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

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900

180

ELSE

ENDIF

CONTINUE

WRITE (i, 180)

FORMAT (78(IH-))

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

WRITE (i, *) CHAR(12)

CLOSE (UNIT = i)

STOP

END

THIS PROGRAM CALCULATES THE DIFFUSION COEFFICIENT OF THE

LIQUID PHASE USING THE WILKE-CHANG METHOD.

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

SUBROUTINE PROGI (DABL, TK, MB, VISB, VA, FACTOR, Y)

DIMENSION VA(I:50), DABL(I:50), u

REAL MB

DO I = i, 12

SUM1 = (7.4*(FACTOR*MB)**0.5*TK)

SUM2 = (VISB*VA(I)**0.6)

DABL(I) = SUMI/SUM2

DABL(I) = DABL(I)/(10**8)

Y(I) = TK/(DABL(I)*VISB*I0**7)

END DO

RETURN

END

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

THIS PROGRAM CALCULATES THE DIFFUSION COEFFICIENT OF THE

GAS PHASE USING THE FULLER, SCHETTLER AND GIDDINGS METHOD

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

SUBROUTINE PROG2 (DABG, TKG, MAG, MBG, VAG, VBG, PRES)

REAL MAG, MBG

SUM3 = ((MAG+MBG)/(MAG*MBG))**0.5

SUM4 = (VAG**0.333+VBG**0.333)**2

DABG = (TKG**I.75*0.001*SUM3)/(PRES*SUM4)

RETURN

END

147

i00

105

ii0

120

PROGRAM PROG24

THIS PROGRAM CALCULATES THE COMPRESSIBILITY FACTOR OF NATURAL

GAS AT A KNOWN SPECIFIC GRAVITY AND TEMPERATURE

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

PP = NATURAL GAS PRESSURE, psia.

SPG = GAS SPECIFIC GRAVITYL, dimensionless

TF = GAS TEMPERATURE, oF.

Z = GAS COMPRESSIBILITY FACTOR.

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

OPEN FILE TO PRINT THE RESULTS.

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

DATA TF /60.0/, SPG /0.550/

WRITE (i, i00)

FORMAT (20X,'COMPRESSIBILITY FACTOR OF NATURAL GAS',

* /IH, 78(IH*))

WRITE (i, 105)

FORMAT (10X, 'TEMPERATURE, oF', 10X, 'SPECIFIC GRAVITY')

WRITE (i,ii0) TF, SPG

FORMAT (10X, F6.0, 20X, F6.3,/)

A1 = 0.001946

A2 = -0.027635

A3 = 0.136315

A4 = -0.238489

A5 = 0.105168

A6 = 3.444"(10"'8)

T = TF + 460.0

WRITE (i, 120)

FORMAT (10X,'PRESSURE psia.',6X,'COMPRESSIBILITY FACTOR Z',

* /, 78(IH-))

PP = I00.0

PI = PP/1000.0

WRITE THE EXPRESSIONS FOR FI, F2, F3, F4, F5

F1 = PI*(0.251*SPG-0.150) - 0.202*SPG + 1.106

F2 = 1.4*EXP(-0.0054*TF)

F3 = (AI*PI**5) + (A2*PI**4) + (A3*PI**3) + (A4*PI**2) + A5*PI

VALI = PI**(3.18*SPG-I.0)

VAL2 = EXP(-0.5*PI)

F4 = (VALI*VAL2)*(0.154-0.152*SPG) - 0.02

VAL3 = -i.039"((Pi-1.8)*'2)

F5 = 0.35*(0.6-SPG)*EXP(VAL3)

VAL4 = 1 + (A6*PI*I0**(I.785*SPG))/(T**3.825)

Z = FI*(I/VAL4+(F2*F3)) + F4 + F5

148

130

140

150

WRITE (i, 130) PP, Z

FORMAT (5X, FI2.0, 15X, F12.5)

PP = PP + i00.0

IF (PP .GT. 5000.0) THEN

GO TO 60

ELSE

GO TO i0

ENDIF

PRINT THE RESULTS ON A NEW PAGE.

WRITE (i, 140)

FORMAT (78(IH-))

WRITE (i, 150)

FORMAT ('I')

TF = TF + i0.0

IF (TF .GT. I00.0) THEN

GO TO 12

ELSE

GO TO 9

ENDIF

= TF -

50.0

SPG = SPG + 0.05

IF (SPG .GT. 0.8) THEN

GO TO 70

ELSE

GO TO 9

ENDIF

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

WRITE (i, *) CHAR(12)

CLOSE (UNIT = i)

STOP

END

149

CHAPTER 3

Fluid Flow

INTRODUCTION

Transportation of fluids is important in the design of chemical pro-

cess plants. In the chemical process industries (CPI), pipework and its

accessories such as fittings, makeup 20% to 30% of the total design

costs and 10% to 20% of the total plant investment. Maintenance

requirements and energy usage in the shape of pressure drop (AP) in the

fluids being pumped add to the cost. Also, these items escalate each

year in line with inflation. As a result, sound pipe sizing practices can

have a substantial influence on overall plant economics. It is the

designer's responsibility to optimize the pressure drops in piping and

equipment and to assess the most economical conditions of operations.

Figures 3-1A and 3-1B illustrate piping layouts in a chemical plant.

The characteristics and complexity of flow pattern are such that most

flows are described by a set of empirical or semi-empirical equations.

These relate the pressure drop in the flow system as a function of flow

rate, pipe geometry, and physical properties of the fluids. The aim in the

design of fluid flow is to choose a line size and piping arrangement that

achieve minimum capital and pumping costs. In addition, constraints

on pressure drop and maximum allowable velocity in the process pipe

should be maintained. These objectives require many trial and error

computations, which can be performed well by a computer.

Flow of Fluids in Pipes

Pressure drop or head loss in a piping system is caused by fluid rising

in elevation, friction, shaftwork (e.g., from a turbine) and turbulence

due to sudden changes in direction or cross-sectional area. Figure 3-2

150

Figure 3-1B. Chemical plant piping layout. Source: I Chem E safer piping training pack-

age (courtesy of the I. Chem E., U.K.)

151

152

Fortran Programs for Chemical Process Design

'4--

-4-"

I.I--

"I::I

1:3

--i-

144xP 1

Tofctt Head Or Energy 5rade Line

Hyd~e Line

_- Pressure heed, P

_- ,q e~.o ci~ ~J beo.d

- ~-~ .---2 o~

=_.-. 9 1 ~

..=--- . .

Etevafion head

~r ArbifrQrY Horizonfc~t Datum Line

Pipe Lengfh ff

h L

v#12g

1/-+4 x P z

144P, #

Zl + p~-- + -2g:-

144P2

- Z 2 + ~-~--+-~-g +h L

Figure 3-2. Distribution of fluid energy in a pipeline.

shows the distribution of energy between two points in a pipeline.

Bernoulli's equation expresses the conservation of the sum of pressure,

kinetic and potential energies.

, f v v+

+ _

(3-1)

Integrating Equation 3-1 gives

2 2

l(p2 P~) + vz-v~ +(z 2 z~)-0 (3-2)

P 2gc

where

P = pressure of fluid, lb/ft 2

p = density of fluid, lbm/ft 3

V - velocity of fluid, ft/s

gc - dimensional constant, 32.174(lbm/lbf)(ft/s 2)

Z = elevation of fluid, ft

subscript 1 -condition at initial point

subscript 2 -condition at final point

Fluid Flow 153

The first, second, and third terms in Equation 3-2 represent pressure

head, velocity head, and static differences respectively. Equation 3-2 is

used for investigating energy distributions or determining pressure dif-

ferentials between any two points in a pipeline. Incorporating the head

loss due to friction, h L, with constant pipe diameter, i.e., V~ = V 2, Equa-

tion 3-2 becomes

1 (P2 - P, ) + (Z2 - Z~ ) - h L (3-3)

Equation 3-3 shows that the head loss, h L, is generated at the expense

of pressure head or static head difference. The static head difference

can be either negative or positive. However, for a negative static

head difference,

AP > h L + (Z 2 - Z l)

(3-4)

In general, pressure loss due to flow is the same whether the pipe is

horizontal, vertical, or inclined. The change in pressure due to the dif-

ference in head must be considered in the pressure drop calculation.

EQUIVALENT LENGTH OF VARIOUS

FITTINGS AND VALVES

The effects of bends and fittings, such as elbow, valves, tees, and

reduction or enlargement of pipes are determined empirically through a

fictituous equivalent length of straight pipe having the same diameter

and they would develop the same pressure drop. The equivalent pipe

length is the most convenient method for determining the overall AP in

a pipe. The drawback to this approach is that, for a given fitting the

equivalent length is not constant but depends on the Reynolds number,

the pipe roughness, the pipe size, and the geometry of the fitting. The

equivalent length is added to the length of actual straight pipe to give

the total length of pipe.

L Total

L ~, + L

eq (3-

where

LTota !

