Confusion sometimes results when reviewing published NPSHR curves. This is especially true when faced with trimming the impeller diameter to match changing operating conditions. A well known fact is that the head-flow relationship varies with the diameter. This can be accurately approximated by the affinity laws. However, what happens to the NPSHR-flow relationship when the diameter changes? This relationship is frequently over looked and can lead to pump cavitation. This Tip of the Month examines the relationship of NPSHR to the impeller diameter and clarifies other misconceptions regarding pump NPSHR curves.
Background
Pump performance may be shown for a single impeller or a range of impeller diameters. In the latter case the pump performance may be shown as multiple curves from the maximum to the minimum diameter, and may show several intermediate impeller sizes. In addition, the pump performance characteristics may show curves for NPSHR, efficiency and required power. The representation of the pump performance varies widely depending on many factors and can lead to design errors and possible confusion.
An example of a typical pump performance curve frequently seen in publications is shown in Figure 1. The pump flow rate is plotted on the horizontal axis, and the head and NPSHR curves, which are a function of flow rate, plotted on the vertical axles. Note that a single-line NPSHR curve starts at the no-flow condition and continually rises to the maximum flow rate. For several reasons that will be discussed later, this type of NPSHR curve is incorrect and can lead to design errors and possible cavitation problems.
Pump cavitation is a complex subject and the topic of many technical papers and books. However, it is widely accepted that this phenomenon begins at the pump inlet. It basically results from the increased velocity and reduced pressure as the fluid enters the impeller. If the fluid static pressure drops below the vapor pressure, gas bubbles form and later collapse as the fluid flows along the impeller vanes. These vapor bubbles can have a significant effect on the head produced by the pump.
It is important to note that fluid temperature also plays an important part in pump cavitation. Obviously, the fluid vapor pressure will vary with temperature. The fluid temperature will also vary with pump efficiency. Temperature rise due to pump efficiency is not significant in the high to mid-range flow rates, however, can be very significant at low flow rates. This is why pump NPSHR values are not given at low flow conditions.
Figure 1 – Pump Performance Curve for a Range of Impeller Diameters
Another important factor in pump cavitation is the fluid velocity. Fluid entering a pump will continually increase in velocity as it passes to the impeller eye. This increase in velocity causes a drop in the fluid static pressure and is analogous to lift on an airfoil. At high to mid-range flow rates the incoming fluid velocity and the impeller rotational velocity are compatible and contributes to stable flow through the pump. However at low flow rates the entering velocity is well below the rotational velocity and may cause the fluid to “recirculation” at the impeller inlet. Fluid recirculation is another form of pump cavitation. This is another reason why NPSHR is not given at low flow rates.
NPSHR Testing
Understanding how NPSHR tests are conducted and how the impeller diameter influences the produced head will help eliminate confusion and possible errors. Pump manufacturers determine the characteristic shape of the NPSHR curve for each impeller through carefully controlled shop testing, hydraulic modeling and computer simulation. Hydraulic Institute Standard 1.6 gives strict guidelines for conducting shop testing and is used by most pump manufactures. Pumps are normally connected to closed-loop piping circuit where water flows from a suction tank (or sump) through the pump and then back to the tank. The discharge flow rate, temperature and pressure are carefully measured and controlled throughout the test. Basically the test is conducted at a fixed flow rate and speed while the suction pressure is reduced. By reducing the suction pressure a point is reached when the water begins to vaporize thus causing the pump to cavitate. The characteristic “cavitation” point is the flow rate that is exhibited by a small drop in head. The test is conducted again at another fixed flow rate and again the resulting suction pressure and flow rate value are recorded at the “cavitation” point. Once the series of tests are completed, a smooth line is drawn through the recorded data and plotted. Figure 2 illustrates a typical series of test results and the resulting NPSHR curve.
Figure 2 – NPSHR Test Curve
A pump cavitation point can be difficult to define. The formation of vapor bubbles is a gradual process, starting slowly and increasing with flow rate. The API-610 defines the cavitation point as a three percent drop in head. This is not to say that pump cavitation does not occur at smaller values, it is just difficult to accurately measure at smaller values. To obtain a single point it is necessary to run a pump for a period of time and allow the testing circuit to stabilize to the reducing suction pressure. Remember, vapor bubbles are forming and instruments need time to react to the fluid dynamics.
Impeller Diameter and Head Relationship
Larger pump impellers produce greater values of head for a given speed. This is because the head is proportional to the tip speed. The relationship of head to tip speed can be approximated by Equation 1.
(Eq. 1)
Tip velocity can also be related to impeller diameter and rotating speed by Equation 2.
(Eq. 2)
From Equations 1 and 2 it can be seen that changes in impeller diameter will have a direct effect on the pump head. For example, reducing the impeller diameter will lower the pump head by a factor of four. Since the cavitation point is identified by a three percent drop in pump head, it is logical that any change in impeller diameter will have a direct effect on the NPSHR value. For this reason, most pump manufacturers provide a single NPSHR curve for a given impeller diameter. Figures 3 and 4 are typical pump performance curves for a range of impeller diameters. Note that a separate NPSHR curve is given for each diameter.
Figure 3 – Typical Pump Performance Curve for a Range of Diameters
Figure 4 – Optional Pump Performance Curve for a Range of Diameters
Conclusions
The following conclusions can be reached from the previous discussion.
Each impeller will have a characteristic NPSHR curve. It will depend on many design factors including the diameter.
At a given flow rate, the NPSHR increases as the impeller diameter is reduced.
The NPSHR is never tested at the shut-off point. The fluid temperature continually rises as the flow rates decreases. This prevents the system from stabilizing sufficiently to obtain accurate measurements.
Pumps may cavitate at low flow rates due to recirculation of fluid at the impeller eye.
The shape of the NPSHR curve is a U-shape. There is a slight rise in values as the flow is reduced and again at higher values. The NPSHR is lowest in the mid-range values.
By: Joe Honeywell
Legend
A Conversion constant = 720 ft/sec (600 m/s)
D Impeller diameter, inches (cm)
H Total pump head, ft (m)
g Gravitational constant, 32.17 ft/sec2 (9.81 m/s2)
n Rotational speed, rev/min
V Impeller tip velocity, ft/sec (m/s)
References
American Petroleum Institute Standard 610, Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries, 10th Ed.
Hydraulic Institute Standard 1.6, Centrifugal Pump Tests, 2000
This is the final part of a two part Tip of the Month (TOTM) series on important aspects related to centrifugal compressor performance testing. The first part dealt with the review of the testing procedure presented in ASME PTC-10 (also referred to as the Code), selection criteria for test gases and factors to consider in a performance testing. This TOTM will review the basic assumptions and performance relationships required for an accurate test. Also discussed are three important principles: volume ratio, Machine Mach Number and Machine Reynolds Number, which also influence the accuracy of the test results.
Introduction
The Code recognizes that the actual testing conditions and the specified design conditions may not be identical. Basic assumptions are made so that test results can be compared to the original design or some other baseline datum. For example, a compressor can have a different efficiency depending on where it is operating on a head-flow curve. However, if the gas composition and operating condition are not the same as the original design, then how accurate are the results? This question will be discussed below.
There are other important parameters utilized by the Code to analyze compressor performance. The first two are called flow coefficient and work coefficient. These are dimensionless parameters that are useful in the interpretation of test results, especially when comparing the test results to the original design or some other datum. Three more important parameters are called volume ratio, Machine Mach Number, and Machine Reynolds Number. These parameters assure that the aerodynamic properties of a compressor are maintained whenever test gases or alternate operating conditions are used. In addition, they establish limits on the operating range and help correct head and efficiency for friction losses. Each parameter will be briefly discussed.
Dimensionless Parameters
Most likely the actual testing conditions and specified design conditions are not identical. To compensate for the differences, the Code utilizes dimensionless parameters called flow coefficient, work coefficient and total work coefficient. The Code also makes assumptions regarding each coefficient and their equivalency at test and specified conditions. Table 1 lists the Code’s principle parameters and the assumptions used to convert test data into values at specified design conditions.
Changes in compressor performance can be determined whenever the speed fluctuates by simply utilizing the affinity laws. If the compressor flow, head and efficiency characteristics are known at a given speed, then merely applying the affinity laws at an alternate speed will produce a new curve representing the compressor performance at that speed. This is the same concept behind head and flow coefficients. In essence, the flow coefficient represents the “normalized flow rate” of the compressor at any speed. Similarly, the work coefficient and total work coefficient represents the “normalized head” of the compressor at any speed. The affinity laws also imply that the efficiency represented at the two equivalent conditions will remain the same. These properties play a major role in shop and field testing of centrifugal compressors.
Table 1 Dimensionless Parameter Assumptions
Dimensionless Parameter1
Description
Mathematical Description1
Flow coefficient
Flow coefficient of the test gas and specified gas are equal using ideal and real gas methods.
Work input coefficient – enthalpy method
Work input coefficients of the test gas and specified gas are equal. Ideal or real gas laws apply.
Work input coefficient – isentropic or polytropic methods
Work input coefficient of the test gas is corrected for the Machine Reynolds Number to obtain the specified work input coefficient. Ideal or real gas laws apply.
Efficiency –isentropic or polytropic methods
The efficiency at the test operating condition is corrected by the Machine Reynolds Number to obtain the specified operating condition.
Total work input coefficient – heat balance or shaft balance methods
The total work input coefficient is equal for test and specified gases.
