20:
142:
In the simplest case of a PFR model, several key assumptions must be made in order to simplify the problem, some of which are outlined below. Note that not all of these assumptions are necessary, however the removal of these assumptions does increase the complexity of the problem. The PFR model can
1232:
When a tracer is injected into a reactor at a location more than two or three particle diameters downstream from the entrance and measured some distance upstream from the exit, the system can be described by the dispersion model with combinations of open or close boundary conditions. For such a
1093:
reactors do not satisfy the idealized flow patterns, back mix flow or plug flow deviation from ideal behavior can be due to channeling of fluid through the vessel, recycling of fluid within the vessel or due to the presence of stagnant region or dead zone of fluid in the vessel. Real plug flow
58:
Fluid going through a PFR may be modeled as flowing through the reactor as a series of infinitely thin coherent "plugs", each with a uniform composition, traveling in the axial direction of the reactor, with each plug having a different composition from the ones before and after it. The key
957:
PFRs are used to model the chemical transformation of compounds as they are transported in systems resembling "pipes". The "pipe" can represent a variety of engineered or natural conduits through which liquids or gases flow. (e.g. rivers, pipelines, regions between two mountains, etc.)
138:
The PFR model works well for many fluids: liquids, gases, and slurries. Although turbulent flow and axial diffusion cause a degree of mixing in the axial direction in real reactors, the PFR model is appropriate when these effects are sufficiently small that they can be ignored.
1119:
The RTD is determined experimentally by injecting an inert chemical, molecule, or atom, called a tracer, into the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of time.
143:
be used to model multiple reactions as well as reactions involving changing temperatures, pressures and densities of the flow. Although these complications are ignored in what follows, they are often relevant to industrial processes.
1373:
1085:
of a reactor is a characteristic of the mixing that occurs in the chemical reactor. There is no axial mixing in a plug-flow reactor, and this omission is reflected in the RTD which is exhibited by this class of reactors.
485:
2086:
1739:
1897:
1227:
305:
1812:
783:
2283:
Colli, A. N.; Bisang, J. M. (September 2015). "Study of the influence of boundary conditions, non ideal stimulus and dynamics of sensors on the evaluation of residence time distributions".
164:(reasonable for some liquids but a 20% error for polymerizations; valid for gases only if there is no pressure drop, no net change in the number of moles, nor any large temperature change)
2446:
Colli, A. N.; Bisang, J. M. (August 2011). "Evaluation of the hydrodynamic behaviour of turbulence promoters in parallel plate electrochemical reactors by means of the dispersion model".
2241:
Colli, A. N.; Bisang, J. M. (August 2011). "Evaluation of the hydrodynamic behaviour of turbulence promoters in parallel plate electrochemical reactors by means of the dispersion model".
933:
63:
in the radial direction but not in the axial direction (forwards or backwards). Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small
706:
1944:
539:
1162:
1580:
1433:
571:
1985:
1005:
1233:
system where there is no discontinuity in type of flow at the point of tracer injection or at the point of tracer measurement, the variance for open-open system is:
2098:
As mentioned before, there are also other boundary conditions that can be applied to the dispersion model giving different relationships for the dispersion number.
1492:
1049:
1025:
814:
117:
93:
1514:
1463:
979:
1242:
404:
1996:
1598:
2483:
Colli, A. N.; Bisang, J. M. (December 2011). "Generalized study of the temporal behaviour in recirculating electrochemical reactor systems".
1821:
1123:
The RTD curve of fluid leaving a vessel is called the E-Curve. This curve is normalized in such a way that the area under it is unity:
1066:). Typically these types of reactors are called packed bed reactors or PBR's. Sometimes the tube will be a tube in a shell and tube
2425:. Vol. 3: Chemical and Biochemical Reactors and Process Control (4th ed.). New Delhi: Asian Books Pvt.Lt. pp. 87–92.
2430:
2382:
2332:
2225:
1176:
205:
95:) of the plug is a function of its position in the reactor. In the ideal PFR, the residence time distribution is therefore a
155:
1753:
725:
869:
2176:
586:
64:
1909:
2348:
796:. Generally, as the temperature increases so does the rate at which the reaction occurs. Residence time,
2398:
Adeniyi, O. D.; Abdulkareem, A. S.; Odigure, Joseph
Obofoni; Aweh, E. A.; Nwokoro, U. T. (October 2003).
