Note: The source of the technical material in this volume is the Professional Engineering Development Program (PEDP) of Engineering Services. Warning: The material contained in this document was developed for Saudi
Aramco and is intended for the exclusive use of Saudi Aramco’s employees. Any material contained in this document which is not
already in the public domain may not be copied, reproduced, sold, given, or disclosed to third parties, or otherwise used in whole, or in part, without the written permission of the Vice President, Engineering Services, Saudi Aramco.
Chapter : Instrumentation For additional information on this subject, contact File Reference: PCI10302 J.R. Van Slooten on 874-6412
CONTENTS PAGE
MANUALLY SIZING CONTROL VALVES FOR LIQUID APPLICATIONS 1
The Importance Of Sizing 1
Undersizing Problems 1
Oversizing Problems 1
Fluid States 2
Fluid States And Sizing Equations 2
Scope Of Presented Equations 2
Guidelines For Capacity vs. Percent Of Rated Travel 3
Sizing For Maximum, Normal, And Minimum Flow Conditions 3
Tendency To Oversize Valves 3
Valve Manufacturer's Guidelines 3
Saudi Aramco Standards 4
Converting Degrees Rotation To Percent Travel 4
The Basic Liquid Flow Equation 5
Predicting Flow Through A Restriction 5
Solving For Required Valve Cv 5
ISA Standards 6
Recognized Valve Sizing Standards 6
ISA Forms Of The Basic Sizing Equation 6
Terms In The ISA Equation 8
Choked Flow 9
Limits Of The Basic Liquid Sizing Equation 9
Pressure And Velocity Profiles 10
Pressure Recovery 11
Saudi Aramco DeskTop Standards
Implications Of Choked Flow For Sizing 15
Calculating the Allowable Pressure Drop 16
Valve Recovery Coefficient 16
Solving For DP Allowable 18
Implementing Choked Flow Equations 21
Piping Geometry 22
Significance Of Pipe Fittings In Valve Sizing 22
ISA Corrections For Swaged Lines 22
Piping Factors And Choked Flow 27
Limitations Of Calculated FLP 28
Alternate Methods For Calculating Swage Effects 30
Viscosity Corrections 31
Flow Regimes 31
Impact Of Flow Regime On Valve Sizing 32
Reynolds Numbers 32
ISA Equations For Non-Turbulent Flow 33
Other Viscosity Correction Methods 35
Summary Of Valve Sizing Equations 36
ISA Method 36
Equations Used By Fisher Controls And Others 38
COMPUTER SIZING CONTROL VALVES FOR LIQUID APPLICATIONS 39
Introduction to the Fisher Sizing Program 39
Benefits Of Computer Sizing Methods 39
Overview Of The Fisher Sizing Program (FSP 1.4) 39
Overview of Program Operation 40
Booting The Program 40
Project Information 40
Main Menu 40
Selecting Units 41
Selecting Variables And Conditions 43
Valve Sizing Calculation Screen 44
Selecting Calculation Options 45
Other Important Operations 48
COMPUTER SIZING CONTROL VALVES FOR GAS AND STEAM APPLICATIONS49
Introduction 49
Differences In Compressible and Incompressible Fluid Flow 49
Use Of Computer Software 49
The ISA Sizing Equations For Compressible Fluids 49
Popular Standard 49
Saudi Aramco Standards 49
Alternate Forms Of The ISA Equation 49
Nomenclature 51
Numerical Constants 51
Basic Equation 52
Choked Flow 53
Expansion Factor: Y 56
Adapting The Equation For Use With Gasses Other Than Air 61
Real Gas Behavior 63
Piping Effects 65
Final Equation Form 67
Summary Of ISA Equation Terms 67
Computer Sizing Control Valves For Gasses Using The ISA Equations 68
Introduction 68
Valve Sizing Methods Available 68
Selecting The Desired Calculation Type 69
Saudi Aramco DeskTop Standards
Fisher And ISA Equation Comparison 72
Equation Basics 73
Equation Limits 74
Pressure Recovery And Critical Flow 75
Blending The Two Equations 76
The C1 Factor 78
Mechanics Of The Sine Term 80
Alternate Forms Of The Universal Sizing Equation 81
Solving for Cg 84
Comparison Of Fisher And ISA Gas Sizing Equations 85 Computer Sizing Control Valves For Gasses Using The Fisher Controls
Equations 86
Valve Sizing Methods Available 86
Selecting A Calculation Type 87
Overview Of Sizing Procedures 87
F3 Options 88
ENTERING VALVE SIZING DATA ON THE SAUDI ARAMCO ISS 91
Body And Flange Size 91
Control Valve Physical Size Information 91
Capacity Ratings 91
Capacity At Minimum, Normal, And Maximum Flow Conditions 91 Valve Travel At Minimum, Normal, And Maximum Flow Conditions 91 WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZE
CONTROL VALVES FOR LIQUID APPLICATIONS 93
Work Aid 1A: Procedures That Are Used To Calculate The Required
Control Valve Cv 93
Work Aid 1B: Procedures That Are Used To Calculate The Allowable
Pressure Drop (DPallow) 94
Work Aid 1C: Procedures That Are Used To Calculate The Effect Of
Work Aid 1D: Procedures That Are Used To Calculate The Effect Of
Laminar Flow On Cv 96
WORK AID 2: PROCEDURES THAT ARE USED TO COMPUTER SIZE
CONTROL VALVES FOR LIQUID APPLICATIONS 97
Work Aid 2A: Procedures That Are Used To Computer Size Control
Valves For Water Applications 97
Work Aid 2B: Procedures That Are Used To Computer Size Control
Valves For Choked Flow 100
Work Aid 2C: Procedures That Are Used To Computer Size Control
Valves For Fluids In The Sizing Database 101 Work Aid 2D: Procedures That Are Used To Computer Size Control
Valves With Piping Factor Correction 103
Work Aid 2E: Procedures Used To Computer Size Control Valves
With Viscosity Correction 105
Work Aid 2F: Procedures That Are Used To Computer Size Control
Valves With Viscosity And Piping Factor Correction 108 Work Aid 2G: Procedures That Are Used To Computer Size Control
Valves For Minimum, Normal, And Maximum Flow
Conditions 110
Work Aid 2G: Procedures That Are Used To Computer Size Control Valves For Minimum, Normal, And Maximum Flow
Conditions, cont'd. 112
WORK AID 3: PROCEDURES THAT ARE USED TO COMPUTER SIZE CONTROL VALVES FOR GAS AND STEAM
APPLICATIONS 114
Work Aid 3A: Procedures That Are Used To Computer Size Control
Valves For Ideal Gasses With The ISA Method 114 Work Aid 3B: Procedures That Are Used To Computer Size Control
Valves For Real Gasses With The ISA Method 115 Work Aid 3C: Procedures That Are Used To Computer Size Control
Valves For Vapors With The ISA Method 116
Saudi Aramco DeskTop Standards
Work Aid 3G: Procedures That Are Used To Computer Size Control
Valves For Vapors With The Fisher Method 120 Work Aid 3H: Procedures That Are Used To Computer Size Control
Valves For Steam With The Fisher Method 121 Work Aid 3I: Procedures That Are Used To Calculate The Effect Of
Compressibility On Valve Size 122
Work Aid 3J: Procedures That Are Used To Computer Size Control
Valves For All Flow Conditions 124
WORK AID 4: PROCEDURES THAT ARE USED TO ENTER VALVE
SIZING DATA ON THE SAUDI ARAMCO ISS 127
LIST OF FIGURES PAGE Figure 1 Fluid States as A Function of Pressure And Heat Content 2 Figure 2 Typical Vendor Recommendations For Percent Travel Versus
Flow 3
Figure 3 Guidelines For Percent Travel At Various Flow ConditionsPer
Section 5.2 of SAES-J-700 4
Figure 4 Units Constants For The ISA Liquid Sizing Equations 7
Figure 5 Pressure And Flow Relationships 9
Figure 6 Pressure And Velocity Profiles Around A Restriction 10
Figure 7 Comparison Of High And Low Recovery Valves 11
Figure 8 Fluid Vaporization When Pvc < Pv 12
Figure 9 Pressure And Flow Relationships 13
Figure 10 Pressure Profiles For Flashing And Cavitating Flows 14 Figure 11 Generalized Relationship Of Pvc To Pv For High And Low
Recovery Valves At Different Pressure Drops 17
Figure 12 Critical Pressure Ratios For Liquids Other Than Water 19
