Control Valve Sizing

Engineering Encyclopedia Saudi Aramco DeskTop Standards

Sizing Control Valves

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 File Reference: PCI10302

For additional information on this subject, contact J.R. Van Slooten on 874-6412

Engineering Encyclopedia

Instrumentation Sizing Control Valves

CONTENTS

PAGE

MANUALLY SIZING CONTROL VALVES FOR LIQUID APPLICATIONS The Importance Of Sizing

1 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 Limits Of The Basic Liquid Sizing Equation

9 9

Pressure And Velocity Profiles

10

Pressure Recovery

11

Fluid Vapor Pressure

12

Mechanics Of Choked Flow

13

Cavitation

15

Flashing

15

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 A Valve Sizing Method

42




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

Overview Of Sizing Procedures

69

Selecting Options

70

The Fisher Universal Gas Sizing Equation Introduction


72 72



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 Body And Flange Size Control Valve Physical Size Information Capacity Ratings

91 91 91 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 Piping Factors On Cv

95




Work Aid 1D: Procedures That Are Used To Calculate The Effect Of Laminar Flow On Cv WORK AID 2:

PROCEDURES THAT ARE USED TO COMPUTER SIZE CONTROL VALVES FOR LIQUID APPLICATIONS

96 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

Work Aid 3D: Procedures That Are Used To Computer Size Control Valves For Steam With The ISA Method

117

Work Aid 3E: Procedures That Are Used To Computer Size Control Valves For Ideal Gasses With The Fisher Method

118

Work Aid 3F: Procedures That Are Used To Computer Size Control Valves For Real Gasses With The Fisher Method

119




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: Work Aid 3J: WORK AID 4:

Procedures That Are Used To Calculate The Effect Of Compressibility On Valve Size

122

Procedures That Are Used To Computer Size Control Valves For All Flow Conditions

124

PROCEDURES THAT ARE USED TO ENTER VALVE SIZING DATA ON THE SAUDI ARAMCO ISS

GLOSSARY


127 128



LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20

Fluid States as A Function of Pressure And Heat Content Typical Vendor Recommendations For Percent Travel Versus Flow Guidelines For Percent Travel At Various Flow ConditionsPer Section 5.2 of SAES-J-700 Units Constants For The ISA Liquid Sizing Equations Pressure And Flow Relationships Pressure And Velocity Profiles Around A Restriction Comparison Of High And Low Recovery Valves Fluid Vaporization When Pvc < Pv Pressure And Flow Relationships Pressure Profiles For Flashing And Cavitating Flows Generalized Relationship Of Pvc To Pv For High And Low Recovery Valves At Different Pressure Drops Critical Pressure Ratios For Liquids Other Than Water Critical Pressure Ratios For Water Flow Limiting Influences Of Reducers And Expanders Piping Factor Effect Vs. Travel For Different Valve Styles R Values That Are Used In The Piping Factor Correction MethodThat Is Included In Section 5.4 Of SAES-J-700 Flow Profiles Of Laminar And Turbulent Flow Regimes Viscosity Conversion Valve Reynolds Number Vs. The Reynolds Number Factor FR Main Menu Of The Fisher Sizing Program


PAGE 2 3 4 7 9 10 11 12 13 14 17 19 19 23 26 30 31 34 35 40



Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42

Screen That Appears When The Units Option Under Config Is Selected Drop-Down Menu That Lists Valve Sizing Methods Options For Variables To Solve For Calculation Screen For ISA Liquid Sizing Calculation Options Pull-Down Menu That Lists Units Options For Q Pull-Down Menu That Lists Fluids In The Sizing Database Table Of Values That Is Displayed When The F9 Key Is Pressed Numerical Constants For The ISA Gas Sizing Equations Gas Flow And Pressure Relationships Choked Flow As A Function Of xT Effects Of k On FKxT And qmax Pressure And Flow Relationships As x Increases From 0.02 To xT Reduced Pressure PVC Leads To Reduced Fluid Density And Reduced Flow Effect of Sonic Velocity On Flow Effect of Vena Contracta Enlargement Relationships Among x, FkxT, And Y Generalized Compressibility Chart Valve Sizing Method Options Available Calculation Types Valve Sizing Screen For The ISA Gas Valve Sizing Method Calculation Options For The ISA Gas Valve Sizing Method


41 42 43 44 45 46 47 48 51 52 53 55 56 57 58 59 60 64 68 69 69 70



Figure 43 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59

Line-By-Line Units Options For Flow Actual Flow Versus Predicted Flow Critical Flow For Low And High Recovery Valves Predicting Low Flow And Critical Flow Tested Values Of Flow Compared To A Sine Curve Comparison of Cv, Cg, and C1 Values C2 Factor Versus k Comparison of ISA and Fisher Sizing Terms Valve Sizing Methods Selection Of A Calculation Type Valve Sizing Screen For The Fisher Real Gas Sizing Method Calculation Options For The Fisher Ideal Gas Sizing Method Calculation Options For The Fisher Real Gas Sizing Method Calculation Options For The Fisher Vapor Sizing Method Calculation Options For The Fisher Steam Sizing Method Pull-Down Menu Options For Temperature The Saudi Aramco ISS


71 74 75 76 77 79 82 85 86 87 87 88 88 89 89 90 92



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.


1



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 the fluid state is at or near any of the boundaries that are shown in Figure 1 above; therefore, this Module will present basic sizing methods for fluids that can be defined as liquids, ideal gasses, and real gasses.


2



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 Normal Maximum

10 20-80 90

Figure 2 Typical Vendor Recommendations For Percent Travel Versus Flow


3



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 Linear Modified Parabolic

80 93 70 90 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).


4



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: ∆P Q = Cv G (1) Where: Q Cv

= The flow rate in gallons per minute (gpm). = 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). G Cv =Q ∆P (2)


5



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: p −p ( 3) q = N1 C v 1 2 Gf To Calculate Control Valve C v - To calculate the control valve Cv that is required to pass a specified flow rate, the equation is as follows: q Gf ( 4) Cv = N1 p1 − p2 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.


6



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 N N1 0.0865

N2 N4 N6

w ---

0.865 1 0.00214 890 76 000 17 300 2.73

------------kg/h

27.3 63.3

kg/h lb/h

Units That Are Used In Equations q d, D p, ∆P γ1 m3/h kPa ----m3/hr bar ----gpm ----m3/h gpm ---

psia --------kPa

--mm in mm in ---

-----

bar psia

-----

----------kg/m3 kg/m3 lb/ft3

ν ----------centistokes centistokes

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 supplemental equations that will be discussed later in this Module.


7



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: G Cv = Q ∆P Generic: (5) Cv =

ISA:

q N1

Gf p1 − p2

(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.


8



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 Flow Relationships.


9



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 Pressure And Velocity Profiles Around A Restriction


10



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 Comparison Of High And Low Recovery Valves


11



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 Fluid Vaporization When Pvc < Pv


12



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 Pressure And Flow Relationships


13



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 Pressure Profiles For Flashing And Cavitating Flows


14



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.


15



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: FL =

ISA: Fisher: Where:

P1 − P2 P1 − Pvc

P −P Km = 1 2 P1 − Pvc

Note that FL2 = Km.

(7)

(8)

FL = The valve recovery coefficient (ISA). Km = An alternate form of the valve recovery coefficient (Fisher Controls and others). Pvc = The fluid pressure at the vena contracta.


16



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 and FL = 0.6 to 0.8.


17



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. P1 − P2 FL = P1 − Pvc arranges to ∆Pchoked = FL2 (P1-Pvc) (9) ISA: P −P Km = 1 2 P1 − Pvc Fisher Controls: 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.


18



Determining The Value Of rc For Non-Water Liquids - For liquids other than water, the plot

Citical Pressure Ratio - rc

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

A4148

.10 .20 .30 .40 .50 .60 .70 .80 .90 1.00 Vapor Pressure - PSIA Critical Pressure - PSIA

Figure 12 Critical Pressure Ratios For Liquids Other Than Water Calculating The Value Of rc For Water - A special rc curve allows the straightforward

Critical Pressure Ratio--r c

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. 1.0 0.9 0.8 0.7 0.6 0.5 0

A4147

500

1000 1500 2000 2500 3000 3500 Vapor Pressure---PSIA

Figure 13 Critical Pressure Ratios For Water


19



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.

Where: FL FF Pv Pvc Km rc

= = = = = =

∆Pallow = Km (P1-Pvc)

(17)

and Pvc=rc Pv

(18)

so ∆Pallow = Km (P1-rc Pv)

(19)

The valve recovery coefficient, dimensionless (ISA). The liquid critical pressure ratio factor, dimensionless (ISA). The liquid vapor pressure, psia. The fluid pressure at the vena contracta, psia. The valve recovery coefficient, dimensionless (Fisher and others). The liquid critical pressure ratio, dimensionless (Fisher and others).

1. Reference ISA Standard S75.01-1985


20



Implementing Choked Flow Equations ISA Sizing Equation For Choked Flow - The ISA standard includes the following

equations: qmax = N1FL C v

p1 − FFp v Gf

q C v = max N1 FL

Gf p1 − FF p v

and (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. q p −p Gf Cv = q = N1 C v 1 2 N1 p1 − p2 Gf and (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. ∆P G Cv =Q Q = Cv ∆P G and (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 Km (FL).


21



Piping Geometry Significance Of Pipe Fittings In Valve Sizing ISA Standards For Testing Valve C v - 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: p1 − p2 q = N1 FP Cv Gf (24)

q Cv = N1 FP


Gf p1 − p2

(25)

22



ISA Standards For Calculating F P - The ISA standard states that when tested values of FP are not available, FP may be estimated as follows: 1

− 2  ΣK C 2  v + 1 FP =   N2 d 4 

(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 = K1 + K 2 + KB 1 − KB 2 (27) •

Figure 14 Flow Limiting Influences Of Reducers And Expanders


23



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: 2  d2  K1 = 0. 5  1− 2  D1  

2  d2  K2 = 1. 0  1− 2   D2 

and or when D1 = D2 2  d2  K1 + K 2 = 1. 5  1− 2   D1 

(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. K and KB 2 are used to compensate for changes in pressure that Bernoulli Coefficients B 1 result from differences in flow stream area and fluid velocity. Each term is calculated by means of the following equations:  d 4  d 4  KB1 = 1−   and KB2 = 1−   D1   D2 

(29)

Refer to Equations 27 and 29, and note that for equal size inlet and outlet piping, KB1 and KB2 cancel out; therefore, only the terms K1 and K2 are needed.


24



Valve Geometry - Refer to Equation 30, and note the relationship between the valve Cv

and the valve inlet diameter d.

1

−  ΣK C 2  2 v FP =  + 1  N2 d 4  (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). C Relative Valve Efficiency = v d2 (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: C If v ≥ 20, account for piping factors d2 (32) Cv If 2 ≤ 20, ignore piping factors d (FP = 1.0) (33)


25



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, slidingstem valves.

Figure 15 Piping Factor Effect Vs. Travel For Different Valve Styles


26



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: q Gf Cv = N1 FP (FL )P p1 − p2 (34)

and, combining terms: FLP = FP (FL )P

(35)

therefore: q Gf Cv = N1 FLP p1 − p2

(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.  K F 2C 2  F LP = FL  i L 4 v + 1  N2 d 

− 12 (37)

The new term Ki includes the loss coefficient (K1) and the Bernoulli coefficient (KB1) on the inlet side of the valve only.


27



FLP And Choked Flow - The factor FLP is used to calculate ∆Pchoked as shown in

Equation 38.

 F LP  2  P1 − FF Pv ∆Pchoked =   FP 

(

)

(38)

Note that the sizing equation (Equation 39) is modified to account for FLP only if flow is choked. q Gf Cv = N1 FLP p1 − p 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.


28



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: Cv =

q N1 FP

Gf p1 − p 2

When ∆Pactual > ∆Pchoked:

1

 ΣK C 2  2 v + 1 FP =  4  N2 d  but

(40) 1

 K F 2C 2  2 i L v  F LP = FL + 1  N 2 d4  but (41) Therefore, several iterations of both equations must be performed as follows: q Cv = N1 FLP

Gf p1 − p2

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.


29



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 C v =

Valve Type

Globe Valves (Flow To Close) Globe Valves (Flow To Open) Angle Valves (Flow To Close) Angle Valves (Flow To Open) Ball Valves Butterfly Valves 90 Degrees Open Butterfly Valves 60 Degrees Open

Calculated C v R

(42) D/d = 1.5

D/d = 2.0

R

R

0.96 0.96 0.85 0.95 0.84 0.77 0.91

0.94 0.94 0.77 0.91 0.80 0.67 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 this consideration, the method can provide useful, if approximate, results.


30



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.

A5615

Laminar Flow

Turbulent Flow

Figure 17 Flow Profiles Of Laminar And Turbulent Flow Regimes


31



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: VDρ R= µ (45)

Inertial influences are: V - fluid velocity D - pipe inside diameter ρ - fluid density The viscous influence is: µ - fluid absolute viscosity


32



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 = N1 FR Cv Cv =

q N1 FR

p1 − p 2 Gf Gf p1 − p2

(46)

(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.