2191:
1094:
reactors with non-ideal behavior have also been modelled. To predict the exact behavior of a vessel as a
1082:
961:
An ideal plug flow reactor has a fixed residence time: Any fluid (plug) that enters the reactor at time
490:
72:
51:
in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of
2522:
Plug flow Tube
Reactor –S2S (A gate way for the plant and process safety ), Copyright -2003 by PHP –Nuke
1132:
55:
of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.
2537:
2400:"Mathematical Modeling and Simulation of a Non-Ideal Plug Flow Reactor in a Saponification Pilot Plant"
1526:
199:
Accumulation is 0 under steady state; therefore, the above mass balance can be re-written as follows:
1387:
2374:
1102:, the most widely used method for the study of axial dispersion, is usually used in the form of:
1051:. A real plug flow reactor has a residence time distribution that is a narrow pulse around the
547:
1949:
1589:
of a continuous distribution measured at a finite number of equidistant locations is given by:
1027:
is the residence time of the reactor. The residence time distribution function is therefore a
132:
2136:
The main problems lies in difficult and sometimes critical start-up and shut down operations.
2421:
Coulson, J M; Richardson, J F (1991). "2 - Flow
Characteristics of Reactors—Flow Modelling".
984:
128:
2366:
2181:
1470:
1034:
1028:
1010:
799:
102:
96:
78:
8:
2367:
1368:{\displaystyle (\sigma _{\theta })^{2}=(\sigma _{t})^{2}/\tau ^{2}=2/P_{e}+8/(P_{e})^{2}}
68:
2342:
1499:
1448:
964:
816:, is the average amount of time a discrete quantity of reagent spends inside the tank.
793:
1438:
which represents the ratio of rate of transport by convection to rate of transport by
175:
A material balance on the differential volume of a fluid element, or plug, on species
2426:
2399:
2378:
2328:
2221:
1073:
When a plug flow model can not be applied, the dispersion model is usually employed.
830:
168:
48:
2496:
2459:
2296:
2254:
2500:
2492:
2463:
2455:
2300:
2292:
2258:
2250:
1099:
1095:
52:
1906:) can be evaluated from the experimental data on C vs. t and for known values of
1052:
949:
at the inlet to the reactor, appearing from the integration boundary condition.
2171:
1067:
60:
2531:
2122:
373:
480:{\displaystyle u={\frac {\dot {v}}{A_{t}}}={\frac {4{\dot {v}}}{\pi D^{2}}}}
2186:
2113:
2327:(3rd ed.). New Delhi - 110 001: Prentice Hall of India. p. 812.
2081:{\displaystyle D_{L}/LU={-1+{\sqrt {1+8(\sigma _{\theta })^{2}}} \over 8}}
1734:{\displaystyle (\sigma _{t})^{2}=\sum t_{i}^{2}C_{i}/\sum C_{i}-\sum ^{2}}
2108:
From the safety technical point of view the PFR has the advantages that
851:
After integration of
Equation 3 using the above assumptions, solving for
2505:
2468:
2305:
2263:
1059:
823:
131:, the solution for which can be calculated providing that appropriate
1439:
1090:
150:
2144:
Plug flow reactors are used for some of the following applications:
1892:{\displaystyle (\sigma _{\theta })^{2}=(\sigma _{t})^{2}/\tau ^{2}}
1586:
1063:
840:
161:
576:
On application of the above to
Equation 1, the mass balance on
382:
is the volumetric source/sink term (the reaction rate), mol/ms.
59:
assumption is that as a plug flows through a PFR, the fluid is
2414:
2397:
859:
we get an explicit equation for the concentration of species
1167:
The mean age of the exit stream or mean residence time is:
19:
1516:= superficial velocity (m/s) based on empty cross-section
715:→ 0 is applied to Equation 2 the mass balance on species
2278:
2276:
2274:
1222:{\displaystyle \tau =\int tE\partial t=\sum tE\nabla t}
300:{\displaystyle F_{i}(x)-F_{i}(x+dx)+A_{t}dx\nu _{i}r=0}
71:
to zero volume. As it flows down the tubular PFR, the
2476:
2439:
2360:
2358:
2271:
2234:
1999:
1952:
1912:
1824:
1756:
1601:
1529:
1502:
1473:
1451:
1390:
1245:
1179:
1135:
1037:
1013:
987:
967:
872:
802:
728:
589:
550:
493:
407:
208:
105:
81:
826:
conditions, or constant temperature (k is constant)
171:
occurring in the bulk of the fluid (homogeneously).
