total head can be plotted. Two pumps in series will generate more discharge pressure than one pump alone. Through use of the pump curve for two pumps and the system resistance curve, the maximum capacity for the new system can be determined.

Figure 13. Series Pump Configuration Performance Curves

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Reduction in Pump Efficiency from Operational Wear - The operation of a centrifugal pump over a period of time will result in wear of internal components, such as impellers, wear rings, interstage seals, shaft end seals, and bearings. Wear of pump components will affect the efficiency of pump operation. As pump components wear, two effects may alter the shape of pump performance curves: 1) a decrease in head produced due to either worn impellers (cavitation or recirculation) or an increase in fluid leakage back to the impeller suction or to the environment, and 2) an increase in pump power required to overcome mechanical losses. All of these effects will result in a change in pump performance curves. If a family of pump performance curves exists for a given pump, information can be obtained regarding the operational condition of the pump by measuring the total head of the pump and determining the total capacity delivered to a system. If a pump is old and has not been overhauled to replace worn parts, the total capacity delivered to the system based on the head of a pump as given by the performance curve will become less accurate because the “as-built” head-capacity curves will no longer reflect the actual pump conditions.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The major cause of a reduction in pump efficiency in centrifugal pumps is wear at the pump wear rings. The increase in wear ring clearance results in an increase in leakage from an impeller discharge to the impeller suction; the ultimate result is a decrease in pump capacity. The effect of and the increase in wear ring clearance is shown in Figure 14. The net capacity of the pump at any given head is reduced by the increase in leakage. Leakage past pump wear rings typically increases with the increase in the pressure differential between the pump discharge and the pump suction and is not constant to all pump heads. The difference in leakage rates at different pump heads is typically negligible and a constant leakage rate is commonly assumed regardless of head. Figure 14 shows a constant leak rate value deducted from the pump capacity for a series of pump heads (HA, HB, HC, and HD), which results in the curve drawn after the leakage has occurred.

Figure 14. Change in Centrifugal Pump Performance Curves from Wear Ring Wear Positive-Displacement Pump Performance Curves

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Positive-Displacement Pump Performance Curves Positive-displacement pump performance curves are different than centrifugal pump performance curves because a positivedisplacement pump generally discharges a constant capacity when operated at a constant speed, regardless of the system pressure or flow resistance. Figure 15 shows a comparison between the performance curves of a centrifugal pump and a rotary positive-displacement pump. The capacity of the rotary pump used in Figure 15 decreases slightly as capacity increases due to slip. Slip is the portion of fluid that “slips” back from the high-pressure side of the pump to the low-pressure side through the internal clearances in a positive-displacement pump. The loss of capacity as pump head increases commonly occurs in positive-displacement pumps. Reciprocating pumps also exhibit a loss of capacity as head increases primarily due to suction and discharge valve leakage and loss of fluid through the clearances between the pump cylinder and the piston rings or plunger.

Figure 15. Rotary and Centrifugal Pump Performance Curve Comparison

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The performance curve shown in Figure 15 will not provide adequate data on positive-displacement pump performance characteristics. Most positive-displacement pump performance characteristic curves are plotted at a constant speed or a constant pressure. Figure 16 shows a rotary pump performance curve for a pump operated at a constant speed. The characteristics of capacity (Q), efficiency (ηP), and power (P) are plotted with regards to the differential pressure across the pump.Head is not plotted for positive-displacement pumps because the head produced by any positive-displacement pump is infinite.

Figure 16. Rotary Pump Performance Curves at a Constant Speed

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Figure 17 shows the performance characteristic curves for the same rotary pump; however, the plot shown in Figure 17 reflects the pump characteristics for a constant differential pressure. The characteristic of capacity, efficiency, and power are plotted with regards to variable pump speeds.