Figure 13 Critical Pressure Ratios For Water 19
Figure 14 Flow Limiting Influences Of Reducers And Expanders 23 Figure 15 Piping Factor Effect Vs. Travel For Different Valve Styles 26 Figure 16 R Values That Are Used In The Piping Factor Correction
MethodThat Is Included In Section 5.4 Of SAES-J-700 30 Figure 17 Flow Profiles Of Laminar And Turbulent Flow Regimes 31
Figure 18 Viscosity Conversion 34
Figure 19 Valve Reynolds Number Vs. The Reynolds Number Factor FR 35
Saudi Aramco DeskTop Standards
Figure 21 Screen That Appears When The Units Option Under Config Is Selected 41
Figure 22 Drop-Down Menu That Lists Valve Sizing Methods 42
Figure 23 Options For Variables To Solve For 43
Figure 24 Calculation Screen For ISA Liquid Sizing 44
Figure 25 Calculation Options 45
Figure 26 Pull-Down Menu That Lists Units Options For Q 46 Figure 27 Pull-Down Menu That Lists Fluids In The Sizing Database 47 Figure 28 Table Of Values That Is Displayed When The F9 Key Is Pressed 48 Figure 29 Numerical Constants For The ISA Gas Sizing Equations 51
Figure 30 Gas Flow And Pressure Relationships 52
Figure 31 Choked Flow As A Function Of xT 53
Figure 32 Effects Of k On FKxT And qmax 55
Figure 33 Pressure And Flow Relationships As x Increases From 0.02 To
xT 56
Figure 34 Reduced Pressure PVC Leads To Reduced Fluid Density And
Reduced Flow 57
Figure 35 Effect of Sonic Velocity On Flow 58
Figure 36 Effect of Vena Contracta Enlargement 59
Figure 37 Relationships Among x, FkxT, And Y 60
Figure 38 Generalized Compressibility Chart 64
Figure 39 Valve Sizing Method Options 68
Figure 40 Available Calculation Types 69
Figure 41 Valve Sizing Screen For The ISA Gas Valve Sizing Method 69 Figure 42 Calculation Options For The ISA Gas Valve Sizing Method 70
Figure 43 Line-By-Line Units Options For Flow 71
Figure 44 Actual Flow Versus Predicted Flow 74
Figure 45 Critical Flow For Low And High Recovery Valves 75
Figure 46 Predicting Low Flow And Critical Flow 76
Figure 47 Tested Values Of Flow Compared To A Sine Curve 77
Figure 48 Comparison of Cv, Cg, and C1 Values 79
Figure 49 C2 Factor Versus k 82
Figure 50 Comparison of ISA and Fisher Sizing Terms 85
Figure 51 Valve Sizing Methods 86
Figure 52 Selection Of A Calculation Type 87
Figure 53 Valve Sizing Screen For The Fisher Real Gas Sizing Method 87 Figure 54 Calculation Options For The Fisher Ideal Gas Sizing Method 88 Figure 55 Calculation Options For The Fisher Real Gas Sizing Method 88 Figure 56 Calculation Options For The Fisher Vapor Sizing Method 89 Figure 57 Calculation Options For The Fisher Steam Sizing Method 89
Figure 58 Pull-Down Menu Options For Temperature 90
Saudi Aramco DeskTop Standards 1
Manually sizing control valves for liquid applications The Importance Of Sizing
While control valve selection is an "art," control valve sizing is closer to a "science". Valve sizing procedures are based on accepted mathematical equations that are used to model flow through ideal restrictions such as orifice plates and flow nozzles. While control valves do not always resemble ideal restrictions, the mathematical models generally give useful results if the specifier inputs accurate data. However, if the service conditions and fluid properties that are used as inputs to the sizing process are not accurate, the specifier may be led to the selection of a control valve that is either undersized or oversized for the application.
Undersizing Problems
Limited Flow Capacity is the primary concern of control valves that are too small. Limited capacity may have economic impact, such as the inability to meet production quotas. Limited capacity may result in process failure because of the inability to supply needed fluids in sufficient quantity. Inadequate capacity can also result in safety hazards; for example, an undersized control valve that is used in a relief application may allow upstream pressure to reach unsafe levels.
Oversizing Problems
Excessive Seat Wear is a common result of oversizing control valves. A valve with excess capacity may spend most of its life throttling near the seat. Sustained throttling with the plug near the seat causes high velocity flow that impinges on and around the seating surfaces. Rapid wear and premature valve failure can result.
Safety is also a key issue; for example, if an oversized valve feeds a relief system, the relief system may have insufficient capacity to control the excess input to the relief system.
Stable Control is another problem that is associated with oversized valves. Process gain is typically quite high when the valve closure member operates near the seat. The high gain can cause large changes in the process variable, which results in instability. In addition, any friction or deadband in the valve has a pronounced effect on
performance at extremely low valve lifts.
Basic Economics are a concern because excess capacity generally comes at an increased, but unnecessary cost.
Fluid States
Fluid States And Sizing Equations
Fluid behavior, including flow rate as a function of pressure and temperature conditions, depends on the fluid state (i.e., whether the fluid is in a liquid, gas, vapor, or other state); accordingly, several different sizing equations are available that can be used to calculate the flow rate or to calculate the required control valve Cv. The chart below (see Figure 1)
illustrates how a fluid state can change as a function of pressure and enthalpy (heat content).
Figure 1
Fluid States As A Function Of Pressure And Heat Content Scope Of Presented Equations
Many complexities are involved in predicting either valve capacity (Cv) or flow rate (q) when
Saudi Aramco DeskTop Standards 3
Guidelines For Capacity vs. Percent Of Rated Travel
Sizing For Maximum, Normal, And Minimum Flow Conditions
While it is sometimes tempting to select and size control valves for the maximum flow condition only, it is equally important to calculate Cv requirements at normal and minimum flow conditions.
Sizing for maximum flow ensures adequate capacity.
Sizing for normal flow conditions allows the specifier to ensure that the valve will normally throttle in a range of travel (or percentage of maximum valve Cv) that provides good control
and sufficient reserve capacity.
Sizing for minimum flow conditions allows the specifier to ensure that the valve is capable of providing stable control at the low-flow condition. Most valves are designed to provide good control down to about 10 percent of rated travel. Throttling below 10 percent travel can cause system instability because of the high valve gain at low lifts, and it can cause high velocity flow that results in accelerated seat wear.
Tendency To Oversize Valves
In many engineering environments, several individuals or groups may have direct or indirect input to the valve sizing process. All too often, each individual or group adds a 'safety margin' when providing information. Specifiers should remain aware that the most common control valve problem is the oversized valve, and they should strive to use actual service conditions when sizing control valves.
Valve Manufacturer's Guidelines
Most valve manufacturers use a rule of thumb that establishes acceptable percentages of travel for the minimum, normal, and maximum flow conditions. The flow versus travel recommendations that are shown in Figure 2 are common.
