Περιβαλλοντική Βιοτεχνολογία- Environmental Biotechnology

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1 Περιβαλλοντική Βιοτεχνολογία- Environmentl Biotechnology Ενότητα 4: Rectors Κορνάρος Μιχαήλ Πολυτεχνική Σχολή Τμήμα Χημικών Μηχανικών

2 Types of rectors Suspended-floc Dispersed growth Fixed-film Attched growth Immobilized cells Fctors for selecting the rector: Physicl nd chemicl chrcteristics of wste Concentrtion of pollutnts Presence or bsence of oxygen Qulittive chrcteristics of runoff Climtic operting conditions Number of processes involved Experience of technicl system opertion Costs for operting time 2

3 Btch rectors Mss rte of substrte ccumultion in control volume = rte of mss in - rte of mss out + rte of mss genertion = = While the microorgnisms re consuming substrte, no substrte is dded or removed from the btch rector. Thus, over this time period the mss of substrte ccumulting in the rector equls the mss of substrte generted within the rector. On the other hnd, the substrte is consumed or destroyed by the microorgnisms, nd genertion hs negtive sign. ds V Vrut dt = Commonly, the rte of substrte utiliztion is ssumed to following Monod kinetics. With this substitution, we obtin: ds qs ˆ V = V X dt K + S ds qs ˆ = X dt K + S 3

4 Btch rectors Mss rte of orgnism ccumultion in control volume = rte of mss in - rte of mss out + rte of mss genertion = = With μ being the net specific growth rte of orgnisms, the mthemticl form is similr to previous eqution: dx V = V( µ X ) dt dx S dx S V = V ˆ µ b X ˆ = µ b X dt K + S dt K + S In the bsence of decy, the orgnism concentrtion t ny time equls the initil concentrtion, X, plus tht which results from substrte consumption during tht time, Y ΔS, or: X = X + Y S or X = X + Y( S S) 4

5 Btch rectors One ordinry differentil eqution is obtined: ds qs ˆ X Y( S S) dt = K + S + This eqution cn be integrted to yield: 1 K 1 K SX 1 t = + X + YS YS X qˆ X YS Y X YS S Y ln ( ) ln ln + + It would be desirble to hve n eqution tht explicitly gives S s function of t, but becuse of the complexity of the eqution, this is not possible. There is computer spredsheet which cn be very useful for solving for S when t is known. 5

6 CSTR rectors with recircultion Effect of recircultion in the system performnce QS + Q S = Q S nd QX + Q X = Q X r i i r r i i From which: S QS + Q S Q QX + Q X Q r r r i i = nd X i = i Also: i r Q = Q+ Q Now, if we do the mss blnce for substrte round the rector control volume, we obtin for the stedy-stte cse: = + i i i QS QS rv ut Then, by mking pproprite substitutions nd simplifying we obtin: = ( ) + ut QS S rv Simple recycle for CSTR does not chnge substrte removl compred with tht obtined without recycle. A mss blnce on microorgnisms cn be performed similrly, nd the result is the sme: Orgnism concentrtions within the rector nd in the rector effluent re not ffected by effluent recycle, since the sme mss flow tht leves the rector returns to the rector. We will see, however, tht this is not the cse with plug-flow rector, where concentrtions re not the sme everywhere. 6

7 Plug-flow rectors Substrte S V = QS Q( S + S) + rut V t X Active microorgnisms V = QX Q( X + X ) + rnet V t Substrte t stedy stte ( A = V / z nd u = Q / A) S u = r z ut Active microorgnisms t stedy stte u X z = r net 7

8 Plug-flow rectors Substrte t stedy stte with Monod kinetics: ds S u = qˆ X dz K + S Active microorgnisms t stedy stte with growth nd decy: dx S u = Yqˆ X bx dz K + S This series of equtions cnnot be solved nlyticlly, nd so numericl pproches must be used. However, if we gin ignore orgnism decy (b = ), then n nlyticl solution is possible. u dx dz ds = uy dz We cncel u nd tke integrls to obtin: dx = Y ds X X S S Integrting gives: X = X + Y( S S) A differentil eqution with only two vribles, S nd z: ds S u qˆ X Y( S S) dz = K + S + 8

9 Plug-flow rectors The rtio dz/u hs dimensions of time nd equls the differentil time, dt, for n element of wter to move long the rector distnce dz. Substituting dt for dz/u in previous eqution yields differentil eqution tht is exctly the sme s for the btch rector. z 1 K 1 K SX 1 = + + u qˆ X YS Y X YS S Y ln { X YS YS} ln ln X + + We obtin n expression for the effluent concentrtion from the btch rector by letting z = L. We lso note tht L/u is equl to V/Q, the hydrulic detention time, θ, for the rector. With these substitutions, the following solution, with θ replcing t, is: 1 K 1 K SX 1 θ = + + qˆ X YS Y X YS S Y e e ln { X YS YS } ln ln X + + 9

10 Plug-flow rectors with recircultion S QS + Q S Q QX + Q X Q r r r i i = nd X i = i i r nd Q = Q + Q It should be noted tht X r =X e nd S=S e. For the cse in which b=, n integrted form of n eqution relting the effluent concentrtions s function of detention time cn be obtined. In this mnner, the effluent concentrtion of X cn be obtined: e e X = X + Y( S S ) With this, the series of equtions cn be combined nd integrted to give: V 1 K 1 K SX 1 Q q X YS Y X YS S Y e i i i e i = ln { } ln ln i + i X + YS YS X i i i ˆ + + Of interest is the impct of recycle on the performnce of PFR. We define the recycle rtio R, s: nd the detention time, θ, s: V V(1 + R) ϑ = = i Q Q R = r Q Q 1

11 CSTR by sedimenttion nd biomss recircultion In order to develop mss blnces for the rector, we gin need some simplifying ssumptions. Assumptions tht we mke here s first exercise re: (1) biodegrdtion of the substrtes tkes plce in the rector only, no biologicl rections tke plce in the settling tnk, nd the biomss in the settler is insignificnt; (2) no ctive microorgnisms re in the influent to the rector.(x = ); nd (3) the substrte is soluble so tht it cnnot settle out in the settling tnk. dx e e w w V = ( Q X + Q X ) + [ Y ( rut ) V bx V ] dt Likewise, mss blnce for substrte gives: ds dt e e w w V = QS ( QS + Q S ) + rv ut ϑ = XV x e e w w QX + Q X We cn rerrnge the bove eqution for the stedy-stte cse to give: e e w w QX+ Q X Y( rut ) = b XV X 11

12 CSTR by sedimenttion nd biomss recircultion 1 Y( rut ) = b ϑ X x We solve this eqution explicitly for S: This eqution is generl for CSTR with settling nd recycle nd cn be pplied whtever the form of the biologicl rection, rut, my be. If we ssume tht it tkes the usul form of the Monod rection, then we obtin the following expression: 1 qs ˆ Y b ϑ = K + S S 1+ bϑ x = K ϑ ( Yqˆ b) 1 x x The finl eqution is identicl with eqution, which ws developed for the chemostt without settling nd recycle. So then, wht is unique bout the CSTR with settling nd microorgnism recycle? The nswer is tht the retention time of the microorgnisms in the system (θ x ) is seprted from the hydrulic detention time (θ). Thus, one cn hve lrge θ x, in order to obtin high efficiency of substrte removl, nd t the snle time hve smll θ, which trnsltes into smll rector volume. 12

13 CSTR by sedimenttion nd biomss recircultion ut X r = Y( rut ) = ϑx 1+ bϑ QS QS Q S V e e w w x For the CSTR, we see tht the substrte concentrtion in the rector, S, is equl to the concentrtion in the effluent S e nd in the wste sludge line, S W, since no rection occurs in the settling tnk. Also, through mss blnce, Q e + Q w = Q. With these substitutions into previous eqution, we obtin: Q ( S S) ( S S) rut = = V ϑ This eqution is nother generl representtion, this time of the utiliztion rte in terms of rector chrcteristics nd performnce. X ϑx Y S S = ϑ 1+ bϑ ( ) ϑ x solids concentrtion rtio ϑ = x 13

14 CSTR by sedimenttion nd biomss recircultion At stedy stte, the mss rte of ctive biomss production (r bp, M/T) must just equl the rte t which biomss leves the system from the effluent strem nd the wste strem: r = QX + Q X e e w w bp r bp = XV ϑ x 14

15 CSTR by sedimenttion nd biomss recircultion For those who re still troubled by this concept, we cn develop nother eqution without using θ x s the mster vrible. We proceed this time by considering the control volume round the rector. At stedy stte, mss blnce for substrte leds to: If Monod kinetics pply nd then substituting ds dt = + = i i i V QS QS rv ut i i qs ˆ Q ( S S) X = K + S V We cn define V/Q i to equl the hydrulic detention time in the rector itself (θ r ) i S S S = ( S K) qx ˆ ˆ ϑ = r qx ϑ << K K 15

16 PFR by sedimenttion nd biomss recircultion X We cn ssume X to be constnt throughout the rector, mking integrtion of previous eqution for the stedy-stte cse much esier. The result is: ds S u = qˆ X dz K + S ϑ r i 1 S i = Kln( ) ( S S) qx ˆ + S We would like to relte tretment efficiency to θ x, since it is much esier to control θ x thn it is to mesure X. We construct mss blnce for ctive microorgnisms round the entire rector, which provides the sme results s for the CSTR with settling nd recycle, repeted here for convenience: 1 ut ϑ x Y( r ) X b 16

17 PFR by sedimenttion nd biomss recircultion 1 YQ ( S S) ϑ x = XV b ϑ r i 1 S i = Kln( ) ( S S) qx ˆ + S Recognizing tht θ r = V/(Q + Q r ), substituting this vlue into eqution, solving for X V, nd then substituting this previous eqution give: qy ˆ S S = b S S ek 1 ( ) x ( ) + ϑ in which e = (1 + R) ln ( S + RS) / (1 + R) / S When R < 1, e pproximtely equls In(S o /S): qy ˆ S S = b, R< 1 S ( S S) + Kln S 1 ( ) ϑ x 17

18 References The imges where their origin is not mentioned re derived from the book: Environmentl Biotechnology : Principles nd Applictions, Bruce E. Rittmnn nd Perry L. McCrty, McGrw-Hill Series in Wter Resources nd Environmentl Engineering 18

19 Τέλος Ενότητας

20 Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί στο πλαίσιο του εκπαιδευτικού έργου του διδάσκοντα. Το έργο «Ανοικτά Ακαδημαϊκά Μαθήματα στο Πανεπιστήμιο Αθηνών» έχει χρηματοδοτήσει μόνο την αναδιαμόρφωση του εκπαιδευτικού υλικού. Το έργο υλοποιείται στο πλαίσιο του Επιχειρησιακού Προγράμματος «Εκπαίδευση και Δια Βίου Μάθηση» και συγχρηματοδοτείται από την Ευρωπαϊκή Ένωση (Ευρωπαϊκό Κοινωνικό Ταμείο) και από εθνικούς πόρους. 2

21 Σημειώματα

22 Σημείωμα Ιστορικού Εκδόσεων Έργου Το παρόν έργο αποτελεί την έκδοση

23 Σημείωμα Αναφοράς Copyright Πανεπιστήμιο Πατρών. Αναπληρωτής Καθηγητής, Μιχαήλ Κορνάρος. «Περιβαλλοντική Βιοτεχνολογία». Έκδοση: 1.. Πάτρα 215. Διαθέσιμο από τη δικτυακή διεύθυνση: 23

24 Σημείωμα Αδειοδότησης Το παρόν υλικό διατίθεται με τους όρους της άδειας χρήσης Cretive Commons Αναφορά, Μη Εμπορική Χρήση Παρόμοια Διανομή 4. [1] ή μεταγενέστερη, Διεθνής Έκδοση. Εξαιρούνται τα αυτοτελή έργα τρίτων π.χ. φωτογραφίες, διαγράμματα κ.λ.π., τα οποία εμπεριέχονται σε αυτό και τα οποία αναφέρονται μαζί με τους όρους χρήσης τους στο «Σημείωμα Χρήσης Έργων Τρίτων». [1] Ως Μη Εμπορική ορίζεται η χρήση: που δεν περιλαμβάνει άμεσο ή έμμεσο οικονομικό όφελος από την χρήση του έργου, για το διανομέα του έργου και αδειοδόχο που δεν περιλαμβάνει οικονομική συναλλαγή ως προϋπόθεση για τη χρήση ή πρόσβαση στο έργο που δεν προσπορίζει στο διανομέα του έργου και αδειοδόχο έμμεσο οικονομικό όφελος (π.χ. διαφημίσεις) από την προβολή του έργου σε διαδικτυακό τόπο Ο δικαιούχος μπορεί να παρέχει στον αδειοδόχο ξεχωριστή άδεια να χρησιμοποιεί το έργο για εμπορική χρήση, εφόσον αυτό του ζητηθεί. 24