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

18

ii

19

12

i0

C

999

COMMON/RES3/

TC, VESWT, WD

COMMON/RES4/

TB, THEAT, F

COMMON/RES5/ REH, REG, SCF, MOMEN

OPEN (UNIT=3, FILE='DATA45.DAT', STATUS='OLD', ERR=I8)

OPEN (UNIT=l, FILE='PRN')

READ

GAS FLOW RATE, FLOW: 10^6 std ft^3/day.

DRYER OPERATING PRESSURE, P: psig.

GAS FLOWING TEMPERATURE, T: oF.

GAS COMPRESSIBILITY FACTOR, Z.

DRYING CYCLE, CYCLE: hr.

WATER CONTENT OF GAS, H2OC: Ib/MM std ft^3.

ALLOWABLE STRESS, S: ib/in^2.

JOINT EFFICIENCY, E: 1.0

DESICCANT WATER CAPACITY, PICKUP: %

DESCICCANT DENSITY, DDEN: ib/ft^3.

DESICCANT BED LENGTH, BL: ft.

HEATER TEMPERATURE, HT: oF.

MOLECULAR WEIGHT OF REGENERATING GAS, MW:

READ ENTHALPY OF REGENERATION GAS BEFORE REGENERATION HEATER,

HI: Btu/ib.

READ ENTHAPLY OF REGENERATION GAS AFTER REGENERATAION HEATER,

H2: Btu/ib.

READ (3, *

, ERR=f9) FLOW, P, T

, ERR=I9) Z, CYCLE, H2OC

, ERR=I9) S, E, PICKUP

, ERR=I9) DDEN, BL, HT

, ERR=I9) MW, HI, H2

GO TO i0

WRITE (~, ii)

FORMAT (6X, 'ERROR MESSAGE IN THE DATA VALUE')

GO TO 999

WRITE (*, 12)

FORMAT (6X, 'DATA FILE DOES NOT EXIST')

GO TO 999

CALCULATE THE REQUIREMENTS FOR A GAS DRYER

CALL DRYER

PRINT THE RESULTS.

CALL OUTPUT

CLOSE (UNIT=3, STATUS='KEEP')

CLOSE (i)

STOP

END

THIS PROGRAM SIZES THE GAS DRYER WITH THE GIVEN DATA VALUES

***************************************************************

327

SUBROUTINE DRYER

PARAMETER (PI=3.1415927)

REAL MW, MOMEN

COMMON/DRY1/ FLOW, P, T

COMMON~DRY2~

Z, CYCLE, H2OC

COMMON/DRY3/ S, E, PICKUP

COMMON/DRY4/ DDEN, BL, HT

COMMON/DRY5/ MW, HI, H2

COMMON/RESI/ H2OL, DESVOL, AREAl

COMMON/RES2/ BD, R, Q, VEL

COMMON/RES3/

TC, VESWT, WD

COMMON/RES4/ TB, THEAT, F

COMMON/RES5/

REH, REG, SCF, MOMEN

CALCULATE TOTAL WATER ADSORBED, H2OL.

H2OL =

(FLOW*CYCLE*H20C)/24.0

CALCULATE DESICCANT VOLUME, DESVOL

DESVOL =

(H2OL*IOO.O)/(PICKUP*DDEN)

CALCULATE DESICCANT CROSS-SECTIONAL AREA, AREAl.

AREAl = DESVOL/BL

CALCULATE BED DIAMETER, BD.

BD = SQRT((4.0*AREAI)/PI)

CALCULATE THE BED AREA, AREA.

AREA = (PI*BD**2)/4.

T1 = T+460.

R = (12.*BD)/2.

P1 = P+14.7

CALCULATE THE ACTUAL GAS FLOW RATE AT FLOWING CONDITIONS, ft^3/min.

Q = (FLOW*TI*Z*I9.6314)/PI

CALCULATE THE SUPERFICIAL GAS VELOCITY, ft./min.

VEL = Q/AREA

CALCULATE THE DRYER SHELL THICKNESS, in.

TC = (P*R)/(S*E-0.6*P)

ASSUME H=2.0 ft. ADDITIONAL SHELL HEIGHT FOR DESICCANT SUPPORT AND

328

C

i00

DISTRIBUTOR.

H = 2.0

R1 = BD/2.0

CALCULATE THE VESSEL WEIGHT., lb.

VESWT = (480.*PI*BD*(TC/12.0)*(BL+H+RI)*I.I)

TB = 0.75*HT+O.25*(HT-50.)