Figure 17. Rotary Pump Performance Curves at a Constant Differential Pressure

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The type of performance curves used for a positivedisplacement pump will vary based on the application of the pump: constant speed-variable differential pressure or variable speed-constant differential pressure. Performance Relationships

The relationships between flow, power, and head for a positivedisplacement pump is dependent on pump speed and discharge pressure. The power of a rotary pump will vary directly with the pump pressure and speed. Brake horsepower is the power that is transferred to the pump element by the driver. Brake horsepower (bhp) is calculated as follows: bhp =

Q d x Ptd 1714 x ηp

bhp

= brake horsepower

Qd

= pump flow rate (gpm)

Ptd

= pump differential pressure (psid)

ηd

= pump efficiency

Where:

For SI units: kW =

Q d x kPa td 60 x ηp

kW

= Kilowatts

Qd

= pump flow rate (m3/min)

Where:

kPatd = pump differential pressure (kilopascals differential) ηd

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The pump flow rate of a positive-displacement pump is related to the displacement and the speed of the pump. With the exception of pressure-compensated pumps, positivedisplacement pumps are constant-capacity pumps for a given speed. As the speed of the pump changes, the rate of pump displacement will change, which results in a change of pump flow rate. Slip or leakage losses must be taken into consideration when determining positive-displacement pump capacity. The capacity of a positive-displacement rotary pump can be determined by the following equation: Q = kDN – S Where: Q

= The capacity of the pump in gallons per minute or cubic meters per minute

k

= Conversion factor, 0.004329 for English units, 0.03471 for SI units

D

= Pump displacement per revolution in cubic feet or cubic meters

N

= Pump speed in revolutions per minute

S

= Slip in gallons per minute or cubic meters per minute

Manufacturers' technical data includes information to predict slip for various combinations of pump speed, pressure, and viscosity. Generally, slip increases at a higher discharge pressure and decreases as viscosity increases. For power pumps, slip is determined from stuffing box losses and valve loss. Because stuffing box losses are considered negligible, the value for valve loss is typically used for power pump slip. Valve loss is the flow of liquid that goes back through a check valve while it is closing or seating. Valve loss will vary with pump speed, pressure, viscosity, and check valve design. Manufacturers’ technical data commonly includes information for determining valve loss.

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Curve Variations

Positive-displacement pump performance curves may vary because of changes in the viscosity of the pumped fluid. Figure 18 shows the effect of viscosity on the performance curves for a screw pump that operates at 3600 rpm and 1800 rpm. The pump capacity is higher at higher viscosity because slip is decreased as viscosity increases.

Figure 18. The Effect of Viscosity on a Screw Pump Performance Curve

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

EFFECTS OF CHANGES IN SYSTEM HEAD CURVES ON PUMP PERFORMANCE Centrifugal and positive-displacement pump design and performance characteristics must be matched to the pumping system. A system head curve is used to show the head versus capacity requirements of a system served by a pump. The head versus capacity curve for a system is commonly called a system curve. The system curve can be plotted on a centrifugal or positive-displacement pump performance characteristic curve. The intersection of the system curve and the pump head versus capacity curve is called the operating point. The operating point indicates the head and the capacity at which the pump will operate in the system. A pump is selected based on the operating point that meets the system requirements for head and flow. Underestimating the system characteristics could result in an inadequate pump selection. A Mechanical Engineer must understand the basis of the system curves to perform the following: •

Ensure that a properly rated pump is selected for a system.

•

Determine the effect of changes to an existing system on an existing pump.

This section of the module will discuss the components of the system head curves and the effect of various pumping system configurations on a pump operating point.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Piping System Head A typical piping system curve is shown in Figure 19. The system curve consists of total static head and friction losses. The static head and the friction components of the system curve are losses to the fluid head and the flow energy that was developed by the pump.

Figure 19. Basic System Curve

The flow of fluid through a pumping system offers resistance to fluid flow through changes in differential suction and discharge pressure, through differential fluid elevation, and through the friction of the fluid in the pipes. The pump selected for a system must be capable of overcoming the resistance to flow from changes in elevation, differential vessel pressures, and friction while providing an adequate amount of flow and head to meet system requirements. The resistance to flow from changes in elevation is referred to as the static head component of a system curve. The resistance to flow from fluid friction in the piping system is referred to as the friction head component of the system curve.