NOTE:
1. See ASME PTC-10 for complete mathematical description of the coefficients.
Basic Performance Relationships
The Code recognizes three methods of determining compressor work (also called head). The first is the enthalpy method and is defined by Equation 2. It represents the difference in the inlet and discharge enthalpy, and results in theactual work supplied to the gas. The next method of determining work is by the isentropic method. This method only determines the ideal compressor work and may be calculated utilizing Equation 3 and 4. The last relationship for determining compressor work is the polytropic method. Only the ideal work is found by this method and may be calculated using Equations 5 and 6. All three methods are commonly used by compressor users and manufacturers.
Volume Ratio
The volume ratio is an important aerodynamic parameter. It maintains similar flow conditions as gas properties and operating conditions change. The best way to describe volume ratio is to consider a multi-stage compressor. The mass of gas entering the first impeller must equal the mass entering other impellers. However, the actual gas volume entering the first stage is not the same for other impellers. The gas is compressed and heated, which results in a reduction of volume. If the gas properties and operating conditions of the test gas are different from the specified gas, then the volume entering and leaving each stage will also be different. Therefore, to duplicate the aerodynamic performance of a compressor at the specified design condition it is important to simulate the equivalent flow of gas through the impellers by carefully matching the volume ratio.
A centrifugal compressor performance test is frequently performed with a gas other than the specified gas. In addition, the compressor may operate at conditions other than the original design. To assure an accurate performance test that simulates the original design, the volume ratio of the specified gas must match the volume ratio of the test gas at the respective operating conditions. Equations 1-6 can be used to determine the conditions that match the test and specified volume ratio. The Code sets limits on deviations of the test gas properties and operating conditions, which is found in Table 2 of Part 1.
Seven variables define the volume ratio relationship between a test gas and the specified gas. The variables and the influence each has to increase or decrease the volume ratio is shown in Table 2. For example, if the k-value of the test gas is greater than the specified gas, the volume ratio will decrease. Similarly, if the test gas suction temperature is less then the volume ratio will increase. Also note another important fact, and that is changes in the suction pressure of the test gas have no effect on volume ratio.
Table 2 – Variable Influence on Volume Ratio
Variable
Change
Volume Ratio
Change
Volume Ratio
Head
Increase
Increase
Decrease
Decrease
Molecular Weight
Increase
Increase
Decrease
Decrease
Suction Temperature
Increase
Decrease
Decrease
Increase
Compressibility
Increase
Decrease
Decrease
Increase
k-value
Increase
Decrease
Decrease
Increase
Speed
Increase
Increase
Decrease
Decrease
Suction pressure
Increase
No change
Decrease
No change
As previously mentioned, the volume ratio of the specified gas must match the volume ratio of the test gas. So if each of the physical properties of the test gas can change the volume ratio, what can be done so that the two volume ratios match? A common practice is to change the test speed to compensate for the mismatch of volume ratios. This practice is illustrated in Figure 1. Note how the compressor speed is decreased so that the volume ratio changes imposed by other variables add up to zero.
In summary, the operating conditions and physical properties of a performance test should be carefully examined. It is critical that the test gas volume ratio closely match the volume ratio of the specified gas. The closer the test gas volume ratio is to the specified gas, the more accurate are the performance test results.
Mach Number
The Mach number influences the maximum amount of gas that can be compressed for a given impeller speed. The limiting flow is known as stonewall (also called choke flow) and is typically found on the compressor characteristic head-flow curve at maximum flow condition for a given speed. As the gas flow rate increases so does the velocity within the compressor’s internal flow path until it approaches the fluid acoustic velocity, thus limiting the flow. Therefore, gas velocities that approach a Mach number of one indicate choke flow inside the compressor.
The Code defines a term called the Machine Mach Number which is the ratio of the outlet blade tip velocity of the first stage impeller to the acoustic velocity at inlet conditions. The Code also sets allowable limits on the deviation between the specified and test gas Machine Mach Numbers. This helps assure the accuracy of the performance test. When shop testing a compressor, the Machine Mach Number at the operating condition is calculated and compared to the difference of the specified gas and test gas. See Figure 2 for allowable deviation limits. If the value exceeds the permitted deviation the test gas operating conditions may need adjusting to comply with to these limits.
Figure 2 – Allowable Deviations for Machine Mach Number
Reynolds Number
The effect that the Reynolds Number has on a compressor is similar to the effect it has on pipes. The gas flowing through the internal passages of a compressor produce friction and energy loss which influences the machine efficiency. For centrifugal compressors, the Code defines a term called the Machine Reynolds Number and places limits on the allowable values during a performance test and is defined by Equation 8. If the Machine Reynolds Number for the test condition and specified condition differs then a correction factor is applied to the test efficiency and head values. See Equation 9 for the correction factor.
The allowable Machine Reynolds Number departure limits between the test gas and specified gas are given in Figure 3.
By Joe Honeywell
Figure 3 – Allowable Machine Reynolds Number Departures References
ASME PTC-10, “Performance test Code on Compressors and Exhausters”, 1997
Short Course “Centrifugal Compressors 201”, Colby, G.M., et al. 38th Turbomachinery Symposium, 2009.
Every centrifugal compressor, whether it is new or has been in service for many years will most likely be tested to verify its thermodynamic performance. For a new machine the testing may be conducted in the manufacturer’s facility under strict controlled conditions or in the field at actual operating conditions. Older compressors that have been placed in service after maintenance or have been operating for an extended period of time may require testing to verify the efficiency and normal operation. This TOTM will review ASME PTC-10 (also referred to as the Code) testing procedure and other topics that contribute to an accurate centrifugal compressor test results.
This two-part series will review the salient aspects of a performance test. Part 1 will review the thermodynamic performance test objectives established in the Code as well as other factors to consider in a testing procedure. While this code is primarily applicable to shop testing it can also apply to field testing. Part 2 will review the Code assumptions and basic performance relationships. It will also examine the three important principles that influence the operating conditions and ultimately influence the accuracy of the performance test. They are volume ratio, Machine Mach Number and Machine Reynolds Number.
Introduction
The purpose of a performance test is to verify that a centrifugal compressor will perform in accordance with the manufacturer’s design at the operating conditions given in the specifications. It also provides a method of confirming the shape of the compressor head-flow curve, efficiency, and the maximum and minimum flow limits at various speeds. Frequently a performance test is conducted under field conditions with the specified gas and operating conditions. However, if the performance test is conducted in the shop it may not be possible to test the compressor with the specified gas because of safety concerns or testing facility limitations. Whether the test is conducted in the field or in the shop, proof of the compressor design is recommended and often necessary to demonstrate contractual obligations and mechanical integrity.
Frequently the gas composition used to confirm a compressor performance differs from the specified gas. This is often the case regardless if the test is conducted in the field or in the shop. For field tests, where the gas composition and operating conditions are set by the process, adjustments must be made in the calculations to confirm the compressor design specifications. Typically, a shop test is conducted with a carefully selected mixture of gases blended together to form a gas that has physical properties that closely resemble the specified gas. Even with a substitute gas, differences remain which influence the test results.
The original compressor design places limits on the thermodynamic performance. The most important of these limits include flow rate, power, temperature, pressure and speed. There are other design restraints which are not as commonly known but will also influence the compressor performance. Such factors are volume ratio, Mach number and Reynolds number. These limits were incorporated in the compressor design and are influenced by gas properties, operating conditions and the mechanical design. To verify the design and operating limits for a compressor, it is necessary to test the machine. For new machines, these tests are commonly performed in the manufacturer’s facility; however, the testing is sometimes performed in the field. It may also be helpful to periodically test a compressor to trend the machine performance. Testing conducted during commissioning will establish a baseline of performance. Periodic field tests are often conducted to verify the overall performance and signal changes that may predict mechanical damage, internal fouling, or other deteriorating conditions.
Summary of ASME PTC-10 – Performance Test Code
The procedure presented in the Code provides a method of verifying the thermodynamic performance of centrifugal and axial compressors. This code offers two types of tests which are based on the deviation between test and specified conditions. A detail procedure is given for calculating and correcting results for differences in gas properties and test conditions. The following briefly describes the guiding principles of the Code.
Type 1 test is conducted with the specified gas at or very near to the specified operating conditions. While the actual and test operating conditions may differ, the permissible deviations are limited. See Table 1, 2 and 3 for deviation limits of testing variables of a Type 1 test.
Type 2 test is conducted with either the specified gas or a substitute gas. The test operating conditions will often differ significantly from the specified conditions. The operating conditions are subject to limitations based on the compressor aerodynamic design. See Table 2 and 3 for permissible deviations of operating conditions and test gas properties.
The calculation method of a Type 1 and Type 2 test may conform to either Ideal or Real Gas laws. Physical property limitations are given in Table 3 if Ideal Gas Law methodology is used.
The Code also gives procedures for calculating and correcting test results for difference between the test conditions and specified conditions. It also gives recommendations for accurate testing including compressor testing schemes, instrumentation, piping configuration and test value uncertainties. The following summarizes each topic.
Thermodynamic calculations may utilize either enthalpy, isentropic or polytropic methods. The Code provides equations and examples for determining compressor work (also referred to as head), gas and overall efficiencies, gas and shaft power, and parasitic losses.
The Code gives a correction procedure for test gases and test operating conditions that deviated from the specified operating conditions.
Compressor testing may be open-loop or closed-loop; however, the test results are subject to limits that may give preference to the test arrangement.
Instrumentation methods and measurement uncertainties (refer to PTC-19 series of standards) used to test compressors are given.
Recommendations for piping layout are also included.
Test Gas Selection
There are many gases commonly used to test compressors. They are selected based on physical properties, toxicity, flammability and environmental concerns. See Table 4 for a list of the most frequently used gases. The manufacturers will sometimes blend the various gases to match the equivalency criteria and the test facilities limitations. Following are recommendations to consider when selecting a test gas.