Flow Condition Percent Of Rated Travel
Minimum 10
Normal 20-80
Maximum 90
Figure 2
Saudi Aramco Standards
Section 5.2 of SAES-J-700 contains guidelines for the percentage of valve travel that
produces the normal and maximum flow rates. The recommended percentages vary with the inherent valve characteristics as shown in Figure 3.
Flow Characteristic Percent Travel At Normal Flow
Percent Travel At Maximum Flow
Equal Percentage 80 93
Linear 70 90
Modified Parabolic 75 90
Figure 3
Guidelines For Percent Travel At Various Flow Conditions Per Section 5.2 of SAES-J-700
Converting Degrees Rotation To Percent Travel
The guidelines for travel versus flow are expressed in percent travel and apply directly to sliding-stem valves; however, travel for rotary-shaft valves is expressed in degrees rotation. In order to apply the recommended percentages listed above to rotary-shaft control valves, percentages of travel must be converted to degrees rotation; for example, if the maximum acceptable travel for a given condition is 93 percent, the equivalent rotation is approximately 84 degrees (0.93% x 90 degrees = 84 degrees).
Saudi Aramco DeskTop Standards 5
The Basic Liquid Flow Equation
Predicting Flow Through A Restriction
Basic (Fisher) Flow Equation - Most sizing procedures are based on concepts and equations that are used to describe flow through orifice plates and flow nozzles. The most common and basic form of the liquid flow equation is as follows:
Q C P G v = ∆ (1) Where:
Q = The flow rate in gallons per minute (gpm).
Cv = A coefficient that is assigned by valve manufacturers to describe how much flow a specific valve will pass under standard conditions (i.e., the test fluid is water with a specific gravity of 1.0, and the pressure drop across the valve is 1 psi).
∆P = The pressure drop across the valve in psi; (∆P = P1-P2). G = The specific gravity of the fluid.
Major Assumption - In reality, the flow rate through a restriction is a function of the pressure drop between upstream pressure and the pressure at the limiting flow area of the restriction, which is called the vena contracta; however, Equation 1 provides the basis for developing the complete equation.
Solving For Required Valve Cv
Rearranging the equation to solve for the control valve Cv results in the base equation that is used for sizing valves for non-compressible fluids (liquids).
C Q G
P
v = ∆
ISA Standards
Recognized Valve Sizing Standards
ISA - One organization that publishes standards that are widely accepted for control valve sizing is the Instrument Society of America (ISA). The ISA standard that includes the valve sizing equations is ANSI/ISA-S75.01-1985.
Section 5.1 Of SAES-J-700 requires the use of the ISA equations for valve sizing, but it also allows the use of other methods that are based on the ISA equations.
ISA Forms Of The Basic Sizing Equation
The ISA forms of the basic equations that have been discussed to this point are:
To Predict Flow - To predict flow, the basic form of the ISA equation is as follows:
q N C p p
G v
f
= 1 1− 2 ( 3 )
To Calculate Control Valve Cv - To calculate the control valve Cv that is required to pass
a specified flow rate, the equation is as follows:
C q N G p p v= f − 1 1 2 ( 4 ) Where:
q = The volumetric flow rate.
N1 = A numerical constant for units of measurement (see Figure 4). Cv = The control valve flow coefficient.
Gf = The liquid specific gravity at upstream conditions; the ratio of the fluid density at the valve inlet to the density of water at 60 degrees F (15.6 degrees C).
p1 = The upstream absolute pressure, psia. p2 = The downstream absolute pressure, psia.
Saudi Aramco DeskTop Standards 7
Units Constants - The following table includes the values of some of the constants that are used in the various forms of the ISA sizing equation.
Constant Units That Are Used In Equations
N w q p, ∆∆P d, D γγ1 νν N1 0.0865 --- m3/h kPa --- --- ---0.865 --- m3/hr bar --- --- ---1 --- gpm psia --- --- ---N2 0.00214 --- --- --- mm --- ---890 --- --- --- in --- ---N4 76 000 --- m3/h --- mm --- centistokes 17 300 --- gpm --- in --- centistokes N6 2.73 kg/h --- kPa --- kg/m3 27.3 kg/h --- bar --- kg/m3 63.3 lb/h --- psia --- lb/ft3 Figure 4
Units Constants For The ISA Liquid Sizing Equations.
The constant N1 is included in Equations 3 and 4 The constants N2 through N6 are used in
Terms In The ISA Equation
ISA Equation Compared To The Generic Equation - The ISA liquid flow sizing equation (Equation 6) differs in minor ways from the generic form of the equation (Equation 5), as shown below: Generic: C Q G P v= ∆ (5) ISA: C q N G p p v = −f 1 1 2 (6)
Minor Differences - Note that the ISA equation uses: • a lower case 'q' for flow rate.
• the term p1-p2 instead of ∆P to describe pressure drop across the valve. • the term Gf instead of G for the specific gravity of the fluid.
• The term N1, which is a units constant. By selecting the proper constant, the specifier may apply the equation by using either metric or English measurement units. Conversions are possible with the generic equation as well. ISA vs. Generic Equation Similarities - Despite minor differences in nomenclature, the two equation forms are algebraically identical, and as a result, they will give identical results. The only exception is the use of the N1 term (units constant) in the ISA
equation; however, a units conversion factor can be applied to any sizing equation. Common Use Of Equation Forms - When reviewing sizing catalogs, technical articles, and other documentation, specifiers will commonly encounter both the ISA nomenclature and minor departures from the ISA nomenclature that some valve manufacturers employ.
Saudi Aramco DeskTop Standards 9
Choked Flow
Limits Of The Basic Liquid Sizing Equation
Predicted Flow - The basic liquid sizing equations that have been discussed to this point predict an increase in flow for every increase in the square root of the pressure drop as shown in Figure 5 below. In reality, the relationship between pressure drop and flow rate only holds true for a limited range of conditions.
Choked Flow - In every application, it is possible to reach a point at which increasing the pressure drop by reducing P2 does not result in a proportional increase in flow. At
some pressure drop limit, a condition of maximum flow is realized in spite of increases in the pressure drop across the valve. The condition of maximum flow is known as choked flow and is represented with Qmax or Qchoked.
Predicting Qmax and ∆∆Pchoked - Equations have been developed that can be used to predict the value of Qmax (Qchoked) with relative certainty. The equations that are used
to predict choked flow make use of a computed value that is referred to either as
∆Pchoked or ∆Pallow. When the computed value of ∆Pchoked or ∆Pallow is larger than
the actual ∆P across the valve, the specifier knows that choked flow exists. When choked flow does exist, the maximum pressure drop that can be used for sizing purposes is the computed value of ∆Pchoked or ∆pallow.
Figure 5
Pressure And Velocity Profiles
A plot that shows mean fluid pressure and mean velocity profiles at and around a control valve helps to explain the mechanics of choked flow. Refer to Figure 6.
Vena Contracta - Recall that as a fluid passes through a restriction such as a control valve, the flowstream continues to neck down to a minimum cross-sectional area. The point of minimum cross-sectional area is known as the vena contracta. The vena contracta may be located at the control valve port, or it may be located downstream of the valve, depending on service conditions and valve style.
Pressure And Velocity At The Vena Contracta - At the vena contracta, fluid velocity increases to a maximum. In accordance with Bernoulli's equation, the increase in velocity is accompanied by a decrease in pressure. The low pressure at the vena contracta is referred to as Pvc.
Figure 6
Saudi Aramco DeskTop Standards 11
Pressure Recovery
Pressure Recovery Defined - The difference between Pvc and P2 is referred to as pressure
recovery. P2 is a fixed value that is dictated by the process, while the pressure at the
vena contracta (Pvc) is a function of valve style and geometry.
High Recovery vs. Low Recovery Control Valves - Low recovery (globe style) control valves produce a relatively small pressure dip at the vena contracta. High recovery valves (ball and butterfly valves) produce a greater pressure dip at the vena contracta. Refer to Figure 7 below. Whether a valve is a high recovery or low recovery type has a significant bearing on the pressure drop at which choked flow occurs.
