PCI20403

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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 not

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

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

without the written permission of the Vice President, Engineering

Services, Saudi Aramco.

Chapter : Instrumentation For additional information on this subject, contact

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

Sizing Control Valves For

Two Phase Flows,Fluids With

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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

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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

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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

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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 ...56 Work 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 Hydrocarbon Liquid 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

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Use Word 6.0c or later to

view Macintosh picture.

Figure 1

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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.

Use Word 6.0c or later to

view Macintosh picture.

Figure 2

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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

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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

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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

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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 7

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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. Any degree 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

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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

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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.,

H

V

g

H

V

g

vc vc 1 1 2 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

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Figure 10

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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 P

vc

is much lower than at P

1

.

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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 (the

available energy is reduced).

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

• The fluid temperature at P

2

is slightly reduced from the temperature at P

1

.

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 = rcPv), 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 P1, 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

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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 density decreases (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

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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

F

Where

C

Therequiredcontrol valveC

C

C for the liquid phase

C

C for the gas or vapor phase

F

a correctionfactor

vr vl vg m vr v vl v vg v m

=

+

=

(

)(

)

:

1

Figure 16

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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

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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.

Use Word 6.0c or later to

view Macintosh picture.

Figure 18

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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 P

T

Q

r g l g

=

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

x

r g g l

=

+



_

1 −



_

where:

V

r

= the gas (vapor) volume ratio

V

g

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

V

l

= specific volume of the liquid, cubic feet per pound

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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

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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.

Use Word 6.0c or later to

view Macintosh picture.

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/ft

3

_.

• 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, P

c

in psia.

• The liquid vapor pressure, P

v

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, P

1

, 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

L

=

K

m

)

•

The value of C

1

(recall that C

1

= C

g

/C

v

Note: The program can be used to size non-Fisher control valves by converting the pressure

recovery coefficient FL to Km with the use

of FL2 = Km, and by calculating the value of C1 with the use of C1=Cg/Cv.

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.

• C

g

- The flow coefficient for the gas or vapor phase.

• C

v

- The flow coefficient for the liquid phase.

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

mixture).

• V

r

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

• F

m

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

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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 A

r

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 terms of 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

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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

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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).

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Figure 25

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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 the

lightest 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 27

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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

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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 Pv 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

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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<P2

The 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

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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 (Cv

max) 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 32

Interpreting 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

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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 fluid

vapor 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.

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Figure 34

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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

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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 the mixture 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

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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-rcPv) where:

rc = 0.96 - 0.28 (pv/Pc).

Recall that rc (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 is

increased, 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 Pc decreases 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 Pv 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 36

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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

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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

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When P1=Pv>Pc

In this scenario, we know that the data is defective. We assume that the stated Pv 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

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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 40

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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:

T

r c = and

P

r 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 Tc are in the same units and P and Pc 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

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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 Tc 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,

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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 42.39

C3H8 .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:

T

r c = and

P

r 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 Tc are in the same units and P and Pc 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 valve

manufacturers 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 Pc, Pv, 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 determine the 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.