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

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Fluid Flow 187

150(1- ~)2 laV 1.75(1- ~) GV

gc - e3

" D 2 +

E 3 9

p Dp

where AP = pressure drop

L = unit depth of packed bed

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

= viscosity of fluid, lb/ft.h

V = superficial fluid velocity, ft/s

Dp- effective particle diameter, ft

E = void fraction of bed

9 = fluid density, lb/ft 3

(3-98)

Equation 3-98 gives the total energy loss in fixed beds as the sum of

viscous energy loss (the first term on the right side of the equation) and

the kinetic or turbulent energy loss (the second term on the right side of

the equation). For gas systems, approximately 80% of the energy loss is

dependent on turbulence and can be represented by the second term of

Equation 3-98. In liquid systems, the viscous term is the major factor.

The Equation

The original Ergun equation of the total energy loss can be rearranged

as follows:

BL 1-E

APT = 9 9

144 ~3

G 2 [ 150(2. 419g)(1 - ~) + 1. 751 (3_99)

Dpgcp DpG

e = fraction void volume of bed,

ft 3 ,

void/ft 3 of packed tower volume

volume of void

volume of bed

I(mass ~ bed / - (mass ~ bed/1

~bed Pcatalyst

mass of bed

Pbed

188

Fortran Programs for Chemical Process Design

= Pc - 9b (3-100)

9c - density of catalyst, lb/ft 3

9b --

density of the packed bed, lb/ft 3

p _ w (3-101)

10.73ZT

6(1-

(3-102)

Dp- S

s - (1-

V 9 Ap

(3-103)

For cylindrical particles

1 pD 2 9 _ 9 PL (3-104)

Vp = 1728 4

1 I/tepD2 1

Ap = ~144 2 + rc 9 PD 9 PL (3-105)

Reynolds number

GDp

NRe = (3-106)

2.419g(1 -- ~)

Friction factor

For laminar flow with

NRe <

150 (3-107)

fp -- NR e

For intermediate Reynolds number

150

f = + 1.75 (3-108)

P NRe

For completely turbulent flow, it is assumed that fp approaches a con-

stant value for all packed beds with the same relative roughness. The

constant is found by experiment to be 1.75 [26].

Fluid Flow 189

Nomenclature

A = cross-sectional area of bed,

ft 2

area of particles, ft 2

B L = bed length, ft

Dp- effective particle diameter, ft

fp- friction factor

gc - gravitational constant - 4.17 x 108((lb m/lbf ) 9 (ft/h 2 ))

G = superficial mass velocity = W/A, lb/h.ft 2

MW = molecular weight of fluid

NRe = Reynolds number, dimensionless

P = fluid pressure, psia

PD - particle diameter, inch

PL = particle length, inch

S = packed bed surface area, ftz/ft 3 bed

T = fluid temperature, ~

Vp- volume of particles, ft 3

W = fluid flow rate, lb/h

Z = compressibility factor

APT = total pressure drop in packed bed, lb/in 2

= fraction voids in packed bed

9 = density of fluid at flowing conditions, lb/ft 3

= fluid viscosity, cP (1 cP = 2.4191b/ft h)

SCREEN HANDLING

The code in this book makes use of a suite of subroutines for screen

handling that have been developed from those given by Ward and

Bromhead [27,28].

In principle, a number of subroutines are invoked by my code, and

these in turn invoke other, lower level subroutines. The top level sub-

routines are called:

GETTXT

GETINT

GETFLO

and

190

Fortran Programs for Chemical Process Design

GETTXT is perhaps the simplest of these. It uses ANSI control

sequences to locate the cursor on the screen, to highlight a box for text

entry, and through assembly-language-coded calls to an MS DOS func-

tion, intercepts individual keypresses and builds them into a text string

in the text entry box.

The low level functions that use the ANSI codes are coded into

GOTOXY Cursor location (FORTRAN)

REVID

Turn reversed video effect on (ASM)

NORMAL Restore normal video (no attributes) (ASM)

SHWTXT Display string (FORTRAN)

From these further calls to assembly language routines that call DOS

functions are made. These routines are:

GETCHR

SHWBYT

Get character from keyboard buffer

Display character string

Analogous routines to GETTXT are provided for inputting INTE-

GER and FLOATING POINT (REAL) variables, and they are called

GETINT and GETFLO. In principle, they are identical to GETTXT,

but they perform the additional tasks of intercepting invalid keypresses

(e.g., no alphabetic characters are permitted nor can the decimal point

be duplicated, etc.) and converting from a text string into a valid num-

ber format. A routine BEEP is provided to send ASCII 07 (BEL) to the

screen, which drives the PC's internal speaker.