Figure 7
Fluid Vapor Pressure
Defined - All subcritical, single-species fluids have a vapor pressure (Pv). Vapor
pressure is the pressure at which a fluid at a stated temperature will begin to change state from the liquid to the vapor phase. The liquid-to-vapor change of state can be thought of as causing a liquid to boil by reducing the fluid pressure, as opposed to increasing the fluid temperature.
Pvc vs Pv - As the pressure at the vena contracta is reduced to the vapor pressure of the fluid (see Figure 8), the fluid will begin to vaporize. The fluid now consists of a mixture of a liquid and vapor. The fluid is no longer incompressible (a liquid); therefore, the basic liquid flow equation is no longer valid.
Figure 8
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Mechanics Of Choked Flow
Increasing Pressure Drop And Fluid Density - Once the Pvc has fallen below the Pv, further
increases in the pressure drop result in additional vapor bubble formation and a further reduction in the density of the fluid mixture. The decrease in fluid density offsets any increase in the velocity of the mixture; as a result, no additional mass flow is realized. Refer to Figure 9. Vapor formation and the subsequent reduction in fluid density help to explain the phenomenon of choked flow.
Figure 9
Associated Phenomenon - Whenever the fluid pressure at the vena contracta falls below the fluid vapor pressure, one of two other phenomena will occur in conjunction with choked flow. The fluid will either be cavitating or flashing, depending, as shown in Figure 10, on the value of P2.
Figure 10
Saudi Aramco DeskTop Standards 15
Cavitation
Cavitation Defined - If downstream pressure (P2) recovers to a pressure that is greater
than the local vapor pressure (Pv) of the fluid, the vapor cavities collapse and the fluid
mixture reverts to a liquid. The entire liquid-vapor-liquid phase change is known as cavitation.
Cavitation Damage results from the collapse of millions of tiny vapor cavities on boundary surfaces. Depending on cavitation intensity, proximity to critical surfaces, and time of exposure, the micro-jets and the shock waves that are associated with the collapse of vapor cavities can produce extreme damage to valves and other
components. Cavitation damage has a characteristic appearance that is rough and cinderlike.
Anti-Cavitation Trim is available for many valves to reduce or eliminate cavitation damage. These special trim designs will be discussed in another module in this course.
Flashing
Flashing Defined - If downstream pressure remains at or below the local vapor pressure of the fluid, the vapor remains in the fluid stream, and the mixture is said to be flashing.
Flashing Damage results from liquid droplets impinging on metal surfaces at high velocity. Flashing damage has a smooth and polished appearance.
Selection Of Valves For Flashing Fluids follows the same general strategy as valve selection for other erosive applications, including the selection of harder body materials, hard trim, flow-down angle bodies, and replaceable liners.
Implications Of Choked Flow For Sizing
It is important for the specifier to identify the presence of choked flow. If the presence of choked flow is not identified and accounted for, the basic flow equation can grossly over predict the flow capacity of the control valve. In addition, choked flow is always accompanied by either flashing or cavitation, which must be considered during valve selection and sizing.
Calculating the Allowable Pressure Drop
All sizing methods include provisions for determining the onset of choked flow. The onset of choked flow is determined by calculating the maximum flow-producing pressure drop
(∆Pallow or ∆Pchoked).
Valve Recovery Coefficient
Pressure Recovery Coefficient Defined - The valve pressure recovery coefficient (or simply, recovery coefficient) plays a major role in calculating the ∆Pallow or the ∆Pchoked. The recovery coefficient accounts for the influence of the valve's internal
geometry on its capacity at the choked flow condition. The equations that are included in ISA Standard S75.01 use the term FL to express the recovery coefficient. Some
manufacturers also use the coefficient Km. Manufacturers determine the value of FL
and/or Km for each valve style by test, and they publish the coefficients along with
other sizing information.
Equation For Determining The Valve Recovery Coefficient - The valve recovery coefficient relates the valve pressure drop to the drop at the vena contracta as follows:
ISA: F P P P P L vc = − − 1 2 1 (7) Fisher: K P P P P m vc = − − 1 2 1 (8) Note that FL2 = Km. Where:
FL = The valve recovery coefficient (ISA).
Km = An alternate form of the valve recovery coefficient (Fisher Controls and others).
Saudi Aramco DeskTop Standards 17
Interpreting Values of Km or FL - Typically, values of Km and FL are much larger for low
recovery globe style valves than for high recovery ball and butterfly valves. Refer to Figure 11 and note that high recovery valves tend to choke at lower pressure drops than low recovery valves do because high-recovery valves produce a greater pressure dip at the vena contracta. Low recovery valves produce a smaller drop at the vena contracta; therefore, more pressure drop can be taken across the valve before Pvc
approaches Pv.
Figure 11
Generalized Relationship Of Pvc To Pv For High And Low Recovery Valves At Different Pressure Drops
Recovery Coefficients For Globe Valves - Most manufacturers usually publish only one pressure recovery coefficient for each style and size of globe valve. The recovery coefficient applies to all percentages of travel. Typical recovery coefficients for sliding stem valves are Km= 0.7 to 0.8 or FL = 0.8 to 0.9. (Remember that FL2 = Km)
Recovery Coefficients Rotary-Shaft Valves - For ball, butterfly, and other high-efficiency (high recovery) valves, the value of the recovery coefficient can vary significantly with the percent of valve travel; therefore, the recovery coefficient for a specific angle of opening must be used in the sizing equations. Typical values are Km = 0.4 to 0.6
Solving For ∆P Allowable
Rearranging The Equation - The usefulness of the equations to calculate the recovery coefficient (Equations 7 and 8) becomes more apparent when the equations are rearranged to solve for the flow limiting pressure drop, as shown in Equations 9 and 10. ISA: F P P P P L vc = − − 1 2 1 arranges to ∆P choked = FL2 (P1-Pvc) (9) Fisher Controls: K P P P P m vc = − − 1 2 1 arranges to ∆Pallow = Km (P1-Pvc) (10)
From the above, it becomes clear that the value of the recovery coefficient can be used to predict ∆Pchoked for a specific set of service conditions.
Problems In Determining Pvc - While Equations 9 and 10 allow the specifier to calculate
∆Pchoked, the problem of how to determine the pressure at the vena contracta (Pvc)
remains.
Calculating Pvc - It has been theoretically established(1) that the Pvc at the choked flow condition can be estimated as a nonlinear function of the fluid vapor pressure
multiplied by the value of the critical pressure ratio. This hypothesis is included in the Appendix of the ISA Standard S75.01 - 1985. The critical pressure ratio is identified in the Fisher nomenclature as rc, and it is identified in the ISA nomenclature as FF. Refer to Equations 11 and 12.
Fisher: Pvc=rc Pv (11)
ISA: Pvc=FF Pv (12)
Where:
FF = rc = The critical pressure ratio. Pv = The vapor pressure of the fluid.
Although the value of rc (FF) is actually a unique function for each fluid and the
prevailing conditions, it has been established that data for a variety of fluids can be generalized, thereby allowing the use of rc (FF) in a wide range of sizing applications.
The value of rc can be determined from plots or with the use of a simple equation.
1. Stiles, G.F., "Development of a Valve Sizing Relationship for Flashing and Cavitation Flow", proceedings of the First Annual Final Control Elements Symposium, Wilmington, Delaware, USA, Delivered May 14-16, 1970.