33



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: 1

F 2 C 2  4 v + 1  L Re v = 1 1 4  υFL 2 C v 2  N2 d N 4 Fd q

(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 m 2/s by 10 6

centipoise

divide centipoise by G f

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.


34



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 performs all of the necessary calculations.


35



Summary Of Valve Sizing Equations ISA Method Basic Flow Equation - For nonchoking, turbulent fluids, Cv is calculated with:

Cv =

q N1

Gf p1 − p2

(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: (51) ∆Pchoked = FL2 (P1 - FF Pv) If choked flow exists (∆Pactual > ∆Pchoked), the required valve Cv is calculated with the

use of the following equation: q C v = max N1 F L

Gf p1 − FF pv

(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: Cv =

q N1 FP

Gf p1 − p2


where

 ΣK C 2  v + 1 FP =  4  N2 d 

− 12

(53)

36



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: 1

Cv =

q max N1 FLP

−  K F 2C 2  2 i L v F LP = FL  + 1  N2 d4 

Gf p1 − p2

where (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. q Gf Cv = N1 FR p1 − p2

(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. 1

F 2 C 2  4 v + 1  L Re v = 1 1  N d  2 4 υFL 2 C v 2 N 4 Fd q

(56)

Only one of the correction factors FR or FP may be used.


37



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. ∆P Q = Cv G

(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 correction factor times the calculated Cv (i.e., CVR = Fv Cv).


38



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.


39



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. Rotact is selected to size rotary-shaft actuators. sTroking is selected to calculate actuator stroking time.


40



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 Screen That Appears When The Units Option Under Config Is Selected


41



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, there is an option that allows manual entry of SG for special circumstances.


42



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 Options For Variables To Solve For


43



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 such as the ∆Pchoked is also shown.


44



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


45



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 Pull-Down Menu That Lists Units Options For Q


46



Pull-Down Menus - F4 Key - Pull-down menu options for several of the input fields can

be accessed by pressing the F4 key; for example, if the cursor is on the field for "Liquid", pressing the F4 key brings down a menu of several different options as shown in Figure 27. Fluids that are preceded with a tilde character (∼) are included in a fixed database. The fixed database also includes sufficient data to allow automatic calculation of the fluid vapor pressure at the service conditions. The fixed database cannot be edited; however, the software does allow the specifier to construct a separate database of fluids and fluid properties that can be edited.

Figure 27 Pull-Down Menu That Lists Fluids In The Sizing Database


47



Other Important Operations For basic operation of the software, knowledge of a few special keystrokes is helpful. Escape Key - The escape key serves several functions. When menus are present, pressing the ESCAPE key has the effect of selecting an option and, then, returning to the calculation screen. Pressing the escape key also allows the specifier to step backwards through the various screens. Clearing An Entry Field - F5 - Pressing the F5 key clears the field at the cursor location. Clearing An Entire Screen - ALT F5 - To clear all data on the screen, the specifier presses the ALT key together with the F5 key. On-Line Help - F1 - The first time F1 is pressed, a context sensitive help screen appears. The help screen displays information about the procedure that was being performed when F1 was pressed. Pressing F1 again brings up an index of topics for which on-line help is available. A topic is selected by moving the cursor and, then, pressing the ENTER key. Table Of Values - F9 - Pressing F9 displays a table of input parameters and calculated results for all flow conditions as shown in Figure 28 below.

Figure 28 Table Of Values That Is Displayed When The F9 Key Is Pressed


48



Computer Sizing control valves for gas and Steam applications Introduction Differences In Compressible and Incompressible Fluid Flow Valve sizing for compressible fluids (gasses and vapors) differs from sizing for noncompressible fluids (liquids) in several ways. The most important difference is that the density of a gas or vapor cannot be assumed to be constant as it passes through the valve. Instead, density is a strong function of pressure and temperature conditions; therefore, the equations that are used to size control valves use several additional terms to account for fluid density. Use Of Computer Software Because of the complexity of the sizing equations that are used for compressible fluids, specifiers typically make use of computer programs to perform sizing calculations; however, to ensure the use of proper sizing techniques, specifiers should develop an understanding of the terms that are used in the sizing equations. The ISA Sizing Equations For Compressible Fluids Popular Standard The equations that are included in Section 6 of ISA Standard S75.01 are broadly accepted both by valve manufacturers and by valve users. The ISA equations are used in virtually all industries, and they are endorsed in most world areas. Saudi Aramco Standards Section 5.1 of SAES-J-700 states that valve sizing procedures shall be based on the equations that are included in the ISA standard that is referenced above. Section 5.1 of SAES-J-700 also allows the use of vendor-supplied, computer-based sizing software that is based on the ISA equations. Alternate Forms Of The ISA Equation The specifier may select from many forms of the ISA equation. The choice of equation form depends on: •

whether the objective is to calculate fluid flow rate or valve Cv

•

whether fluid flow is expressed in terms of volumetric flow or mass flow

•

the terms that are used to express fluid density

•

the units of measurement (SI or English unit systems)


49



Mass Flow - To solve for mass flow (w), equations that account for fluid density with

specific weight (γ) or molecular weight (M) are used. These equations are sometimes referred to as the 'vapor' forms of the equation. xM w = N 8 Fp C v p1 Y w = N 6 Fp C v Y xp1 γ 1 T1 Z (59) or Volumetric Flow - To solve for volumetric flow (q), either specific gravity (Gg) or molecular weight (M) can be used to account for fluid density. x x q = N7 Fp C v p1 Y q = N9 Fp C v p1 Y G g T1 Z MT1 Z or (60) Control Valve Cv - For valve sizing, the equations above are rearranged to solve for Cv. When the fluid flow rate is specified in terms of mass flow (w) and density is specified in terms of specific weight () or in terms of molecular weight (M), Cv is calculated with the use of one of the following equations: w T1 Z w Cv = Cv = N 6 Fp Y xp1 γ 1 N 8 Fp p1 Y xM or (61) When the flow rate is specified in terms of volumetric flow (q) and fluid density is specified in terms of specific gravity (Gg) or molecular weight (M), Cv is calculated with the use of one of the following equations: Gg T1 Z MT1 Z q q Cv = Cv = x x N 7 Fp p1 Y N 9 Fp p1 Y or (62) Units Systems - The various N terms in the equations allow the specifier to use the desired engineering units such as psi or bar for pressure, and scfm or kg/m3 for flow rate.


50



Nomenclature The terms that are used in Equations 59 through 62 are described below. Cv Fp Gg M Nx pX T1 w x Y Z 1

control valve flow coefficient piping geometry factor; dimensionless gas specific gravity; dimensionless (i.e., density of gas to density of air at reference conditions, or ratio of molecular weight of a gas to molecular weight of air) molecular weight; atomic mass units constants for units of measure; see table below p1 = static fluid pressure upstream of the valve; p2 = static fluid pressure downstream of the valve; see the table below for units absolute temperature of fluid at valve inlet; degrees K or R mass flow rate; kg/h or lb/h - see the table below for units pressure drop ratio ∆ p p1 ; dimensionless expansion factor; dimensionless compressibility factor; dimensionless specific weight of the fluid at valve inlet; see the table below for units Numerical Constants

The values of the various N terms are shown below. Constant

Units N w q* T1 d, D p1, p2, ∆p γ N5 0.00241 ----------mm 1000 ----------in N6 2.73 kg/h --kPa kg/m3 ----27.3 kg/h --bar kg/m3 ----63.3 lb/h --psia lb/ft3 ----N7 4.17 --m3/h kPa --K --417 --m3/h bar --K --1360 --scfh psia --°R --N8 0.948 kg/h --kPa --K --94.8 kg/h --bar --K --19.3 lb/h --psia --°R --N9 22.5 --m3/hr kPa --K --2250 --m3/hr bar --K --7320 --scfh psia --°R --* cubic feet per hour at 14.73 psia and 60 degrees F, or cubic meters per hour at 101.3 kPa and 15.6 degrees C

Figure 29 Numerical Constants For The ISA Gas Sizing Equations


51



Basic Equation To help develop an understanding of the ISA sizing equations, the complete equation for volumetric flow (Equation 63) will be stripped to its most basic form, and each term will be explained as it is added to the basic equation. x q = N7 Fp Cv p 1 Y G gT1 Z

(63) Flow Rate: A Function Of Pressure Drop Ratio - Recall that for liquid flow, q is a function

of the square root of the pressure drop, as shown below. ∆P q = Cv G

(64)

Similarly, gas flow is a function of pressure conditions and Cv. Over a limited set of conditions, tests show that the basic relationship between gas flow, Cv, and pressure conditions is as follows: q = Cv p1 x (65) Where: x=

∆P p1

Equation 65 predicts a flow rate that is a linear function of

(66)

x as shown in Figure 30.

Figure 30 Gas Flow And Pressure Relationships


52



Choked Flow Overview Of Choked Flow - The equation that was just shown predicts an increase in flow

for every increase in the value of x; however, when the value of the square root of x becomes greater than about 0.02, the observed increases in flow rate become less than the equation predicts. Refer to Figure 31. Ultimately, there is a point of choked flow. At the choked flow condition, increases in x (by reducing downstream pressure) do not produce any increase in flow rate. Choking occurs when the jet stream at the vena contracta achieves sonic velocity. The choked flow rate is associated with a flow limiting value of x, which is known as xT. Pressure Drop Ratio Factor xT - The flow limiting value of x (refer to Figure 31) is called the pressure drop ratio factor, or xT (T stands for terminal). The value of xT is related to valve style and geometry; therefore, valve manufacturers determine xT values by test, and they publish them in sizing catalogs and other documents. The values of xT are different for every different valve style and size. xT values also change as a function of the percentage of valve travel.

Figure 31 Choked Flow As A Function Of xT


53



xT And The Ratio Of Specific Heats Factor - Manufacturers test valves for xT values at standard conditions and with standard fluids. The test fluid is air. To make the value of xT meaningful with fluids other than air, the sizing equations account for properties of flowing fluids that are different than the properties of air. One of the significant fluid properties of any compressible fluid is its specific heat ratio, which is expressed as k. k represents the ratio of a fluid's specific heat at a constant pressure to its specific heat at a constant volume. When a valve is used with a fluid other than air, the value of xT value should be corrected for the specific heat of the flowing gas. The correction factor is called the ratio of specific heats factor and it is referred to as Fk. Fk is simply the specific heat ratio for the flowing gas (k) divided by the specific heat ratio (k) of air, which is 1.4. Refer to Equation 67. k Fk = 1. 4 (67) Where: Fk = The ratio of specific heats factor. k = The specific heat ratio of the flowing gas. 1.4 = The specific heat ratio (k) of air at standard conditions. To correct the value of xT for the ratio of specific heats of the flowing gas, the value of xT becomes FkxT. The value of xT that is used in any sizing equation should be limited to the value of FKxT. Locating k Values - k values are included in many standard references such as the Gas Processor's Handbook, and they are also included in the fluid databases of many sizing programs. Specifiers should note that k values vary with service temperature, and that these values can change dramatically (generally increase) at high temperatures.


54



Use Of FKxT - To prevent overpredicting flow or undersizing valves, the value of x that

is used in any of the sizing equations must not exceed the value of FKxT. Refer to Equation 68. q = Cv p1 FK xT q = Cv p1 x becomes (68) Effect Of Fk on XT - Refer to Figure 32 and note that larger values of k result in higher values of FKxT, and vice versa. The values of qmax are similarly affected. Note that the effects that are shown are exaggerated to help illustrate the concept.

Figure 32 Effects Of k On FKxT And qmax Us Of FK In Valve Sizing - Many hydrocarbon gasses and vapors have k values that range

from 1.2 to 1.5 at moderate temperatures. k values in this range typically have a very small impact on valve sizing; therefore, many specifiers ignore the specific heat correction when k is between 1.2 and 1.5, and they assume that FK is equal to 1.0.


55



Expansion Factor: Y Application of x and xT - At the beginning of this discussion, the basic gas flow equation

was presented as:

q = Cv p1 x , where

x=

∆p p1

(69)

It has been shown that the x can be used to predict flow when x < 0.02, that choked flow can be predicted when x is limited to xT, and that xT can be further modified to account for the thermodynamic properties of the fluid. Refer to Equation 70. q = Cv p1 FK xT (70)

The equations above do not express the non-linear relationship between the region where x>0.02 and x
x and q in

q Versus x When x > 0.02 and x < F KxT - The expansion factor, Y, is included in the ISA

equations to account for the relationship of q to x when x > 0.02 and x < FKxT. The expansion factor (Y) helps to account for the following: •

Changes in fluid density that result from increased fluid velocity and reduced fluid pressure at the vena contracta.

•

The effect of vena contracta enlargement.

These conditions are discussed in the following sections.

