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

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Compressors 427

V- C, (6-26)

where V = mole volume, ft3/(lb mol)

For the polytropic head,

Hp,

V can be substituted in Equation 6-25. The

polytropic head is defined by

Hp - fpP: C__~_~ dP

(6-27)

Integrating Equation 6-27,

becomes

n En-' n-, n

Hp - C 1

P2 n -- Pl

n-1

(6-28)

__tin )!~/ p2 n

n-1 p -1

(6-29)

where

1 I

p~'V~ - p~V 2 - C~ and Rc = P__z_2 (6-30)

Substituting these into Equation 6-29, to eliminate C~ gives

n --

Hp -

n - 1 PlVI

Rcn --

1 (6-31)

Using the gas law relationship

plVi- -- ZIRTI (6-32)

where Z~ = compressibility factor at suction

T~ = absolute temperature at suction, ~

M w = molecular weight, (lb/lb mol)

R = gas constant

428

Fortran Programs for Chemical Process Design

Substituting Equation 6-32 into Equation 6-31, the polytropic head,

Hp,

becomes"

Z~RT~ n --

Hp - Mw n-1 Re n -1 (6-33)

If the compressibility factor, Z2, for the gas at discharge conditions is

significantly different from that of the suction, then the average com-

pressibility factor, Zavg ' is used to calculate the polytropic head.

Z - _ Z~ + Z 2 (6-34)

avg

The polytropic head is defined by

Z avgRTl n R n -- 1 (6-35)

Mw n-1 c

This can also be expressed as:

1545. Z~vg. Tl n -

H p M w n-1 Re -1 (6-36)

The discharge temperature, ~ is given by

(Hp)(Mw) (n- l/+ t (6-37)

t2=

(Zavg~R ~ n '

There is a limit on the temperature as in the olefin or butadiene plants to

prevent polymerization. At temperatures greater than 450 - 500~ the

approximate mechanical limit, problems of sealing and casing growth

could occur. High temperature requires a special, high machine cost.

Therefore, multistage compressors are designed within the temperature

range of 250~ 300~ In addition, a single-stage polytropic compres-

sor can handle 7,000 to 11,000 feet of liquid, depending on the gas prop-

erties and inlet temperature [4].

The gas horsepower is expressed as

w.H

m P

Ghp -

1.98 x 106.

(6-38)

Compressors 429

The polytropic efficiency is used to compare adiabatic with polytropic

performance. This is defined by

n /k/E

n 1 k 1

(6-39)

Figure 6-2 shows the relationship between the polytropic efficiency and

adiabatic (isentropic) efficiency of a perfect gas.

Adiabatic Compressor

The performance of reciprocating (piston) compressors with large

valve area, or where valve losses are evaluated, is considered as close to

Figure 6-2. The relationship between the polytropic efficiency and the adiabatic effi-

ciency for a perfect gas (Z = 1 ). (Source: A. K. Escoe,

Mechanical Design of Process

Systems,

Volume 2, Gulf Publishing Company.)

430

Fortran Programs for Chemical Process Design

adiabatic behavior as can be measured. The thermodynamic definition

of an adiabatic process requires that no heat be added or removed from

a system in which a change of state occurs. The adiabatic head produces

the following equation, which is similar to the polytropic head of Equa-

tion 6-33. This is expressed as:

(z R T//k/[k: 1

__ avg"

Rc k

- 1

Had

Mw k - 1

(6-40)

This can also be given by

1545.

Zavg~

T l k R k

Had --

~I Z k- 1

(6-41)

The discharge temperature is:

T2-

The adiabatic gas horsepower is"

W, Had

1.98 x 106 .

gad

The adiabatic efficiency,

Ead ,

is:

(6-42)

(6-43)

k-l)

Ead=R -~- -1

R n --1

where

(6-44)

MwC

- P

(6-45)

MwC p -

1. 986

Generally, if the compression ratio for piston machines is less than 5 or

6, single-stage compression is used. If the total compression ratio is

between 6 and 36, two-stage compression will be required. Three or

more stages may be required for compression ratios greater than 36. For

two-stage compression, calculate the square root of the total compres-

sion ratio. Then assume that the compression ratio per stage will be

equal to the square root of the total compression [2].

