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ed stream, since there is no heat loss to the surroundings in an adiabatic reactor. The heat capacity of the catalyst and the reactor wall are not included in the heat balance, since once the steadystate temperature profile is established, the solids cannot store any more energy, and all the heat released must be absorbed by the flowing gas. From Eqs. () and (), () () 57 Adiabatic Reactors 00()()AFMpAAAFMpF x HTTFcF FCC x HTTFc???????????since , another form of Eq. () is 58 Adiabatic Reactors 0s l o p e = ( )A M pC H c????59 Adiabatic Reactors ? ? ? ?20 2 12AFMpC H x xTTc???? ???If a higher conversion is needed, the gases are cooled in an external exchanger and sent to a second bed. The temperature change in the second bed is proportional to the increase in conversion, and the slope is generally taken to be the same as for the first bed: () In some cases, three or four beds in series are used to get nearly plete conversion. 60 Adiabatic Reactors 0Ay? ?0100 of e a c h ga s i n t he pr odu c t a v e r a ge he a t c a pa c i t y f or ( T )AFFi piipi Fy x H TTTncw he ren m ol e scT?????????Taking 100 moles of feed as a basis, with mole fraction A, the heat balance can be written as () 61 Adiabatic Reactors The temperature pattern is then of the type shown in Figure for a threestage converter with two quenches. This type of converter is used for ICI’s lowpressure methanol synthesis [6]. send only part of the feed to the first stage and to use the rest of the feed to mix with and cool the hot gases between stages. 62 Adiabatic Reactors T but too high a feed temperature can lead to rapid catalyst fouling or greater formation of byproducts maxx63 Optimum Reaction Temperature 64 Optimum Reaction Temperature 12/11/2212 r rA t 0 or E RTA B A BE RTC D C DoptA B C Dk P P ae P Pk P P be P PTdr drdrdT dT dT??????????When both reactions have simple kiics and follow the Arrhenius relationship, an equation for can be obtained. Consider the reaction optT65 Optimum Reaction Temperature 1212// 12221211 11 c a nc e l i ng te r m s a nd r e pl a c i ng the e xpo ne nti a l t e r m s wit h k a nd k giv e s A B C DE RT E RTA B C DA B Cdk dkP P P PdT dTEEP P ae P P beR T R TP P k E P???? ? ? ?? ? ? ?? ? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ??221221 1122 A t e quil i br i um , k a nd =optDCDABat TCDA B C D e qABP k EPPkEk P P EPP kP P k P P KP P k? ? ? ? ? ??? ? ? ? ? ?? ? ? ? ? ???At constant position, () 66 Optimum Reaction Temperature ? ?? ?? ?? ?122 T1TT1 T2T2 2 2 T1 1 1 L HS : = = e = e R HS : e E optopt optoptoptoptCDeqatABEE HRReqHRCDeqABPP EKP P Ek aaKk b bPP E E EaKP P E E b E? ?????? ? ? ??? ? ? ?? ? ? ?? ? ? ? ? ???? ? ? ? ? ?? ? ? ? ? ?TT21q u a t i n g t e r m s : e e opt optHHRREaab b E???????????therefore () 67 Optimum Reaction Temperature TT212121 t e r m s : e eT a ki ng t he na t ur a l l oga r i t hm : l nTT11 l n TT a known T ,Eq.( ) c a n beo p t e qH R H Rop t e qop t e qeqEquati ngEaab b EEHHR R EE HERFor? ? ? ????????????????????????? ?????????? sol v e f or T :opt() 68 Optimum Feed Temperature The amount of catalyst needed depends on the feed temperature and the conversion 69 Optimum Feed Temperature 70 PRESSURE DROP IN PACKED BEDS ? ?22002 331 5 0 ( 1 ) 1 .7 5 1()spspuuPLd d??????? ? ?????The pressure drop in a fixed bed can be calculated from the Ergun equation [10]: () 71 End