Himmelblau 5th ed Ex 2.30

Himmelblau 5th ed Ex 2.30 - omputer Sec 2.7 201 1 i.e the...

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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 wo-stage 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--.'~~I----l..-__ , 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 -R-P=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 I-a (_a_) I-a 0 100 l eading to the solution A 100(_1_) I-a R = 1 00(_a_) I-a 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 equation-solving code such as o ne o f those in the disk pocket in the back o f t he book . Self-Assessment 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 uter-based e quation-solving 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 rentice-Hall, E nglewood Cliffs, N .J., 1976 . NASH, L ., Stoichiometry, Addison-Wesley, 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 cGraw-Hill , New York, 1970 . RAo, Y. K ., Stoichiometry and Th ermodynamics 01 Metallurgical Processes, C ambridge Uni­ versity P ress, New York, 1985. ...
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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.

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