3210:
1416:
1332:, or exit age distribution. Not all fluid particles will spend the same amount of time within the reactor. The exit age distribution (E(t)) defines the probability that a given fluid particle will spend time t in the reactor. Similarly, the cumulative age distribution (F(t)) gives the probability that a given fluid particle has an exit age less than time t. One of the key takeaways from the exit age distribution is that a very small number of fluid particles will never exit the CSTR. Depending on the application of the reactor, this may either be an asset or a drawback.
4926:
1374:. The presence of corners or baffles in a reactor often results in some dead space where the fluid is poorly mixed. Similarly, a jet of fluid in the reactor can cause short-circuiting, in which a portion of the flow exits the reactor much quicker than the bulk fluid. If dead space or short-circuiting occur in a CSTR, the relevant chemical or biological reactions may not finish before the fluid exits the reactor. Any deviation from ideal flow will result in a residence time distribution different from the ideal distribution, as seen at right.
5556:
1400:
6055:
106:
1345:
6067:
1321:
93:. In a perfectly mixed reactor, reagent is instantaneously and uniformly mixed throughout the reactor upon entry. Consequently, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and reaction rate. The CSTR is the ideal limit of complete mixing in reactor design, which is the complete opposite of a
4922:
PFRs, which may be a challenge in applications where space is limited. However, one of the added benefits of dilution in CSTRs is the ability to neutralize shocks to the system. As opposed to PFRs, the performance of CSTRs is less susceptible to changes in the influent composition, which makes it ideal for a variety of industrial applications:
3225:
must be taken into account. As seen above, an increase in the number of CSTRs in series will decrease the total reactor volume. Since cost scales with volume, capital costs are lowered by increasing the number of CSTRs. The largest decrease in cost, and therefore volume, occurs between a single CSTR
1390:
To model systems that do not obey the assumptions of constant temperature and a single reaction, additional dependent variables must be considered. If the system is considered to be in unsteady-state, a differential equation or a system of coupled differential equations must be solved. Deviations of
4921:
CSTRs facilitate rapid dilution of reagents through mixing. Therefore, for non-zero-order reactions, the low concentration of reagent in the reactor means a CSTR will be less efficient at removing the reagent compared to a PFR with the same residence time. Therefore, CSTRs are typically larger than
1048:
in the reactor and the rate constant. A key assumption when modeling a CSTR is that any reactant in the fluid is perfectly (i.e. uniformly) mixed in the reactor, implying that the concentration within the reactor is the same in the outlet stream. The rate constant can be determined using a known
1494:
is the molar flow rate of the feed. When the same process is applied to a cascade of CSTRs as seen in the graph with three CSTRs, the volume of each reactor is calculated from each inlet and outlet fractional conversion, therefore resulting in a decrease in total reactor volume. Optimum size is
1340:
While the ideal CSTR model is useful for predicting the fate of constituents during a chemical or biological process, CSTRs rarely exhibit ideal behavior in reality. More commonly, the reactor hydraulics do not behave ideally or the system conditions do not obey the initial assumptions. Perfect
31:
3336:. Therefore the total reactor volume is independent of the number of CSTRs for a zeroth order reaction. Therefore, cost is not a function of the number of reactors for a zeroth order reaction and does not decrease as the number of CSTRs increases.
3230:
and controls, construction, installation, and maintenance that accompany larger cascades. Therefore as the number of CSTRs increases, the operating cost increases. Therefore, there is a minimum cost associated with a cascade of CSTRs.
2514:
1387:(PFRs) either in series or in parallel. For examples, an infinite series of ideal CSTRs is hydraulically equivalent to an ideal PFR. Reactor models combining a number of CSTRs in series are often termed tanks-in-series (TIS) models.
4511:
82:. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and
3128:
1299:
2779:
3837:
1382:
Although ideal flow reactors are seldom found in practice, they are useful tools for modeling non-ideal flow reactors. Any flow regime can be achieved by modeling a reactor as a combination of ideal CSTRs and
526:
1341:
mixing is a theoretical concept that is not achievable in practice. For engineering purposes, however, if the residence time is 5–10 times the mixing time, the perfect mixing assumption generally holds true.
1674:
3199:
2298:
1352:
Non-ideal hydraulic behavior is commonly classified by either dead space or short-circuiting. These phenomena occur when some fluid spends less time in the reactor than the theoretical residence time,
919:
2198:
When the volumes of the individual CSTRs in series vary, the order of the CSTRs does not change the overall conversion for a first order reaction as long as the CSTRs are run at the same temperature.
202:
2194:
2115:
4265:
840:
4154:
1579:
1391:
the CSTR behavior can be considered by the dispersion model. CSTRs are known to be one of the systems which exhibit complex behavior such as steady-state multiplicity, limit cycles, and chaos.
3307:
2036:
1972:
1871:
1205:
3629:
3546:
2372:
751:
4815:
2852:
658:
5086:. Tchobanoglous, George,, Stensel, H. David,, Tsuchihashi, Ryujiro,, Burton, Franklin L. (Franklin Louis), 1927-, Abu-Orf, Mohammad,, Bowden, Gregory (Fifth ed.). New York, NY.
1138:
3992:
3958:
980:
1462:
3409:
3381:
4355:
4310:
3719:
3674:
6040:
4731:
4691:
4591:
4551:
3877:
3334:
1030:, is always equal to the reactor volume divided by the fluid flow rate. See the next section for a more in-depth discussion on the residence time distribution of a CSTR.
2810:
5386:
Hurtado, F.J.; Kaiser, A.S.; Zamora, B. (March 2015). "Fluid dynamic analysis of a continuous stirred tank reactor for technical optimization of wastewater digestion".
4903:
4881:
4859:
4837:
4775:
4753:
3921:
3899:
4651:
4621:
1905:
1785:
1728:
1492:
4046:
4019:
3463:
3436:
1755:
1694:
1371:
1027:
944:
423:
2388:
1060:
for an ideal CSTR. The values of the outlet concentration and residence time are major design criteria in the design of CSTRs for industrial applications.
1499:
with two CSTRs, equal volumes should be used. As the number of ideal CSTRs (n) approaches infinity, the total reactor volume approaches that of an ideal
4360:
3213:
Cost initially decreases with the number of CSTRs as volume decreases but as operational costs increase, the total cost eventually begins to increase.
1056:
Equation 6 can be solved by integration after substituting the proper rate expression. The table below summarizes the outlet concentration of species
5465:
17:
5167:
5115:
2866:
1008:
is the total amount of time a discrete quantity of reagent spends inside the reactor. For an ideal reactor, the theoretical residence time,
1216:
2532:
3724:
429:
1495:
achieved when the area above the rectangles from the CSTRs in series that was previously covered by a single CSTR is maximized. For a
1584:
5545:
4930:
5512:
3143:
2213:
97:(PFR). In practice, no reactors behave ideally but instead fall somewhere in between the mixing limits of an ideal CSTR and PFR.
846:
5721:
143:
5446:
5370:
5293:
5143:
5091:
2122:
2043:
224:(valid for most liquids; valid for gases only if there is no net change in the number of moles or drastic temperature change)
767:
4159:
4051:
1514:
138:
3246:
1977:
1913:
1812:
1149:
5345:
5049:
2305:
3551:
3468:
6030:
679:
6071:
6035:
3345:
2815:
592:
4786:
5879:
5646:
5317:
Stokes, R. L.; Nauman, E. Bruce (1970). "Residence Time
Distribution Functions for Stirred Tanks in Series".
1087:
3349:
950:
3963:
3929:
3226:
and having two CSTRs in series. When considering operating cost, operating cost scales with the number of
5869:
5505:
5007:
1430:
1005:
5473:
6093:
5726:
3386:
3358:
5540:
79:
4696:
4656:
4556:
4516:
4315:
4270:
3842:
3679:
3634:
3312:
3209:
1348:
Exit age distribution E(t) and cumulative age distribution F(t) functions for a CSTR with dead space
5896:
5575:
5535:
4780:
5792:
5570:
5012:
4910:
3137:
1500:
1407:
Cascades of CSTRs, also known as a series of CSTRs, are used to decrease the volume of a system.
1384:
1328:
An ideal CSTR will exhibit well-defined flow behavior that can be characterized by the reactor's
94:
2786:
89:
The behavior of a CSTR is often approximated or modeled by that of an ideal CSTR, which assumes
6059:
5964:
5949:
5777:
5671:
5651:
5498:
2302:
When the cascade of CSTRs is isothermal with identical reactors, the concentration is given by
1874:
1424:
1415:
4886:
4864:
4842:
4820:
4758:
4736:
3904:
3882:
4626:
4596:
3879:
and B is the desired product, the cascade of CSTRs is favored with a fresh secondary feed of
1697:
5230:
Monsen, Nancy E.; Cloern, James E.; Lucas, Lisa V.; Monismith, Stephen G. (September 2002).
1880:
1760:
1703:
1467:
5989:
5852:
5716:
5666:
5395:
5243:
5194:
4997:
4947:
4024:
3997:
3441:
3414:
2855:
1733:
1679:
1356:
1324:
Exit age distribution E(t) and cumulative age distribution F(t) functions for an ideal CSTR
1012:
929:
331:
75:
2509:{\displaystyle C_{Ai}={\frac {-1+{\sqrt {1+4k_{i}\tau _{i}C_{A(i-1)}}}}{2k_{i}\tau _{i}}}}
2382:
8:
5874:
5857:
5837:
5817:
5232:"A comment on the use of flushing time, residence time, and age as transport time scales"
1496:
1053:. Generally, as the temperature increases so does the rate at which the reaction occurs.
5399:
5247:
5198:
4925:
2207:
5884:
5630:
5261:
5161:
5109:
4962:
4955:
1800:
1423:
As seen in the graph with one CSTR, where the inverse rate is plotted as a function of
1050:
6009:
6004:
5959:
5782:
5656:
5442:
5419:
5411:
5366:
5341:
5299:
5289:
5212:
5149:
5139:
5097:
5087:
5045:
274:
5265:
3239:
From a rearrangement of the equation given for identical isothermal CSTRs running a
1803:
first order, constant density reaction in a cascade of identical CSTRs operating at
5939:
5906:
5661:
5403:
5251:
5202:
5183:"A note on the concepts of age distribution and transit time in natural reservoirs"
4943:
71:
2861:
From this, the cumulative residence time distribution (F(t)) can be calculated as
5772:
5767:
5757:
5407:
4506:{\displaystyle {\frac {d}{d}}={\frac {k_{1}}{k_{2}}}^{n_{1}-n_{2}}^{m_{1}-m_{2}}}
2527:
can be calculated. At the concentration at the jth reactor in series is given by
5338:
Introduction to
Chemical Engineering Kinetics and Reactor Design, Second Edition
5944:
5921:
5827:
5822:
5762:
5747:
5711:
5596:
5207:
5182:
3222:
2524:
1419:
As the number of CSTRs in series increases, the total reactor volume decreases.
1329:
90:
5256:
5231:
4733:
and B is the desired product, a cascade of CSTRs with a high concentration of
4593:
and B is the desired product, a cascade of CSTRs with an inlet stream of high
6087:
5842:
5797:
5706:
5521:
5415:
5303:
5216:
5153:
5101:
4906:
1788:
565:
5994:
5979:
5891:
5832:
5731:
5701:
5610:
5423:
5002:
4979:
3218:
1804:
4861:
but CSTRs in general are typically not chosen when the desired product is
5984:
5974:
5969:
4267:, respectively, we can obtain a relationship between the two by dividing
3631:, respectively, we can obtain a relationship between the two by dividing
3123:{\displaystyle F(t)={\frac {C_{n}}{C_{o}}}=1-e^{-{\frac {nt}{\bar {t}}}}}
1399:
5555:
5911:
5864:
5787:
5696:
263:
5136:
Water quality engineering : physical/chemical treatment processes
2385:
at steady state in a cascade of CSTRs, the general design equation is
118:
A continuous fluid flow containing non-conservative chemical reactant
1294:{\displaystyle C_{A}={\frac {-1+{\sqrt {1+4k\tau C_{Ao}}}}{2k\tau }}}
2774:{\displaystyle {\frac {C_{j}}{C_{o}}}=1-e^{-{\frac {nt}{\bar {t}}}}}
6014:
5916:
3832:{\displaystyle {\frac {d}{d}}={\frac {k_{1}}{k_{2}}}^{n_{1}-n_{2}}}
3133:
1049:
empirical reaction rate that is adjusted for temperature using the
1034:
227:
5288:. Davis, Robert J. (International ed.). Boston: McGraw-Hill.
1344:
521:{\displaystyle 2.{\frac {dN_{A}}{dt}}=F_{Ao}-F_{A}+V\nu _{A}r_{A}}
105:
5954:
5847:
5625:
5620:
221:
5490:
5441:(second ed.). Boca Raton, FL, USA: CRC Press. p. 181.
5999:
5591:
4984:
83:
1669:{\displaystyle \tau _{i}={\frac {C_{A(i-1)}-C_{Ai}}{-r_{Ai}}}}
34:
Diagram showing the setup of a continuous stirred-tank reactor
6041:
List of largest biomedical companies by market capitalization
5901:
5084:
Wastewater engineering : treatment and resource recovery
1320:
5615:
3926:
For a parallel reaction with two or more reactants such as
3227:
3194:{\displaystyle \sigma _{t}^{2}={\frac {{\bar {t}}^{2}}{n}}}
2293:{\displaystyle C_{Am}=C_{Ao}-\sum _{i=1}^{m}k_{i}\tau _{i}}
5229:
914:{\displaystyle 6.\ r_{A}={\frac {1}{\tau }}(C_{Ao}-C_{A})}
5605:
5601:
5340:. Hoboken, new Jersey: Wiley. pp. 241–253, 349–358.
4952:
Lagoon treatment systems for natural wastewater treatment
1581:, we can determine that for a single CSTR in series that
1044:, is generally dependent on the concentration of species
2206:
At steady state, the general equation for an isothermal
197:{\displaystyle {\Bigl (}{\frac {dN_{A}}{dt}}=0{\Bigr )}}
2189:{\displaystyle C_{Am}={\frac {C_{Ao}}{(1+k\tau )^{m}}}}
2110:{\displaystyle C_{A2}={\frac {C_{Ao}}{(1+k\tau )^{2}}}}
666:
can then be rewritten in terms of the concentration of
30:
4260:{\displaystyle {\frac {d}{dt}}=k_{2}^{n_{2}}^{m_{1}2}}
3132:
As n → ∞, F(t) approaches the ideal PFR response. The
2812:
is the average residence time of the cascade given by
961:
835:{\displaystyle 5.\ r_{A}={\frac {Q}{V}}(C_{Ao}-C_{A})}
4889:
4867:
4845:
4823:
4789:
4761:
4739:
4699:
4659:
4629:
4599:
4559:
4519:
4363:
4318:
4273:
4162:
4149:{\displaystyle {\frac {d}{dt}}=k_{1}^{n_{1}}^{m_{1}}}
4054:
4027:
4000:
3966:
3932:
3907:
3885:
3845:
3727:
3682:
3637:
3554:
3471:
3444:
3417:
3389:
3361:
3315:
3249:
3146:
2869:
2818:
2789:
2535:
2391:
2308:
2216:
2125:
2046:
1980:
1916:
1907:
is the outlet concentration of A from the first CSTR
1883:
1815:
1763:
1736:
1706:
1682:
1587:
1517:
1470:
1433:
1359:
1219:
1152:
1090:
1015:
953:
932:
849:
770:
682:
595:
432:
334:
146:
3339:
2783:
where n is the total number of CSTRs in series, and
1574:{\displaystyle \tau ={\frac {C_{Ao}-C_{A}}{-r_{A}}}}
5385:
3348:, utilizing a cascade of CSTRs can achieve greater
3309:, the volume of each individual CSTR will scale by
2040:Plugging in the first CSTR equation to the second:
5081:
4897:
4875:
4853:
4831:
4809:
4769:
4747:
4725:
4685:
4645:
4615:
4585:
4545:
4505:
4349:
4304:
4259:
4148:
4040:
4013:
3986:
3952:
3915:
3893:
3871:
3831:
3713:
3668:
3623:
3540:
3457:
3430:
3403:
3375:
3328:
3301:
3193:
3122:
2846:
2804:
2773:
2508:
2366:
2292:
2188:
2109:
2030:
1966:
1899:
1865:
1779:
1749:
1722:
1688:
1668:
1573:
1486:
1456:
1365:
1293:
1199:
1132:
1021:
974:
938:
913:
834:
745:
652:
520:
417:
196:
5133:
3302:{\displaystyle \tau ={\frac {C_{Ao}-C_{Am}}{mk}}}
2031:{\displaystyle C_{A2}={\frac {C_{A1}}{1+k\tau }}}
1967:{\displaystyle C_{A1}={\frac {C_{Ao}}{1+k\tau }}}
1866:{\displaystyle C_{A1}={\frac {C_{Ao}}{1+k\tau }}}
1503:for the same reaction and fractional conversion.
189:
149:
6085:
3217:When determining the cost of a series of CSTRs,
1511:From the design equation of a single CSTR where
1200:{\displaystyle C_{A}={\frac {C_{Ao}}{1+k\tau }}}
1001:is the reactor/outlet concentration of species A
5283:
4974:Loop reactor for production of pharmaceuticals
1315:
291:is converted to products via chemical reaction
5506:
5466:"Visual Encyclopedia of Chemical Engineering"
5437:Kadlec, Robert H.; Wallace, Scott D. (2009).
5436:
5286:Fundamentals of chemical reaction engineering
4958:for the stabilization of wastewater biosolids
3624:{\displaystyle {\frac {d}{dt}}=k_{2}^{n_{2}}}
3541:{\displaystyle {\frac {d}{dt}}=k_{1}^{n_{1}}}
2518:
2367:{\displaystyle C_{Am}=C_{Ao}-mk_{i}\tau _{i}}
755:Equation 4 can then be rearranged to isolate
580:Applying the assumptions of steady state and
5336:Hill, Charles G.; Root, Thatcher W. (2014).
5316:
5181:Bolin, Bert; Rodhe, Henning (January 1973).
4937:
4755:in the feed and small secondary streams of
2119:Therefore for m identical CSTRs in series:
746:{\displaystyle 4.\ 0=QC_{Ao}-QC_{A}-Vr_{A}}
5513:
5499:
5363:Chemical Reaction Engineering, 3rd Edition
5360:
5180:
5166:: CS1 maint: location missing publisher (
5138:. Lawler, Desmond F. Hoboken, New Jersey.
5114:: CS1 maint: location missing publisher (
5035:
5033:
3901:in order to maximize the concentration of
1377:
5255:
5206:
4810:{\displaystyle {\ce {A -> B -> C}}}
3234:
2847:{\displaystyle {\bar {t}}={\frac {V}{Q}}}
1506:
653:{\displaystyle 3.\ 0=F_{Ao}-F_{A}-Vr_{A}}
552:is the molar flow rate outlet of species
313:Integral mass balance on number of moles
5546:Competitions and prizes in biotechnology
5335:
5319:Canadian Journal of Chemical Engineering
4931:Newtown Creek Wastewater Treatment Plant
4924:
4883:as the back mixing from the CSTR favors
3208:
1464:where V is the total reactor volume and
1414:
1398:
1343:
1319:
540:is the molar flow rate inlet of species
104:
29:
5039:
5030:
4968:
1133:{\displaystyle C_{A}={C_{Ao}}-{k\tau }}
1064:Outlet Concentration for an Ideal CSTR
992:is the inlet concentration of species A
14:
6086:
5077:
5075:
5073:
5071:
5069:
5067:
5065:
5063:
5061:
4961:Treatment wetlands for wastewater and
1757:is the outlet concentration of A, and
5494:
5460:
5458:
5129:
5127:
5125:
5044:. New York: Oxford University Press.
5042:The Engineering of Chemical Reactions
3987:{\displaystyle {\ce {A + D -> C}}}
3953:{\displaystyle {\ce {A + D -> B}}}
2210:at in a cascade of CSTRs is given by
975:{\displaystyle \tau ={\tfrac {V}{Q}}}
266:conditions, or constant temperature (
6066:
5279:
5277:
5275:
1410:
1394:
64:continuous-flow stirred-tank reactor
5058:
1457:{\displaystyle {\frac {V}{F_{Ao}}}}
946:is the theoretical residence time (
24:
5455:
5122:
1427:, the area in the box is equal to
211:is the number of moles of species
25:
6105:
5520:
5272:
5082:Metcalf & Eddy (2013-09-03).
3404:{\displaystyle {\ce {A -> C}}}
3376:{\displaystyle {\ce {A -> B}}}
3340:Selectivity of parallel reactions
3240:
1335:
109:Cross-sectional diagram of a CSTR
6065:
6054:
6053:
5554:
5470:encyclopedia.che.engin.umich.edu
5134:Benjamin, Mark M. (2013-06-13).
1730:is the feed concentration of A,
1051:Arrhenius temperature dependence
662:The molar flow rates of species
587:= −1, Equation 2 simplifies to:
252:is the concentration of species
6031:Index of biotechnology articles
5430:
5379:
4916:
4913:is chosen for these reactions.
4350:{\displaystyle {\frac {d}{dt}}}
4305:{\displaystyle {\frac {d}{dt}}}
3714:{\displaystyle {\frac {d}{dt}}}
3669:{\displaystyle {\frac {d}{dt}}}
2376:
2201:
245:is the reaction rate constant,
122:enters an ideal CSTR of volume
40:continuous stirred-tank reactor
18:Continuous stirred tank reactor
6036:List of biotechnology articles
5354:
5329:
5310:
5223:
5174:
4817:also have selectivity between
4800:
4794:
4726:{\displaystyle m_{1}<m_{2}}
4686:{\displaystyle n_{1}>n_{2}}
4653:is favored. In the case where
4638:
4632:
4608:
4602:
4586:{\displaystyle m_{1}>m_{2}}
4546:{\displaystyle n_{1}>n_{2}}
4474:
4465:
4436:
4427:
4394:
4386:
4378:
4370:
4333:
4325:
4288:
4280:
4238:
4229:
4213:
4204:
4177:
4169:
4130:
4121:
4105:
4096:
4069:
4061:
3977:
3943:
3872:{\displaystyle n_{1}>n_{2}}
3800:
3791:
3758:
3750:
3742:
3734:
3697:
3689:
3652:
3644:
3605:
3596:
3569:
3561:
3522:
3513:
3486:
3478:
3394:
3366:
3355:For a given parallel reaction
3329:{\displaystyle {\frac {1}{m}}}
3174:
3117:
3102:
3094:
3076:
3067:
3055:
3025:
3017:
2999:
2974:
2950:
2941:
2879:
2873:
2825:
2796:
2768:
2753:
2745:
2727:
2718:
2706:
2676:
2668:
2650:
2625:
2601:
2592:
2471:
2459:
2174:
2158:
2095:
2079:
1794:
1624:
1612:
908:
879:
829:
800:
412:
398:
392:
378:
372:
358:
352:
338:
13:
1:
5880:Genetically modified organism
5647:Biotechnology industrial park
5023:
100:
5408:10.1016/j.watres.2014.11.053
2525:residence time distributions
260:is the order of the reaction
7:
5870:Environmental biotechnology
5361:Levenspiel, Octave (1998).
5008:Oscillatory baffled reactor
4991:
3140:into a cascade of CSTRs is
3136:associated with F(t) for a
1330:residence time distribution
1316:Residence time distribution
1308:Numerical solution required
113:
70:), is a common model for a
10:
6110:
5236:Limnology and Oceanography
5208:10.3402/tellusa.v25i1.9644
5040:Schmidt, Lanny D. (1998).
2805:{\displaystyle {\bar {t}}}
2519:Non-ideal cascade of CSTRs
566:stoichiometric coefficient
6049:
6023:
5930:
5810:
5740:
5689:
5680:
5639:
5584:
5563:
5552:
5541:Timeline of biotechnology
5528:
5257:10.4319/lo.2002.47.5.1545
4938:Environmental engineering
4898:{\displaystyle {\ce {C}}}
4876:{\displaystyle {\ce {B}}}
4854:{\displaystyle {\ce {C}}}
4832:{\displaystyle {\ce {B}}}
4770:{\displaystyle {\ce {D}}}
4748:{\displaystyle {\ce {A}}}
3916:{\displaystyle {\ce {A}}}
3894:{\displaystyle {\ce {A}}}
2523:With non-ideal reactors,
670:and the fluid flow rate (
80:environmental engineering
5897:Microbial biodegradation
5576:Industrial biotechnology
5536:History of biotechnology
5018:
4646:{\displaystyle {\ce {}}}
4616:{\displaystyle {\ce {}}}
27:Type of chemical reactor
5571:Colors of biotechnology
5284:Davis, Mark E. (2003).
5013:Plug flow reactor model
4933:in Greenpoint, Brooklyn
4929:Anaerobic digesters at
3352:for a desired product.
3204:
1403:A series of three CSTRs
1378:Modeling non-ideal flow
324:in a reactor of volume
135:perfect or ideal mixing
5965:Biomedical engineering
5672:Pharmaceutical company
5652:Biotechnology products
4934:
4899:
4877:
4855:
4833:
4811:
4771:
4749:
4727:
4687:
4647:
4617:
4587:
4547:
4507:
4351:
4306:
4261:
4150:
4042:
4015:
3988:
3954:
3917:
3895:
3873:
3833:
3715:
3670:
3625:
3542:
3459:
3432:
3405:
3377:
3330:
3303:
3235:Zeroth order reactions
3214:
3195:
3124:
2848:
2806:
2775:
2510:
2368:
2294:
2269:
2190:
2111:
2032:
1968:
1901:
1900:{\displaystyle C_{A1}}
1867:
1781:
1780:{\displaystyle -r_{A}}
1751:
1724:
1723:{\displaystyle C_{Ao}}
1690:
1670:
1575:
1507:Ideal cascade of CSTRs
1488:
1487:{\displaystyle F_{Ao}}
1458:
1420:
1404:
1367:
1349:
1325:
1295:
1201:
1134:
1023:
976:
940:
915:
836:
747:
654:
522:
419:
198:
110:
35:
4928:
4900:
4878:
4856:
4834:
4812:
4772:
4750:
4728:
4688:
4648:
4618:
4588:
4548:
4508:
4352:
4307:
4262:
4151:
4043:
4041:{\displaystyle k_{2}}
4016:
4014:{\displaystyle k_{1}}
3989:
3955:
3918:
3896:
3874:
3834:
3716:
3671:
3626:
3543:
3460:
3458:{\displaystyle k_{2}}
3433:
3431:{\displaystyle k_{1}}
3406:
3378:
3331:
3304:
3241:zeroth order reaction
3212:
3196:
3125:
2849:
2807:
2776:
2511:
2383:second order reaction
2369:
2295:
2249:
2208:zeroth order reaction
2191:
2112:
2033:
1969:
1902:
1868:
1782:
1752:
1750:{\displaystyle C_{A}}
1725:
1691:
1689:{\displaystyle \tau }
1671:
1576:
1489:
1459:
1425:fractional conversion
1418:
1402:
1368:
1366:{\displaystyle \tau }
1347:
1323:
1296:
1202:
1135:
1037:, the reaction rate,
1035:order of the reaction
1024:
1022:{\displaystyle \tau }
977:
941:
939:{\displaystyle \tau }
916:
837:
748:
655:
523:
420:
418:{\displaystyle 1.=-+}
273:single, irreversible
199:
108:
33:
5990:Chemical engineering
5853:Reproductive cloning
5717:Hybridoma technology
5667:Human Genome Project
4998:Laminar flow reactor
4969:Chemical engineering
4948:wastewater treatment
4887:
4865:
4843:
4821:
4787:
4759:
4737:
4697:
4657:
4627:
4597:
4557:
4517:
4513:. In the case where
4361:
4316:
4271:
4160:
4052:
4025:
3998:
3964:
3930:
3905:
3883:
3843:
3839:. In the case where
3725:
3680:
3635:
3552:
3469:
3442:
3415:
3387:
3359:
3313:
3247:
3144:
2867:
2856:volumetric flow rate
2816:
2787:
2533:
2389:
2306:
2214:
2123:
2044:
1978:
1914:
1881:
1813:
1761:
1734:
1704:
1680:
1585:
1515:
1497:first order reaction
1468:
1431:
1357:
1217:
1150:
1088:
1013:
951:
930:
847:
768:
680:
593:
576:is the reaction rate
430:
332:
144:
76:chemical engineering
5875:Genetic engineering
5858:Therapeutic cloning
5838:Bionic architecture
5818:Animal cell culture
5585:Biological concepts
5400:2015WatRe..71..282H
5248:2002LimOc..47.1545M
5199:1973Tell...25...58B
4956:Anaerobic digesters
4048:and rate equations
3465:and rate equations
3161:
1065:
343:Net accumulation of
5931:Interdisciplinary
5885:Molecular genetics
5631:Selective breeding
5439:Treatment Wetlands
4963:storm water runoff
4935:
4895:
4873:
4851:
4829:
4807:
4767:
4745:
4723:
4683:
4643:
4613:
4583:
4543:
4503:
4347:
4302:
4257:
4146:
4038:
4011:
3984:
3950:
3913:
3891:
3869:
3829:
3711:
3666:
3621:
3538:
3455:
3428:
3401:
3373:
3346:parallel reactions
3326:
3299:
3215:
3191:
3147:
3120:
2844:
2802:
2771:
2506:
2381:For an isothermal
2364:
2290:
2186:
2107:
2028:
1964:
1897:
1863:
1777:
1747:
1720:
1686:
1666:
1571:
1484:
1454:
1421:
1405:
1385:plug flow reactors
1363:
1350:
1326:
1291:
1197:
1130:
1063:
1019:
972:
970:
936:
911:
832:
743:
650:
518:
415:
194:
111:
56:mixed flow reactor
36:
6094:Chemical reactors
6081:
6080:
6010:Nanobiotechnology
6005:Molecular biology
5806:
5805:
5657:Biotechnology law
5448:978-1-56670-526-4
5372:978-0-471-25424-9
5295:978-1-62870-437-2
5145:978-1-118-63227-7
5093:978-0-07-340118-8
4893:
4871:
4849:
4827:
4805:
4799:
4793:
4765:
4743:
4637:
4607:
4471:
4433:
4425:
4398:
4392:
4376:
4345:
4331:
4300:
4286:
4235:
4210:
4189:
4175:
4127:
4102:
4081:
4067:
3982:
3976:
3970:
3948:
3942:
3936:
3911:
3889:
3797:
3789:
3762:
3756:
3740:
3709:
3695:
3664:
3650:
3602:
3581:
3567:
3519:
3498:
3484:
3399:
3393:
3371:
3365:
3344:When considering
3324:
3297:
3189:
3177:
3099:
3097:
3074:
3022:
3020:
2997:
2979:
2977:
2946:
2944:
2907:
2842:
2828:
2799:
2750:
2748:
2725:
2673:
2671:
2648:
2630:
2628:
2597:
2595:
2558:
2504:
2476:
2184:
2105:
2026:
1962:
1873:, where k is the
1861:
1664:
1569:
1452:
1411:Minimizing volume
1395:Cascades of CSTRs
1313:
1312:
1289:
1275:
1195:
1033:Depending on the
969:
877:
855:
798:
776:
688:
601:
461:
408:
404:
403:Net generation of
390:
386:
370:
366:
348:
344:
217:closed boundaries
179:
95:plug flow reactor
46:), also known as
16:(Redirected from
6101:
6069:
6068:
6057:
6056:
5907:Pharmacogenomics
5687:
5686:
5681:Basic techniques
5662:Green Revolution
5640:General concepts
5558:
5515:
5508:
5501:
5492:
5491:
5485:
5484:
5482:
5481:
5472:. Archived from
5462:
5453:
5452:
5434:
5428:
5427:
5383:
5377:
5376:
5358:
5352:
5351:
5333:
5327:
5326:
5314:
5308:
5307:
5281:
5270:
5269:
5259:
5242:(5): 1545–1553.
5227:
5221:
5220:
5210:
5178:
5172:
5171:
5165:
5157:
5131:
5120:
5119:
5113:
5105:
5079:
5056:
5055:
5037:
4944:Activated sludge
4904:
4902:
4901:
4896:
4894:
4891:
4882:
4880:
4879:
4874:
4872:
4869:
4860:
4858:
4857:
4852:
4850:
4847:
4838:
4836:
4835:
4830:
4828:
4825:
4816:
4814:
4813:
4808:
4806:
4803:
4797:
4791:
4781:Series reactions
4776:
4774:
4773:
4768:
4766:
4763:
4754:
4752:
4751:
4746:
4744:
4741:
4732:
4730:
4729:
4724:
4722:
4721:
4709:
4708:
4692:
4690:
4689:
4684:
4682:
4681:
4669:
4668:
4652:
4650:
4649:
4644:
4642:
4641:
4635:
4622:
4620:
4619:
4614:
4612:
4611:
4605:
4592:
4590:
4589:
4584:
4582:
4581:
4569:
4568:
4552:
4550:
4549:
4544:
4542:
4541:
4529:
4528:
4512:
4510:
4509:
4504:
4502:
4501:
4500:
4499:
4487:
4486:
4472:
4469:
4464:
4463:
4462:
4461:
4449:
4448:
4434:
4431:
4426:
4424:
4423:
4414:
4413:
4404:
4399:
4397:
4393:
4390:
4381:
4377:
4374:
4365:
4356:
4354:
4353:
4348:
4346:
4344:
4336:
4332:
4329:
4320:
4311:
4309:
4308:
4303:
4301:
4299:
4291:
4287:
4284:
4275:
4266:
4264:
4263:
4258:
4256:
4255:
4251:
4250:
4236:
4233:
4228:
4227:
4226:
4225:
4211:
4208:
4203:
4202:
4190:
4188:
4180:
4176:
4173:
4164:
4155:
4153:
4152:
4147:
4145:
4144:
4143:
4142:
4128:
4125:
4120:
4119:
4118:
4117:
4103:
4100:
4095:
4094:
4082:
4080:
4072:
4068:
4065:
4056:
4047:
4045:
4044:
4039:
4037:
4036:
4020:
4018:
4017:
4012:
4010:
4009:
3993:
3991:
3990:
3985:
3983:
3980:
3974:
3968:
3959:
3957:
3956:
3951:
3949:
3946:
3940:
3934:
3922:
3920:
3919:
3914:
3912:
3909:
3900:
3898:
3897:
3892:
3890:
3887:
3878:
3876:
3875:
3870:
3868:
3867:
3855:
3854:
3838:
3836:
3835:
3830:
3828:
3827:
3826:
3825:
3813:
3812:
3798:
3795:
3790:
3788:
3787:
3778:
3777:
3768:
3763:
3761:
3757:
3754:
3745:
3741:
3738:
3729:
3720:
3718:
3717:
3712:
3710:
3708:
3700:
3696:
3693:
3684:
3675:
3673:
3672:
3667:
3665:
3663:
3655:
3651:
3648:
3639:
3630:
3628:
3627:
3622:
3620:
3619:
3618:
3617:
3603:
3600:
3595:
3594:
3582:
3580:
3572:
3568:
3565:
3556:
3547:
3545:
3544:
3539:
3537:
3536:
3535:
3534:
3520:
3517:
3512:
3511:
3499:
3497:
3489:
3485:
3482:
3473:
3464:
3462:
3461:
3456:
3454:
3453:
3437:
3435:
3434:
3429:
3427:
3426:
3410:
3408:
3407:
3402:
3400:
3397:
3391:
3382:
3380:
3379:
3374:
3372:
3369:
3363:
3335:
3333:
3332:
3327:
3325:
3317:
3308:
3306:
3305:
3300:
3298:
3296:
3288:
3287:
3286:
3271:
3270:
3257:
3200:
3198:
3197:
3192:
3190:
3185:
3184:
3179:
3178:
3170:
3166:
3160:
3155:
3129:
3127:
3126:
3121:
3116:
3115:
3100:
3098:
3090:
3088:
3080:
3075:
3073:
3050:
3033:
3032:
3023:
3021:
3013:
3011:
3003:
2998:
2996:
2985:
2980:
2978:
2970:
2968:
2960:
2949:
2948:
2947:
2945:
2937:
2935:
2927:
2908:
2906:
2905:
2896:
2895:
2886:
2853:
2851:
2850:
2845:
2843:
2835:
2830:
2829:
2821:
2811:
2809:
2808:
2803:
2801:
2800:
2792:
2780:
2778:
2777:
2772:
2767:
2766:
2751:
2749:
2741:
2739:
2731:
2726:
2724:
2701:
2684:
2683:
2674:
2672:
2664:
2662:
2654:
2649:
2647:
2636:
2631:
2629:
2621:
2619:
2611:
2600:
2599:
2598:
2596:
2588:
2586:
2578:
2559:
2557:
2556:
2547:
2546:
2537:
2515:
2513:
2512:
2507:
2505:
2503:
2502:
2501:
2492:
2491:
2478:
2477:
2475:
2474:
2450:
2449:
2440:
2439:
2421:
2409:
2404:
2403:
2373:
2371:
2370:
2365:
2363:
2362:
2353:
2352:
2337:
2336:
2321:
2320:
2299:
2297:
2296:
2291:
2289:
2288:
2279:
2278:
2268:
2263:
2245:
2244:
2229:
2228:
2195:
2193:
2192:
2187:
2185:
2183:
2182:
2181:
2156:
2155:
2143:
2138:
2137:
2116:
2114:
2113:
2108:
2106:
2104:
2103:
2102:
2077:
2076:
2064:
2059:
2058:
2037:
2035:
2034:
2029:
2027:
2025:
2011:
2010:
1998:
1993:
1992:
1973:
1971:
1970:
1965:
1963:
1961:
1947:
1946:
1934:
1929:
1928:
1906:
1904:
1903:
1898:
1896:
1895:
1872:
1870:
1869:
1864:
1862:
1860:
1846:
1845:
1833:
1828:
1827:
1789:rate of reaction
1786:
1784:
1783:
1778:
1776:
1775:
1756:
1754:
1753:
1748:
1746:
1745:
1729:
1727:
1726:
1721:
1719:
1718:
1700:of the reactor,
1695:
1693:
1692:
1687:
1675:
1673:
1672:
1667:
1665:
1663:
1662:
1661:
1645:
1644:
1643:
1628:
1627:
1602:
1597:
1596:
1580:
1578:
1577:
1572:
1570:
1568:
1567:
1566:
1553:
1552:
1551:
1539:
1538:
1525:
1493:
1491:
1490:
1485:
1483:
1482:
1463:
1461:
1460:
1455:
1453:
1451:
1450:
1435:
1372:
1370:
1369:
1364:
1300:
1298:
1297:
1292:
1290:
1288:
1277:
1276:
1274:
1273:
1246:
1234:
1229:
1228:
1206:
1204:
1203:
1198:
1196:
1194:
1180:
1179:
1167:
1162:
1161:
1139:
1137:
1136:
1131:
1129:
1118:
1117:
1116:
1100:
1099:
1066:
1062:
1028:
1026:
1025:
1020:
981:
979:
978:
973:
971:
962:
945:
943:
942:
937:
920:
918:
917:
912:
907:
906:
894:
893:
878:
870:
865:
864:
853:
841:
839:
838:
833:
828:
827:
815:
814:
799:
791:
786:
785:
774:
762:and simplified:
752:
750:
749:
744:
742:
741:
726:
725:
710:
709:
686:
659:
657:
656:
651:
649:
648:
633:
632:
620:
619:
599:
527:
525:
524:
519:
517:
516:
507:
506:
491:
490:
478:
477:
462:
460:
452:
451:
450:
437:
424:
422:
421:
416:
406:
405:
402:
391:
388:
384:
371:
368:
364:
346:
345:
342:
228:n-order reaction
203:
201:
200:
195:
193:
192:
180:
178:
170:
169:
168:
155:
153:
152:
72:chemical reactor
21:
6109:
6108:
6104:
6103:
6102:
6100:
6099:
6098:
6084:
6083:
6082:
6077:
6045:
6019:
5960:Biopharmacology
5932:
5926:
5802:
5773:Electrophoresis
5768:Kidney dialysis
5758:Crystallization
5736:
5682:
5676:
5635:
5580:
5559:
5550:
5524:
5519:
5489:
5488:
5479:
5477:
5464:
5463:
5456:
5449:
5435:
5431:
5384:
5380:
5373:
5359:
5355:
5348:
5334:
5330:
5315:
5311:
5296:
5282:
5273:
5228:
5224:
5179:
5175:
5159:
5158:
5146:
5132:
5123:
5107:
5106:
5094:
5080:
5059:
5052:
5038:
5031:
5026:
5021:
4994:
4971:
4940:
4919:
4890:
4888:
4885:
4884:
4868:
4866:
4863:
4862:
4846:
4844:
4841:
4840:
4824:
4822:
4819:
4818:
4790:
4788:
4785:
4784:
4762:
4760:
4757:
4756:
4740:
4738:
4735:
4734:
4717:
4713:
4704:
4700:
4698:
4695:
4694:
4677:
4673:
4664:
4660:
4658:
4655:
4654:
4631:
4630:
4628:
4625:
4624:
4601:
4600:
4598:
4595:
4594:
4577:
4573:
4564:
4560:
4558:
4555:
4554:
4537:
4533:
4524:
4520:
4518:
4515:
4514:
4495:
4491:
4482:
4478:
4477:
4473:
4468:
4457:
4453:
4444:
4440:
4439:
4435:
4430:
4419:
4415:
4409:
4405:
4403:
4389:
4382:
4373:
4366:
4364:
4362:
4359:
4358:
4337:
4328:
4321:
4319:
4317:
4314:
4313:
4292:
4283:
4276:
4274:
4272:
4269:
4268:
4246:
4242:
4241:
4237:
4232:
4221:
4217:
4216:
4212:
4207:
4198:
4194:
4181:
4172:
4165:
4163:
4161:
4158:
4157:
4138:
4134:
4133:
4129:
4124:
4113:
4109:
4108:
4104:
4099:
4090:
4086:
4073:
4064:
4057:
4055:
4053:
4050:
4049:
4032:
4028:
4026:
4023:
4022:
4005:
4001:
3999:
3996:
3995:
3994:with constants
3967:
3965:
3962:
3961:
3933:
3931:
3928:
3927:
3908:
3906:
3903:
3902:
3886:
3884:
3881:
3880:
3863:
3859:
3850:
3846:
3844:
3841:
3840:
3821:
3817:
3808:
3804:
3803:
3799:
3794:
3783:
3779:
3773:
3769:
3767:
3753:
3746:
3737:
3730:
3728:
3726:
3723:
3722:
3701:
3692:
3685:
3683:
3681:
3678:
3677:
3656:
3647:
3640:
3638:
3636:
3633:
3632:
3613:
3609:
3608:
3604:
3599:
3590:
3586:
3573:
3564:
3557:
3555:
3553:
3550:
3549:
3530:
3526:
3525:
3521:
3516:
3507:
3503:
3490:
3481:
3474:
3472:
3470:
3467:
3466:
3449:
3445:
3443:
3440:
3439:
3422:
3418:
3416:
3413:
3412:
3411:with constants
3390:
3388:
3385:
3384:
3362:
3360:
3357:
3356:
3342:
3316:
3314:
3311:
3310:
3289:
3279:
3275:
3263:
3259:
3258:
3256:
3248:
3245:
3244:
3237:
3223:operating costs
3207:
3180:
3169:
3168:
3167:
3165:
3156:
3151:
3145:
3142:
3141:
3105:
3101:
3089:
3081:
3079:
3054:
3049:
3028:
3024:
3012:
3004:
3002:
2989:
2984:
2969:
2961:
2959:
2936:
2928:
2926:
2922:
2918:
2901:
2897:
2891:
2887:
2885:
2868:
2865:
2864:
2854:where Q is the
2834:
2820:
2819:
2817:
2814:
2813:
2791:
2790:
2788:
2785:
2784:
2756:
2752:
2740:
2732:
2730:
2705:
2700:
2679:
2675:
2663:
2655:
2653:
2640:
2635:
2620:
2612:
2610:
2587:
2579:
2577:
2573:
2569:
2552:
2548:
2542:
2538:
2536:
2534:
2531:
2530:
2521:
2497:
2493:
2487:
2483:
2479:
2455:
2451:
2445:
2441:
2435:
2431:
2420:
2410:
2408:
2396:
2392:
2390:
2387:
2386:
2379:
2358:
2354:
2348:
2344:
2329:
2325:
2313:
2309:
2307:
2304:
2303:
2284:
2280:
2274:
2270:
2264:
2253:
2237:
2233:
2221:
2217:
2215:
2212:
2211:
2204:
2177:
2173:
2157:
2148:
2144:
2142:
2130:
2126:
2124:
2121:
2120:
2098:
2094:
2078:
2069:
2065:
2063:
2051:
2047:
2045:
2042:
2041:
2012:
2003:
1999:
1997:
1985:
1981:
1979:
1976:
1975:
1948:
1939:
1935:
1933:
1921:
1917:
1915:
1912:
1911:
1888:
1884:
1882:
1879:
1878:
1847:
1838:
1834:
1832:
1820:
1816:
1814:
1811:
1810:
1797:
1771:
1767:
1762:
1759:
1758:
1741:
1737:
1735:
1732:
1731:
1711:
1707:
1705:
1702:
1701:
1681:
1678:
1677:
1654:
1650:
1646:
1636:
1632:
1608:
1604:
1603:
1601:
1592:
1588:
1586:
1583:
1582:
1562:
1558:
1554:
1547:
1543:
1531:
1527:
1526:
1524:
1516:
1513:
1512:
1509:
1475:
1471:
1469:
1466:
1465:
1443:
1439:
1434:
1432:
1429:
1428:
1413:
1397:
1380:
1358:
1355:
1354:
1338:
1318:
1309:
1278:
1266:
1262:
1245:
1235:
1233:
1224:
1220:
1218:
1215:
1214:
1181:
1172:
1168:
1166:
1157:
1153:
1151:
1148:
1147:
1122:
1109:
1105:
1104:
1095:
1091:
1089:
1086:
1085:
1076:
1069:Reaction Order
1042:
1014:
1011:
1010:
999:
990:
960:
952:
949:
948:
931:
928:
927:
902:
898:
886:
882:
869:
860:
856:
848:
845:
844:
823:
819:
807:
803:
790:
781:
777:
769:
766:
765:
760:
737:
733:
721:
717:
702:
698:
681:
678:
677:
644:
640:
628:
624:
612:
608:
594:
591:
590:
585:
574:
562:
550:
538:
512:
508:
502:
498:
486:
482:
470:
466:
453:
446:
442:
438:
436:
431:
428:
427:
401:
387:
367:
341:
333:
330:
329:
318:
305:
298:
282:
250:
239:
220:constant fluid
209:
188:
187:
171:
164:
160:
156:
154:
148:
147:
145:
142:
141:
116:
103:
52:backmix reactor
28:
23:
22:
15:
12:
11:
5:
6107:
6097:
6096:
6079:
6078:
6076:
6075:
6063:
6050:
6047:
6046:
6044:
6043:
6038:
6033:
6027:
6025:
6021:
6020:
6018:
6017:
6012:
6007:
6002:
5997:
5992:
5987:
5982:
5977:
5972:
5967:
5962:
5957:
5952:
5950:Bioengineering
5947:
5945:Bioelectronics
5942:
5936:
5934:
5928:
5927:
5925:
5924:
5922:Tissue culture
5919:
5914:
5909:
5904:
5899:
5894:
5889:
5888:
5887:
5882:
5872:
5867:
5862:
5861:
5860:
5855:
5845:
5840:
5835:
5830:
5828:Bioinformatics
5825:
5823:Biofabrication
5820:
5814:
5812:
5808:
5807:
5804:
5803:
5801:
5800:
5795:
5790:
5785:
5780:
5775:
5770:
5765:
5763:Chromatography
5760:
5755:
5750:
5748:Centrifugation
5744:
5742:
5741:Chemical field
5738:
5737:
5735:
5734:
5729:
5724:
5719:
5714:
5712:Flow cytometry
5709:
5704:
5699:
5693:
5691:
5684:
5678:
5677:
5675:
5674:
5669:
5664:
5659:
5654:
5649:
5643:
5641:
5637:
5636:
5634:
5633:
5628:
5623:
5618:
5613:
5608:
5599:
5594:
5588:
5586:
5582:
5581:
5579:
5578:
5573:
5567:
5565:
5561:
5560:
5553:
5551:
5549:
5548:
5543:
5538:
5532:
5530:
5526:
5525:
5518:
5517:
5510:
5503:
5495:
5487:
5486:
5454:
5447:
5429:
5388:Water Research
5378:
5371:
5353:
5346:
5328:
5309:
5294:
5271:
5222:
5173:
5144:
5121:
5092:
5057:
5050:
5028:
5027:
5025:
5022:
5020:
5017:
5016:
5015:
5010:
5005:
5000:
4993:
4990:
4989:
4988:
4982:
4976:
4975:
4970:
4967:
4966:
4965:
4959:
4953:
4950:
4939:
4936:
4918:
4915:
4905:. Typically a
4802:
4796:
4720:
4716:
4712:
4707:
4703:
4680:
4676:
4672:
4667:
4663:
4640:
4634:
4610:
4604:
4580:
4576:
4572:
4567:
4563:
4540:
4536:
4532:
4527:
4523:
4498:
4494:
4490:
4485:
4481:
4476:
4467:
4460:
4456:
4452:
4447:
4443:
4438:
4429:
4422:
4418:
4412:
4408:
4402:
4396:
4388:
4385:
4380:
4372:
4369:
4343:
4340:
4335:
4327:
4324:
4298:
4295:
4290:
4282:
4279:
4254:
4249:
4245:
4240:
4231:
4224:
4220:
4215:
4206:
4201:
4197:
4193:
4187:
4184:
4179:
4171:
4168:
4141:
4137:
4132:
4123:
4116:
4112:
4107:
4098:
4093:
4089:
4085:
4079:
4076:
4071:
4063:
4060:
4035:
4031:
4008:
4004:
3979:
3973:
3945:
3939:
3866:
3862:
3858:
3853:
3849:
3824:
3820:
3816:
3811:
3807:
3802:
3793:
3786:
3782:
3776:
3772:
3766:
3760:
3752:
3749:
3744:
3736:
3733:
3707:
3704:
3699:
3691:
3688:
3662:
3659:
3654:
3646:
3643:
3616:
3612:
3607:
3598:
3593:
3589:
3585:
3579:
3576:
3571:
3563:
3560:
3533:
3529:
3524:
3515:
3510:
3506:
3502:
3496:
3493:
3488:
3480:
3477:
3452:
3448:
3425:
3421:
3396:
3368:
3341:
3338:
3323:
3320:
3295:
3292:
3285:
3282:
3278:
3274:
3269:
3266:
3262:
3255:
3252:
3236:
3233:
3206:
3203:
3188:
3183:
3176:
3173:
3164:
3159:
3154:
3150:
3138:pulse stimulus
3119:
3114:
3111:
3108:
3104:
3096:
3093:
3087:
3084:
3078:
3072:
3069:
3066:
3063:
3060:
3057:
3053:
3048:
3045:
3042:
3039:
3036:
3031:
3027:
3019:
3016:
3010:
3007:
3001:
2995:
2992:
2988:
2983:
2976:
2973:
2967:
2964:
2958:
2955:
2952:
2943:
2940:
2934:
2931:
2925:
2921:
2917:
2914:
2911:
2904:
2900:
2894:
2890:
2884:
2881:
2878:
2875:
2872:
2841:
2838:
2833:
2827:
2824:
2798:
2795:
2770:
2765:
2762:
2759:
2755:
2747:
2744:
2738:
2735:
2729:
2723:
2720:
2717:
2714:
2711:
2708:
2704:
2699:
2696:
2693:
2690:
2687:
2682:
2678:
2670:
2667:
2661:
2658:
2652:
2646:
2643:
2639:
2634:
2627:
2624:
2618:
2615:
2609:
2606:
2603:
2594:
2591:
2585:
2582:
2576:
2572:
2568:
2565:
2562:
2555:
2551:
2545:
2541:
2520:
2517:
2500:
2496:
2490:
2486:
2482:
2473:
2470:
2467:
2464:
2461:
2458:
2454:
2448:
2444:
2438:
2434:
2430:
2427:
2424:
2419:
2416:
2413:
2407:
2402:
2399:
2395:
2378:
2375:
2361:
2357:
2351:
2347:
2343:
2340:
2335:
2332:
2328:
2324:
2319:
2316:
2312:
2287:
2283:
2277:
2273:
2267:
2262:
2259:
2256:
2252:
2248:
2243:
2240:
2236:
2232:
2227:
2224:
2220:
2203:
2200:
2180:
2176:
2172:
2169:
2166:
2163:
2160:
2154:
2151:
2147:
2141:
2136:
2133:
2129:
2101:
2097:
2093:
2090:
2087:
2084:
2081:
2075:
2072:
2068:
2062:
2057:
2054:
2050:
2024:
2021:
2018:
2015:
2009:
2006:
2002:
1996:
1991:
1988:
1984:
1960:
1957:
1954:
1951:
1945:
1942:
1938:
1932:
1927:
1924:
1920:
1894:
1891:
1887:
1859:
1856:
1853:
1850:
1844:
1841:
1837:
1831:
1826:
1823:
1819:
1809:For one CSTR:
1796:
1793:
1774:
1770:
1766:
1744:
1740:
1717:
1714:
1710:
1685:
1660:
1657:
1653:
1649:
1642:
1639:
1635:
1631:
1626:
1623:
1620:
1617:
1614:
1611:
1607:
1600:
1595:
1591:
1565:
1561:
1557:
1550:
1546:
1542:
1537:
1534:
1530:
1523:
1520:
1508:
1505:
1481:
1478:
1474:
1449:
1446:
1442:
1438:
1412:
1409:
1396:
1393:
1379:
1376:
1362:
1337:
1336:Non-ideal CSTR
1334:
1317:
1314:
1311:
1310:
1306:
1302:
1301:
1287:
1284:
1281:
1272:
1269:
1265:
1261:
1258:
1255:
1252:
1249:
1244:
1241:
1238:
1232:
1227:
1223:
1212:
1208:
1207:
1193:
1190:
1187:
1184:
1178:
1175:
1171:
1165:
1160:
1156:
1145:
1141:
1140:
1128:
1125:
1121:
1115:
1112:
1108:
1103:
1098:
1094:
1083:
1079:
1078:
1074:
1070:
1040:
1018:
1006:Residence time
1003:
1002:
997:
993:
988:
984:
968:
965:
959:
956:
935:
910:
905:
901:
897:
892:
889:
885:
881:
876:
873:
868:
863:
859:
852:
831:
826:
822:
818:
813:
810:
806:
802:
797:
794:
789:
784:
780:
773:
758:
740:
736:
732:
729:
724:
720:
716:
713:
708:
705:
701:
697:
694:
691:
685:
647:
643:
639:
636:
631:
627:
623:
618:
615:
611:
607:
604:
598:
583:
578:
577:
572:
568:
560:
556:
548:
544:
536:
515:
511:
505:
501:
497:
494:
489:
485:
481:
476:
473:
469:
465:
459:
456:
449:
445:
441:
435:
414:
411:
400:
397:
394:
383:
380:
377:
374:
363:
360:
357:
354:
351:
340:
337:
316:
311:
310:
303:
296:
292:
285:
280:
271:
261:
248:
237:
225:
218:
215:
207:
191:
186:
183:
177:
174:
167:
163:
159:
151:
136:
115:
112:
102:
99:
91:perfect mixing
26:
9:
6:
4:
3:
2:
6106:
6095:
6092:
6091:
6089:
6074:
6073:
6064:
6062:
6061:
6052:
6051:
6048:
6042:
6039:
6037:
6034:
6032:
6029:
6028:
6026:
6022:
6016:
6013:
6011:
6008:
6006:
6003:
6001:
5998:
5996:
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5971:
5968:
5966:
5963:
5961:
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5938:
5937:
5935:
5929:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5886:
5883:
5881:
5878:
5877:
5876:
5873:
5871:
5868:
5866:
5863:
5859:
5856:
5854:
5851:
5850:
5849:
5846:
5844:
5843:Cell immunity
5841:
5839:
5836:
5834:
5831:
5829:
5826:
5824:
5821:
5819:
5816:
5815:
5813:
5809:
5799:
5798:Sedimentation
5796:
5794:
5791:
5789:
5786:
5784:
5781:
5779:
5776:
5774:
5771:
5769:
5766:
5764:
5761:
5759:
5756:
5754:
5751:
5749:
5746:
5745:
5743:
5739:
5733:
5730:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5708:
5707:Cultured meat
5705:
5703:
5700:
5698:
5695:
5694:
5692:
5690:Biology field
5688:
5685:
5679:
5673:
5670:
5668:
5665:
5663:
5660:
5658:
5655:
5653:
5650:
5648:
5645:
5644:
5642:
5638:
5632:
5629:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5603:
5600:
5598:
5595:
5593:
5590:
5589:
5587:
5583:
5577:
5574:
5572:
5569:
5568:
5566:
5562:
5557:
5547:
5544:
5542:
5539:
5537:
5534:
5533:
5531:
5527:
5523:
5522:Biotechnology
5516:
5511:
5509:
5504:
5502:
5497:
5496:
5493:
5476:on 2013-12-14
5475:
5471:
5467:
5461:
5459:
5450:
5444:
5440:
5433:
5425:
5421:
5417:
5413:
5409:
5405:
5401:
5397:
5393:
5389:
5382:
5374:
5368:
5364:
5357:
5349:
5347:9781118368251
5343:
5339:
5332:
5325:(6): 723–725.
5324:
5320:
5313:
5305:
5301:
5297:
5291:
5287:
5280:
5278:
5276:
5267:
5263:
5258:
5253:
5249:
5245:
5241:
5237:
5233:
5226:
5218:
5214:
5209:
5204:
5200:
5196:
5192:
5188:
5184:
5177:
5169:
5163:
5155:
5151:
5147:
5141:
5137:
5130:
5128:
5126:
5117:
5111:
5103:
5099:
5095:
5089:
5085:
5078:
5076:
5074:
5072:
5070:
5068:
5066:
5064:
5062:
5053:
5051:0-19-510588-5
5047:
5043:
5036:
5034:
5029:
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5011:
5009:
5006:
5004:
5001:
4999:
4996:
4995:
4986:
4983:
4981:
4978:
4977:
4973:
4972:
4964:
4960:
4957:
4954:
4951:
4949:
4945:
4942:
4941:
4932:
4927:
4923:
4914:
4912:
4908:
4907:batch reactor
4782:
4778:
4718:
4714:
4710:
4705:
4701:
4678:
4674:
4670:
4665:
4661:
4578:
4574:
4570:
4565:
4561:
4538:
4534:
4530:
4525:
4521:
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4296:
4293:
4277:
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4247:
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4218:
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4195:
4191:
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4182:
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4077:
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4033:
4029:
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3822:
3818:
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3809:
3805:
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3764:
3747:
3731:
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3660:
3657:
3641:
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3583:
3577:
3574:
3558:
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3508:
3504:
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3475:
3450:
3446:
3423:
3419:
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3351:
3347:
3337:
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3318:
3293:
3290:
3283:
3280:
3276:
3272:
3267:
3264:
3260:
3253:
3250:
3242:
3232:
3229:
3224:
3220:
3211:
3202:
3186:
3181:
3171:
3162:
3157:
3152:
3148:
3139:
3135:
3130:
3112:
3109:
3106:
3091:
3085:
3082:
3070:
3064:
3061:
3058:
3051:
3046:
3043:
3040:
3037:
3034:
3029:
3014:
3008:
3005:
2993:
2990:
2986:
2981:
2971:
2965:
2962:
2956:
2953:
2938:
2932:
2929:
2923:
2919:
2915:
2912:
2909:
2902:
2898:
2892:
2888:
2882:
2876:
2870:
2862:
2859:
2857:
2839:
2836:
2831:
2822:
2793:
2781:
2763:
2760:
2757:
2742:
2736:
2733:
2721:
2715:
2712:
2709:
2702:
2697:
2694:
2691:
2688:
2685:
2680:
2665:
2659:
2656:
2644:
2641:
2637:
2632:
2622:
2616:
2613:
2607:
2604:
2589:
2583:
2580:
2574:
2570:
2566:
2563:
2560:
2553:
2549:
2543:
2539:
2528:
2526:
2516:
2498:
2494:
2488:
2484:
2480:
2468:
2465:
2462:
2456:
2452:
2446:
2442:
2436:
2432:
2428:
2425:
2422:
2417:
2414:
2411:
2405:
2400:
2397:
2393:
2384:
2374:
2359:
2355:
2349:
2345:
2341:
2338:
2333:
2330:
2326:
2322:
2317:
2314:
2310:
2300:
2285:
2281:
2275:
2271:
2265:
2260:
2257:
2254:
2250:
2246:
2241:
2238:
2234:
2230:
2225:
2222:
2218:
2209:
2199:
2196:
2178:
2170:
2167:
2164:
2161:
2152:
2149:
2145:
2139:
2134:
2131:
2127:
2117:
2099:
2091:
2088:
2085:
2082:
2073:
2070:
2066:
2060:
2055:
2052:
2048:
2038:
2022:
2019:
2016:
2013:
2007:
2004:
2000:
1994:
1989:
1986:
1982:
1958:
1955:
1952:
1949:
1943:
1940:
1936:
1930:
1925:
1922:
1918:
1908:
1892:
1889:
1885:
1876:
1875:rate constant
1857:
1854:
1851:
1848:
1842:
1839:
1835:
1829:
1824:
1821:
1817:
1807:
1806:
1802:
1792:
1790:
1772:
1768:
1764:
1742:
1738:
1715:
1712:
1708:
1699:
1683:
1658:
1655:
1651:
1647:
1640:
1637:
1633:
1629:
1621:
1618:
1615:
1609:
1605:
1598:
1593:
1589:
1563:
1559:
1555:
1548:
1544:
1540:
1535:
1532:
1528:
1521:
1518:
1504:
1502:
1498:
1479:
1476:
1472:
1447:
1444:
1440:
1436:
1426:
1417:
1408:
1401:
1392:
1388:
1386:
1375:
1373:
1360:
1346:
1342:
1333:
1331:
1322:
1307:
1304:
1303:
1285:
1282:
1279:
1270:
1267:
1263:
1259:
1256:
1253:
1250:
1247:
1242:
1239:
1236:
1230:
1225:
1221:
1213:
1210:
1209:
1191:
1188:
1185:
1182:
1176:
1173:
1169:
1163:
1158:
1154:
1146:
1143:
1142:
1126:
1123:
1119:
1113:
1110:
1106:
1101:
1096:
1092:
1084:
1081:
1080:
1077:
1071:
1068:
1067:
1061:
1059:
1054:
1052:
1047:
1043:
1036:
1031:
1029:
1016:
1007:
1000:
994:
991:
985:
982:
966:
963:
957:
954:
933:
926:
925:
924:
921:
903:
899:
895:
890:
887:
883:
874:
871:
866:
861:
857:
850:
842:
824:
820:
816:
811:
808:
804:
795:
792:
787:
782:
778:
771:
763:
761:
753:
738:
734:
730:
727:
722:
718:
714:
711:
706:
703:
699:
695:
692:
689:
683:
675:
673:
669:
665:
660:
645:
641:
637:
634:
629:
625:
621:
616:
613:
609:
605:
602:
596:
588:
586:
575:
569:
567:
563:
557:
555:
551:
545:
543:
539:
533:
532:
531:
528:
513:
509:
503:
499:
495:
492:
487:
483:
479:
474:
471:
467:
463:
457:
454:
447:
443:
439:
433:
425:
409:
395:
381:
375:
361:
355:
349:
335:
327:
323:
319:
309:
306:
299:
293:
290:
287:All reactant
286:
283:
276:
272:
269:
265:
262:
259:
255:
251:
244:
240:
233:
229:
226:
223:
219:
216:
214:
210:
184:
181:
175:
172:
165:
161:
157:
140:
137:
134:
133:
132:
131:
127:
125:
121:
107:
98:
96:
92:
87:
85:
81:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
32:
19:
6070:
6058:
5995:Microbiology
5980:Biochemicals
5892:Gene therapy
5833:Biosynthesis
5811:Applications
5752:
5732:Spectroscopy
5702:Cell culture
5611:Fermentation
5478:. Retrieved
5474:the original
5469:
5438:
5432:
5391:
5387:
5381:
5362:
5356:
5337:
5331:
5322:
5318:
5312:
5285:
5239:
5235:
5225:
5193:(1): 58–62.
5190:
5186:
5176:
5135:
5083:
5041:
5003:Microreactor
4980:Fermentation
4946:process for
4920:
4917:Applications
4779:
4777:is favored.
4357:. Therefore
3925:
3721:. Therefore
3354:
3343:
3238:
3216:
3131:
2863:
2860:
2782:
2529:
2522:
2380:
2377:Second order
2301:
2205:
2202:Zeroth order
2197:
2118:
2039:
1909:
1808:
1805:steady state
1798:
1510:
1422:
1406:
1389:
1381:
1353:
1351:
1339:
1327:
1072:
1057:
1055:
1045:
1038:
1032:
1009:
1004:
995:
986:
947:
922:
843:
764:
756:
754:
676:
671:
667:
663:
661:
589:
581:
579:
570:
558:
553:
546:
541:
534:
529:
426:
325:
321:
314:
312:
307:
301:
294:
288:
278:
270:is constant)
267:
257:
253:
246:
242:
235:
231:
212:
205:
139:steady state
130:Assumptions:
129:
128:
123:
119:
117:
88:
67:
63:
59:
55:
51:
47:
43:
39:
37:
5985:Biorobotics
5975:Biomimetics
5970:Biomedicine
5394:: 282–293.
3350:selectivity
1910:Two CSTRs:
1795:First order
320:of species
5940:Bioeconomy
5912:Stem cells
5865:Embryology
5788:Filtration
5778:Extraction
5697:Bioreactor
5480:2020-04-30
5024:References
4987:production
1801:isothermal
1698:space time
264:isothermal
101:Ideal CSTR
5783:Fed Batch
5683:and tools
5416:0043-1354
5365:. Wiley.
5304:880604539
5217:0040-2826
5162:cite book
5154:856567226
5110:cite book
5102:858915999
4801:⟶
4795:⟶
4489:−
4451:−
3978:⟶
3944:⟶
3815:−
3395:⟶
3367:⟶
3273:−
3251:τ
3175:¯
3149:σ
3110:−
3095:¯
3062:−
3018:¯
2975:¯
2942:¯
2924:−
2916:−
2826:¯
2797:¯
2761:−
2746:¯
2713:−
2669:¯
2626:¯
2593:¯
2575:−
2567:−
2495:τ
2466:−
2443:τ
2412:−
2356:τ
2339:−
2282:τ
2251:∑
2247:−
2171:τ
2092:τ
2023:τ
1959:τ
1858:τ
1765:−
1684:τ
1648:−
1630:−
1619:−
1590:τ
1556:−
1541:−
1519:τ
1361:τ
1286:τ
1260:τ
1237:−
1192:τ
1127:τ
1120:−
1017:τ
955:τ
934:τ
896:−
875:τ
817:−
728:−
712:−
635:−
622:−
500:ν
480:−
376:−
241:), where
6088:Category
6060:Category
6015:Virology
5917:Telomere
5564:Branches
5424:25635665
5266:11505988
4992:See also
4783:such as
3134:variance
1676:, where
1305:Other n
275:reaction
204:, where
114:Modeling
84:slurries
62:), or a
6072:Commons
5955:Biology
5848:Cloning
5626:Protein
5621:Plasmid
5529:History
5396:Bibcode
5244:Bibcode
5195:Bibcode
3219:capital
1799:For an
1787:is the
1696:is the
564:is the
222:density
6000:Mining
5933:fields
5592:Allele
5445:
5422:
5414:
5369:
5344:
5302:
5292:
5264:
5215:
5187:Tellus
5152:
5142:
5100:
5090:
5048:
4985:Biogas
4156:and
3548:and
1791:of A.
923:where
854:
775:
687:
600:
530:where
407:
385:
365:
347:
6024:Lists
5902:Omics
5262:S2CID
5019:Notes
3228:pumps
284:= −1)
68:CFSTR
5753:CSTR
5722:HPLC
5616:Gene
5597:Cell
5443:ISBN
5420:PMID
5412:ISSN
5367:ISBN
5342:ISBN
5300:OCLC
5290:ISBN
5213:ISSN
5168:link
5150:OCLC
5140:ISBN
5116:link
5098:OCLC
5088:ISBN
5046:ISBN
4839:and
4711:<
4693:and
4671:>
4623:and
4571:>
4553:and
4531:>
4021:and
3960:and
3857:>
3438:and
3383:and
3221:and
3205:Cost
1974:and
1877:and
1211:n=2
1144:n=1
1082:n=0
256:and
78:and
48:vat-
44:CSTR
38:The
5793:PFR
5727:NMR
5606:RNA
5602:DNA
5404:doi
5252:doi
5203:doi
4911:PFR
4909:or
4312:by
3676:by
1501:PFR
674:):
389:out
74:in
60:MFR
50:or
6090::
5468:.
5457:^
5418:.
5410:.
5402:.
5392:71
5390:.
5323:48
5321:.
5298:.
5274:^
5260:.
5250:.
5240:47
5238:.
5234:.
5211:.
5201:.
5191:25
5189:.
5185:.
5164:}}
5160:{{
5148:.
5124:^
5112:}}
5108:{{
5096:.
5060:^
5032:^
3923:.
3243::
3201:.
2858:.
989:Ao
851:6.
772:5.
684:4.
597:3.
537:Ao
434:2.
369:in
336:1.
300:=
254:A,
236:kC
234:=
126:.
86:.
54:,
5604:/
5514:e
5507:t
5500:v
5483:.
5451:.
5426:.
5406::
5398::
5375:.
5350:.
5306:.
5268:.
5254::
5246::
5219:.
5205::
5197::
5170:)
5156:.
5118:)
5104:.
5054:.
4892:C
4870:B
4848:C
4826:B
4804:C
4798:B
4792:A
4764:D
4742:A
4719:2
4715:m
4706:1
4702:m
4679:2
4675:n
4666:1
4662:n
4639:]
4636:D
4633:[
4609:]
4606:A
4603:[
4579:2
4575:m
4566:1
4562:m
4539:2
4535:n
4526:1
4522:n
4497:2
4493:m
4484:1
4480:m
4475:]
4470:D
4466:[
4459:2
4455:n
4446:1
4442:n
4437:]
4432:A
4428:[
4421:2
4417:k
4411:1
4407:k
4401:=
4395:]
4391:C
4387:[
4384:d
4379:]
4375:B
4371:[
4368:d
4342:t
4339:d
4334:]
4330:C
4326:[
4323:d
4297:t
4294:d
4289:]
4285:B
4281:[
4278:d
4253:2
4248:1
4244:m
4239:]
4234:D
4230:[
4223:2
4219:n
4214:]
4209:A
4205:[
4200:2
4196:k
4192:=
4186:t
4183:d
4178:]
4174:C
4170:[
4167:d
4140:1
4136:m
4131:]
4126:D
4122:[
4115:1
4111:n
4106:]
4101:A
4097:[
4092:1
4088:k
4084:=
4078:t
4075:d
4070:]
4066:B
4062:[
4059:d
4034:2
4030:k
4007:1
4003:k
3981:C
3975:D
3972:+
3969:A
3947:B
3941:D
3938:+
3935:A
3910:A
3888:A
3865:2
3861:n
3852:1
3848:n
3823:2
3819:n
3810:1
3806:n
3801:]
3796:A
3792:[
3785:2
3781:k
3775:1
3771:k
3765:=
3759:]
3755:C
3751:[
3748:d
3743:]
3739:B
3735:[
3732:d
3706:t
3703:d
3698:]
3694:C
3690:[
3687:d
3661:t
3658:d
3653:]
3649:B
3645:[
3642:d
3615:2
3611:n
3606:]
3601:A
3597:[
3592:2
3588:k
3584:=
3578:t
3575:d
3570:]
3566:C
3562:[
3559:d
3532:1
3528:n
3523:]
3518:A
3514:[
3509:1
3505:k
3501:=
3495:t
3492:d
3487:]
3483:B
3479:[
3476:d
3451:2
3447:k
3424:1
3420:k
3398:C
3392:A
3370:B
3364:A
3322:m
3319:1
3294:k
3291:m
3284:m
3281:A
3277:C
3268:o
3265:A
3261:C
3254:=
3187:n
3182:2
3172:t
3163:=
3158:2
3153:t
3118:]
3113:1
3107:n
3103:)
3092:t
3086:t
3083:n
3077:(
3071:!
3068:)
3065:1
3059:n
3056:(
3052:1
3047:+
3044:.
3041:.
3038:.
3035:+
3030:2
3026:)
3015:t
3009:t
3006:n
3000:(
2994:!
2991:2
2987:1
2982:+
2972:t
2966:t
2963:n
2957:+
2954:1
2951:[
2939:t
2933:t
2930:n
2920:e
2913:1
2910:=
2903:o
2899:C
2893:n
2889:C
2883:=
2880:)
2877:t
2874:(
2871:F
2840:Q
2837:V
2832:=
2823:t
2794:t
2769:]
2764:1
2758:j
2754:)
2743:t
2737:t
2734:n
2728:(
2722:!
2719:)
2716:1
2710:j
2707:(
2703:1
2698:+
2695:.
2692:.
2689:.
2686:+
2681:2
2677:)
2666:t
2660:t
2657:n
2651:(
2645:!
2642:2
2638:1
2633:+
2623:t
2617:t
2614:n
2608:+
2605:1
2602:[
2590:t
2584:t
2581:n
2571:e
2564:1
2561:=
2554:o
2550:C
2544:j
2540:C
2499:i
2489:i
2485:k
2481:2
2472:)
2469:1
2463:i
2460:(
2457:A
2453:C
2447:i
2437:i
2433:k
2429:4
2426:+
2423:1
2418:+
2415:1
2406:=
2401:i
2398:A
2394:C
2360:i
2350:i
2346:k
2342:m
2334:o
2331:A
2327:C
2323:=
2318:m
2315:A
2311:C
2286:i
2276:i
2272:k
2266:m
2261:1
2258:=
2255:i
2242:o
2239:A
2235:C
2231:=
2226:m
2223:A
2219:C
2179:m
2175:)
2168:k
2165:+
2162:1
2159:(
2153:o
2150:A
2146:C
2140:=
2135:m
2132:A
2128:C
2100:2
2096:)
2089:k
2086:+
2083:1
2080:(
2074:o
2071:A
2067:C
2061:=
2056:2
2053:A
2049:C
2020:k
2017:+
2014:1
2008:1
2005:A
2001:C
1995:=
1990:2
1987:A
1983:C
1956:k
1953:+
1950:1
1944:o
1941:A
1937:C
1931:=
1926:1
1923:A
1919:C
1893:1
1890:A
1886:C
1855:k
1852:+
1849:1
1843:o
1840:A
1836:C
1830:=
1825:1
1822:A
1818:C
1773:A
1769:r
1743:A
1739:C
1716:o
1713:A
1709:C
1659:i
1656:A
1652:r
1641:i
1638:A
1634:C
1625:)
1622:1
1616:i
1613:(
1610:A
1606:C
1599:=
1594:i
1564:A
1560:r
1549:A
1545:C
1536:o
1533:A
1529:C
1522:=
1480:o
1477:A
1473:F
1448:o
1445:A
1441:F
1437:V
1283:k
1280:2
1271:o
1268:A
1264:C
1257:k
1254:4
1251:+
1248:1
1243:+
1240:1
1231:=
1226:A
1222:C
1189:k
1186:+
1183:1
1177:o
1174:A
1170:C
1164:=
1159:A
1155:C
1124:k
1114:o
1111:A
1107:C
1102:=
1097:A
1093:C
1075:A
1073:C
1058:A
1046:A
1041:A
1039:r
998:A
996:C
987:C
983:)
967:Q
964:V
958:=
909:)
904:A
900:C
891:o
888:A
884:C
880:(
872:1
867:=
862:A
858:r
830:)
825:A
821:C
812:o
809:A
805:C
801:(
796:V
793:Q
788:=
783:A
779:r
759:A
757:r
739:A
735:r
731:V
723:A
719:C
715:Q
707:o
704:A
700:C
696:Q
693:=
690:0
672:Q
668:A
664:A
646:A
642:r
638:V
630:A
626:F
617:o
614:A
610:F
606:=
603:0
584:A
582:ν
573:A
571:r
561:A
559:v
554:A
549:A
547:F
542:A
535:F
514:A
510:r
504:A
496:V
493:+
488:A
484:F
475:o
472:A
468:F
464:=
458:t
455:d
448:A
444:N
440:d
413:]
410:A
399:[
396:+
393:]
382:A
379:[
373:]
362:A
359:[
356:=
353:]
350:A
339:[
328::
326:V
322:A
317:A
315:N
308:V
304:A
302:C
297:A
295:N
289:A
281:A
279:ν
277:(
268:k
258:n
249:A
247:C
243:k
238:A
232:r
230:(
213:A
208:A
206:N
190:)
185:0
182:=
176:t
173:d
166:A
162:N
158:d
150:(
124:V
120:A
66:(
58:(
42:(
20:)
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