Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation
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Rate of Reaction
AT - dP/20,000 - 105/20,000 - 5K
Rate at set pressure, (dT/dt) s - 6.0 K/min
Rate at maximum pressure - 6.6 K/min
Average rate - 6.3 K/min
= 0.105 K/s
Instrument Sizing 387
Solution
Using Fauske's nomograph of Figure 5-12 at a self heat rate of 6.3 K/
min. and a set pressure of 217.5 psia, the corresponding vent area per
1,000 kg of reactants = 0.0008m 2.
The vent area of 8,000 kg reactants = 0.0064m 2
The vent size
d (4Area) ~
- -
90.27 mm
(3.6 in. )
If Figure 5-12 is applicable for F=0.5, then for F= 1.0, the area is
0"5 m 2
A-(0.0064m2) ~ _0.0032
The area assumes a 20% absolute overpressure.
The result can be adjusted for other overpressures by multiplying the
area by a ratio of 20/(new absolute percent overpressure).
Using the Leung's method:
Assuming L/D - 0, F - 1.0
Two-phase mass flux from Equation 5-58
G-(0.9)(1.0)(20,000)( 1" 0 x 443" 15) ~
= 6918.1
kg
m.s 2
Rate of heat generation: q
dT( J.K ) W_315W
q - Cp-~ ~ - (3,000)(0.105) kg k---g
388
Fortran Programs for Chemical Process Design
From Equation 5-63, the vent area, A, is:
A .__
8,000 x 315
6918.1{( 10
8,000
0.5 / 2
x 443.15 x 20,000 / + (3' 000 x 5.0)~
A = 7.024 x 10 -3 m2
d = 94.56mm (3.72 in. )
The vent size is about 4.0 in.
Using the Fauske's method:
Assuming ~z = 1.0, ~0 = 0.0, F = 1.0
AP = 1 bar = 105N/m 2
From Equation 5-68, the vent area, A, is
1
A --- ~ 9
2
(8, ooo)(o. o5)(1 - o)
443.15 / 0.5 05
(1.0) 31()-0-6 (1)(1 - 0)
A = 10.927x10 -3m 2
d = 117.95mm (4.64 in. )
References
1. Miller, R.W., "Flow Measurement Engineeing Handbook," McGraw-
Hill Book Co., New York, 1983.
2. Perry, R.H.,
et. al., Perry's Chemical Engineers'Handbook,
6th ed.,
McGraw-Hill Book, Co., 1984.
3. Buckingham, E., "Notes on the Orifice Meter: the Expansion Fac-
tor for Gases," J.
Res. Nat. Burr, Stand.,
1932, Vol 9., p. 61.
4. Mink, W.H., "Program Calculates Orifice Sizes for Gas Flows,"
Chem. Eng.,
Aug. 25, 1980, Vol. 87, No. 17, p. 91.
5. Langford, C.G., "Installing, Maintaining and Troubleshooting Con-
trol Valves,"
Chem. Eng.,
September 5, 1983, pp. 101-103.
Instrument Sizing 389
6. Driskell, L., "Predicting Flow Through Control Valves,"
Chem. Eng.
September 5, 1991, pp. 94-28.
7. Collins, S., "How to Size, Specify and Apply Control Valves,"
Power,
January, 1991, pp. 25-28.
8. Monsen, J.F., "Program Sizes Control Valves for Liquids,"
Chem.
Eng.
May 18, 1981, pp. 159-163.
9. Kern, R., "Control Valves in Process Plants,"
Chem. Eng.,
April 14,
1975, pp. 85-93.
10. Blackwell, W.W., "Chemical Process Design on a Programmable
Calculator," McGraw-Hill Book Co., N.Y., 1984.
11. Coker, A.K., "Size Relief Valves Sensibly,"
Chem. Eng. Prog.,
August, 1992, pp. 20-27.
12.
Sizing, Selection, and Installation of Pressure-Relieving Devices in
Refineries: Part l~Sizing and Selection,
API Recommended Prac-
tice 520 5th ed., American Petroleum Institute, Washington, D.C.,
1990.
13. Crozier, Jr., R.A., "Sizing Valves for Fire Emergencies,"
Chem. Eng.,
Oct 28, 1985, p. 49.
14. Coker, A.K., "Size Relief Valves Sensibly~Part 2,"
Chem. Eng.
Prog.,
Nov., 1992, pp. 94-102.
15. Boyle, W.J., "Sizing Relief Area for Polymerization Reactors,"
Chem. Eng. Prog.,
63 (8), 1967, p. 61.
16. Huff, J.E., "C.E.E Loss Prevention Technical Manaul," 7, 1973.
17. Fisher, H.G., "An Overview of Emergency Relief System Design
Practice," Plant/Operations Progress, 10 (1), Jan. 1991, pp. 1-12.
18. Fauske, H.K., "Generalized Vent Sizing Monogram for Runaway
Chemical Reactions,"
Plant~Operations Progress,
Vol. 3, No.4,
October 1984.
19. Crowl, D.A. and J.E, Louvar,
Chemical Process Safety Fundamen-
tal with Applications,
Prenctice-Hall, Inc., New Jersey, 1990.
20. Leung, J.C., "Simplified Vent Sizing Equations for Emergency
Relief Requirements in Reactors and Storage Vessels,"
AIChEJ.,
32
(10), 1986, pp. 1622-1633.
21. Leung, J.C. and H.K. Fauske,
Plant~Operations Progress,
6 (2), 1987,
pp. 77-83.
22. Duxbury, H.A. and A.J. Wilday, "The Design of Reactor Relief Sys-
tems,"
Trans. IChemE.,
Vol 68, Part B, Feb, 1990, pp. 24-30.
i0
PROGRAM PROG51
ORIFICE SIZING FOR FLUID FLOWS.
THIS PROGRAM CALCULATES AN ORIFICE DIAMETER FOR BOTH LIQUID AND GAS
FLOWS USING FULL-SCALE FLOWRATES IN EITHER Ib/s. OR ft^3/min. AND THE
FULL-SCALE PRESSURE DROPS IN EITHER PSI. OR INCH-H20.
THE PROGRAM APPLIES TO CORNER, FLANGE, VENA-CONTRACTA, AND
1/2 DIAMETER TAPS.
ACFM = FULL-SCALE FLOWRATE AT UPSTREAM CONDITIONS, ft^3/min.
CD = COEFFICIENT OF DISCHARGE.
D = INSIDE PIPE DIAMETER, inch.
OD = ORIFICE DIAMETER FOR FULL-SCALE PRESSURE DROP, inch.
FA = AREA THERMAL-EXPANSION FACTOR. ACCOUNTS FOR THE
EXPANSION OF THE ORIFICE WITH TEMPERATURE CHANGES.
Hw = FULL-SCALE ORIFICE PRESSURE-DIFFERENTIAL. INCH-H20 AT
68oF.
K = SPECIFIC HEAT RATIO (CONSTANT PRESSURE TO CONSTANT VOLUME).
G = FULL-SCALE FLOWRATE, ib/s.
UP = UPSTREAM PRESSURE, psia.
DELP = FULL-SCALE ORIFICE PRESSURE-DIFFERENTIAL, psi.
Y = EXPANSION FACTOR.
BETA = RATIO OF ORIFICE DIAMETER TO PIPE INTERNAL DIAMETER.
DEN = UPSTREAM FLUID DENSITY, Ib/ft^3.
CHOICE = DETERMINES WHETHER THE ORIFICE PRESSURE DROP IS PSI
OR INCH-H20.
FLOW = CHECKS WHETHER THE FLOW CONDITION IS LIQUID OR GAS.
***********************************************************************
CHARACTER*I0 CHOICE, FLOW
REAL K, ID, OD, N, L, FMASS
COMMON/DATAI/FLOW,
CHOICE
OPEN (UNIT=3, FILE ='DATA51.DAT', STATUS ='OLD', ERR=IS)
OPEN (UNIT=l, FILE ='PRN')
CHECK WHETHER THE DATA FOR THE ORIFICE PRESSURE DROP IS PSI. OR
INCH-H20.
CHOOSE TYPE OF FLOW FOR SIZING (LIQUID/GAS)
READ (3, 5, ERR=I9) FLOW
FORMAT (A)
IF (FLOW .EQ. 'LIQUID' .OR. FLOW .EQ. 'liquid') THEN
GO TO 20
ELSEIF (FLOW .EQ. 'GAS' .OR. FLOW .EQ. 'gas') THEN
ENDIF
CHOOSE TYPE OF PRESSURE DROP.
READ (3, I0, ERR=I9) CHOICE
FORMAT (A)
390
20
30
D
UP
K
DEN
VISG
= PIPE INTERNAL DIAMETER, inch.