The compressor mechanical design may impose constraints on the test. Consider the machine rotor dynamics, overspeed, maximum temperature and power limitations when selecting a test gas.
Avoid flow rate mismatch of impellers. The volume ratio equivalency is the most important parameter in selecting a test gas. This may also place limitations on the operating conditions. More on this subject in Part 2. of this series.
The test gas molecular weight should closely match the molecular weight of the specified gas.
The test gas k-value should closely match the specified gas to duplicate the Machine Mach Number. If this is not practical then the test k-value should be slightly greater to avoid possible stonewall limitations.
Select a test gas with minimum Reynolds Number deviation from the specified gas. This will minimize the efficiency and head correction factors. This is especially important for machines with a low Machine Reynolds Number.
Table 4 Typical Test Gas Mediums (1)
Test Gas
Molecular Weight
k-Value (2)
Absolute Viscosity-cP (2)
Helium
4.003
1.667
0.0194
Nitrogen
28.014
1.401
0.0174
Air (dry)
28.959
1.401
0.0175
Carbon Dioxide
44.010
1.299
0.0145
R134a
102.0
1.124
0.0114
Natural Gas (4)
17.1 (3)
1.26 (3)
0.010 (3)
Propane
44.096
1.141
0.00789
Note:
From “Compressors 201” course at Turbomachinery Conference, 2009
Values from National Institute of Standards and Technology and Gas Processors Suppliers Association
Values at 60 0F (15.6 C) and 14.696 psia (101.3 kPa)
Gas composition and physical properties varies with local utility
Test Objectives
The following are some factors to consider as part of the performance test procedure.
API 617 requires a minimum of five test points to be taken at the operating speed to demonstrate the surge point, stonewall, required operating point and two alternate points. The user may optionally request additional test points to verify compressor performance at alternate speeds. For example, extra data points may be needed to verify the surge line or critical process operating conditions for variable speed machines.
The test may be performed as a Type 1 or Type 2 test. Type 1 is normally more accurate and is typically reserved when test conditions can be made to closely match the specified operating conditions. A Type 2 test is typically a shop test utilizing a substitute gas.
If a Type 2 test is recommended, the test gas may be a pure gas such as those listed in Table 4, or a mixture of gases. The composition of the test gas should be agreed upon before testing. In addition, the composition of the test gas should be sampled before, during and after the test. Some gas mixtures tend to stratify and give erroneous results.
The physical properties of the test gas are critical to the outcome especially if it is a mixture of selected gases. An agreement on the physical properties is recommended.
Normally an agreement is made as to the “equation of state” used to calculate the results of the test. Not all EOS programs give the same results, nor is there industry agreement as to which method is best.
Discuss the specific driver used in the test. Will a shop driver or the specified driver be used? Will the driver be fixed or variable speed? If it is variable speed, will it be motor, gas turbine or steam turbine?
If a gear is part of the test, will it be manufacturer or user supplied? Is the efficiency of the gear known? Tests can be performed to verify gear efficiency.
Will the gas be cooled with a water-cooled or air-cooled exchanger? Is there temperature limitations on the coolant used in the test?
Is the allowable working pressure of equipment and piping systems adequate for the test? Will a pressure safety valve be needed to protect the system and is it properly sized?
An agreement on how the input power will be measured is important. Options include, heat balance, calibrated driver, dynamometer, and torque meter. Review the specific method of measuring input power with the manufacturer.
A piping and instrument schematic is recommended. The drawing should show details of the test loop including the placement of major equipment, number and location of instruments, and piping size. This is especially important for compressors with multiple sections, inlet sidestream, or back-to-back configuration.
Before proceeding with a performance test a written procedure is recommended that outlines how the test will be conducted. The procedure should clearly convey the scope of the test, the responsibilities of each party, test piping and instrument arrangement, measurement methods, uncertainty limits, calibration, taking of test data and how to interpret results, and acceptance criteria.
By Joe Honeywell
References
ASME PTC-10, “Performance test Code on Compressors and Exhausters”, 1997.
API Standard 617, “Centrifugal compressors for Petroleum, Chemical, and Gas Services Industries”, 1995.
Kurz, R., Brun, K, & Legrand, D.D., “Field Performance Testing of Gas Turbine Driven Compressor Sets”, Proceeding of the 28th Turbomachinery Symposium, 1999.
Short Course “Centrifugal Compressors 201”, Colby, G.M., et al. 38th Turbomachinery Symposium, 2009.
National Institute of Standards and Technology, Web Site for Properties of Fluids.
In the August 2009 Tip of the Month (TOTM), it was shown that pumping power requirement varies as the crude oil °API changes. Increasing °API or line average temperature reduces the crude oil viscosity. The viscosity reduction caused higher Reynolds number, lower friction factor and in effect lowered pumping power requirements. Since the objective of the August 2009 TOTM was to study the effect °API and the line average temperature have on the pumping power requirement, the effect of crude oil viscosity on pump performance was ignored and in the course of calculation a constant pump efficiency of =0.75 was used for all cases. In this TOTM, we will consider the crude oil viscosity effect on a selected pump performance. The Hydraulic Institute Standards [1] procedures and the guideline presented in the August 2006 TOTM written by Honeywell were applied to correct the pump efficiency.
As in the August 2009 TOTM, we will study crude oil °API and the pipeline average temperature and how these effect the pumping requirement. For a case study, we will consider a 160.9 km (100 miles) pipeline with an outside diameter of 406.4 mm (16 in) carrying crude oil with a flow rate of 0.313 m3/s or 1,126 m3/h (170,000 bbl/day or 4958 GPM). The pipeline design pressure is 8.963 MPa (1300 psia) with a maximum operating pressure of 8.067 MPa (1170 psia). The wall thickness was estimated to be 6.12 mm (0.24 in). The wall roughness is 51 microns (0.002 in) or a relative roughness (e/D) of 0.00013. The procedures outlined in the March 2009 TOTM were used to calculate the line pressure drop due to friction. Then corrected pumping efficiency was used to calculate the required pumping power. Since the objective was to study the effect °API and the line average temperature have on the pumping power requirement, we will ignore elevation change. The change in pumping power requirements due to changes in crude oil °API and line average temperature for this case study will be demonstrated.
Viscosity Effect on Centrifugal Pump Performance
There are several papers investigating and presenting procedures for correcting centrifugal pump curves [2-3]. According to Turzo et al. [2], three models are available for correcting performance curves: Hydraulic Institute, Stepanoff, and Paciga. Turzo et al. [2] also presented a computer applications for correcting pump curves for viscosity effect. In this review, the Hydraulic Institute [1], HI, procedure was applied and is described briefly here.
HI uses a performance factor, called Parameter B which includes terms for viscosity, speed, flow rate and total head. The method uses a new basis for determining the correction factors CH, CQ, and C. The basic equation for Parameter B is given as Equation 1.
B = Performance factor K = 16.5 for SI units
= 26.5 for USCS (FPS) vis = Viscous fluid Kinematic viscosity – cSt HBEP-W = Water head per stage at BEP – m (ft) QBEP-W = Water flow rate at BEP – m3/h (gpm) N = Pump shaft speed – rpm
Correction factors are applied to capacity (CQ), head (CH), and efficiency (C). Calculation of these Correction Factors is dependent on the calculated value of Parameter B. For the cases considered in this study, the B values were less than 1; therefore, based on the HI guideline, the correction factors for head and capacity were set equal to 1 and the correction factor for efficiency, C, was calculated by Equation 2.
BEP-W = Pump efficiency at BEP Vw = Water kinematic viscosity – cSt
Figures 1 and 2 present the water-based pump curves used in this study. For computer calculations, these two curves were fitted to polynomials of degrees 3 and 2 for head vs capacity and efficiency vs capacity, respectively.
In Equations 3 and 4, H is in m (ft) and Q is in m3/h (GPM). For this pump:
Case Study 1: Effect of Line Average Temperature (Seasonal Variation)
To study the effect of the line average temperature on the pumping power requirement, an in house computer program called OP&P (Oil Production and Processing) was used to perform the calculations outlined in the March 2009 TOTM. For a 35 °API crude oil in the pipeline described the required pumping power was calculated for line average temperature ranging 21.1 to 37.8 °C (70 to 100 °F). For each case, the parameter B was calculated by Equation 1 and since its value was less than 1, the efficiency correction factor was calculated by Equation 2. Then, the pump efficiency calculated by Equation 4 was multiplied by the correction factor for the subsequent calculations. The corrected efficiency ranged from 0.70 to 0.72. The required pumping power was compared with an arbitrary base case (85 °F or 29.4 °C and constant = 0.75) and the percentage change in the pumping power requirement was calculated. Figure 3 presents the percent change in power requirement as a function of line average temperature. There is about 5% change (for constant =0.75) and more than 8% change (for corrected efficiency) in the pumping power requirement for the temperature range considered.
Note that as the line average temperature increases the power requirement decreases. This can be explained by referring to Figure 4 in which the oil viscosity decreases as the temperature increases. Lower viscosity results in higher Reynolds (i.e. Reynolds number which is the ratio of inertia force to viscous force); therefore, the friction factor decreases (refer to the Moody friction factor diagram in the March 2009 TOTM).
Case Study 2: Effect of Variation of Crude Oil °API
In this case, the effect of crude oil °API on the total pump power requirement for three different line average temperatures was studied. For each line average temperature, the crude oil °API was varied from 30 to 40 and the total pumping power requirement was calculated and compared to the base case (35 °API and average line temperature of 29.4°C=85°F).