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

Static Head Component

The static head component of a system curve accounts for the difference in head between a pump’s suction and its discharge from the difference in the fluid elevation and pressure in the vessels. The head at the pump suction due to elevation and the head at the pump discharge due to elevation are considered fixed system heads, which are also called static heads. Static heads do not change with the rate of flow, but they will vary with changes in the elevation and pressure of the fluid at the pump’s suction and at its discharge. Figure 20 shows a simple diagram of a pumping system that illustrates a positive static head component and the associated system curve. The static head is considered positive if the increase in head is in the direction of flow.

Figure 20. Positive Static Head

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

A positive static head does not affect the shape or the slope of the system curve, but the positive static head defines the head of the system curve with no flow. Figure 21 shows a simple diagram of a pumping system that illustrates a negative static head component and the associated system curve. The static head is considered negative when the increase in head is in the opposite direction of the flow.

Figure 21. Negative Static Head

In Figure 21, a certain amount of fluid flow will occur by gravity head alone. The system curve is plotted from the negative static head value, and it shows that there is a flow rate even at zero head.

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Static head can also include pressure head. Pressure head is generated by pressure exerted on top of the surface of a liquid. In Figures 20 and 21, the surface of the liquid at the suction and at the discharge was exposed to atmospheric pressure. Because the surface of the liquid at both the suction and at the discharge is exposed to the same pressure, the resulting differential head from the pressure was zero. Figure 22 shows a simple diagram of a pumping system that illustrates the effect of pressure head.

Figure 22. Pressure Head

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The surface of the discharge fluid from the pump in Figure 22 is under pressure. The pressure adds static head to the pump discharge. The static head can be determined from the pressure by means of the following equations: H = ∆P ×

144 w

H = ∆P ×

2.31 s

or

Where: ∆P

= The differential gauge pressure on the fluid surface in pounds per square inch

w

= The specific weight of the fluid in pounds per cubic foot

s

= The specific gravity of the fluid

H

= Head in feet

Friction Head Component

The friction head component is always a variable head component because the value changes with the flow rate. In the system example shown in Figure 23, the friction resistance is caused by the orifice, the heat exchanger, the filter, and by the fluid friction from the liquid through the pipe.

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Figure 23. System Resistance Example

The friction of a fluid flowing through a pipe is caused by the viscous shear stresses in the fluid and by fluid turbulence at the pipe wall. There are two types of flow that will impact the amount of fluid friction in a pipe: laminar flow and turbulent flow. Laminar flow occurs in a pipe when the average fluid velocity is low and the energy head is lost due to the viscosity of the fluid. Laminar flow is defined as a series of flow layers. The flow layers nearest the pipe wall have less fluid velocity than the flow layers in the center of the pipe. The flow layers toward the center of the pipe have the fastest fluid velocity. The result of fluid flow layers moving at different velocities increases the fluid friction. An analogy of laminar flow can be described as multiple sleeves inside of a tube. Each sleeve is traveling at a different velocity, and the outer sleeves travel slower than the inner sleeves. Friction is generated at the outside diameter of each sleeve. The total friction is the sum of the friction generated between all of the sleeves and the tube wall.

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The laminar flow layers decrease in thickness as fluid velocity increases. As the laminar flow layers become thinner, surface imperfections on the pipe wall begin to increase fluid flow turbulence. As fluid velocity continues to increase, more turbulent flow is created. Turbulent flow occurs when the average fluid velocity in a pipe is high and energy head is lost to the turbulence generated by the surface imperfections on the pipe walls. The total amount of fluid friction is less for turbulent flow than laminar flow. Figure 24 shows a velocity profile of laminar and turbulent fluid flow through a pipe.

