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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 notalready in the public domain may not be copied, reproduced, sold, given,

or disclosed to third parties, or otherwise used in whole, or in part,

without the written permission of the Vice President, Engineering

Services, Saudi Aramco.

Chapter : Instrumentation For additional information on this subject, contact

File Reference: PCI20403 E. W. Reah on 875-0426

Engineering EncyclopediaSaudi Aramco DeskTop Standards

Sizing Control Valves For

Two Phase Flows,Fluids With

Dissolved Gasses, And Hydrocarbon Mixtures

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Engineering Encyclopedia Instrumentation

Sizing Control Valves for 2 Phase

Flows, Fluids with Dissolved Gasses, etc.

Saudi Aramco DeskTop Standards

CONTENTS PAGES

BASICS OF FLUID THERMODYNAMIC BEHAVIOR, ASSUMPTIONS FOR

CONTROL VALVE SIZING MODELS, AND CONTROL VALVE SIZING EQUATIONS ......1

Basics of Fluid Thermodynamic Behavior.......................................................................1

Pressure-Enthalpy Phase Diagrams ....................................................................1

Axis Identification..............................................................................................1

Chart Data ..........................................................................................................3

Phase Dome And Fluid States ............................................................................3

Lines Of Constant Temperature .........................................................................4

Change In Enthalpy............................................................................................5

Lines Of Constant Entropy.................................................................................6

Lines Of Specific Volume ..................................................................................7

Critical Point ......................................................................................................8

Assumptions For Control Valve Sizing Models ..............................................................9

Importance Of Identifying Conditions At The Control Valve Vena

Contracta ............................................................................................................9

Assumptions Concerning Entropy That Are Used In Control Valve Sizing.....10

Assumptions Concerning Enthalpy That Are Used In Control Valve Sizing ...11

Gas Flow Example ...........................................................................................13

Liquid Flow Example.......................................................................................15

Control Valve Sizing Equations.....................................................................................16

Fluid States For Which The Standard ISA Sizing Equations Are Applicable ..16

Fluid States That Require Special Sizing Techniques ......................................17

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SIZING CONTROL VALVES FOR TWO PHASE FLOWS ......................................................18

Types Of Two Phase Flows And Implications For Valve Sizing ...................................18

Types Of Two Phase Flows..............................................................................18

Implications For Valve Sizing..........................................................................19

Two-Phase Flow Sizing Assumptions And Sizing Methods ..........................................20

Best Case Assumptions: Homogenous Mixture ...............................................20

ISA Standard S75.01 ........................................................................................20

Fisher Methods For Sizing Control Valves For Two-Phase Flows ................................20

Overview Of The Two-Phase Sizing Procedure ...............................................20

Determining Flow Rates At The Valve Inlet ....................................................24

Unique Problems For Vapor/Liquid Flows ......................................................25

Computer Sizing Two Phase Flows ...............................................................................26

Method Selection Criteria ................................................................................26

Inputs To The Vapor/Liquid Two-Phase Sizing Method .................................27

Calculated Results With The Vapor/Liquid Two-Phase Sizing Method ..........28

Differences Between The Vapor/Liquid Method And The Gas/Liquid

Method .............................................................................................................29

SIZING CONTROL VALVES FOR FLUIDS WITH DISSOLVED GASSES ...........................30

Mechanics Of Outgassing And Implications For Valve Sizing......................................30

Dissolved Gas Defined.....................................................................................30

Mechanics Of Outgassing ................................................................................30

Outgassing Versus Flashing .............................................................................31

Outgassing Versus Cavitation ..........................................................................32

Indicators Of The Presence Of Dissolved Gasses .............................................32

Implications For Valve Sizing..........................................................................34

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Bracketing Approach To Valve Sizing For Dissolved Gas Applications .......................35

General Concept ...............................................................................................35

Calculating The Minimum Valve Size .............................................................36

Calculating Maximum Valve Size....................................................................37

Evaluation Of The Minimum And Maximum Cv Calculations .......................38

Valve Style Selection Guidelines .....................................................................38

SIZING CONTROL VALVES FOR HYDROCARBON MIXTURES .......................................39

Introduction ...................................................................................................................39

Unique Sizing Problems With Liquid Mixtures.............................................................39

Multiple Pressure-Enthalpy Diagrams..............................................................39

Defining Fluid Properties .................................................................................40

Common Anomalies In The Values Of Fluid Properties ..................................42

Sensitivity Of Sizing Calculations To Accurate Fluid Properties .....................43

Liquid Mixture Sizing Techniques ................................................................................44

When Pv<Pc<P1 ..............................................................................................44

When P1=Pv<Pc ..............................................................................................45

When P1>Pv>Pc ..............................................................................................46

When P1=Pv>Pc ..............................................................................................47

Features And Limitations Of The Sizing Techniques .......................................48

Gas Mixture Sizing ........................................................................................................49

Review Of Ideal Gasses And Real Gasses........................................................49

Determining The Value Of Z For Gas Mixtures...............................................52

Computer Sizing ..............................................................................................54

Seeking Assistance ........................................................................................................55

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WORK AID 1: PROCEDURES FOR THE USE OF THE TWO-PHASE SIZING OPTION

OF THE FISHER SIZING PROGRAM ......................................................................................56

Work Aid 1A: Procedures That Are Used To Size Control Valves For Vapor/Liquid

Flows .............................................................................................................................56Work Aid 1B: Procedures That Are Used To Size Control Valves For Gas/Liquid

Flows .............................................................................................................................58

WORK AID 2: PROCEDURES FOR THE USE OF A BRACKETING TECHNIQUE

THAT IS USED TO SIZE CONTROL VALVES FOR FLUIDS WITH DISSOLVED

GASSES ......................................................................................................................................60

WORK AID 3: GUIDELINES FOR ADJUSTING THE VALUES OF FLUID

PROPERTIES THAT ARE USED TO SIZE CONTROL VALVES FOR HYDROCARBON

MIXTURES.................................................................................................................................62

Work Aid 3A: Guidelines That Are Used To Size Control Valves For HydrocarbonLiquid Mixtures .............................................................................................................62

Work Aid 3B: Guidelines That Are Used To Size Control Valves For Hydrocarbon

Gas Mixtures..................................................................................................................63

GLOSSARY................................................................................................................................64

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Saudi Aramco DeskTop Standards 1

BASICS OF FLUID THERMODYNAMIC BEHAVIOR, ASSUMPTIONS FOR CONTROL VALVE

SIZING MODELS, AND CONTROL VALVE SIZING EQUATIONS

Basics of Fluid Thermodynamic Behavior

Pressure-Enthalpy Phase Diagrams

A pressure-enthalpy diagram (see Figure 1) is useful in predicting the behavior of a specific fluid as it passes

through a control valve. A unique phase diagram is available for most common fluids; e.g., methane, ethane,

pentane, carbon dioxide, water, etc.. The pressure-enthalpy diagram enables the specifier to determine whether

a fluid is a liquid, a gas, or a two-phase fluid. The phase diagram that is shown in Figure 1 is taken from the

GPSA (Gas Processors Suppliers Association) Handbook.

Axis Identification

Pressure - The fluid pressure in psia is listed on the ordinate.

Enthalpy - The enthalpy, H, is shown on the abscissa. Enthalpy is defined as the heat contained in the

fluid. Enthalpy is often measured in Btu/lb.

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Use Word 6.0c or later to

view Macintosh picture.

Figure 1

Pressure-Enthalpy Diagram For Methane

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Chart Data

The information that is included on the pressure-enthalpy chart that is shown in Figure 1 includes the following:

• Lines of constant temperature, T, degrees F

• Lines of constant entropy, S, [(Btu/lb) (degrees R)]

• Lines of specific volume, V, cu ft/lb

Phase Dome And Fluid States

The simplified plot that is shown in Figure 2 shows the two-phase dome. The dome serves to separate distinct

regions of the plot that define whether a fluid is a liquid, a gas, a two-phase fluid, or a supercritical fluid.



Figure 2

Two-Phase Dome And Fluid States

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Lines Of Constant Temperature

The simplified plot that is shown in Figure 3 includes lines of constant temperature. Notice that when a

temperature line intersects the phase dome, the line moves horizontally across the two-phase dome.



Figure 3

Simplified Phase Diagram With Lines Of Constant Temperature

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Change In Enthalpy

To better understand the effect of a change in the heat content of a fluid, (a change in enthalpy), refer to Figure

4 and the discussion that follows.



Figure 4

Relationship Of Temperature And Enthalpy

A. At point A, the fluid is at some defined inlet pressure, temperature, and enthalpy.

B. As heat is added under conditions of constant pressure, the fluid temperature increases from point A to point B. When the temperature increases to the point where the temperature line intersects the saturated

liquid line of the two-phase dome (point B), the liquid begins to vaporize.

