CBE 450 Chemical Reactor Fundamentals Fall, 2009 Homework Assignment #4 Solutions

Transcription

1 CBE 450 Chemicl ectr Fundmentl Fll, 2009 Hmewrk ignment #4 Slutin 1. Btch ectr nlyi vi nlyticl Exprein Cnider the fllwing imeriztin rectin B with n elementry mechnim uch tht the rte i r kc where the rte cntnt i given by E k k exp T The temperture i 300 K. The ctivtin energy i 5000 J/ml. The rte cntnt prefctr i The initil cncentrtin f i 10.0 ml/liter. () Prvide n nlyticl exprein fr the reidence time required t chieve pecified cnverin fr thi rectin in btch rectr. (b) Wht reidence time i required t rech cnverin f 95? (c) Wht reidence time i required t rech cnverin f 95 if the rectin rte prefctr i (d) Wht reidence time i required t rech cnverin f 95 if the ctivtin energy i (e) Wht reidence time i required t rech cnverin f 95 if the rectr vlume i (f) Wht reidence time i required t rech cnverin f 95 if the inlet cncentrtin i (g) Wht cnverin will ne btin if the reidence time i 10? (h) Wht rectr vlume i required t prduce 10 ml/ f B t 95 cnverin? (i) Wht rectr vlume i required t prduce 10 ml/ f B t 98 cnverin? Slutin: () Prvide n nlyticl exprein fr the reidence time required t chieve pecified cnverin fr thi rectin in btch rectr. Frm Fgler pge 150

2 1 1 t ln k 1 X (b) Wht reidence time i required t rech cnverin f 95? k k E exp T 10exp * t ln ln 2. k 1 X (c) Wht reidence time i required t rech cnverin f 95 if the rectin rte prefctr i 1 k k E exp T 20exp * t ln ln 1. k 1 X (d) Wht reidence time i required t rech cnverin f 95 if the ctivtin energy i 1 k k E exp T 10exp * t ln ln 16. k 1 X (e) Wht reidence time i required t rech cnverin f 95 if the rectr vlume i eidence time den t depend n rectr ize fr thi rectin. t ln ln 2. k 1 X (f) Wht reidence time i required t rech cnverin f 95 if the inlet cncentrtin i eidence time den t depend n initil cncentrtin fr thi rectin. 1

3 t ln ln 2. k 1 X (g) Wht cnverin will ne btin if the reidence time i 10? 1 1 t ln k 1 X kt 1 exp1.347 X exp (h) Wht rectr vlume i required t prduce 10 ml/ f B t 95 cnverin? The initil cncentrtin i 10 ml/liter r 10,000 ml/m 3. If we cnvert 95 f thi, then ur cncentrtin f B i 9500 ml/m 3. If ur reidence time i ecnd, then we cn prduce ml 1 ml m m In rder t get 10 ml/, ml 4271 V m 3 10 ml the vlume i m 3 r liter. (i) Wht rectr vlume i required t prduce 10 ml/ f B t 98 cnverin? If we wnt 98 cnverin, the reidence time i t ln ln 2. k 1 X The initil cncentrtin i 10 ml/liter r 10,000 ml/m 3. If we cnvert 98 f thi, then ur cncentrtin f B i 9800 ml/m 3. If ur reidence time i ecnd, then we cn prduce ml 1 ml m m In rder t get 10 ml/, 3374 ml ml V m 3 10 the vlume i m 3 r liter.

4 2. Btch ectr nlyi vi Numericl Methd Cnider the fllwing rectin + B C with n elementry mechnim uch tht the rte i r kc C B where the rte cntnt i given by E k k exp T The temperture i 300 K. The ctivtin energy i 5000 J/ml. The rte cntnt prefctr i The rectr h vlume f 1 m 3. The initil cncentrtin f i 10.0 ml/liter. The initil cncentrtin f B i 15.0 ml/liter. () Ue Mtlb t crete plt f the cncentrtin f, B nd C functin f time fr the firt 7200 f the rectin. Lbel, B nd C n the plt. Prvide yur input file fr ydeinput.m. (b) Ue thi plt (r the tbulr frm f the dt in the plt) t determine wht reidence time i required t rech cnverin f 95? (c) Wht reidence time i required t rech cnverin f 95 if the ctivtin energy i (d) Wht cnverin will ne btin if the reidence time (with the riginl ctivtin energy) i 1000? (e) Wht rectr vlume i required t prduce 10 ml/hr f C t 95 cnverin? Slutin: () Ue Mtlb t crete plt f the cncentrtin f, B nd C functin f time fr the firt 7200 f the rectin. functin dydt = ydeinput(x,y,nvec); hmewrk fur prblem 2 + B --> C nu = -1; nub = -1; nuc = 1; C = y(1); CB = y(2);

5 CC = y(3); k = 1.0e-3; ^-1 E = 5000; J/ml = 8.314; J/ml/K T = 300; K k = k*exp(-e/(*t)); rte = k*c*cb; blnce n in term f cnc f dydt(1) = nu*rte; blnce n B in term f cnc f B dydt(2) = nub*rte; blnce n C in term f cnc f C dydt(3) = nuc*rte; The cmmnd I ued w yde(2,1000,0,7200,[10,15,0]); which generted thi plt: y x legend: blck =, red = B, blue = C. (b) Ue thi plt (r the tbulr frm f the dt in the plt) t determine wht reidence time i required t rech cnverin f 95?

6 If the initil cncentrtin f w 10 ml/liter, then fter 95 cnverin, the cncentrtin f C i 9.5 ml/liter. Frm the dt file, yde.ut, x y(1) y(2) y(3) e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e+000 S, the reidence time i but 2959 ec t rech 95 cnverin. (c) Wht reidence time i required t rech cnverin f 95 if the ctivtin energy i functin dydt = ydeinput(x,y,nvec); hmewrk fur prblem 2 + B --> C nu = -1; nub = -1; nuc = 1; C = y(1); CB = y(2); CC = y(3); k = 1.0e-3; ^-1 E = 10000; J/ml = 8.314; J/ml/K T = 300; K k = k*exp(-e/(*t)); rte = k*c*cb; blnce n in term f cnc f dydt(1) = nu*rte; blnce n B in term f cnc f B dydt(2) = nub*rte; blnce n C in term f cnc f C dydt(3) = nuc*rte; The cmmnd I ued w yde(2,1000,0,30000,[10,15,0]);

7 x y(1) y(2) y(3) e e e e e e e e e e e e e e e e e e e e+000 S the reidence time fr 95 cnverin i 21,960 ec. (d) Wht cnverin will ne btin if the reidence time (with the riginl ctivtin energy) i 1000? Frm the utput file, yde.ut, f the firt run, we hve x y(1) y(2) y(3) e e e e e e e e e e e e e e e e e e e e+000 S t 1000, the cnverin i but (e) Wht rectr vlume i required t prduce 10 ml/hr f C t 95 cnverin? t 95 cnverin f C, we btin 9.5 ml/liter f C fter 2959 ec. 9.5 ml 1 ml ml ml l 2959 l l l hr In rder t get 10 ml/hr, ml ml V 10 l hr hr the vlume i liter. 3. CST nlyi vi nlyticl Exprein Cnider the fllwing imeriztin rectin B with n elementry mechnim uch tht the rte i r kc where the rte cntnt i given by

8 E k k exp T The temperture i 300 K. The ctivtin energy i 5000 J/ml. The rte cntnt prefctr i The inlet flwrte i 2 liter/ec. The cncentrtin f in the inlet trem i 10 ml/liter. () Prvide n nlyticl exprein fr the reidence time required t chieve pecified cnverin fr thi rectin in btch rectr. (b) Wht i the Dmköhler number fr 95 cnverin? (c) Wht reidence time i required t rech cnverin f 95? (d) If the vlume f the rectr i 1 liter, wht i the vlumetric flwrte f the inlet trem? (e) If the inlet flwrte i 2 liter/ec, wht vlume i required t btin 95 cnverin? (f) If the rectr i perting t 95 cnverin nd yu wnt t prduce 10,000 ml/hr f B, determine the vlume f the rectr nd the vlumetric flwrte required. Slutin: () Prvide n nlyticl exprein fr the reidence time required t chieve pecified cnverin fr thi rectin in btch rectr. X D 1 D k 1 k errnging thi fr the reidence time yield 1 X k 1 X (b) Wht i the Dmköhler number fr 95 cnverin? errnge the bve exprein. D X X (c) Wht reidence time i required t rech cnverin f 95? k k E exp T 10exp * D kt

9 t D k (d) If the vlume f the rectr i 1 liter, wht i the vlumetric flwrte f the inlet trem? V t F V 1 l F t 14.1 (e) If the inlet flwrte i 2 liter/ec, wht vlume i required t btin 95 cnverin? The reidence time fr 95 cnverin i V tf liter (f) If the rectr i perting t 95 cnverin nd yu wnt t prduce 10,000 ml/hr f B, determine the vlume f the rectr nd the vlumetric flwrte required. We wnt 10,000 ml/hr f B, which t 95 cnverin require ml/hr f. cme in t 10 ml/liter. S we need FC N F N C ml liter liter F hr 10ml hr The reidence time fr 95 cnverin i 14.1 r hr. V tf liter