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

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CALCULATE THE VAPOR RATE

WF=Q/LAT

CALCULATE THE ORIFICE AREA FOR FIRE CONDITIOn[.

CALL VAPOR (WF, SP5, OP5, TS, ZS, MWS, NS)

RETURN

END

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

THIS PROGRAH PRINTS THE RESULTS OF FIRE RELIEF SIZING ONTO A

PRINTER

SUBROUTINE OUT5 (F, AREA, LAT, SPS, OP5, T5, ZS, MW5, N5)

C}IARACTER COUNT(14),REGIME(14), REG(14)

C}IARACTER* 14 COUNT1 ( 14 ), COU~[LL ( 14 ), ACOUNT ( ! 4 )

CHARACTER* i0 CHOICE

COMMON/NAME/I, Y, IJK

COMMON/DATAI/WGMAX,ADESI,ACALI,CI

COHMON/DATAg/COUNT,REGIME,COUNTI,COUNLL,REG,ACOUNT

COMMON/DATA5/FORCE

CO~4ON/DATAT/Q,WF

COMMON CHOICE

DIMENSION Y(14)

REAL LAT,OPS,MWS,N5

WRITE(I, 1500)

FORMAT(20X,'FIRE RELIEF VALVE SIZING')

WRITE(I, 1600)

FOFdiAT(IH ,76(iH*))

WRITE (I, 1650)CHOICE

FORMAT (3X,'BASIS OF SELECTION:', T65, A)

WRITE(I, 1700) F

FORMAT(3X,'ENVIRONMENTAL FACTOR:',T65,Fg.3)

~ITE(I, 1800) AREA

FORMAT(3X,'WETTED SURFACE AREA OF VESSEL, ft^2:',T65,Fg.3)

h~ITE(I, 1900) LAT

FORMAT(3X,'LATENT HEAT OF VAPORIZATION, Btu/Ib:',T65,F9.3)

WRITE(l, 2000) SP5

FORMAT(3X,'VALVE SET PRESSURE, psig:',T65,F9.3)

WRITE(I, 2100) OP5

FORMAT(3X,'PERCENTAGE OF OVERPRESSURE, (%):',T65,Fg.3)

~TRITE(I, 2200) T5

FOR~T(3X,'FLUID TEMPERATURE, DEG. F:',T65,F9.3)

WRITE(I, 2300) Z5

FORMAT(3X,'FLUID COMPRESSIBILITY FACTOR:',T65,F9.3)

WRITE(I, 2400) }~5

FORMAT(3X,'FLUID MOLECULAR WEIGHT:',T65,F9.3)

WRITE(l, 2500) N5

FORMAT(3X,'RATIO OF SPECIFIC HEATS OF FLUID:',T65,F9.3)

WRITE(l, 2600) CI

FORMAT(3X,'GAS CONSTANT DETERMINED BY RATIO OF Cp/Cv:',T65,F9.3)

WRITE(l, 2700) WE

FORMAT(3X,'VAPOR RELIEF FLOW RATE, ib/h.:',T65,F12.0)

WRITE(l, 2800) ACALI

FORMAT(3X,'CALCULkTED VALVE ORIFICE AREA, in^2: ' , T65,F9.3)

WRITE(l, 2900) ADESI

FORMAT(3X,'NEAREST STANDARD ORIFICE AREA, in^2: ' , T65,F9.3)

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WRITE(l, 3000) REGIME(I)

FORMAT(3X,'NEAREST STANDARD ORIFICE SIZE:',T65,A)

WRITE(l, 3100) COUNTI(I)

FORMAT(BX,'PREFERRED VALVE BODY SIZE, (IN-OUT) inches:',T65,A14)

WRITE(l, 3200) WGMAX

FORMAT(3X,'MAXIMUM VAPOR FLOWRATE WITH STD. ORIFICE ib/hr.:',

T65,FI2.0)

WRITE(l, 3300) FORCE

FORMAT(3X,'REACTION FORCE, Ib:',T65,FI2.0)