2391:
2373:(Third ed.). John Wiley & Sons. pp.
2355:
2080:
1979:
1938:
1891:
1806:
1733:
1574:
1508:
1486:
1457:
1427:
1367:
1221:
1156:
1098:, RTD or stimulus response technique is used. The
1043:
1019:
999:
973:
927:
808:
777:
700:
565:
533:
479:
299:
111:
87:
2420:
788:The temperature dependence of the reaction rate,
2529:
1807:{\displaystyle \tau =\sum t_{i}C_{i}/\sum C_{i}}
778:{\displaystyle u{\frac {dC_{i}}{dx}}=\nu _{i}r}
1076:
366:is the tube transverse cross sectional area, m
2318:
2316:
1058:A typical plug flow reactor could be a tube
928:{\displaystyle C_{A}(x)=C_{A0}e^{-k\tau }\,}
711:When like terms are cancelled and the limit
2482:
2445:
2404:Assumption University Journal of Technology
2282:
2240:
701:{\displaystyle A_{t}u+A_{t}dx\nu _{i}r=0\,}
127:The stationary PFR is governed by ordinary
2364:
2313:
2504:
2467:
2325:Elements of Chemical Reaction Engineering
2304:
2262:
2211:
2209:
2207:
1744:Where mean residence time τ is given by:
1494:= effective dispersion coefficient ( m/s)
924:
697:
530:
2198:
1520:Vessel dispersion number is defined as:
323:the differential thickness of fluid plug
23:Schematic diagram of a plug flow reactor
18:
2518:
2516:
2215:
1939:{\displaystyle (\sigma _{\theta })^{2}}
1062:with some solid material (frequently a
390:(m/s) and the concentration of species
2530:
2322:
2204:
2154:Homogeneous or heterogeneous reactions
2220:. New York: Oxford University Press.
2218:The Engineering of Chemical Reactions
2095:can be estimated (L = packed height)
952:
317:is the reactor tube axial position, m
2513:
2091:Thus axial dispersion coefficient D
534:{\displaystyle F_{i}=A_{t}uC_{i}\,}
13:
1213:
1195:
1157:{\displaystyle \int E\partial t=1}
1142:
343:is the molar flow rate of species
14:
2549:
1987:can be obtained from eq. (3) as:
1083:residence-time distribution (RTD)
1575:{\displaystyle 1/P_{e}=D_{L}/LU}
945:is the concentration of species
2497:10.1016/j.electacta.2011.09.058
2460:10.1016/j.electacta.2011.06.047
2297:10.1016/j.electacta.2015.07.019
2255:10.1016/j.electacta.2011.06.047
2177:Continuous stirred-tank reactor
2139:
122:
65:continuous stirred tank reactor
2061:
2047:
1974:
1953:
1927:
1913:
1865:
1851:
1839:
1825:
1722:
1680:
1616:
1602:
1428:{\displaystyle P_{e}=LU/D_{L}}
1356:
1342:
1286:
1272:
1260:
1246:
981:will exit the reactor at time
889:
883:
656:
653:
638:
622:
616:
603:
398:(mol/m) can be introduced as:
256:
241:
225:
219:
47:) is a model used to describe
1:
2369:Chemical Reaction Engineering
1055:residence time distribution.
792:, can be estimated using the
573:is the volumetric flow rate.
7:
2365:Levenspiel, Octave (1998).
2192:Oscillatory baffled reactor
2164:
1465:= characteristic length (m)
1077:Residence-time distribution
863:as a function of position:
10:
2554:
2216:Schmidt, Lanny D. (1998).
2160:High-temperature reactions
566:{\displaystyle {\dot {v}}}
386:The flow linear velocity,
374:stoichiometric coefficient
37:continuous tubular reactor
2323:Fogler, H. Scott (2004).
1980:{\displaystyle (1/P_{e})}
2347:: CS1 maint: location (
1946:, the dispersion number
16:Reactor simulation model
2118:It is well controllable
1000:{\displaystyle t+\tau }
357:is the tube diameter, m
29:plug flow reactor model
2148:Large-scale production
2125:areas can be installed
2082:
1981:
1940:
1893:
1808:
1735:
1576:
1510:
1488:
1459:
1429:
1369:
1223:
1158:
1045:
1021:
1001:
975:
929:
810:
779:
702:
567:
535:
481:
330:refers to the species
301:
129:differential equations
113:
99:with a value equal to
89:
24:
2199:Reference and sources
2157:Continuous production
2083:
1982:
1941:
1894:
1809:
1736:
1577:
1511:
1489:
1487:{\displaystyle D_{L}}
1460:
1430:
1370:
1224:
1159:
1046:
1044:{\displaystyle \tau }
1022:
1020:{\displaystyle \tau }
1002:
976:
930:
829:single, irreversible
811:
809:{\displaystyle \tau }
780:
703:
568:
536:
482:
302:
114:
112:{\displaystyle \tau }
90:
88:{\displaystyle \tau }
22:
2423:Chemical Engineering
2182:Laminar flow reactor
1997:
1950:
1910:
1822:
1754:
1599:
1527:
1500:
1471:
1449:
1388:
1243:
1177:
1133:
1035:
1029:Dirac delta function
1011:
985:
965:
870:
841:first-order reaction
800:
726:
587:
548:
491:
405:
206:
103:
97:Dirac delta function
79:
45:piston flow reactors
2485:Electrochimica Acta
2448:Electrochimica Acta
2285:Electrochimica Acta
2243:Electrochimica Acta
1645:
133:boundary conditions
35:, sometimes called
2078:
1977:
1936:
1889:
1804:
1731:
1631:
1572:
1506:
1484:
1455:
1425:
1365:
1219:
1154:
1041:
1017:
997:
971:
953:Operation and uses
925:
806:
794:Arrhenius equation
775:
698:
563:
531:
477:
297:
109:
85:
49:chemical reactions
25:
2538:Chemical reactors
2454:(21): 7312–7318.
2432:978-0-08-057154-6
2384:978-0-471-25424-9
2334:978-81-203-2234-9
2249:(21): 7312–7318.
2227:978-0-19-510588-9
2112:It operates in a
2076:
2070:
1509:{\displaystyle U}
1458:{\displaystyle L}
974:{\displaystyle t}
757:
560:
475:
456:
436:
424:
53:chemical reactors
2545:
2523:
2520:
2511:
2510:
2508:
2480:
2474:
2473:
2471:
2443:
2437:
2436:
2418:
2412:
2411:
2395:
2389:
2388:
2372:
2362:
2353:
2352:
2346:
2338:
2320:
2311:
2310:
2308:
2280:
2269:
2268:
2266:
2238:
2232:
2231:
2213:
2087:
2085:
2084:
2079:
2077:
2072:
2071:
2069:
2068:
2059:
2058:
2037:
2025:
2014:
2009:
2008:
1986:
1984:
1983:
1978:
1973:
1972:
1963:
1945:
1943:
1942:
1937:
1935:
1934:
1925:
1924:
1898:
1896:
1895:
1890:
1888:
1887:
1878:
1873:
1872:
1863:
1862:
1847:
1846:
1837:
1836:
1813:
1811:
1810:
1805:
1803:
1802:
1790:
1785:
1784:
1775:
1774:
1740:
1738:
1737:
1732:
1730:
1729:
1720:
1719:
1707:
1702:
1701:
1692:
1691:
1673:
1672:
1660:
1655:
1654:
1644:
1639:
1624:
1623:
1614:
1613:
1581:
1579:
1578:
1573:
1565:
1560:
1559:
1547:
1546:
1537:
1515:
1513:
1512:
1507:
1493:
1491:
1490:
1485:
1483:
1482:
1464:
1462:
1461:
1456:
1434:
1432:
1431:
1426:
1424:
1423:
1414:
1400:
1399:
1374:
1372:
1371:
1366:
1364:
1363:
1354:
1353:
1341:
1330:
1329:
1320:
1309:
1308:
1299:
1294:
1293:
1284:
1283:
1268:
1267:
1258:
1257:
1228:
1226:
1225:
1220:
1163:
1161:
1160:
1155:
1100:tracer technique
1096:chemical reactor
1050:
1048:
1047:
1042:
1026:
1024:
1023:
1018:
1006:
1004:
1003:
998:
980:
978:
977:
972:
934:
932:
931:
926:
923:
922:
907:
906:
882:
881:
815:
813:
812:
807:
784:
782:
781:
776:
771:
770:
758:
756:
748:
747:
746:
733:
707:
705:
704:
699:
687:
686:
671:
670:
637:
636:
615:
614:
599:
598:
572:
570:
569:
564:
562:
561:
553:
540:
538:
537:
532:
529:
528:
516:
515:
503:
502:
486:
484:
483:
478:
476:
474:
473:
472:
459:
458:
457:
449:
442:
437:
435:
434:
425:
417:
415:
347:at the position
306:
304:
303:
298:
287:
286:
271:
270:
240:
239:
218:
217:
179:of axial length
118:
116:
115:
110:
94:
92:
91:
86:
2553:
2552:
2548:
2547:
2546:
2544:
2543:
2542:
2528:
2527:
2526:
2521:
2514:
2481:
2477:
2444:
2440:
2433:
2419:
2415:
2396:
2392:
2385:
2363:
2356:
2340:
2339:
2335:
2321:
2314:
2281:
2272:
2239:
2235:
2228:
2214:
2205:
2201:
2196:
2167:
2142:
2094:
2064:
2060:
2054:
2050:
2036:
2026:
2024:
2010:
2004:
2000:
1998:
1995:
1994:
1968:
1964:
1959:
1951:
1948:
1947:
1930:
1926:
1920:
1916:
1911:
1908:
1907:
1905:
1883:
1879:
1874:
1868:
1864:
1858:
1854:
1842:
1838:
1832:
1828:
1823:
1820:
1819:
1798:
1794:
1786:
1780:
1776:
1770:
1766:
1755:
1752:
1751:
1725:
1721:
1715:
1711:
1703:
1697:
1693:
1687:
1683:
1668:
1664:
1656:
1650:
1646:
1640:
1635:
1619:
1615:
1609:
1605:
1600:
1597:
1596:
1561:
1555:
1551:
1542:
1538:
1533:
1528:
1525:
1524:
1501:
1498:
1497:
1478:
1474:
1472:
1469:
1468:
1450:
1447:
1446:
1442:or dispersion.
1419:
1415:
1410:
1395:
1391:
1389:
1386:
1385:
1359:
1355:
1349:
1345:
1337:
1325:
1321:
1316:
1304:
1300:
1295:
1289:
1285:
1279:
1275:
1263:
1259:
1253:
1249:
1244:
1241:
1240:
1178:
1175:
1174:
1134:
1131:
1130:
1079:
1036:
1033:
1032:
1012:
1009:
1008:
986:
983:
982:
966:
963:
962:
955:
943:
912:
908:
899:
895:
877:
873:
871:
868:
867:
856:
846:
836:
801:
798:
797:
766:
762:
749:
742:
738:
734:
732:
727:
724:
723:
682:
678:
666:
662:
632:
628:
610:
606:
594:
590:
588:
585:
584:
552:
551:
549:
546:
545:
524:
520:
511:
507:
498:
494:
492:
489:
488:
468:
464:
460:
448:
447:
443:
441:
430:
426:
416:
414:
406:
403:
402:
397:
376:, dimensionless
364:
340:
282:
278:
266:
262:
235:
231:
213:
209:
207:
204:
203:
125:
104:
101:
100:
80:
77:
76:
61:perfectly mixed
17:
12:
11:
5:
2551:
2541:
2540:
2525:
2524:
2512:
2475:
2438:
2431:
2413:
2390:
2383:
2354:
2333:
2312:
2270:
2233:
2226:
2202:
2200:
2197:
2195:
2194:
2189:
2184:
2179:
2174:
2172:Flow chemistry
2168:
2166:
2163:
2162:
2161:
2158:
2155:
2152:
2151:Fast reactions
2149:
2141:
2138:
2134:
2133:
2131:
2127:
2126:
2119:
2116:
2106:
2105:
2103:
2092:
2089:
2088:
2075:
2067:
2063:
2057:
2053:
2049:
2046:
2043:
2040:
2035:
2032:
2029:
2023:
2020:
2017:
2013:
2007:
2003:
1992:
1976:
1971:
1967:
1962:
1958:
1955:
1933:
1929:
1923:
1919:
1915:
1903:
1900:
1899:
1886:
1882:
1877:
1871:
1867:
1861:
1857:
1853:
1850:
1845:
1841:
1835:
1831:
1827:
1817:
1814:
1801:
1797:
1793:
1789:
1783:
1779:
1773:
1769:
1765:
1762:
1759:
1749:
1742:
1741:
1728:
1724:
1718:
1714:
1710:
1706:
1700:
1696:
1690:
1686:
1682:
1679:
1676:
1671:
1667:
1663:
1659:
1653:
1649:
1643:
1638:
1634:
1630:
1627:
1622:
1618:
1612:
1608:
1604:
1594:
1583:
1582:
1571:
1568:
1564:
1558:
1554:
1550:
1545:
1541:
1536:
1532:
1518:
1517:
1505:
1495:
1481:
1477:
1466:
1454:
1436:
1435:
1422:
1418:
1413:
1409:
1406:
1403:
1398:
1394:
1383:
1376:
1375:
1362:
1358:
1352:
1348:
1344:
1340:
1336:
1333:
1328:
1324:
1319:
1315:
1312:
1307:
1303:
1298:
1292:
1288:
1282:
1278:
1274:
1271:
1266:
1262:
1256:
1252:
1248:
1238:
1230:
1229:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1182:
1172:
1165:
1164:
1153:
1150:
1147:
1144:
1141:
1138:
1128:
1117:
1116:
1113:
1110:
1107:
1078:
1075:
1068:heat exchanger
1040:
1016:
996:
993:
990:
970:
954:
951:
941:
921:
918:
915:
911:
905:
902:
898:
894:
891:
888:
885:
880:
876:
854:
849:
848:
844:
838:
834:
827:
805:
774:
769:
765:
761:
755:
752:
745:
741:
737:
731:
696:
693:
690:
685:
681:
677:
674:
669:
665:
661:
658:
655:
652:
649:
646:
643:
640:
635:
631:
627:
624:
621:
618:
613:
609:
605:
602:
597:
593:
559:
556:
542:
541:
527:
523:
519:
514:
510:
506:
501:
497:
471:
467:
463:
455:
452:
446:
440:
433:
429:
423:
420:
413:
410:
395:
384:
383:
377:
367:
362:
358:
352:
338:
334:
324:
318:
296:
293:
290:
285:
281:
277:
274:
269:
265:
261:
258:
255:
252:
249:
246:
243:
238:
234:
230:
227:
224:
221:
216:
212:
197:
196:
173:
172:
165:
158:
153:
124:
121:
108:
84:
73:residence time
15:
9:
6:
4:
3:
2:
2550:
2539:
2536:
2535:
2533:
2519:
2517:
2507:
2502:
2498:
2494:
2490:
2486:
2479:
2470:
2465:
2461:
2457:
2453:
2449:
2442:
2434:
2428:
2424:
2417:
2409:
2405:
2401:
2394:
2386:
2380:
2376:
2371:
2370:
2361:
2359:
2350:
2344:
2336:
2330:
2326:
2319:
2317:
2307:
2302:
2298:
2294:
2290:
2286:
2279:
2277:
2275:
2265:
2260:
2256:
2252:
2248:
2244:
2237:
2229:
2223:
2219:
2212:
2210:
2208:
2203:
2193:
2190:
2188:
2185:
2183:
2180:
2178:
2175:
2173:
2170:
2169:
2159:
2156:
2153:
2150:
2147:
2146:
2145:
2137:
2132:
2129:
2128:
2124:
2123:heat transfer
2120:
2117:
2115:
2111:
2110:
2109:
2104:
2101:
2100:
2099:
2096:
2073:
2065:
2055:
2051:
2044:
2041:
2038:
2033:
2030:
2027:
2021:
2018:
2015:
2011:
2005:
2001:
1993:
1990:
1989:
1988:
1969:
1965:
1960:
1956:
1931:
1921:
1917:
1884:
1880:
1875:
1869:
1859:
1855:
1848:
1843:
1833:
1829:
1818:
1815:
1799:
1795:
1791:
1787:
1781:
1777:
1771:
1767:
1763:
1760:
1757:
1750:
1747:
1746:
1745:
1726:
1716:
1712:
1708:
1704:
1698:
1694:
1688:
1684:
1677:
1674:
1669:
1665:
1661:
1657:
1651:
1647:
1641:
1636:
1632:
1628:
1625:
1620:
1610:
1606:
1595:
1592:
1591:
1590:
1588:
1569:
1566:
1562:
1556:
1552:
1548:
1543:
1539:
1534:
1530:
1523:
1522:
1521:
1503:
1496:
1479:
1475:
1467:
1452:
1445:
1444:
1443:
1441:
1420:
1416:
1411:
1407:
1404:
1401:
1396:
1392:
1384:
1381:
1380:
1379:
1360:
1350:
1346:
1338:
1334:
1331:
1326:
1322:
1317:
1313:
1310:
1305:
1301:
1296:
1290:
1280:
1276:
1269:
1264:
1254:
1250:
1239:
1236:
1235:
1234:
1216:
1210:
1207:
1204:
1201:
1198:
1192:
1189:
1186:
1183:
1180:
1173:
1170:
1169:
1168:
1151:
1148:
1145:
1139:
1136:
1129:
1126:
1125:
1124:
1121:
1114:
1111:
1108:
1105:
1104:
1103:
1101:
1097:
1092:
1087:
1084:
1074:
1071:
1069:
1065:
1061:
1056:
1054:
1038:
1030:
1014:
994:
991:
988:
968:
959:
950:
948:
944:
936:
919:
916:
913:
909:
903:
900:
896:
892:
886:
878:
874:
864:
862:
858:
842:
839:
832:
828:
825:
822:
821:
820:
817:
803:
795:
791:
786:
772:
767:
763:
759:
753:
750:
743:
739:
735:
729:
720:
718:
714:
709:
694:
691:
688:
683:
679:
675:
672:
667:
663:
659:
650:
647:
644:
641:
633:
629:
625:
619:
611:
607:
600:
595:
591:
581:
579:
574:
557:
554:
525:
521:
517:
512:
508:
504:
499:
495:
469:
465:
461:
453:
450:
444:
438:
431:
427:
421:
418:
411:
408:
401:
400:
399:
393:
389:
381:
378:
375:
371:
368:
365:
359:
356:
353:
350:
346:
342:
335:
333:
329:
325:
322:
319:
316:
313:
312:
311:
308:
294:
291:
288:
283:
279:
275:
272:
267:
263:
259:
253:
250:
247:
244:
236:
232:
228:
222:
214:
210:
200:
194:
193:
192:
190:
186:
182:
178:
170:
166:
163:
159:
157:
154:
152:
149:
148:
147:
146:Assumptions:
144:
140:
136:
134:
130:
120:
106:
98:
82:
74:
70:
66:
62:
56:
54:
50:
46:
42:
38:
34:
30:
21:
2488:
2484:
2478:
2451:
2447:
2441:
2422:
2416:
2407:
2403:
2393:
2368:
2324:
2288:
2284:
2246:
2242:
2236:
2217:
2187:Microreactor
2143:
2140:Applications
2135:
2114:steady state
2107:
2097:
2090:
1901:
1743:
1584:
1519:
1437:
1377:
1231:
1166:
1122:
1118:
1115:Random input
1112:Cyclic input
1088:
1080:
1072:
1057:
960:
956:
946:
939:
937:
865:
860:
852:
850:
818:
789:
787:
721:
716:
712:
710:
582:
577:
575:
543:
391:
387:
385:
379:
369:
360:
354:
348:
344:
336:
331:
327:
320:
314:
309:
201:
198:
188:
184:
180:
176:
174:
156:Steady state
145:
141:
137:
126:
123:PFR modeling
57:
44:
40:
36:
32:
28:
26:
2506:11336/74029
2491:: 406–416.
2469:11336/74207
2410:(2): 65–74.
2306:11336/45663
2291:: 463–471.
2264:11336/74207
1106:Pulse input
195:= - + -
135:are known.
2102:Advantages
1109:Step input
824:isothermal
326:the index
2343:cite book
2056:θ
2052:σ
2028:−
1922:θ
1918:σ
1881:τ
1856:σ
1834:θ
1830:σ
1792:∑
1764:∑
1758:τ
1709:∑
1678:∑
1675:−
1662:∑
1629:∑
1607:σ
1440:diffusion
1302:τ
1277:σ
1255:θ
1251:σ
1214:∇
1205:∑
1196:∂
1187:∫
1181:τ
1143:∂
1137:∫
1091:plug flow
1039:τ
1015:τ
995:τ
920:τ
914:−
804:τ
764:ν
680:ν
626:−
580:becomes:
558:˙
462:π
454:˙
422:˙
280:ν
229:−
160:Constant
151:Plug flow
107:τ
83:τ
2532:Category
2165:See also
2130:Concerns
1587:variance
1064:catalyst
1007:, where
843:(r = k C
831:reaction
819:Assume:
719:becomes
183:between
169:reaction
69:limiting
1902:Thus (σ
1378:Where,
372:is the
351:, mol/s
310:where:
191:gives:
167:Single
162:density
2429:
2381:
2377:–265.
2331:
2224:
2121:Large
1060:packed
938:where
544:where
189:x + dx
1089:Real
837:= -1)
487:and
43:, or
2427:ISBN
2379:ISBN
2349:link
2329:ISBN
2222:ISBN
1585:The
1081:The
1053:mean
187:and
27:The
2501:hdl
2493:doi
2464:hdl
2456:doi
2375:260
2301:hdl
2293:doi
2289:176
2259:hdl
2251:doi
1991:(8)
1816:(7)
1748:(6)
1593:(5)
1382:(4)
1237:(3)
1171:(2)
1127:(1)
1031:at
866:4.
857:(x)
722:3.
583:2.
394:, C
341:(x)
202:1.
41:CTR
33:PFR
2534::
2515:^
2499:.
2489:58
2487:.
2462:.
2452:56
2450:.
2406:.
2402:.
2357:^
2345:}}
2341:{{
2315:^
2299:.
2287:.
2273:^
2257:.
2247:56
2245:.
2206:^
1070:.
942:A0
935:,
833:(ν
785:,
713:dx
708:.
321:dx
307:.
181:dx
119:.
67:,
39:,
2509:.
2503::
2495::
2472:.
2466::
2458::
2435:.
2408:7
2387:.
2351:)
2337:.
2309:.
2303::
2295::
2267:.
2261::
2253::
2230:.
2093:L
2074:8
2066:2
2062:)
2048:(
2045:8
2042:+
2039:1
2034:+
2031:1
2022:=
2019:U
2016:L
2012:/
2006:L
2002:D
1975:)
1970:e
1966:P
1961:/
1957:1
1954:(
1932:2
1928:)
1914:(
1904:θ
1885:2
1876:/
1870:2
1866:)
1860:t
1852:(
1849:=
1844:2
1840:)
1826:(
1800:i
1796:C
1788:/
1782:i
1778:C
1772:i
1768:t
1761:=
1727:2
1723:]
1717:i
1713:C
1705:/
1699:i
1695:C
1689:i
1685:t
1681:[
1670:i
1666:C
1658:/
1652:i
1648:C
1642:2
1637:i
1633:t
1626:=
1621:2
1617:)
1611:t
1603:(
1570:U
1567:L
1563:/
1557:L
1553:D
1549:=
1544:e
1540:P
1535:/
1531:1
1504:U
1480:L
1476:D
1453:L
1421:L
1417:D
1412:/
1408:U
1405:L
1402:=
1397:e
1393:P
1361:2
1357:)
1351:e
1347:P
1343:(
1339:/
1335:8
1332:+
1327:e
1323:P
1318:/
1314:2
1311:=
1306:2
1297:/
1291:2
1287:)
1281:t
1273:(
1270:=
1265:2
1261:)
1247:(
1217:t
1211:E
1208:t
1202:=
1199:t
1193:E
1190:t
1184:=
1152:1
1149:=
1146:t
1140:E
992:+
989:t
969:t
947:A
940:C
917:k
910:e
904:0
901:A
897:C
893:=
890:)
887:x
884:(
879:A
875:C
861:A
855:A
853:C
847:)
845:A
835:A
790:r
773:r
768:i
760:=
754:x
751:d
744:i
740:C
736:d
730:u
717:i
695:0
692:=
689:r
684:i
676:x
673:d
668:t
664:A
660:+
657:]
654:)
651:x
648:d
645:+
642:x
639:(
634:i
630:C
623:)
620:x
617:(
612:i
608:C
604:[
601:u
596:t
592:A
578:i
555:v
526:i
522:C
518:u
513:t
509:A
505:=
500:i
496:F
470:2
466:D
451:v
445:4
439:=
432:t
428:A
419:v
412:=
409:u
396:i
392:i
388:u
380:r
370:ν
363:t
361:A
355:D
349:x
345:i
339:i
337:F
332:i
328:i
315:x
295:0
292:=
289:r
284:i
276:x
273:d
268:t
264:A
260:+
257:)
254:x
251:d
248:+
245:x
242:(
237:i
233:F
226:)
223:x
220:(
215:i
211:F
185:x
177:i
75:(
31:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