= THE UPSTREAM PRESSURE, psia.
= THE RATIO OF SPECIFIC HEAT CAPACITIES,
Cp/Cv.
= THE GAS DENSITY, ib/ft^3.
= THE GAS VISCOSITY, cP.
READ (3, *, ERR=I9) D, UP
READ (3, *, ERR=I9) K, DEN
READ (3, *, ERR=I9) VISG
IF (CHOICE .EQ. 'INCH-H20' .OR. CHOICE .EQ. 'inch-H20') THEN
READ THE ORIFICE PRESSURE DROP IN INCH-H20 AND THE FLUID FLOW
RATE IN Ib/s.
READ (3, *, ERR=I9) DELP2, G2
CALCULATE THE ORIFICE PRESSURE DROP IN PSI.
CALCULATE THE GAS FLOW RATE IN ft^3/min.
DELPI=0.036063*DELP2
Sl = (G2*60.0)/DEN
GO TO 25
ELSEIF (CHOICE .EQ. 'PSI' .OR. CHOICE .EQ. 'psi') THEN
READ THE ORIFICE PRESSURE DROP IN PSI. AND THE GAS
FLOW RATE IN ft^3/min.
READ (3, *, ERR=f9) DELPI, G1
GAS FLOWRATE, (G2) IN Ib/sec.
ORIFICE PRESSURE DROP (DELP2) IN INCH-H20
G2 = (GI*DEN)/60.0
DELP2 = 27.72925*DELPI
ENDIF
GO TO 25
READ (3, 30, ERR=I9) CHOICE
FORMAT (A)
IF (CHOICE .EQ. 'INCH-H20' .OR. CHOICE .EQ. 'inch-H20') THEN
ID
DELP
DEN
Q
VISL
= PIPE INTERNAL DIAMETER, inch.
=
ORIFICE PRESSURE DROP, INCH-H20
= LIQUID DENSITY, ib/ft^3.
= LIQUID FLOWRATE, ft^3/min.
= LIQUID VISCOSITY, cP.
391
18
i00
19
ii0
25
READ (3, *, ERR=I9) ID, DELP
READ (3, *, ERR=I9) DEN, Q, VISL
CALCULATE THE ORIFICE PRESSURE DROP IN PSI.
CALCULATE THE LIQUID FLOW RATE IN Ib/sec.
DELPI = O.036063*DELP
FMASS = (Q*DEN)/60.O
CALL LIQUIDF (ID, DELP, DELPI, DEN, Q, FMASS, VISL)
GO TO 999
ELSEIF (CHOICE .EQ. 'PSI' .OR. CHOICE .EQ. 'psi') THEN
ID = PIPE INTERNAL DIAMETER, inch.
DELPI = ORIFICE DIFFERENTIAL PRESSURE, PSI.
DEN = LIQUID DENSITY, ib/ft.^3.
FMASS = LIQUID FLOW RATE, ib/sec.
VISL = LIQUID VISCOSITY, cP.
READ (3, *, ERR=Ig) ID, DELPI
READ (3, *, ERR=I9) DEN, FMASS, VISL
CALCULATE THE ORIFICE PRESSURE DROP IN INCH-H20
CALCULATE THE LIQUID FLOW RATE IN ft^3/min.
DELP = 27.72925*DELPI
Q = (FMASS*60.0)/DEN
CALL LIQUIDF (ID, DELP, DELPI, DEN, Q, FMASS, VISL)
ENDIF
GO TO 999
WRITE (*, i00)
FORMAT (3X,'DATA FILE DOES NOT EXIST')
GO TO 999
WRITE (*, 1107
FORMAT (3X,'ERROR MESSAGE IN THE DATA VALUE')
GO TO 999
N = 1.0-(0.41*DELPI)/(UP*K)
T = (0.35*DELPI)/(UP*K)
SRT
= (DEN
*DELPI ) *'0.5
L = G2/(0.3255*(D**2)*SRT)
P = (2.0*N)/T
Q = (N**2+L**2)/(T*T)
392
120
130
140
150
160
R=-(L**2)/(T*T)
A = (3.0*Q-(P*P))/3.0
B = ((2.0*(P**3))-(9.0*P*Q)+(27.0*R))/27.0
SUM1 = (((B**2)/4.0)+((A**3)/27.0))**0.5
VALI = (-B/2.0+SUMI)**(I.0/3.0)
Y = VALI + ((-B/2-SUMI)**(I.0/3.0))
Y = ABS(Y-(2.0*N)/(3.0*T))
OD = D*(Y**0.25)
USING THE ORIFICE DIAMETER, CHECK WHETHER THE CALCULATED GAS
RATE IS THE SAME AS THE INITIAL GAS RATE.