Figure 24. Fluid Velocity Profile

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Pumps Pump and Pump/Piping System Performance as Depicted in Performance Curves

The friction head component is determined by calculating the fluid friction at various flow rates through the system pipes and components. The loss of head from fluid friction (commonly called head loss) can be calculated using several methods for both laminar and turbulent flow. One method for determining head loss uses the following equation known as Darcy’s equation: LV 2 = f hf D2g

Where: hf

= Head loss in feet of liquid

L

= Pipe length in feet

D

= Average inside diameter of the pipe in feet

V

= Average pipe velocity in ft/sec

g

= Gravitational constant (32.174 ft/sec2)

f

= Friction factor

The friction factor can be calculated by means of several methods, or it can be determined from charts or graphs. The easiest method of determining head loss in pipes and components is to use head loss charts that have been derived from the various mathematical methods or by empirical methods. The value for head loss can be read directly from the charts. The charts are available from many sources, and they contain head loss values for viscous fluids at various flow rates. Charts are available for different pipe, pipe fittings, and pipe component materials. Head loss charts for fittings are based on the equivalent length of pipe method used to estimate head loss through a valve or fitting. The equivalent length of pipe is the length of straight pipe that would provide the same head loss as flow through the fitting or valve. The ratio of L/D from Darcy’s equation has been experimentally determined for various pipe components. When the L/D ratio is multiplied by the inside diameter of a pipe of specified schedule for a pipe component, the result is an equivalent length of pipe that is used to calculate the head loss.

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Pump Operating Point As mentioned previously, the system curve can be plotted on a centrifugal or positive-displacement pump performance characteristic curve. The intersection of the system curve and the pump head versus capacity curve is called the operating point. The operating point indicates the head and capacity at which the pump will operate in the system. For the most efficient operation of a pumping system, a pump should be selected so that the operating point is close to the BEP for the pump. The operating point of a pump is typically a dynamic point. Changes in the static and friction components of the system curve may cause the operating point to change position. Several factors affect the control of the operating point: throttling flow, pump speed, and pump minimum flow requirements. Throttling Flow

System valves must also be taken into consideration when determining system curves. The resistance to flow in the pump discharge piping is the main constituent in the friction head component. Valves installed in pump discharge piping increase the resistance to flow, even when the valve is wide open. The effect of throttling a discharge valve is shown in Figure 25. If a downstream control valve is throttled from the wide-open position, the friction head component of the system curve will increase, and the change in the slope of the system curve will increase. As the system curve rises rapidly, the operating point on the pump characteristic curve will shift to a higher value of head and a lower value of capacity.

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Figure 25. Effect of Discharge Valve Throttling on a System Curve

The rate of the slope change for a system curve due to throttling a discharge control valve will vary with the flow characteristics of the valve. Throttling a pump suction valve will also affect the system curve. The inlet static head of the pump will be reduced due to the pressure drop across the valve. A reduction in the inlet static head will increase the difference in head (∆H) from the pump suction to the discharge. An increase in the ∆H across the pump will raise the static head component of the system curve. Because throttling a pump suction valve affects the static head component of the system curve, the shape of the curve (due to friction) will remain the same, but the curve will be located at a lower head. The pump curve will intersect the system curve (operating point) at a lower head and flow rate. Throttling a pump suction valve is not recommended for centrifugal pumps because it changes the net positive suction head (NPSH) to the pump. NPSH is discussed in detail in MEX 211.03.

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Throttling flow control is not used on positive-displacement pumps because the capacity of a positive-displacement pump is independent of head. Changing the system head loss through the use of a throttle valve on a positive-displacement pump discharge will result in a change in pump head (the operating point will move up or down the pump curve), but pump capacity will effectively remain the same (capacity may vary slightly due to the effect of slip). Pump Speed

Changing pump speed has a similar effect on the operating point for both centrifugal and positive-displacement pumps. As shown by the following pump Affinity Laws, centrifugal pump capacity and head are affected by pump speed. Q1 N1 = Q 2 N2 H1  N1  =  H2  N2 

2

The effect of changing positive-displacement pump speed has a similar effect on pump flow rate, but the pump head will not be affected.

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Changing the speed of a centrifugal pump will change the pump flow rate and head, which moves the operating point on the system curve. Figure 26 shows the effect of changing pump speed on the pump operating point.