For each case the percent change in total power requirement was calculated and is presented in Figure 5. As shown, when °API increases the total power requirement decreases. This also can be explained by referring to Figure 4 in which the crude oil viscosity decreases as ° API increases. The effect of viscosity is more pronounced at lower line average temperature (i.e. 21.1 °C or 70°F). Figure 5 also indicates that there is about 30 % change in total power requirement as °API varies from 30 to 40 °API. This is a significant variation and suggests that it should be considered during design of crude oil pipelines.
Discussion and Conclusions
The analysis of Figures 3 and 5 indicates that for the oil pipeline, the pumping power requirement varies as the crude oil °API changes. Increasing °API or line average temperature reduces the crude oil viscosity (see Figure 4). The reduction of viscosity results in higher a Reynolds number, lower friction factor and in effect lowers pumping power requirements.
For the cases studied in this TOTM, the effect of crude oil viscosity on the performance of pump was considered. It was found that no correction was required for the capacity and head but a correction factor in the range of 0.95 to 0.98 was required to adjust the pump efficiency for crude oil applications.
A sound pipeline design should consider expected variations in crude oil °API and the line average temperature. In addition, the pump performance curves should be corrected for the effect of viscosity.
During the life cycle of a crude oil pipeline the properties of transported oil change, because in gathering systems the produced oils come from different wells. New wells may be added or some wells may go out of production for maintenance and repair. Production rates during the life of wells vary, too. In addition the properties of crude oil change during production. Due to seasonal variation, the average line temperature may also change. As it is shown in the proceeding sections, viscosity of crude oil is a strong function of API gravity and temperature.
In the March 2009 tip of the month (TOTM), procedures for calculation of friction losses in oil and gas pipelines were presented. The sensitivity of friction pressure drop with the wall roughness factor was also demonstrated.
In this TOTM, we will study crude oil °API and the pipeline average temperature and how they effect the pumping requirement. For a case study, we will consider a 160.9 km (100 miles) pipeline with an outside diameter of 406.4 mm (16 in) carrying crude oil with a flow rate of 0.313 m3/s (170,000 bbl/day). The pipeline design pressure is 8.963 MPa (1300 psia) with a maximum operating pressure of 8.067 MPa (1170 psia). The wall thickness was estimated to be 6.12 mm (0.24 in). The wall roughness is 51 microns (0.002 in) or a relative roughness (e/D) of 0.00013. The procedures outlined in the March 2009 TOTM were used to calculate the line pressure drop due to friction. Then assuming 75 % pumping efficiency, the required pumping power was calculated. Since the objective was to study the effect °API and the line average temperature have on the pumping power requirement, we will ignore elevation change. The change in pumping power requirements due to changes in crude oil °API and line average temperature for this case study will be demonstrated.
Case Study 1: Effect of Line Average Temperature (Seasonal Variation)
To study the effect of the line average temperature on the pumping power requirement, an in house computer program called OP&P (Oil Production and Processing) was used to perform the calculations as outlined in the March 2009 TOTM. For a 35 °API crude oil in the pipeline described in the preceding section, the required pumping power was calculated for the line average temperature ranging from 21.1 to 37.8 °C (70 to 100 °F). For each case, the required pumping power was compared with an arbitrary base case (85 °F or 29.4 °C) and the percentage change in the pumping power requirement was calculated, accordingly. Figure 1 presents the percent change in power requirement as a function of line average temperature. There is about 5% change in the pumping power requirement for the temperature range considered.
Note as the line average temperature increases, the power requirement decreases. This can be explained by referring to Figure 2 in which the oil viscosity decreases as the temperature increases. Lower viscosity results in higher Reynolds (i.e. Reynolds number is the ratio of inertia force to viscous force); therefore, the friction factor decreases (refer to the Moody friction factor diagram in the March 2009 TOTM).
Case Study 2: Effect of Variation of Crude Oil API
In this case, the effect of crude oil °API on the total pump power requirement for three different line average temperatures was studied. For each line average temperature, the crude oil °API was varied from 30 to 40 and the total pumping power requirement was calculated and compared to the base case (35 °API and average line temperature of 29.4°C=85°F).
For each case the percent change in total power requirement was calculated and is presented in Figure 3. As shown in this figure, when °API increases the total power requirement decreases. This also can be explained by referring to Figure 2 in which the crude oil viscosity decreases as ° API increases. The effect of viscosity is more pronounced at lower line average temperature (i.e. 21.1 °C or 70°F). Figure 3 also indicates that there is about 25 % change in total power requirement as °API varies from 30 to 40 °API. This is a big change and should be considered during design of crude oil pipelines.
Discussion and Conclusions
The analysis of Figure1-3 indicates that for the oil pipeline, the pumping power requirement varies as the crude oil °API changes. Increasing °API or line average temperature reduces the crude oil viscosity (see Figure 2). The reduction of viscosity results in higher Reynolds number, lower friction factor and in effect lower pumping power requirements.
In practical situations, an originating station takes crude out of storage and the midline stations taking suction from the upstream section of pipeline. In some parts of the world, the suction temperature to the originating pumps is +38 °C (+100 °F) but the temperature to the midline station is ground temperature (this assumes a buried line below the frost line) approximately 18 °C (65 °F). The originating station will always be more affected by temperature because storage will follow ambient – whereas the midline station will operate at notionally constant temperature +/- 5.5 °C (+/- 10 °F) in the lower 9 °C (48 °F). For the case studied in this TOTM, the number of pumping stations varied from 2.5 to 3.2.
In light of the above discussion, a sound pipeline design should consider expected variation in crude oil °API and the line average temperature.
One of the most important physical properties of a gas is the ratio of specific heats. It is used in the design and evaluation of many processes. For compressors, it is used in the design of components and determination of the overall performance of the machine. Engineers are frequently asked to evaluate a compressor performance utilizing traditional equations of head, power and discharge temperature. While these simplified equations may not give exact results, they give useful information needed to troubleshoot a machine, predict operating conditions, or a long-term trend analysis. The accuracy of the performance information will depend on the proper selection of the ratio of specific heats. This Tip of the Month (TOTM) will investigate the application of the ratio of specific heats to compressors, its sensitivity to the determination of machine performance and give recommendations for improved accuracy.
Background of k-value
The ratio of specific heats is a physical property of pure gases and gas mixtures and is known by many other names including: adiabatic exponent, isentropic exponent, and k-value. It is used to define basic gas processes including adiabatic and polytropic compression. It also appears in many of the traditional equations commonly used to determine a compressor head, gas discharge temperature, gas power, and polytropic exponent. The k-value also influences the operating speed of a compressor, but we will simplify the present analysis by deleting speed from our evaluation. The following commonly used compressor performance equations show how the k-value is utilized in the design and evaluation of compressors.
Note: The actual Z-value will vary from the suction to discharge conditions. ZS is sometimes replaced with ZAVE to approximate the variations in compressibility value [1, 5]. See the nomenclature at the end of this TOTM.
The above equations are written in terms of the adiabatic process with the exception of Equation 5, which refers to the polytropic process. Both compression processes are similar and will give the same actual results. The adiabatic and polytropic methods are extensively used by manufacturers to design compressors, and make use of k-values to calculate their performance. However, as will be seen, the effect of the k-value and the calculated results will influence both compression processes alike. For simplicity, this Tip of the Month will use the adiabatic process.
It can be seen from Equations 1-5 that the k-value has an effect on a compressor head, temperature, power, and polytropic exponent. In order to determine how small changes in the k-value can influence a compressor performance, let us first define the k-value of a pure gas. The thermodynamic definition of a gas k-value is given by Equation 6. It shows the relationship to the specific heat at constant volume, CV and specific heat at constant pressure, CP. Both values vary with temperature and pressure.
For a pure gas there are many references that give CP and CV values at various conditions. One useful source is National Institute of Standards and Technology. Their website is http://webbook.nist.gov/chemistry/fluid/
The method of determining the k-value for gas mixtures is more complex. The major difference is that a gas mixture does not behave as any one of its components but as an “equivalent” gas. Therefore, to determine the k-value of the mixture, we must know the mole fraction of each component, Yi and the molar specific heat at constant pressure for each component, M CPi. Equation 7 can be used to determine the k-value of an ideal gas mixture [1, 5]. Real gases may deviate from the calculated value.
While Equations 1-7 are applicable for manual calculations methods, it is important to note that process simulation packages determine the compressor head and discharge temperature utilizing equations of state. The results are the same but the methods are very different.
K-value Sensitivity Analysis
In the compression process the temperature and pressure of the process gas both increase. Not knowing what k-value to select for evaluating the compression process can lead to errors. For example, a typical propane compressor may have a k-value at suction conditions of 1.195. At the compressor discharge conditions the k-value is 1.254. The difference in the two values varies by 4.94 percent and can have a significant influence in the performance evaluation. The following example illustrates how minor changes in the k-value can influence the calculated compressor head, temperature, power and the polytropic coefficient.
Example 1: A natural gas compressor is operating at the conditions given below. Only the k-value is varied from 1.20 to 1.28, all other given parameters remain constant. Figure 1 illustrates how the “apparent” performance of a compressor can change by varying the k-value.
It can be seen from Figure 1 that the discharge temperature deviated over 18.8 percent by only changing the k-value by 6.7 percent. In this case the k-value varied from a value of 1.20 to 1.28; which is the typical range for natural gas. Similarly, the power changed by 2.5 percent, polytropic exponent by 9.5 percent, and adiabatic head by 2.5 percent for the same variation of the k-value. The changes in compressor performance described in Figure 1 can be much larger depending on the gas composition and the operating temperature and pressure.