The subroutine MENU displays a list of mnemonics on the screen at

predefined locations. In my code, these mnemonics are usually in a ver-

tical stack, and they are all accompanied by a line of explanatory text

per mnemonic. Use of the cursor keys causes a highlighted bar to step

through the mnemonics. Pressing the RETURN key selects the option

equivalent to the currently selected mnemonic.

In addition to the GETxxx subroutines, I sometimes need to display

text or numbers at predefined locations on the screen. The GOTOXY

and SHWTXT calls are put together in DISTXT, DISINT, and DISFLO

(DIS implying DISplay). Some other routines which are used to create

special effects are

BORDER

COLORS

Fluid Flow 191

BORDER

permits me to draw rectangular boxes on the screen using

the extended character set line-drawing characters (both single and

double). COLORS uses the ANSI codes to set foreground and back-

ground colors. The advantage of using the ANSI screen control system

is that it makes many of the jobs involved in screen control simple for

the FORTRAN programmer, but at a cost: the computer on which the

software is run must have ANSI.SYS loaded. Under DOS 5 or DOS 6,

ANSI.SYS can be loaded "high," which prevents it from taking up valu-

able conventional DOS memory. There are various "enhanced

ANSI.SYS" utilities which are public domain or shareware, including

FANSI and NANSI. Another useful utility is ANSI.COM (PC Maga-

zine, Ziff Davies Publishing), which has the advantage of being

unloadable if the user wishes to reclaim the small amount of memory

that it consumes.

Title Screen and Keyboard Utilities

CSSANDK SEGMENT

PUBLIC

CLS

CLRSTRG

CLS

PROC

PUSH

MOV

INT

POP

ENDP

PUBLIC PARA 'CODE'

ASSUME CS:CSSANDK

FAR

AH, 9

DH, SEG CLRSTRG

DS, DX

DX, OFFSET CLSRTRG

21H

1BH,'[2J$'

REVID

PUBLIC

PROC

PUSH

MOV

INT

REVID

FAR

AH, 9

DX, SEG REVSTR

DS, DX

DX, OFFSET REVSTR

21H

192 Fortran Programs for Chemical Process Design

REVSTR

REVID

POP DS

RET

DB 1BH,'[7m$'

ENDP

NORMAL

NORSTR

NORMAL

PUBLIC

PROC

PUSH

MOV

INT

POP

RET

ENDP

NORMAL

FAR

AH, 9

DX, SEG NORSTR

DS, DX

DX, OFFSET NORSTR

21H

1BH,'[0m$'

SHWBYT

PUBLIC

PROC

PUSH

MOV

LDS

INT

POP

RET

ENDP

SHWBYT

FAR

AH, 09H

BP, SP

DX, [BP+6]

21H

04H

GETCHR

PUBLIC

PROC

PUSH

MOV

INT

MOV

LES

XOR

MOV

POP

RET

ENDP

GETCHR

FAR

AH, 08H

21H

BP, SP

BX, DWORD PTR[BP+6]

AH, AH; this zeroes AH

ES:[BX], AX; better than MOV

04H

Fluid Flow 193

KBCLEAR

WHILE:

RETURN:

KBCLEAR

PUBLIC KBCLEAR

PROC FAR

PUSH BP

MOV BP, SP

MOV

INT

MOV

INT

JMP

AH, 0BH

21H

AL, AL

SHORT RETURN

AH, 08H

21H

SHORT WHILE

POP

RET

ENDP

CURSOF

PUBLIC

PROC

PUSH

MOV

INT

POP

RET

ENDP

CURSOF

FAR

CX, 2000H

AH, 1

10H

CURSBLK

PUBLIC

PROC

PUSH

MOV

INT

POP

RET

ENDP

CURSBLK

FAR

CX, 0007H

AH, 1

10H

CURSON

PUBLIC

PROC

PUSH

MOV

CURSON

FAR

CX, 0607H

194

Fortran Programs for Chemical Process Design

CURSON

CSSANDK

MOV

INT

POP

RET

ENDP

AH, 1

10H

ENDS

END

Fortran Subroutines

SUBROUTINE CLS

WRITE(*, 100) CHAR(27)//'[2J'

