Fluid_Flow_Rules_of_Thumb_for_Chemical

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Fluid Flow

Veloci ty He a d ............................................................... 3 Fu l l Plant Piping ......................................................... 4 P a r t i a l l y Fu l l Ho r i z o n t a l P i pe s .................................. 5 Equivalent Length ....................................................... 6 R e c omme n d e d Veloci t ies ............................................ 7 Two - p h a s e F l ow ........................................................... 9 Comp r e s s i b l e F l ow - - S h o r t (P l an t ) L i ne s ................. 12 Comp r e s s i b l e F l ow - - L o n g P i pe l i ne s ........................ 18 Son i c Ve loc i ty ............................................................... 21 Metering ....................................................................... 21 Con t r o l Va lves ............................................................. 22 Sa f e t y Re l i e f Va lves ..................................................... 25

Fluid Flow

3

Velocity Head

Sonic Velocity

Two of the most useful and basic equations are

For the situations covered here, compressible fluids might reach sonic velocity. When this happens, further decreases in downstream pressure do not produce addi- tional flow. Sonic velocity occurs at an upstream to down- stream absolute pressure ratio of about 2 : 1 . This is shown by the formula for sonic velocity across a nozzle or orifice.

U2

(1)

/ ~h ~

2g

Au 2 AP ( V ) + ~ +ZKZ+E = 0 2g

(2)

where

critical pressure r a t i o - P2/P~ - [ 2 / ( K + 1)]K//K-~) when K - 1.4, r a t i o - 0.528, so P~/P2 - 1.89

Ah = Head loss in feet of flowing fluid u = Velocity in ft/sec g = 32.2 ft/sec 2 P = Pressure in lb/ft2 V = Specific volume in ft3/lb Z - Elevation in feet E = Head loss due to friction in feet of flowing fluid

To determine sonic velocity, use

Vs - (KgRT) ~

where

Vs = Sonic velocity, ft/sec K = Cp/Cv, the ratio of specific heats at constant pres- sure to constant volume g = 32.2 f t ]sec 2 R = 1,544/mol.wt. T = Absolute temperature, ~ P1, P2 = Inlet, outlet pressures, psia Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very high. For sonic velocity in piping see the section on "Com- pressible Flow." Still more mileage can be gotten out of Ah = u2/2g when using it with Equation 2, which is the famous Bernoulli equation. The terms are 1. The PV change 2. The kinetic energy change or "velocity head" 3. The elevation change 4. The friction loss Bernoulli Equation

Applications

In Equation 1 Ah is called the "velocity head." This expression has a wide range of utility not appreciated by many. It is used "as is" for

1. Sizing the holes in a sparger 2. Calculating leakage through a small hole 3. Sizing a restriction orifice 4. Calculating the flow with a pilot tube

With a coefficient it is used for

1. Orifice calculations 2. Relating fitting losses, etc.

Why a Coefficient?

For a sparger consisting of a large pipe having small holes drilled along its length Equation 1 applies directly. This is because the hole diameter and the length of fluid travel passing through the hole are similar dimensions. An orifice, on the other hand, needs a coefficient in Equation 1 because hole diameter is a much larger dimen- sion than length of travel (say 1/8 in for many orifices). Orifices will be discussed under "Metering" in this chapter.

These contribute to the flowing head loss in a pipe. However, there are many situations where by chance, or

4

Rulesof Thumb for Chemical Engineers

Calculations:

on purpose, uZ/2g head is converted to PV or vice versa. We purposely change uZ/2g to PV gradually in the fol- lowing situations" 1. Entering phase separator drums to cut down on turbulence and promote separation 2. Entering vacuum condensers to cut down on pressure drop We build up PV and convert it in a controlled manner to uZ/2g in a form of tank blender. These examples are dis- cussed under appropriate sections.

Use AH - u2/2g. Flow is sonic, so use AP - 100 - 50 - 50 psi (2" 1 pressure drop). Hole d i ame t e r - 1/8 i n - 0.125 in Hole area - n • (0.1252)/4 - 0.0123 in2 = 0.0000852 ft2 Densi ty of me t h a n e - (161b/76ft 3) x (100/76) x [(460 + 76)/(460 + 60)] - 0.285 lb/ft 3 (See "Approximate Physical Properties" in Section 25, "Properties," for the rule-of-76.) AH - 50 lb/in 2 x 144 in2/ft2 x f t 3 / 0 . 2 8 5 lb - 25,263 ft u2 - 25 , 263 ( 64 . 4 ) - 1,626,900 u - 1275 ft/sec F l ow - 1275 ft/sec x 0.0000852 ft2 x 0.285 lb/ft 3 x 3600 sec/hr - 111 lb/hr

Example

Given:

Methane (Mw = 16) Line @ 100 psia and 60~ Hole in the line of 1/8 in diameter Hole discharges to atmosphere (15 psia) Assume Z - compr es s i b i l i t y- 1.0

Source

Branan, C.R. The Process Engineer's Pocket Handbook, Vol. 1, Gulf Publishing Co., Houston, Texas, p. 1. 1976.

Find:

Flow through the hole in lb/hr

Full Plant Piping

exchanger tubeside pressure drop calculations), a con- stant of 23,000 should be used instead of 20,000. The equation applies to:

A handy relationship for turbulent flow in full com- mercial steel pipes is:

AP F - W 18~ . . L~

Liquids Compressible fluids at: Non-critical flow AP less than 10% of inlet pressure

where:

APF - Frictional pressure loss, psi/lO0 equivalent ft of pipe W = Flow rate, lb/hr

It was derived from the Fanning equation:

~t = Viscosity, cp 9 - Density, lb/ft 3 d - Internal pipe diameter, in.

