Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation
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Fluid Flow 207
Table 3-18
Input Data and Computer Output for for
Pressure Drop in a Packed Bed
DATA38.DAT
0.134 60.0 104.4
0.25 0.25 0.45
0.413 0.0278
PRESSURE DROP IN A PACKED BED
PACKED BED DIAMETER, ft.:
LENGTH OF PACKED BED, ft.:
FLUID FLOWRATE THROUGH PACKED BED, ib/h.:
PARTICLE DIAMETER,
inch.:
PARTICLE LENGTH,
inch.:
FRACTIONAL VOIDS IN PACKED BED:
DENSITY OF FLUID, ib/ft^3:
FLUID VISCOSITY,
cP:
CROSS-SECTIONAL AREA OF BED, ft^2:
SUPERFICIAL MASS VELOCITY, ib/h.ft^2:
AREA OF PARTICLES, ft^2:
VOLUME OF PARTICLES, ft^3:
THE PACKED BED SURFACE AREA, ft^2/ft^3 BED:
EFFECTIVE PARTICLE DIAMETER, ft.:
FLUID REYNOLDS NUMBER:
FRICTION FACTOR FOR INTERMEDIATE FLOW:
TOTAL PRESSURE DROP IN PACKED BED, ib/in^2:
.134
60.000
104.4
.250
.250
.450
.4130
.0278
.0141
7402.9
.2045E-02
.7102E-05
158.400
.0208
4170.
1.7860
68.603
density 9 - 0.413
lbm/ft 3
viscosity ~t - 0.0278 cP
Table 3-17 gives the Reynolds number, friction factor, and pressure drop
of catalyst pellets of 0.25 inch and at different particle length. Table 3-18
shows a typical input data and computer output with PL = 0.25 inch.
The simulation exercise gives a pressure drop of 68.603 lb/in 2. The
results show that the pressure drop in a packed bed depends on size and
shape of the particles.
References
1. Hooper, W. B., "The two-K Method Predicts Head Loss in Pipe
Fittings,"
Chem Eng.,
August 24, 1981, pp. 96-100.
2. Crane Technical paper 410,
Crane Co. Flow of Fluid Through Valves,
Fittings, and Pipe,
Imperial ed., 1984.
3. Simpson, L. L., "Sizing Piping for Process Plants,"
Chem. Eng.,
June 17, 1968, pp. 192-214.
4. Hooper, W. B., "Calculate Head Loss Caused by Change in Pipe
Size,"
Chem. Eng.,
Nov. 7, 1988, pp. 89-92.
208
Fortran Programs for Chemical Process Design
5. Colebrook, C. F., "Turbulent Flow in Pipes with Particular Refer-
ences to the Transition Region Between the Smooth and Rough Pipe
Laws," J. Inst., of Civil Eng. (London) vol. 11, 1938-1939, p. 133.
6. Coker, A. K., "Sizing Process Piping for Single-Phase Fluids," The
Chemical Engineer, October 10, 1991, pp. 19-25.
7. Gregory, G. A. and M. Fogarasi, "Alternate to Standard Friction
Factor Equation," Oil & Gas J., April 1, 1985, pp. 120-127.
8. Powley, M. B., "Flow of Compressible Fluids," Can J. Chem. Eng.,
1958, pp. 241-245.
9. API, Recommended Practice for the Design and Installation of Pres-
sure Relieving Systems in Refineries, 4th ed., RP 520, API, 1976.
10. Lapple, C. E., "Isothermal and Adiabatic Flow of Compressible
Fluids," Trans. AIChE J. Vol. 39, 1943, pp. 385-428.
11. Coker, A. K., "Determine Process Pipe Sizes," CEP, March, 1991,
pp. 33-39.
12. Mak, H. Y., "New Method Speeds Pressure Relief Manifold
Design," Oil & Gas J., Nov. 20, 1978, pp. 166-172.
13. Janett, E., "How to Calculate Back pressure in Ventlines," Chem.
Eng., Sept. 2., 1963, pp. 83-86.
14. Kirkpatrick, D. M., "Simpler Sizing of Gas Piping," Hydrocarbon
Process., Dec., 1969, pp. 135-138.
15. Baker, Ovid, "Simulataneous Flow of Oil and Gas," Oil & Gas J.,
July, 26, 1954, pp. 185-189.
16. Chenoweth, J. M. and M. W. Martin, "Turbulent Two-Phase Flow,"
Petroleum Refiner, Vol. 34, No. 10, 1955, pp. 151-155.