100 FORMAT(A4/)

RETURN

END

SUBROUTINE REVlD

WRITE(*, 100) CHAR(27)//'[7m'

100 FORMAT(A4/)

RETURN

END

SUBROUTINE NORMAL

WRITE(*, 100) CHAR(27)//'[0m'

100 FORMAT(A4/)

RETURN

END

SUBROUTINE SHWBYT (STR, NSTR)

CHARACTER*(*) STR

WRITE(*, 100) STR(I:NSTR)

100 FORMAT(A/)

RETURN

END

PROBLEMS AND SOLUTIONS

Problem 3-1

A piping isometric (Figure 3-8) shows a 6-inch (Schedule 40) line

with six 90~ elbows and two flow-through tees. The actual length of

Fluid Flow 195

" ALL DIMENSIONS ARE IN FEET

~~ USE LONG RADIUS ELBOWS

~41~

ACTUAL LENGTH

long

rodius elbows

2 flow-ihrough lees

0-. s

Figure 3-8. Piping isometric layout.

pipe is 78 ft. The fluid flow is 75,000 lb/h and its physical properties are

viscosity B = 1.25 cP, density P = 64.30 lb/ft 3, and pipe roughness e =

0.00015 ft. Calculate the equivalent length of pipe fittings, total length

of the pipe, velocity head, head loss, and the overall pressure drop.

Solution

The computer program PROG31 is a subroutine in the screen handling

suites of programs used to calculate the parameters for the 6-inch (Sched-

ule 40) pipe. The software program PIPECAL is run to determine the

total length of the pipe (i.e., the sum of the straight length of the pipe

and the equivalent length due to pipe fittings), the head loss, the pres-

sure drop per 100 ft of pipe, and the overall pressure drop. Table 3-8

gives the computer output from the screen handling software program.

The equivalent length due to pipe fittings is 38.3 ft, the total pipe length

is 116.3 ft, the excess head loss is 0.196 ft, the pressure drop per 100 ft

of the pipe is 0.075 psi, and the overall pressure drop is 0.088 psi.

196 Fortran Programs for Chemical Process Design

Table 3-8

Computer Output From the Screen Handling Programs

PRESSURE DROP CALCULATION OF AN INCOMPRESSIBLE FLUID IN A PIPE LINE

PIPE INTERNAL DIAMETER,

inch:

MASS FLOW RATE,

ib/h:

VOLUMETRIC FLOW RATE,

gal/min.:

FLUID VISCOSITY,

cP:

FLUID DENSITY, Ib/ft.^3:

FLUID VELOCITY,

ft/sec.:

VELOCITY HEAD LOSS DUE TO FITTINGS:

EQUIVALENT LENGTH OF PIPE,

ft:

ACTUAL LENGTH OF PIPE,

ft:

TOTAL LENGTH OF PIPE, ft.:

REYNOLDS NUMBER:

PIPE ROUGNESS, ft.:

DARCY FRICTION FACTOR:

EXCESS HEAD LOSS,

ft:

PIPE PRESSURE DROP/100 ft, psi/100ft:

OVERALL PRESSURE DROP OF PIPE,

psi:

___

6.065

75000.00

145.44

1.2500

64.3000

1.614

1.5960

38.3099

78.0000

116.3099

62424.

.000150

.0211

.1961

.0754

.0877

Running Pipecal

The computer program PIPECAL, as well as the other programs

described in the screen handling, has been compiled to calculate the

equivalent length due to pipe fittings, the total length of the pipe, veloc-

ity head, the head loss, the pressure drop per 100 ft of pipe, and the

overall pressure drop for any given pipe size, fluid flow rate, and its

physical properties. To run the program from either the floppy diskette

or a hard drive, type after the A or C:\> prompt from the command line,

PIPECAL.EXE (or PIPECAL) followed by a return key.

For example, A or C:\>PIPECAL.EXE (or PIPECAL)

A title is displayed and the user then presses any key from the PC con-

sole to continue. Once the screen is cleared, a list of eight options is

displayed as follows:

1. OPEN

2. CREATE

3. SAVE

4. CALCS

5. PRT RES

6. SAVE RES

7. FINISH

8 QUIT

Open a pre-existing file

Create a new data file

Save the data file you just edited

Start calculating

Print the result file

Save the result file

Next problem?

Exit to DOS

PIPECAL is user-friendly and the procedure in running the program is

as follows: