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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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
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.02
05
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025
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016 ~
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.0001 .00008 .00006 .00005 .00004 .00003
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.00002
.009
.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
I . I
1.1
Pseudo reduced temperature
1,0
1.0 1.05
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0.95
0.9
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8
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1.1
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MW<40
[ i i l
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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