WD = DDEN*DESVOL

THEAT = 1.05*(VESWT*0.12*(TB-T)+WD*O.25*(TB-T)+H2OL*I400.)

F = ALOG((HT-T)/50.)

CALCULATE TOTAL REGENERATION GAS REQUIREMENT AND STANDARD CUBIC

FEET OF REGENERATION GAS

REH = THEAT*F

REG = REH/(HI-H2)

SCF = (REG*380.0)/MW

CALCULATE ALCOA'S MOMENTUM FOR MAXIMUM DOWNFLOW

VELOCITIES i.e. DESICCANT ATTRITION SHOULD NOT BE A PROBLEM

IF THE MOMEMTUM IS EQUAL TO OR LESS THAN 30,000.

MOMENTUM = (V)(MOL.WT) (P. Atms)

MOMEN = VEL*MW*(PI/14.7)

RETURN

END

THIS PROGRAM PRINTS THE OUTPUT OF THE RESULTS

SUBROUTINE OUTPUT

REAL MOMEN, MW

COMMON~DRY1~

FLOW, P, T

COMMON~DRY2~

Z, CYCLE, H2OC

COMMON/DRY3/ S, E, PICKUP

COMMON/DRY4/ DDEN, BL, HT

COMMON/DRY5/ MW, HI, H2

COMMON/RESl/ H2OL, DESVOL, AREAl

COMMON/RES2/ BD, R, Q, VEL

COMMON/RES3/

TC, VESWT, WD

COMMON/RES4/

TB, THEAT, F

COMMON/RES5/ REH, REG, SCF, MOMEN

WRITE (i, i00)

FORMAT (///,35X, 'GAS DRYER DESIGN',/IH ,78(IH*))

329

ii0

120

130

140

150

160

170

180

190

200

210

WRITE (i, ii0) FLOW, P, T

FORMAT (5X, 'GAS FLOW RATE, 10^6 std. ft^3/day: ' , T60, F12.3,/,

5X,'DRYER OPERATING PRESSURE, psig.:', T60, F12.3,/,

5X,'GAS FLOWING TEMPERATURE, oF:', T60, FI2.1)

WRITE (i, 120) Z, CYCLE, H2OC

FORMAT (5X,'GAS COMPRESSIBILITY FACTOR:', T60, F12.4,/,

5X,'DRYING CYCLE, hr.:', T60, FI2.1,/,

5X,'WATER CONTENT OF GAS, Ib/10^6 std.ft^3:',T60,Fl2.0)

WRITE (i, 130) S, E, PICKUP

FORMAT (5X,'ALLOWABLE STRESS, psi:', T60, FI2.1,/,

* 5X,'JOINT EFFICIENCY:', T60, FI2.1,/,

* 5X,'USEFUL DESIGN CAPACITY OF DESICCANT, (%):', T60, FI2.1)

WRITE (i, 140) DDEN, HT

FORMAT (SX, 'DESICCANT DENSITY, Ib/ft^3: ' , T60, FI2.1,/,

5X, 'HEATER OUTLET TEMPERATURE, oF:', T60, FI2.1)

WRITE (i, 150) MW, HI, H2

FORMAT (5X, 'MOLECULAR WEIGHT OF REGENERATION GAS:',T60,FI2.1,/,

*5X,'ENTHALPY OF GAS BEFORE REGENERATION HEATER, Btu/Ib:',T60,

*FI2.1,/,5X,'ENTHALPY OF GAS AFTER REGENERATION HEATER, Btu/ib:',

*T60, FI2.1)

WRITE (i, 160) H2OL, DESVOL, AREAl

FORMAT (SX,'TOTAL WATER ADSORBED, ib/h.:', T60, F12.3,/,

5X,'DESICCANT VOLUME, ft^3.: ' , T60, F12.4,/,

5X,'CALCULATED CROSS-SECTIONAL AREA, ft^2.: " , T60, F12.4)

WRITE (i, 170) BD, R, BL, Q, VEL

FORMAT (5X,'BED DIAMETER, ft.:', T60, F8.4,/,

* 5X,'BED RADIUS, ft.:', T60, F8.4,/,

*

5X,'BED LENGTH, ft.:', T60, F8.2,/,

* 5X,'ACTUAL GAS FLOW RATE, ft^3/min.: 9 , T60, F12.3,/,

* 5X,'SUPERFICIAL GAS VELOCITY, ft./min.:', T60, F12.3)

WRITE (i, 180) TC, VESWT, WD

FORMAT (5X,'DRYER SHELL THICKNESS, in.:', T60, F12.4,/,

5X,'VESSEL WEIGHT, lb.:', T60, FI2.0,/,

5X,'DESICCANT WEIGHT, lb.:', T60, FI2.0)

WRITE (i, 190) TB, THEAT, F

FORMAT (5X,'TEMPERATURE OF DESICCANT BED, oF:', T60, F12.3,/,

5X,'TOTAL HEAT REQUIRED TO REGENERATE DRYER, Btu:', T60,

E14.6,/, 5X, 'LOSS FACTOR:', T60, F12.4)

WRITE (i, 200) REH, REG, SCF, MOMEN

FORMAT (5X,'HEAT ADDED TO REGENERATION GAS:', T60, E14.6,/,

* 5X,'TOTAL REGENERATION GAS REQUIREMENT, ib:',T60, E14.6,

* /,5X,'STANDARD CUBIC FEET OF REGENERATION GAS, std.ft^3: " ,

* T60, EI4.6,/,5X,'MOMENTUM:', T60, E14.6)

WRITE (i, 210)

FORMAT (76(IH-))

FORM FEED THE PRINTING PAPER TO THE TOP OF THE NEXT PAGE.

WRITE (i, *) CHAR(12)

RETURN

END

330

CHAPTER 5

Instrument Sizing

INTRODUCTION

Instruments are used to monitor the pertinent process variables dur-

ing plant operation. They may be part of automatic control loops or

used for the manual monitoring of the process operation. Instruments

that monitor critical process variables are fitted with automatic alarms

to alert the operators to critical and hazardous situations. Miller [ 1] and

Perry [2] provide details of process instruments and control equipment.

This chapter considers orifice sizing for liquid and gas flows, control valve

design for liquid, vapor, steam services, and two-phase flow. The chapter

further reviews relief valve sizing for vapor, steam, liquid, air, and fire con-

ditions. The effect of the pressure drop (AP) on pipework design, noise

suppression, discharge reactive forces, and relief valve location is consid-

ered. In addition, the chapter discusses two-phase flow relief sizing involv-

ing runaway reactions. For all the sizing procedures, the chapter develops

the engineering equations for ease in preparing computer programs.

Orifice Sizing For Liquid and Gas Flows

In process design, an orifice or a nozzle is usually sized for known

flow rate and pressure drop (AP). Nozzles and orifices are used to restrict

the flow of fluids. Thus, a reduction in cross-sectional area can cause

significant changes in the pressure and temperature of a compressible

fluid as it flows through the constriction. The magnitude of the change

depends on the linear velocity of the fluid or the Mach number at the

constriction. An orifice is usually designed to develop a full-scale

pressure differential at maximum flow. Alternatively, it can be designed

to a square-edged or sharp-edged cut.

331

332

Fortran Programs for Chemical Process Design

A square-edged or sharp-edged orifice is a clean cut square-edge hole

with straight walls perpendicular to the flat upstream face of a thin plate

placed crosswise of the channel. The stream issuing from such an ori-

fice attains its minimum cross section (vena-contracta) at a distance

downstream of the orifice. This varies with the ratio, [3, of the orifice to

the pipe diameter. All measurements of the distance from the orifice are

made from the upstream face of the plate for the corner, radius, pipe,

and vena contracta taps.

Corner Taps.

Static holes are drilled, one in the upstream and the

other in the downstream flange. The opening is as close as possible to

the orifice plate.

Radius Taps. Static holes are located one pipe diameter upstream

and one-half diameter downstream from the plate.

1

Pipe Taps. Static holes are located 2 ~ pipe diameters upstream and 8

pipe diameters downstream from the plate.

1

Vena-Contracta Taps. The upstream static hole is ~ to 2 pipe diam-

eters from the plate; the downstream tap is located at the position of

minimum pressure.

Flange Taps. Static holes are located 1 inch upstream and 1 inch

downstream of the plate.