C. As additional heat is added, the fluid temperature remains constant but more vapor is produced in the

mixture.

D. When the saturated vapor line is reached (point C) , no liquid remains and the fluid is a gas or vapor.

E. As additional heat is added, the fluid temperature increases (points D and E).

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Lines Of Constant Entropy

Figure 5 includes several lines of constant entropy (S). Entropy is defined as the permanent and irreversible

change in the amount of available energy. A change in energy is often caused by friction. A process in which

no energy is given up is referred to as isentropic (entropy remains constant). Note that the isentropic lines (lines

of constant entropy) pass through the two-phase dome.



Figure 5

Simplified Phase Diagram With Lines Of Constant Entropy

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Lines Of Specific Volume

Figure 6 includes several lines of specific volume (V). Specific volume is given in terms of cubic volume per a

unit of mass; e.g., cubic feet per pound. Specific volume is the inverse of fluid density; i.e.:

Density (pounds per cubic feet) = 1/V



Figure 6

Simplified Phase Diagram With Lines Of Specific Volume

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Critical Point

The critical point is defined as the temperature and pressure at which the liquid and vapor specific volumes, or

densities, become equal. As shown in Figure 7, the critical point is determined by the intersection of the fluid’s

critical pressure and its critical temperature. It is impossible to identify supercritical fluids as a liquid or a vapor;

accordingly, they have been referred to as ‘dense gasses’ or ‘compressible liquids’. Supercritical fluids can

present unique challenges for the valve specifier.



Figure 7Critical Point Defined By The Critical Pressure And The Critical Temperature

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Assumptions For Control Valve Sizing Models

Importance Of Identifying Conditions At The Control Valve Vena Contracta

Pressure-enthalpy diagrams are useful in predicting fluid behavior as the fluid passes through a control valve.

However, one must make some assumptions concerning fluid flow before one can gain insight from the

diagrams.

Sizing Pressure Drop Vs. Valve Capacity - The pressure drop that creates fluid flow is the pressure

differential between the upstream pressure P1 and the pressure at the control valve vena contracta, Pvc.

The vena contracta is the point, following a restriction to flow, at which the cross-sectional area of the

flow stream is at its minimum value, the fluid velocity is at a maximum value, and the fluid pressure

(Pvc) is reduced. Because the value of Pvc is rarely known, valve sizing equations include choked flow

calculations in order to predict the pressure value of Pvc. Precise determination of the value of Pvc is

made difficult by the fact that in many valves, there may be several vena contractas. In addition, the

location of the vena contracta(s) often changes as the service conditions change.

Fluid State At The Vena Contracta Vs. Valve Capacity - The fluid pressure at the vena contracta

determines the whether the fluid at the vena contracta is a liquid, vapor, or a two-phase mixture. Anydegree of fluid vaporization at the vena contracta will reduce the fluid density and, as density

decreases, larger and larger valve sizes will be required to pass a given flow rate. For this reason, it is

useful to devise means of predicting the fluid state at the vena contracta.



Figure 8

Sizing Pressure Drop P1 - Pvc Versus Valve Pressure Drop P1-P2

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Assumptions Concerning Entropy That Are Used In Control Valve Sizing

Valve Inlet To The Vena Contracta - Most valve sizing procedures are based on the assumption that

as the fluid passes from the valve inlet to the valve vena contracta, any fluid expansion that occurs as a

result of increased velocity is isentropic; i.e., there is no change in the available energy. Refer to Figure

9.

Valve Vena Contracta To Outlet - As the fluid flows from the valve vena contracta to the valve

outlet, some of the pressure energy is converted to heat because of friction. The pressure loss is

permanent and irreversible; therefore, there is an increase in entropy. Refer to Figure 9.



Figure 9

Entropy Assumptions

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Assumptions Concerning Enthalpy That Are Used In Control Valve Sizing

For the discussion that follows, refer to Figure 10 on the next page.

Valve Inlet To The Vena Contracta - The assumptions concerning enthalpy are based on the first

Law Of Thermodynamics; i.e.,

HV

gH

V

gvc

vc1

12 2

2 2+ = +

where:

H enthalpy, Btu/lb

V fluid velocity, ft/sec

g gravitational constant

subscript 1 upstream conditions

subscript vc vena contracta conditions

Fluid velocity always increases as fluid flows from the valve inlet to the valve vena contracta.

Referring to the above equation, if the velocity at the vena contracta (Vvc) increases, Hvc must

decrease.

Vena Contracta To The Valve Outlet - As the fluid flows from the vena contracta to the valve outlet,

the fluid velocity decreases. According to the equation that is shown above, the decrease in velocity

must be accompanied by a corresponding increase in enthalpy.

Valve Inlet To The Valve Outlet: Isenthalpic, Adiabatic Process - For valve sizing purposes, the

assumption is made that there is no actual transfer of heat from the fluid to the valve because of the

very short time that the fluid undergoes the change in enthalpy. Because there is no actual transfer of heat from the fluid to the valve, the flow is considered to be adiabatic.

And, because velocity decreases from the vena contract to the valve outlet, the flow is assumed to be

isenthalpic (enthalpy is constant) from the valve inlet to the valve outlet, even though there is a

temporary change in enthalpy at the vena contracta.

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Figure 10

Isenthalpic Flow

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Gas Flow Example

The assumptions that were previously described can be used in conjunction with the data that is included in the

pressure-enthalpy diagrams to determine the state of the fluid as it passes through a control valve. Figure 11

shows the thermodynamic behavior of a gas as it passes through a control valve.



Figure 11

Thermodynamic Analysis Of Gas Flow Through A Control Valve

Valve Inlet To The Vena Contracta - As a gas passes from the valve inlet to the valve vena contracta,the pressure changes from P1 to Pvc. According to the assumption of isentropic flow from P1 to Pvc,

Pvc and P1 will both be located on the same entropy line. Also note the following:

• The fluid temperature at Pvc is much lower than at P1.

• The fluid velocity at the vena contracta increases; therefore, the enthalpy is lower.

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Vena Contracta To The Valve Outlet - The assumption of isenthalpic flow across the valve means

that P2 and P1 will both be located on the same enthalpy line. Also note the following:

• Significant pressure energy is converted to heat, noise, and vibration. The loss of

pressure energy is permanent and irreversible; therefore entropy increases (theavailable energy is reduced).

• Because the fluid velocity decreases, its enthalpy will increase.

• The fluid temperature at P2 is slightly reduced from the temperature at P1.

Summary - From the above, it should be clear that if one knows the inlet pressure and temperature, the

vena contracta pressure (calculated by the choked flow equation Pvc = r cPv), and the outlet pressure, a

wealth of information can be determined, including:

• The fluid state at the vena contracta.

• The temperature of the fluid at the valve outlet.• The fluid specific volume and therefore the fluid density at the valve outlet.

It must be stated that while the specific points of P 1, Pvc, and P2 can be clearly identified on the chart, the exact

path of the traverse from P1 to P2 is unknown. The traverse may occur in a direct path as shown in Figure 11,

or it may dip and rise in a fashion that is totally unpredictable.

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Liquid Flow Example

Figure 12 illustrates the thermodynamic behavior of a liquid as it passes through a control valve. The only

difference between the liquid expansion that is shown in Figure 12 and the gas expansion that was previously

discussed is that the liquid expansion takes place in the liquid region of the phase diagram.



Figure 12

Thermodynamic Analysis Of Liquid Flow Through A Control Valve

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Control Valve Sizing Equations

Fluid States For Which The Standard ISA Sizing Equations Are Applicable

The applicability of the control valve sizing equations that are endorsed by the ISA is limited to specific fluid

states and conditions. The applicability of a particular equation is determined by the fluid state at the valve inlet .

The equations and the fluids states to which they apply are shown in Figure 13 and they are discussed below.



Figure 13

Fluid States And Applicable Sizing Equations

Liquids - If P1, Pvc, and P2 are all located to the left of the two-phase dome, the liquid will not

vaporize as it passes through the control valve. Fluid density will remain constant and the standard

liquid sizing equation can be applied.

Flashing Liquids - If P1 is in the liquid region and if P2 is inside the two-phase dome, the liquid will

be flashing. The decrease in fluid density means that a larger valve may be required to pass the flow.

To determine if the flow is choked, the choked flow pressure drop is calculated and compared with the

actual pressure drop. The valve is sized with the use of the lesser of the two pressure drops.

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Cavitating Liquids - If P1 and P2 are outside the two-phase dome but Pvc dips inside the two-phase

dome, fluid vaporizes and then reverts to a liquid; i.e., the fluid cavitates. Cavitation is also

accompanied by the potential for choked flow.