Figure 26. Effect of Changing Centrifugal Pump Speed on the Pump Operating Point

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Pump Minimum Flow Arrangements

Although a constant-speed centrifugal pump will operate over a wide range of capacities, low flow conditions can cause the following problems in pump operation: •

An increase in the pumped fluid temperature. Increasing the pumped fluid temperature may cause the fluid to flash to vapor in the pump. Fluid flashing to vapor in the pump will result in pump cavitation damage, vibration, or dry running the pump. Dry running the pump will result in pump seizure.

•

Cavitation and pump vibration damage can also be caused by suction or discharge recirculation.

•

High axial-thrust loads on the pump bearings from the high head condition at low flow.

•

Shaft vibration, excessive wearing of the wear rings, shaft breakage, bearing failure, or seal failure caused by singlevolute pump radial forces.

•

For axial-flow pumps, driver overload can occur.

Pumping system controls are often installed to prevent pump operation at low flow while meeting system head and flow requirements. Typically, the minimum flow rate that can be tolerated by a pump with a single-suction impeller is 20% to 25% of the design flow of the pump. Minimum flow controls are typically designed to maintain the pump operating point above an established low flow setpoint while maintaining the proper flow to the pumping system. For double-suction pumps, minimum flows can be considerably higher (40% to 60% of BEP). The more common minimum flow controls used in pumping systems are: •

Integral minimum flow control

•

Variable bypass control

•

Continuous bypass control

•

Low flow signal switch

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Integral Minimum Flow Control - An example of an integral minimum flow control valve system is shown in Figure 27. The integral minimum flow lift check valve is installed in the pump discharge. The operation of the lift check valve controls an integral pilot valve through a mechanical linkage. The integral pilot valve controls an integral bypass flow control orifice. If the system head is greater than the head discharged by the pump, the check valve will close to prevent backflow of fluid through the pump. The integral pilot valve will bypass pump discharge through the control orifice to allow a minimum flow back to the suction source. The integral minimum flow control valve can be set as an on-off control or modulating control.

Figure 27. Integral Minimum Flow Control

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Variable Bypass Control - The variable bypass control is typically

used on high head pumps. The variable bypass control consists of a modulating bypass valve, a flow or pressure sensor, and a control loop. The pressure or flow sensor senses the pump discharge flow or pressure and signals the control loop. The control loop compares the flow or pressure signal to the minimum flow setpoint and then provides a control signal to the modulating bypass control valve. The modulating bypass control valve throttles bypass flow from the pump discharge back to the suction source. The variable bypass control system is capable of reducing the harmful effects of sudden flow changes while conserving power by only bypassing flow when necessary. Continuous Bypass Control - The continuous bypass control is a

simple method of maintaining minimum flow through a pump. The continuous bypass control system typically consists of a bypass line from the pump discharge to the suction source and a metering device. The metering device can be a manual throttle valve or an orifice. The continuous bypass control is the least efficient and is typically used on small pumps with low pressure drops. The function of the continuous bypass is similar to the operation of the integral minimum flow control. Low Flow Signal Switch - Low flow signal switches can be used

in two different types of minimum flow systems: minimum flow shutoff systems and on-off bypass systems. The minimum flow shutoff system typically consists of a pressure switch or a flow (differential pressure) switch connected to the pump motor relay. If the discharge head reaches the pressure switch setpoint, the relay turns off the pump motor. A similar function occurs with the flow switch if pump flow approaches the minimum flow setpoint. Pump restart can be controlled manually, automatically by a timer, or automatically when system conditions warrant a pump restart. The on-off bypass control typically consists of a low flow signal switch, a transmitter, and a solenoid bypass valve (fails open). The flow switch (differential pressure) provides a signal to a transmitter to open the bypass valve when the minimum flow condition occurs.

