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

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Compressors 437

the optimum height and co-ordinate pump requirements, where pumps

take suction from vessels or drums with the height above the pump.

Where friction loss through piping forms a significant part of the total

head, the designer should influence the selection of the allowable pres-

sure drop (AP). In addition, volatile liquids, hot liquids, viscous liquids,

and slurries will require a special approach and selection methods. If

the pump is installed in a sump or a pit, essential factors require the

correct sizing of the pit. These involve the flow requirements as the

liquid flows toward the pump, and the positioning of the pump in the pit

with sufficient baffles and spacing. Pump selection and troubleshooting

are illustrated by Garay [6], McGuire [7], McNaughton [8], and have

appeared in the literature [9,10,11 ].

This chapter considers the design of centrifugal pumps for given flow

rates and physical properties.

Hydraulics of the System

The required factors in pump hydraulics are:

Density. The weight per unit volume of a substance, sometimes called

specific weight. The density of water is 62.3 pounds per cubic foot.

Specific Gravity

(SpGr). The ratio of the density or specific weight

of a substance to that of some standard substance. For liquids, the stan-

dard is water usually at 60~ In the petrochemical industry, API gravity

use is 10 ~ API. This corresponds to a specific gravity of 1.0.

SpGr(relative to water at 60 ~ F) =

141.5

131.5+ ~ API

(6-57)

In the chemical industry, degrees Baume" are commonly used. For liq-

uids lighter than water,

141.5

SpGr - (6-58)

130 + degrees Baume'

For liquids heavier than water,

145

SpGr = (6-59)

145 -

degrees Baume'

Pressure.

The force exerted per unit area of a fluid, often designated

as pounds per square inch (psi).

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Fortran Programs for Chemical Process Design

Barometric Pressure.

The atmospheric pressure at the pump loca-

tion. It changes with the weather conditions.

Gauge Pressure

(psig). The gauge pressure is the pressure above

atmospheric (or below in a vacuum).

Atmospheric Pressure

(psi). The force exerted on a unit area by the

weight of the atmosphere. The pressure at sea level due to the atmos-

phere is 14.7 psi.

Absolute Pressure (psia).

The sum of atmospheric and gauge pres-

sures. Absolute pressure in a perfect vacuum is 0, and at the atmosphere

at sea level is 14.7 psi (0 psig).

1 atmosphere (bar) = 14.7 psi = 34 ft of water

conversion factor = 34/14.7 = 2.31

psi - head in feet • SpGr (6-60)

2.31

Vapor Pressure.

The pressure at which a liquid at a specified tem-

perature is in equilibrium with the atmosphere or with its vapor in a

closed system. At pressures below the vapor pressure at a given tem-

perature, the liquid will start to vaporize. This is due to a reduced pres-

sure at the surface of the liquid.

Head.

The height of a fluid column, measured in feet, to ascertain

the gauge pressure at the bottom of the column.

Head, ft - 2.31 (pressure, psi) (6-61)

(SpGr)

Friction Head.

The pressure to overcome the resistance to the flow

in the pipe and fittings. It is expressed as lbs/sq, in. or feet of liquid.

Static Head.

Fluid elevation above or below the datum line. For

horizontal centrifugal pumps, static head is calculated from the pump

center line; with vertical pumps, it is taken from the eye of the first-

stage impeller.

Velocity Head.

The kinetic energy of a flowing fluid. It is defined by

V 2

k =

(6-62)

Compressors 439

Suction

Lift. The manometer reading in feet of liquid at the pump

suction (corrected to a datum), minus the velocity head. This term

expresses the suction head when it is below atmospheric pressure.

Static Suction Lift.

The vertical distance from the center line of the

pump down to the free level of the liquid source.

Net or Dynamic Suction Lift.

Static suction lift, friction head, and

velocity head.

Suction Head.

Occurs when the source of supply is above the center

line of the liquid.

Static Discharge Head.

The vertical elevation from the center line

of the pump to the point of free discharge.

Dynamic Discharge Head.

The static discharge head plus dynamic

suction lift or minus dynamic suction head.

Total Discharge Head.

The pressure reading at the pump discharge

in feet of liquid, corrected to a datum, plus the velocity head.

Total Head.

The algebraic difference between the discharge and suc-

tion heads. A suction lift is added to the total discharge head; a positive

suction head is subtracted from the discharge head.

Head Losses.

The frictional head losses caused by fluid flow through

pipes, fittings, valves, and nozzles.

NPSH. The net positive suction head is the most critical factor in a

pumping system. A sufficient NPSH is essential, whether working with

centrifugal, rotary, or reciprocating pumps. Marginal or inadequate NPSH

will cause cavitation, which is the formation and rapid collapse of

vapor bubbles in a fluid system. Collapsing bubbles place an extra load

on pump parts and can remove a considerable amount of metal from

impeller vanes. Cavitation often takes place before the symptoms

become evident. Factors that indicate cavitation are increased noise,

loss of discharge head, and reduced fluid flow.