Ideal Gasses - If P1, Pvc, and P2 are located at a considerable distance to the right of the two-phase

dome, the fluid is an ideal gas. In this region, the temperature lines are parallel to the vertical lines of

constant enthalpy. As a result, the relationships of pressure, volume, and temperature are constant, as

expressed with PV=RT, where R is a gas constant.

Real Gasses - If P1, Pvc, and P2 are all located to the right of the two-phase dome and below the

critical pressure and if one or more of the three points is near the two-phase dome, the gas will exhibit

real gas behavior. In this region, the temperature lines are not parallel to the lines of constant enthalpy.

The compressibility factor, Z, compensates for real gas behavior which is described with PV=ZRT.

Fluid States That Require Special Sizing Techniques

A number of flow conditions are commonly encountered for which the standard ISA sizing equations are not

applicable.

Two Phase Flows: Liquid/Vapor Or Liquid/Gas - If either P1 or P2 is located inside the two-phase

dome, a two-phase flow is present. For a single-species fluid, the flow consists of a liquid and its

vapor. If the fluid is a binary fluid (two different substances) the flow may consist of a liquid and a gas.

Fluids With Dissolved Gasses (Outgassing Fluids) - Many fluids include dissolved gasses that come

out of solution as a result of agitation (such as occurs when the fluid passes through a control valve) or

pressure reduction. With regard to valve sizing, the impact of an outgassing fluid is similar to that of a

flashing fluid; i.e., the decrease in fluid density at the vena contracta has a flow-limiting effect.

Fluid Mixtures: Gas Mixtures And Liquid Mixtures - The ISA sizing equations are based on the

flow of single-species fluids; e.g., water, pentane, etc.. The equations may not accurately predict the

flow rate if the fluid is comprised of two or more gasses or two or more liquids.

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SIZING CONTROL VALVES FOR TWO PHASE FLOWS

Types Of Two Phase Flows And Implications For Valve Sizing

Types Of Two Phase Flows

A two-phase flow consists of a liquid and either a gas or a vapor as shown in Figure 14.



Figure 14

Two-Phase Flows

Vapor/Liquid Flow - For a single species fluid such as water, two-phase flow is encountered when

some portion of the fluid is in the liquid state and some portion of the fluid is in the vapor state. Steam

is a common example of a vapor/liquid flow.

Gas/Liquid Flow (Binary Fluid) - In many applications, the flow consists of two different

components (a binary fluid). If one component is in the liquid state and another is in the gaseous state

under the prevailing conditions, the flow is referred to as a gas/liquid flow. A common example of a

binary fluid is air and water.

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Implications For Valve Sizing

Special considerations for two-phase flows are listed in Figure 15 and they are discussed below.

Specific Volume Of The Mixture - All sizing equations for liquid and gas flows include a factor for

the fluid density. As the ratio of the gas or vapor phase to the liquid phase increases, the fluid densitydecreases (specific volume increases) and increased valve capacity may be required to pass the

specified flow rate. With two phase flows, the determination of the fluid density that will be useful in

the valve sizing equations is an important step.

Gas Velocity Versus Liquid Velocity (Slip) - Gasses tend to flow at higher velocities than liquids.

The phenomenon of a gas moving faster than a liquid in the same flowstream is referred to as “slip”.

Because fluid velocity determines flow rate, “slip” must be considered when calculating valve

capacities for two-phase flows.

Choked Flow And The Valve Sizing Pressure Drop - The value of the flow-limiting pressure drop

(choked ∆P, critical ∆P) can be somewhat different for liquids and for gasses. Accordingly, any two-

phase sizing procedure must include a method for determining the pressure drop that is effective for

sizing purposes.



Figure 15

Two-Phase Flow Sizing Considerations

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Two-Phase Flow Sizing Assumptions And Sizing Methods

Best Case Assumptions: Homogenous Mixture

A two-phase sizing procedure is most feasible to develop for a homogenous flow (bubble, mist, or spray flow).

For plug or slug flows in which the flowstream is alternately all liquid and then all gas or vapor, development

of a universal equation would be virtually impossible.

ISA Standard S75.01

The ISA sizing standard (S75.01) does not include equations for two-phase sizing. In the absence of industry-

wide standards, valve manufacturers and others have developed systematic procedures for sizing control valves

for two-phase flows. This Module will introduce the two-phase sizing procedure that has been developed by

Fisher Controls. The method is documented in the manufacturer’s sizing catalogs (Fisher Catalogs 10 and 12)

and it is included in the Fisher Sizing Program.

Fisher Methods For Sizing Control Valves For Two-Phase Flows

Overview Of The Two-Phase Sizing Procedure

The basic approach for sizing two-phase flows is shown in Figure 16 and it is discussed below.

1. Calculate the Cv for the liquid phase of the flowstream (Cvl).

2. Calculate the Cv for the gas or vapor phase of the flowstream (Cvg).

3. Sum Cvg and Cvl.

4. Apply a correction factor (1+Fm) to the sum of the Cv’s to determine the Cv required (Cvr ).

C C C F

Where

C Therequiredcontrolvalve C

C C for the liquid phase

C C for the gas or vapor phase

F a correctionfactor

vr vl vg m

vr vvl v

vg v

m

= + +

===

=

( ) ( )

:

1

Figure 16

The Fisher Controls Two-Phase Valve Sizing Equation

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Valve Sizing Pressure Drops - To ensure that flow is not overestimated (and that valve size is not

underestimated) when calculating valve sizes for two-phase flows, the valve sizing ∆P must be limited

for each phase. The pressure drop that is used for valve sizing purposes is selected according to the

information that is shown in Figure 17. Note that the value of ∆Pc is determined by:

1. Finding the critical pressure drop ratio (∆P/P1) from the chart below. The ratio is a function of the

value of C1 (C1 = Cg/Cv).

2. Multiplying the inlet pressure (P1) by the value that is determined in the above step.

Fluid Phase Conditions Sizing ∆∆P

Vapor/Gas All Lesser of ∆Pactual or ∆Pc

Liquid If ∆Pactual ≥ ∆Pc ∆Pc

If ∆Pactual ≤ ∆Pc Lesser of ∆Pactual or ∆Pallow



Figure 17

Sizing ∆P’s That Are Used In Two-Phase Sizing

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Correction Factor, Fm - Figure 18 shows the correction curve that is used to determine the correction

factor Fm. To determine the value of Fm, the point at which the volume ratio, Vr , intersects the plot is

determined and the value of Fm is read off the left axis of the chart.



Figure 18

Gas Volume Ratio, Vr Versus Cv Correction Factor, Fm

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Volume Ratio Vr For Gas/Liquid Flows - The volume ratio for gas/liquid flows is calculated as

follows:

V

Q

Q PT

Qr

g

lg= +284 1

1

where:

Vr = the gas volume ratio

Qg = gas flow, scfh

Ql = liquid flow, gpm

T1 = inlet temperature, degrees R (Degrees R = Degrees F + 460)

P1 = fluid pressure at the control valve inlet, psig

Volume Ratio Vr For Vapor/Liquid Flows - The volume ratio for vapor/liquid flows is calculated as

follows:

V

V

V Vx

x

r

g

g l=

+−

1

where:

Vr = the gas (vapor) volume ratio

Vg = specific volume of the gas or vapor, cubic feet per pound

Vl = specific volume of the liquid, cubic feet per pound

x = mixture quality, dimensionless

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Determining Flow Rates At The Valve Inlet

Establishing Service Conditions At The Valve Inlet - It should be clear from the previous discussion

that in order to apply the two-phase sizing equation, the flow rates of the liquid and the gas

components at the valve inlet must be known. For most applications, the respective flow rates of the

liquid and the gas at the valve inlet are assumed to be the same as the flows at the downstream

conditions as shown in Figure 19. Although flow rate information is often difficult to obtain, it should

be available from process engineers and experienced operations personnel. In many instances, the flow

rates can be determined by studying the downstream process.



Figure 19

Inlet Flow Assumptions

Fm Values - The values of Fm range from 0 to 1.0. When the value of Vr is near 0, the fluid is mostly

liquid and the correction factor Fm is small. As the volume ratio increases (the flowstream consists of

increasing amounts of gas or vapor), the correction factor Fm also increases. At the maximum value of

Fm, the Cvr is double that of the uncompensated value of Cv. Notice that when the volume ratio is

greater than 0.9, the correction curve displays a steep downward slope. The steep slope is partially

related to the phenomenon of slip; i.e., the much higher velocity of a gas or vapor as compared to the

velocity of a liquid under the same conditions.

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Unique Problems For Vapor/Liquid Flows

Transfer Of Mass And Energy Between Phases - Refer to Figure 20 and note that the horizontal

traverse of the constant temperature line across the two-phase dome can be viewed as an indicator of

quality, x. When the quality (x) of a fluid is 0, the fluid is entirely in the liquid state and when the

quality is 1.0 the fluid is entirely in the vapor state. If only the pressure and temperature of a vapor are

known, the fluid state could be defined by any point on the horizontal temperature line that passes

across the two-phase dome. For this reason, either the value of x or the enthalpy must be known in

order to determine the density of a vapor. Because the enthalpy value is often difficult to obtain, the

value of x is commonly used for valve sizing purposes.



Figure 20

Enthalpy And x Versus Pressure And Temperature

Available Data Vs. Actual Conditions At The Valve Inlet - The service conditions that are provided

to the valve specifier - including the value of x - are often the conditions that were determined for the

fluid at some upstream location. Because of pressure losses, heat losses, and changes in operating

parameters, the pressure conditions, temperature conditions, and the value of x at the valve inlet may

be substantially different than the given data. Any such discrepancy can result in erroneous

calculations for Vr and Cvr . When sizing valves for vapor/liquid flows, specifiers should make an

additional effort to ensure that accurate data is available.

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Computer Sizing Two Phase Flows

Method Selection Criteria

Refer to Figure 21 and note that there are two two-phase sizing methods within the Fisher Sizing Program: a

vapor/liquid method and a gas/liquid method. The criteria for selection of a particular method is discussed

below.

Units For Fluid Density - If the fluid density is given in units of mass (M, lb/ft3, kg/m3, etc.), the

vapor/liquid option should be selected.

Gas And Liquid Chemical Structure (Single Species Vs Binary Fluid) - As a generalization, the

vapor/liquid method is selected for single species fluids (water/steam) while the gas/liquid method is

commonly selected for binary fluids.



Figure 21

Fisher Sizing Program Menu Screen

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Inputs To The Vapor/Liquid Two-Phase Sizing Method

The sizing screen for the vapor/liquid method is shown in Figure 22 . The entry fields and the calculated results

are discussed below.



Figure 22

Fisher Sizing Program Screen For The Vapor/Liquid Sizing Method

Vapor Phase Information - The fluid data that is required to size the vapor phase of the flow is shown

in Figure 22. The required inputs are:

• The vapor name.

• The density of the vapor, lb/ft3.

• The flow rate, lb/hr.

Liquid Phase Information - The fluid data that is required to size the liquid phase of the flow is

shown in Figure 22. The required inputs are:

• The liquid name.

• The liquid critical pressure, Pc in psia.

• The liquid vapor pressure, Pv in psia.

• The liquid specific gravity, SG.

• The liquid flow rate, Q lb/hr.

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Mixture Service Conditions

The mixture service conditions that must be entered are:

• The inlet pressure, P1, in psia.

• The pressure drop, dP, in psid.• The temperature of the mixture at the valve inlet, T, in degrees F.

Note: The measurement units for many of the entry fields can be changed by pressing the F8 key, and,

then, selecting the desired units from the list that is shown.

Valve Specifications - The valve specifications that must be input are:

• The value of K m (recall that F KL m= )

• The value of C1 (recall that C1 = Cg/CvNote: The program can be used to size non-Fisher control valves by converting the pressure

recovery coefficient F L to K m with the use of F L2 = K m , and by calculating the value of C 1 with the use of C 1=C g /C v .

Calculated Results With The Vapor/Liquid Two-Phase Sizing Method

The software automatically calculates the valve size and displays the results of the various calculations.

Calculated Parameters - The results that are calculated and displayed include the following:

• dP Critical - The flow-limiting pressure drop for the gas phase.

• dP allowable - The flow limiting pressure drop for the liquid phase.

• r c - The critical pressure ratio that defines the vena contract pressure.

• Cg - The flow coefficient for the gas or vapor phase.

• Cv - The flow coefficient for the liquid phase.

• Quality - The value of x (x = the weight fraction of vapor in a vapor-liquid

mixture).

• Vr - The volume ratio (the percent by volume of gas to liquid).

• Fm - The correction factor that is included in the two-phase sizing equation.

• Cvr - The required control valve Cv, corrected for two-phase flow.

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Notes On Other Sizing Parameters - Many of the sizing options that are normally available by

pressing the F3 key are not active in the two-phase sizing methods. For example:

• The option to calculate the sound pressure level is not available because even at

critical flow, excessive SPL is generally not a problem with two-phase flows.Furthermore, the standard noise prediction equations do not yield accurate results

for two-phase flows.

• Cavitation damage is rarely a problem for two-phase flows because the high vapor

content provides a cushioning effect that protects against cavitation bubble

implosion. Accordingly, the options to evaluate the cavitation indices of K c and Ar

are not available in the two-phase sizing methods.

Differences Between The Vapor/Liquid Method And The Gas/Liquid Method

The basic difference between the vapor/liquid method and the gas/liquid sizing method is the units that are used

to express density of the gas or vapor phase. In the vapor/liquid method, the vapor density is expressed in termsof mass flow (lb/ft3, etc.). In the gas/liquid method, the vapor density is expressed in terms of specific gravity

(SG) or molecular weight (M). Refer to Figure 23.



Figure 23

Fisher Sizing Program Screen For The Gas/Liquid Sizing Method

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SIZING CONTROL VALVES FOR FLUIDS WITH DISSOLVED GASSES

Mechanics Of Outgassing And Implications For Valve Sizing

Dissolved Gas Defined

Figure 24 shows that gasses can be forced into solution in a liquid. The amount of gas that can be dissolved in a

solution is partially dependent upon the fluid pressure and the amount of time that the fluid is under pressure.

Dissolved gasses are typically found in high pressure streams of untreated, multi-component fluids. Crude oil is

a common example of a liquid that includes dissolved gasses. An example that is found in daily life is a

carbonated drink in a sealed bottle or can.

Mechanics Of Outgassing

Gas molecules may come out of solution (outgas) if the fluid pressure is reduced or if the fluid is agitated. A

common example of outgassing occurs when a can or bottle of a carbonated beverage is shaken and then

opened. Similarly, pressure letdown and the creation of turbulence are two of the operating mechanisms of a

high-pressure separator that is used in oil field operations.



Figure 24

Mechanics Of Outgassing

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Outgassing Versus Flashing

Refer to Figure 25 and compare the thermodynamic analysis of a flashing liquid with an outgassing liquid.

With flashing fluids, Pvc must fall below Pv and P2 must remain inside the two-phase dome. With outgassing

fluids, P1, Pvc, and P2 may all be on the liquid side of the two-phase dome. A slight reduction in fluid pressure

or the occurrence of agitation is all that is required to cause a gas to come out of liquid solution (outgas).



Figure 25

Outgassing Versus Flashing

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Outgassing Versus Cavitation

If the local pressure of a liquid falls below the liquid’s Pv and then rises above the liquid’s Pv, the fluid will

vaporize and then revert to the liquid state; i.e., the fluid will cavitate. If the local pressure of an outgassing

liquid decreases and subsequently increases, the gaseous portion of the fluid may not go back into solution.

Often, additional time is required for the increased pressure to force the gas back into the liquid solution. Refer

to Figure 26.



Figure 26

Outgassing Versus Cavitation

Indicators Of The Presence Of Dissolved Gasses

Stated Pv = P1 - Whenever the stated Pv of a liquid is equal to P1, one may deduce that the liquid

includes dissolved gasses that will come out of solution upon any reduction in pressure. The exception

is when both the true vapor pressure and the inlet pressure happen to fall on the saturated vapor line of

the two-phase dome. In this case, flashing rather than outgassing may be the greatest consideration.

Pv=P1>Pc - Even though it is a physical impossibility for the value of Pv to be larger than the value of

Pc, there are two common reasons for the occurrence of such defective data. (1) The value that is given

as the fluid’s Pv is actually the fluid’s bubble point. The bubble point is the pressure at which thelightest fluid components will come out of solution, or outgas. (2) The value that is given for the

critical pressure is actually the fluid’s pseudocritical pressure. Pseudocritical pressures will be

discussed later in this Module.

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Figure 27Fluid Properties As Indicators Of Outgassing

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Implications For Valve Sizing

Valve Capacity As A Function Of Gas Volume Ratio - Pressure reductions and turbulence in the

valve can cause varying amounts of dissolved gasses to come out of solution. Depending on the

amount of dissolved gas in the liquid and the degree of outgassing that occurs, fluid expansion at the

valve vena contracta can have a choking effect on flow capacity. If the effects of outgassing are not

considered, the valve may be undersized. The challenges that are encountered during valve sizing are

shown in Figure 28 and they are listed below.

• There is no simple method that can be used to accurately determine the amount of gas that is

dissolved in the liquid.

• There is no simple method to determine the extent of outgassing that will occur under various

service conditions.

• There is no scientific method for precisely calculating the impact of outgassing on valve capacity.



Figure 28

Sizing Considerations For Fluids With Dissolved Gasses

Absence Of Sizing Standards For Dissolved Gasses - No standards body (ISA, IEC, etc.) has

endorsed a method for compensating for dissolved gasses. Experience and the application of practical

techniques are the only guides that are available to the specifier.

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Bracketing Approach To Valve Sizing For Dissolved Gas Applications

General Concept

A common approach to valve sizing for outgassing liquids is to perform two or more sizing calculations that are

based on different assumptions regarding the state of the fluid. Then, the results of the two calculations are

compared and a subjective assessment is made in order to estimate the appropriate valve size. A common

technique is illustrated in Figure 29 and it is introduced below.

1. First, in order to determine the smallest possible valve size, the specifier sizes the valve as if it were a pure,

non-choked, liquid flow.

2. Next, in order to determine the largest possible valve size, the specifier assumes that the gas that does come

out of solution is present at the valve inlet. This is accomplished through the use of the two-phase sizing

procedure that was previously discussed.

3. The results of the two sizing calculations are compared and a valve size is selected on the basis of

experience and engineering judgment.



Figure 29

Basic Concept Of A Bracketing Approach To Valve Sizing

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Calculating The Minimum Valve Size

Assumption: Fluid Remains In Liquid State - In order to determine the smallest possible valve size,

the assumption is made that the fluid will remain in a liquid state; i.e., no vaporization will occur. Refer

to Figure 30.

Sizing Technique - To size the fluid as a liquid, the value of Pv is set to an arbitrarily low value; e.g.,

Pv = 0 (or a very low pressure value). After setting Pv to 0, the minimum valve size is calculated with

the use of the standard liquid sizing equations. Figure 30 shows that by setting P v to 0 or a value that is

near 0, there is little chance that the pressure at the vena contracta (Pvc) will drop below the fluid vapor

pressure (Pv). In other words, the sizing equations will not allow for fluid vaporization (choked flow).

The calculated results will lead to the smallest possible valve size. In fact, if outgassing occurs within

the valve, the valve may be undersized.



Figure 30

Sizing For The Minimum Valve Size

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Calculating Maximum Valve Size

Assumption: Upstream Gas/Liquid Fraction = Downstream Gas/Liquid Fraction

The maximum valve size is calculated with the use of a two-phase sizing method - most likely the

gas/liquid method. In order to calculate the maximum valve size, the gas/liquid fraction or the volume

ratio of the gas at downstream conditions must be known. For valve sizing purposes, the gas/liquid

volume ratio at the valve inlet is assumed to be equal to the gas/liquid volume ratio at the valve outlet

as shown in Figure 31.

Assumption: Pv<P2The two-phase sizing method will make sufficient allowance for fluid expansion that is caused by

outgassing. To ensure that the sizing equations do not make additional allowances for fluid expansion

by calculating the choked flow pressure drop, the value of Pv is set to an arbitrary value such as the

value of P2.



Figure 31

Sizing For The Maximum Valve Size

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Evaluation Of The Minimum And Maximum Cv Calculations

After the minimum and maximum Cv’s have been calculated, they are evaluated according the information that

is shown in Figure 32.

Cv min ∼∼ Cv max - If the minimum calculated Cv (Cv min) and the maximum calculated Cv (Cvmax) lead one to the selection of the same valve size, that valve size can be selected with reasonable

confidence.

Broadly Differing Values Of Cv max and Cv min - If the results of the calculations indicate valve

sizes that are significantly different, the specifier should consult with the valve vendor or manufacturer.

Difference In Valve Size That Is

Required By Cv min And Cv max

Confidence In

Sizing Method

Action

None High Select Indicated Valve Size

1 Valve Size Medium Select The Larger Valve Size

More Than 1 Valve Size Low Contact The Valve Vendor

Figure 32Interpreting The Results Of The Sizing Technique

Valve Style Selection Guidelines

Selection Of Replaceable Trim - Because of uncertainties in the sizing calculations, one should select

top-entry valves and cage-style trim in order to allow for field changes of trim size if necessary.

Body And Trim Material Selection - The physical effects of an outgassing fluid are similar to those

of a flashing fluid; i.e., when gasses come out of solution, localized areas of high-velocity flow

increase the potential for erosion damage. Accordingly, the body and trim materials for an outgassing

application should be selected as if the application were flashing; i.e., hardened trim and alloy bodies.

Cavitation Considerations

In a majority of applications where the gas/volume ratio is relatively high, the presence of dissolved

gasses can have a cushioning effect on any cavitation that may be occurring within the valve and

piping. Many specifiers assume that the dissolved gas will absorb most of the energy that is released

during cavitation and the issue of cavitation is ignored. This is the case with many unstabilized crude

oils. However, if the gas/liquid volume ratio is very low (VR < 0.2) and cavitation is predicted,

cavitation resistant trim should be considered.

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SIZING CONTROL VALVES FOR HYDROCARBON MIXTURES

Introduction

Many hydrocarbon fluids are mixtures. For example, crude oil may contain several different liquid components

and several different gaseous components. Most natural gasses are actually mixtures of several different

components (methane, ethane, propane, etc.).

Unique Sizing Problems With Liquid Mixtures

Multiple Pressure-Enthalpy Diagrams

Each component of a liquid mixture has a unique saturated liquid line, a unique critical point, and a unique

saturated vapor line. The challenge to the valve specifier is that the valve sizing equations require a single value

for the mixture vapor pressure and a single value for the mixture critical pressure.



Figure 33

Multiple Pressure-Enthalpy Diagrams For A Liquid Mixture

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Defining Fluid Properties

In order to establish single values for the fluid properties of mixtures, several different averaging techniques

may be applied.

Bubble Point Versus Vapor Pressure - For a single-species fluid at a specific temperature, the fluidvapor pressure defines a relatively precise pressure at which the fluid will begin to vaporize. With

mixtures, however, each mixture component may begin to vaporize at a different pressure. The

pressure at which the lightest component of a mixture begins to vaporize is often referred to as the

bubble point . If a vapor pressure for a liquid mixture is given as a single value, that value often is the

bubble point. The bubble point may be determined by testing, with the use of computer simulation

programs, or by calculation. When evaluating liquid mixtures, the saturated liquid line on a pressure-

enthalpy diagram may be replaced with a bubble line as shown in Figure 34.



Figure 34

Pressure-Enthalpy Diagram For A Liquid Mixture

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Pseudocritical Pressure and Pseudocritical Temperature - Each component in a liquid mixture has a

unique critical pressure and a unique critical temperature. For a mixture, the critical point is defined by

the intersection of the “pseudocritical” pressure and the “pseudocritical” temperature. Refer to Figure

34. One method of determining the pseudocritical pressure and the pseudocritical temperature is

through the use of a molar averaging technique. The pseudocritical properties are determined by:

1. Multiplying the mole fraction of each component times the values of Pc and Tc of each

component. The result is the pseudocritical property of each component.

2. Summing the values of the pseudocritical properties of each component to obtain the

pseudocritical properties of the mixture.

Pseudocritical pressures and temperatures may also be determined by test, by calculation, or with the

use of process simulation software. Although the pseudocritical point may not fall exactly on the phase

line, it does provide information that is reasonably effective in the valve sizing calculations.

Dew Line Vs. Saturated Vapor Line - For mixtures, there is not a single saturated vapor line on the

pressure-enthalpy diagram. Instead, the “dew line” describes the conditions under which the mixture

begins to change from the gaseous to the two-phase state and vice versa. Refer to Figure 34.

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Common Anomalies In The Values Of Fluid Properties

P1=Pv - When one is performing valve sizing calculations for mixtures, it is common to receive data

that indicates that P1=Pv. If P1=Pv, then one of two conditions may be present:

1. The fluid includes dissolved gasses which will come out of solution upon any reduction in pressure. In this situation, the stated vapor pressure is actually the bubble point. Refer to Figure 35.

2. Pressure P1 is at or very near the vapor pressure of the lightest component in the mixture. In this

instance, fluid vaporization rather than outgassing is the result. Depending on the conditions, fluid

vaporization may be accompanied by flashing, by cavitation, and/or by choked flow. Refer to

Figure 35.

3.

Unless a complete thermodynamic analysis is performed, it is difficult to distinguish between the two

conditions that are described above. However, a vapor pressure value that is equal to the valve inlet

pressure is the “classic” indication of the presence of an outgassing fluid.

Pv>Pc - Specifiers may receive data that indicates the fluid Pv is greater than the fluid Pc; however, it

is a physical impossibility for Pv to be greater than Pc. When these conditions are given, some of themixture components are above their critical temperatures (are not liquid) and they are dissolved in

heavier liquid components. The value that is given for Pc is probably the pseudocritical pressure. The

true critical pressure of some of the components will be higher. In addition, the value of the Pv that is

given may be the bubble point ; i.e., the pressure at which the lightest components begin to vaporize.



