Appendix B: Shortcut Calculations and Graphical Compressor ...

507

* Reprinted from a 1994 Elliott Company sales bulletin. The reference information contained herein is providedas an assist to developing your application. However, Elliott reserves the right to modify the design or construc-tion of the equipment described and to furnish it, as altered, without further reference to the illustrations or infor-mation contained herein.

APPENDIX B

SHORTCUT CALCULATIONS ANDGRAPHICAL COMPRESSOR SELECTION PROCEDURES

B.1 SELECTION GUIDE FOR ELLIOTT MULTISTAGE CENTRIFUGAL COMPRESSORS*

A Practical Guide to Compressor Technology, Second Edition, By Heinz P. BlochCopyright © 2006 John Wiley & Sons, Inc.

APPNB.qxd 7/29/06 2:33 PM Page 507

508 APPENDIX B


SHORTCUT CALCULATIONS AND SELECTION PROCEDURES 509


510 APPENDIX B




512 APPENDIX B




514 APPENDIX B



516 APPENDIX B




518 APPENDIX B




520 APPENDIX B



B.2 QUICK SELECTION METHODS FOR MULTISTAGE COMPRESSORS*

Among the many purely graphical methods of rapidly selecting multistage compressors isone developed around 1965 by Don Hallock of the Elliott Company, Jeannette, Pa. To usethese charts, the following quantities must be known:

1. W—weight flow, in lb/min or scfm (standard ft3/min).

2. P1—inlet pressure, in psia

3. Rp—pressure ratio (discharge psia/inlet psia)

4. t1—inlet temp., in °F

5. M—mole weight

6. K—ratio of specific heats

Determine the Inlet cfm, Q1. If W is known, use Fig. B.1, proceeding through P1, t1, andM to find Q1.

If scfm is known, use Fig. B.2, proceeding through P1, t1, and “temperature standard” tofind Q1.

Determine the Head H. On Fig. B.3, enter Rp and proceed through K, t1, and M as shown.If head H exceeds 80,000 to 90,000, more than one compressor body will be required.

Determine the Number of Stages Required. On Fig. B.4, enter head H and proceed throughM to read the number of stages required. Round this off to the next-higher even number.

Determine the Speed and Size of the Machine. On Fig. B.5, enter Q1 and read the maxi-mum width in inches. Proceed to the stepped lines and read the rpm and flange sizes.Proceed through the number of stages and read the length of the machine in inches. In theexample shown, the icfm is 45,000 and the gas is between propane and chlorine in moleweight. The speed is shown to be 4000 rpm and the flanges are 36 and 24 in. A slightlyhigher flow requires 3500 rpm and 42- and 30-in. flanges.

Determine the Horsepower Requirement. On Fig. B.6, enter W, proceed through Q1 andH, and read HP. If W is not known, work backward from Q1 on Fig. B.1 to find W beforeusing Fig. B.6.

For uncooled, constant weight flow compression, such as alkylation, wet gas, recycle, orair under 50 psia, the foregoing is sufficient to determine price, size, and driver require-ment. For cooled or variable weight flow compression, proceed as follows:

Cooled Compression. Assume one cooler and two compression sections, each sectionhandling a pressure ratio equal to the square root of the overall pressure ratio.

● Determine discharge temperature t2 from Fig. B.7, proceeding through Rp, Q1, K, and t1.● Assuming that this t2 is satisfactory, proceed through all the figures for each of the

separate sections. Speed and width of the compressor will be dictated by the first sec-tions. The total horsepower is the sum of the sections.

* Developed and contributed by Don Hallock, Elliott Company, Jeannette, Pa. Adapted by permission of HP andthe Elliott Company. Originally published in the October 1965 issue of Hydrocarbon Processing.


522 APPENDIX B

● If one cooler does not depress t2 sufficiently, or if still more horsepower saving isdesired, try two coolers or more. Rp per section for a two-cooler three-sectionarrangement is the cube root of the overall Rp; for a three-cooler four-section arrange-ment, it is the fourth root. Bear in mind that more than one set of cooler openings isseldom available on a single compressor body. When more than one cooler is chosen,therefore, more than one compressor body is likely to be required.

Considerable judgment is required in choosing the number of coolers to use. Once thetemperature limits are satisfied, the use of additional coolers becomes a matter of econom-ics between compressor and cooler cost, and horsepower evaluation.

Variable Weight Flow. For applications having side flows either in or out, it is necessaryto consider each constant flow compression section separately. Mixture temperature to thesecond section after the first “inward” side flow must be calculated by finding the discharge

FIGURE B.1 If the weight flow of gas W is known, use this chart to find the inlet flow Q1 (icfm).



temperature of the first section from Fig. B.7, multiplying by the first section weight flow,adding in the product of the sidestream temperature and weight flow, and dividing by thesum of the weight flows. With mixture t1, P1, W, M, and K known, the figures can now beused for the second section, and so on through the machine.

M and K of the sidestream will generally be the same or quite close to those of the inlet,so mixture calculations for these quantities will normally be unnecessary. For extractionside flows, the second section inlet conditions are the same as the first section dischargeconditions, except for W.

Normally, the first section will “see” the largest Q1, in which case the first section Q1

will dictate the size and speed of the machine. An occasional refrigeration process, how-ever, will show the second section Q1 to be the largest. In this case, that Q1 will dictatemachine size and speed.

To determine the number of stages required, add the stages for each compression sectionand add in a blank stage for each large side load. It is impossible to give criteria for exactlywhat constitutes a “large” side load, but experience has shown that a typical propylene unit

FIGURE B.2 If the scfm value is known, use this chart to find the inlet flow Q1 (icfm).


524 APPENDIX B

FIGURE B.3 Enter this chart at Rp, the pressure ratio (discharge/inlet, psia), to find the head H.

FIGURE B.4 Enter this chart with the H value on Fig. B.3 to find the number of stages required.



will require a blank stage for the first sideload only, whereas a typical ethylene machinemay require two blank stages. If the total number of stages, including blanks, exceeds nine,a second machine will probably be required.

B.3 DELAVAL ENGINEERING GUIDE TO COMPRESSOR SELECTION*

FIGURE B.5 Enter this chart at the Q1 value from Fig. B.1 or B.2 and find the speed, width, length,and flange sizes.

* Reprinted by permission of IMO Industries, Inc., DeLaval Turbine Division, Trenton, N.J.


526

FIG

UR

E B

.6E

nter

this

cha

rt a

t the

wei

ght f

low

of

gas

Wan

d pr

ocee

d to

fin

d th

e co

mpr

esso

r ho

rsep

ower

req

uire

d.



FIGURE B.7 The discharge temperature can be found on this chart.


528 APPENDIX B




530 APPENDIX B




532 APPENDIX B




534 APPENDIX B




536 APPENDIX B




538 APPENDIX B


539


540 APPENDIX B

B.4 SHORTCUT (GRAPHICAL) METHOD OF DETERMININGAPPROXIMATE PERFORMANCE OF SULZER CENTRIFUGALCOMPRESSORS*

The calculation procedures given in the following pages permit

To determine: Compressor size and type● Nominal diameter D (m)● Number of stages zPower input P (kW)Speed n (r/min)Absolute discharge temperature T2 (K)

Using: Mass flow m (kg/s)Suction pressure p1 (bar abs)Absolute suction temperature T1 (K)Relative humidity �1 (%)Discharge pressure p2 (bar abs)Molecular mass M (kg/kmol)Isentropic exponent kCompressibility factor Z

The following factors, symbols and indices are also used:

Actual suction volume flow V1 (m3/s)Absolute humidity xPeripheral speed u (m/s)Head (polytropic) hp (kJ/kg)Temperature difference

(�T � Tc � T1) �T (K)Intercooling power factor f

Indices Suction conditions 1Discharge conditions 2Dry tWet fPolytropic pper casing Gper group of stages

(between two coolings) SUncooled *After cooling cTotal TNumber of casings iNumber of intercoolings j

How to Use the Diagrams A guide to the selection diagrams and two examples are givenin Table B.1, one with air in one casing, the other with gas in two casings.

* These graphical methods are intended for screening studies only. Contact the manufacturer for more definitivelayout and performance prediction.




542 APPENDIX B




544 APPENDIX B




546 APPENDIX B




548

TAB

LE

B.1

Sele

ctio

n an

d P

erfo

rman

ce C

alcu

lati

on o

f a

Cen

trif

ugal

Com

pres

sor

Tra

in

Cal

cula

tion

Exa

mpl

e 1:

Cal

cula

tion

Exa

mpl

e 2:

Air

Com

pres

sor,

One

Cas

ing

Gas

Com

pres

sor,

Two

Cas

ings

Giv

en:

Cap

acity

m. t�

10kg

/sm. t

�23

.66

kg/s

Suct

ion

pres

sure

p 1�

1 ba

r ab

sp 1

�0.

92 b

ar a

bsSu

ctio

n te

mpe

ratu

reT

1�

293

KT

1�

333

K

Rel

ativ

e hu

mid

ity�

1�

90%

�1

�0%

Dis

char

ge p

ress

ure

p 2�

5 ba

r ab

sp 2

�16

.1 b

ar a

bsD

ry m

olec

ular

mas

sM

t�

28.9

5kg

/km

olM

t�

17.0

3kg

/km

olIs

entr

opic

exp

onen

t cp/

c vk

�1.

4k

�1.

29C

ompr

essi

bilit

y fa

ctor

Z�

1Z

�1

Cal

cula

tion

inst

ruct

ions

1.D

eter

min

atio

n of

the

abso

lute

hum

idity

xx

�0.

016

x�

0(f

rom

T1,

p1,

�1,

Mt)

with

Dia

gram

12.

Det

erm

inat

ion

of th

e w

et m

olec

ular

mas

sM

f�

28.7

kg/k

mol

Mt�

Mf�

17.0

3kg

/km

olM

f(f

rom

x, M

t) w

ith D

iagr

am 2

3.C

alcu

latio

n of

the

wet

mas

s fl

ow . m

f�

. m

t(1

�x)

m. f�

10(1

�0.

016)

f�

10.1

6kg

/sm. f

�m. t

�23

.66

kg/s

4.D

eter

min

atio

n of

the

max

. per

mis

sibl

e pe

riph

eral

spe

edE

lect

ric

mot

or u

max

�32

0m

/sE

lect

ric

mot

or u

max

�32

0m

/su m

ax(f

rom

Z, k

, T1,

Mf)

with

Dia

gram

3T

urbi

ne u

max

�29

0m

/sT

urbi

ne u

max

�29

0m

/s

For

furt

her

calc

ulat

ion,

mot

or d

rive

has

bee

n se

lect

ed.

5.D

eter

min

atio

n of

the

tota

l pol

ytro

pic

head

h* p

Th*

pT�

186

kJ/k

gh*

pT�

722.

8kJ

/kg

(fro

m k

, p2,

p1,

Z, M

f, T

1) w

ith D

iagr

am 4

6.D

eter

min

atio

n of

the

max

. pol

ytro

pic

head

obt

aina

ble

h pG

max

�30

0kJ

/kg

h pG

max

�30

0kJ

/kg

per

casi

ng h

pG m

ax(f

rom

um

ax)

with

Dia

gram

57.

Cal

cula

tion

of n

umbe

r of

cas

ings

i i�

h pT/h

pG m

ax, w

ith h

pT�

i�1

i�2

with

fT

�0.

73h*

pT�

f T, w

here

by f

Tha

s to

be

estim

ated

with

Dia

gram

6

8.D

eter

min

atio

n of

the

pres

sure

rat

io p

er c

asin

g p 2

/p1G

with

p 2

/p1T

�p 2

/p1G

�5

p 2/p

1G�

4.27

Dia

gram

79.