Figure 33 Pressure And Flow Relationships As x Increases From 0.02 To xT


56



Density Changes - As the value of x increases, fluid velocity at the vena contracta increases and

fluid pressure decreases. See Figures 33 and 34. The reduction in local fluid pressure causes the fluid to expand, which results in a reduction in fluid density. Because fluid density decreases with each incremental increase in x, incremental increases in x no longer produce proportional increases in flow rate.

Figure 34 Reduced Pressure PVC Leads To Reduced Fluid Density And Reduced Flow


57



Vena Contracta Enlargement - When the fluid velocity becomes sonic, a shock wave is

created that limits velocity to a maximum (terminal) value. Flow rate becomes a function of sonic (terminal) velocity and the effective flow area at the vena contracta. Refer to Figures 33 and 35.

Figure 35 Effect of Sonic Velocity On Flow


58



After the fluid attains sonic velocity, a decrease in P2 may produce a limited increase in flow rate, depending on the valve style. The increase in flow rate occurs because an increase in x reduces backpressure and causes the vena contracta to move upstream to the valve throat as shown in Figure 36. The flow area at the valve throat is typically larger than the flow area of an unconstrained vena contracta that is located in the piping downstream of the control valve; therefore, some increase in flow rate may occur.

Figure 36 Effect of Vena Contracta Enlargement Inclusion Of Y In Sizing Equations - The ISA equation accounts for the conditions listed

above by means of the expansion factor Y. The Y term is used in the sizing equation as follows: q = Cv p1 Y x (71)


59



Calculating Y - Y can be taken as a linear function of x. The equation to calculate Y is

as follows: Y =1 −

x 3FK x T

(72) Relationships of x, xT, Fk, And Y - The relationships between the values of x, xT, and Y

are best shown graphically as in Figure 37. Note that the value of Y will always fall in a range between 0.67 and 1.0.

Figure 37 Relationships Among x, FkxT, And Y Basis For Y - For compressible fluids, the expansion factor can be defined as the ratio of

the flow coefficient for a gas to the flow coefficient for a liquid. When the value of Y is 1.0, there is no difference in the liquid and gas flow coefficients. Values of Y that are less than 1.0 indicate a flow limiting effect due to density changes that result from fluid expansion. In other words, as x approaches zero (very low pressure drop ratios), flow resembles that of an incompressible fluid (a liquid); accordingly, fluid expansion has a small effect on flow, and Y approaches 1.0. As x approaches xT, the fluid becomes less dense. The expansion factor Y becomes smaller to account for the reduction in density. As x approaches xT, Y approaches 0.67, thereby signaling the maximum flow-limiting effect of fluid expansion and the presence of choked flow.


60



Dimensionless Terms - Refer to Equation 72 and note that all of the terms that are used to

calculate Y are dimensionless; therefore, Y is also dimensionless. Equation Development - At this point of discussion, the flow equation takes the form: q = Cv p1 Y x (73) This equation: •

predicts flow at low pressure drop ratios ( p1 x )

•

predicts critical flow (with the use of xT)

•

predicts the effect of density changes that result from fluid expansion due to low pressure at the vena contracta. Adapting The Equation For Use With Gasses Other Than Air

Ideal Gasses - The equation that has been discussed to this point (Equation 73) is based on the flow of air at standard conditions. It can be generalized for any gas at any temperature with a simple modification to account for fluid specific gravity and temperature as shown in Equation 74. x q = Cv p1 Y Gg T1 (74)

Where: Gg = The specific gravity of the flowing gas; the ratio of the density of the gas at the valve inlet to the density of air, where both the flowing gas and the reference fluid (air) are at standard conditions of 60 degrees F and 14.7 psia. T1 = The absolute temperature of the fluid at the valve inlet in degrees Rankine or in Kelvin.


61



The manner in which fluid density is included in the gas sizing equations is different than the method that is used for liquid sizing. Recall that for liquid sizing, fluid density is included in the equation as the actual SG of the liquid at the valve inlet; that is, the SG of the liquid must be corrected for temperature before the sizing equations are used. For gas sizing, the fluid density that is used in the sizing equations is the fluid density at standard conditions (i.e., 14.7 psia and 60 degrees F). The sizing equation corrects the density for the flowing conditions according to the ideal gas law, which states that: pV = RT (75) Where: p = The absolute fluid pressure, psia. V = The specific volume (e.g., m3/kg, ft3/lb, etc.). R = A gas constant that is unique for each fluid. T = The fluid's absolute temperature, Kelvin, degrees Rankine, etc. The relationships that are shown in Equation 75 are valid only for gasses that follow the ideal gas law. Note also that the correction is not necessary when the mass flow forms of the equation are used, and density is expressed in terms of specific weight () at the valve inlet (e.g., lbs/ft3, kg/m3, etc.).


62



Real Gas Behavior Real Versus Ideal Gasses - Many gasses and vapors do not behave according to ideal gas

law of pV = RT, and those gasses that do not exhibit ideal gas behavior are referred to as real gasses. The most significant aspect of real gas behavior is that specific volume (V) may not change as a linear function of either temperature or pressure, i.e.: RT V≠ p (76) Non-linear changes in the relationships between p, V, and T are a result of a phenomenon known as compressibility. Valve specifiers are interested in compensating for the effects of fluid compressibility because of the direct relationship of fluid specific volume to fluid density and because of the impact of fluid density on flow and Cv calculations. To obtain precise results when calculating Cv or flow rates, the compressibility factor Z must be included in any equation where the specific weight is a computed value. The correction for fluid compressibility is not necessary when density is expressed in terms of specific weight at the valve inlet (e.g., lbs/ft3, kg/m3, etc.). Compressibility Factor Z - For real gasses at a specific set of service conditions, the effects of compressibility can be calculated with the use of the compressibility factor, Z. pV = ZRT (77) The compressibility factor is included in the basic flow equation to correct for the behavior of a non-ideal gas as follows: x q = Cv p1 Y Gg T1 Z (78)

Note that a compressibility factor of 1.0 indicates ideal gas behavior (i.e., there are no compressibility effects), whereas a lower value of Z (e.g., Z= 0.8) would indicate a tendency toward incompressible (liquid) flow. Also, note that lower values of Z will result in an increase in flow (q). Application Of Z Factor - The correction for fluid compressibility is not necessary when the flowing gas displays ideal gas behavior or when fluid density is expressed in terms of specific weight.


63



Calculating Z - Z can be determined in many ways. One popular approach is to calculate

the reduced pressure (pr) and the reduced temperature (Tr) and, then, to locate the value of Z from a generalized compressibility chart (refer to Figure 38). As shown in Equation 79, the reduced pressure (pr) is the ratio of inlet pressure to the fluid critical pressure, and the reduced temperature (Tr) is the ratio of inlet temperature to the fluid critical temperature. All values are expressed in absolute units. pr =

p1 T1 Tr = pc and Tc

(79)

To determine the value of Z, the value of pr is located on the X axis. At the point where pr intersects the appropriate Tr plot, the value of Z is read at the Y axis of the chart.

Figure 38 Generalized Compressibility Chart Maximum Impact Of Z - Refer to Figure 38 and note that compressibility effects become most significant when the inlet pressure approaches the fluid critical pressure (i.e., as pr approaches 1.0), and/or as the inlet temperature approaches or falls below the fluid critical temperature.


64



Piping Effects Piping Factor FP - When expanders and reducers are used, the piping factor FP is

included in the equation as shown below: q = Fp C v p1 Y

x Gg T1 Z

(80)

The following equation is used to calculate Fp. The equation is the same equation that is used for liquids.  ΣK C 2  v Fp =  1  +  N2 d4 

−1 2

(81) XT Plus Piping Factor FP = xTP - The value of XT is also affected by inlet reducers.

Outlet expanders are considered as part of the valve for purposes of determining XT. When the factor XT is modified to account for an inlet reducer, it becomes xTP, and it is calculated with the following: −1  xT  x T Ki C v2 x TP = 2  + 1 F p  N5 d 4 

(82)

Where: Ki = The inlet loss coefficients only (K1 + KB1).

Effect of XTP On Valve Sizing - The use of inlet reducers rarely affects the value of xT

significantly; therefore, it is often ignored, except in the case of large, highly efficient valves. Experienced specifiers often ignore the effect of inlet reducers on xT except when the ratio of Cv to d (ratio of valve capacity to valve size) becomes very large (as it does with ball and butterfly valves), and the valve inlet is much smaller than the pipe size. In these situations, the value of x that is used in the sizing equations should be limited to the value of xTP.


65



Calculating XTP - The equation that is used to calculate control valve Cv through the use of the xTP factor (see Equation 83) is highly iterative. Note that the equation to calculate Cv requires the terms Fp and xTP; however, the equations that are used to calculate Fp and xTP both include the Cv term. Therefore, an estimated value of Cv must be calculated (without consideration of Fp and with the use of xT instead of xTP). The estimated Cv is then used to initially solve for both Fp and xTP. The calculated values Fp and xTP are then used to solve for Cv. Several iterations of the equations

must be solved until the solutions converge on a useful result. Generally speaking, only two or three iterations are necessary to arrive at a useful result. When successive iterations of the calculations result in very small differences in the calculated Cv, the specifier knows that accuracy has been achieved Gg T1 Z q Cv = x TP N 7 Fp p1 Y (83)

but  ΣK C 2  v + 1 Fp =   N 2 d4 

− 12

and

−1  xT  x T Ki C v2 x TP = 2  + 1 F p  N5 d 4 

(84)

Although manual sizing involves the use of many calculations, the necessary calculations are performed easily and quickly with personal computers and appropriate software.


66



Final Equation Form Numerical Constants - The final term in the ISA equation is the term N7, or the units

constant. The specifier selects a units constant that allows use of either the metric or the English units system. x G g T1 Z

q = N7 Fp C v p1 Y

(85)

Solving For Cv - For purposes of valve sizing, Equation 85 is arranged to solve for Cv as

follows:

Cv =

q N 7 Fp p1 Y

Gg T1 Z x

(86)

Summary Of ISA Equation Terms Following is a quick review of terms in the equation. q

flow rate (scfh, lbs/hr, kg/hr depending on the units constant, N7)

N2

units constant that is used in the equation to calculate Fp; N2 allows pipe and valve inside diameters to be expressed in mm (N2=0.00214) or in inches (N2=890); refer to Figure 4

N5

units constant that is used in the equation to calculate XTP; N5 allows pipe and valve inside diameters to be expressed in mm (N2=0.00214) or in inches (N2=890); refer to Figure 29

N7

units constant to determine units for pressure, flow, and temperature measurements; refer to Figure 29

Fp

piping geometry factor, dimensionless

Cv

control valve flow coefficient

p1

inlet pressure, absolute Y = 1−

x 3Fk x T where F = ratio of specific heats factor k

Y

expansion factor.

Gg

gas specific gravity (ratio of the density of the flowing gas to the density of air, with both at standard conditions)

T1

inlet temperature, absolute

Z

compressibility factor, dimensionless

x

pressure drop ratio ( ∆P / p1 ); limited to xT for choked flow, FKxT to account for specific heat ratio, and xTP to correct for piping factors


67



Computer Sizing Control Valves For Gasses Using The ISA Equations Introduction The procedures that are used to operate the Fisher Sizing Program when sizing control valves for compressible fluids are similar to the procedures that are used with the liquid sizing method. The major differences are the required inputs, the entries in the Intermediate Results section, and the results that are displayed in the Calculated Results section. Valve Sizing Methods Available When the main menu item Valves is selected, the specifier is presented with several sizing options as shown in Figure 39. The ISA options are as follows: ISA Gas - Selecting the ISA Gas method causes the software to use the equations in which fluid density is expressed in terms of SG or M. ISA Vapor - Selecting the ISA Vapor method causes the software to use the equations in which fluid density is expressed in terms of specific weight (e.g., lbs/ft3. kg/m3, etc.) The Vapor method calculates the most accurate results with the fewest inputs.

Figure 39 Valve Sizing Method Options


68



Selecting The Desired Calculation Type After a valve sizing method has been selected, the specifier selects the type of calculation that will be performed. Refer to Figure 40. Choices include valve sizing, fluid velocity calculations, and various noise calculations.

Figure 40 Available Calculation Types Overview Of Sizing Procedures Valve Sizing Screen - Selecting the Valve Sizing & LpA option brings up the sizing

screen. This screen is divided into several sections as shown in Figure 41 below.

Figure 41 Valve Sizing Screen For The ISA Gas Valve Sizing Method


69



Fluid And Service Conditions - In this section, the specifier enters the fluid type, and fluid

properties such as critical pressure, critical temperature, and Fk. Service conditions are also entered in this section. Intermediate Results - Any intermediate results that the software calculates are displayed in the Intermediate Results section. Examples include the calculated values of Y and Z. Valve Specification - In this section, the specifier enters any needed valve data such as xT and sizing data for the valve and piping if piping corrections are necessary. Calculated Results - After all fluid properties, service conditions, and valve data are entered in the appropriate locations, the specifier presses the function key F2 to calculate the required control valve Cv. The results of the sizing calculations appear in the calculated results section. In addition to valve Cv, other important information such as the ∆Pchoked and the pressure drop ratio (x) is also shown. Selecting Options F3 Options - During the sizing procedure, the specifier may choose from several

different sizing options by pressing the function key F3. The options menu for the ISA Gas method is shown in Figure 42. 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.