Figure 35

Common Anomalies In Fluid Properties

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Sensitivity Of Sizing Calculations To Accurate Fluid Properties

Sensitivity Of Valve Sizing Calculations To Pc - The valve sizing procedure for liquid flows requires

a value for the critical pressure (Pc) in order to permit calculation of the choked flow pressure drop

(∆Pallow or ∆Pchoked).

∆Pallow or ∆Pchoked = FL2 (P1-r cPv)

where:

r c = 0.96 - 0.28 (pv/Pc).

Recall that r c (the critical pressure ratio) is a measure of pressure reduction below the vapor pressure at

the vena contracta that provides the energy that is required to vaporize an amount of liquid. Fluid

vaporization can have a significant impact on the valve size that is required. In addition, choked flow

may be accompanied by flashing or cavitation. Given the significance of proper valve sizing and of

flashing and cavitation, the determination of useful values of Pc and Pv for the purpose of valve sizing

is essential.

Impact of Pc on ∆∆Pchoked (∆∆Pallow) - If all other parameters are fixed and the value of Pc isincreased, the choked flow equation will predict that choked flow will occur at smaller and smaller

pressure drops. As a result, the Cv that is calculated will increase. Similarly, if the value of P cdecreases while other parameters remain constant, larger and larger pressure drops may occur before

the flow becomes choked and a smaller value of Cv will be calculated.

Sensitivity Of Valve Sizing Calculations To Pv - If all other parameters are held constant and the

value of Pv is increased, the equation will predict that choked flow will occur at smaller pressure drops.

If a Pv is given which actually describes the mixture bubble point, the actual liquid Pv may be much

lower. The result is that the choked flow equation will predict total vaporization and choked flow

when, in fact, only a portion of the fluid stream will be vaporizing or outgassing. The result is that the

sizing equation will calculate a conservative Cv; i.e., the valve will not be undersized.

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Liquid Mixture Sizing Techniques

Many different techniques have been developed in order to address the challenges of sizing control vales for

liquid mixtures. Only a few will be presented in this Module. The techniques that are presented below are

designed to given an estimate of the valve size that will be required. For mixtures and other difficult sizing

problems, specifiers should always seek assistance from valve manufacturers and others who can apply

advanced sizing tools and techniques.

When Pv<Pc<P1

The relative values of Pv, Pc, and P1 that are shown in Figure 36 are what one would expect to find in a normal

liquid sizing situation. Because Pv does not equal P1, dissolved gas is not present. And, Pv is below the value

of Pc, which is to be expected. Because the fluid is known to be a mixture, the assumption is that the P v is

actually the bubble point and the Pc is actually the pseudocritical pressure. This mixture would be sized with

the use of the standard liquid sizing equations. If choked flow or flashing are not indicated, the fluid remains in

the liquid phase and the Cv that is calculated is accurate. If choked flow or flashing are indicated, the Cv that is

calculated will be conservative because only a portion of the mixture will actually vaporize. The major problem

is that it is difficult to precisely determine the extent of fluid vaporization.



Figure 36When Pv<Pc<P1

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When P1=Pv<Pc

In this example, because P1=Pv, we know that either (1) dissolved gasses are present, or (2) P1 is at the vapor

pressure of the mixture component with the highest Pv. If dissolved gasses are present, some outgassing will

occur upon any reduction of pressure at the vena contracta. If a fluid component’s vapor pressure is equal to P1,

then some flashing or cavitation could occur. However, the intensity of the flashing or cavitation may not be

significant if only a small fraction of the fluid is vaporizing.

The recommended sizing technique is the bracketing method that was previously discussed, i.e.:

1. Size the mixture as a non-choked liquid by setting the value of Pv to 0 or 1.

2. Size the mixture as a two-phase flow after setting the value of Pv to the value of P2.

3. Evaluate the results. If the difference in the valve size that is indicated by the two techniques is within one

valve size, select the larger valve size. If the difference in valve size is greater than one valve size, seek

assistance.



Figure 37

When P1=Pv<Pc

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When P1>Pv>Pc

In this scenario, the data is defective because no fluid can have a Pv that is greater than the Pc. The value that is

given for the critical pressure is actually the pseudocritical pressure. Because some of the components are above

their critical temperatures, they remain dissolved in heavier liquid components. (A fluid at a temperature that is

above its critical temperature cannot exist as a liquid). To calculate a valve size for this situation, the value of

the pseudocritical pressure Pc is set to equal the value of Pv. Then, the calculation is performed with the use of

the standard liquid sizing equations. Increasing the value of the critical pressure has the effect of reducing the

∆Pallow. This is a conservative approach and, in most instances, there is little danger of undersizing the valve.

An alternative is to set the value of Pv equal to the value of Pc. However, this method often produces a much

less conservative result.



Figure 38

When P1>Pv>Pc

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When P1=Pv>Pc

In this scenario, we know that the data is defective. We assume that the stated P v is actually the bubble point

and that the stated critical pressure is actually the pseudocritical pressure. This is the worst-case state for high

pressure crude oil. The fluid is a solution of light hydrocarbons in heavy, the fluid is at its bubble point when

entering the valve, and any reduction in pressure will result in some outgassing. There are two basic approaches

to sizing:

• Increase the critical pressure to equal the vapor pressure (bubble point) and proceed with the liquid sizing.

The calculated choked flow Cv will be conservative because it assumes that all of the liquid vaporizes

when, in fact, only the lightest components will flash or outgas.

• If the gas/liquid volume ratio of the mixture at the valve outlet is known, assume that two phase flow

occurs at the valve inlet and proceed with a two phase sizing procedure . Also set the value of Pv to the

value of P2 in order to prevent the flashing calculations from over-compensating for fluid expansion. By

assuming two-phase flow at the inlet, the fluid expansion of outgassing or flashing adequately considered.

If the choked flow equations are also applied, the calculated Cv will be overly conservative (too large).



Figure 39

When P1>Pv>Pc

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Features And Limitations Of The Sizing Techniques

The sizing techniques that have been presented in this Module will generally ensure the calculation of a

conservative Cv; i.e., the techniques will result in adequate or more than adequate valve capacity and they will

generally not undersize a control valve. While the techniques can be useful in estimating the valve size that is

required, specifiers should always remember the following:

• The techniques that have been presented are meant to provide an estimate of valve size only. It is strongly

recommended that specifiers obtain the most accurate data that is available and, then, obtain assistance

valve manufacturers and others who can apply more sophisticated sizing tools and methods.

• Specifiers should provide engineering attention in proportion to the size of the valve. For example, a small

sizing error in a 2-inch valve may not lead to significant sizing problems or significant additional costs.

However, a sizing error in a 12 or 20 inch valve could lead to significant operating problems and

substantial, unnecessary costs.

• Because the sizing techniques that have been presented are conservative, specifiers should remain alert to

problems that can occur with oversized valves. For example, if an oversized valve is located in a header

that feeds a vent valve, the flow rate of the fluid to the vent valve may be much greater than the capacity of the vent valve and an unsafe situation could easily occur.

• For critical and/or severe service applications, it is highly recommended that specifiers seek assistance from

valve vendors and sizing experts who are employed by valve manufacturers.

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Gas Mixture Sizing

Review Of Ideal Gasses And Real Gasses

Ideal Gasses - The ideal gas laws define a constant relationship between pressure, temperature, and

volume. The ideal gas law is expressed as:

PV=RT

where:

P = fluid pressure, psia

V = volume, cu ft

R = gas constant; 10.73(psia x cu

ft)/(degrees R x lb mole)

T = fluid temperature, degrees R

Real Gasses - As the pressure and temperature of the gas approach the critical point (see Figure 40),

the ideal gas laws do not accurately describe the relationships of P, V, and T. In order to more precisely

define the relationship of P, V, and T in real gasses, the compressibility factor, Z, is included in the

equation.

PV=ZRT



Figure 40Review Of Ideal Gasses Versus Real Gasses

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Determining The Value Of Z - The value of Z can be determined by:

1. Performing the calculations to determine the values of the reduced pressure (Pr ) and the reduced

temperature (Tr ).

2. Using the values of Pr and Tr to determine the value of Z from a compressibility chart.

The values of Pr and Tr are calculated as follows:

TT

Tr

c

= and PP

Pr

c

=

where:

T = the actual fluid

temperature

Tc = the critical

temperature of the fluid

P = the actual fluid pressure

Pc = the critical pressure of

the fluid

Note: Any units of absolute pressure or temperature may be used provided that T and T c are in the

same units and P and P c are in the same units.

