Idealize Bioreactor CSTR vs. PFR... 3 Analysis of a simple continuous stirred tank bioreactor... 4 Residence time distribution... 4 F curve:...

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1 Idealize Bioreaor CSTR vs. PFR... 3 Analysis of a simple oninuous sirred ank bioreaor... 4 Residene ime disribuion... 4 F urve:... 4 C urve:... 4 Residene ime disribuion or age disribuion... 4 Residene ime disribuion and reaion kineis... 5 Well mixed oninuous sirred ank reaor... 6 Plug Flow Bioreaor... 7 Example:

2 Idealize Bioreaor CSTR vs. PFR Well mixed CSTR Exi onenraion he same as in reaor. Insananeous mixing upon addiion of raer o he reaor. Plug flow reaor (PRFR) Pison flow No bak mixing No dispersion due o moleular diffusion 3

3 Analysis of a simple oninuous sirred ank bioreaor Residene ime disribuion F urve: no raes < Sep inpu of raer of onenraion C on he fluid sream enering he vessel. The ime reord of raer in he exi sream measured as C is alled F urve. 1 2 C C urve: Pulse inpu, an impulse or dela f n, ino a oninuous reaor wih a inflow and oufow raes of F The onenraion urve a he oule C Toal area M/F Toal inpu M M = CFd normalized response urve o he impulse C Cd = d 1 = M / F C is a populaion densiy funion Residene ime disribuion or age disribuion Analyze a lose vessel: fluid eners and leaves as plug flow, no bah diffusion, eddies a he enrane and exi. E; age disribuion of fluid leaving a vessel or residene ime disribuion Age: he ime spen by an elemen of he exi sream in he vessel Ed = 1 D C C Toal area=1 4

4 1 fraion of exi sream of age beween and +d is Ed Ed = 1 1 Ed In a losed vessel (no bak mixing in he enrane and exi), C urve and E urve are idenial. Assume he flow ino he reaor a < is whie fluid, and a is swihed o red fluid. The onenraion of red fluid will rise in he exi sream over ime. The red fluid onenraion in he ouflow sream afer normalizaion gives F urve. A any given ime of >, red fluid and only red fluid in he exi sream has an age shorer hen. (fraion of red fluid in he exi sream)=(fraion of exi seam younger hen age ) f = Ed The mean residene ime is = Ed Residene ime disribuion and reaion kineis In a bah reaor, he rae of reaion wih a reaan onenraion d d = r If he onenraion a ime is C a any given ime C ε = d= rd C In a reaor, an elemen of fluid whih has a residene ime will hus have a reaan onenraion of ε. If he age disribuion of ha elemen is E, he disribuion funion of he reaan onenraion in ha elemen of fluid is Cε Ed By inegraing all elemens hrough he age disribuion urve one ges C = CoExp( k) Ed 5

5 For firs order reaion d k d = C = CoExp( k) The reaan onenraion a he oule of he reaor is C = CoExp( k) Ed I an be see ha he E funion is muliplied by he expression of for a bah reaor in he inegraion over all age disribuion. Well mixed oninuous sirred ank reaor dv d = F in F ou dv if Fin = Fou = F = d dv ( ) = Fin Fou d V ons, well mixed F in d F = d V V in = d F = d V d Fd = V Iniial ondiions: = = Solve: ln = F V 6

6 ime ons: V F when V = F.368 = ln 1 = onenraion dereased by 63% When he reaion wih a reaion rae r ours in he reaor: F in d F = + r r = reaion rae/volume d V V Plug Flow Bioreaor F U = A Δ( z A Δ z) = UA z UA z+δz + A Δ zr Δ Assume onsan area and express he equaion in a differenial form, ( U) = + r z A seady sae, he onenraion hanges wih posiion, bu no ime. We assume ha he veloiy of he liquid flow is onsan. Then U = r z If we define z E = and subsiue ino he above equaion hen, U U = = r z I is lear ha he equaion looks jus like ha for a bah reaor. In a bioreaor for ell growh he reaion ha we are ineresed in is basially ha for ell growh and for subsrae onsumpion. 7

7 We an express he growh rae dependene on subsrae onenraion in a Mono-kinei equaion, hen he equaions beome dx μm xs 1 = dz K + s U s ds 1μ max xs 1 = dz Y ( K + s) U s Le he iniial ondiions be z=, x=x, s=s, he onenraion profiles of ell and subsrae an be solved jus like a bah reaor and are shown in Figure. Example: Aerobi miroorganism growing in a plug flow bioreaor. The onenraion of oxygen and ells a he inle are: s =.2 mmole and x l = 1 g. The maximum speifi l growh rae is 1 hr -1. The onsumpion of oxygen an be assume o follow Monod kineis wih Ks =.1mmole and he yield oeffiien of biomass based on oxygen is l 1gells Yx =. The ross seional area of he reaor is 3mmole2 Wha is he maximum reaor lengh ha an be used for he flow rae (F) of 1 l? min Assumpions: (i) ons volume (ii) well mixed (iii) oxygen is he e growh-limiing nurien 2 A = 1m. 1 l and min I is lear ha oxygen onenraion will be used quikly depleed in a plug flow reaor used for ell ulivaion. Therefore, plug flow reaor is rarely used for large sale operaion of ell ulivaion. Raher, a sirred ank or oher mixing vessel ype of reaors wih a oninuous supply of oxygen from he gas phase by air sparging, are frequenly used. Plug flow reaor is more ofen used in enzymai reaions and in bioseparaions. 8

8 They are also used in appliaions whih are relaively small in sale, suh as in issue engineering appliaions. 9