Compressors

431

Mechanical Losses

After the gas horsepower is calculated by either the polytropic or

adiabatic compression method, horsepower losses due to friction in bear-

ings, seal, and speed increasing gears should be added. Although, there

is no accurate method in estimating mechanical losses from gas power

requirements, Table 6-1 gives approximate mechanical losses as a per-

centage of the gas power requirement [5].

The mechanical losses can be calculated by

Mechanical losses - (Ghp)(% mechanical losses)

(6-46)

The brake horsepower is:

B hp - Ghp + mechanical losses

(6-47)

The volumetric flow rate at suction or inlet condition can be expressed as"

Q~-(ICFM)-[ (MMSCFD) x10660 x 24 ][14"71[P~ 5-~T~ ]

IZsl

)< 1~ ft 3/min

(6-48)

The actual mass flow rate is

G-Q. I

P,'Mw

lb/min

(6-49)

Table 6-1

Approximate Mechanical Losses as a Percentage

of a Gas Power Requirement

Gas Power Requirement

English (hp)

0-3,000

3,000-6,000

6,000-10,000

10,000+

Metric (kW)

0-2,500

2,500-5,000

5,000-7,500

7,500+

Mechanical Losses %

2.5

1.5

432

Fortran Programs for Chemical Process Design

The accuracy of the developed polytropic head and efficiency curve

may be reduced due to volume ratio effects. These effects are the influ-

ences that the performance of one impeller has on those of the impellers

downstream. Lapina [ 1 ] stated these effects are greater as the number of

impellers within a compression section increases. He proposed some

guidelines to assess the volume-ratio effects for differences in the inlet

conditions. An equation to calculate the value of 0 for both the old or refer-

ence inlet conditions and the proposed new inlet conditions is given by

O-[(26I)(Mw)I~

(6-50)

MULTICOMPONENT GAS STREAMS

The design of a gas compressor for a gas mixture involves estimating

the thermodynamic properties. The procedure for calculating the prop-

erties of a gas mixture is to use the weighted molal average of the prop-

erty. These thermodynamic properties are estimated as follows:

Molecular weight

Mw,mixtur e =

~ y~M~ (6-51)

i=l

Reduced temperature

Tr,mixtur e = ~ YiTr,i

(6-52)

i=l

Reduced pressure

Pr,mixture --

s Yi Pr,i

(6-53)

i--I

Molal heat capacity

MCp,mixtur ~ - s yiMCp,i

(6-54)

i=l

Ratio of molal heat capacities

k mixtur e =

p, mixture

MC v, mixture

p, mixture

(MC p,mixture -- 1. 986)

(6-55)

Compressors 433

Compressibility factor

Zmixtur e :

f(T~,Pr) for the mixture

(6-56)

where Yi = mole fraction of component i.

Table 6-2 summarizes the differences between reciprocating and cen-

trifugal compressors.

Surge Control of Compressors

All dynamic compressors have a limited range of capacity for a given

selection of impellers at a fixed speed. Below the minimum value of

50 to 70% of the rated flow, the compressor will surge, that is, it will

become unstable in operation. Excessive vibration and possibly sudden

failure or shutdown may arise.

It is essential that all compressor systems be designed to avoid pos-

sible surge operation. This is done by incorporating some type of

antisurge control system. This is to ensure that the flow into the com-

pressor is sufficient to maintain stability at the required pressure drop

across the compressor. The surge control system should be used only

for surge control and must not be linked with other functions of the

process control system; otherwise, this could result in the damage of

the compressor.

Table 6-2

Comparison of Reciprocating and Centrifugal Compressors

Centrifugal Compressors

1. Lower installed first cost where

pressure and volume conditions are

favorable.

2. Lower maintenance cost.

3. Greater continuity of service and

dependability.

4. Less operating attention.

5. Greater volume capacity per unit

of plot area.

6. Adaptability to high speed low

maintenance cost drivers.

Reciprocating Compressors

1. Greater flexibility in capacity and

pressure range.

2. High compressor efficiency and

lower power cost.

3. Capability of delivering higher

pressure.

4. Capability of handling smaller

volumes.

5. Less sensitive to changes in gas

composition and density.

434

Fortran Programs for Chemical Process Design

Another surge control may be a blow off valve. This is automatically

controlled to open or blow off excess capacity to the atmosphere if the

process flow requirement is too low. In some cases, suction control valves

are used. For gases that cannot be designed to atmosphere, a bypass

control is the common antisurge control. This action bypasses unwanted

flow back to the suction source. However, because the gas has already

been compressed, its temperature is increased, and must therefore be

cooled before entering the compressor a second time. In this case, a

bypass cooler may be installed. The cooler may be avoided where the

suction source is large or far away and the heat is dissipated by mixing

or radiation. Figure 6-2A shows generalized flow characteristics of a

compressor. In this figure, as the system resistance decreases, the com-

pressor-system operating point moves to the right with a corresponding

increase in the volumetric gas flow. However, the gas flow through the

compressor cannot increase without a limit. This limit is known as "stone-

wall," and is caused by the choking of the gas as it exits from the com-

pressor. These two operating limits are shown in Figure 6-2A. The

designer should ensure that the system compressor curve-intersection

point is well away from the surge or stonewall for efficient operation.

Head

Surge

Normal operating zone

Stonewall

, ,

Flow Q

Figure

6-2A. Generalized flow characteristics of a compressor.

Compressors 435

Treatment of Compressor Fluids

The discharge from any compressor is a dirty corrosive liquid. Remov-

ing the sludge from a compressor air system can effect the following:

9 reduce installation costs incurred or drain traps, pipe and fittings,

filters and regulators.

9 reduce the maintenance of drain trap and the failure rate of pneu-

matic equipment, which is caused by dirt and moisture in the

supply line.

9 increase the life of pneumatic equipment.

Cases of high performance equipment require high quality of clean

and dry compressed air. Compressed air contains water, oil, and dirty

particles, which affects the performance of pneumatic equipment. Com-

pressed air dryers are used to remove water vapor and to dry the air.

Two main types of dryers are used in the CPI: refrigerant and desiccant

dryers. Desiccant dryers use an adsorbent material, such as activated

alumina, or molecular sieves to remove moisture from the compressed

air. Also, desiccant dryers can be either heat regenerated or heatless.

The main advantage of desiccant dryers is their ability to cool the air to

a very low temperature. They are more expensive in terms of both capi-

tal and running costs. They are important when higher quality air is

required. These dryers are widely used in offshore oil industry, where

extreme ambient conditions are required. The design of desiccant

dryers for removing water vapor from a natural gas is explained in

Chapter Four.

Nomenclature

Bhp- brake or shaft horsepower, bhp

C = constant

Cp- specific heat at constant pressure, Btu/lb~

Cv = specific heat at constant volume, Btu/lb~

D = impeller diameter or rotor, ft

D s = specific diameter, ft

Ead-

adiabatic efficiency

Ep -

polytropic efficiency (try 0.75 for preliminary work)

G = gas flowrate, lb/min

Ghp - gas horsepower, actual compression horsepower, exclud-

ing mechanical losses, hp

H = head, (ft. lbf)/lb m

436 Fortran Programs for Chemical Process Design

Had-

adiabatic head, (ft lbf)/lb m

Hp- polytropic head, (ft lbf)/lb m

ICFM - volume flow referred to inlet condition, ft3/min

k- adiabatic (isentropic) exponent, Cp/C v

MCp - molar specific heat at constant pressure, Btu/(lb tool~

MC v - molar specific heat at constant volume, Btu/(lb tool~

M w - molecular weight

MMSCFD - million standard cubic feet per 24-hour day

N- speed, rpm

N~- specific speed, rpm

n- polytropic exponent

P- absolute pressure, psia

P~ - suction pressure, psia

P2 - discharge pressure, psia

P~- suction pressure, psia

Q - volume flow, ft3/s

Q~= volume flow, ft3/min

R- universal gas constant

= 10.73(psia ft3/lb mole ~

= 1545[(lb ft 2) ft3/lb mole ~ or ft lb/lb mole ~

= 1.986(Btu/lb mole ~

R c - compression ratio, P2/P~

T~ - suction temperature, ~

T 2 - discharge temperature, ~

T~- suction temperature, ~

t~ - inlet temperature, ~

t 2 -

discharge temperature, ~

W- workdone, Btu/lb-mole

w - gas flow, lb/h

Zavg -- average compressibility factor for gas from suction to dis-

charge conditions. A value of 1.0 will give conservative

results.

CENTRIFUGAL PUMP HYDRAULICS

Introduction

Selecting the correct pump requires a knowledge of the system in

which the pump must operate. In the chemical process industries (CPI),

the engineer should start from the process flow sheets and schematics

such as piping and instrument diagrams. The engineer must determine