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Figure 28 shows the pump performance characteristic curve and the system head curve for a system that uses a constant minimum flow orifice. There are two system curves: a normal operation system curve based on the friction and static head of the operating system and a bypass system curve. The bypass system curve is based on the head loss of the bypass piping and a wide open bypass valve. The use of a minimum flow bypass valve is the same operating a system with parallel branch lines. Each branch line has its own system curve based on the head loss in each branch. The sum of the flows from the system and bypass curves at a constant head provides a combined curve. When the bypass valve is open, the operating point will become the point at which the combined system curve intersects the pump characteristic curve. The flow rate through the pump will be the sum of the fluid flow to the system and the fluid flow through the bypass.

Figure 28. Pump Performance Characteristic Curve and System Head Curve for a System that uses a Constant Minimum Flow Orifice

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Figure 29 shows the same system as flow rate approaches zero, the operating point has moved to the left, but the bypass flow rate is constant. When the system flow rate becomes zero, the operating point will be located where the bypass system curve intersects the pump characteristic curve.

Figure 29. Operating Point in Bypass System as System Flow Approaches Zero

The operation of a modulating bypass valve is similar to the bypass system previously described. The exception of a modulating bypass valve is that the bypass flow does not stay constant. The bypass flow is minimized when the system flow demand is high; the bypass flow is maximized as the system flow approaches zero. The combined system curve in a modulating bypass system only changes slightly until the bypass valve is fully open. As a result, the pump operating point is maintained in the relatively same location on the pump characteristic curve until the bypass valve is fully open.

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Typical System Curves for Refineries and Pipelines The following section provides examples of typical pump performance and system curves for refinery systems and pipelines. The examples can be used to evaluate the type of pumping system that should be installed in different applications. The four common pump performance and system curves are as follows: •

High static head, low friction head

•

Low static head, high friction head

•

Parallel pump operation

•

Series pump operation

High Static, Low Friction

Figure 30 shows a typical system curve for a high static head, low friction head system overlaid on a pump head-capacity curve. A high static head, low friction head system is typical of pumping to high elevations or pressures with a low frictional pressure drop. Note that the characteristic of this system is a flat curve. If the pump core is also flat, this type of system will be unstable.

Figure 30. High Static Head, Low Friction Head System Curve

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Low Static, High Friction

Figure 31 shows a typical system curve for a low static head, high friction head system overlaid on the same pump capacity curve previously shown in Figure 30. A low static head, high friction head system is typical of pumping at the same elevation or pressure but with many piping turns, valves, and system components installed in the line, which result in a high frictional pressure drop.

Figure 31. Low Static Head, High Friction Head System Curve

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Parallel Pump Operation

Figure 32 shows a system curve overlaid on the head-capacity curves for two identical pumps arranged in a parallel configuration.

Figure 32. Parallel Pump Operation Head-Capacity and System-Head Curves

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Series Pump Operation

Figure 33 shows the same system curve previously shown in Figure 32 overlaid on the head-capacity curves for the same two identical pumps arranged in a series configuration.

Figure 33. Series Pump Operation Head-Capacity and System-Head Curves

An evaluation of when to use a parallel pump configuration and when to use a series pump configuration depends on the shape of both the system-head curve and the pump head-capacity curve. If the static head component represents a large portion of the system head and friction losses are low (high static head, low friction head), parallel pump operation is a preferable method of increasing system capacity. If the system head consists almost entirely of friction (low static head, high friction head), operating pumps in series will provide more flow through the system than if the same pumps were operated in parallel.

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Figure 34 shows a graphical representation of exaggerated characteristics for pumps and systems plotted to percent rated capacity versus percent rated head. Figure 34 shows two system curves. Curve 1 is relatively flat, which indicates a low friction component, and curve 2 is steep, which indicates a high friction component. Flat head-capacity curves are provided for a single pump (curve A), for two pumps in parallel (curve B), and for two pumps in series (curve C). The following examples illustrate how system and head-capacity curves relate when specifying pump configurations.