Pump Hydraulics Calculations

Pump sizing computation requires the following information on the

process flow diagram or a pump calculation sheet: service, size and type,

fluid, pump temperature, density at pump temperature, design capacity

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Fortran Programs for Chemical Process Design

in gpm at pump temperature, suction head, discharge head, design dif-

ferential, NPSH (net positive suction head) and power requirements.

Calculating the suction condition of a pump comprises the following:

1. vessel pressure (original pressure).

2. add the suction head or minus for a suction lift, S.Hd.

3. minus the line pressure drop, L loss.

That is

Suction pressure = orig. pres. + S.Hd.- L. loss

The discharge condition of a pump considers the following:

(6-63)

1. delivery pressure

2. static head

3. control valve pressure drop

4. exchanger pressure drop

5. orifice pressure drop

6. furnace pressure drop

7. line pressure drop

8. other pressure drop

The NPSH = (orig. pres. - vapor pres.) + S.Hd - L. loss, ft (6-64)

The net head at the suction of the pump impeller must not exceed a

certain value to prevent formation of vapor and cause cavitation of the

metal. This minimum head is called the available NPSH a, and must be

greater than the required NPSH~ for a stable pump operation.

Pump discharge pres. = del. pres. + Shd.

+ AP Cont. v. + AP exch.

+ AP orif. + AP furn.

+ AP line + AP Other.

(6-65)

Total pump AP = pump discharge pres.- pump suction pres. (6-66)

Bhp (brake horsepower) =

(flow rate, gpm)(pump AP, psi)

(1715)(EFF)

(6-67)

Bhp =

(gpm)(H)(SpGr)

(3960)(EFF)

(6-68)

Compressors

441

where H = total discharge head

Table 6-3 shows a pump hydraulic design calculation data sheet.

Centrifugal Pump Efficiency

The design engineer must use the expected pump efficiency provided in

the pump performance curve to evaluate the required brake horsepower

for a centrifugal pump. In the early stages of the design, it is customary

to estimate a value for the efficiency. Final values depend on the speci-

fied pump and the operating conditions that are encountered. Branan

[4] has developed an equation to calculate the centrifugal pump effi-

ciency and pump horsepower. The equation was based on pump effi-

ciency curves of the NGPSA Engineering Data Book. These efficiency

Table 6-3

Pump Hydraulic Design Calculation Sheet

Fluid

Viscosity at Pumping temperature (RT), cP

Vapor Pressure at pumping temperature

(RT), psia

Specific gravity, (SpGr) at RT.

Density at RT., lb/ft 3

Operating flow at ET., gpm

Design Flow at ET., gpm

Suction

Vessel pressure, Orig. Pres., psia

Static head S.Hd., psi

- Line loss APf, psi.

Suction pres. = Orig. pres. + S.Hd.

27.7

5.4

0.23

Gas Oil

0.6

0.01

250.0

Discharge

Delivery pressure, psia. 28.2

Static head S.Hd., psi 14.86

AP Control valve, psi 10.0

AP Exchanger, psi 5.0

L. line

32.78

NPSH = (orig. pres.- vapor pres.) +

S.Hd.- L.loss, psia.

32.77

AP Orifice, psi 2.0

AP Furnace, psi

Line loss AP psi 4.38

Other AP, contigency, psi

250.0

64.87

1.04

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Fortran Programs for Chemical Process Design

curves give good results with the vendor data (the range of developed

heads, 50ft to 300ft, and the flow rates, 100 to 1000 gpm). The equation

for calculating the pump efficiency is expressed as"

EFF - (80- 0. 2855H + 3.78 x 10 -4 HQ

- 2.38 x 10 -THQ 2 + 5.39 x 10 -4H 2

- 6.39 x 10 -7 HZQ + 4 x 10 -'~ HZQ 2 )(1/100) (6-69)

The actual brake horsepower required for pump operation Bhp is"

Bhp- HBhp

EFF (6-70)

where EFF = pump efficiency (decimal fraction)

H = developed pump head, ft

Q = flow rate through pump, gpm

HBhp = hydraulic brake horsepower, hp

B hp - actual brake horsepower required for pump operation, hp

Using Equation 6-69, Figure 6-3 shows typical characteristic curves for

a 6-inch centrifugal pump operating at 1750 rpm. Equation 6-69 gives

160

140

120

100

EFFICIENCY

HEAD

BHP

0 100 200 300 400 600 600 700 800 900 1000

FLOWRATE

gpm

Figure

6-3. Typical characteristic curves for a 6-inch centrifugal pump operating at

1750 rpm.

Compressors 443

results within 7% of the actual pump curves for the range of applicabil-

ity (H = 50 to 300 ft, Q = 100 to 1000 gpm). For flows in the range of 25

to 99 gpm, an approximate efficiency can be obtained by solving Equa-

tion 6-69 for 100 gpm and then subtracting 0.35% gpm times the differ-

ence between 100 gpm and the low flow rate in gpm. For low flow

rates, near 25-30 gpm, this will give results within about 15% for

the middle of the head range (pump AP) and 25% at the extremes. The

horsepower at the 25-30 gpm level is normally below 10 [4].

AFFINITY LAWS

The affinity laws express the mathematical relationship between the

variables involved in a pump's performance. By applying the principles

of dimensional analysis on the physical properties affecting pump

operation, the relationship is:

f{ Q NQ ~ oQD}

(gcH)O.SD2,(gcH)O.7 5 , ~-~ - 0

(6-71)

where the dimensionless expressions are:

n, = Q (6-72)

(gcH~ 2

NQ 0.5

n2 = (6-73)

(gcH) ~

pQD (6-74)

71~ 3 =

~D 2

For true dynamic similarity, n~, n2, and

n 3

must be constant for similar

pumps or for the same pump at different speeds, n 3, which is the Reynolds

number, cannot be maintained constant with changes in pump speed or

size if the same liquid is pumped. Therefore, for practical application,

the Reynolds number can be neglected when considering the conditions

for dynamic similarity.

The conditions for dynamic similarity are constant values of n~ and

n 2. Equation 6-71 can be altered by appropriate mathematical operation

to yield

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Fortran Programs for Chemical Process Design

ff Q No}

(gcH)O.5D2,(gcH)O.5 - 0

(6-75)

where

/ m

rc 2 - (6-76)

(gcH) ~

Therefore, for conditions of similarity of flow rt,, T[~2, and rt~ are con-

stant. Stepanoff [12] has shown that the velocity diagrams at the impel-

ler are geometrically similar when the pumps are operating at the same

efficiency for similar pumps or for the same pump at different speeds.

Applications of Affinity Laws

For the same pumps or geometrically similar pumps, Q/(gcH)~ 2,

NQ~176 and ND/(g~H) ~ have unique values corresponding to each

efficiency. In addition, these values remain constant despite the impeller

diameter or pump speed. For the same pump operating at different speeds

the impeller diameter, D, is constant.

That is

D - constant

Therefore at any given efficiency

Capacity"

and ND

(g~H)~ D 2 (gcH) ~

are constant

Q /ND

(g~H)~ D 2 (gcH) ~

Therefore

= Constant

(6-77)

ND 3

= Constant - K

But D is constant

Therefore

Q- K'N

(6-78)

(6-79)

Compressors 445

where K" and K are constants

Therefore

Q2 ~ N2

Ql NI

Head"

(6-80)

(gcH) ~

= Constant

- J

(6-81)

N2D 2

= J' (6-82)

where J and

are constants.

Therefore at a constant diameter

(/2

H2 _ N2

H1 - -~l

(6-83)

Break horsepower (Bhp)

Bhp ~ QH c~

N 3

at constant D

Therefore

( )3

BhP2 _ N2

(6-84)

These laws apply only for efficiencies of the same value.

For geometrically similar pumps with different impeller diameters

but same speeds:

From Equation 6-78

Q- KND 3 (6-85)

At constant speed

Q - K"D 3 where K and K" are constants.

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Fortran Programs for Chemical Process Design

Q2 D2

Head:

At constant speed from Equation 6-82

H2 D2

Brake horsepower (Bhp)

/ / 5

BhP2 _ D2

(6-86)

(6-87)

(6-88)

Specific Speed

One dimensionless expression in the affinity laws is:

NQ ~

(gcH) ~

= constant at a given efficiency

It is often used by designers in sizing and selecting the type of pump or

compressor. The performance of centrifugal pumps is related to a

parameter called specific speed. It is a correlation of capacity, head, and

speed at optimum efficiency that classifies pump impellers with respect

to their geometric similarity. Specific speed is a number expressed alge-

braically as:

_ NQ ~

N~-

HO.75

(6-89)

where N s = specific speed of the pump

N = pump speed, rpm

Q = flow at optimum efficiency, gpm

H = head per impeller, ft

The specific speed of an impeller is the rotation in rpm. This is a geo-

metrically similar impeller that would run if it were of such size as to

discharge 1 gpm against a total head of 1 ft. Specific speed is used to

determine the NPSH required by a given impeller. Those that produced

high total dynamic head (TDH) have low specific speeds, and conversely,