Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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Instrument Sizing 337

The orifice sizing applies to corner, flange, vena-contracta and 1/2-

diameter taps.

Nomenclature

C D - coefficient of discharge

d = orifice diameter for full scale AP, inch

D = internal pipe diameter, inch

F a = area thermal-expansion factor. Takes into account the expansion

of the orifice with temperature changes

h w = full-scale orifice pressure differential, in.

H20 at

68~

k- specific heat ratio (constant pressure to constant volume Cp/Cv)

P = upstream pressure, psia

AP = full-scale orifice pressure-differential, psi

Q = full-scale flow rate at upstream conditions, ft3/min

Wtrue = true full-scale flow rate, lb/s

Y = expansion factor

]3 = d/D, ratio of orifice diameter to pipe I.D.

9 = upstream fluid density, lb/ft 3

CONTROL VALVE SIZING

Introduction

Valves and piping represent about 25 percent of the total capital expen-

diture for materials and equipment in the chemical process industries

(CPI). These industries employ valves in a wide range of flowing media

from granula solids to industrial wastes. The most important character-

istics in the selection of valves are viscosity, corrosiveness, and

abrasiveness. In addition, a designer must consider the process param-

eters. These may be predictable short-term upset conditions, handling

more than one fluid with the same valve, or potentially high pressures

resulting from a fluid being entrapped in a valve body that then vapor-

izes due to heat gain. Selecting the right control valve for an application

involves four basic styles of throttling: cage-style globe valves, ball

valves, eccentric-disk valves, and butterfly valves. Globe valves are the

standards of the control valves. These may be hand operated or power

actuated types for automatic control. The common feature of these valves

is their internal construction, which consists of a disc or plug recipro-

cating within the valve body. Figure 5-2A shows a typical globe valve,

and Figure 5-2B shows a globe valve with cage-style trim.

Figure 5-2B. A globe valve with cage-style trim.

338

Instrument Sizing 339

Langford [5] has reviewed the installation, maintenance and trouble-

shooting of control valves, while Driskell [6] studied the various

aspects of two-phase flow, non-turbulent, non-Newtonian and flashing

liquids. Recently, Collins [7] listed the main basic conditions for select-

ing control valves. These include (1) characteristics of the controlled

fluid, (2) system pressures, (3) maximum differential pressure, (4) fluid

operating temperature and range, (5) line size, (6) valve size, (7) valve

type, (8) valve C v, (9) allowable leakage, (10) end connections, (11)

valve environment (outside temperature and range), (12) seat material,

body material, (13) actuation medium, (14) flow characteristics, and

(15) rangeability.

Correctly sized control valves achieve a high quality of control. A

valve that is too small will not allow the required flow, and a valve that

is too large will cost more than a correctly sized smaller valve and the

flow will be uncontrollable because its full control range will not be

used. The procedure for sizing a control valve is [8]:

1. Calculate the required valve sizing coefficient, Cv, based on pro-

cess data and manufacturers' valve data.

2. Consult valve manufacturers' table of C v against size. Then select

the smallest valve with a C~ rating greater than or equal to the

required C v.

3. Check that the reducers required installing the valve will not

change the valve selection. Choose a new valve with a greater C v

if necessary.

4. Check that the flow through the valve is not choked.

When the liquid flow is turbulent, and the effects of choked flow and

reducers are ignored, the expression for C~ reduces to

)0.5

C = q SpGrf (5-28)

v KD AP

Pressure Drop For Sizing

The pressure drop

(APsizing)

used for sizing the control valve is the

actual pressure drop across the valve at the sizing flow rate. This is

obtained by starting with the system pressure drop

(APsystem).

The pres-

sure drop at the sizing flow rate of all pipe, fittings, and equipment in

the flow system is subtracted from

APsystem.

The remainder is the actual

pressure drop across the control valve at the sizing flow rate.

340

Fortran Programs for Chemical Process Design

Choked Flow

As the flow of liquid passes the point of greatest restriction inside the

control valve, its velocity reaches a maximum and its pressure falls to a

minimum. If the pressure falls below the vapor pressure of the liquid,

vapor bubbles form within the valve. Increasing

APsizing across

the valve

beyond the point where vapor bubbles form would not alter the flow.

This suggests choked flow. The AP at which choked flow begins is called

the terminal, AP T . AP T is used instead for sizing the control valve when

APsizing across the valve is greater than AP T.

Flashing and Cavitation

Choked flow produces either flashing or cavitation. Flashing occurs

when the pressure downstream of the valve is below the vapor pressure

of the liquid, AP v. Pipe and internal valve erosion often occur because

the velocity of flashing the vapor-liquid stream is higher than the inlet

liquid velocity. A cavitation will occur if the downstream pressure is

above the liquid's vapor pressure. This results in the collapse of the

vapor bubbles as they leave the point of greatest restriction in the valve.