Corrected k-Value Recommendations
The k-value sensitivity for a single-stage machine is not nearly the problem as a multi-stage compressor. For a single-stage machine, the pressure ratio is typically lower and the temperature and pressure changes are less. As a result the changes in k-value are not as great and accurate results can be obtained by approximating the k-value at the suction conditions. However, for multi-stage machines, where the pressure and temperature ratios are higher, the k-value sensitivity is more of a factor in evaluating compressor performance. Most compressor manufacturers calculate the k-value for each stage of compression and avoid errors introduced by utilizing an overall k-value. Without their software, we are left with a corrected k-value by empirical methods.
There are many useful approximations that will correct for changes in the k-value as the process gas passes through the compressor. Normally the k-value will decrease during compression but not always. Utilizing the suction conditions to estimate the k-value will generally give higher values of temperature, heat, and power. The polytropic exponent generally decreases as the adiabatic exponent decreases. To avoid potential discrepancies, a k-value correct may be warranted. The following are six methods of determining the corrected k-value commonly used in industry.
At TS and PS: This method determines the k-value at suction conditions and is useful for single stage compressors or applications where there is little change in the k-value. The k-value is easy to determine and tends to overestimate results, especially if the temperature and pressure do not change significantly. For greater values of RP the results may become so conservative they become useless.k = ks at suction conditions
At TD and PD: This method determines the k-value at discharge conditions. The k-value is less conservative and tends to underestimate results. The k-value may be difficult to determine, especially if the discharge temperature is unknown. For gases with highly variable k-values, an iterative solution may be required to estimate the discharge temperature and corrected k-value.k = kD at discharge conditions
At TAVE and PSTD [5]: This method utilizes the average operating temperature at standard pressure and determines the k-value. Numerous reference books propose this method. Errors are introduced because the k-value at standard pressure may not accurately represent values at the operating pressure.k = at average operating temperature and standard pressure
At TAVE and PAVE: This method utilizes the k-value at the average operating temperature and pressure.k = at average operating temperature and pressure
Average value [1, 3]: This empirical method takes the average k-value at compressor inlet conditions and outlet conditions. Utilizing the average k-value will result in performance values that are closer to the actual performance of the compressor.
Weighted average value [4]: This empirical method takes the weighted average of the suction, mid-point and discharge conditions. Note that the mid-pressure is determined by equivalent pressure ratios, . The mid-temperature is estimated from the mid-pressure. This method considers the staged k-value to change with diverging isentropic and pressure lines shown on a Mollier chart.
Example 2 illustrates the various methods used to determine corrected k-values given above. It also compares the range of the resulting values.
Example 2: A propane compressor is operating at the given conditions shown below. Table 1 lists the k-values attributed to various operating and reference conditions [6].
Summary
This Tip of the Month has defined the physical property of process gases called the k-value or ratio of specific heats. It has shown that small changes in the k-value can have a significant effect on the calculated values of head, power, gas discharge temperature, and polytropic exponent. Recommendations were also given to improve the accuracy by utilizing different k-value methods.
In the February 2007 tip of the month (TOTM), Joe Honeywell [1] presented a procedure for calculating fluid pressure drop for liquid in a piping system due to friction. Continuing Honeywell’s TOTM, we will outline procedures for calculation of friction losses in oil and gas pipelines. From an engineer’s point of view the question may arise “how sensitive is friction pressure drop with the wall roughness factor?” Of course the answer is “it depends”. To explain this answer quantitatively and qualitatively, we will study the effect of wall roughness factor for two case studies in this month’s TOTM. In the first case study, an oil pipeline with a flow rate of 0.313 m3/s (170,000 bbl/day) and in the second case, a natural gas pipeline with a flow rate of 22.913 Sm3/s (70 MMSCFD) will be studied and calculation results will be presented in tabular and graphical format.
Friction Factor
The Moody diagram in Figure 1 is a classical representation of the fluid behavior of Newtonian fluids and is used throughout industry to predict fluid flow losses. It graphically represents the various factors used to determine the friction factor. For example, for fluids with a Reynolds number of 2000 and less, the flow behavior is considered a stable laminar fluid and the friction factor is only dependent on the Reynolds number [2]. The friction factor, f, for the Laminar zone is represented by:
Where Re is the Reynolds number and is expressed as the ratio of inertia force to viscous force and mathematically presented as.
Fluids with a Reynolds number between 2000 and 4000 are considered unstable and can exhibit either laminar or turbulent behavior. This region is commonly referred to as the critical zone and the friction factor can be difficult to accurately predict. Judgment should be used if accurate predictions of fluid loss are required in this region. Either Equation 1 or 3 are commonly used in the critical zone. If the Reynolds number is beyond 4000, the fluid is considered turbulent and the friction factor is dependent on the Reynolds number and relative roughness. For Reynolds numbers beyond 4000, the Moody diagram identifies two regions, transition zone and completely turbulent zone. The friction factor represented in these regions is given by the Colebrook formula which is used throughout industry and accurately represents the transition and turbulent flow regions of the Moody diagram.
The Colebrook formula for Reynolds number over 4000 is given in equation 3.
The roughness factor is defined as the absolute roughness divided by the pipe diameter or . Typical values of absolute roughness are 5.9x10-4 in (0.0015 mm) for PVC, drawn tubing, glass and 0.0018 in (0.045 mm) for commercial steel/welded steel and wrought iron [3].
The Colebrook equation has two terms. The first term, ()/3.7, is dominate for gas flow where the Re is high. The second term, , is dominate for fluid flow where the relative roughness lines converge (smooth pipes). In the “Complete Turbulence” region, the lines are “flat”, meaning that they are independent of the Reynolds Number. In the “transition Zone”, the lines are dependent on Re and . When the lines converge in the “smooth zone” the fluid is independent of relative roughness.
Liquid (Incompressible) Flow
For liquid flow, equation 4 has been used by engineers for over 100 years to calculate the pressure drop in pipe due to friction. This equation relates the various parameters that contribute to the friction loss. This equation is the modified form of the Darcy-Weisbach formula which was derived by dimensional analysis.
The friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using an iterative method or a trial and error procedure.
Gas (Compressible) Flow
For gas flow, density is a strong function of pressure and temperature, and the gas density may vary considerably along the pipeline. Due to the variation of density, equation 5 should be used for calculation of friction pressure drop.
Again, the friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using a trial and error procedure. Actual volume flow rate is needed to calculate the velocity of gas in the line from which the Reynolds number is calculated. Equation 6 may be used to convert the volume flow rate at standard condition to the actual volume flow rate.
Case Study 1: Oil Pipeline
Consider a 16-inch (inside diameter of 395 mm) oil export line for transportation of 170,000 bbl/day (0.313 m3/s) of a 43 API crude oil (relative density of 0.81) from an offshore platform to the shore oil terminal. The total length of pipe is 55 km. The ambient temperature is 5 °C and the crude oil viscosity at the average pipe temperature is 0.001 cP. The pipe line inlet pressure is 14.9 MPa (absolute). Since the objective is to study the effect of roughness factor on friction pressure drop, we will ignore elevation change.
To study the effect of roughness factor on friction pressure drop, was varied from 1x10-6 to 1x10-3. The roughness factor of = 1x10-6 represents a very smooth pipe. The calculated friction pressure drop as a function of the roughness factor is plotted in Figure 2. For each value of roughness factor, the percent change in frictional pressure drop was calculated in comparison to a very smooth pipe (= 1x10-6) and the results are presented in Figure 3. The calculated results are also presented in Table 1.
Case Study 2: Gas Pipeline
Let’s consider an 8-inch (inside diameter of 190 mm) gas export line for transportation of 70 MMSCFD (22.913 Sm3/s) of natural gas with a molecular weight of 19.3 (relative density of 0.67) from an offshore platform to the shore. The total length of pipe is 43 km. The ambient temperature is 5°C and the gas viscosity at the average pipeline temperature is 1.1x10-6 cP. The gas inlet temperature is 35°C and pressure is 13.0 MPa (absolute). Since the objective is to study the effect of roughness factor on friction pressure drop, we will again ignore elevation change.
Similar to the oil pipeline, the roughness factor, was varied from 1×10-6 to 0.006. Note, for a roughness factor greater than 0.006, a higher inlet pressure, a larger diameter or lower flow rate was needed. The calculated friction pressure drop as a function of roughness factor is presented in Figure 2. For each value of roughness factor, the percent change in frictional pressure drop in comparison to a very smooth pipe (= 1×10-6) was calculated and the results are presented in Figure 3.
Discussion and Conclusions
The analysis of Figure 2 indicates that for the oil pipeline, the friction pressure drop is almost independent of the roughness factor in the range of 1×10-6< <1×10-4; however, for >1×10-4, it will increase with . For liquid lines, the Reynolds number is normally in the range of 5×104 to 1×106. For this range, the friction factor curves in Figure 1 approach close to each other so the values of friction factors become close to each other.
Contrary to the oil pipeline, the friction pressure drop for the gas pipeline is a strong function of . As can be seen in Figure 2, friction pressure drop increases very rapidly with the roughness factor. Figure 3 shows the comparison of percent change of friction pressure drop between oil and gas pipelines as a function of roughness factor. For the liquid pipeline, the maximum change is 20 % but for the gas pipeline the maximum change is more than 200 %. Again this can be explained by referring to Figure 1. For gas pipelines, the Reynolds number is higher than in the liquid line and the range is normally 5×106<Re<1×108. For this range, the friction factor curves in Figure 1 are apart from each other, so the friction factors are not close.
In summary, contrary to liquid pipelines the gas pipelines are very sensitive to wall roughness and using smooth pipe can reduce friction pressure drop considerably. This in turn lowers the OPEX. Therefore, regular pigging to clean the pipe surface is done to lower the roughness factor. The modern gas transmission companies will add a Fusion Bounded Epoxy (FBE) liner to gas pipelines because the pipe is sensitive to roughness. This lowers OPEX for the long term. It should be noted that the smoother the pipe, the higher the CAPEX, so as always, detailed total cost analysis should be performed for engineering applications.