Figure 42 Calculation Options For The ISA Gas Valve Sizing Method


70



F3 Options For The ISA Gas Sizing Method - Options for the gas sizing method are as

follows: Line 1: Solve for Cg, Cs, or Cv. Other options: Solve For Flow, Solve For dP (pressure drop) Line 2: Calculate Z. Option: Input Z Line 3: Calculate Fp. Other options: Input Fp & Xtp, Omit Fp & Xtp Line 4: LpA (SPL) OFF. Option: Calculate LpA (SPL) Line 5: Pipe: Size/Sched. Option Pipe: Diameter/Thickness Line 6 Warnings ON. Option: Warnings OFF F3 Options For The ISA Vapor Sizing Method - Options for the vapor sizing method are the same as for the gas method, except that there is no option for calculating Z. Recall that compressibility effects are not considered when the vapor form of the equation. Options And Input Fields - As various options are selected, the input fields on the sizing screen will change; for example, if the option to calculate Z is selected, the software will require values for critical pressure and temperature, and it will display the calculated value of Z. Units-Selection - As explained previously, engineering units can be changed globally through the selection of Units from the Config heading on the main menu. The specifier may also change units for any input parameter by placing the cursor on that parameter and pressing F8. Pressing F8 produces a sub-menu (refer to Figure 43) of available options.

Figure 43 Line-By-Line Units Options For Flow


71



The Fisher Universal Gas Sizing Equation Introduction Many valve specifiers use the Fisher Universal Gas Sizing Equation as an alternative to the ISA equations. The Fisher Universal Gas Sizing Equation gained popularity immediately after its introduction in 1951 because it was easier to use than other techniques that were available at that time. During this era, specifiers sized valves manually, either by calculation or with slide rules. At a later date, the programmable calculator gained popularity for valve sizing. The Universal Gas Equation was easily adapted for use with the programmable calculator because of its straightforward, non-iterative nature. Today, control valve specifiers size valves with computers and sizing software; accordingly, equation complexity is less of an issue. Fisher And ISA Equation Comparison While the Fisher and ISA equations differ in many ways, they both model the gas flow process in a similar fashion and they give nearly identical results. With rare exception, any discrepancies in calculated results are within the limits of accuracy of any sizing technique. In virtually all instances, either equation will direct the specifier to the same valve size. Key differences between the Fisher and ISA equations include the following: •

For gasses and vapors, the Fisher equation uses the flow coefficient Cg, rather than Cv. Cg relates critical flow to absolute inlet pressure.

•

The Fisher equation uses a sine term to account for fluid expansion in the region between linear flow and choked flow. This approach eliminates the need to calculate the value of an expansion factor (Y).

Terms to account for the influences of piping factors, compressibility, and specific heat ratios other than 1.0 are not included in the basic equation; instead, they are considered on an as-needed basis. The Fisher Universal Sizing equation for an ideal gas is as follows:   3417  ∆ P  520  Q= Cg P1 C2 SIN    C1 C2  P1  GTZ •

Degrees


(87)

72



Equation Basics To gain an understanding of equation mechanics and the terms that are used in the equation, the equation will be discussed by starting with its most basic form. Basic Liquid Flow Equation - All early efforts to derive a useful gas sizing equation began with the basic liquid sizing equation (see Equation 88). ∆P Q(GPM) = Cv G (88) Adding A Constant To Change From GPM To SCFH - The first step in adapting the equation for use with compressible fluids is to add a conversion factor to change units from gallons-per-minute to cubic-feet-per-hour. In addition, specific gravity is related in terms of pressure, which is more meaningful for gas flow. Refer to Equation 89. Note that the ratio of ∆P to P1 is known as the pressure drop ratio and that the pressure drop ratio is identical to the x term in the ISA equation. The result is as follows: ∆P Qscfh = 59. 64 Cv P1 P1 (89) Provisions For Any Specific Gravity And Temperature - With the inclusion of a modification

that is based upon Charles' Law for gasses, the equation is generalized to account for any gas at any temperature as shown in Equation 90. ∆ P 520 Q scfh= 59. 64 C v P1 P1 GT (90)

Where: 520 G T

= The product of the specific gravity and the absolute temperature of air at standard conditions (i.e., the specific gravity is 1.0 and the temperature is 520 degrees Rankine, which corresponds to 60 degrees F). = The specific gravity of the flowing gas at standard conditions (60 degrees F and 14.7 psia). = The temperature of the flowing gas in degrees Rankine.


73



Equation Limits Pressure Drop Ratio Limits - Equation 90 predicts a flow rate that is a linear function of

the square root of the pressure drop ratio (the same as the flow rate that is predicted by the x term in the ISA equation); however, at pressure drop ratios that are greater than approximately 0.02, tests show smaller and smaller incremental increases in actual flow for every incremental increase in the pressure drop ratio. Refer to Figure 44. Critical Flow - Tests also indicate a point of critical flow, which is the same as choked flow in ISA terminology. Critical flow is defined as the point where increasing the pressure drop ratio by reducing downstream pressure does not produce any increase in flow rate.

Figure 44 Actual Flow Versus Predicted Flow


74



Pressure Recovery And Critical Flow The next challenge was to determine a method that could be used to predict the critical flow rate. As it turns out, critical flow is a function of valve geometry. A comparison of plots that relate critical flow to the pressure drop ratio for two different valve styles illustrates the concept. Refer to Figure 45. Note that the two valves have identical Cv ratings, but one of the valves is a high recovery type and the other valve is a low recovery type.

Figure 45 Critical Flow For Low And High Recovery Valves Low Recovery Valves (or globe style valves) reach critical flow at a pressure drop ratio of approximately 0.5. High Recovery Valves reach critical flow at much lower pressure drop ratios. Flow Coefficient Cg and Critical Flow - Because of the problems in using Cv to predict critical flow in both high and low recovery valves, Fisher Controls developed a standard for testing flow capacity with air as well as with water. From these tests, a gas sizing coefficient Cg was defined that relates gas critical flow to the absolute inlet pressure. Cg is experimentally determined for each valve style and size; therefore, Cg can be used to accurately predict critical flow (using air as a test fluid) with the following: Qcritical = Cg P1 (91)

To make the critical flow equation useful for any gas at any temperature, the correction factor that was shown previously is applied: 520 Qcritical = Cg P1 GT (92)


75



Blending The Two Equations Impracticality Of Using Two Equations - At this point, Fisher had two equations. See

Figure 46. Equation A (see Equation 93) accurately predicted flow at very low pressure drop ratios only. Note that this equation uses the flow coefficient Cv. ∆P 520 Q = 59. 64 C v P1 P1 GT (93)

Equation B (see Equation 94) predicted critical flow only. Note that this equation uses the flow coefficient Cg. 520 Qcritical = Cg P1 GT (94) Although the equations provided utility, neither equation accounted for the transition region between low flow conditions and critical flow; i.e., when ∆P/P1 > 0.02 and Q < Qcritical. In addition, the process of using two equations and two flow coefficients was inefficient.

Figure 46 Predicting Low Flow And Critical Flow


76



Tests And Data Plotting - To arrive at a single equation, Fisher Controls completed an

extensive testing procedure to analyze flow versus pressure relationships in the region between low pressure drop ratios and critical (choked) flow. Tests were performed on high recovery valves, low recovery valves, and valves that can be called intermediate recovery valves. Test results were normalized with respect to critical flow, and data was plotted. Sine Curve - Analysis revealed that the test points in the transition region between low flow and critical flow fell on a curve that closely approximates the first quarter cycle of a standard sine curve. See Figure 47 below.

Figure 47 Tested Values Of Flow Compared To A Sine Curve Combining The Equations - Capitalizing on this finding, Fisher Controls used a sine function to mathematically model flow in the transition region. The sine function effectively blends Equation 93 and Equation 94 into one, as shown in Equation 95. Note that the result of the sine function must be limited to a maximum of 90 degrees so that the equation does not predict decreasing flow after critical flow is achieved.   3417  DP  520  Q= C g P1 SIN   GT   C  P  1


1 Degrees

(95)

77



The C1 Factor Note the inclusion of the C1 factor in Equation 96.   3417  520  Q= C g P1 SIN   GT  C  1 

∆P  P1 

Degrees

(96)

Role of C1 - The role of C1 is to allow the use of a single sizing coefficient (Cg) in a

universal equation that combines the equation that is used to calculate the flow of incompressible fluids (Equation 97) with the equation that is used to calculate the critical flow of a gas (Equation 98). A fundamental obstacle in blending Equations 97 and 98 is that the liquid flow equation uses the flow coefficient Cv, while the gas flow equation uses the flow coefficient Cg. ∆P 520 Q = 59. 64 C v P1 P1 GT Liquid Flow (97) 520 Q= C g P1 GT Gas Flow (98) Equations 97 and 98 could have been combined in their original forms; however, the specifier would have to supply both the Cv coefficient and the Cg coefficient. During the development of the Fisher equation, the decisions were made that a single coefficient would be used and that a factor to account for the differences in liquid and gas flow through a particular valve would be included in the equation. The factor C1 is used for this purpose. As shown in Equation 99, C1 is defined simply as the ratio of the gas flow coefficient, Cg to the liquid flow coefficient, Cv. Cg C1= Cv (99)


78



Differences In Gas And Liquid Capacity - In order to better understand the significance of

the C1 term, consider a comparison of the Cg and Cv flow coefficients for a high recovery valve, and the Cg and Cv flow coefficients for a low recovery valve that are shown in Figure 48. Liquid flow (Cv) is heavily influenced by valve geometry (i.e., whether the flow path is tortuous or streamlined). Gas flow (Cg) is largely a function of the flow area of the valve. The difference in the factors that determine capacity for liquid flow and for gas flow explain why two valves with identical Cg's can have substantially different Cv's (and why two valves with identical Cv's can have substantially different Cg's). TYPICAL C1 VALUES FOR HIGH AND LOW RECOVERY VALVES High Recovery Valve

Low Recovery Valve

Cg = 4680

Cg = 4680

Cv = 254

Cv = 135

C1 = Cg/Cv

C1 = Cg/Cv

= 4680/254

=4680/135

=18.4

=34.7

Figure 48 Comparison of Cv, Cg, and C1 Values Locating C1 Values - Manufacturers that use C1 values determine them by test, and they

publish them in sizing catalogs along with other sizing information. For globe valves, the value of C1 is the same at all percentages of travel. For rotary-shaft control valves, the value of C1 depends on the degrees of rotation.


79



Mechanics Of The Sine Term Concept - A close look at the sizing equation reveals that the quantity of the sine

function is essentially used as a multiplier with the simple equation for critical flow. Refer to Equation 100.   3417  ∆P  520  Q= C g P1 SIN   GT   C1  P1  Degrees

(100) Predicts Qcritical Serves as a multiplier Low Pressure Drop Ratio Example - Assuming a C1 value of 35 and a pressure drop ratio

of 0.02, the value of the bracketed terms is as follows:   3417   0. 02  SIN  = SIN [98 × 0.141]Degrees = SIN 13 = 0. 225   35   Degrees

(101)

The flow rate that is predicted by the critical flow equation is multiplied by 0.225; therefore, the calculated value of Q will be relatively small. Higher Pressure Drop Ratios - As the pressure drop ratio increases, the sine function, at the end of the first quarter cycle, tends towards its maximum value of 1.0. If the result of the sine function is 1.0, the equation is functionally reduced to the equation for critical flow as illustrated in the following equation.   3417  ∆P  520 ∆P  Q= C g P1 SIN   = 1. 0 GT   C1  P1 Degrees P1 and 102) If   3417   520 SIN  1  ≈ SIN 90° = 1. 0 Q= C g P1    35  GT then and (103) Intermediate Pressure Drop Ratios - At intermediate pressure drop ratios, the sine function

models flow in the transition region between low flow and critical flow.


80



Alternate Forms Of The Universal Sizing Equation Ideal (Perfect) Gas Law Assumptions - The equation that has been discussed to this point is

based on the ideal gas laws. As was discussed previously, real gas behavior can differ markedly from ideal behavior. Real Gasses - The real gas form of the Fisher equation uses two correction factors. The corrections are for compressibility and for the ratio of specific heats. Both corrections are similar to the real gas corrections that are used in the ISA sizing equations. The Z Factor And Real Gas Compressibility - When the compressibility of a real gas does not follow the ideal gas law of pV = RT, the term Z is used to correct the ideal gas equation. pV = ZRT (104) The value of Z can be determined from generalized compressibility charts (refer back to Figure 38) after establishing the reduced pressure and temperature with the use of the following equations: P T Preduced = actual and Treduced = actual Pcritical Tcritical (105)

The Z term is included in the equation as follows:   3417  ∆P  520  Q= Cg P1 SIN   GTZ   C1  P1 

Degrees


(106)

81



C2 And The Ratio Of Specific Heats - In the Fisher equation, allowance is made for thermodynamic properties (the ratio of specific heats) with the term C2. C2 serves the same function as the Fk factor in the ISA equations. C2 is included in

the equation as follows: Q=

  3417  520  Cg P1 C2 SIN   GTZ  C C  1 2

∆P  P1 

Degrees

(107)

In the ISA equation, the Fk factor suggests a linear relationship between k and Fk (i.e., Fk = k/1.4). This relationship is typically valid for k values between 1.2 and 1.6 only. The Fisher equation uses a somewhat more precise correction. Although C2 values are found to be a strong function of k, the relationship is not precisely linear. For a specific value of k, the specific value of C2 can be determined from the chart that is shown in Figure 49.