Saudi Aramco DeskTop Standards 19
Determining The Value Of rc For Non-Water Liquids - For liquids other than water, the plot that is shown in Figure 12 is used. The ratio of the fluid vapor pressure to the fluid critical pressure is shown on the X axis. At the point where the vapor pressure to critical pressure ratio intersects the curve, the critical pressure ratio (rc) is read from the Y axis. 1.0 0.9 0.8 0.7 0.6 0.5 0 .10 .20 .30 .40 .50 .60 .70 .80 .90 1.00 Vapor Pressure - PSIA
Critical Pressure - PSIA
Citical Pressure Ratio - r
c
A4148
Figure 12
Critical Pressure Ratios For Liquids Other Than Water
Calculating The Value Of rc For Water - A special rc curve allows the straightforward determination of rc for water (see Figure 13). Vapor pressure is shown on the X axis. At the point where the vapor pressure intersects the curve, the critical pressure ratio (rc) is read from the Y axis.
Critical Pressure
Ratio--r c 1.0 0.9 0.8 0.7 0.6 0.5 0 500 1000 1500 2000 2500 3000 3500 Vapor Pressure---PSIA A4147 Figure 13
Locating Values - The vapor pressure and critical pressure of the fluid may be
supplied to the valve specifier in a description of the process, or they may be found in any one of a number of references that give properties of fluids.
Equation For rc - An equation has also been developed that allows the specifier to calculate an approximate value of rc for a variety of fluids (1).
rc = FF = 0.96 - 0.28 (Pv/Pc )1/2 (13)
Calculating ∆∆Pchoked (∆∆Pallow) - Because the pressure at the vena contracta (Pvc) can be
calculated, the equations to calculate the flow-limiting pressure drop can be completed. The ISA equations are as follows:
∆Pchoked = FL2 (P1-Pvc) (14)
and Pvc=FF Pv (15)
so ∆Pchoked = FL2 (P1-FF Pv) (16)
The Fisher equations (as shown below) are similar in appearance and are functionally identical to the ISA equations.
∆Pallow = Km (P1-Pvc) (17)
and Pvc=rc Pv (18)
so ∆Pallow = Km (P1-rc Pv) (19)
Where:
FL = The valve recovery coefficient, dimensionless (ISA).
FF = The liquid critical pressure ratio factor, dimensionless (ISA). Pv = The liquid vapor pressure, psia.
Pvc = The fluid pressure at the vena contracta, psia.
Km = The valve recovery coefficient, dimensionless (Fisher and others). rc = The liquid critical pressure ratio, dimensionless (Fisher and others).
Saudi Aramco DeskTop Standards 21
Implementing Choked Flow Equations
ISA Sizing Equation For Choked Flow - The ISA standard includes the following equations: q N F C p F p G L v F v f max= 1 1− and C q N F G p F p v L f F v = − max 1 1 (20)
Two options are available for use of the equations. If it is known that flow is choked, the equations that are shown above may be used directly. If it has not yet been determined if choked flow exists, the specifier may first calculate the ∆Pchoked by
using Equation 16. Then, the lesser of either the actual ∆P or the ∆Pchoked is used in
the basic sizing equations.
C q N G p p v= f − 1 1 2 and q N C p p G v f = 1 1− 2 (21)
Fisher Controls Sizing Equation - The standard procedure for use of the Fisher equation is to first calculate the allowable pressure drop with:
∆Pallow = Km (P1-rc Pv) (22)
The smaller of either the ∆Pactual or the ∆Pallow is then used in the basic sizing
equations. C Q G P v= ∆ and Q C P G v = ∆ (23)
Iterative Nature Of Sizing Calculations - The procedures that are used to calculate Cv
through the use of the ∆Pallow are as follows:
1. Using an estimated value of Km(FL), calculate the ∆Pallow.
2. Use the lesser of the ∆Pallow or ∆Pactual to calculate the required Cv.
3. Select a valve size, and determine the percent of travel that will provide the required Cv. Observe the actual Km (FL) of the selected valve size at the travel that was just determined.
4. If the actual Km (FL) is different than the estimated Km (FL), use the actual value of Km (FL) to recalculate the ∆Pallow, and recalculate the required Cv. 5. Repeat steps 2 through 4 until the estimated Km (FL) is the same as the actual
Piping Geometry
Significance Of Pipe Fittings In Valve Sizing
ISA Standards For Testing Valve Cv - Valve manufacturers determine control valve Cv
ratings according to ISA test standards. These standards specify the use of test piping that is the same diameter as the nominal valve size. In many applications, the valve size is smaller than the pipe size, and reducers and expanders (swages) are used. Swages can have a considerable effect on valve capacity.
Fittings, Pressure Drop, And Flow Rate - The net effect of a reducer, an expander, or the combination of a reducer and an expander is a reduction in the apparent pressure drop and a corresponding reduction in flow rate. The reduction in flow capacity that results from the use of swages results in decreased flow and increased valve Cv requirements.
ISA Corrections For Swaged Lines
Piping Geometry Factor FP - The ISA equation uses the piping geometry factor FP to
account for the flow-limiting effect of swages. For maximum accuracy, FP values must
be determined by test.
Use of FP Factor - The piping geometry factor FP is included in the ISA equations as
follows: q N F C p p G P v f = 1 1− 2 (24) C q N F G p p v P f = − 1 1 2 (25)
Saudi Aramco DeskTop Standards 23
ISA Standards For Calculating FP - The ISA standard states that when tested values of FP
are not available, FP may be estimated as follows:
FP = ΣK Cv2 N2 d4 + 1 −1 2 (26) Where:
FP = The piping geometry factor, dimensionless.
ΣK = The sum of all loss coefficients, dimensionless.
N2 = A dimensionless units constant for pipe and valve size (N2 = 890 for inches; N2 = 0.00214 for mm); see Figure 4.
d = The inside diameter of the valve inlet, specified in inches or mm according to the value of N2.
Calculating K - K is the algebraic sum of all the loss coefficients that influence flow through the fittings that are attached to the control valve. The coefficients are: • Friction coefficients that account for turbulence and friction (K1 and K2)
• Bernoulli coefficients that account for pressure and velocity changes (KB1 and KB2)
Refer to Equations 26 and 27, and to Figure 14.
ΣK K= 1+K2+KB1−KB2 (27)
Figure 14
Resistance Coefficients K1 and K2 account for the pressure that is lost to turbulence and
friction in the inlet and outlet fittings respectively. K1 and K2 values may be found in
standard piping references such as Crane Company's Flow of Fluids Through Valves,
Fittings, and Pipe. Alternatively, K1 and K2 can be calculated by means of the
following equations: K1=0. 5 1− d2 D12 2 and K2=1. 0 1− d2 D22 2 or when D1 = D2 K1+K2=1. 5 1− d2 D12 2 (28) Where:
K1 = The resistance coefficient of the inlet fitting(s). K2 = The resistance coefficient of the outlet fitting(s). d = The inside diameter of the valve inlet.
D1 = The inside diameter of the upstream pipe. D2 = The inside diameter of the downstream pipe.
Equation 28 illustrates that the ratio of d to D (valve inlet diameter to pipe diameter) is the key flow-limiting influence. As D increases relative to d, the flow limiting effects increase.
Note that the combined equation (to solve for K1 + K2) can be used only when inlet
and outlet piping are the same size. Note also that all the K terms are dimensionless. Bernoulli Coefficients KB1 andKB2 are used to compensate for changes in pressure that
result from differences in flow stream area and fluid velocity. Each term is calculated by means of the following equations:
KB1=1− d D1 4 and KB2=1− d D2 4 (29)
Refer to Equations 27 and 29, and note that for equal size inlet and outlet piping, KB1
Saudi Aramco DeskTop Standards 25
Valve Geometry - Refer to Equation 30, and note the relationship between the valve Cv
and the valve inlet diameter d.
FP = ΣK Cv2 N2 d4 + 1 −1 2 (30)
When isolated from the remainder of the equation, the Cv and d terms can be seen as an indicator of relative valve efficiency, (i.e., a large Cv and a small valve inlet
diameter (d) indicates a high efficiency valve such as a ball or butterfly valve).