The shock waves and noise caused by the collapsing bubbles cause rapid

and severe damage to the valve or piping.

CONTROL VALVE SIZING FOR LIQUID, GAS,

STEAM,

AND TWO-PHASE FLOW

The valve flow coefficients,C v for a given valve depend on the internal

dimensions of the valve and the smoothness of the valve's internal sur-

face. Control valve manufacturers establish the C v for their valves through

a series of tests using water or air at a given pressure differential across

the valve. Manufacturers define C v as the capacity index. This indicates

the flow of water (gpm at 60~ that will pass through a completely

open valve under a pressure differential between the inlet and outlet

flanges. Control valve coefficients for single and double seated valves

are given in Table 5-1 [9].

Liquid Sizing

The equation for sizing valve for liquid service is given by

( /

SpGr~

Cv-Q, i~-~- 2

(5-29)

Instrument Sizing

341

Table 5-1

Flow Coefficients for Control Val~es

Flow Coefficient Cv

Size, in. Single-Seat Double-Seat

3/4 8

1 9

1 1/4 14 18

1/2 21 28

2 36 48

2 1/2 54 72

3 75 110

4 124 195

6 270 450

8 480 750

10 750 1160

12 1080 1620

14 1470 2000

16 1920 2560

Alternatively, for a given C v, the liquid flow rate can be defined by

/ 0.5

Q1 C v ( PIspG~-

(5-3o)

Equation 5-29 is valid for liquid flowing below its saturation tempera-

ture in the turbulent zone with a viscosity value that is close to that of

water and size of pipe. Also, the control valve must be the same. Equa-

tion 5-29 can also be applied, if the vapor pressure of the liquid at the

flowing temperature is equal to or less than one-half the upstream pres-

sure. For this case, the vapor pressure of the liquid is substituted for

downstream pressure,

P2,

and the valve coefficient is calculated. The

calculated Cv must be corrected by a critical flow factor, Cf, where Cvcorr

is defined by

Cvcalc

Cvcorr --

(5-31)

The value of Cf is between 0.85 and 0.98. Flow capacity of a control

valve placed between pipe reducers is slightly decreased. In subcritical

342 Fortran Programs for Chemical Process Design

flow, this is accounted for by a correction factor, R. In critical flow, the

correction factor is Cfr. This replaces Cf in the sizing calculations. In

addition, R, Cf, and Cf~ depend on the ratio between pipe size and valve

size. Table 5-2 lists values of R, Cf, and Cfr for single-seated and double-

seated control valves [9].

Gas Sizing

The following equations are used for sizing control valves for gas

and steam conditions. These equations apply to both subcritical and criti-

cal flow conditions [10].

For subcritical condition, C v, is defined by

0.5

C = Qg{(SpGrg)(T) )}0.5 (5-32)

v 1360{(P, - P2)(P2

Table 5-2

Correction Factors for Control Valve Flow Coefficient

Single Seat Double Seat

Condition

Equal- Equal-

Factor Percentage V-Port Percentage V-Port

Critical

flow line

size control

valve

Cf 0.98 or .85 0.98 0.98 0.98

Critical

flow (control

valve between

pipe reducers)

Cfr 0.86 0.94 0.86 0.94

Subcritical

flow D/d = 1.5

R 0.96 0.96 0.96 0.94

Subcritical

flow D/d = 2

(Control valve

between pipe

reducers)

R 0.94 0.94 0.94 0.94

Instrument Sizing 343

The gas flow rate is computed for a given C v, and is defined by

C v (1360){(P, - P })o!P2)}~

Qg - {(Sparg )(T) (5-33)

Critical Condition

For critical flow, the downstream pressure of the control valve is less

than one-half the upstream pressure. Therefore, the term {(P~-

Pz)(P2)}0.5

reduces to 0.5P~ in Equations 5-32 and 5-33. Cv is then defined by

Cv Q {(SpGrg)(T)} ~

= g (5-34)

1360(0.5P~)

The gas flow rate is:

Q : C v(1360)(0.~P~) (5-35)

g {(Sparg)(T)

Steam Sizing

The following equations are used to size control valves for saturated

and superheated steam flow. For saturated steam flow, a value of zero is

used for ~ superheat.

Subcritical Condition. The control valve coefficient, C v, is defined by

Cv = (W)(K)

3{(P1 - P: )(P2 )}0.5 (5-36)

The steam flow rate, W, is defined by

W = (3)(Cv){(P' - Pz)(P2)}05

(5-37)

Critical Condition. The control valve coefficient and the steam flow

rate are expressed as:

Cv = (W)(K) (5-38)

1.5P I

344 Fortran Programs for Chemical Process Design

and

W - 1.5(P. )(C v ) (5-39)

where

K = 1 + (0.0007 x ~ superheat)

(5-40)

Two-Phase Flow

Sizing a control valve for liquid-gas mixtures introduces incorrect

valve coefficient, C v, if C v for each of the two fractions is calculated

separately, and then added. This method assumes that the liquid and gas

are passing through the valve orifice independently and at greater dif-

ferent velocities.

Driskell [6] has given a plausible assumption that the two fluids travel

through the throttling orifice as a homogeneous mixture at approximately

the same velocity. He applied the gas expansion factor to the gas frac-

tion only, and not to the total mixture. C v for liquid-gas mixtures can be

expressed as follows:

Divide the specific volume of the inlet gas, Vg, by the square of the

expansion factor Y. This gives an effective incompressible specific vol-

ume, while the liquid specific volume, Vl, is unaffected.

That is,

+ v ! (5-41)

where

Vg =

1/pg and v~ =

1/p~

Add the effective volumes of the two fluids in proportion to their mass

fraction, f, in the mixture to obtain the effective specific volume of the

stream, v e.

fg. Vg

V e = y2 + fl'vl (5-42)

where the expansion factor is:

Y = 1- (5-43)

(3FkXT)

Instrument Sizing 345

and

x = AP/P 1

x T = pressure drop ratio factor (from manufacturer)

F k =

ratio of specific heats factor (k/1.40)

k = ratio of specific heats (Cp/Cv)

= P1 - P2,

psi

P~ = inlet pressure, psia

P2 = outlet pressure, psia

The valve coefficient, C v, is:

C v = 0.5 (5-44)

63.3( A__p_P)ve

Alternatively, for a given Cv, the flow rate in lb/h is:

/0.5

W - 63.3(C v) AmP

V e

(5-45)

Installation

Control valves form an important equipment item in process plants,

and therefore, a lot of money can be saved by ensuring that the right

valves are installed. Selecting the right control valve for any application

starts with defining the valve's functions. For example, if an on-off inter-

lock valve is to be used, then the primary criteria for selection are reli-

ability and simplicity. If very fast and precise modulation is required,

such as for a compressor antisurge vent, a high quality valve is chosen.

Factors that affect the selection of control valves are:

9 Defining the type of fluid.

This includes the physical properties

(density and viscosity), corrosive properties, and the nominal pres-

sures, temperatures and flow rate. In the case of fluids, it is neces-

sary to know the vapor pressures to check for flashing and cavitation.

Also a high temperature increase can severely damage some types

of gaskets and packings.

9 The valve size.

This can be defined using standard calculation meth-

ods. The operating conditions and calculations may eliminate cer-

346 Fortran Programs for Chemical Process Design

tain valve styles from consideration. Cavitation is more evident

with the high-recovery rotary type valves and sometimes can be

avoided by selecting a globe valve. In addition, a valve that is too

small will not permit the required amount of flow. Alternatively, a

valve that is too large will be expensive and may create trim wear

and control problems.

9 Access for maintenance. This must be provided during the design

phase, retained during construction, and considered during the

revision stage. Maintenance can be both problematic and expen-

sive if a valve is difficult to reach or to work on. A substantial

change in the fluid-momentum (e.g., a flow through an angle valve

or a large fluid-velocity change) causes high reaction forces. This

can cause serious damage to the valves. The valve should be

installed between one and three feet above the grade or platform to

control the process.

9 Excessive stress on a valve body. This can cause leakage and

prevent normal operation of the moving parts resulting in the break-

age of the flange or valve body. Poor pipe alignment is the most prob-

able cause of excess stress. Also, heavy valves require support in order

to reduce the stress and to make removal and reinstallation easier.

Noise

Cavitation refers to the formation and subsequent collapse of vapor

bubbles in the flowing liquid stream at a point of higher pressure. This

causes erosion of the valve parts. It generates extremely high pressure

shock waves that hammer against the valve outlet and piping. Pressures

in these collapsing cavities can be as high as 500,000 psi in magnitude,

and often result in severe and rapid damage to the valve and piping.

Noise from control valves is often caused by pressures, flows, and

temperatures involving compressible flow. Valves control flow by caus-

ing turbulence, thereby converting much of the energy to heat and a

small fraction to sound. The control valve manufacturers have devel-

oped noise reducing valve trims and high-capacity valve configuration.

Langford [5] suggested that noise may be reduced by as much as 20 dB

by installing acoustic insulation at the valve and downstream, or alter-

natively by using heavier wall pipe downstream.

Nomenclature

C v = capacity coefficient for fully open control valve

fg- mass fraction in the gas phase