Figure 49 C2 Factor Versus k


82



Density Form Of Equation (Mass Flow/Vapor) - When the specific weight (weight per unit

of volume) of the fluid at the valve inlet is known, a more generalized form of the equation can be used. The density form of the equation, (see Equation 108) eliminates the need to correct for the effects of pressure and temperature on density, and it also eliminates the need for the Z term.   3417  ∆P   Q = 1. 06 d1P1 C g SIN     C1  P1  Degrees

(108)

Where: Q = Gas, steam, or vapor flow (lbs/hr, kg/hr, etc.). d1 = The density of the gas at the valve inlet (lbs/ft3, kg/m3, etc.). The density form of the equation is commonly used for steam and other vapor applications. Special Steam Equation (Below 1000 PSIG) - Because steam applications are quite common, a special form of the equation, which is shown in Equation 109, is also available.   3417  ∆P    C s P1  QLB/HR = SIN    1+ 0. 00065 T sh    C  P1  1

Degrees

(109)

Where: Cs = The steam sizing coefficient. Tsh = The degrees of superheat (degrees F). Note that Equation 109 uses the flow coefficient Cs (s is for steam). Fisher Controls publishes Cs values for most valves. The relationship between Cs, Cg, and Cv is as follows: Cg Cs = C g = C s x 20 20 therefore (110) Note also that Equation 109 can be used only for steam below 1000 psig.


83



Solving for Cg Rearranging The Equations - While the equations have been discussed in forms that

predict flow rate, any of the equations that are used to predict flow can be arranged to solve for the required control valve Cg as shown in Equation 111. Q scfh Cg =  3417 ∆P  520 P1 C 2 SIN  C1 C2 P1  GTZ Degrees

(111) Initial Assumptions For C1 Values - When solving for Cg, the specifier must initially select a valve style and estimate a value of C1. After calculating Cg and selecting a specific valve type and size, the actual C1 values for the selected valve are used in the equation to ensure maximum accuracy. Specifiers typically use initial (estimated) C1 values of approximately 35 for standard globe style valves, and C1 values of

approximately 15 to 20 for ball and butterfly valves. Converting Cg To Cv - It may occasionally be desirable to convert a flow coefficient from Cg to Cv; for example, it may be useful to size non-Fisher valves by means of the Fisher Sizing Program, or it may be useful to convert Cg to Cv for comparative studies of capacity or other valve attributes. Recall that C1 is calculated as follows: Cg C1= Cv (112) Therefore, after a Cg has been calculated, it can be converted to Cv as follows: Cg Cv = C1 (113)


84



Comparison Of Fisher And ISA Gas Sizing Equations Both the ISA and the Fisher equations model the same process and typically produce nearly identical results. Although minor differences in the calculated flow coefficient may occur, the use of either equation will virtually always lead the specifier to the same valve size. The table below summarizes how the two equations account for various aspects of flow through the control valve. Parameter

Flow equation

ISA Equation

q = N7 Fp C v p 1Y

Flow Coefficient

Cv (water test)

Flow when ∆P / p1 ≤ 0. 02

Cv

x G g T1 Z

∆P p1 (liquid equation)

Fisher Equation Q=

  3417 C g P1 C 2 SIN     C 1 C 2 GTZ 520

Cg (air test) Cv

Cv =

   

∆P   P1 

Degrees

Cg C1

∆P p1 (liquid equation)

Critical Flow For Specific Valve Style

p 1 xT

p1 Cg

Published xT tested by manufacturer

Published Cg tested at critical flow

Fluid Expansion

Y x

Sine function

Piping Factor

FP factor

Swaged capacities for rotaryshaft valves published in sizing information

Calculated by specifier or tested and published by manufacturer Compressibility (real gasses) Thermodynamic behavior (k)

Z=

pV RT

F k xT

Can use FP Z=

pV RT

C2

Figure 50 Comparison of ISA And Fisher Sizing Terms


85



Computer Sizing Control Valves For Gasses Using The Fisher Controls Equations Valve Sizing Methods Available When the main menu item Valves is selected, the specifier is presented with several sizing methods as shown in Figure 51. The available methods are: Fisher Ideal Gas - The Fisher Ideal Gas method assumes ideal gas behavior; accordingly, the corrections for compressibility (Z) and for non-ideal thermodynamic properties (C2) are not used. In this sizing method, Z is assumed to be 1.0, and k is assumed to be 1.4. Fluid density is expressed in terms of SG or M. Fisher Real Gas - The Fisher Real Gas method includes options for the use of Z factors and C2 coefficients. This method is similar to the ISA Gas method. Fisher Vapor - The Fisher Vapor method is similar to the ISA Vapor method except that there is no option for the piping factor correction. Fluid density is entered in terms of lbs/ft3 or kg/m3, and there are options for the use of Z and C2 factors. The vapor method is also commonly used for steam. Fisher Steam - The Fisher Steam method uses the special equation for steam applications under 1 000 psig.

Figure 51 Valve Sizing Methods


86



Selecting A Calculation Type After a specific valve sizing method has been selected, the specifier can choose the type of information that is being sought. As shown in Figure 52, choices include valve size, fluid velocity, and various noise calculations.

Figure 52 Selection Of A Calculation Type Overview Of Sizing Procedures Valve Sizing Screen - Selecting the Valve Sizing & LpA option brings up the actual

sizing screen, which is illustrated in Figure 53. The sizing screen is divided into four distinct sections.

Figure 53 Saudi Aramco DeskTop Standards

87



Valve Sizing Screen For The Fisher Real Gas Sizing Method


88



F3 Options Fisher Ideal Gas - As shown in Figure 54 below, there are no sizing options for the Ideal Gas Method that affect how the flow coefficient is determined.

Figure 54 Calculation Options For The Fisher Ideal Gas Sizing Method Fisher Real Gas - The calculation options for the Fisher Real Gas Method (see Figure 55) present the specifier with several choices for the use of Z and C2 factors. The choices are as follows: • Input Z, omit C2 • Input Z, calculate C2 (C2 is calculated from k) • Calculate Z, C2 (Z is calculated from Pc and Tc)

Figure 55 Calculation Options For The Fisher Real Gas Sizing Method Saudi Aramco DeskTop Standards

89



Fisher Vapor - As shown in Figure 56, there are no sizing options for the Fisher Vapor

Method that affect the calculation of the flow coefficient.

Figure 56 Calculation Options For The Fisher Vapor Sizing Method Fisher Steam - The only option in the Fisher Steam Method is the choice of whether the

specifier will input steam temperature or assume that the steam is saturated. See Figure 57.

Figure 57 Calculation Options For The Fisher Steam Sizing Method


90



Options And Input Fields - As various options are selected, the input fields on the sizing

screen will change; for example, if the option to calculate Z is selected, the software will require values for critical pressure and temperature. Refer to Figure 58. Units-Selection - As explained previously, engineering units can be changed globally by selecting Units from the Config heading on the main menu; in addition, the specifier may change the units for any input parameter by placing the cursor on that parameter and pressing F8. Figure 58 illustrates the available units options for fluid temperature.

Figure 58 Pull-Down Menu Options For Temperature


91



eNTERING VALVE SIZING DATA ON THE SAUDI ARAMCO ISS To complete a Saudi Aramco Instrument Specification Sheet (ISS), the specifier must calculate and enter information that describes both the physical size of the valve and information that describes the capacity of the valve. For purposes of illustration, the discussion that follows is based on the ISS for globe and angle control valves (Refer to Saudi Aramco Form 8020-711-ENG.) Body And Flange Size Control Valve Physical Size Information Body And Port Size - After a particular valve size is selected, the body size and port size

are entered on line 49. Flange Sizes and Ratings - The inlet flange size, rating, and style are specified on line 50.

The outlet flange size, rating, and style and rating are specified on line 51. Face-To-Face Dimensions - are entered on line 72. The face-to-face dimension for a particular valve style and size is included in the appropriate valve specification bulletin. Capacity Ratings Capacity At Minimum, Normal, And Maximum Flow Conditions Cv At Minimum, Normal, And Maximum Flow Conditions is specified on lines 62 through

64.

Maximum Rated Cv of the valve is specified on line 65. Percent of Rated Cv At Min, Norm, and Max Flow Conditions is also entered on lines 62

through 64. Each value is simply the calculated Cv at each flow condition divided by the maximum rated Cv of the selected valve. Valve Travel At Minimum, Normal, And Maximum Flow Conditions Throttling Range is shown on line 66. The lower value of the range is defined by the

percent of valve travel that provides the minimum Cv requirement, and the upper value of the range is the percent of valve travel that provides the maximum Cv requirement. Valve Opening At Normal Flow is the percent of valve travel that provides the required Cv at normal flow conditions.


92



Figure 59 The Saudi Aramco ISS


93



WORK AID 1: PROCEDURES THAT ARE USED TO MANUALLY SIZE CONTROL VALVES FOR LIQUID APPLICATIONS Work Aid 1A: 1.

Procedures That Are Used To Calculate The Required Control Valve Cv

Use the following ISA and Fisher equations to solve for Cv. G Cv =Q ∆P Fisher: Cv =

ISA:

q N1

Gf p1 − p2

To determine the appropriate value N1, refer to the table below. Constant N

N1

2.

0.0865 0.865 1

Units That Are Used In Equations d, D γ1 p, ∆P

w

q

-------

m3/h m3/hr gpm

kPa bar psia

-------

ν

-------

-------

Refer to Fisher Catalog 10 or to other manufacturer's catalog and locate the appropriate pages for the valve types that are described in the Exercise. For each valve type, browse through the Cv table and locate a valve size that will provide the required capacity. Ensure that you select a valve size that will provide the required Cv at a percentage of travel that is consistent with the guidelines that are given in Section 5.2 of SAES-J-700. The guidelines are summarized in the table below. Extrapolate the degrees of rotation or the percent of travel that provides the required Cv. For rotary-shaft valves, convert the degrees of rotation to percent of travel by dividing the degrees of rotation that provide the required Cv by 90 degrees.

Guidelines For Percent Travel At Various Flow Conditions Per Section 5.2 of SAES-J-700 Flow Characteristic

Equal Percentage Linear Modified Parabolic


Percent Travel At Normal Flow

Percent Travel At Maximum Flow

80 70 75

93 90 90

94



Work Aid 1B:

Procedures That Are Used To Calculate The Allowable Pressure Drop (∆Pallow)

Perform the following procedures to complete Exercise 1B. 1.

2.

Locate the required fluid properties from the Fisher Control Valve Handbook as follows: SG

Properties of Water table, page 135

Pv

Properties of Water table, page 135 (given as Saturation Pressure)

Pc

Physical Constants of Various Fluids table, page 134

Using the following equation, calculate the ∆Pallow. ∆Pallow = Km (P1-rc Pv) Locate the values that are required to solve the equation as follows:

3.

Km

Use the value that is listed in the Exercise under the heading "Valve Specifications."

P1

Use the value that is listed in the Exercise under the heading "Service Conditions."

Pv

Use the value that was recorded during step 1. of this Exercise.

rc

Refer to Fisher Catalog 10, section 2, page 10, Figure 1.

Using the Fisher Sizing equation that is included in Work Aid 1A, calculate the required Cv. Use the lesser of the actual ∆P or the ∆Pallow. Refer to the page in Fisher Catalog 10 that lists the Cv's for the selected valve and select the smallest valve size that will provide the required Cv at a percentage of travel that is consistent with the guidelines that are given in Section 5.2 of SAES-J-700 (refer to Work Aid 1A). Extrapolate and record the percent of travel at which the Cv requirements are met. Note and record the Km of the selected valve.

4.

Using the value of Km that was determined in step 2, recalculate the ∆Pallow.

5.

Using the new value of ∆Pallow, recalculate the required Cv.

6.

Select a valve size that will meet the Cv requirements.

7.

Extrapolate and record the percent of travel at which Cv requirements are met.


95



Work Aid 1C:

Procedures That Are Used To Calculate The Effect Of Piping Factors On Cv

Perform the following procedures to complete Exercise 1C. 1.

Locate the appropriate pages in Fisher Catalog 10 for the valve that is described in the Exercise. Ensure that you locate the page for the line-to-body size ratio that is given in the Exercise. Browse through the Cv column and locate a valve that provides the maximum Cv at less than the percent of travel guideline that is included in Section 5.2 of SAES-J-700. Note: For rotary valves, the percentages of travel that are listed in Section 5.2 of SAES-J-700 can be converted to degrees of rotation as follows: % travel x 90 degrees

2.