Figure 5-1 shows the locations and names of the orifice taps. The true

mass flow rate for both liquids and gases is obtained by multiplying the

theoretical mass flow equation by the discharge coefficient, the gas

expansion factor, and the thermal-expansion factor. This is expressed as:

W - 0.52502(

CDYd2Fa

) )0.5

true

~/1

-- ~4

(pAP (5-1)

where the coefficient of discharge, C D, is

true flow rate

C D = (5-2)

theoretical flow rate

C D for a given orifice type is a function of the Reynolds number

(NRe)

and the diameter ratio ]3. CD is constant at Reynolds number greater

than 30,000. For square-edged or sharp-edged concentric circular

Instrument Sizing 333

il

2 1/2 D and 8D taps (pipe taps)

2 1/2 I_..,

1 in. LI~

Ill

I

Flow

Ill

i

I Ill

//

v

1 in.

8 D .~1~.

// !I !

taps Corner

/ ,

\\ I,

I

---, D/2

il I

D and D/2 taps

Figure

5-1. Orifice pressure tap locations. 2 1/2D and 8D pipe taps are not recom-

mended in ISO 5167 or ASME fluid meters. D and D/2 taps are now used in place of

vena-contracta taps.

orifices, C D falls between 0.595 and 0.62. The discharge coefficient cor-

rects the theoretical equation for the influence of velocity profile (NRe),

assuming no energy loss between the taps and pressure-tap location.

The thermal expansion factor

Fa:

The material of primary element

and pipe expands or contracts with temperature. The pipe and bore

diameters are measured at room temperature, but will be larger or smaller

when used at other temperatures. F~ is introduced to correct for

these differences.

The Expansion Factor Y. This corrects for density changes between

taps. Y depends on the adiabatic exponent (k - Cp/Cv), absolute pres-

sure ratio (AP/P,), and the ratio, 13, between restriction diameter and the

inside pipe diameter. For liquid flow, Y = 1.0. For gas flow, Buckingham

derived the equation [3]:

Y - 1 - (0.41 + 0.35134

) --

AP

Pk

(5-3)

334 Fortran Programs for Chemical Process Design

Orifice Sizing For Liquid Flows

For liquid sizing, Y= 1.0, and the following assumptions

are F a -

1.0,

C D - 0.62 [4]

Equation 5-1 is re-arranged in the form

~Jl--~ 4

0.52502(CD)

d 2

W

true

(pAP) ~ (5-4)

where

Z ~.

O. 52502 (C D )

W

true

(pAP) ~ (5-5)

and

d

- (5-6)

D

Equation 5-4 is expressed by

1E (d 4]~

d2 1- ~

- Z (5-7)

squaring both sides of Equation 5-7

1

1 d) 4 -

d4I -(~

1 22

(5-8)

1 1 = Z 2

d4- D4

(5-9)

1

1 = Z2 + (5-10)

d 4 D 4

The orifice size, d, is expressed by

D4

) 0.25

d - 1+

D4Z 2

(5-11)

Instrument Sizing 335

Orifice Sizing For Gas Flows

Using Equations 5-1 and 5-3

That is,

CDYd2Fa /

Wtrue -- 0" 52502 ~]1_~4 (PAp)~

and

Y = 1 - (0.41 +

0.35[34 )

AP

Pk

The following substitutions are made:

y-J3 4

W

true

0.52502(D 2 )(pAP)~

(5-1)

(5-3)

(5-12)

(5-13)

n= 1-0.41

AP

P.k

(5-14)

t = 0.35~

AP

P.k

(5-15)

Equation 5-1 and Equation 5-3 are modified and combined to give

1 - ( ny'/2 - ty3/2 ) (5-16)

(1-

y)l/2

Squaring both sides and dividing by t 2, Equation 5-16 is expressed in

cubic form as:

y3

2n. y2 n 2 + 12 12

- t + t --------F--- y t2 = 0 (5-17)

Equation 5-17 is solved for y by finding roots of the cubic equation

using the following substitutions.

Let

2n

p = (5-18)

t

336

Fortran Programs for Chemical Process Design

q - ( n2

+,2)

t ~

12

r-

t 2

y3 _ 2py2 + qy _ r - 0

and

a -

3q-p

312 _ n 2

3t 2

(5-19)

(5-20)

(5-21)

(5-22)

b - (2p3 - 9pq + 27r)

27

(2n 3 + 18nl 2 + 27tl 2)

27t 3

The solution to Equation 5-17 yielding a real number is:

{b2 / b2 a3/"2}"3

y - __+ +

4 27

{b (b2 a3/"2}"3 2n

+ -2-- 4- +27 3t

the orifice diameter, d, is expressed by

d- Dy I/4

Conversions:

AP - 0.03613(h w )

Wtru e

_ (Q.P)60.0

(5-23)

(5-24)

(5-25)

(5-26)

(5-27)

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

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