Det

erm

inat

ion

of th

e po

lytr

opic

hea

d pe

r ca

sing

h* p

Gh*

pG�

h*pT

�18

6kJ

/kg

h*pG

�29

3kJ

/kg

(fro

m k

, p2/

p 1G

, Z, M

f, T

1) w

ith D

iagr

am 4


549

Fro

m n

ow o

n if

two

or m

ore

casi

ngs

are

nece

ssar

y, th

e ca

lcul

atio

n ha

s to

be

mad

e fo

r ea

ch c

asin

g se

para

tely

(on

e af

ter

the

othe

r).

Firs

t cas

ing

Seco

nd c

asin

g

10.

Det

erm

inat

ion

of th

e in

flue

nce

of in

terc

oolin

g f

�0.

9 w

ith �

T�

20

f�

0.91

with

�T

�0

f�

0.91

with

�T

�0

on th

e re

quir

ed s

haft

pow

er (

from

p2/

p 1G

, K, �

T, T

1an

d j�

1an

d j�

1an

d j�

1an

d es

timat

ed n

umbe

r of

inte

rcoo

lings

per

cas

ing

j)w

ith D

iagr

am 6

11.

Cal

cula

tion

of th

e fi

ctiv

e po

lytr

opic

hea

dh p

G�

186

�0.

9h p

G�

293

� 0.

91H

pG�

293

� 0.

91h p

G�

h*pG

�f

�16

7.4

kJ/k

g�

266.

6 �

267

kJ/k

g�

266.

6 �

267

12.

Det

erm

inat

ion

of th

e nu

mbe

r of

sta

ges

z pe

r ca

sing

z�

4z

�6

z�

6an

d th

e de

fini

te p

erip

hera

l spe

ed u

(fr

om h

pG, z

→u)

u�

295

m/s

u�

304

m/s

u�

304

m/s

with

Dia

gram

8 (

roun

d of

f z

to w

hole

num

ber

and

corr

ect p

erip

hera

l spe

ed c

orre

spon

ding

ly)

13.

Det

erm

inat

ion

of th

e ac

tual

suc

tion

volu

me

V. 1V. 1

�8.

59m

3 /sV. 1

�41

.8m

3 /sV. 1

�10

.2m

3 /s(f

rom

. mf,

p 1, T

1, M

f, Z

) w

ith D

iagr

am 9

14.

Sele

ctio

n of

the

com

pres

sor

size

(no

min

al d

iam

eter

D)

D�

56cm

D�

112

cmD

�56

cmas

a f

unct

ion

of V

. 1w

ith D

iagr

am 1

0

15.

Type

des

igna

tion

(fro

m s

teps

10,

12,

14)

RZ

56-

4R

Z 1

12-6

RZ

56-

6

16.

Cal

cula

tion

of th

e sp

eed

n�

n�

n�

n�

17.

Det

erm

inat

ion

of th

e po

wer

inpu

t P (

from

hpG

, m. f)

P�

2173

kWP

�81

00kW

P�

8100

kWw

ith D

iagr

am 1

1

Tota

l tra

in 1

6200

kW

18.

Det

erm

inat

ion

of th

e di

scha

rge

tem

pera

ture

T2

T2

�42

4K

T2

�41

3K

T2

�41

3K

(fro

m p

2/p 1

betw

een

inte

rcoo

ling,

k, T

1) w

ithw

ith T

1�

333

Kw

ith T

1�

333

Kw

ith T

1�

333

KD

iagr

am 1

2 w

here

by T

1is

the

suct

ion

tem

pera

ture

and

p 2/p

1�

2.3

and

p 2/p

1�

2.1

and

p 2/p

1�

2.1

afte

r pr

eced

ing

inte

rcoo

ling

and

pres

sure

rat

io p

2/p 1

betw

een

inte

rcoo

ling

has

to b

e de

term

ined

with

Dia

gram

7

60

304

0.

5610

368

r/m

in�

��

�60

30

4

1.

1251

84r/

min

�

��

�60

29

5

0.

5610

060

r/m

in�

��

�60

u

D

(D i

n m

eter

s)�

��

�


Appendix B: Shortcut Calculations and Graphical Compressor ...

Documents