APE - - (2f U2 L 9) / (32.2 D)

and the approximate relationship: 2

This relationship holds for a Reynolds number range of 2,100 to 1 0 6. For smooth tubes (assumed for heat

f - 0.054/Re ~

Fluid Flow

5

Sources

where:

u = velocity, ft/sec L = length, ft f = Fanning friction factor = Moody' s / 4 D = diameter, ft Re = Reynold' s Number

1. Branan, C. R., Rules of Thumb for Chemical Engi- neers, But terworth-Heineman, 2002, p. 4. 2. Simpson, L.L., "Sizing Piping for Process Plants", Chemical Engineering, June 17, 1968, p. 197.

Partially Full Horizontal Pipes

Example

The equations in the previous section are, of course, intended for use with full pipes. Durand provides a rapid way to estimate whether a horizontal pipe carrying liquid is full. The criteria are If Q/d 25 _> 10.2 the pipe is full. If Q/d 25 < 10.2 do a partially full flow analysis as follows. Let x = In (Q/d 25) and find the height of liquid in the pipe by:

Given:

Horizontal pipe d = 4 in ID Q = 100 gpm

Find:

Is the pipe full? If not, what is the liquid height? Also, what is the pipe's equivalent diameter?

H/D - 0.446 + 0.272x + 0.0397x 2 - 0.0153x 3 - 0.003575x 4

Find the "equivalent diameter" by:

Calculations:

De /D - - 0 . 01130+ 3.040 ( H / D ) - 3.461 (H/D) 2 + 4.108 (H/D) 3 - 2.638 (H/D) 4

Q/ d 25 - 1 0 0 / 3 2 - 3.125 Not full since Q/ d 25 < 10.2

[This is an empirical way to avoid getting De from De = 4 (cross-sectional flow area/wetted perimeter)] Note that for 1.0 > H/D > 0.5, De/D > 1.0. My calcu- lations and all references confirm this. De is substituted for D in subsequent flow analysis.

x = ln(3.125) = 1.1394 H/D = 0.779 H = 0.779 (4)= 3.12 in

De /D = 1 . 2 2 7 D e = 1 . 227 ( 4 ) = 4.91 in

Nomenclature

Source

D = pipe diameter, ft De = equivalent diameter, ft H - height of liquid in the pipe, ft Q = flow rate, gpm

Durand, A. A. and M. Marquez-Lucero, "Determining Sealing Flow Rates in Horizontal Run Pipes", Chem- ical Engineering, March 1998, p. 129.

d = pipe diameter, in q = flow rate, ft/sec u = velocity, ft/sec

6

Rules of Thumb for Chemical Engineers

Equ i v a l en t

Leng t h

The following table gives equivalent lengths of pipe for various fittings.

Table 1 Equivalent Length of Valves and Fittings in Feet

Contraction

En l a r gemen t

90 ~

Short Long Hard So f t rad. rad. T. T. el l el l

45 ~

9

9

Std. red.

Std. red.

mi t e r bends

Sudden

Sudden

o -->

~

"~

el l

-~- ~

_~

=>

.~o

>

Equiv. L in terms of small d

r ' N~

r

0

0 0

~

!

9

" - -

" ~

>

r

~0 z ~

"~

'

~:o

~, t '-

o 0")

= ~. ,

o :

0

i~. o=

<

c

O

"o T

. -

. ~

.

.

.

.

.

.

.

~

~

~

~

E

E

E

a "O

a

a "O

a

a "O

a

a "O

a "O

a "O

~1

03

~ "

"O

, "O

"O

11/2

55

26

13

7

1

1 2

3 5

2 3

8 9 2 3

5

3

1

4

1

3

2

1

1

2

70

33

17

14

2

2 3

4 5

3 4 10 11 3 4 i

7

4

1

5

1

3

3

1

1

21/2

80 i 40

20

11

2

2 . .

5 . .

3 . . ~ 12

3 . .

8

5

2

6

2

4

3

2

2

3

100

50

25

17

2

2

6

4

14

4

10

6

2

8

2

5

4

2

2

4

130

65 ' 32

30

3

3

7

5

19

5

12

8

3

10

3

6

5

3

3

18

12

4

14

4

9

7

4

4

1

6

200 100

48

70

4

4

11

8

28

8

8

260 125

64

120

6

6

15

9

37

9

25

16

5

19

5

12

9

5

5

2

10

330 ! 160

80

170

7

7

18

12

47

12

31

20

7

24

7

15

12

61 6

2

12 I 400 190

95

170

9 i 9

22

14

55 ~ 14

28 21

20

37

24

8

28

8

18

14

7

7

2

,

i

14

450 210

105

80 i 10 ' 10 ' 26

16

62 , 16

32 24

22

42

26

9

- -

- -

20

16

8

- -

16

500 240

120

1 4 5 ' 11

11

29 ~ 18

72

18 ' 38 27

24

47

30

10

- -

m

24

18

9

- -

- -

18

550 280

140

160

12

12

33

20

82

20 i 42 30

28

53

35

11

~

~

26

20

10

m

20

650 300

155

210

14

14

36

23

90

23

46 33

32

60

38

13

~

30

23

11

22 ! 688 335 ~ 170

225

15

15

40

25

100

25

52 36

34

65

42

14

~

~

32

25

12

24

750 370

185 i 254

16

16

44

27

110

27

56 39

36

70

46

15

~

~ ' 35

27

13

30

~

m

312

21

21 i 55

40 ' 140

40

70 ~ 51

44

:

i

'

i

;

36

m

~

~

25

25

66 i 47 i 1 7 0

47

84 60

52

!

I

l

42

~

~

! 30

30

77

55

200

55

98 69

64

48 54

m

~ ~

35 40

35 40

88 99

65 70

220 250

65 70

112 81 126 90

72 ] 80 i

~

60

~

~

45

45

110

80

260

80

190 99

92

Sources

1. GPSA Engineering Data Book, Gas Processors Sup- pliers Association, 10th Ed. 1987. 2. Branan, C. R., The Process Engineer's Pocket Hand- book, Vol. l, Gulf Publishing Co., p. 6, 1976.

Fluid F l ow

7

RecommendedVelocities

Here are various recommended flows, velocities, and pressure drops for various piping services.

Sizing Cooling Water Piping in New Plants Maximum Allowable Flow, Velocity and Pressure Drop

MAINS

LATERALS

Flow GPM

Vel.

Flow GPM

AP

Vel.

AP

Pipe Size in.

ft/sec, f t / lO0'

ft/sec,

ft/100'

7O

3.04 3.53 4.22 4.17 4.48 5.11 5.13 5.90 6.23 6.67 7.82 8.67

2.31 2.22 1.92 1.36 1.19 1.23 1.14 1.16 1.17 1.17 1.19 1.11

100 200 500 900

4.34 5.05 5.56 5.77 6.10 6.81 7.20 7.91 8.31

4.47 4.29 3.19 2.48 2.11 2.10 2.10 2.09 1.99

3 4 6 8

140 380 650

Sizing Steam Piping in New Plants Maximum Allowable Flow and Pressure Drop

1,100 1,800 2,200 3,300 4,500 6,000

1,500 2,400 3,100 4,500 6,000

10 12 14 16 18 20 24 30

Laterals

Mains

Pressure, PSIG Density, #/CF

600 0.91

175 0.41 0.70

30

600 0.91 0.70

175

30

0.106

1.41 0.40

0.106

0.50

0.30

AP, PSI/100'

1.0

11,000 19,000

Nominal Pipe Size, In.

Maximum Lb/Hr • 10 3

7.5

3.6 7.5

1.2 3.2 8.5

6.2

2.7 5.7

0.9 2.5 6.6

3 4 6 8

15 40 76

12 33 63

Sizing Piping for Miscellaneous Fluids

21 42 76

16 32 58 87

18 32 50 70

14 25 39 54 78

t0 12 14 16 18 20

130 190 260 360

108 158 217 300

100 ft/sec 60 ft/sec

Dry Gas Wet Gas

115 155 220 300

117 166 227

150 ft/sec 100 ft/sec 100 ft/sec Max. velocity 0.3 mach 0.5 psi/100 ft 0.5 ft head total suction line

High Pressure Steam Low Pressure Steam Air Vapor Lines General

100 130 170

9

. . .

101 132

. . . . . .

. . . . . .

Note: (1) 600PSIG steam is at 750~ 175PSIG and 30PSIG are saturated. (2) On 600PSIG flow ratings, internal pipe sizes for larger nominal diameters were taken as follows: 18/16.5"; 14/12.8", 12/11.6", 10/9. 75": (3) If other actual I.D. pipe sizes are used, or if local superheat exists on 175PSIG or 30 PSIG systems, the allowable pressure drop shall be the governing design criterion.

Light Volatile Liquid Near Bubble Pt. Pump Suction Pump Discharge, Tower Reflux Hot Oil Headers Vacuum Vapor Lines below 50 MM Absolute Pressure

3 - 5 psi/100 ft 1.5 psi/100 ft Allow max. of 5%

absolute pressure for friction loss

8

Rules of Thumb for Chemical Engineers

Suggested Fluid Velocities in Pipe and Tubing (Liquids, Gases, and Vapors at Low Pressures to 50psig and 50~176

The velocities are suggestive only and are to be used to approxi- mate line size as a starting point for pressure drop calculations.

The final line size should be such as to give an economical balance between pressure drop and reasonable velocity.

Suggested Trial Velocity

Suggested Trial Velocity

Fluid

Pipe Material

Fluid

Pipe Material

Acetylene (Observe pressure limitations) Air, 0 to 30 psig Ammonia Liquid Gas Benzene Bromine Liquid Gas Calcium Chloride Carbon Tetrachloride Chlorine (Dry) Liquid Gas Chloroform Liquid Gas EthyleneGas Ethylene Dibromide Ethylene Dichloride EthyleneGlycol Hydrogen Hydrochloric Acid Liquid Gas Methyl Chloride Liquid Gas Natural Gas Oils, lubricating Oxygen (ambient temp.) (Low temp.) Propylene Glycol

Sodium Hydroxide 0-30 Percent 30-50 Percent 50-73 Percent Sodium Chloride Sol'n. No Solids With Solids

4000 fpm 4000 fpm

Steel Steel

6 fps 5 fps 4

Steel and Nickel

6 fps 6000 fpm 6 fps

Steel Steel Steel Glass Glass Steel Steel

5 fps (6 Min.- 15 Max.) 7.5 fps 6 fps

Steel

Monel or nickel

4 fps 2000 fpm

Perchlorethylene Steam

Steel

4 fps 6 fps

0-30 psi Saturated* 30-150 psi Satu- rated or super- heated* 150 psi up

4000-6000 fpm

Steel

5 fps 2000-5000 fpm

Steel, Sch. 80 Steel, Sch. 80

6000-10000 fpm

6 fps 2000 fpm 6000 fpm 4 fps 6 fps 6 fps 4000 fpm

Copper & Steel Copper & Steel Steel Glass

superheated *Short lines

6500-15000 fpm 15,000 fpm (max.)

