Unformatted text preview: omputer Sec. 2.7 201 1 ( i.e., the output
2. The modu
Ivergence may be
of one mOl
nal costs may be
slower tha
high.
3 . To specify
j have to place a
control bl e
such that design
specificatioll:> a le meL 1 nls arrangement creates a loop. I f the values of many
design variables are to be determined , you might end up with several nested
loops of calculation. Consequently, the concept of t earing has evolved in connection with modular
flowsheeting codes to solve material (and energy) balances. Tearing involves decou
piing the interconnections between the modules so that sequential information flow
takes place. Tearing is required because o f loops of information created by recycle
streams. What you do in tearing is to provide guesses for values of some of the un
knowns (the t ear variables), usually the recycle streams, and then calculate the val
ues o f the tear variables from the modular subroutines. These calculated values form
new guesses , and so on, until the differences between the guessed values and the
calculated values are sufficiently small.
We cannot go into all of the detail s of flowsheeting program construction and
application here. Refer to Chapter 5 and the to supplementary references at the end
of this chapter for further information. However , let us look at an example of a very
simple process with recycle to compare the simultaneous equation and modular solu
tion techniques just to illustrate the concepts. EXAMPLE 2 .30 C omparison o f Simultaneous Equation and Modular Techniques o f Solving \1aterial Balances Figure E 2.30 i llustrates a t wostage p ro cess with one recycle stream. T h e o bjective is to use
the total m aterial b alances for t he p roce ss to calculate the a mount o f the recycle s tream R as
a function o f a , t he fraction o f A r ecycled. Use a = and a = 0 .90 for the c omparison. 1 R F = 100 _l..l.'~~Il..__
, P Q R = A Figure E2.30 Sulution
T he m aterial b alances a re
U nit I :
Unit 2: 100 +R = A A =R+P (a)
(b) T he f raction recycle is
A ll' = R (c) M aterial Balances 202 C hap. 2 We have three independent equations to be solved containing three variables whose values are
unknown. A ny o f t he methods mentioned in Appendix L might be used to solve the equa
tions. Gaussian elimination starts with the format = 100 A R (a') A RP=O
erA  R (b') (c') =0 o I I 100]
I0
oI 0 I ]
] a nd successive e lementary o perations result in the matrix o 0 1 00(]) 0 100 o
o Ia (_a_)
Ia 0 100 l eading to the solution A 100(_1_)
Ia
R = 1 00(_a_) Ia P = ] 00
F or t he t wo g iven values o f a , a =!
) 150
50
100 A
R
P a = 0.9
1000
900
100 Next. the modular approach to the solution o f the problem would involve solving unit I
for A first assuming a value for R, t he tear variable. Then unit 2 would be solved, the value o f
R c alculated, and the value calculated c ompared with the assumed value. I f t he e rror is nO[
s mall enough , the new value o f R f rom unit 2 would become the assumed value o f R for unit
1, unit 1 solved again for A , and unit 2 solved again. The sequence o f s olutions would be re
peated until the error in R b ecame sufficiently small. Because R is initially not known, sup
pose that we start with R = 0 and A = 100 as the initial guesses. Thereafter
Unit I: (d J Unit 2: (e ) w here k d esignates the stage in the iteration. 3i B alances C hap. 2 C hap. 2 203 S upplementary R eferences S uccessive calculations yield a riab les whose values a re
= used to solve the equa Ct' ( a') A =~ = a = 0.9 100 + R = (b') k R (c ' ) I
2
3
4 0
33 .33
4 4.44
4 8 .15 100
133.33
144.44
148.15 3 3.33
4 4.44
4 8.15
4 9.38 5 0.00 1 50.00 5 0.00 A 0
90
171
2 43.9 9 00 R Aa R = 100 + R R 100
190
271
3 43.9 1 000 = Aa 90
171
2 43.9
3 09.5 9 00 I nsofar as this book is concerned , if you a re not familiar with a ftowsheeting c ode, you
will find it will be more trouble to solve a material balance problem using a ftowsheeting
code than it will be to use a standard equationsolving code such as o ne o f those in the disk
pocket in the back o f t he book . SelfAssessment Test
1. S olve o ne o r t wo o f t he examples in Sec. 2 .6 a nd 2 .7 using
(a)
(b)
(c)
(d)
(e) A
A
A
A
A personal c omp uterbased e quationsolving code
code from the disk in the pocket in the back o f this book
c ode t aken f rom y our c omputer c enter l ibrary
spreadsheet p rogram
ftowsheeting code S UPPLEMENTARY REFERENCES
G eneral
BENSON , S . W ., C hemical Calculations, 2 nd e d., W iley, New York, 1963. ;Juld involve solving unit I
Jl d be solved , the value o f
value. I f t he e rror is not
5umed value o f R f or unit
o f s olutions would be re
initially not k nown, sup
Thereafter (di
(el FELDER , R. M ., a nd R. W. ROUSS EAU, Elementary Principles 01 Chemical Processes, 2 nd e d., Wiley, New York, 1986 .
HUS AIN, ASGHAR, C hemical Process Simulation , H alstead (Wiley) , New Delhi, 1986.
MYERS, A . L. , and W. D. SEIDER, Introduction to Chemical Engineering and Computer Calcu
lations , P renticeHall, E nglewood Cliffs, N .J., 1976 .
NASH, L ., Stoichiometry, AddisonWesley, Reading , M ass., 1966.
National Technical Information Service, Flue Gases: Detection, Sampling, Analysis, PB 86
8712901GAR, N TIS, S pringfield, Va., 1986 .
RANZ , W. E ., D escribing Chemical Engineering Systems, M cGrawHill , New York, 1970 .
RAo, Y. K ., Stoichiometry and Th ermodynamics 01 Metallurgical Processes, C ambridge Uni
versity P ress, New York, 1985. ...
View
Full
Document
This note was uploaded on 09/26/2011 for the course CH E 2002 taught by Professor Mc,f during the Fall '08 term at The University of Oklahoma.
 Fall '08
 Mc,F

Click to edit the document details