CALCULATE THE EXPANSION FACTOR, Y1
BETA = OD/D
Y1 = 1.0-(0.41+0.35*(BETA**4))*(DELPI/(UP*K))
FA = 1.0
CD = 0.62
VALI = (1.0-(BETA**4))**0.5
G = 0.52502*CD*YI*(OD**2)*FA*SRT
GR = G/VALI
CALCULATE THE REYNOLDS NUMBER
REG = (6.31*3600.0*G2)/(D*VISG)
WRITE (i, 120)
FORMAT (25X,'ORIFICE SIZING FOR GAS FLOWS', /IH ,76(IH*))
WRITE (i, 130)FLOW
FORMAT (5X,'TYPE OF FLOW:', T65, A)
WRITE (i, 140) CHOICE
FORMAT (5X,'TYPE OF PRESSURE DROP:', T65, A)
WRITE (i, 150) D, UP, DELP2, DELPI, K, DEN, VISG, GI, G2
FORMAT (5X,'INSIDE PIPE DIAMETER, inch:', T65, F8.3,/,
* 5X,'UPSTREAM PRESSURE, psia.:', T65, F8.3,/,
*
5X,'ORIFICE PRESSURE DROP, INCH-H20:', T65, F8.3,/,
* 5X,'ORIFICE PRESSURE DROP, psi.:', T65, F8.3,/,
* 5X,'SPECIFIC HEAT RATIO (k=Cp/Cv):', T65, F8.4,/,
* 5X,'UPSTREAM FLUID DENSITY, ib/ft^3: ' , T65, F8.3,/,
* 5X,'GAS VISCOSITY, cP:', T65, F8.4,/,
* 5X,'GAS FLOW RATE, ft^3/min.: ' , T65, F8.3,/,
* 5X,'GAS MASS RATE, ib/sec.:', T65, F8.3)
WRITE (i, 160)Y, OD, GR, REG
FORMAT (5X,'EXPANSION FACTOR:', T65, F8.4,/,
5X,'ORIFICE DIAMETER, inch:', T65, F8.3,/,
5X,'FULL SCALE GAS FLOWRATE, ib/sec.:', T65, F8.3,/,
393
170
999
180
190
200
5X, 'REYNOLDS NUMBER: ' , T65, FI2.0)
WRITE (i, 170)
FORMAT (IH ,76(IH-) )
FORM FEED THE PRINTING PAPER TO THE TOP OF NEXT PAGE.
WRITE (i, *) CHAR(12)
CLOSE (UNIT=3, STATUS='KEEP')
CLOSE (I)
STOP
END
************************************************************
THE FORMULA FOR CALCULATING THE ORIFICE PLATE FOR LIQUID
FLOW IS:
M = 0.52502((Cd.Y.d^2.Fa)(SQRT(DEN.DELP)/(SQRT(I-(DO/D)^4)
WHERE FOR LIQUID FLOW, Cd=0.62, Fa=l.0 AND Y=I.0
DO = ORIFICE DIAMETER
D = PIPE INTERNAL DIAMETER
DEN = DENSITY OF LIQUID, Ib/ft^3.
DELP = PRESSURE DROP ACROSS THE ORIFICE, inch-H20 OR psi.
M = MASS FLOW RATE, ib/s.
************************************************************
SUBROUTINE LIQUIDF (ID, DELP, DELPI, DEN, Q, FMASS, VISL)
CHARACTER*I0 FLOW, CHOICE
COMMON/DATAI/FLOW, CHOICE
REAL ID, OD
CALCULATE THE ORIFICE DIAMETER, inch.
PRESSURE DROP ACROSS THE ORIFICE (DELPI), PSI.
LIQUID FLOW RATE (FMASS), ib/sec.
Z = (0.52502*0.62*(DEN*DELPI)**0.5)/FMASS
RATIO = (ID**4)/(I+((ID**4)*(Z**2)))
OD = RATIO**0.25
CALCULATE THE REYNOLDS NUMBER, REL
REL = (6.31*3600.0*FMASS)/(ID*VISL)
PRINT THE RESULTS OF ORIFICE SIZING FOR LIQUID FLOW.
WRITE (i, 180)
FORMAT (20X, 'ORIFICE SIZING FOR LIQUID FLOW', /IH ,76(IH*))
WRITE (I, 190) FLOW
FORMAT (LX,'TYPE OF FLOW:', T65, A)
WRITE (i, 200)CHOICE
FORMAT (LX,'TYPE OF PRESSURE DROP:',T65, A)
394
210
220
WRITE (i, 210) ID, DELP, DELPI, DEN, VISL, Q, FMASS, OD, REL
FORMAT (SX,'INTERNAL PIPE DIAMETER, inch:', T65, F8.3,/,
*
5X,'ORIFICE PRESSURE DROP, inch-H20:',T65,F8.3,/,
*
5X,'ORIFICE PRESSURE DROP, psi:', T65, F8.3,/,
* 5X,'LIQUID DENSITY, ib/ft^3: ' , T65, F8.3,/,
*
5X,'LIQUID VISCOSITY, cP:', T65, F8.4,/,
* 5X,'LIQUID VOLUMETRIC RATE, ft^3/min.:',T65,FS.3,/,
* 5X,'LIQUID MASS RATE, ib/sec.:', T65, F8.3,/,
* 5X,'ORIFICE SIZE, inch:',T65, F8.3,/,
* 5X,'REYNOLDS NUMBER:', T65, FI2.0)
WRITE (i, 220)
FORMAT (IH ,76(IH-))
FORM FEED THE PRINTING PAPER TO TOP OF THE NEXT PAGE.
WRITE (i, *) CHAR(12)
RETURN
END
395
ii
22
33
PROGRAM PROG52
THIS PROGRAM CALCULATES THE CONTROL VALVE CAPACITY COEFFICIENT (Cv)
OR MAXIMUM FLUID RATE FOR LIQUID, VAPOR AND STEAM IN PROCESS
OPERATIONS. IF THE CONTROL-VALVE COEFFICIENT(Cv) IS ALREADY KNOWN,
THE PROGRAM WILL CALCULATE THE MAXIMUM FLUID FLOW RATE (LIQUID,
VAPOR OR STEAM) THAT CAN PASS THROUGH THE VALVE FOR A GIVEN SET
OF PROCESS CONDITIONS.
TO COMPUTE THE FLUID FLOW FOR LIQUID, GAS AND STEAM CONDITIONS,
VALUES OF THE VALVE CAPACITY COEFFICIENT MUST BE KNOWN (i.e. Cv>0)
*******************************************************************
Cv = CAPACITY COEFFICIENT FOR FULLY OPEN VALVE
DELP = CONTROL VALVE PRESSURE DROP, psi.
V = LIQUID FLOW, GPM
SPL = SPECIFIC GRAVITY OF LIQUID
Q = GAS FLOW, ft^3/h @ 14.7 psia and 60 oF
SPG = SPECIFIC GRAVITY OF GAS = (M.W. gas/M.W, air)
P1 = INLET PRESSURE, psia
P2 = OUTLET PRESSURE, psia
T = FLOWING TEMPERATURE, oF
W = STEAM FLOW, ib/h
K = SUPERHEAT CORRECTION FACTOR
CHARACTER*I0 CHOICE
COMMON/DATA1/ V, PI, P2, DELPL, SPL, CVL
COMMON~DATA2~
Q, P21, P22, DELPG, SPG, T, CVG
COMMON/DATA3/ W, P31, P32, DELPS, F, CVS
OPEN (UNIT=3, FILE='DATA52.DAT', STATUS='OLD', ERR=I8)
OPEN (UNIT=l, FILE='PRN')
READ (3, 6)CHOICE
FORMAT (A)
IF (CHOICE .EQ. 'LIQUID' .OR. CHOICE .EQ. "liquid') THEN
GO TO ii
ELSEIF (CHOICE .EQ. 'GAS' .OR. CHOICE .EQ. 'gas') THEN
GO TO 22
ELSEIF (CHOICE .EQ. 'STEAM' .OR. CHOICE .EQ. 'steam') THEN
GO TO 33
ENDIF
READ(3,*,ERR=IO) V, CVL
READ(3,*,ERR=I0) PI, P2, SPL
GO TO 44
READ(3,*,ERR=IO) Q, CVG
READ(3,*,ERR=I0) P21, P22, SPG, T
GO TO 55
READ(3,*,ERR=I0) CVS
396