Due to the sensitivity of gas pipelines to roughness factor and other operation parameters, there are numerous gas flow equations (e.g. Weymouth, Panhandle A and B, AGA) to best fit certain design conditions [1].
To learn more about similar cases and how to minimize operational problems, we suggest attending our ME44 (Overview of Pumps and Compressors in Oil and Gas Facilities), ME46 (Compressor Systems – Mechanical Design and Specification), PL4 (Fundamental Pipeline Engineering), G40 (Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), and PF4 (Oil Production and Processing Facilities) courses.
By: Dr. Mahmood Moshfeghian
Reference:
Honeywell, Joe, “Friction Pressure Drop Calculation,” Campbell Tip of the Month, Feb 2007
Campbell, J. M., “Gas Conditioning and Processing, Vol. 1, the Basic Principals, 8th Ed., Campbell Petroleum Series, Norman, Oklahoma, 2001
Menon, E.S, Piping Calculations Manual, McGraw-Hill, New York, 2005
In this tip of the month, we will discuss how miscalculations and incorrect analysis of potential process upsets can affect process safety. There are many aspects in facility design engineering and process safety engineering that should be considered when designing a new facility or debottlenecking an existing one. During these times of compressed schedules and budgets, it can become difficult to ensure all project deliverables receive the proper amount of checking and documentation. Mistakes in engineering design and operations of the following systems can result in serious safety incidents which must be avoided. Quality control, technical training, calculation checking and method verifications can aid in minimizing safety risks in these systems. This months’ tip will focus on Pressure Relief Systems.
A primary process system in oil and gas facilities requiring careful attention is the Pressure Relief System. The most common components in upstream pressure relief systems are:
Protected Equipment
Emergency Shut Down Valves
Depressurization Valves
Pressure Safety Valves (PSV)
Pressure Safety Valves Inlet and Discharge Piping
Flare Header
Flare Knock Out Drum
Flare Stack / Tip
The primary purpose of the pressure relief system is to ensure that the operation’s personnel and equipment are protected from overpressure conditions that happen during process upsets, power failures, and from external fires. In some locations and facilities, it is accepted practice to vent the pressure safety valves directly to atmosphere provided the process fluid is discharged at sufficient velocity to ensure good dispersion and that the fluids molecular weight is lighter than air. In this TOTM we will be discussing components in the pressure relief system in which detailed engineering calculations must be completed to select and install properly.
Pressure Safety Valves:
The purpose of a pressure safety valve is to protect equipment and / or piping from any possible overpressure scenario. There are multiple industry recommended practices and standards that govern the sizing, selection and installation of pressure safety valves. Many of these are referenced in this TOTM. A study that was conducted by Berwanger, et al. [1] determined that only 65% of upstream processing facility pressure safety valves meet the existing standards. Accurate pressure safety valve relieving requirements, scenario analysis and installation design is critical to ensure safety of the equipment and the operations staff during an upset condition. The American Institute of Chemical Engineering found that roughly 30% of process industry losses have been found to be partially attributed to deficient pressure relief systems [2]. If an upset process condition occurs with a system that has a pressure safety valve that is missing, undersized, or not properly installed, there is a potential that the equipment will not be protected and will mechanically fail. This could result in a significant loss of fluid containment and potential fatalities depending upon the fluids contained within the process.
On March 4, 1998, there was a major vessel failure at a Sonat Exploration facility in Pitkin Louisiana. The vessel failure and subsequent fire resulted in four deaths. A cause of the incident was failure of a low pressure vessel open to a high pressure gas source that was not provided with any pressure relief devices [3].
In determining the relevant relieving scenarios for a pressure relief valve, it is essential that the engineer doing the evaluation has a solid understanding of the process and the process control design within the facility. If the lead engineer is conducting an existing plant review or working on the design of a new facility, it is critical that they evaluate all potential relieving scenarios that may be required. If a scenario is missed, then there is a possibility that the system will not be protected if that missed scenario was the limiting case. ANSI / API Standard 521 ISO 23251, 5th Edition [5] specifies requirements and provides guidelines for examining the principal causes of overpressure; determining individual relieving rates; and selecting and designing disposal systems, including the details on specific components of the disposal system. Only with experience and training do engineers develop the competency level to complete these evaluations effectively. Participation in Process Safety Hazards Reviews and Analyses promote the development of an engineer’s skills in identifying and resolving potential process hazards, and can help develop a junior engineer’s skills and understanding of the evaluation of these systems.
API Recommended Practice 520, 7th Edition, Part 1 [4], and the International Organization for Standardization (ISO) Standards in the 4126 series (will not all be referenced here, and it should be noted that these only apply to systems designed and installed in the European Union Member States), addresses the methods to determine the pressure safety valve sizing requirements for the different relieving scenarios and provides guidance on how to select the proper relief valve type. Both over-sizing and under-sizing a relief valve can result in mechanical failures, thus it is critical that the valve sizing and selection are correct.
If a facility is being debottlenecked and modified all pressure safety valves that will be affected by the modification must be checked for adequate capacity. Many facilities are not applicable to the U.S. Occupational Safety and Health Administration (OSHA) Process Safety Management (PSM) Standard 29 CFR 1910.119 [6].It is strongly recommended that a Management of Change (MOC) procedure be used to ensure that no facility modification will pose a safety risk or undermine the existing safety equipment provided within the facility. Pressure safety valves for all modified systems must be verified to safely handle the new required rates and compositions that result from debottlenecking the facility.
In addition, it is essential that operation’s personnel are trained in the proper handling and testing of relief valves. There have been cases when operations and maintenance personnel have increased the set pressure on a pressure relief valve that was frequently relieving. The increase in set pressure results in the vessel operating above the stamped maximum allowable working pressure and may result in mechanical failure. Trained staff will understand that the solution to the problem is to correct the process condition that is resulting in the high pressure, not increase the set point on the pressure safety valve.
PSV Inlet and Discharge Piping
Another area that requires close attention is the proper design of the inlet and discharge piping of the pressure safety valves. API Recommended Practice 520, 5th Edition, Part 2 [7], and ANSI / API Standard 521 [5] provide guidance on the installation and design of the inlet and discharge piping for pressure safety valves.
For inlet piping to pressure safety valves, the recommended practice is to maintain the inlet hydraulic losses at no more than 3% of the set pressure of the pressure safety valve. This is because the relief valve is designed to normally close at 97% of the set pressure. A PSV with no inlet flow will sense the same pressure as exists in the protected equipment. Once open however, the pressure at the inlet to the relief will be the pressure at the protected equipment minus the friction loss in the inlet line. If this friction loss exceeds 3%, the valve will close and then reopen once the flow stops. This chattering can destroy the valve. Over sizing of a pressure safety valve can also result in “chatter” from essentially the same phenomenon. There is a potential for pressure relief valve or piping failure from prolonged “chattering” due to mechanical fatigue and potentially thermal fatigue.
If the inlet piping design cannot be configured to meet this requirement, then the use of a remote sensing pilot pressure safety valve can be used. This is not preferred due to the potential for the sensing line to plug or freeze.
Typically, relief valves are mounted almost directly on the equipment they protect. You will often find, however, that in existing plants this is not always the case. Some pressure safety valves may be located remotely with long inlet lines and the 3% criteria must be carefully checked. Even with new plant designs, there are times when the piping designer must locate the pressure safety valve remotely. It is important to always check the inlet line losses by utilizing the piping isometric drawings.
A study conducted by Berwanger, et al [1], found that 16% of all pressure safety valve installations reviewed were out of compliance with accepted engineering practices and standards as a result of improper installations. 35.5 % of these valves were out of compliance due to excessive inlet pressure drop. Experience indicates that in many older plants, the pressure safety valve inlet and discharge piping is set at the inlet size and outlet size of the pressure safety valve and the pressure drop calculations were not performed – or were performed on incorrect assumptions for inlet pipe routing. A crude oil fire occurred in a Shell facility as a result of improper inlet piping design. This caused severe vibration and caused a 6” flange to fail, losing containment of the process stream [8].
For systems with 600# ratings and above, the valve manufacturer may supply a relief valve with an inlet flange rating of 600# and an outlet flange rating of 300#. Be aware that a “typical” 150# flange rating on the PSV discharge piping is not always acceptable for the higher pressure systems. The velocity at the outlet of the pressure safety valve can not exceed sonic. Thus, for high pressure systems the flow through the relief valve may require a pressure greater than the max pressure rating of a 150# system to maintain sonic flow. It is important to check the pressure required to maintain sonic based on the size of the pressure safety valve outlet. If a 300# flange is required then a 300# pipe fitting is installed to expand the pipe to a diameter where the pressure corresponding to a 150# system is not exceeded. For large systems, it is recommended to use a flare network software program to predict the backpressure at the outlet of each pressure safety valve for various relief scenarios. During a fire, several reliefs may open simultaneously and the backpressure must be known at the outlet of each relieving pressure safety valve under these circumstances.