Tr and Pr are factors that normalize the actual pressure and temperature of a specific fluid to the critical

pressure and the critical temperature of that fluid. In this context, normalizing means that all fluids with

equal values of Tr and Pr will exhibit the same thermodynamic fluid. The advantage of normalizing the

data is that a single chart (see Figure 41) or a single equation can be used to determine the value of Z

for a broad range of fluids.

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Figure 41

Chart That Is Used To Determine The Value Of Z From Pr and Tr

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Determining The Value Of Z For Gas Mixtures

Multiple Phase Diagrams - As shown in Figure 42, each component in a gas mixture will have a

different critical point (a different value of Tc and a different value of Pc). In order to calculate the

value of Z, a means of establishing a single value of T c and a single value of Pc for the mixture must

be defined.



Figure 42

Phase Diagrams For The Components In A Gas Mixture

Determining Pseudocritical Pressures And Temperatures - In order to determine a single value of

Pc and Tc for the gas mixture, the pseudocritical temperature and the pseudocritical pressure are

calculated. The pseudocritical pressure and the pseudocritical temperature are the molar averages of the

critical pressure and the critical temperature, respectively, of all of the components in the gas mixture.

As shown in Figure 43, the pseudocritical values for the mixture are obtained by:

1. Multiplying the mole fraction of each component times the value of Tc and the value of Pc of each

component, and, then,

2. Summing the pseudocritical values of Tc and Pc for each component.

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Component Mole

Fraction

Tc, degrees R Pseudocritical

Tc, degrees R

Pc, psia Pseudocritical Pc,

psia

CH4 0.90 343.0 308.7 666.4 599.76

C2H6 .06 549.6 32.9 706.5 42.39C3H8 .04 665.7 26.6 616 24.64

Pseudocritical values 368.2 666.79

Figure 43

Calculation Of The Pseudocritical Pressure And The Pseudocritical Temperature

Of A Gas Mixture

Determining The Value of Z - The pseudocritical values are used to calculate the pseudocritical

reduced pressure and the pseudocritical reduced temperature. The calculations are:

TT

Tr

c

= and PP

Pr

c

=

where:

Tr and Pr Pseudocritical reduced pressure and temperature

T and P Actual inlet temperature and pressure

Tc and Pc Pseudocritical temperature and pressure

Note: Any units of absolute pressure or temperature may be used provided that T and T c are in the

same units and P and P c are in the same units.

To determine the value of Z, the reduced pseudocritical properties (Tr and Pr ) are used in conjunction

with a chart such as the one that is shown in Figure 41 on a previous page. The chart that is shown in

Figure 41 is valid for many natural gasses with minor amounts of non-hydrocarbon constituents up to

pressures of approx. 10, 000 psig. The accuracy of the chart decreases if the mixture contains more

than 3 percent CO2 or H2S or if the mixture contains significant amounts of water. The chart is not

valid for two-phase flows.

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Computer Sizing

Most valve sizing programs will automatically calculate the value of Z if either the critical pressure and

temperature or the pseudocritical pressure and temperature are entered as inputs to the program.

Real Gas Sizing Methods - A real gas sizing method will produce the most accurate sizing

calculations. The inputs that are required for real gas sizing are:

• The value of Z.

• The value of either the specific heats ratio, k, which is used in the Fisher sizing equations, or the

specific heats ratio factor Fk (Fk = k/1.4) that is included in the ISA sizing equations. If the value

of k is not known, k can be set to 1.25 (Fk = .89), which is typical for many gasses that consist

primarily of methane and ethane.

Ideal Gas Sizing - If the values of Z and k (Fk ) are unknown, which is often the case with natural gas

mixtures, the valve may be sized by with the use of an ideal gas sizing method. The ideal gas sizing

method assumes that Z=1 and that k = 1.4 (Fk =1). Ideal gas sizing methods will typically produce

results that are conservative; i.e., the valve will not be undersized.

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Seeking Assistance

Calculation of an accurate valve size for hydrocarbon mixtures can be very challenging and may require

information and resources that are not readily available. Specifiers commonly seek assistance when they size

control valves for hydrocarbon mixtures. Some of the resources that are available to Saudi Aramco Engineers

are discussed below.

Internal Aramco Resources - Within the Saudi Aramco, the Process and Control Systems Department

includes a Process Engineering Division that in turn is segmented into units with responsibilities for

highly specific areas. The units are:

• The Upstream Process Unit (crude, NGL, GOSPS).

• The Refining Unit.

• The Process Engineering Service Unit (which can simulate any process, pipeline, or facility).

The units that are listed above may be able to supply information concerning fluid properties and

service conditions.

Control Valve Vendors - Assistance in control valve sizing is also available through valvemanufacturers and vendors. When communicating with these external resources, it is necessary to

supply as much information as possible concerning the process, the service conditions, the

composition and physical properties of the fluid, and any other fluid and application information that is

available.

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WORK AID 1: PROCEDURES FOR THE USE OF THE TWO-PHASE SIZING OPTION OF THE

FISHER SIZING PROGRAM

Work Aid 1A: Procedures That Are Used To Size Control Valves For Vapor/Liquid Flows

Note: The information that is listed in Exercise 1A does not include values for P c , P v , or SG. However, because

the fluid is a two-phase water and steam mixture, the properties can be located in various steam table and other resources. These resources are identified in the step-by-step procedures that are listed below.

1. Launch the Fisher Sizing Program.

2. Select the Vapor/Liquid two-phase sizing option.

3. Enter the sizing inputs as follows:

Vapor Phase Information

a. Enter the vapor name as “steam”.

b. Refer to the Properties Of Saturated Steam table that begins on page 136 of the Fisher

Control Valve Handbook and determine the specific volume of 90 psig steam. Convert the

specific volume to steam density with the use of the equation density = 1/V. Also determinethe temperature of the steam at the inlet pressure and enter the temperature in the appropriate

field in the section of the screen that is titled Mixture Service Conditions.

c. Enter the mass flow rate, W, of the steam. If necessary, change the units by pressing the F8

key and, then, selecting the desired units.

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Liquid Phase

a. Place the cursor in name field in the Liquid Phase section of the screen, press the F4 key to

access the fluid database, and select water vapor.

b. The Pc of water will automatically be entered as a result of selecting the fluid from the fluid

database in the previous step.

c. Because some of the fluid enters the valve as a vapor, the fluid vapor pressure is the same as

the inlet pressure. If the inlet pressure is expressed in psig, convert the inlet pressure value to

an absolute pressure value by adding 14.5 to the value of P1. Enter this value as the vapor

pressure.

d. Refer to the Properties Of Water table on page 135 of the Fisher Control Valve Handbook and

determine the specific gravity of water at the temperature of the steam.

e. Enter the mass flow rate, Q, of the liquid phase. If necessary, change the units by pressing the

F8 key and, then, selecting the desired units.

Mixture Service Conditionsa. Enter the value of P1.

b. Enter the pressure drop (∆P or dP).

c. Note: The temperature value was entered in a previous step.

Valve Specifications

For the purpose of initial sizing, enter the estimated values of K m and C1.

Note: For non-Fisher valves, convert F L to K m and calculate C 1 as follows:

F L2 = K m

C 1 = C v /C g

4. Calculate the required Cv by pressing the F2 key.

5. Locate the manufacturers catalog page that lists the flow coefficients for the desired valve type and,

then, select a valve that will provide the required Cv at less than 90 percent valve travel.

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Work Aid 1B: Procedures That Are Used To Size Control Valves For Gas/Liquid Flows

The following procedure describes the steps that are taken to size a gas/liquid two-phase flow.

1. Launch the Fisher Sizing Program.

2. Select the Gas/Liquid two-phase sizing option.

3. Enter the sizing inputs as follows:

Gas Phase Information

a. Place the cursor in name field in the Gas Phase section of the screen, press the F4 key to

access the fluid database, and select air.

b. The SG of air will automatically be entered as a result of selecting the fluid from the fluid

database in the previous step.

c. Enter the volumetric flow rate of the gas phase. If necessary, change the units by pressing the

F8 key and selecting the desired units.

Liquid Phase

a. Place the cursor in name field in the Liquid Phase section of the screen, press the F4 key to

access the fluid database, and select water vapor.

b. The Pc of the water phase will automatically be entered as a result of selecting the fluid from

the fluid database in the previous step

c. The Pv of the water phase is listed on page 135 of the Fisher Control Valve Handbook.

d. The SG of the water phase is listed on page 135 of the Fisher Control Valve Handbook.

e. Enter the flow rate, Q, of the liquid phase. If necessary, change the units by pressing the F8

key and selecting the desired units.

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Mixture Service Conditions

a. Enter the value of P1.

b. Enter the pressure drop (∆P or dP).

c. Enter the fluid temperature.

Valve Specifications

For the purpose of initial sizing, enter the estimated values of K m and C1.