Relative Valve Efficiency C d v =
2
(31)
Note also that high recovery (high efficiency) valves will result in lower values of FP.
Many experienced specifiers examine the ratio of the Cv to inlet diameter to determine
whether or not to account for swage effects. One rule of thumb is expressed by the following:
If C
d account for piping factors v
2 ≥ 20,
(32) If C
d ignore piping factors
v
2 ≤ 20,
Equation Analysis - Given the mathematical relationship of the Cv and d terms, it follows
that FP will have the largest impact on high efficiency (high recovery) valves such as
rotary valves. Refer to Figure 15 and note that FP will have the greatest effect on flow
when high efficiency valves are operated near their full rated capacity. Generally speaking, swage effects diminish rapidly as valve position is reduced to about 50% of rated travel.
For sliding-stem valves, the impact of swages on control valve sizing is generally in the range of 2-5 percent. This margin of error is within the accuracy limits of the sizing equation; therefore, swage effects are commonly ignored for low recovery, sliding-stem valves.
Figure 15
Saudi Aramco DeskTop Standards 27
Piping Factors And Choked Flow
Calculating FLP - When a valve is used with swages, the pressure recovery coefficient (FL or Km) is not the same as the coefficient for the valve alone. Section 5.3 of ISA
Standard S75.01-1985 describes the use of an additional coefficient FLP. FLP is a
coefficient that is the product of the recovery coefficient that has been corrected for piping factors (FL)P and the piping geometry factor FP as shown in the following
equations: C q N F F G p p v P L P f = − 1 ( ) 1 2 (34)
and, combining terms:
FLP=F FP( L P) (35) therefore: C q N F G p p v LP f = − 1 1 2 (36) Where:
FP = The piping factor.
(FL)P = FL corrected for piping factor.
FLP = The combined coefficient for pressure recovery and piping factors. The ISA Standard states that, for maximum accuracy, the value of FLP should be
determined by test. The standard also states that if tested values are not available, reasonable accuracy can be achieved with the use of Equation 37.
FLP =FL Ki FL2Cv2 N2 d4 + 1 −1 2 (37)
The new term Ki includes the loss coefficient (K1) and the Bernoulli coefficient (KB1)
FLP And Choked Flow - The factor FLP is used to calculate ∆Pchoked as shown in Equation 38. ∆Pchoked = FLP FP 2
(
P1−FFPv)
(38)Note that the sizing equation (Equation 39) is modified to account for FLP only if flow
is choked. C q N F G p p v LP f = − 1 1 2 (39) Limitations Of Calculated FLP
Imprecise Results - For maximum accuracy, the value of FLP must be determined by test.
The value of FLP that is calculated through the use of the ISA equation indicates only
an approximation of swage effects, and it generally over-predicts the impact of reducers and expanders. The lack of precision is caused by several factors, including the following:
• Difficulty in obtaining precise values for the K terms.
• The equations are based on liquid flow across abrupt transitions (as opposed to the smooth transitions of most expanders and reducers).
• The combined effects of swages and specific valve geometry are not accounted for.
Saudi Aramco DeskTop Standards 29
Iterative Nature Of FP, FLP, And Cv Calculations - When calculating control valve Cv
requirements, the FP and FLP terms are used in the equation to size for Cv; however,
the unknown Cv also appears in the equations to solve for FP and FLP. Refer to
Equations 40 and 41. When ∆Pactual < ∆Pchoked:
C q N F G p p v P f = − 1 1 2 but FP = ΣK Cv2 N2 d4 +1 1 2 (40)
When ∆Pactual > ∆Pchoked:
C q N F G p p v LP f = − 1 1 2 but FLP =FL Ki FL2Cv2 N2d4 + 1 1 2 (41)
Therefore, several iterations of both equations must be performed as follows: 1. Using an estimated FL (Km) or FLP, calculate the required Cv. 2. Using the Cv that was calculated above, calculate FP or FLP.
3. Using the calculated value of FP or FLP and the actual FL (or Km) of the selected valve, solve for Cv again.
4. Using actual values for FL (Km) and the calculated values for Cv and FP or FLP, repeat steps 2 and 3 until the results converge on a final value of Cv.
Alternate Methods For Calculating Swage Effects
Swage Effects That Are Tested By Manufacturers - According to the ISA standard,
maximum accuracy is achieved when the effect of fittings on valve Cv and FL (Km) is
determined by test for each valve type and line-to-valve size ratio. Many
manufacturers publish rotary valve FL, Km, and Cv values that have been corrected for
swage effects.
Calculating Swage Effects With Sizing Software - Most valve sizing software includes options for calculating FP and FLP factors. The computer can quickly perform the
iterations of the calculation that are necessary to arrive at useful (though approximate) results.
Section 5.4 of SAES-J-700 states that when no specific vendor data is available for valves that are mounted between pipe reducers, a correction factor will be used. The standard includes a table of correction factors (R) for D/d ratios (pipe diameter to valve size) of 1.5 and 2.0 for a variety of valve styles. Refer to Figure 16. The R factors are applied as follows: Required Cv = Calculated Cv R (42) Valve Type D/d = 1.5 D/d = 2.0 R R
Globe Valves (Flow To Close) 0.96 0.94
Globe Valves (Flow To Open) 0.96 0.94
Angle Valves (Flow To Close) 0.85 0.77
Angle Valves (Flow To Open) 0.95 0.91
Ball Valves 0.84 0.80
Butterfly Valves 90 Degrees Open 0.77 0.67
Butterfly Valves 60 Degrees Open 0.91 0.85
Figure 16
R Values That Are Used In The Piping Factor Correction Method That Is Included In Section 5.4 Of SAES-J-700
R-Value Considerations - Because R factors are derived without consideration for valve Cv or the percent of rated travel, the correction will not be as accurate as a correction
that is calculated with the ISA method. (Recall the significance of Cv/d2). In spite of
Saudi Aramco DeskTop Standards 31
Viscosity Corrections Flow Regimes
The sizing equations that have been presented to this point are based on the assumption that the flowing fluid is turbulent, as opposed to laminar.
Laminar Flow - In laminar flow, the fluid flows in smooth, ordered layers. Refer to Figure 17 below. Fluid velocity is highest in the layers in the center of the pipe, while drag forces cause a reduction in the fluid velocity nearer the pipe wall. Laminar flow is also referred to as viscous flow. Although effects other than fluid viscosity may cause laminar flow, most laminar flow occurs with high viscosity fluids.
Turbulent Flow - In turbulent flow, the uniform layers disappear and the flowstream is made up of turbulent eddies that occur randomly in the fluid stream as shown in Figure 17. The flow profile is more blunt, and the velocity at the center of the pipe and the velocity near the pipe wall are nearly equal.
Transitional Flow - Between laminar and turbulent flow, a condition of transitional flow exists. The transitional flow regime has characteristics of both laminar and turbulent flow.
Laminar Flow Turbulent Flow
A5615
Figure 17
Impact Of Flow Regime On Valve Sizing
Pressure Drop Vs. Flow Rate - The valve specifier's interest in flow regimes centers on the relationship between energy losses in the valve (pressure drop) and flow rate. For turbulent flow, the standard sizing equation describes a relationship in which the flow rate is proportional to the square root of the pressure drop across the valve as follows:
For Turbulent Flow: Q∝ ∆P (43)
In the laminar flow regime, tests confirm that the flow rate is directly proportional to pressure drop as described with the following:
For Laminar Flow: Q ∝ ∆P (44)
For fluids in the laminar regime, either a larger valve or a larger pressure drop will be required to produce a flow rate that is equal to the flow rate of a fluid flowing in the turbulent regime.
Depending on the magnitude of the viscous effects, the flow rate of a fluid in the transitional regime will fall somewhere between the flow rate of a fluid in the laminar regime and a fluid in the turbulent flow regime.
Reynolds Numbers
Inertial And Viscous Influences - The physical quantities that determine the flow regime can be represented as a ratio of inertial to viscous forces. This ratio is a dimensionless parameter that is known as the Reynolds number, R. To illustrate the concept, the Reynolds number for a straight piece of piping is represented with the following:
R=VDρ
µ (45)
Inertial influences are: V - fluid velocity
D - pipe inside diameter
ρ - fluid density
The viscous influence is:
Saudi Aramco DeskTop Standards 33
Influences On Reynolds Numbers - Note that a decrease in fluid velocity, pipe diameter, or fluid density will result in a lower Reynolds number and a tendency toward laminar flow. Also, note that increasing fluid viscosity will result in a lower Reynolds number and a tendency toward laminar flow.
ISA Equations For Non-Turbulent Flow
Reynolds Number Factor FR - The ISA Standard uses a Reynolds number factor FR to
account for the effects of viscous flow. The factor FR is included in the basic sizing
equation as follows: q N F C p p G R v f = 1 1− 2 (46) C q N F G p p v R f = − 1 1 2 (47)
The FR factor expresses the ratio of the nonturbulent flow rate to the turbulent flow
rate that is predicted by the basic sizing equation. Note also that Equations 46 and 47 do not include the piping correction factor FP. The effect of valve fittings and swages
on nonturbulent flow is currently not well understood; therefore, when the ISA equations are used, the specifier may correct for piping factors or viscous effects, but not for both.
Reynolds Number Vs. Flow Regime - A chart that relates the valve Reynolds number to the value of FR helps to illustrate the effect that laminar flow can have on the calculated
flow rate or the control valve Cv. The plot that is shown in Figure 19 illustrates that
when the valve Reynolds is 12 000 or larger, the flow is fully turbulent; accordingly, there is no flow limiting effect and the value of FR is 1.0. As the Reynolds number
falls below 12 000, the flow-limiting effects of laminar flow increase, and the value of FR decreases.
Section 5.5 Of SAES-J-700 requires an evaluation of viscous effects whenever the Reynolds number is below 12 000.
Calculating FR - Calculating the value of FR is a two step process.
1. The first step is to calculate a valve Reynolds number, Rev, as shown below: Rev= N4Fdq υFL12 Cv12 FL2 Cv2 N2d4 +1 1 4 (48)
Note that the equation is iterative because Rev, Cv, and FL are all unknown at the
beginning of the process. Estimates must be made for all values, and, then, several iterations are performed to arrive at useful results.
Note also the use of the term Fd. Fd is a valve style modifier. Currently, the ISA
Standard recognizes only two values of Fd. A value of 0.7 is used for double ported
globe valves and for butterfly valves. For all other valve styles, Fd is 1.0.
Kinematic viscosity, υ, is expressed in centistokes. If fluid viscosity is specified in
terms other than centistokes, it is necessary to convert the viscosity to centistokes with the use of the methods that are shown in the table below:
Viscosity Expressed As: Convert to Centistokes by:
m2/s Multiply m2/s by 106
centipoise divide centipoise by Gf
Figure 18 Viscosity Conversion
2. The calculated valve Reynolds number (Rev) is used to enter a plot (see Figure 19) that relates Rev to a value of FR. The value of FR is used as shown in Equations 46 and 47.
Saudi Aramco DeskTop Standards 35 Figure 19
Valve Reynolds Number Vs. The Reynolds Number Factor FR Other Viscosity Correction Methods
Viscosity Correction Nomograph - To avoid time-consuming calculations, valve
manufacturers provide simplified approaches to obtain low Reynolds number (viscous liquid) correction factors. Fisher Controls provides a simple nomograph that allows the specifier to compensate for viscous effects when performing flow, pressure drop, and Cv calculations. The nomograph uses known inputs of valve Cv, flow rate, and fluid
viscosity to arrive at a Reynolds number NR. The value of NR is then used to identify a
correction factor Fv. Fv is used to correct the initial Cv calculation to arrive at a
corrected value of Cvr (Cv required ). For purposes of selecting an appropriately sized
control valve, the value of Cvr is used instead of Cv.
Cvr = Fv Cv (49)
Where:
Cvr = The Cv that has been adjusted for fluid viscosity.
Fv = A correction factor, dimensionless, from the Fisher nomograph. Cv = The uncorrected Cv.
Sizing Software such as the Fisher Sizing Program and other sizing programs include options that automatically check for the effects of viscous (laminar) flow. The specifier enters the fluid viscosity along with other service conditions, and the software
Summary Of Valve Sizing Equations ISA Method
Basic Flow Equation - For nonchoking, turbulent fluids, Cv is calculated with:
C q N G p p v= −f 1 1 2 (50)
Choked Flow Sizing Equation - To determine if choked flow exists, the specifier
calculates the ∆Pchoked, compares ∆Pchoked to the actual ∆P, and uses the lesser of the
two drops for sizing purposes. The ∆Pchoked is calculated as follows:
∆Pchoked = FL2 (P1 - FF Pv) (51)
If choked flow exists (∆Pactual > ∆Pchoked), the required valve Cv is calculated with the
use of the following equation: Cv =qmax
N1FL
Gf p1−FFpv
(52)
Alternatively, the basic flow equation (Equation 50) may be used for choked flow sizing if the ∆Pchoked is used as the sizing pressure drop.
Piping Correction For Non-Choked Flow Applications - In applications where the flow is not choked, the flow limiting effect of piping reducers and expanders is calculated with the use of the piping correction factor FP as follows:
C q N F G p p v P f = − 1 1 2 where FP = ΣK Cv2 N2 d4 + 1 −1 2 (53)
Saudi Aramco DeskTop Standards 37
Piping Correction For Choked Flow Applications - To compensate for piping factors under conditions of choked flow, a single coefficient FLP is used to compensate for both
choked flow and piping factors as follows:
C q N F G p p v LP f = − max 1 1 2 where FLP =FL Ki FL2Cv2 N2 d4 + 1 −1 2 (54)
Viscosity Corrections FR - The effect of nonturbulent (laminar) flow is included in the sizing equation with the Reynolds number factor, FR, as shown in Equation 55.
C q N F G p p v R f = − 1 1 2 (55)
The value of FR is determined by first calculating the valve Reynolds number with the
use of Equation 56 and, then, locating a value of FR from the chart that was shown
previously in Figure 19. Rev= N4Fdq υFL12 Cv12 FL2 Cv2 N2d4 +1 1 4 (56)
Equations Used By Fisher Controls And Others
Basic Flow Equation - The basic flow equation that is used by many manufacturers (refer to Equation 57) is similar in form to the ISA equation.
Q C P
G v
= ∆
(57)
Checking for Choked Flow - The potential for choked flow is investigated by calculating the ∆Pallow and comparing the result with the actual ∆P across the valve. If the actual ∆P is greater than the ∆Pallow, choked flow exists and the ∆Pallow is used as the sizing
pressure drop in Equation 57. The ∆Pallow is calculated with:
∆Pallow = Km (P1-rc Pv) (58)
Km values are published in manufacturers' literature. The value of rc can be found
from tables or calculated with a simple equation.
Piping Corrections - The effect of reducers and expanders on valve capacity is determined by testing each type and size of valve with different line-to-body size ratios. Corrected Cv's are then published for rotary valves. Corrected values of Km are
also published. The effect of reducers and expanders on globe valve capacity and recovery characteristics is negligible; therefore, no corrections are published or are necessary.
Viscosity Corrections - During a manual sizing procedure, viscosity corrections are easily made with the use of a nomograph that relates valve Cv, flow rate, and viscosity to a
correction factor Fv. The Cv required (CVR) is calculated by taking the product of the
Saudi Aramco DeskTop Standards 39
Computer sizing control valves for liquid applications Introduction to the Fisher Sizing Program
Benefits Of Computer Sizing Methods
Valve specifiers generally make use of available sizing software that runs on PC's. The many advantages of computer sizing include the following:
• Ease and speed of computation • Computational accuracy
• Elimination of need to remember numerous sizing equations • The ability to construct a database of fluids and fluid properties • The ability to save data and sizing calculations on disk
• The ability to generate various reports and specification sheets Overview Of The Fisher Sizing Program (FSP 1.4)
Sizing Equations - The sizing software that is used in this Module has the ability to perform sizing calculations according to the ISA sizing equations and the equations that are used by Fisher Controls and by other manufacturers. The ability to perform calculations with the use of either method will be helpful in demonstrating various sizing approaches.
Generic Sizing Engine - The Fisher Sizing Program uses accepted equations, does not rely on proprietary valve specifications, and calculates results that are useful during the selection of any valve - regardless of manufacturer - provided that valve recovery coefficients are expressed in terms of FL or Km. The flexibility of the software
becomes most apparent in special sizing applications.
Other Capabilities - The program allows the specifier to select a system of units, to build a database of common fluids and fluid properties, and to print both standard and custom reports and specification sheets; however, only those features that directly relate to valve sizing will be discussed in this Module. Participants with ongoing responsibility for valve sizing will benefit from exploring other options that are included in this software.
Overview of Program Operation Booting The Program
After the PC is set to the appropriate directory, the program is launched by typing the executive (exec) file "FSP" and, then, pressing the ENTER key.
Project Information
After launching the program, a main menu and identification screen appears as shown in Figure 20. This screen allows for specifier identification, project identification, equipment tag number, and other information.
Figure 20
Main Menu Of The Fisher Sizing Program Main Menu
A menu at the top of this screen lists several different sizing activities and functions. The specifier selects a specific sizing activity by moving the cursor to the desired selection and pressing the ENTER key or by pressing the capitalized letter of the desired activity.
Valve is selected to size control valves, calculate flow rate, or calculate pressure drop. Ssact is selected to size sliding-stem actuators.
Saudi Aramco DeskTop Standards 41
rEport is selected to print a report of the service conditions, fluid properties, and the results of the sizing calculations.
sPecsheet - is selected to print out a standard or custom specification sheet. File is selected to import or export text files to or from a specification sheet. Other is selected to gain access to a notepad and other miscellaneous options. Config is selected to change units from English to metric, to select printers, to set atmospheric pressure, and to establish other system and sizing defaults.
eXit is selected to quit the program. Selecting Units
The specifier may select the default engineering units by selecting Config from the main menu and, then, selecting the Units option. See Figure 21. Each entry may be changed individually by highlighting it and pressing ENTER. Also, notice the option at the bottom of the screen to make all units either English (by pressing the F2 key) or metric (by pressing the F3 key). Pressing the F10 key exits this screen.
Figure 21
Selecting A Valve Sizing Method
When the menu item Valve is selected, the specifier is presented with several options for sizing gasses, liquids, and vapors. Each option uses different equations within the computer
program. The three available methods for liquid sizing are shown in Figure 22 and are described below.
Figure 22
Drop-Down Menu That Lists Valve Sizing Methods
ISA Liquid - When the ISA Liquid method is selected, the software uses the ISA sizing equations.
Fisher Liquid - When the Fisher Liquid method is selected, the software uses the same fundamental equations that are used in the ISA method, except that the terms Km and
rc are used instead of FL and FF, respectively. In the Fisher Liquid method, there is no
option for calculating FP because piping effects are included in the valve Cv's that are
published by Fisher Controls.
Fisher Water - The Fisher Water method takes advantage of the fact that the SG (specific gravity) and Pv (vapor pressure) for water can be calculated from other
information that is entered by the specifier. The Fisher Water method saves time because it eliminates the need for the specifier to input values for SG and Pv; however,
Saudi Aramco DeskTop Standards 43
Selecting Variables And Conditions
Selecting Variables To Solve For - After a sizing method has been selected, the specifier selects the variable to solve for. Refer to Figure 23. The choices are as follows: • Valve Sizing and LpA (noise prediction)
• Velocity
• LpA vs. Q (Noise prediction at various flow rates)
• Cv Simple (for estimating Cv with no corrections for choked flow, viscosity, piping, etc.)
Selecting Conditions - On the same screen, the specifier selects whether the sizing calculations will be performed for the minimum, normal, or maximum flow conditions, or for some other condition (identified by the column header 'OTH'). Copying Conditions - The software performs calculations for one service condition (min, norm, max, or OTH) at a time, and the active condition is indicated with a check mark. Parameters for one condition can be copied to another to eliminate redundant entry of inputs. Copying parameters from one condition to another is performed by pressing the cursor keys until the cursor is on the target condition, pressing ALT C, and selecting the condition from which data will be copied.
Figure 23
Valve Sizing Calculation Screen
Selecting the Valve Sizing and LpA option of the ISA Liquid sizing method brings up the actual sizing screen (shown in Figure 24). This screen is divided into several sections.
Figure 24
Calculation Screen For ISA Liquid Sizing
Liquid Properties And State - This section is where the specifier enters the fluid and fluid properties such as the fluid critical pressure (Pc), vapor pressure (Pv), and specific
gravity (SG).
Service Conditions - In this section, the specifier enter pressure, flow, and temperature information.
Intermediate Results - Any intermediate results such as the calculated values of FF, FR,
Rev, or FP are displayed in this area.
Valve Specification - In this section, the specifier enters any needed valve data such as the value of FL. When pipe and valve size are required for calculating FP or FR, they
are also entered in this section.
Calculated Results - After all data have been entered, the specifier presses the function key F2 to calculate the required valve Cv. The results of the sizing calculations appear
in the Calculated Results section. In addition to valve Cv, other important information
Saudi Aramco DeskTop Standards 45
Selecting Calculation Options
The F3 Options Key - At any time, the specifier may choose from several different sizing options (see Figure 25) by pressing the function key F3. Options are toggled by
highlighting the appropriate line and pressing ENTER. The option that is visible when the option menu is stored (by pressing the ESCAPE key) is the option that will be used in sizing. The options menu for the ISA liquid sizing method includes the following: • Line 1: Solve for Cg, Cs, or Cv - Other options: Solve For Flow Rate, Solve
For Pressure Drop
• Line 2: LpA (SPL) OFF - Option: Calculate LpA (SPL) • Line 3: Omit Fp - Other options: Calculate Fp, input Fp
• Line 4: Viscous Correction OFF - Option: Viscous Correction ON • Line 5: Pipe: Size/Sched - Option: Pipe: Diameter/Thickness
• Line 6: Input Pv - Option: Calculate Pv (Note that the software can only calculate the Pv for fluids for which data have been included in the permanent database; for other fluids, the specifier must enter the Pv.)
• Line 7: Warnings ON - Option: Warnings OFF
Figure 25 Calculation Options
As various options are selected, the fields for inputs and for calculated results will change; for example, if the Viscous Correction option is set to ON, the program will require the specifier to input fluid viscosity and valve inlet diameter. In addition, the calculated values of Rev and FR will be displayed in the Intermediate Results section.
Line-By-Line Units Selection - F8 Key - The specifier may change units of measurement for any input parameter by placing the cursor on that parameter and pressing F8. Pressing F8 produces a sub-menu that lists all possible choices. Refer to Figure 26. A choice is made by positioning the cursor on the desired unit and pressing the ENTER key. The option that is visible when the option menu is stored (by pressing the ENTER key) is the option that is used in the program.
Figure 26