The piping design for the inlet and discharge of pressure safety valves should be reviewed to determine that the piping can meet the mechanical and thermal stresses that will develop when the pressure safety valves relieve. Threaded connections for high set pressure safety valves or on pressure safety valves that are installed near vibrating equipment are not recommended. The threaded connections have a tendency to fail or become “unscrewed” from the vibrations, and / or forces during relieving
Proper valve and discharge piping support design is essential. Piping and valve support becomes more critical on larger pressure safety valves and pressure safety valves that have high set pressures discharging to atmosphere. The reaction forces that can develop from the valves relieving to atmosphere can be significant. Even though the outlet piping may not be excessively long, the internal thrust created at the 90 degree elbow as the discharge piping turns up can be excessive. The flow will most likely be sonic velocity at the elbow and the discharge vent must be adequately supported to prevent failure. One incident occurred when the inlet piping on a 4X6 pressure safety valve set at 1350 psig failed. The valve became a projectile as a result. Fortunately, no one was hurt by flying debris and the gas line was isolated before the vapor cloud was ignited. This “near miss” was likely the direct result of poor welding and poor support on the valve installation.
The reaction forces in closed systems tend to be less, but in some cases the reaction forces in a closed system can become significant if there are sudden large pipe expansions or during unsteady flow conditions within the piping. Inadequate design and supports for pressure safety valves and the associated piping can result in mechanical failure during a relieving event.
Flare Header Design
If the pressure safety valve discharges into a flare header the superimposed and built up back pressure is critical and can impact the valves relieving capacity if the actual back pressure is higher than the originally calculated or assumed back pressure. The maximum allowable back pressure at which a pressure safety valve can function properly depends upon the type of the pressure safety valve. A study conducted by Berwanger, et al [1], found that almost 24% of all PSV installations reviewed were out of compliance with accepted engineering practices and standards because of improper installations. 12 % of these valves were out of compliance due to the outlet pressure drop being too high. If the built up back pressure is greater than the maximum value the valve can function with, then the upstream pressure of the valve will increase above the set pressure of the valve as a result. This condition increases the likelihood of a failure.
A flare network software program should be used to calculate backpressure in large relief systems. For most pressure safety valves the maximum flow that can pass through the orifice size is larger than the required relieving flow. The maximum flow must be used to calculate the inlet line loss and the resulting backpressure. Modulating pilot valves can be used, if required, to control the maximum flow that is required to be relieved. In the design of the flare system, several types of valves are available, as explained in API 520 Part 1 [4]. Conventional, bellows, and pilot valves are typically used. The valve manufacturer must be consulted to define the maximum flow and backpressure requirements for each type of valve. The final flare design can not be completed until the actual pressure safety valves have been selected.
Depending upon the fluids which are being relieved and the pressures involved, it is possible to have relieving events that require stainless steel discharge piping, Flare Header, Flare KO Drum and Flare Stack because of cryogenic relieving temperatures from the Joule-Thompson Effect through the pressure safety valve. There have been multiple cases where carbon steel flare headers have failed due to the cryogenic relieving temperatures that developed during relieving events. The failure of a flare header completely undermines the purpose of the Pressure Relief System, and can result in a catastrophic event.
In today’s’ market, the recovery of NGL’s from natural gas is quite common. Particular attention is required in designing the relief systems for the cryogenic vessels. The pressure safety valves most likely will be relieving cold (at -20 F or below) two phase fluids. The pressure safety valve downstream piping will be exposed to very cold temperatures when the valves relieve. The recommended method for sizing two phase flow valves is by utilizing the DIERS equations. API 520 Part 1, Appendix D [4] summarizes these equations and provides an example calculation. The calculation procedure is long and tedious but it is recommended to perform a hand calculation before utilizing in house spreadsheets. The couple of hours spent performing the calculation will provide valuable insight to the key parameters used in the equations and will serve as a verification check of a spreadsheet.
There should be no dead legs in any piping from the discharge of the relief valve to the Flare KO Drum. Any pockets or dead legs can fill with liquids which may result in excess back pressure during relieving events There may also be large reaction forces in the flare header as a result of the slug of liquids forced down the header. In 1999, the flare header of a Tosco refinery in California was overpressured due liquid accumulation at a low point in the flare header. This resulted in a facility shutdown.There were no injuries reported [9].
Flare KO Drum and Flare Stack / Tip
Flare KO Drum and Flare Stack sizing is also critical to the safety of the plant. Oil and Gas Industry Flares are designed to destroy vapor streams only and require an adequately sized Flare KO Drum to prevent flammable liquids from raining out of the flare tip. In determining the sizing, it is important that a Flare Study be conducted to determine the worst case scenario for Flare KO Drum and Stack capacity and to select the proper droplet size separation criteria that the selected flare tip can adequately destroy. ANSI / API Standard 521[5] provides guidance on sizing, design and selection of this equipment.
A good example of the consequences of liquids flowing out of a Vent Stack was the Texas City Refinery explosion of 2005. This catastrophic incident resulted in a process upset where the amount of liquids that flowed to the KO Drum overwhelmed the drum size, and flowed up the vent stack and to the surrounding atmosphere which resulted in the tragic explosion [10]. If a Flare would have been installed in the Texas City Refinery rather than a Vent Stack, the consequences of the event would have been reduced. The vapor phase hydrocarbons that were originally flowing to the vent stack would have been destroyed in the Flare Tip, and the vapor cloud that exploded would have been prevented. Flowing liquid hydrocarbons to a Flare Tip is still a dangerous situation. If a Flare KO Drum were overwhelmed with hydrocarbon liquids the Flare Stack would likely be raining fire, and not liquid hydrocarbons.
Based on the stack sizing, ANSI / API Standard 521 [5] outlines procedures to estimate the radiation effect from the flare. With today’s’ specialized design of flare stacks, consultation with the flare manufacturer is recommended for the radiation confirmation.
Depressurization Valves
In the gas processing industry, it has become a standard practice to block in the treating facility with Emergency Shut Down (ESD) Valves rather than depressure the entire facility to the flare. One primary reason for this philosophy is that natural gas fires are not equivalent to liquid hydrocarbon pool fires. Natural gas fire protection and mitigation requires different protection methods than for those used for fighting liquid hydrocarbon pool fires, which can be extinguished using a fire water system or a foam system. . It is standard natural gas industry practice to isolate the hydrocarbon gas sources to the facility and evacuate all personnel from the facility. Once the source of the gas is isolated, the feed to the fire is terminated and the fire is quickly extinguished from lack of fuel.
In the case where a facility must be depressurized in an upset condition, careful attention must be given to the design of the depressurization valves, their timing and flare capacity. There exists the potential to overwhelm the Flare Tip if the Tip was not designed for the high depressurization rates. In addition, consideration for required depressurization time, resulting Flare Header temperatures, and depressurization control schemes must be given close attention. These systems can be highly complex due to the transient nature of the process and require careful design procedures to ensure a safe Depressurization System.
By: Kindra Snow-McGregor
Senior Process Consultant and Instructor
References:
Non-Conformance of Existing Pressure Relief Systems with Recommended Practices, A Statistical Analysis, Patrick C. Berwanger, PE, Robert A Kreder, and Wai-Shan Lee. Berwanger, Inc., 2002.
AIChE. Emergency Relief System (ERS) Design Using DIERS Technology. American Institute of Chemical Engineers, New York, NY, 1995.
U.S. Chemical Safety and Hazard Investigation Board, Investigation Report, Catastrophic Vessel Overpressurization, Report No. 1998-002-I-LA.
Sizing, Selection, and Installation of Pressure-Relief Devices in Refineries, Part 1 – Sizing and Selection, API Recommended Practice 520, 7th Edition, January 2000.
ANSI / API Standard 521, / ISO 23251, Pressure Relieving and Depressuring Systems, 5th Edition, January 2007.
Occupational Safety and Health Standards, Process Safety Management of Highly Hazardous Chemicals, 29-CFR-OSHA-1910.119, 57 FR 23060, June 1, 1992; 61 FR 9227, March 7, 1996.
Sizing, Selection, and Installation of Pressure-Relief Devices in Refineries, Part 2 – Installation, API Recommended Practice 520, 5th Edition, August 2003.
Poor Relief Valve Piping Design Results in Crude Unit Fire, Politz, FC., API Mid-year Refining Meeting, 14 May 1985, Vol / Issue 64.
In this tip of the month (TOTM) we will present the results of several case studies showing the effect of gas molecular weight on the performance and efficiencies of centrifugal compressors. We have considered several “what if” scenarios such as variation of compressor speed as a function of molecular weight, while maintaining the same suction and discharge pressures and mass flow rate. Variation of polytropic head and efficiencies as a function of gas molecular weight for a given compression ratio, and compressor speed has also been studied. In addition, the impact of thermodynamic properties package has been studied.
Compressors can be generally classified in two categories:
Positive displacement; this type of compressor includes reciprocating, rotary screw, sliding vane, liquid ring and rotary lobe. The compression principle is volumetric displacement – reducing the gas volume increases pressure.
Kinetic or Dynamic: this type of compressor includes centrifugal and axial compressors. The compression principle is acceleration and deceleration of the gas – kinetic energy is converted to pressure rise.
Reciprocating and centrifugal compressors are the most popular compressors used in E & P applications. Rotary screw compressors are gaining in popularity in low to moderate pressure gas boosting service, refrigeration systems and fuel gas compression for gas turbines. Further detail may be found in reference [1].
From a calculation viewpoint alone, the power calculation is particularly sensitive to the specification of flow rate, inlet temperature and pressure, and outlet pressure. Gas composition is important but a small error here is less important providing it does not involve the erroneous exclusion of corrosive components. A compressor is going to operate under varying values of the variables affecting its performance. Thus the most difficult part of a compressor calculation is specification of a reasonable range for each variable and not the calculation itself. Maddox and Lilly [2] emphasize that using a single value for each variable is not the correct way to evaluate a compression system.
Normally, the thermodynamic calculations are performed for an ideal (reversible process). The results of a reversible process are then adapted to the real world through the use of an efficiency. In the compression process there are three ideal processes that can be visualized: 1) an isothermal process, 2) an isentropic process and 3) a polytropic process. Any one of these processes can be suitably used as a basis for evaluating compression power requirement by either hand or computer calculation. The isothermal process, however, is seldom used as a basis because the normal industrial compression process is not even approximately carried out at constant temperature.
Due to practical limitation the compression ratio per stage is often in the range between 2 and 6. For large overall compression ratio applications multistage compressors are used. The choice of the interstage pressure is an economic decision and can be estimated by equal compression ratios for each section but may be adjusted to minimize total power requirement.
In order to study the effect of feed gas molecular weight on the performance of centrifugal compressors, several computer simulations using HYSYS [3] were performed.The gas mixtures with the composition shown in Table 1 with molecular weights ranging from 18.2 to 23.17, corresponding to relative density of 0.63 to 0.80, respectively, were used in this study. The characteristics curves for the centrifugal compressors used in this study are shown in Figures 1 and 2. These performance curves were supplied to the simulation software and used in the course of simulations.
Case 1: Effect of Molecular Weight on Flow Rate for Fixed ?P (Constant Speed)
For a fixed inlet pressure of 700 kPa, 35 °C, and 15000 RPM, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In order to maintain the outlet pressure, the feed flow rate has to vary. We are essentially fixing P1 and P2 and wanting to see the effect on the compressor of varying molecular weight feed. The set up shown in Figure 3 was used to generate the simulation results. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figure 4. The PR EOS [4] is used for thermodynamic properties calculations.
Figure 4 indicates that as the relative density decreased, the flow rate must decrease. Note, for the case of compression ratio of 2.5, no convergence could be achieved for relative density of 0.63 and 0.65 due to the fact the surge limit had been reached. For the same case, the required power as a function of relative density is shown in Figure 5. Since, the flow rate decreased with decreasing relative density, the required power decreased.
Finally, the variation of polytropic head as a function of inlet actual volumetric flow rate is shown in Figure 6. Note that the relative densities are identified on this diagram to show their influence on the performance of the compressor.
Case 2: Variable Speed
As in the case 1, for a fixed inlet pressure of 700 kPa, 35 °C, and mass flow rate of 1000 kmol/hr, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In this case, the compressor is varying speed to maintain flow rate at the P speed imposed on it. The schematic setup to generate simulation results is shown in Figure 7. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figures 8 and 9. In addition to the results by the PR EOS, the results obtained by BWRS are shown on these diagrams. The difference between the results of these two EOS for these cases is negligible.
As shown in Figure 8, as the relative density increases, the compressor speed dropped. However, as relative density or molecular weight increased, the required power increased, see Figure 9.
As shown in Figures 10 and 11, the polytropic efficiency and head decrease with relative density. More detail of simulation results can be found in Reference [5].
Conclusions
The impact of relative density (molecular weight) on the performance of a centrifugal compressor was studied by performing a series of computer simulations. Based on the simulation results, it is found that:
For the same feed condition, compression ratio, compressor speed, the flow rates must decrease as the relative density decreases, and will eventually approach a surge condition.
For the same feed condition, compression ratio, compressor speed, as the relative density increases, the flow rate increases which results in more power consumption.
For the same feed condition and rate, and compression ratio, the compressor speed decreases with molecular weight but as expected, the power requirement increases.
The PR EOS and BWRS EOS produced the same simulation results
Campbell, J. M., “Gas Conditioning and Processing, Vol. 2, the Equipment Modules, 8th Ed., Campbell Petroleum Series, Norman, Oklahoma, 2001
Maddox, R. N. and L. L. Lilly, “Gas conditioning and processing, Volume 3: Advanced Techniques and Applications,” John M. Campbell and Company, 2nd Ed., Norman, Oklahoma, USA, 1990.
Peng, Y. D., Robinson, D. B., “A New Two-Constant Equation of State,” Ind. Eng. Chem. Fund., 15, 59, 1976
Moshfeghian, M., Bothamley, M., and Lilly, L.L., “Feed gas molecular weight affects performance of centrifugal efficiency,” Oil and Gas J., May 10, 2008
Engineers are frequently asked to calculate the fluid pressure drop in a piping system. Many software programs are available for solving complicated hydraulic problems; however’ they can be complex and difficult to use. In addition, there are many tables or shortcut methods that give adequate answers but they usually apply to predefined conditions which are sometimes misleading or less accurate. This “Tip of the Month” discusses a method of calculating friction pressure losses for liquid lines. A spreadsheet is presented that gives friction losses based on this method.
Background Information
Equation 1 is known as the Darcy-Weisbach (sometimes called the Darcy) equation and has been used by engineers for over 100 years to calculate fluid flow pressure loss in pipe. This equation is derived by dimensional analysis and relates the various parameters that contribute to the friction loss. A correction factor, called the Moody friction factor, is included which compensate theoretical results with the experimental results.
Where:
hL = Head loss due to friction, m [ft]
f = Moody friction factor
L = Pipe length, m [ft]
V = Velocity, m/s [ft/sec]
g = Gravitational acceleration, 9.81 m/sec2 [32.2 ft/sec2]
D = Inside diameter, m [ft]
The task of determining the friction factor can be difficult due to the many variables that influence flow behavior. For example, the friction factor is significantly different if the fluid flow exhibits Newtonian or non-Newtonian behavior, or if the flow is laminar or turbulent. Other variables that influence the friction factor are properties of the pipe represented by absolute roughness and inside diameter, and fluid parameters such as flow rate, viscosity and density.
The Moody diagram given in Figure 1 is a classical representation of the fluid behavior of Newtonian fluids and is used throughout industry to predict fluid flow losses. It graphically represents the various factors used to determine the friction factor. For example, fluids with a Reynolds number of 2000 and less, the flow behavior is considered a stable laminar fluid, and the friction factor is only dependent on the Reynolds number. The friction factor for the Laminar Zone is represented by Equation 2. Fluids with a Reynolds number between 2000 and 4000 are considered unstable and can exhibit either laminar or turbulent behavior. This region commonly referred to as the Critical Zone, and the friction factor can be difficult to accurately predict. Judgment should be used if accurate predictions of fluid loss are required in this region. Either Equation 2 or 3 are commonly used in the Critical Zone. Beyond 4000, the fluid is considered turbulent and the friction factor is dependent on the Reynolds number and relative roughness. For Reynolds numbers beyond 4000, the Moody diagram identifies two regions, Transition Zone and Completely Turbulent Zone. The friction factor represented in this region is given by Equation 3.
Figure 1. Moody Friction Factor Diagram
Where:
Re = Reynolds Number
V = Fluid velocity, m/s [ft/sec]
D = Inside diameter, m [ft]
e = absolute pipe roughness, m [ft]
? = Fluid density, kg/m3 [lbm/ft3]
µ = Fluid viscosity, kg/(m-s) [lbm/(ft-sec)]
The Method
The Colebrook formula, Equation 3, is used throughout industry and accurately represents the Transition and Turbulent flow regions of the Moody Diagram. However, this implicit equation is difficult to solve by manual methods. Typically an iterative method is used to solve the Colebrook equation. One method of solving this equation is with numerical analysis technique called Newton-Raphson’s1 Method. This successive approximation approach is represented by Equation 5, and involves 1) the Colebrook formula, 2) the first derivative of the Colebrook formula and 3) an initial guess. Since the Colebrook formula is a convergent equation, the solution is usually determined with less than four iterations.
A macro that solves the Colebrook formula is given in this spreadsheet. It is easily adapted to programmable calculators. The iterative method assumes that the following input variables are available:
Pipe inside diameter – mm [in]
Pipe length – m [ft]
Absolute roughness – m [ft]
Absolute viscosity – cP
Fluid relative density
Fluid flowrate – m3/h [gpm]
Example Problem
The macro begins with inputting the variables needed to solve for the Moody friction factor. Next, the macro determines the Reynolds Number. If the Reynolds value is below 2000 the flow is considered laminar and a simplified friction formula shown in Equation 2 is used. Above 2000 the flow is considered turbulent and the Colebrook formula is used. Finally, the Moody friction factor is determined and combined with the Darcy formula, Equation 1, to determine the fluid friction losses.
Numerous results were checked against values given in “Cameron Hydraulic Data Book”2 and found to vary by less than one percent. A term called “Delta-F” is also given in the spreadsheet which gives an indication of the variance in the Colebrook equation and the calculated value. Values of Delta-F less then 0.05 indicates an accuracy of three or more decimal places.
Alternate Method:
An alternate method of determining the friction factor is given by Chen3. His method of calculating the friction factor is explicit and does not require iterations to solve. This method has been by studied by Gregory and Fogarasi4, and found to give satisfactory values compared to the Colebrook equation. For those interested in this alternate approach, see Equation 6.
Where:
f = Fanning friction factor (1/4 of Moody friction factor)
D = Inside diameter, m [ft]
e = absolute pipe roughness, m [ft]
Re = Reynolds Number
To learn more about friction factor and its impact on piping and pipeline calculation, design and surveillance, refer to JMC books and enroll in our ME41, PL4, PL61, and G4 courses.
By: Joe Honeywell
Instructor & Consultant
References:
“Elementary Numerical Analysis”, by S. D. Conte, McGraw-Hill Book Company, 1965, pp 30
“Cameron Hydraulic Data Book”, by Ingersoll-Rand Company, Woodcliff, N. J., 15 ed., pp 3-49 to 3-85
Chen, N.H., An Explicit Equation for Friction Factor in Pipe, Ind. Eng. Chem. Fund., 18, 296,1979
Gregory, G.A. and Fogarasi, F., Alternate to Standard Friction Factor Equation, Oil & Gas Jour. Apr. 1 1985, pp 127.