17. Mandhane, J. M., G. A. Gregory, and K. Aziz, "A Flow Pattern Map
for Gas-Liquid Flow in Horizontal Pipes," Inst. J. Multiphase Flow,
Vol. 1, 1974, pp. 537-553.
18. Coker, A. K., "Understand Two-Phase Flow in Process Piping," CEP,
November 1990, pp. 60-65.
19. Lockhart, R. W. and R. C. Martinelli, "Proposed Correlation of Data
for Isothermal Two-Phase, Two-Component Flow in Pipes," CEP,
Vol. 45, No. 1, 1949, pp. 39-48.
20. Blackwell, W. W., Chemical Process Design on a Programmable
Calculator, McGraw-Hill, New York, 1984, p. 22.
21. Coulson, J. M., et al., Chemical Engineering, Vol. 1, 3rd ed.,
Pergamon Press, New York, 1978, pp. 91-92.
22. Ludwig, E. E., Applied Process Design for Chemical and Petro-
chemical Plants, Vol. 1, 2nd ed., Gulf Publishing, Houston, 1977,
p. 85.
Fluid Flow 209
23. Duckler, A. E., Wicks, M., and Cleveland, R. C., "Frictional Pres-
sure Drop in Two-Phase Flow" An Approach Through Similarity
Analysis," AIChE. J, Vol. 10, 1964, pp. 44-51.
24. Ruskin, R. E, "Calculating Line Sizes for Flashing Steam Conden-
sate," Chem Eng., August, 18, 1975, pp. 101-103.
25. Ergun, Sabri, "Fluid Flow Through Packed Columns," Chem. Eng.
Prog., Vol. 48, No. 2, 1952 pp. 89-92.
26. Bennett, C. O., and Myers, J. E., Momentum, Heat and Mass Trans-
fer, McGraw-Hill Book Co., New York, 1982.
27. Ward T., and Bromhead, E. N., Fortran and the Art of PC Program-
ming, John Wiley & Sons, Chichester, 1989.
28. Bromhead, E. N., Private Communications.
29. Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice-
Hall Inc., New Jersey, 1986.
SUBROUTINE PROG31
*********************************************************************
* THIS PROGRAM CALCULATES PRESSURE DROP IN A PIPE INCLUDING *
* PIPE FITTINGS SUCH AS VALVES AND ELBOWS. THE PROGRAM USES THE *
* CHEN'S METHOD TO DETERMINE THE FRICTION FACTOR FC. THE DARCY *
* FRICTION FACTOR IS 4 x Chen'S FRICTION FACTOR (F = 4FC). THE *
*
PROGRAM INCORPORATES THE TWO K-METHOD TO DETERMINE THE NUMBER OF *
* VELOCITY HEADS AND THUS CALCULATES THE EQUIVALENT PIPE LENGTH *
* DUE TO PIPE FITTINGS. FROM THE TOTAL LENGTH OF THE PIPE, THE *
* OVERALL PRESSURE DROP OF THE PIPE IS CALCULATED. *
*********************************************************************
*********************************************************************
* AREA =
PIPE INTERNAL CROSS-SECTIONAL AREA, ft^2. *
* ID = PIPE INTERNAL DIAMETER, ft. *
* ED = PIPE EXPANSION DIAMETER, ft. *
* CD = PIPE CONTRACTING DIAMETER, ft. *
* F = DARCY FRICTION FACTOR *
* L = TOTAL FITTING EQUIVALENT LENGTH PLUS STRAIGHT *
* PIPE LENGTH,ft. *
* LEQ = FITTINGS EQUIVALENT LENGTH, ft. *
* LST = STRAIGHT PIPE LENGTH, ft. *
* NF = NUMBER OF FITTINGS OF A GIVEN TYPE *
* RE = REYNOLDS NUMBER *
* P = P1 OR P2 (DEPENDING ON INPUT) *
* Pl = PIPE INLET PRESSURE, psia. *
* P2 = PIPE OUTLET PRESSURE, psia. *