Sulfuric Acid 88--93 Percent 93-100 Percent

Steel Steel Steel

4 fps 4 fps

S. S.-316, Lead Cast Iron & Steel, Sch. 80

Sulfur Dioxide Styrene Trichlorethylene Vinyl Chloride Vinylidene Chloride Water Average service Boiler feed

4000 fpm 6 fps 6 fps 6 fps 6 fps

Steel Steel Steel Steel Steel Steel Steel Steel

5 fps 4000 fpm

Rubber Lined R. L., Saran, Haveg

6 fps 4000 fpm 6000 fpm 6 fps 1800 fpm Max. 4000 fpm

Steel Steel Steel Steel Steel (300 psig Max.) Type 304 SS

3-8 (avg. 6) fps 4-12 fps 1-5 fps

Pump suction lines Maximum economi- cal (usual) Sea and brackish water, lined pipe Concrete

7-10 fps

Steel R. L., concrete, asphalt-line, saran- lined, transite

5 fps

Steel

5-8 fps~ 3 5-12 fpsJ (Min.)

Note: R. L. = Rubber - l ined s t ee l

Fluid Flow

9

Typical Design Vapor Velocities* (ft./sec.)

Typical Design* Velocities for Process System Applications

Line Sizes

Fluid

<_6"

8"-12"

_>14"

Velocity, ft./sec.

Service

Saturated Vapor 0 to 50 psig

4-6.5 1-5

Average liquid process Pump suction (except boiling) Pump suction (boiling) Boiler feed water (disch., pressure) Drain lines Liquid to reboiler (no pump) Vapor-liquid mixture out reboiler Vapor to condenser Gravity separator flows

30-115

50-125

60-145

Gas or Superheated Vapor 0 to 10 psig

0.5-3 4-8 1.5-4 2-7

50-140 40-115

90-190 75-165 60-150

110-250 95-225 85-165

11 to 100 psig 101 to 900 psig

30-85

15-30 15-80 0.5-1.5

*Values listed are guides, and final line sizes and flow velocities must be determined by appropriate calculations to suit circumstances. Vacuum lines are not included in the table, but usually tolerate higher velocities. High vacuum conditions require careful pressure drop evaluation.

*To be used as guide, pressure drop and system environment govern final selection of pipe size. For heavy and viscous fluids, velocities should be reduced to about values shown. Fluids not to contain suspended solid particles.

Usual Allowable Velocities for Duct and Piping Systems*

Suggested Steam Pipe Velocities in Pipe Connecting to Steam Turbines

Velocity, ft./min.

Service/Application

Typical range, ft./sec.

Service--Steam

Forced draft ducts

2,500-3,500 2,000-3,000

Induced-draft flues and breeching

Inlet to turbine

100-150 175-200 400-500

Chimneys and stacks Water lines (max.)

2,000

Exhaust, non-condensing

600

Exhaust, condensing

High pressure steam lines Low pressure steam lines Vacuum steam lines Compressed air lines Refrigerant vapor lines High pressure

10,000

12,000-15,000

25,000

Sources

2,000

1. Branan, C. R., The Process Engineer's Pocket Hand- book, Vol. 1, Gulf Publishing Co., 1976. 2. Ludwig, E. E., Applied Process Design for Chemical and Petrochemical Plants, 2nd Ed., Gulf Publishing Co. 3. Perry, R. H., Chemical Engineer's Handbook, 3rd Ed., p. 1642, McGraw-Hill Book Co.

1,000-3,000 2,000-5,000

Low pressure

Refrigerant liquid

200 400

Brine lines

Ventilating ducts Register grilles

1,200-3,000

500

*By permission, Chemical Engineer's Handbook, 3rd Ed., p. 1642, McGraw-Hill Book Co., New York, N.Y.

Two-phaseFlow

Two-phase (liquid/vapor) flow is quite complicated and even the long-winded methods do not have high accuracy. You cannot even have complete certainty as to which flow regime exists for a given situation. Volume 2 of Ludwig's design books I and the GPSA Data Book2 give methods for analyzing two-phase behavior. For our purposes, a rough estimate for general two- phase situations can be achieved with the Lockhart and Martinelli 3 correlation. Perry's 4 has a writeup on this cor- relation. To apply the method, each phase's pressure drop is calculated as though it alone was in the line. Then the following parameter is calculated:

x - [ a P c / a P o 1'/2

where: APL and APG are the phase pressure drops The X factor is then related to either YL or YG. Whichever one is chosen is multiplied by its companion pressure drop to obtain the total pressure drop. The fol- lowing equation5is based on points taken from the YL and YG curves in Perry's 4 for both phases in turbulent flow (the most common case):

YL - 4.6X-178 + 12.5X-~ + 0.65 YG- X2yL

10

Rulesof Thumb for Chemical Engineers

10.0 8.0 6.0

4.0

2.0

3.0 2.0

0 o ~.0 ~9 0.8 Q_ ~- 0.6 0 "~ 0 . 4

g

o _

1.0 ~ 0.8 ~- 0 0.6 5. 0.4 u 0 0.3 > . _

m

~-

0 . 2

0.1 0.08 0.06 0.05

0.2

p l

2 3 4 6 8 1 1.5 2 3 4

6 8 1 1 . 52

3 4 6 8 1 1 . 52

3 4

6 8 1 1 . 52

3 4

6 8 1

J ~

J

-

9 .... T -

- - -

~ X 1,000

"- X 10,000

100,000

X 1 0 0

- ~ . . . . . . . .

'

J ~

Flowrate, Ib/h

Sizing Lines for Flashing Steam-Condensate

The X range for Lockhart and Martinelli curves is 0.01 to 100. For fog or spray type flow, Ludwig ~ cites Baker 's 6 suggestion of multiplying Lockhart and Martinelli by two. For the frequent case of flashing steam-condensate lines, Ruskan 7 supplies the handy graph shown above. This chart provides a rapid estimate of the pressure drop of flashing condensate, along with the fluid velocities. Example: If 1,000 lb/hr of saturated 600-psig condensate is flashed to 200 psig, what size line will give a pressure drop of 1.0psi/100ft or less? Enter at 600psig below insert on the fight, and read down to a 200psig end pressure. Read left to intersection with 1,000 lb/hr flowrate, then up verti-

cally to select a 1~2 in for a 0.28psi/100ft pressure drop. Note that the velocity given by this lines up if 16.5 ft/s are used; on the insert at the right read up from 600psig to 200psig to find the velocity correction factor 0.41, so that the corrected velocity is 6.8 ft/s.

Lockhart and Martinelli Example

Given:

Saturated 600 psig condensate flashed to 200 psig 1]/2 in line, sch. 80 (ID - 1.500 in) Flow - 1000 lb/hr

Fluid Flow

11

Condensate

Steam

Vapor APF - (135) ~8 (0.015)~

4.8 (0.468)]

Sat. 615 psia

T, ~

489

489

= 0.045 psi /100 ft

V, ft3/lb 0.7504 0.0202 H, btu/lb 1203.0 474.7

Cameron 8 = 0.05

Liquid APF -(865)18(0.14)~

Sat. 2 1 5 psia

000(1.5)4"8(55.5)]

T V H

388

388

= 0.017 psi /100 ft

2.135

0.018

Cameron 8 = 0.02 Crane9 = 0.01

1199.3 361.9

It, cp

0.015

0.14

Total Pressure Drop

Find:

X - [APL/APG]0.5 _ [0.017/0.045] 0.5 - 0.615

)-0.68

The flash amounts of steam and condensate, lb/hr Individual pressure drops if alone in the line, psi/100 ft Total pressure drop, psi/100 ft

YL 4.6(0.615) -1"78

-

+ 12.5(0.615

+0.65 - 29

Total AP - 29(0.017) - 0.49 psi /100 ft Ruskan7 = 0.28

Sources

Calculations:

1. Ludwig, E. E., Applied Process Design For Chemical and Petrochemical Plants, Vol. 1, Gulf Publishing Co. 2nd Edition., 1977. 2. GPSA Data Book, Vol. II, Gas Processors Suppliers Association, 10th Ed., 1987. 3. Lockhart, R. W., and Martinelli, R. C., "Proposed Correlation of Data for Isothermal Two-Phase, Two- Component Flow in Pipes," Chemical Engineering Progress, 45:39-48, 1949. 4. Perry, R. H., and Green, D., Perry's Chemical Engineering Handbook, 6th Ed., McGraw-Hill Book Co., 1984. 5. Branan, C. R., The Process Engineer's Pocket Hand- book, Vol. 2, Gulf Publishing Co., 1983. 6. Baker, O., "Multiphase Flow in Pipe Lines," Oil and Gas Journal, November 10, 1958, p. 156. 7. Ruskan, R. E, "Sizing Lines For Flashing Steam- Condensate," Chemical Engineering, November 24, 1975, p. 88. 8. Cameron, Hydraulic Data, Ingersoll-Rand Co., 17th Ed. 9. Flow of Fluids, Technical Paper No. 410, Crane CO., 1981.

Flash

Let X - lb/hr vapor Y - lb/hr liquid

X + Y = 1000 1199.3X + 361.9Y = 474.7(1000)

Solving: X - 135 lb/hr Y - 865 lb/hr

Individual pressure drops

APF - - W '8 ~~ /(20, 000 d 48 p)(See "Full Plant Piping" in Section 1, "Fluid Flow")

where

APF = psi/100 ft W = lb/hr ~t = cp

d - i n 9 = lb/ft3

12

Rules of Thumb for Chemical Engineers

Compressible Flow--Short (Plant) Lines

For compressible fluid flow in plant piping, one can use Mak's ~ Isothermal flow chart (Figure 1). Mak's chart was provided originally for relief valve manifold design and adopted by API. 2 The relief valve manifold design method, and its derivation, is discussed in Section 20, "Safety." Mak's methods can be applied to other common plant compressible flow situations. Since Mak's Isothermal flow chart is intended for relief manifold design, it supports calculations starting with Pz, the outlet pressure, that is atmospheric at the flare tip, and back-calculates each lateral's inlet pressure, P1. These inlet pressures are the individual relief valves' back pres- sures. The chart parameter is M2, the Mach number at the pipe outlet. Having M2 is very useful in monitoring prox- imity to sonic velocity, a common problem in compress- ible flow. For individual plant lines the fol lowing cases are easily solved with Figure 1 and the tabulated steps.

2. Determine fL/D. 3. Obtain Z. Figures 5, 6, and 7 are provided for convenience. 4. Calculate Pz/P~.

2. Same. 3. Same.

4. Calculate M2.

See Equation 3. If M2 > 1 flow is choked, so set M2 at 1 and determine a reduced W. Read at the reset value o f M2 = 1 i f applicable. Note: This case (given P2 and W) is the same as an individual lateral in relief manifold design.

5. Get M2 from Figure 1. If below the

5. Get Pz]P1 from Figure 1.

critical flow line, use M2 = 1. 6. Calculate W. See Equation 3.

6. Calculate P~.

Given: P2 and P~ Find: W Steps: 1. Get f from GPSA graph (Figure 4).

P2 and W P~ 1. Same.

Based on outlet pressure

1.0 - ==E

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40 SO 60 7080 I00 90

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Figure 1. Isothermal flow chart based on M2.

Fluid Flow

13

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14

Rulesof Thumb for Chemical Engineers

M~ Graph

fL/D - (1/M22)(p1/P2)2 [1 - (P2/p1)2 ] - ln(P1/P2) 2

(4)

100

- , , - M-0.1 - , , - M- 0 . 2 I o M-0.3 I -~- M- 0 . 4 I - * - M- 0 . 5 I - ~ M-O.6 I - ~ M-O.7 I ...,.,.. M- 0 . 8 I [] M-O.9 I - - - Cr i t i ca l I

\ \

Critical pressure at the pipe outlet in psia

10

~ ~ ~ i i l l i ~ m m m ~ m m m m m ~ ' ~ m m m m m ~ ~ ~ ~ ~ ~ m m ~ ~ m m m m m ~ ~ m m ~ ~ ~ ~ ~ mmmmmi .Emmmm i l i ~

(5)

- (W/408d 2)(ZT/Mw)~

P c r i t

For comparison the author has generated an Excel | plot (Figure 3) using the data from Figure 2. This is for those readers who work with this popular spreadsheet.

m m m m m m m m m m m m ~

0.1

m m m m m m m m m m m m m k ~ m m m m m m m m m m m m m m

0.01

Example

0.1

0.2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

P2/P1

Given (see sketch following):

Figure 3. Excel| version of M1 chart.

Calculate how much gas will flow to the vessel through the 1 in line with the normally closed hand valve fully opened. Use the psv full open pressure of 136 psia as the vessel pressure. The equivalent length of 200 ft includes the fully opened hand valve. The 1 in pipe's inside diameter is 1.049 in. Assume Z = 1.0.

The Mak Isothermal flow chart is such a useful tool that the author has used it for cases where P1 is known instead of P2 with a trial and error approach. The author has now generated a graph (Figure 2) based upon M~ using Equa- tion 2. The Isothermal flow chart (Figure 1) based on M2 uses Equation 4. Figure 2 facilitates the following case.

Given: Find: Steps:

P1 and W

P2 1. Get f from GPSA graph (Figure 4). 2. Determine fL/D. 3. Obtain Z. Figures 5, 6, and 7 are provided for convenience. 4. Calculate M1. See Equation 1. 5. Get Pz/P1 from Figure 2. The critical curve indicates where M1 -- P2/Pl. When this happens M2 = 1 since M2 = Ml(P1/P2). The design pipe diameter might have to be changed to provide a possible set of conditions. 6. Calculate P2.

Calculations:

Note that if the AP was across a restriction orifice, sonic velocity would occur since the AP is greater than 2 : 1 (315/136 = 2.31). However, the AP is along a length of pipe, so we will use Mak' s method. For commercial steel pipe:

f - 0.023 id - 1.049in - 0.0874 ft

P2/P1 - 136/135 - 0.43 fL/D - 0.023(200)/0.0874 - 52.6 M2 - 0 . 2 8 ( f r om Figure 1)

Some calculations require knowing the critical pres- sure at which sonic velocity occurs. This is calculated with Equation 5. The applicable equations are

Note that if the flow were critical, M2 would be 1.

M2 - 1.702 x 10-5[W/(PzDZ)][ZT/Mw] ~ P2 - 136 psia D 2 - 0 . 0 8 7 4 2 - 0.00764 T - 460 + 60 - 520 ~ Mw - 1 6 Z - 1.0 (given)

Based on M1

(1)

M1 - 1.702 • 10-5[W/(P1D 2)](ZT/Mw)~

(2)

fL/D = (l/M12)[1 - (P2/p1)2] _ ln(P~/P2):

0 . 28 - 1.702 x 10-5[W/(136 x 0.00764)][1.0(520)/16] 0.5

Based on M2

(3)

W - 0.28 x 1.039 x 105/(5.70 x 1 . 702) - 30001b/hr

M2 - 1.702 • 10-5[W/(P2D 2)](ZT/Mw)~

Fluid Flow

15

Pipe Diameter, in Fee t -D

4 5

(J 25

.05 .04 .03

0~/

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.02

05

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025

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d 018 ~

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.0001 .00008 .00006 .00005 .00004 .00003

012

.00002

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.00001 I .000008 .000006 .000005 1

008

5 6 8 10

20

30 40 506---0

80 100

200 300

Pipe Diameter, in Inches- d

Figure 4. Friction factor chart.

16

Rules of Thumb for Chemical Engineers

Pseudo-reduced Pressure, Pr

$

3

4

5

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2

0

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Pseudo reduced temperature

1,0

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MW<40

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1.0

1.0

Compressil0il;ty of natural gases Jan.l,1941

0.1

0.9

10

11

12

13

14

15

Pseudo-reduced pressure, Pr

Figure 5. Z factor for natural gas.

Fluid F l ow

17

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18

Rules of Thumb for Chemical Engineers

Example sketch

Mw = Gas molecular weight P1,P2 = Inlet and outlet line pressures, psia Pc r i t - Critical pressure for sonic velocity to occur, psia T = Absolute temperature, ~ W = Gas flow rate, lb/hr Z - Gas compressibi l i ty factor

psv set @ 110 psig x 1.1 accumulation = 121 psig = 136 psia

/ .

/ .

15 psia

l

NC ~[

]

60 ~ 1O0 psig

Sources

lin

0

1. Mak, Henry Y., "New Method Speeds Pressure-Rel ief Manifold Design," Oil and Gas Journal, Nov. 20, 1978, p. 166. 2. API Recommended Practice 520, "Sizing, Selection, and Installation of Pressure Rel ieving Devices I Refineries," 1993. 3. "Flow of Fluids through Valves, Fittings, and Pipe," Crane Co. Technical paper 410, 1981. 4. Crocker, Sabin, Piping Handbook, McGraw-Hi l l , Inc., 1945. 5. Standing, M.B. and D. L. Katz, Trans. AIME, 146, 159 (1942).

200 equiv, ft

C1

300 psig = 315 psia 60 ~

Nomenclature

D = Pipe diameter, ft d - Pipe diameter, in f = Moody friction factor L = Line equivalent length, ft M1,M2 = Mach number at the line inlet, outlet

CompressibleFlow--Long Pipelines

Equations CommonlyUsed for Calculating Hydraulic Data for Gas Pipe Lines

Weymouth.

0.5 Q- 433.5x (Yb/Pb)XI p12GLTz-p22 I X D2"667 x E

Panhandle A.

Qb 435.87 x (TB/PB)1"0778 D2.6182 - x x E x

Pavg -- 2/3[P~ + P2 - (P1 x P2)/1:'1 + P2]

pl 2 _ p2 2 _ 0.0375 x G x (h2 - hi) M Pavg2 0.5394 Tavg X Zavg 6 0.8539 • L x Tavg x Zavg

Pavg is used to calculate gas compressibi l i ty factor Z

Nomenclature for Panhandle Equations

Qb = f l ow r a t e , SCFD P b - base pressure, psia Tb " - b a s e temperature, ~ Tavg = average gas temperature, ~

Panhandle B.

P1 = inlet pressure, psia P2 - outlet pressure, psia G = gas specific gravity (air = 1.0) L = line length, miles Z = average gas compressibi l i ty D = pipe inside diameter, in. h2 - elevation at terminus of line, ft

Qb 737 X (Tb/Pb)L~176 - X D 2s3 • E

_ 0.0375 x G x (h2 - hi) x Pavg2 0.51

pl 2 _ p22

Tavg X Zavg 6 0"961X L x Tavgx Zavg

x

Fluid Flow

19

Panhandle A.

h~ = elevation at origin of line, ft Pavg- average line pressure, psia E = efficiency factor E = 1 for new pipe with no bends, fittings, or pipe diameter changes E - 0.95 for very good operating conditions, typically through first 12-18 months

Qb 435.87 X (520/14.7) 1~ X (4.026) 26182 - x l x

( 2 , 000 ) 2 _ ( 1 , 500 ) 2 _ 0 . 0375 X 0.6 X 100 X (1 , 762) 2 0.5394 560 x 0.835 (0.6) .8539 X 20 x 560 x .835

E = 0.92 for average operating conditions E - 0.85 for unfavorable operating conditions

Qb - 16,577 MCFD

Nomenclature for WeymouthEquation

Panhandle B.

Q = flow rate, MCFD Tb = base temperature, ~ Pb = base pressure, psia G = gas specific gravity (air = 1)

Qb 737 X (520/14.7) 1~176 - • (4.026) 2.53x 1 x

0.51

- - 000)2 (1,500)2 0.0375 x 0.6 x 100 x (1,762) 2 560 x 0.835 (0.6) "961X 20 X 560 X .835

(2,

L = line length, miles T = gas temperature, ~

Z = gas compressibi l i ty factor D = pipe inside diameter, in. E = efficiency factor. (See Panhandle nomenclature for suggested efficiency factors)

Qb - 17,498 MCFD

Weymouth.

Q - 0 . 4 3 3 x ( 520 / 14 . 7 ) • [ (2 , 000) 2 - ( 1 , 5 0 0 ) 2 /

Sample Calculations

(0.6 x 20 x 560 x 0.835) ] 1/2 • (4 . 026) 2.667

Q - ? G - 0 . 6 T - 100~ L - 20 miles P 1 - 2,000psia P 2 - 1,500psia

Q - 11,101 MCFD

Source

Pipecalc 2.0, Gulf Publ ishing Company, Houston, Texas. Note: Pipecalc 2.0 will calculate the compressibil- ity factor, minimum pipe ID, upstream pressure, down- stream pressure, and flow rate for Panhandle A, Panhandle B, Weymouth, AGA, and Colebrook-Whi te equations. The flow rates calculated in the above sample calculations will differ slightly from those calculated with Pipecalc 2.0 since the viscosity used in the examples was extracted from Reference 2. Pipecalc uses the Dranchuk et al. method for calculating gas compressibility.

Elev diff. - 100 ft

D - 4.026-in. Tb -- 60~ Pb -- 14.7 psia E - 1.0 Pavg- 2/3(2,000 + 1,500 - (2,000 x 1,500/2,000 + 1,500)) = 1,762 psia

Z at 1,762psia and 100~ - 0.835.

20

Rules of Thumb for Chemical Engineers

Equivalent Lengths for Multiple Lines Based on Panhandle A

dl, d2, d3 & dn - internal diameter of individual line corresponding to lengths L1, L2, L3 & Ln

Condition I. A single pipe line which consists of two or more dif- ferent diameter lines. LE -- equivalent length L1, L2 , . . . Ln - length of each diameter D1, D2 , . . . Dn = internal diameter of each separate line corresponding to L1, L2 , . . . Ln DE = equivalent internal diameter IDE14"8539 "DE -'4"8539 ,-DE --4.8539 Let

1.8539

2.6182

dE 2.6182+ d22.6182+d326182+. . . dn2"6182

LE - L l [ d 1

i]18539

90 9

2.6182

dE

2.6182

2.6182

2.6182

E Ln d12.6182-k-d2

+d3

+. . .dn

+. . . gnl-~nnI

t e - gl[_-~-ij

+ L2 [-~2 ]

when L1 - length of unlooped section

L2 - length of single looped section L3 - length of double looped section dE - dl - d2

Example. A single pipe line, 100 miles in length con- sists of 10 miles 10~4-in. OD; 40 miles 123/4-in. OD and 50 miles of 22-in. OD lines. Find equivalent length (LE) in terms of 22-in. OD pipe.

then"

.8539

i ]1 LE - L1 + 0.27664 L2 + L3 2dl 2"6182-k-d326182 d12.6182

L- - 50+E 40[ 215 -'4"8 3912.;51 +1 01215 -'4"853910.;5J

= 50 + 614 + 364 = 1,028 miles equivalent length of 22-in. OD

when dE- d l - d2 - d3 then LE- L1 + 0.27664 L2 + 0.1305 L3

Example. A multiple system consisting of a 15 mile section of 3-85/8-in. OD lines and 1-103/4-in. OD line, and a 30 mile section of 2-85/8-in. lines and 1-103/4-in. OD line. Find the equivalent length in terms of single 12-in. ID line.

Condition II. A multiple pipe line system consisting of two or more parallel lines of different diameters and different lengths. LE= equivalent length L1, L2, L3, . . . Ln- length of various looped sections dl, d2, d3, 9 9 9 = internal diameter of the individ- ual line corresponding to length L1, L2, L3 82 Ln i dE2.6182 ]1.8539 LE -- L1 dl2"6182+ d226182+d326182-t-... dn2"6182 Let

122.6182

11"8539

LE -- 15 3(7.981)2.6182+ 10.022"6182 I 22.6182

]1.8539

+ 30 2(7.981)2.16182 + 10.022"6182 = 5 . 9 + 18.1 = 24.0 miles equivalent of 12-in. ID pipe

0 9 9

dE2.6182

11"8539

Example. A multiple system consisting of a single 12-in. ID line 5 miles in length and a 30 mile section of 3-12-in. ID lines. Find equivalent length in terms of a single 12-in. ID line.

Ln dl2"6182-k-8226182+d326182+. . . dn2"6182

LE - - equivalent length L1, L2, L3 82 Ln- length of various looped sections

Let

Fluid Flow

21

2. McAllister, E. W., Pipe Line Rules of Thumb Handbook, 3rd Ed., Gulf Publishing Co., pp. 247-248, 1993. 3. Branan, C. R., The Process Engineer's Pocket Hand- book, Vol. 1, Gulf Publishing Co., p. 4, 1976.

LE - 5 + 0.1305 X 30 = 8.92 miles equivalent of single 12-in. ID line

References

1. Maxwell, J. B., Data Book on Hydrocarbons, Van Nostrand, 1965.

Sonic Velocity

To determine the critical pressure ratio for gas sonic velocity across a nozzle or orifice use

To determine sonic velocity, use

V~ - ~/KgRT

critical pressure ratio - [ 2 / ( K + 1)]k/(k-~)

where

If pressure drop is high enough to exceed the critical ratio, sonic velocity will be reached. When K - 1.4, ratio - 0.53.

Vs = Sonic velocity, ft/sec K = Cp/Cv the ratio of specific heats at constant pressure to constant volume. This ratio is 1.4 for most diatomic gases. g = 32.2ft/sec 2 R = 1,544/mol. wt. T = Absolute temperature in ~

Source

Branan, C. R., The. Process Engineer's Pocket Hand- book, Vol. 1, Gulf Publishing Co., 1976.

Metering

2g - 64.4 ft]sec 2 Ah - Orifice pressure drop, ft of fluid D - Diameter Co - Coefficient. (Use 0.60 for typical application where Do/Op is between 0.2 and 0.8 and Re at vena con- tracta is above 15,000.)

Orifice

1/2

Uo - Up2

- Co (2gAh) 1/2

Permanent head loss % of Ah Permanent Do/Dr Loss 0.2 95 0.4 82 0.6 63 0.8 40

Venturi

Same equation as for orifice:

Co - 0.98

One designer uses permanent loss - Ah (1 - Co)

Permanent head loss approximately 3-4% Ah.

where

Uo - Velocity through orifice, ft/sec Up - Velocity through pipe, ft/sec

22

Rules of Thumb for Chemical Engineers

Rectangular Weir

Pitot Tube

Z~ - u2/2g

Fv - 3.33(L - 0.2H)H 3/2

Source

where

Branan, C. R., The Process Engineer's Pocket Handbook Vol. 1, Gulf Publishing Co., 1976.

F v - Flow in f t 3 / s e c L - Width of weir, ft H - Height of liquid over weir, ft

Control Valves

where

Notes"

APa]low = Maximum allowable differential pressure for sizing purposes, psi Km = Valve recovery coefficient (see Table 3) re = Critical pressure ratio (see Figures 1 and 2) P~ = Body inlet pressure, psia Pv = Vapor pressure of liquid at body inlet tempera- ture, psia This gives the maximum AP that is effective in produc- ing flow. Above this AP no additional flow will be pro- duced since flow will be restricted by flashing. Do not use a number higher than APa]low in the liquid sizing formula.

1. References 1 and 2 were used extensively for this section. The sizing procedure is generally that of Fisher Controls Company. 2. Use manufacturers' data where available. This hand- book will provide approximate parameters applicable to a wide range of manufacturers. 3. For any control valve design be sure to use one of the modem methods, such as that given here, that takes into account such things as control valve pres- sure recovery factors and gas transition to incom- pressible flow at critical pressure drop. Across a control valve the fluid is accelerated to some maximum velocity. At this point the pressure reduces to its lowest value. If this pressure is lower than the liquid's vapor pressure, flashing will produce bubbles or cavities of vapor. The pressure will rise or "recover" downstream of the lowest pressure point. If the pressure rises to above the vapor pressure, the bubbles or cavities collapse. This causes noise, vibration, and physical damage. When there is a choice, design for no flashing. When there is no choice, locate the valve to flash into a vessel if possible. If flashing or cavitation cannot be avoided, select hardware that can withstand these severe condi- tions. The downstream line will have to be sized for two phase flow. It is suggested to use a long conical adaptor Liquid Flow

Critical Pressure Ratios For Water

1.0

~U ~_ o.9 i . . -

0.8 r~

V) I,SJ o= 0.7 o.. . . J

U

0.6"

n t ,

U

-

O.5

500 1000 1500 2000 2500 3000 3500 VAPOR PRESSURE-PSIA

o

Figure 1. Enter on the abscissa at the water vapor pres- sure at the valve inlet. Proceed vertically to intersect the curve. Move horizontally to the left to read rc on the ordi- nate (Reference 1).

from the control valve to the downstream line. When sizing liquid control valves first use

nPa l l o w - K m (P1 - rc Pv )

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