Figure 34. Pump Characteristics and System Head Curve Comparisons Example 1 - For a system head composed mainly of friction (curve 2), two pumps operating in parallel would operate at point 2B and would provide 105% of the capacity obtained with a single pump. The same two pumps in series would operate at point 2C and provide 128% of single pump capacity. This

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example shows the advantage of series pumps, which are commonly found in pipeline systems. Example 2 - If the same two pumps in series were installed in a system with a flat system curve (curve 1), the operating point would be at point 1C. The operation of series pumps in a system with a flat system curve still has better capacity than the same two pumps installed in parallel, as indicated by point 1B. However, the advantage is only slight and other factors, such as the following, must be taken into consideration:

•

The brake horsepower in a series pump configuration would total 230% of the rated horsepower for one pump. The power input will provide 148% of single pump capacity, which results in a power-to-capacity ratio of 1.55. The brake horsepower for parallel pump operation is 164% with a capacity of 138% of single pump capacity, which results in a power capacity ratio of 1.19. Parallel pumps would provide a greater advantage over series pumps in terms of cost per gallon of fluid pumped.

•

When two pumps are operated in series at point 1C, each pump must handle 148% of normal capacity. Pumping greater than 100% of normal capacity may cause problems in achieving adequate NPSH. For parallel pump operation at point 1B, each pump would handle only 69% of normal capacity, which minimizes the problem of inadequate NPSH.

•

If the pump driver had been selected without any margin over the power requirement at rated capacity, series pump operation at point 1C will overload the driver.

Figure 35 shows the same system head curves 1 and 2 but with a pump that has a steep head-capacity curve. In this scenario, the capacity advantage of using series pumps is diminished. The series pump operating point in a high friction system (point 2C) is only 122% of single pump capacity compared with 115% for parallel pump operation (point 2B). Unlike example 1, the total power consumption is less for the greater capacity obtained from series pump operation than it would be for the smaller capacity of parallel pump operation. The drop in the total power consumption is caused by the shape of the brake horsepower curve for pumps with steep head-capacity curves in series. The brake horsepower curve lowers as capacity increases.

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Using the flat system curve, parallel operation, with 160% of single capacity at point 1B, provides the advantage over series operation, with 134% of single capacity at point 1C.

Figure 35. Steep Head-Capacity Curve .

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GLOSSARY best efficiency point (BEP)

The point on the map of head, capacity, and impeller diameter at which hydraulic efficiency is maximum.

brake horsepower

The quantity of power required to turn the shaft of a pump. The power loading on the shaft between the pump and its driver.

capacity

The quantity of fluid actually delivered from a pump per unit of time. Typical units include gallons per minute, liters per minute, cubic meters per hour and cubic meters per minute.

cavitation

The implosion of vapor bubbles in a liquid inside a pump on the pumping component (e.g., impeller or plunger).

efficiency

The hydraulic (pressure) energy added to the liquid divided by the power input to the shaft.

gpm

Flow rate in gallons per minute.

head

The quantity used to express the energy content of a liquid per unit weight of the liquid, which is referred to any arbitrary datum in feet or meters.

momentum

In mechanics, the quantity of motion of a body. The linear momentum of a body is the product of its mass and velocity. The angular momentum of a body rotating about a point is equal to the product of its mass, its angular velocity, and the square of the distance from the axis of rotation. Both linear and angular momentum of a body or system of bodies are conserved if no external force acts on the body of the system.

Net Positive Suction Head Available (NPSHA)

Actual pressure at the pump suction minus vapor pressure of the liquid.

Net Positive Suction Head Required (NPSHR)

The amount of pressure drop that occurs from the pump suction flange to the pumping element.

orifice

A device for measuring fluid flow rate in a pipe. This

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device consists of a restriction orifice in the pipe, pressure taps upstream and downstream of the orifice, and a gauge to measure the ∆P. performance curve

Graphs that show the produced head, the required power, the NPSH required, and the efficiency as functions of flow rate.

specific gravity

The density of a liquid divided by the density of water at 60°F.

torque

A quantity expressing the effectiveness of a force to change the net rate of rotation of a body. Torque is equal to the product of the force acting on the body and the distance from its point of application to the axis around which the body is free to rotate. Units of torque include the foot-pound (or pound-foot), the dyne-centimeter, and the newton-meter.

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