* DELP = PRESSURE DROP psi/100 ft. *
* RHO = FLUID DENSITY, Ib/ft^3. *
* Q = FLUID FLOW RATE, gal/min. *
* W = GAS FLOWRATE, ib/h. *
* G = ACCELERATION DUE TO GRAVITY, 32.174 ft/sec^2 *
* PR = ABSOLUTE ROUGHNESS OF PIPE WALL, 0.00015ft. *
* V = FLUID VELOCITY, ft/sec. *
* VIS = VISCOSITY OF GAS, cP. *
* EE = RELATING TO ENTRANCE AND EXIT LOSSES *
* ETV = RELATING TO ELBOW, TEES AND VALVES *
* FIT = PIPE FITTINGS. *
*********************************************************************
1
2
3
* GATE VALVE 4
* BALL VALVE 5
* PLUG VALVE 6
* GLOBE VALVE 7
* DIAPHRAM, DAM TYPE VALVE 8
* BUTTERFLY VALVE 9
* SWING CHECK VALVE i0
* RUN THRU TEE (flanged/welded)ll
* RUN THRU TEE (stub in type
* branch 12
* PIPE ENTRANCE 13
* FITTING TYPE FITTING NO. K1 KL *
* 180o ELBOWS (long radius) i000.0 0.30 *
* 90o ELBOWS (long radius) 800.0 0.20 *
* 45o ELBOWS (long radius) 500.0 0.15 *
300.0 0.i0 *
500.0 0.15 *
i000.0 0.25 *
1500.0 4.00 *
i000.0 2.00 *
800.0 0.25 *
1500.0 1.50 *
150.0 0.05 *
,
i00.0
0.00 *
160.0 0.50 *
210
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ii
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* PIPE EXIT 14 0.0 1.00 *
CHARACTER*30 INFILE, OUTFIL
CHARACTER CHOICE
DIMENSION CHOFIT (14, 4)
LOGICAL FITT
COMMON /FILES/ INFILE, OUTFIL
COMMON/DSCRI/
PID, RLST, Q, W, DEN, VIS, Z, PRI
COMMON/DSCR2/ V, LEQ, LST, L, DELTAH, DELP, DELPT
COMMON~DATA1~
PR, D, RE
COMMON/DATA2/ ICOUNT
COMMON/DATA3/ CHOFIT
COMMON/DATA4/ CD, ED, OD, CHOICE
COMMON/DATA5/ F, K, KOT
COMMON~DATA6~
THETAI, THETA2, PI
REAL L, LEQ, RLST, K, OD, KOT, KTOTAL
CALCULATE PIPE CROSS-SECTIONAL AREA, ft^2
KTOTAL = 0.0
LEQ = 0.0
PR = 0.00015
G = 32.2
PI = 3.1415927
n = PID/12
AREA = (PI*(D**2))/4.0
CHECK WHETHER THE PIPE ROUGHNESS IS FOR CARBON STEEL
(i.e. PR = 0.00015ft).
IF ( PR .NE. PRI) THEN
PR = PRI
ENDIF
CHECK WHETHER FLUID FLOW RATE IS IN VOLUMETRIC OR MASS RATE.
IF ( Q .GT. 0.0) THEN
GO TO ii
ELSEIF (W .GT. 0.0) THEN
GO TO 12
ENDIF
CALCULATE REYNOLDS NUMBER BASED ON VOLUMETRIC RATE
RE = (50.6*DEN*Q)/(PID*VIS)
CALCULATE FLUID VELOCITY ft/sec.
V = (0.408*Q)/PID**2
CALCULATE THE FLUID MASS FLOW RATE, ib/hr
W = (V*(PID**2)*DEN)/.0509
211
12
C
21
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31
32
GO TO 21
CALCULATE REYNOLDS NUMBER BASED ON MASS FLOW RATE, ib/hr.
RE = (6.31*W)/(PID*VIS)
CALCULATE FLUID VELOCITY, ft/sec.
V = (0.0509*W)/(DEN*(PID**2))
CALCULATE THE FLUID VOLUMETRIC FLOW RATE, gal/min.
Q = W/(8.02*DEN)
CALCULATE THE DARCY FRICTION FACTOR
IF (RE .GT. 2000.0) THEN
GO TO 31
ELSE
F1 = 64.0/RE
F = F1
ENDIF
GO TO 32
CALCULATE THE FRICTION FACTOR USING THE CHEN'S EQUATION
A1 = ((PR/D)/3.7+(6.7/RE)**0.9)
B1 = -4.0*ALOGI0((PR/(3.7*D))-(5.02/RE)*ALOGI0(AI))
CALCULATE THE DARCY FRICTION FACTOR. F
F = 4.0/BI*,2
CHECK WHETHER THERE ARE FITTINGS
IF FIT IS TRUE THEN CALL THE PROGRAM SFIT
FITT = .TRUE.