~ITE (I, 34007

FORMAT (76(iH-))

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

WRITE (i, *)CHAR(12)

RETURN

STOP

END

THIS PROGRAM STORES THE MANUFACTURERS' ORIFICE SIZES

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

SUBROUTINE MANUF (ADES)

CHARACTER COUNT(14),REGIME(14),REG(14)

CHARACTER*I4 COUNTI(14),ACOUNT(14),COUNLL(14)

COMMON/NAME/I,Y, IJK

COMMON/DATA4/COUNT,REGIME,COUNTI,COUNLL,REG, ACOUNT

DIMENSION Y(14)

DO I0 I=i,14

IF (ADES .EQ. Y(I)) THEN

REGIME(I)=COUNT(I)

COUNLL(I)=COUNTI(I)

GO TO 20

ELSE

ENDIF

CONTINUE

RETURN

END

THIS PROGRAM STORES THE MANUFACTURERS' ORIFICE SIZES

SUBROUTINE AMANU (ADES3)

CHARACTER COUNT(14),REGIME(14),REG(14),REGI(14)

CHARACTER*I4 COUNTI(14),ACOUNT(14),COUNLL(14),ACONT(14)

COMMON/NAME/I,Y,IJK

COMMON/DATA/REGI,ACONT

COMMON/DATA4/COUNT,REGIME,COUNTI,COUNLL, REG, ACOUNT

DIMENSION Y(14)

DO I0 I=i,14

IF (ADES3 .EQ. Y(I)) THEN

REG~I)=COUNT(I)

ACOUNT(I)=COUNTI(I)

ELSE

ENDIF

CONTINUE

418

RETURN

END

THIS PROGRAM STORES THE MANUFACTURERS' ORIFICE SIZES

SUBROUTINE MANUEL (ADES3, ADES31)

CHARACTER COUNT(14),REGIME(14),REG(14)

CHARACTER*I4 COUNTI(14),ACOUNT(14),COUNLL(14)

COMMON/NAME/I,Y,IJK

COMMON/DATA4/COUNT,REGIME,COUNTI,COUNLL, REG, ACOUNT

DIMENSION Y(14)

DO i0 I=l, 14

IF (ADES3 .EQ. Y(I)) THEN

REG(I)=COUNT(I)

ACOUNT(I)=COUNTI(I)

ELSE

ENDIF

CONTINUE

DO 20 I=i,14

IF (ADES31 .EQ. Y(I)) THEN

REGIME(I)=COUNT(I)

COUNLL(I)=COUNTI(I)

GO TO 30

ELSE

ENDIF

CONTINUE

RETURN

END

THIS PROGRAH DETERMINES THE REACTION FORCES IN ~

OPEN DISCHARGE SYSTEM

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

SUBROUTINE REACTF (WG, N, T, MW)

REAL N,MW

COMMON/DATAS/FORCE

VALI=(N*T)/((N+I.0)*MW)

FORCE=(WG*SQRT(VALI))/366.0

RETURN

END

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

BLOCK DATA

REAL Y(14)

COMMON/NAME/I,Y,IJK

DATA

Y(1)/O.II/,Y(2)/O.196/,Y(B)/O.BOT/,Y(4)/0.503/

DATA

Y(B)/O.785/,Y(6)/I.287/,Y(7)/I.838/,Y(8)/2.853/

DATA

Y(9)/B.60/,Y(IO)/4.B4/,Y(II)/6.38/,Y(12)/II.05/

DATA Y(IB)/16.00/,Y(14)/26.00/

END

419

CHAPTER 6

Compressors

INTRODUCTION

Compressors are gas movers and devices where mechanical work is

done on the gas resulting in an ~ increased pressure. Centrifugal com-

pressors are used in a variety of chemical process industries (CPI). Their

performance often varies with changes in process conditions. Some-

times the performance curves supplied by the manufacturer as discharge

pressure and power requirement against an inlet volumetric flow may

not be valid for variations in process conditions. Lapina [1] has pro-

vided a technique of obtaining a usable performance curve that is valid

for the actual process conditions. Gas compressor applications are

employed in the following duties:

9 refrigeration

9 gas injection

9 gas transmission

9 gas lift

9 wellhead separator boosting

There is no single type of compressor that can be adapted to a particular

application. The operating conditions, space, and weight restrictions must

be reviewed before the appropriate compressor is selected. In addition,

the type of driver requires selection because its selection and process

conditions are interrelated.

Compressors can be classified into two basic types: reciprocating and

centrifugal. The reciprocating compressor is well suited for high pres-

sures and low volume flow rates, while the centrifugal is preferred for

lower pressures and high volume flow rates. A centrifugal compressor

420

Compressors 421

uses the relationship between the velocity and pressure to increase the

gas pressure. The gas enters a rotating impeller at the eye. The vanes

force the gas to the outside rim, and subsequently throw it away from

the rim at a high velocity. The gas is flung into the surrounding diffuser

and volute passageways with a large volume, resulting in a reduced

velocity. The velocity energy is thus changed into pressure energy and

subsequently increases the gas pressure.

CENTRIFUGAL COMPRESSORS

In a centrifugal compressor, at least half the driver power (e.g., an elec-

tric gas or a steam turbine or a gas engine) is changed into gas velocity

energy. The increased velocity can be carried forward to the next impel-

ler for further increase in the velocity. A centrifugal compressor uses

the impeller to furnish rotational pressure, which squeezes the gas out-

ward and closer together, resulting in some pressure increase. As the

impeller is rotated faster, more energy is expended from the driver. Fig-

ure 6-1 shows the flow of gas in a centrifugal compressor. The amount

of pressure a compressor impeller can develop depends on its speed and

diameter. Increased velocity and pressure are required for .high speed,

large diameter impellers. The impeller metal will have the same cen-

trifugal force as the gas flowing through it. Also the impeller metal can

tear apart if the diameter is too large or the impeller turns too rapidly.

Therefore, the pressure that is developed with a single impeller is

CENTRIFUGAL FORCE

Gas Outlet

F7Z,

Figure 6-1. Gas flow in centrifugal compressor.

422

Fortran Programs for Chemical Process Design

limited by the strength of the impeller metal. An additional impeller is

used where one impeller is incapable of providing the required pres-

sure. The gas leaving one rim enters the next stage eye of the impeller,

consequently boosting its pressure.

RECIPROCATING COMPRESSORS

Reciprocating compressors are furnished as single stage or multi-

stage with ratings from fractional to more than 20,000 horsepower per

unit. The pressures range from a low vacuum at suction to 30,000 psi

and higher at discharge. The number of stages depends on the overall

compression ratio. The compression ratio per stage is limited by the

discharge temperature and does not exceed four [2].

Multistage compressors are provided with intercoolers between stages

and with an aftercooler at the compressor discharge. These are heat

exchangers that remove the heat of compression from the gas and

reduce its temperature to approximately the temperature existing at the

compressor intake. In certain cases, aftercooling and interstage cooling

are not always beneficial. If the gas must be heated before entering a

reactor, downstream heaters can be designed for a lower duty if the heat

of compression is not removed. Multistage compressors are intercooled

when the inlet temperature of the gas and the required compression

ratio are such that the discharge temperature of the gas exceeds 300~

The coolers reduce the actual volume of gas flowing to the high pres-

sure cylinders, the horsepower requirement, and keep the temperature

within safe operating limits. In instances where a compressor with

intercoolers is used to compress gases with condensable vapors, the com-

bined effect of compression and cooling can condense out the liquid.

Therefore, the liquid condensate must be removed by installing a knock-

out pot after the intercooler. This will prevent damage to the down-

stream of the compressor.

THE EQUATIONS

Compressors are rated in feet of compression head developed. This

is the energy conveyed to a gas stream by a compressor. It is observed

by the increase in gas pressure as the gas passes through the compressor.

Centrifugal compressors more nearly follow polytropic operation and

are widely used to handle large volumes of gas at pressure ranges of 0.5

to several hundred psi.

Compressors 423

There are two ways to carry out the thermodynamic calculations for

compression, namely by assuming:

1. An adiabatic (isentropic) reversible path: A process during which

there is no heat added or removed from the system. The entropy

is constant.

That is

pV k -

Constant (6-1)

2. A polytropic reversible path: A process in which changes in gas

characteristics during compression are reviewed.

That is

pV n - Constant (6-2)

The constant temperature process is a case when n= 1, which is equiva-

lent to isothermal compression, the constant pressure process n = 0; and

the constant volume process n = ~,. Generally, it is impractical to build

sufficient heat transfer equipment into the design of most compressors

to convey the bulk of the heat of compression. Therefore most machines

tend to operate along a polytropic path that approaches the adiabatic.

Most compressor calculations are based on the adiabatic curve [3].

Relationships may be developed between the temperature, pressure,

and volume for a polytropic process between state 1 and state 2. The

ideal gas law states that:

pV- RT (6-3)

That is

p,V~ - pzg2 (6-4)

RT 1 RT 2

Pl = , P2 - (6-5)

V 1 V 2

Rearranging p~ and P2 in Equation 6-5

Pl Tl V2

For a polytropic process between states 1 and 2,

(6-6)

424

Fortran Programs for Chemical Process Design

Pl V2

/ n

p; -(~

(6-7)

Substituting Equation 6-6 into Equation 6-7

V 2

(6-8)

Therefore

)n-I

Tl _ V2

Y~- 7,

(6-9)

(6-10)

Substituting Equation 6-10 into Equation 6-7

In-'

(6-11)

The compression work can be calculated from the pressure-volume re-

lationship as follows"

W- s (6-12)

and

pV n -

C for a polytropic process

ffl dV

W- C

(6-13)

Integrating Equation 6-13

I n l-n 1

fj2 CV'2- - CVl

W -- C

V-ndv - i-n

(6-14)

Compressors 425

n n

C- P2V2 -

plVl

Therefore Equation 6-14 can be expressed as

W-[ p2V21-n- plV' ]

(6-15)

Using the ideal gas laws,

p2V2-

mRT 2

and

PlV1 -

mRT~

Equation 6-15 is given by

W = mR(T2 - Tl )

1-n

(6-16)

For the polytropic compression, work done is defined by

W = nR(T2 - Tl )

1-n

(6-17)

The polytropic compression work can be expressed as:

W = ~[plVl - P2V2]

n-1

(6-18)

Since the process from 1 to 2 is polytropic, then

n n

plVl

P2V2

and

(6-19)

Pl )n

(6-20)

From Equation 6-18

w: n [ p2V2]

n-lPlVl 1 P[-VI

(6-21)

426 Fortran Programs for Chemical Process Design

and

n-I

p2v2/p2/

pTV7- 7

Substituting Equation 6-22 into Equation 6-21

W .__

n-1

I1-

P2 1

p,v,

where R c = pz/pl = compression ratio

Equation 6-23 is given by

n-l]

W _ ~n _ R~ n

n- 1 pjV~ 1

(6-22)

(6-23)

(6-24)

Polytropic Compressor

Real compression processes operate between adiabatic and isother-

mal compression. Actual compression processes are polytropic processes.

This is because the gas being compressed is not at constant entropy as

in the adiabatic process, or at constant temperature as in the isothermal

processes. Generally, compressors have performance characteristics that

are analogous to those of pumps. Their performance curves relate flow

capacity to head. The head developed by a fluid between states 1 and 2

can be derived from the general thermodynamic equation.

H- IpP: VdP (6-25)

where H = head, ft of fluid

p = pressure, psi

V = specific volume of the fluid, ft3/lb

For polytropic compression, the pressure-volume relationship is

pV n =

constant