Chapter 5 Analysis and Design of Biochemical Reactors
Chapter 5 Analysis and Design of Biochemical Reactors
Chapter 5 Analysis and Design of Biochemical reactors 5.cOncept of Design of Bioch. Reactors 5.1.cLassification Bioch. Reactors Batch Semi-Batch operation Continua operation operation Bio-block Reactors Bio-membrane reactors Full mix Plug flow Full mix Plug flow patter pattern pattern pattern, Stir tank Plug flow Fluid flow reactor Immobilized reactor reactor Cycle pipe reactor bio-disc Cycle reactor Bubble reactor Full mix membrane Leaching filter Loop reactor Multi-cascade reactor reactor Mem brane reacto
Chapter 5 Analysis and Design of Biochemical Reactors 5.1 Concept of Design of Bioch. Reactors 5.1.1Classification Bioch. Reactors Stir tank reactor Cycle reactor Loop reactor Plug flow reactor Bubble reactor Multi-cascade reactor Fluid flow reactor Cycle pipe reactor Full mix membrane reactor Immobilized bio-disc Leaching filter Membrane reactor Batch operation Semi-Batch operation Continual operation Bio-block Reactors Bio-membrane reactors Plug flow pattern Full mix pattern Full mix pattern Plug flow pattern
Diagram of Divers Enzymatic Reactors Operations 参阅《生化反应动力学与反应器》P285-290 Cycle Packed K immobilized X bed bed Batch Continuous Multi-cascade operation reactor 出切 ○ Multi-cascade semi- Stir vessel--super- operation Piping filter integration set P Coil immobilized Fluid flow Loop n membrane bed bed flow reactor reactor
Diagram of Divers Enzymatic Reactors & Operations 参阅《生化反应动力学与反应器》P285-290 Batch operation Continuous Multi-cascade reactor Fluid flow bed Stir vessel—superfilter integration set Multi-cascade semioperation Loop flow reactor Coil membrane reactor Packed bed Cycle immobilized bed Piping immobilized bed
5.1.2 Basic Equation for Design of Bio-Reaction (1) Mass balance(Accumulatn is o under steady state Calculation of Mass balance for substrates and products converted Input Output Accumulation components components components+ /unit of components /unit volume /unit volume /unit volume volume Calculation of mass balance for cells Input Output Grown Died cels cells cells Accumulate ceus /unit /unit /unit d cellls /unit /unit volume volume volume volume volume
5.1.2 Basic Equation for Design of Bio-Reaction （1）Mass balance（Accumulatn is 0 under steady state) Calculation of Mass balance for substrates and products Input components /unit volume = converted components /unit volume Output components /unit volume + + Accumulation of components /unit volume Grown cells /unit volume Accumulate d cells /unit volume Died cells /unit volume Output cells /unit volume Input cells /unit volume = + + + Calculation of Mass balance for cells
(2) Energy balance(Heat balance In a definite time: Reaction Input heat Output heat Accumulated heat /unit /unit time /unit time + heat /unit time time (3)Momentum balance It is usually negligible for bioreactors because of operation conducted under constant pressure. In conclusion each balance in the same model as follows: Input output consumption +accumulation
（2）Energy balance (Heat balance ) In a definite time: Input heat /unit time Output heat /unit time Reaction heat /unit time Accumulated = + + heat /unit time (3) Momentum balance It is usually negligible for bioreactors because of operation conducted under constant pressure. In conclusion, each balance in the same model as follows: Input = output + consumption +accumulation
5.2 Batch Stirring Tank Reactor( BSTR) 52.1ca|cu| ation of the reaction time“t” For BSTR, Calculation of mass balance The rate of converted The accumulation components r rate of components rrS 1 dN yn at (5-5) R Effective volume in the reactor Quantity of substrate, mol
5.2 Batch Stirring Tank Reactor( BSTR ) 5.2.1 Calculation of the reaction time “ t ” For BSTR， Calculation of mass balance dt dN V r S R S = − dt dN V r s R s 1 = − VR − Ns − （5-5） Quantity of substrate，mol Effective volume in the reactor The rate of converted components rs = —The accumulation rate of components
Reaction in liquid phase dc S 7 dt (5-6) let t=O, Cs=Cso; t=t,, CS=CS S05 After integration of isolated variable obtain cs d 5-7) The conversion rate is expressed by X then comes out:
Reaction in liquid phase (5-6) let After integration of isolated variable， obtain (5-7) The conversion rate is expressed by , then comes out： = − s s o C C s s r r dC t dt dC r S s = − 0, ; , , S S 0 r CS CS0 t = C = C t = t = Xs
rs dX (5-8) S 式4(5-7)和(5-8)表示了反应物S反应到了一定 程度时所需要的反应时间t的大小,为一普遍关 系式,对不同的反应有不向的r形式,带入上式, 即可求得t的值。 (1) Homogenous enzymatic reaction. when the non inhibition reaction of single substrate carried out, substituteM-Mequation into(5-8) x dx t=C 产(+m)x max S maX kn+C
式（5-7）和（5-8）表示了反应物S反应到了一定 程度时所需要的反应时间 的大小，为一普遍关 系式，对不同的反应有不同的 形式，带入上式， 即可求得 的值。 （1）Homogenous enzymatic reaction.when the non inhibition reaction of single substrate carried out, substituteM－M equation into (5-8)， s r r t s X s m X s m s s s r s dX C k r C k C r C dX t C s s (1 ) 0 0 max max 0 = + + = = s o X s s r s r dX t C 0 （5-8） r t
After integration, obtain nmtn=C。X。+Kmln (5-9) 1-X (C5-C,)+Km (5-10 When C. > K Ft=C.Ⅹ=C.-C.(5-12)
After integration ，obtain (5-10) When When s s r s s m C C r t C C K 0 0 ( ) ln max = − + （5-9） Cs0 Km （5-11） s s m s r m C C K X r t K 0 ln 1 1 ln max = − = Cs0 Km r Cs Xs Cs Cs r t = = − max 0 0 （5-12） s r s s m X r t C X K − = + 1 1 ln max 0
对不同X值,以1~C/Kn对应作图,得到图 1。从图中可以看出当C。/Kn较小时,近似为 一级反应。当X一定,乙将不随CKm 值而变化;当C/K较大时,近似为零级 反应,此时z将随C/K值成比例增加。 如果在酶催化过程中,酶发生失活现象, 若为不可逆失活,则 rx =k2 ce=k.. exp(-kat) 1(5-13) 带入式(5-8),积分得 ,==,In1-[Csx+kmh- KO +2E0 1-X (5-14)
对不同 值，以 对应作图，得到图 1。从图中可以看出当 较小时，近似为 一级反应。当 一定， 将不随 值而变化；当 较大时，近似为零级 反应，此时 将随 值成比例增加。 如果在酶催化过程中，酶发生失活现象， 若为不可逆失活，则 带入式（5-8），积分得 Xs Xs Cs Km / 0 Cs Km / 0 r t Cs Km / 0 r t Cs Km / 0 exp( ) max 2 2 0 E e d r r = k C = k C −k t + + r Cs Km t ~ / 0 （5-13） ]} 1 1 ln{1 [ ln 1 0 2 0 s s s m E d d r X C X K k C k k t − = − − + + (5-14)