Refer to Section 5.4 of SAES J-700. Locate the value of R for the valve type that is described in the Exercise. Calculate the required Cv through use of the following equation: Re quired C v =

Calculated C v R

Using the required Cv that was just calculated, refer to the appropriate page in Fisher Catalog 10, and select a valve size. Note: The required Cv has already been corrected; therefore, ensure that you select a valve size from the page for the 1:1 line-to-body size ratio. Also, ensure that the selected valve provides the maximum required Cv at a travel that is consistent with the guidelines that are listed in Section 5.2 of SAES-J700. (Refer to the note in step 1, above.)


96



Work Aid 1D:

Procedures That Are Used To Calculate The Effect Of Laminar Flow On Cv

Perform the following procedures to complete Exercise 1D. 1.

Without attempting to compensate for fluid viscosity, calculate the required Cv for the application that is described. Use the following equation. Cv =Q

2.

G ∆P

To compensate for viscous effects, locate the Viscosity Correction Nomograph in Fisher Catalog 10, Section 2, pages 26 and 27 and follow the instructions that are included in the nomograph. Use the value of Cv that was calculated in step 1.


97



Work Aid 2:

Procedures That Are used to Computer size con trol valves for liquid Applications

Work Aid 2A:

Procedures That Are Used To Computer Size Control Valves For Water Applications

1.

2.

Use the following procedures to complete part 1. a.

If necessary, press ESCAPE to return to the main menu.

b.

From the main menu, select Valve.

c.

Press and hold the ALT key and press F5 to clear all sizing inputs.

d.

Select the Fisher Water method.

e.

From the menu that appears, select the Cv Simple method.

f.

Ensure that the engineering units on the calculation screen match the units that are used to describe the application. If the units do not match for any field, move the cursor to that field, press the F8 key, and select the desired units. Press ESCAPE.

g.

Enter the pressure drop (dP). dP = P1 minus P2.

h.

Locate the SG of water at 100 degrees F from the table on page 135 of the Fisher Control Valve Handbook. Enter the value of SG in the appropriate field.

i.

Enter the flow rate.

j.

Press F2 to calculate the valve sizing information. Record the values that are requested in the Exercise.


Press ESCAPE.

b.

Select the Valve Sizing and LpA option.

c.

Press F3 and ensure that the options are selected as follows: •

Solve for Cg, Cs, or Cv

•

LpA (SPL) OFF

•

Calculate SG


98



•

Cavitation Check OFF

•

Warnings OFF

d.

Ensure that all of the fluid properties and the service conditions are accurately entered.

e.

Enter an estimated value of Km. Select a value from the table below. Typical Values Of Km and FL

Valve Style

Globe And Angle Rotary-Shaft f. 3.

4.

Typical Km

0.75 0.45

Typical FL

.87 0.67



Press ESCAPE twice.

b.

Select the Fisher Liquid method.

c.


d.

Press F3 and ensure that the Input Pv option is selected.

e.

Enter the value of Pv that was recorded during step 2 above.

f

Obtain the value of Pc from the table on page 134 of the Control Valve Handbook

g.

Ensure that all service conditions and fluid properties are accurately entered.

h.



Press ESCAPE twice.

b.

Select the ISA Liquid method.

c.



99



d.

Determine an estimated value of FL through the use of the equation that follows or by selecting a value from the table below. Estimated FL = Estimated K m Typical Values Of Km and FL Valve Style

Globe And Angle Rotary-Shaft

Typical Km

0.75 0.45

Typical FL

.87 0.67

e.

Enter the estimated FL.

f.

Ensure that all service conditions and fluid properties are accurately entered.

g.



100



Work Aid 2B:

Procedures That Are Used To Computer Size Control Valves For Choked Flow

Use the following procedures to complete Exercise 2B. 1.

Return to the main menu.

2.


3.

From the menu that appears, select the Fisher Liquid method.

4.

Press and hold the ALT key and press F5 to clear any sizing inputs.

5.


6.

Press F3 and ensure that the option Input Pv is selected.

7.

Enter the fluid name as "HC liquid."

8.

Enter the fluid properties and the service conditions.

9.

Enter the estimated Km. (Refer to the table in step 4 of Work Aid 2A.)

10.

Press F2 to calculate the valve sizing information.

11.

Refer to the appropriate page in Catalog 10 and select a valve size that will provide the maximum Cv at a percentage of travel that is consistent with the guidelines that are listed in Section 5.2 of SAES-J-700. (Refer to the table in Work Aid 1A).

12.

Record the information that is requested under the heading "Initial Calculations and Valve Selection."

13.

Using the Km of the initially selected, recalculate the valve sizing information. Note that the calculated Cv may now allow the selection of a smaller valve. To determine if a smaller valve will pass the required flow, use the Km of the smaller valve to recalculate the sizing information.

14.

Record the information that is requested under the heading "Final Calculations and Valve Selection."


101



Work Aid 2C:

1.

2.

Procedures That Are Used To Computer Size Control Valves For Fluids In The Sizing Database


Return to the main menu.

b.


c.

From the menu that appears, select the Fisher Liquid method.

d.

Press and hold the ALT key and press F5 to clear any sizing inputs.

e.


f.

Press F3 and ensure that the option Input Pv is selected.

g.

Enter the fluid name as "Liquid Propane."

h.

Refer to page 130 of the Fisher Control Valve Handbook, and locate the values of Pc, Pv, and SG for the liquid. Enter these values in the proper fields on the calculation screen. Note: The value of Pv that is included in the table is for the fluid at a temperature of 100 degrees F; however, this value of Pv will be used because it is the only value that is available.

i.

Enter all of the service conditions.

j.

Enter an estimated value of Km. (Refer to the table in part 4 of Work Aid 2A.)

k.

Press F2 to calculate the valve sizing information. Record the information that is requested under the heading Calculated Results.


Place the cursor on the appropriate fields and press the F5 key to clear the values that were previously entered for Pv and Pc.

b.

Press F3 and select the Calculate Pv option.

c.

Place the cursor in the Fluid field and press F4 to display a list of fluids. From the pull-down menu, select Propane.

d.



102



3.

4.


Without clearing the calculation screen, change the temperature and the SG to to the values that are stated in part 3.

b.



Without clearing the calculation screen, change the Km to 0.75.

b.

Press the F2 key to calculate the valve sizing information. Record, under the heading Calculated Results on the Exercise Sheet, the information that is requested.


103



Work Aid 2D:

1.

2.

3.

Procedures That Are Used To Computer Size Control Valves With Piping Factor Correction


Press ESCAPE to return to the menu that gives choices of sizing methods.

b.

Select the Fisher Water sizing method.

c.

Press and hold the ALT key, and press the F5 key to clear all sizing inputs.

d.


e.

Press F3. Ensure that the option Calculate SG is selected.

f.

Enter the service conditions.

g.

Enter an estimated value of Km. (To determine an estimated Km, refer to the table in step 4 of Work Aid 2A).

h.

Press F2 to calculate the valve sizing information. Record the calculated Cv.


Locate the page in Fisher Catalog 10 that describes the valve that is specified. Ensure that you locate the page that lists capacities for the appropriate line-tobody size ratio.

b.

Select a valve size that provides the maximum required Cv at a percentage of travel (or degrees of rotation) that is consistent with Section 5.2 of SAES-J700. (Refer to the table in part 2 of Work Aid 1A.)

c.

Record the information that is requested in the Exercise.


Locate the page in Fisher Catalog 10 that describes the valve that is specified. Ensure that you use the page that lists capacities for the appropriate line-tobody size ratio.

b.

Select a valve size that provides the maximum required Cv at a percentage of travel (or degrees of rotation) that is consistent with Section 5.2 of SAES-J700. (Refer to the table in part 2 of Work Aid 1A.)

c.

Record the information that is requested in the Exercise.


104



4.



b.

Select the ISA Liquid sizing method.

c.

From the menu that appears, select the Valve Sizing and LpA option.

d.

Press F3. Ensure that the options Calculate FP, Viscous Correction OFF, and Input

Pv, are selected.

e.

Ensure that fluid properties and the service conditions are accurately entered.

f.

Enter an estimated FL. Determine an estimated value of FL through the use of the equation that follows or by selecting a value from the table below. Estimated FL = Estimated K m Typical Values Of Km and FL Valve Style Typical Km

Globe And Angle Rotary-Shaft

0.75 0.45

Typical FL

.87 0.67

g.

Enter an assumed valve inlet size, d. Use the valve size that was previously selected.

h.

Enter the appropriate values for D1 and D2.

i.

Press F2 to calculate the valve sizing information. Record the value of Cv.

j.

Select an appropriate valve size. Note: Because the calculated Cv includes the necessary correction for piping factors, ensure that you select a valve size from the table that lists capacities for a 1:1 line-to-body size ratio. Also, ensure that you select a valve size that is consistent with the percentage of travel guidelines that are listed in Section 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)


105



Work Aid 2E:

1.

Procedures Used To Computer Size Control Valves With Viscosity Correction



b.

Select the Fisher Liquid sizing method.

c.

Press and hold the ALT key, and press F5 to clear any sizing inputs.

d.


e.

Press F3. Ensure that the options Viscous Correction OFF and Input Pv are selected.

f.

Enter the fluid name.

g.

Ensure that the engineering units that are displayed on the calculation screen match the units that are used in the description of the application. If necessary, change the units for any field by moving the cursor to the field, pressing F8, and selecting the desired units.

h.


i.

Enter an estimated value of Km. (Refer to the table in part 4 of Work Aid 2A.)

j.


k.

Locate the page in Fisher Catalog 10 that describes the valve that is specified in the Exercise.

l.

Select a valve size that satisfies the Cv requirement according to the travel guidelines that are given in Section 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)

m.

Record the requested values.


106



2.

3.


Do NOT clear the calculation screen.

b.

Press F3. Ensure that the options Input Pv, and Viscous Correction ON are selected.

c.


d.

Ensure that all fluid properties and service conditions are accurately entered.

e.


f.

Refer to the appropriate page in Fisher Catalog 10, and select a valve size that satisfies the Cv requirement according to the travel guidelines that are given in Section 5.2 of SAES-J-700. (Refer to the table in part 2 of Work Aid 1A.)

g.

Record the requested values.


Do NOT clear the calculation screen.

b.

Press ESCAPE twice to return to the sizing methods menu.

c.


d.


e.

Press F3. Ensure that the options Omit FP, Viscous Correction ON, and Input Pv are selected.

f.

Note that the software may have calculated a value of FL from the Km that was included in the previous calculation. If the software has not calculated this value, calculate FL from the value of Km that was used previously; i.e., FL = square root of Km. Alternatively, an estimated value of FL may be obtained from the table that is included in part 4 of Work Aid 2A.


107



g.

Enter the appropriate value of Fd for a globe valve. To view a Help Screen that explains Fd values, press the F1 key twice, press "v" to view a list of valve sizing Help Screens, select Valve Sizing: Sizing Parameters, and press Page Down until the explanation of Fd appears. (Note that for most globe valves, Fd = 1.0).

h.

Assume that the valve size is equal to the line size, and enter an appropriate value for d.

i.

Press F2 to calculate the valve sizing information, and note the Cv.

j.

Refer to Fisher Catalog 10, and ensure that the valve size that is assumed above can provide the required capacity. If it appears that a smaller valve can provide the need capacity, change the value of d, calculate Cv, and again refer to the sizing tables. Ensure that you select a valve that is consistent with the guidelines in Section 5.2 of SAES-J-700 (see the table in part 2 of Work Aid 1A).


108



Work Aid 2F:

1.

Procedures That Are Used To Computer Size Control Valves With Viscosity And Piping Factor Correction

Use the following procedures to complete part 1. Calculating Cv with Viscous Correction a.

Press ESCAPE until the valve sizing method menu appears. b.


c.

Clear all values by pressing ALT-F5.

d.


e.

Press F3. Ensure that the options Omit FP, Viscous Correction ON and Input Pv are selected.

f.


g.


h.

Enter an estimated value of FL. An estimated value of FL can be obtained from the table in part 4 of Work Aid 2A.

i.

Enter the appropriate value of Fd. Refer to step g. in part 3. of Work Aid 2E.

j.

Assume that the valve size is equal to the line size, and enter the appropriate value for d.

k.


l.

Refer to the appropriate page in Fisher Catalog 12, and select a control valve size that provides the required Cv at a percentage of travel that is consistent with Section 5.2 of SAES-J-700. Refer to the table in part 2 of Work Aid 1A.

m.

Record the selected valve size and the degrees of rotation at which the valve will provide the maximum Cv requirement.


109



Calculating Cv with Piping Factor Correction

2.

a.

Press F3. Ensure that the options Calculate FP and Viscous Correction OFF are selected.

b.

Initially assume that the required valve size is equal to line size, and enter the appropriate value of d.

c.

Enter the appropriate values for D1 and D2.

d.


e.

Refer to the appropriate page in Fisher Catalog 12, and select a control valve size. Evaluate the assumed valve size as well as smaller sizes. If a smaller than initially selected valve size appears to have sufficient capacity, recalculate the valve sizing information with the use of the appropriate value of d and the actual value of FL.

f.

Record the selected valve size and the degrees of rotation at which the valve provides the maximum Cv requirements.


If the calculations that consider piping factors lead to the selection of one valve size and the calculations that consider the effects of laminar flow lead to the selection of another valve size, select the larger valve.


110



Work Aid 2G:

Procedures That Are Used To Computer Size Control Valves For Minimum, Normal, And Maximum Flow Conditions

Use the following procedures to complete Exercise 2G. Setup

a.

Press ESCAPE until the valve sizing method menu appears.

b.


c.

Press ALT-F5 to clear all of the data.

d.

With the cursor on the Valve Size and LpA Option, press F3 and ensure that the options are set to LpA (SPL) OFF, Omit FP, Viscous Correction OFF, Pipe: Size, Sched., Input P v, and Warnings OFF. Note that the FP option will not be used to initially select a valve size.

Initial Sizing

a.

Select the MIN (minimum) condition. Enter the fluid properties and the service conditions. To determine an estimated value of FL, browse through the FL values that are listed on the Catalog 12 page that describes the selected valve type. Select a value of FL that is typical for the valve type and size.

b.


c.

Press ESCAPE. On the screen that appears, move the cursor to the NRM (normal) flow condition column.

d.

Press ALT-C. From the menu that appears, select 1 to copy the sizing information from the minimum flow calculation screen to the normal flow calculation screen. Press ENTER.

e.

Change the pressure and flow conditions to the values that are given for the normal flow condition.

f.


g.

Press ESCAPE. On the screen that appears, move the cursor to the MAX (maximum) flow condition column.

h.

Press ALT-C. From the menu that appears, select 2 to copy the sizing information from the normal flow calculation screen to the maximum flow calculation screen. Press ENTER.


111



i.

Change the pressure and flow conditions to the values that are given for the maximum flow condition.

j.


Display The Calculated Results And Select A Valve Size

a.

Press F9 to display a table of calculated values.

b.

Note the minimum and maximum Cv values. Refer to the Catalog 12 page for the selected valve. Locate the smallest valve size that can provide the maximum Cv according to the guidelines in Section 5.2 of SAES-J-700 (refer to the table in part 2 of Work Aid 1A).


112



Work Aid 2G:

Procedures That Are Used To Computer Size Control Valves For Minimum, Normal, And Maximum Flow Conditions, cont'd.

Intermediate Sizing With The Calculate F P Option

a.

Press ESCAPE twice to return to the menu screen from which the Valve Sizing And LpA calculations are selected.

b.

Press F3 and select the Calculate FP option. (Note that selecting an option from this screen invokes the option for all calculation screens (MIN, NRM, and MAX); selecting an option from a particular sizing screen invokes the option for that specific condition only.)

c.

Select the minimum flow condition. Enter the appropriate values for d, D1, and D2. Press F2 to calculate the valve sizing information.

d.

Repeat the step immediately above for the normal and the maximum flow conditions.

e.

Press F9 to display a table of calculated Cv's that have been corrected for piping factors. Refer to the appropriate Catalog 12 page, and compare the corrected Cv's that are displayed on the screen to the Cv's that are published for the initially selected valve. Ensure that the selected valve can provide the Cv's that are required at the minimum and maximum flow conditions according to the guidelines in Section 5.2 of SAES-J-700 (refer to the table in part 2 of Work Aid 1A). Record the valve size as requested on the Exercise Sheet.

Final Sizing and Selection

a.

Select the minimum flow condition sizing screen and note the calculated Cv.

b.

Refer to the appropriate page in Catalog 12 and estimate the degrees of rotation at which the Cv requirement will be met.

c.

Extrapolate a value of FL for the degrees of rotation that were estimated in step b. Enter the extrapolated value of FL in the appropriate field on the sizing screen, and press F2 to calculate the valve sizing information.

d.

If the Cv that was calculated in step c. is different than the Cv that was calculated in step b., the degrees of rotation at which the required Cv is obtained will be different and the value of FL may have also changed; therefore, steps b. and c. must be repeated. If the Cv's that were calculated in steps b. and c. are the same (or nearly the same), record the information that is requested on the Exercise Sheet, and proceed to the next step.


113



e.

Select the normal flow condition and note the value of the calculated Cv. Perform steps b., c., and d. for the normal flow condition.

f.

Select the maximum flow condition and note the calculated Cv. Perform steps b., c., and d. for the maximum condition.

g.

Ensure that you have recorded all the information that is requested on the Exercise Sheet.

h.

If it is necessary to review the calculated results, press F9.


114



work aid 3:

Procedures that are used to Computer size control valves for gas and steam applications

Work Aid 3A:

Procedures That Are Used To Computer Size Control Valves For Ideal Gasses With The ISA Method

Perform the following procedures to complete Exercise 3A. a.

If necessary, press ESCAPE to return to the main menu.

b.


c.

From the menu that appears, select the ISA Gas method.

d.


e.

Press F3, and select the Input Z option.

f.

Enter the service conditions, the fluid properties, and the value of xT. •

Note that Fk = k divided by 1.4. If k is unknown, enter 1.0 for FK.

•

Because Tc and pc are not included in the description of the fluid properties, Z cannot be calculated; therefore, enter a value of 1.0 for Z.

g.


h.

Record the values that are requested in the Exercise.


115



Work Aid 3B:

Procedures That Are Used To Computer Size Control Valves For Real Gasses With The ISA Method

Perform the following procedures to complete Exercise 3B. Note: It is not necessary to clear the existing sizing inputs. a.

Press ESCAPE to return to the sizing method menu.

b.


c.


d.

Press F3, and select the Calculate Z option.

e.

Ensure that the correct information is entered in the fields for the service conditions, fluid properties, and the value of xT. Remember that Fk = k divided by 1.4.

f.


g.



116



Work Aid 3C:

Procedures That Are Used To Computer Size Control Valves For Vapors With The ISA Method

Perform the following procedures to complete Exercise 3C. a.


b.

From the menu that appears, select the ISA Vapor method.

c.


d.

Ensure that the engineering units on the calculation screen match the units that are used to describe the service conditions. If the units do not match for any field, move the cursor to that field, press the F8 key, and select the desired units.

e.

Enter the fluid properties, the service conditions, and xT. Remember that FK = k/1.4.

f.


g.



117



Work Aid 3D:

Procedures That Are Used To Computer Size Control Valves For Steam With The ISA Method

Perform the following procedures to complete Exercise 3D. a.


b.

From the menu that appears, select the ISA Vapor method.

c.


d.

Press and hold the ALT key, and press F5 to clear all sizing inputs.

e.


f.

Using the chart in Fisher Catalog 10, Section 2, page 39, determine the density of the steam.

g.

Enter the fluid properties, the service conditions, and the value of xT.

h.


i.



118



Work Aid 3E:

Procedures That Are Used To Computer Size Control Valves For Ideal Gasses With The Fisher Method

Perform the following procedures to complete Exercise 3E. 1.

2.

Fisher Ideal Gas sizing method a.

Press ESCAPE to return to the main menu.

b.


c.

From the menu that appears, select the Fisher Ideal Gas method.

d.


e.


f.


g.

Enter the required service conditions, the fluid properties, and the value of C1.

h.


i.

To convert the Cg to Cv, divide the value of Cg by the value of C1.

j.


Fisher Real Gas sizing method Note: It is not necessary to clear the existing sizing inputs. a.


b.

From the menu that appears, select the Fisher Real Gas method.

c.


d.

Press F3. If there is insufficient to calculate Z and C2, select the option Input Z, Omit C2.

e.

Enter the service conditions, the fluid properties, and the value of C1.

f.

To ignore the effects of real gas compressibility, enter a value of 1.0 for Z.

g.


h.

To convert Cg to Cv, divide Cg by C1.

i.



119



Work Aid 3F:

Procedures That Are Used To Computer Size Control Valves For Real Gasses With The Fisher Method

Perform the following procedures to complete Exercise 3F. 1.

Fisher Real Gas sizing method Note: It is not necessary to clear the existing sizing inputs. a.


b.


c.


d.

Press F3, and select the Calculate Z, C2 option.

e.

Enter the service conditions, the fluid properties, and the value of C1.

f.


g.


h.



120



Work Aid 3G:

Procedures That Are Used To Computer Size Control Valves For Vapors With The Fisher Method

Perform the following procedures to complete Exercise 3G. 1.

Fisher Vapor sizing method a.


b.

From the menu that appears, select the Fisher Vapor method.

c.


d.

Ensure that the service conditions and the value of C1 are entered correctly.

e.


f.


g.



121



Work Aid 3H:

Procedures That Are Used To Computer Size Control Valves For Steam With The Fisher Method

Use the following procedures to complete Exercise 3H. 1.

2.

Fisher Vapor sizing method a.


b.

From the menu that appears, select the Fisher Vapor method.

c.


d.

Ensure that the service conditions and C1 are entered correctly.

e.


f.


g.


Fisher Steam sizing method a.


b.

From the menu that appears, select the Fisher Steam method.

c.


d.

Ensure that the service conditions and C1 are entered correctly.

e.


f.

To convert Cs to Cg, multiply Cs by 20.

g.


h.



122



Work Aid 3I:

Procedures That Are Used To Calculate The Effect Of Compressibility On Valve Size

Use the following procedures to perform the sizing calculations for Exercise 3I. 1.

2.

Fisher Ideal Gas sizing method a.

Press ESCAPE to return to the valve sizing method menu.

b.

From the menu that appears, select the Fisher Ideal Gas method.

c.


d.


e.

Move the cursor to the Gas entry field, and press F4. From the menu that appears, select N-Butane.

f.

Enter the service conditions and the value of C1.

g.


h.


i.


Fisher Real Gas sizing method a.


b.


c.


d.

It is not necessary to clear existing sizing inputs.

e.

Press F3, and select the Calculate Z, C2 option.

f.

Ensure that the sizing inputs are entered correctly.

g.


h.


i.



123



3.

ISA Gas sizing method a.


b.


c.


d.

It is not necessary to clear existing sizing inputs.

e.

Press F3, and select the Calculate Z option.

f.

Ensure that the sizing inputs are entered correctly.

g.


h.



124



Work Aid 3J:

Procedures That Are Used To Computer Size Control Valves For All Flow Conditions

Setup

a.

Press ESCAPE until the valve sizing method menu appears.

b.

Select the ISA Gas sizing method.

c.

Press ALT-F5 to clear all data.

d.

With the cursor on the Valve Sizing and LpA Option, press F3 and ensure that the options are set to Input Z, Omit FP and xTP, LpA (SPL) OFF, and Warnings OFF. Note that the FP option will not be used to initially select a valve size.

e.

If it is necessary to change engineering units for any of the input fields, ensure that the screen that is displayed is the screen from which Valve Sizing and LpA are selected. Press F8 to display a list of sizing parameters. Move the cursor to the parameters for which units must be changed. To display a list of options for a particular parameter, place the cursor on the parameter, and, then, press ENTER. Move the cursor to the desired option, and press ENTER. After the units for the appropriate parameters have been selected, press ESCAPE.

Initial Sizing

a.

Select the MIN (minimum) condition and enter the required sizing inputs. Assume ideal gas behavior; i.e., set Fk to 1.0, and set Z to 1.0. To determine an estimated xT, browse through the xT values that are listed on the Catalog 12 page that describes the selected valve and select a value of xT that is typical for the selected valve type.

b.


c.

Press ESCAPE. On the screen that appears, move the cursor to the NRM (normal) flow condition column.

d.

Press ALT-C. From the menu that appears, select 1 to copy the sizing information from the minimum flow calculation screen to the normal flow calculation screen. Press ENTER.

e.

Change the pressure and the flow conditions to the values that are included in the application description.

f.



125



g.

Press ESCAPE. On the screen that appears, move the cursor to the MAX (maximum) flow condition column.

h.

Press ALT-C. From the menu that appears, select 2 to copy the sizing information from the normal flow calculation screen to the maximum flow calculation screen. Press ENTER.

i.

Change the pressure and the flow conditions to the values that are included in the application description.

j.


Display The Calculated Results And Select A Valve Size

a.

Press F9 to display a table of calculated values.

b.

Note the minimum and maximum Cv values. Refer to the appropriate Catalog 12 page, and locate the smallest valve size that can provide the required Cv at the maximum flow condition. Ensure that you observe the percentage of travel guidelines that are included in Section 5.2 of SAES-J-700. Refer to the table in part 2 of Work Aid 1A.

Intermediate Sizing With The Calculate F P Option

a.

Press ESCAPE twice to return to the menu screen from which the Valve Sizing And LpA calculations are selected.

b.

Press F3 and select the Calculate FP option. (Note that selecting an option from this screen invokes the option for all calculation screens (MIN, NRM, and MAX); selecting an option from a particular sizing screen invokes the option for that specific condition only.)

c.

Select the minimum flow condition. Enter the appropriate values for d, D1, and D2. Press F2 to calculate the Cv.

d.

Repeat step c. for both the normal and maximum flow conditions.

e.

Press F9 to display a table of calculated Cv's that have been corrected for piping factors. Refer to the appropriate Catalog 12 page, and compare the corrected Cv's that are displayed on the screen to the Cv's that are published for the initially selected valve. Ensure that the initially selected valve has adequate capacity and that it conforms to the guidelines in Section 5.2 of SAES-J-700 (refer to the table in part 2 of Work Aid 1A). Record the valve size on the Exercise Sheet.


126



Final Sizing and Selection

a.

Select the minimum flow condition. Note the calculated Cv.

b.

Refer to appropriate page in Catalog 12, and estimate the percentage of travel at which the Cv requirement will be met.

c.

Extrapolate a value of xT for the percent travel that was estimated in step b. Enter the extrapolated value of XT in the appropriate field on the sizing screen, and press F2 to calculate the sizing information.

d.

If the Cv that was calculated in step c. is different than the Cv that was calculated in step b., the percent of travel at which the required Cv is obtained will be different and the value of XT may have also changed; therefore, steps b. and c. must be repeated. If the Cv's that were calculated in steps b. and c. are the same (or nearly the same), record the information that is requested and proceed to the next step.

e.

Select the normal flow condition and note the value of the calculated Cv. Perform steps b., c., and d. for the normal flow condition.

f.

Select the maximum flow condition and note the calculated Cv. Perform steps b., c., and d. for the maximum condition.

g.

Ensure that you have recorded the information that is requested on the Exercise Sheet. Press F9 to review the calculated results if necessary.


127



WORK AID 4: PROCEDURES THAT ARE USED TO Enter Valve Sizing Data on the saudi Aramco ISS Enter the information on the ISS as follows: Line 49: Enter the valve body size and the valve port size. Line 50: Enter the inlet flange size, the inlet flange ANSI Class rating, and the flange style (enter the abbreviation RF for a raised-face flange style). Line 51: Enter outlet flange size, the ANSI Class rating, and the flange style. Line 61: Circle the entry that indicates whether flow tends to close or open the valve. Line 62: Enter the minimum flow Cv. Divide the Cv at the minimum flow condition by the maximum Cv rating of the valve. Enter the result as a percentage. Line 63: Enter the normal flow Cv. Divide the Cv at the normal flow condition by the maximum Cv rating of the valve. Enter the result as a percentage. Line 64: Enter the maximum flow Cv. Divide the Cv at the maximum flow condition by the maximum Cv rating of the valve. Enter the result as a percentage. Line 65: Enter the maximum Cv rating of the valve. Line 66: Enter the percentages of travel at which the valve provides the Cv's that are required at the minimum and maximum flow conditions. Line 67: Enter the percentage of travel at which the valve provides the Cv that is required at the normal flow condition. Line 72: Refer to the appropriate specification bulletin and determine the face-to-face dimension of the selected valve. Enter the dimension on the ISS, and circle the appropriate units of measurement (mm or inches).


128



GLOSSARY γ1 ∆Pallow ∆Pchoked C1 C2 capacity cavitation centipoise centistokes Cg choked flow

compressibility critical flow critical pressure critical pressure ratio critical temperature Cs Cv Cvr

D d D1 Saudi Aramco DeskTop Standards

Specific weight of the fluid at the valve inlet. Pressure drop at which choked flow limits flow to Qmax; same as ∆Pchoked. Pressure drop at which choked flow limits flow to Qmax; same as ∆Pallow. Term that is used in the Fisher Gas Sizing Equation to account for differences in liquid and gas coefficients for high and low recovery valve types. Term that is used in the Fisher Gas Sizing Equation to account for the ratio of specific heats. C2 serves the same function as Fk in the ISA equations. Rate of flow through a valve under stated conditions. In liquid service, the noisy and potentially damaging phenomenon that accompanies bubble formation and collapse in the flowstream. Unit of measure of viscosity (Cs). Unit of measure of viscosity (Cp). Gas flow coefficient that is used by Fisher Controls. Maximum flow rate through a restriction. Choked flow results in liquid flows as pressure reductions cause decreases in fluid density and thus offset any increase in velocity. In gasses, choked flow is achieved when fluid velocity is sonic. Condition that occurs in gasses as increasing pressure compacts molecules of the flowing gas. Condition when gas flow is at sonic velocity and further reductions in downstream pressure produce no increase in flow rate. The pressure of the liquid-vapor point. Ratio that is used in liquid sizing to calculate Pvc and allowable pressure drop (∆Pchoked). Temperature of the liquid-vapor critical point (i.e., the temperature above which the fluid has no liquid-vapor transition. Steam flow coefficient that is used by Fisher Controls. Flow coefficient that is commonly used for liquids. Cv required; a value of Cv that has been corrected to account for the effects of fluid viscosity on the calculated Cv. This term is used in conjunction with the Fisher Controls nomograph that is used to determine viscosity corrections. Term that represents nominal pipeline diameter. Term that represents nominal valve size (generally the valve inlet diameter). Diameter of the piping that is connected to the valve inlet. 129



D2 density

downstream ∆P Fd FF FL FLP flashing

flow characteristic

flow coefficient (Cv) flow rate FLP FR FP Fv

fluid fluid expansion FP Saudi Aramco DeskTop Standards

Diameter of the piping that is connected to the valve outlet. Weight per unit of volume of a fluid. May be given as relative density (specific gravity SG, molecular weight M, or in terms of specific weight (weight per unit of volume, such as kgs/m3, lbs/ft3, etc.). Any point that is located away from a reference point in the direction of fluid flow. The pressure drop. in psi, across the valve (∆P = P1-P2). Valve style modifier that is used in ISA equation to calculate valve Reynolds number. ISA term for critical pressure ratio; same as rc, which is used by Fisher and others. Term that is used in ISA equations to describe valve recovery coefficient. Similar to Km, which is used by Fisher. FL corrected for piping factor. A phenomenon that is observed in liquid service when the pressure of the fluid falls below its vapor pressure and it does not recover to a pressure above its vapor pressure. Flashing commonly produces, in control valve components, damage that has the appearance of erosion damage (smooth, polished cavities on the affected components). Relationship between flow through the valve and percent of rated travel as the latter is varied from 0 to 100 percent. This term is a special term. It should always be designated as either inherent flow characteristic or installed flow characteristic. Common flow characteristics are linear, equal percentage, and quick opening. The number of U.S. gallons per minute of 60 degree F water that will flow through a valve with a pressure drop of one pound per square inch. The amount (mass, weight, or volume) of fluid flowing through a regulator per unit of time. ISA term that represents a recovery coefficient (liquid flow) that is corrected for piping factors. Reynolds number factor that is used in the ISA equations. Piping factor that is used in the ISA equations. Viscosity correction factor that is used by Fisher Controls to compensate for the effects of viscous flow. The value of Fv is determined from a nomograph, and it is applied as follows: Cvr (Cv required) = FvCv, where Cv is an initially calculated value. Substance in a liquid, gas, or vapor state. Expansion that results from a decrease in pressure as a gas flows through a control valve. ISA term that represents the piping factor. See Piping Factor. 130



FSP G Gf Gg

high-recovery valve

ideal gas ISA Km laminar flow

low-recovery valve

M Nx p1 p2 piping factor pr


Fisher Sizing Program The specific gravity of the fluid. Identical to the SG and the ISA terms Gf and Gg. Liquid specific gravity at upstream conditions; ratio of fluid density at flowing temperature to density of water at 60 degrees F (15.6 degrees C). Gas specific gravity; ratio of density of gas at flowing conditions to density of air at reference conditions; ratio of molecular weight of a gas to molecular weight of air; dimensionless. A valve design that dissipates relatively little flow-stream energy because of streamlined internal contours and minimal flow turbulence. Valves, such as rotary-shaft ball and butterfly valves, are typically high-recovery valves. In these designs, the pressure dip at the vena contracta is larger than in low-recovery valves. A gas that obeys the ideal gas law of pV=RT. Instrument Society of America. Liquid flow valve recovery coefficient that is used by Fisher Controls; similar to FL in ISA equations. A flow regime characterized by smooth, ordered layers. The layers in the center of the pipe have the highest velocity, while drag forces result in reduced velocity nearer the pipe wall. Laminar flow is also referred to as viscous flow. The term viscous flow is somewhat of a misnomer because effects other than fluid viscosity can cause laminar flow. A valve design that dissipates a considerable amount of flowstream energy because of turbulence created by the contours of the flowpath. Globe valves are typical. In these designs, the pressure dip at the vena contracta is not as great as in high-recovery valves. molecular weight, atomic mass units. Used in ISA equations, N terms are numerical constants that allow the use of the equations with different engineering units. Fluid pressure upstream of the valve. Fluid pressure downstream of the valve. Ratio of flow through a valve with swaged connections to flow through a valve with a 1:1 line-to-body size ratio. Represented in the ISA equations with term FP. The reduced pressure, determined by dividing the actual pressure of the fluid (psia) by the fluid's critical pressure psia). The value of Pr and the value of Tr (the reduced temperature) may be used to determine the value of the compressibility factor, Z. 131



pressure pressure differential pressure drop pressure drop ratio pressure drop ratio factor pressure drop, allowable

pressure drop, choked

PSI or psi Pv Pvc Q or q R Rev rated Cv ratio of specific heat factor rc

real gas SG sonic velocity


Force exerted per unit of area. The difference in pressure between two locations in a fluid system. The difference between upstream pressure and downstream pressure that represents the amount of flow stream energy that the control valve must be able to withstand. Ratio of inlet pressure P1 to pressure drop across the valve. The limiting value of x that is used in the ISA sizing equations. Referred to with xT (t stands for terminal). The value of xT is related to valve style and geometry. It is determined by test and published with other valve sizing information. The pressure drop at which choked flow limits flow to Qmax. This term is used by Fisher Controls and others. It is equivalent to the term "choked pressure drop" that is used in the ISA equations. The pressure drop at which choked flow limits flow to Qmax. This term is used in the ISA equations. It is equivalent to the term "allowable pressure drop" that is used by Fisher and others. Pounds per square inch. For a liquid, the pressure of the vapor in equilibrium with the liquid. Pressure at the vena contracta. flow rate Gas constant that is used in the equation to describe pressure, volume, and temperature relationships of ideal gasses. R = 1545/molecular weight (M) of the fluid. Reynolds number for valve. The value of Cv at the rated full-open position. The factor that is used in the ISA gas sizing equations to account for thermodynamic fluid behavior. It is represented by Fk. Fk is equal to the ratio of the specific heat for the flowing gas to the specific heat of air, which is 1.4 (i.e., Fk = k/1.4). A term that is used by Fisher Controls and others to represent the critical pressure ratio. The term rc is equivalent to the term FF in the ISA sizing equations. The critical pressure ratio and the fluid vapor pressure (Pv) are used to estimate the fluid pressure at the vena contracta according to: Pvc = rc Pv. A gas for which deviations form the ideal gas law are taken into account. specific gravity The upper velocity limit of a flowing gas. It is equal to the speed of sound in the flowing gas.

132



specific gravity specific heat ratio

swage T or T1 throttling range Tr

transitional flow travel

turbulent flow vena contracta

w x xT

Y Z


Measure of density, generally expressed as SG or M. See SG and M. Represented with the term k. The ratio of the amount of heat that is required to raise a mass of material 1 degree in temperature to the amount of heat that is required to raise an equal mass of a reference substance (usually water) 1 degree in temperature. Both measurements are made at a specific temperature and at constant volume or pressure. A piping expander or reducer that allows the installation of a control valve in a pipeline whose diameter is greater than the diameter of the control valve inlet and outlet fittings. Temperature of the fluid at the valve inlet. The range defined by the percent valve travel that provides the minimum Cv requirement and the percent valve travel that provides the maximum Cv requirement. The reduced temperature, determined by dividing the actual temperature of the fluid by the fluid's critical temperature. The value of Tr and the value of Pr (the reduced pressure) may be used to determine the value of the compressibility factor, Z. A flow regime with characteristics of both laminar and turbulent flow. The amount of movement (linear or rotational) of the valve closure member between the closed and open positions, generally expressed in degrees of rotation for rotary-shaft valves and in percent of travel for sliding-stem valves. A flow regime characterized by turbulent eddies that occur randomly in the fluid stream. Fluid velocity at the center of the pipe and the velocity near the pipe wall are nearly equal. The location where cross-sectional area of the flowstream is at its minimum size, where fluid velocity is at its highest level, and fluid pressure is at its lowest level. (The vena contracta normally occurs just downstream of the actual physical restriction in a control valve.) Mass flow rate (lbs/hr, kg/s, etc.) Pressure drop ratio ( ∆P / p1 ); limited to value of xT for choked flow and xTP to correct for piping factors, dimensionless. Flow limiting pressure drop that is used in ISA gas sizing equations. x Y = 1− 3Fk x T , where F = ratio of specific Expansion factor k heats. Compressibility factor; dimensionless.

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Control Valve Sizing

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