Note: For non-Fisher valves, convert F L to K m and calculate C 1 as follows:

F L2 = K m

C 1 = C v /C g

4. Calculate the valve sizing information by pressing the F2 key.

5. Locate the manufacturers catalog page that lists flow coefficients for the desired valve, and, then, select

a valve that will provide the required Cv at less than 90 percent valve travel.

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WORK AID 2: PROCEDURES FOR THE USE OF A BRACKETING TECHNIQUE THAT IS USED

TO SIZE CONTROL VALVES FOR FLUIDS WITH DISSOLVED GASSES

To estimate an appropriate valve size for a fluid with dissolved gasses, perform two sizing calculations and,

then, evaluate the results. The procedure is outlined below.

1. Size the valve with the use of a liquid sizing model by setting the value of Pv very close to 0.0 and,

then, performing the normal liquid sizing calculations.

If the Liquid Sizing method of the Fisher Sizing Program is selected, press the F3 key and ensure that

all options and warnings are set to OFF. Also ensure that the Input P v option is selected. Note that the

Fisher Sizing Program will not accept a value of 0 for Pv. If Pv is set to 0, the program will raise the

value to 2 psia.

Enter the results of the liquid sizing procedure in the table that is located on the next page.

2. Size the valve with the use of a two-phase sizing model after making the following adjustments and

assumptions:

a. Assume that the gas flow rate and the liquid flow rate at the valve inlet are the same as the gasflow rate and the liquid flow rate at the valve outlet.

b. By assuming two-phase flow at the valve inlet, the expansion that results from outgassing

within the valve will be sufficiently accounted for. To prevent the choked flow equations from

over-compensating for fluid expansion, set the value of Pv equal to the value of P2. If

necessary, change the pressure units.

c. After setting the value of Pv equal to the value of P2, ensure that the value of Pc is equal to or

greater than the value of Pv. If Pc < Pv, the program will halt. If necessary, raise the value of

Pc to the value of Pv and proceed with the calculations.

Note: If the Fisher Sizing Program is used to size non-Fisher valves, convert F L to K m with

F L2 = K m and calculate the value of C 1 with C v /C g

Enter the results of the two-phase sizing calculation in the table that is located on the following page.

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Liquid Sizing Model Two-Phase Sizing Model

Min Flow Max Flow Min Flow Max Flow

Calculated Cv or

Cvr Assumed Pv, psia

Assumed Pc, psia

Required Valve

Size

-inch -inch

3. If the valve size that is determined with the use of the two-phase sizing model is within one valve size

of the valve size that is determined with the use of the liquid sizing model, one may have reasonable

confidence in the sizing technique and the larger valve size should be selected. If the difference is

greater than one valve size, assistance should be sought from the manufacturer or from other sizing

specialists.

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WORK AID 3: GUIDELINES FOR ADJUSTING THE VALUES OF FLUID PROPERTIES THAT

ARE USED TO SIZE CONTROL VALVES FOR HYDROCARBON MIXTURES

Work Aid 3A: Guidelines That Are Used To Size Control Valves For Hydrocarbon Liquid Mixtures

Relationship of Pv, Pc, and P1Comment Sizing Technique

Scenario 1

Pv < Pc ; P1>PvUse Word 6.0c or later to


Normal liquid flow conditions.

Flashing or cavitation may

occur.

Normal liquid sizing.

Sizing ∆P = lesser of ∆Pactual or ∆Pallow

∆Pallow = K m (P1 - r cPv)

where:

r c = 0.96 - 0.28 (Pv/Pc)1/2

Scenario 2

Pv = P1; Pv<PcUse Word 6.0c or later to


Pv is probably the bubble point

and the fluid is outgassing.

Size with a bracketing technique.

1. Set Pv=0 and size as a liquid2. Set Pv = P2 and size as a 2-

phase flow assuming that the

gas and liquid flow at the inlet

are the same as at the outlet.

3. Evaluate the results and select

the larger valve size.

Scenario 3

Pv > Pc; Pv < P1Use Word 6.0c or later to


Data is defective.

1. The Pc is the pseudocritical

Pc. The Pc of some

components may be higher.

2. Pv may be the “bubble

point”; i.e., somecomponents are above their

Tc (cannot exist as liquids)

and are in solution in

heavier liquid components.

Raise Pc to Pv and size with the

normal liquid sizing equations.

Allow for choked flow.

Scenario 4

Pv > Pc; Pv = P1Use Word 6.0c or later to


Combination of Scenarios 2 and

3. Typical for high pressure

crude oil.

Data is defective.

• Pc is the pseudo-critical

pressure.

• Pv is probably the "bubble-

point" and the fluid will

outgas.

Size with the use of the dissolved

gas bracketing technique (see

scenario 2).

1. Set Pv=0 and size as a liquid

2. Set Pv = P2. If Pv is still > Pc,

raise Pc to Pv, and size as a 2-

phase flow assuming that the

gas and liquid flow at the inlet

are the same as at the outlet.Evaluate the results and select the

larger valve size.

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Work Aid 3B: Guidelines That Are Used To Size Control Valves For Hydrocarbon Gas Mixtures

In order to perform accurate sizing calculations for a gas mixture, the real gas equations must be used. When

one is making use of the Fisher Sizing Program, the means by which the sizing calculations are performed

depends upon whether one has selected the Fisher Real Gas method or the ISA/EN Gas Sizing method.

Fisher Real Gas Method

• The values of Tc and Pc must be entered.

• The value of the ratio of specific heats, k, is entered. If the value of k is not known, an estimated value of

1.25 will generally provide reasonably accurate results with most natural gas mixtures.

ISA Sizing Methods

• The values of Tc and Pc must be entered.

• The specific heats ratio factor Fk must is entered. Note that Fk = k/1`.4. If the value of k (and therefore, Fk )

is not known, an estimated value of 0.89 will generally provide reasonably accurate results with most

natural gas mixtures.

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GLOSSARY

adiabatic A process in which there is no transfer of heat.

binary fluid A fluid that is comprised of two or more unique substances.

bubble point In a solution of two or more components, the conditions of temperature

and pressure at which the first bubbles of gas appear; a conceptual

equivalent to the vapor pressure of a single-species fluid.

critical point The point that is defined by the intersection of the critical temperature and

critical pressure on a phase diagram.

critical pressure The pressure at which the vapor density and the liquid density of a

substance are the same.

critical temperature The temperature at which the vapor density and the liquid density of a

substance are the same.

enthalpy A measure of heat content of a fluid, H, that is typically expressed in termsof Btu/lb.

entropy A thermodynamic quantity, S, that describes any permanent and

irreversible change in the available energy.

isentropic A process in which there is no change in entropy.

outgassing The phenomenon that occurs when a dissolved gas comes out of solution

as a result of turbulence, agitation, or reduced fluid pressure.

phase diagram A diagram that plots fluid pressure, entropy, enthalpy, specific volume,

and temperature as a function of any two of those parameters. Also

referred to as a Mollier diagram.

Pr

The reduced pressure; determined by dividing the actual absolute fluid

pressure by the fluid critical pressure; P/Pc.

pressure-enthalpy

diagram

A phase diagram that plots the values of entropy, temperature, and specific

volume of a specific fluid versus the pressure and enthalpy values of the

same fluid.

pseudocritical

pressure

The molar average of the critical pressures of each component in a fluid

mixture..

pseudocritical

temperature

The molar average of the critical temperatures of each component in a

fluid mixture.

quality The weight fraction of vapor in a vapor-liquid mixture; expressed as X

where X(100) = the percent vapor..

single-species fluid A fluid that is comprised of a single component; e.g., water.

specific volume The volume of a substance per a unit of mass. The inverse of fluid density.

supercritical A fluid state in which the fluid exhibits the characteristics of both a liquid

and a vapor; i.e., the state in which there is no distinction between the

liquid characteristics of the fluid and the vapor characteristics of the fluid.

thermodynamics The branch of physics that deals with the transformation of heat into other

forms of energy.

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Tr The reduced temperature; determined by dividing the actual absolute fluid

temperature by the fluid critical temperature; T/Tc.

two-phase dome A region on a phase diagram, generally in the shape of a modified

parabola, that distinguishes among the liquid, two phase, and gaseousstates of a fluid. It also encloses a region where both vapor and liquid

coexist as a two-phase mixture.

two-phase flow A flow that is comprised of a liquid and a gas or a liquid and a vapor.

vena contracta The point, following a flow restriction, at which the cross-sectional area of

the flowstream is at its minimum value, the fluid velocity is at its

maximum value, and the fluid pressure is reduced.

volume ratio In a two-phase flow, the ratio of the volume of a gas or vapor to the

volume of the total liquid/gas or liquid/vapor mixture.

X see quality

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