IF (FITT) THEN
THEN CALL FITTINGS
CALL SFIT(K)
GO TO 33
ELSE
K = 0.0
GO TO 34
ENDIF
FITT = .FALSE.
CALCULATE THE TOTAL EQUIVALENT LENGTH , ft.
212
33
C
34
44
C
35
LEQ = LEQ + (K*D)/F
CALCULATE THE TOTAL VELOCITY HEAD
KTOTAL = KTOTAL + K + (F*RLST/D)
CALCULATE TOTAL FITTING EQUIVALENT LENGTH PLUS
STRAIGHT PIPE LENGTH, ft
L = RLST + LEQ
IF ( RE .LT. 2000.0) THEN
GO TO 35
ELSE
ENDIF
CALCULATE THE FLUID PRESSURE DROP PER i00 ft. OF PIPE BASED ON THE
MASS FLOW RATE, ib/hr.
IF (Q .GT. 0.0) THEN
GO TO 44
ELSE
DELP = (0.000336*F*(W**2))/((PID**5)*DEN)
ENDIF
CALCULATE THE OVERALL PRESSURE DROP OF THE PIPE
DELPT = (DELP*L)/100.0 + ((Z'DEN)/144.0)
GO TO 55
CALCULATE THE FLUID PRESSURE DROP PER 100ft OF PIPE BASED ON THE
VOLUMETRIC RATE. gal/min.
DELP = (0.0216*F*DEN*(Q**2))/(PID**5)
CALCULATE THE OVERALL PRESSURE DROP OF THE PIPE
DELPT = (DELP*L)/100.0 + ((Z'DEN)/144.0)
GO TO 55
CALCULATE THE PRESSURE DROP FOR LAMINAR FLOW
IF (Q .GT. 0.0) THEN
DELP = (0.0273*VIS*Q)/(PID**4)
CALCULATE THE OVERALL PRESSURE DROP psi.
DELPT = (DELP*L)/100.0 + ((Z'DEN)/144.0)
CALCULATE THE TOTAL HEAD LOSS, ft.
DELTAH = (0.0393*VIS*L*Q)/(PID**4*DEN) + Z
213
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55
66
GO TO 66
CALCULATE THE PRESSURE DROP BASED ON THE MASS FLOW RATE.
THE PRESSURE DROP IN psi. PER 100ft OF PIPE
ELSEIF (W .GT. 0.0) THEN
DELP = (0.0034*VIS*W)/((PID**4)*DEN)
CALCULATE THE OVERALL PRESSURE DROP IN psi.
DELPT = (DELP*L)/100.0 + ((Z'DEN)/144.0)
CALCULATE THE TOTAL HEAD LOSS, ft.
DELTAH = (0.0049*VIS*L*W)/((PID**4)*(DEN**2)) + Z
ENDIF
GO TO 66
CALCULATE THE TOTAL HEAD LOSS ft.
DELTAH = (0.000483*F*L*(W**2))/((PID**5)*(DEN**2)) + Z
RETURN
END
****************************************************************
* THIS PROGRAM USES THE TWO-K METHOD TO CALCULATE THE TOTAL *
* THE VELOCITY HEAD FOR THE FITTINGS: *
* CONSTANTS FOR THE TWO-K METHOD *
SUBROUTINE SFIT (KALL)
CHARACTER CHOICE
DIMENSION CHOFIT (14, 4)
COMMON/DATA1/ PR, D, RE
COMMON/DATA3/ CHOFIT
COMMON/DATA4/ CD, ED, OD, CHOICE
COMMON/DATA5/ F, K, KOT
COMMON/DATA6/ THETAI, THETA2, PI
COMMON/DSCRI/ PID, RLST, Q, W, DEN, VIS, Z, PRI
REAL KALL, KSUM, KLSUM, KEEl, KEE2, KEET, KTOTAL
REAL KEX, KCT, KOD, KOT, OD, K
CHOFIT (6, 3) = CHOFIT (i, 3)
CHOFIT (8, 3) = CHOFIT (i, 3)
CHOFIT (9, 3) = CHOFIT (2, 3)
CHOFIT (5, 3) = CHOFIT (3, 3)
CHOFIT (i0, 3) = CHOFIT (7, 3)
CHOFIT (5, 4) = CHOFIT (3, 4)
CHOFIT (9, 4) = CHOFIT (6, 4)
214
i0
20
ii
22
KSUM = 0.0
KLSUM = 0.0
KEEl = 0.0
KEE2 = 0.0
KTOTAL = 0.0
KEX = 0.0
KCT = 0.0
KOD = 0.0
DO i0 I = i, 12
KSUM = KSUM + CHOFIT (I, 2)*CHOFIT (I, 3)
KLSUM = KLSUM + CHOFIT (I, 2)*CHOFIT (I, 4)
CONTINUE
KTOTAL = KTOTAL + (KSUM/RE+ (KLSUM* ( i. 0+ ( i. 0/PID) ) ) )
KEEl=KEEl+( CHOFIT( 13,2 ) *CHOFIT( 13,3 )+CHOFIT( 14,2 ) *CHOFIT( 14,3 ) )
MEE2=KEE2+(CHOFIT( 13,2 ) *CHOFIT( 13,4 )+CHOFIT( 14,2 ) *CHOFIT( 14,4 ) )
MEET = (KEEl/RE + EKE2)
MALL = KTOTAL + MEET
CALCULATE THE K VALUES OF THE SUDDEN CHANGES
IN PIPE ENLARGEMENT/REDUCTION WITH TAPERED ANGLES OR
WITHOUT TAPERED ANGLES.
IF ( CHOICE .EQ. 'Y' .OR. CHOICE .EQ. 'y') THEN
GO TO 20
ELSEIF (CHOICE .EQ. 'N' .OR. CHOICE .EQ. 'n') THEN
GO TO 75
ENDIF
IF ( ED .EQ. 0.0) THEN
BETA1 = 0.0
GO TO 30
ELSE
BETA1 = PID/ED
ENDIF
IF (THETAI .EQ. 0.0) THEN
GO TO Ii
ELSEIF (THETAI .LE. 45.0) THEN
CALl = 2.6*SIN((THETAI*PI)/(180.0*2.0))
GO TO 22
ELSEIF (THETAI .GT. 45.0) THEN
ENDIF
IF (RE .LE. 4000.0) THEN
BETA1 = 2.0,(1.0 - (BETA1)**4)
GO TO 30
ELSEIF (RE .GT. 4000.0) THEN
BETA1 = (i.0 + 0.8*F)*(I.0 - (BETA1**2))**2
GO TO 30
ENDIF
IF (RE .LE. 4000.0) THEN
BETA1 = CALl*2.0*(1.0 - (BETA1)**4)
215
3O
35
45
55
40
GO TO 30
ELSEIF (RE .ST. 4000.0) THEN
BETA1 = CALI*(I.0+0.8*F)*(I.0-(BETAI**2))**2
ENDIF
KEX = KEX + BETA1
IF (CD .EQ. 0.0) THEN
BETA2 = 0.0
GO TO 40
ELSE
BETA2 = PID/CD
ENDIF
IF (THETA2 .EQ. 0.0) THEN
GO TO 35
ELSEIF (THETA2 .LT. 45.0) THEN
CAL2 = 1.6*SIN((THETA2*PI)/(180.0*2.0))
GO TO 45
ELSEIF (THETA2 .GT. 45.0 .OR. THETA2 .LT. 180.0) THEN
CAn3 = SIN((THETA2*PI)/(180.0*2.0))
CAL3 = SQRT(CAL3)
GO TO 55
ENDIF
IF (RE .LE. 2500.0) THEN
BETA2 = (1.2 + 160.0/RE)*((BETA2**4) - 1.0)
GO TO 40
ELSEIF (RE .GT. 2500.0) THEN
BETA2 = (0.6+0.48*F)*(BETA2**2)*((BETA2**2)-I.0)
GO TO 40
ENDIF
IF (RE .LE. 2500.0) THEN
BETA2 = CAL2*(I.2+I60.0/RE)*((BETA2**4)-I.0)
GO TO 40
ELSEIF (RE .GT. 2500.0) THEN
BETA2 = CAL2*(0.6+0.48*F)*(BETA2**2)*((BETA2**2)-I.0)
GO TO 40
ENDIF
IF (RE .LE. 2500.0) THEN
BETA2 = CAL3*(I.2+I60.0/RE)*((BETA2**4)-I.0)
GO TO 40
ELSEIF (RE .ST. 2500.0) THEN
BETA2 = CAL3*(0.6+0.48*F)*(BETA2**2)*((BETA2**2)-I.0)
ENDIF
KCT = KCT + BETA2
IF (OD .EQ. 0.0) THEN
BETA3 = 0.0
GO TO 41
ELSE
BETA3 = OD/PID
ENDIF
IF (RE .LE. 2500.0) THEN
VAn1 = (2.72+((BETA3**2)*(120.0/RE-I.0)))
216