L~t

Leq

= total length of pipe, ft

= length of straight pipe, ft

- equivalent length of pipe, ft

The pressure drop equation can be expressed as:

154

Fortran Programs for Chemical Process Design

( ) v_i

AP- fD~+~K 928 ~

and the head loss equation can be expressed as"

L ) v 2

AH- fD~+ZK 2gc

where D - internal diameter of pipe, ft

fD- Darcy friction factor

K- Excess head loss

L- pipe length, ft

(3-6)

(3-7)

Excess Head Loss

K is a dimensionless factor defined as the excess head loss in a pipe

fitting, and expressed in velocity heads. The velocity head is the amount

of kinetic energy contained in a stream or the amount of potential energy

required to accelerate a fluid to its flowing velocity. Most published K val-

ues apply to fully developed turbulent flow because at high Reynolds num-

ber, K is found to be independent of Reynolds number. However, the two-K

technique includes a correction factor for low Reynolds number. Hooper

[1] gives a detailed analysis of his method compared to others [2,3], and

has shown that the two-K method is the most suitable for any pipe size. In

general, the two-K method is independent of the roughness of the fittings,

but it is a function of Reynolds number and of the exact geometry of the

fitting. The method can be expressed as:

( '/

K- K~ +Koo 1+~ (3-8)

NRe

where K~ - K for fitting

at NRe -

K - K for a large fitting

at NRe - oo

d - internal diameter of attached pipe, inch

The conversion between equivalent pipe length and the resistance coef-

ficient, K, can be expressed as ....

K- fD eq (3-9)

Table 3-1 lists values of K~ and Ko~ for the two-K method.

Table 3-1

Velocity Head Factors of Pipe Fittings

Elbows

Tees

Valves

Fitting Type

Standard (R/D - 1), screwed

Standard (R/D - 1), flanged/welded

Long-radius (R/D- 1.5, all types

90 ~

Mitered elbows

(R/D- 1.5)

45 ~

180 ~

Used as

elbow

Run-

through

tee

Gate,

ball, plug

1 Weld (90 ~ angle)

2 Weld (45 ~ angles)

3 Weld (30 ~ angles)

4 Weld (22 1/2 ~ angles)

5 Weld (18 ~ angles)

Standard (R/D = 1), all types

Long-radius (R/D = 1.5), all types

Mitered, 1 weld, 45 ~ angle

Mitered, 2 weld, 22 1/2 ~ angles

Standard (R/D- 1), screwed

Standard (R/D - 1), flanged/welded

Long radius (R/D - 1.5) all types

Standard, screwed

Long-radius, screwed

Standard, flanged or welded

Stub-in-type branch

Screwed

Flanged or welded

Stub-in-type branch

Full line size, 13- 1.0

Reduced trim, 13- 0.9

Reduced trim, 13 - 0.8

800

1000

800

500

1000

500

800

1000

Kcx~

0.40

0.25

0.20

1.15

0.35

0.30

0.27

0.25

0.20

0.15

0.25

0.15

0.60

0.35

0.30

0.70

0.40

0.80

1.00

200 0.10

150 0.05

100 0.00

300 0.10

500 0.15

1000 0.25

Globe, standard 1500 4.00

Globe, angle or Y-type 1000 2.00

Diaphragm, dam type 1000 2.00

Butterfly 800 0.25

Lift 2000 10.00

Check Swing 1500 1.50

Tilting-disk 1000 0.50

Note: Use R/D = 1.5 values for R/D = 5 pipe bends, 45 ~ to 180 ~ Use

appropriate tee values for flow through crosses.

Source: Hooper [1]

155

156

Fortran Programs for Chemical Process Design

Pipe Reduction and Enlargement

The velocity head is v2/2gc . For any velocity profile the true velocity

represents the integral of the local velocity head across the pipe diam-

eter. It is found by dividing the volumetric flow rate by the cross-sec-

tional area of the pipe and multiplying by a correction factor. For laminar

flow this factor is 2; for turbulent flow the factor depends on both the

Reynolds number and the pipe roughness and (1 + 0.8fD) [4]. Therefore,

when the pipe size changes, the velocity head also changes. Because the

velocity is inversely proportional to the flow area and thus to the diam-

eter squared, K is inversely proportional to the velocity squared.

/ / 4

D 2

K 2 - K l -~,

(3-10)

Although the potential energy provides the flowing fluid with kinetic

energy at the pipe entrance, the kinetic energy is later recovered. This

indicates that the measured pipe pressure will be lower than the calcu-

lated pressure by one velocity head. If the kinetic energy is not recovered

at the pipe exit, the exit counts as a loss of one velocity head. Table 3-2

shows how K varies with changes in pipe size.

PRESSURE DROP CALCULATIONS FOR

SINGLE-PHASE INCOMPRESSIBLE FLUIDS

The pressure drop of flowing fluids can be calculated from the Darcy

friction factor:

AP _ fD

9

9 V2

- (3-11)

L D 2g c

where fD = Darcy friction factor

9 = density of fluid,

lbm/ft 3

V - velocity of fluid in the pipe, ft/s

gc = dimensional constant, 32.174(lbm/lbf)(ft/s 2)

L - length of pipe, ft

Friction Factor

The friction factor is related to the Reynolds number by a set of corre-

lations and depends on whether the flow regime is laminar, transitional,

or turbulent. The Reynolds number is: