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 10.0-1. 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
1 1 t ln k 1 X (b) Wht reidence time i required t rech cnverin f 95? k k E exp T 10exp 5000 8.314*300 1.347 t 1 1 1 1 ln ln 2. k 1 X 1.347 1 0.95 224 (c) Wht reidence time i required t rech cnverin f 95 if the rectin rte prefctr i 1 k k E exp T 20exp 5000 8.314*300 2.694 t 1 1 1 1 ln ln 1. k 1 X 2.694 1 0.95 112 (d) Wht reidence time i required t rech cnverin f 95 if the ctivtin energy i 1 k k E exp T 10exp 10000 8.314*300 0.1815 t 1 1 1 1 ln ln 16. k 1 X 0.1815 1 0.95 51 (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 1 1 1 1 ln ln 2. k 1 X 1.347 1 0.95 224 (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
t 1 1 1 1 ln ln 2. k 1 X 1.347 1 0.95 224 (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 10 0.9999986 1 (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 2.224 ecnd, then we cn prduce ml 1 ml 9500 4271 3 3 m 2.224 m In rder t get 10 ml/, ml 4271 V m 3 10 ml the vlume i 0.002341 m 3 r 2.341 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 1 1 1 1 ln ln 2. k 1 X 1.347 1 0.98 904 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 2.904 ecnd, then we cn prduce ml 1 ml 9800 3374 3 3 m 2.904 m In rder t get 10 ml/, 3374 ml ml V m 3 10 the vlume i 0.002963 m 3 r 2.963 liter.
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 0.001-1. 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);
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: 15 10 y 5 0 0 1000 2000 3000 4000 5000 6000 7000 8000 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?
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) 2.9304000e+003 5.1040049e-001 5.5104005e+000 9.4895995e+000 2.9376000e+003 5.0768060e-001 5.5076806e+000 9.4923194e+000 2.9448000e+003 5.0497654e-001 5.5049765e+000 9.4950235e+000 2.9520000e+003 5.0228819e-001 5.5022882e+000 9.4977118e+000 2.9592000e+003 4.9961545e-001 5.4996155e+000 9.5003845e+000 2.9664000e+003 4.9695822e-001 5.4969582e+000 9.5030418e+000 2.9736000e+003 4.9431639e-001 5.4943164e+000 9.5056836e+000 2.9808000e+003 4.9168986e-001 5.4916899e+000 9.5083101e+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]);
x y(1) y(2) y(3) 2.1900000e+004 5.0299964e-001 5.5029996e+000 9.4970004e+000 2.1930000e+004 5.0149525e-001 5.5014952e+000 9.4985048e+000 2.1960000e+004 4.9999576e-001 5.4999958e+000 9.5000042e+000 2.1990000e+004 4.9850117e-001 5.4985012e+000 9.5014988e+000 2.2020000e+004 4.9701144e-001 5.4970114e+000 9.5029886e+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) 9.8640000e+002 2.6110780e+000 7.6110780e+000 7.3889220e+000 9.9360000e+002 2.5918983e+000 7.5918983e+000 7.4081017e+000 1.0008000e+003 2.5729072e+000 7.5729072e+000 7.4270928e+000 1.0080000e+003 2.5541020e+000 7.5541020e+000 7.4458980e+000 1.0152000e+003 2.5354802e+000 7.5354802e+000 7.4645198e+000 S t 1000, the cnverin i but 74.3. (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 0.003211 0.003211 11. 56 l 2959 l l l hr In rder t get 10 ml/hr, ml ml 11.56 V 10 l hr hr the vlume i 0.865 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
E k k exp T The temperture i 300 K. The ctivtin energy i 5000 J/ml. The rte cntnt prefctr i 10.0-1. 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 0.95 1 X 1 0.95 19 (c) Wht reidence time i required t rech cnverin f 95? k k E exp T 10exp 5000 8.314*300 1.347 1 D kt
t D 19 14. k 1.347 1 (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 0.07089 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 14.1. V tf 14.1 2 28. 2liter (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 10526 ml/hr f. cme in t 10 ml/liter. S we need FC N F N C ml liter liter F 10526 1053 hr 10ml hr The reidence time fr 95 cnverin i 14.1 r 0.003917 hr. V tf 0.003917 1053 4. 124liter