11
Jong Min Lee
School of Chemical and Biological Engineering Seoul National University
Heuristics (“Rules of Thumb”)
Heuristics 11
Use of Experienced-Based Principles to:
Check new process designs
Provide equipment size and performance estimates
Help with troubleshooting problems with existing systems Verify computer simulations and results
Provide initial estimates for simulator inputs Use as a starting place for initial designs Develop preliminary process layouts
However, keep in mind that a heuristic:
Doesn’t guarantee a solution May contradict other heuristics
Can reduce the time to solve problems Depends on the context in which it is used
Examples of Heuristics Usage
What is the density of water in SI units? In English units?
What does a gallon of milk weigh? What about 4 gallons of milk?
What does a cubic meter of air weigh?
The ratio of is approximately _______?
3
⇢
L/⇢
v<latexit sha1_base64="Dd21mv5tJZA0hve/QNpG1n6FCtI=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFc1Zkq6MJFwY0LFxXsA9qhZNJMG5pJxiRTKEO/w40LRdz6Me78G9PpLLT1wOUezrmX3Jwg5kwb1/12VlbX1jc2C1vF7Z3dvf3SwWFTy0QR2iCSS9UOsKacCdowzHDajhXFUcBpKxjdzvzWmCrNpHg0k5j6ER4IFjKCjZX8rhrK3v151sa9UtmtuBnQMvFyUoYc9V7pq9uXJImoMIRjrTueGxs/xcowwum02E00jTEZ4QHtWCpwRLWfZkdP0alV+iiUypYwKFN/b6Q40noSBXYywmaoF72Z+J/XSUx47adMxImhgswfChOOjESzBFCfKUoMn1iCiWL2VkSGWGFibE5FG4K3+OVl0qxWvItK9eGyXLvJ4yjAMZzAGXhwBTW4gzo0gMATPMMrvDlj58V5dz7moytOvnMEf+B8/gCSVJHz</latexit>
Heuristics 11
Creation of Heuristics / Shortcuts
1. Predict. (assumptions, heuristics, back of the envelope calculations) 2. Authenticate/Analyze (equations, simulations, operational data) 3. Reevaluate/Rethink (compare, revise)
Example-11.1
Suppose you calculated a turbulent heat transfer coefficient inside a 1.5” pipe as:
5250 W/[m2·℃], for water at 21℃ and a velocity of 1.83 m/s.
Estimate a heat transfer coefficient when the water temperature is 93℃ and a velocity of 3.05 m/s.
5
1. Predict: assume the velocity and temp. have no effect. Predicted Heat Transfer Coef. = 5250 W/[m2·℃]
2. Authenticate: Find appropriate equation for calculation of Nusselt number.
Solution-11.1
Re = u⇢Dpipe/µ= (1.83)(997.4)(1.5)(0.0254)/(9.8⇥10 4) = 71⇥103
<latexit sha1_base64="kusx9KQHMqwm6C3CVFonjTIKmHI=">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</latexit>
For highly turbulent flow, use the _______________ equation hD/k = (0.023)(Du⇢/µ)0.8(Cpµ/k)1/3
<latexit sha1_base64="rI4KY5mS/fmMQK2O8lLSSwzLSBU=">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</latexit>
h0/h = (D0/D)0.2(u0/u)0.8(⇢0/⇢)0.8(µ0/µ)0.47(Cp0/Cp)0.33(k0/k)0.67
<latexit sha1_base64="UzA9hE1WuWcjkNk3/lM30Fgh1+0=">AAACTHicbZBLSysxFMcz1euj10fVpZtguczcTWemFSuCUKgLlwpWhbaWTJo6ocnMkIdQhvmAbly481O4uYsrIpiZzsLXgeT88zvnkOQfJIxK5XlPVmVh8dfS8spq9ffa+sZmbWv7UsZaYNLDMYvFdYAkYTQiPUUVI9eJIIgHjFwF025ev7ojQtI4ulCzhAw5uo3ohGKkDBrVcGi7ITyGzontnvy9Sb1GM3O07epCH2bOQISxDd08lQg6A65zxOdN++3M6Y4S2zVbAVqtzJna7rQ4HLSzUa3uNbwi4Hfhl6IOyjgb1R4H4xhrTiKFGZKy73uJGqZIKIoZyaoDLUmC8BTdkr6REeJEDtPCjAz+MWQMJ7EwK1KwoB8nUsSlnPHAdHKkQvm1lsOfan2tJofDlEaJViTC84smmkEVw9xZOKaCYMVmRiAsqHkrxCESCCvjf9WY4H/98ndx2Wz4rUbzfL/eOSrtWAG7YA84wAdt0AGn4Az0AAb34Bn8By/Wg/XPerXe5q0Vq5zZAZ+isvQOBvWrvQ==</latexit>
= (1)(1.50)(0.973)(1.73)(1.00)(1.08) = 2.725<latexit sha1_base64="/maFZZlv1jxJRD5H8GXwqJHIhTA=">AAACFnicbVDLSgMxFM3UV62vUZdugkWYLhxmppZWQSi4cVnBPqAdSibNtKGZB0lGKEO/wo2/4saFIm7FnX9jpu1CWw/kcnLuuST3eDGjQlrWt5ZbW9/Y3MpvF3Z29/YP9MOjlogSjkkTRyziHQ8JwmhImpJKRjoxJyjwGGl745us334gXNAovJeTmLgBGobUpxhJJfX1c3gNDbtk2GbFKhmWeVktZ5d5taxZrZWUyTGrTqWvFy2lZoCrxF6QIlig0de/eoMIJwEJJWZIiK5txdJNEZcUMzIt9BJBYoTHaEi6ioYoIMJNZ2tN4ZlSBtCPuDqhhDP190SKAiEmgaecAZIjsdzLxP963UT6NTelYZxIEuL5Q37CoIxglhEcUE6wZBNFEOZU/RXiEeIIS5VkQYVgL6+8SlqOaZdN5+6iWL9axJEHJ+AUGMAGVVAHt6ABmgCDR/AMXsGb9qS9aO/ax9ya0xYzx+APtM8fD+CWjA==</latexit>
h0 = (2.725)(5250) W/m2 C = 14,300W/m2 C
<latexit sha1_base64="PbPXyGL3uXTC/YM8dfFQbaOhBaY=">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</latexit>
(11.2)
Heuristics 11
3. Reevaluate/Rethink (compare, revise) Solution-11.1
• The temperature effect on viscosity must be evaluated.
• The effects of temperature on Cp, ⍴, and k are negligible.
• Pipe diameter has a small effect on h (all other things being equal)
• Results are limited to the range where the Sieder-Tate equation is valid
With these assumption, the values for water at 21℃ are substituted into Eq. (11.2). This creates a useful heuristic for evaluating the heat transfer coefficients for water
Follow the logic carefully…
7
From Rules 9 and 12
u = 0.0305r850
8 1 = 0.313 m/s
<latexit sha1_base64="xWiz2t5VnHnX0zqVforLuAo/+vU=">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</latexit>
uact = (0.75)(0.313) = 0.23 m/s
<latexit sha1_base64="nMDMZHBCljPGar5SNUq2QSRj0fA=">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</latexit>
Mass flow rate of vapor = 9200 kg/h = 9200/3600 (kg/s) = 2.56 (kg/s)
uact⇢v⇡D2/4 = 2.56 ! D = 1.33 m<latexit sha1_base64="l6ksFaoH4uEAD19TConQNOpVGDA=">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</latexit>
From Rule 5, the volume of the liquid =
0.5L⇡D2/4 = 0.726L m3<latexit sha1_base64="KeH+cD51FFeFFgRQ6BEJHDDag24=">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</latexit>
5 min of liquid flow
= (5 min)(60 sec/min)(11,570 kg/hr)/(850 kg/m
3)/3600 (hr/sec) = 1.13 m
3Equating the two results above, L = 1.56 m
Heuristics 11
Rule 1: Set F = 0.9
Rule 6: min 𝛥 T = 10℃; but E-105 has 8℃ (ignore for now) Rule 7: Water enters at 30℃ and leaves at 40℃
Rule 8: U = 850 W/m
2℃
T
lm= [(112 40) (38 30)]/ ln[(112 40)/(38 30)] = 29.1 C
<latexit sha1_base64="Z0kWP8uD7NOeMq2vZ6bzsUuouFQ=">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</latexit>
Q = 1085MJ/h = 301kW from Table 1.7
<latexit sha1_base64="wam2SUOCzRHMrRuGFGifadwjW8k=">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</latexit>
A = Q
F U T
lm= 301, 000
0.9 ⇥ 850 ⇥ 29.1 = 13.52 m
2<latexit sha1_base64="f9kr7a/+akZWb61kmAZn2x6O0vo=">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</latexit>
From Rule 9, this heat exchanger should be double-pipe or multiple- pipe design
In Table 1.7, E-105 is multiple-pipe design with the area of 12 m
29
Rule 2:
Fs = u⇢0.5v = 1.2 1.5 m/s(kg/m3)0.5<latexit sha1_base64="DWU+8I7+vuhKOmNKhB3L+QigTLM=">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</latexit> ( )
Rule 3:
Ptray = 0.007 bar<latexit sha1_base64="EaaFDfHtqtDFvNYDOsivrNQEn9M=">AAACCnicbVA9SwNBEN2LXzF+nVrarAbBKtxFIRYKAS0sI5gPSEKY22ySJXsf7M4J4YitjX/FxkIRW3+Bnf/GvSSFJj4YeLw3w8w8L5JCo+N8W5ml5ZXVtex6bmNza3vH3t2r6TBWjFdZKEPV8EBzKQJeRYGSNyLFwfckr3vDq9Sv33OlRRjc4SjibR/6gegJBmikjn3YuuYSgVY6CSoYjekldQqOU3pIWsqnHqhxx86nSgq6SNwZyZMZKh37q9UNWezzAJkErZuuE2E7AYWCST7OtWLNI2BD6POmoQH4XLeTyStjemyULu2FylSAdKL+nkjA13rke6bTBxzoeS8V//OaMfbO24kIohh5wKaLerGkGNI0F9oVijOUI0OAKWFupWwAChia9HImBHf+5UVSKxbc00Lx9ixfvpjFkSUH5IicEJeUSJnckAqpEkYeyTN5JW/Wk/VivVsf09aMNZvZJ39gff4AFB+ZOA==</latexit>
Rule 4:
"tray = 60 90%<latexit sha1_base64="f2wNkVtqt64ORNGj8ogtphDbc0M=">AAACB3icbVDLSgMxFM3UV62vUZeCBEvBjWWmig9QKLhxWcE+oDOUTJq2oZkHyZ3CMHTnxl9x40IRt/6CO//GtJ2Fth64cHLOveTe40WCK7CsbyO3tLyyupZfL2xsbm3vmLt7DRXGkrI6DUUoWx5RTPCA1YGDYK1IMuJ7gjW94e3Eb46YVDwMHiCJmOuTfsB7nBLQUsc8dEZEskhxoV8pSJKM8Q0+t/AJvrKcUscsWmVrCrxI7IwUUYZax/xyuiGNfRYAFUSptm1F4KZEAqeCjQtOrFhE6JD0WVvTgPhMuen0jjEuaaWLe6HUFQCeqr8nUuIrlfie7vQJDNS8NxH/89ox9C7dlAdRDCygs496scAQ4kkouMsloyASTQiVXO+K6YBIQkFHV9Ah2PMnL5JGpWyfliv3Z8XqdRZHHh2gI3SMbHSBqugO1VAdUfSIntErejOejBfj3fiYteaMbGYf/YHx+QOTWJfF</latexit>
x<latexit sha1_base64="AUHygUqOawO2OsD/95c1w9r8X30=">AAACDHicbVDLSgMxFM34rPVVdekmWAQXUmZa0RYUCm5cVrAPaIeSyWTa0EwyJJliGerejb/ixoUibv0Ad/6NaTsLbT0QOJxzLjf3eBGjStv2t7W0vLK6tp7ZyG5ube/s5vb2G0rEEpM6FkzIlocUYZSTuqaakVYkCQo9Rpre4HriN4dEKir4nR5FxA1Rj9OAYqSN1M3l77uJGPb9MbyCdqFSOS+ePhjJE3qm2CW7bFKGTAEXiZOSPEhR6+a+Or7AcUi4xgwp1XbsSLsJkppiRsbZTqxIhPAA9UjbUI5CotxkeswYHhvFh4GQ5nENp+rviQSFSo1CzyRDpPtq3puI/3ntWAdlN6E8ijXheLYoiBnUAk6agT6VBGs2MgRhSc1fIe4jibA2/WVNCc78yYukUSw4pULx9ixfvUzryIBDcAROgAMuQBXcgBqoAwwewTN4BW/Wk/VivVsfs+iSlc4cgD+wPn8Aa3WYoA==</latexit> ovhd = 0.9962, xbot = 0.0308
↵ovhd = 2.44, ↵bot = 2.13, ↵geom ave =p
2.44⇥2.13 = 2.28
<latexit sha1_base64="7PSUU6hecJZOdHuLzE+qJo9i+J8=">AAACR3icbZDBaxNBFMZnU1trbOtqj14Gg9BDCbsx0BwUCl56rGDaQjYubycvydDZne3M20BYkr/Oi9fe+i948VApPTqbjaKtDwY+ft/7mJkvyZW0FAQ3XmPjyebW0+1nzec7u3sv/JevzqwujMC+0EqbiwQsKplhnyQpvMgNQpooPE8uP1b++QyNlTr7TPMchylMMjmWAsih2P8SgcqnEJd6Nh0t+AfeaXe7h8vfNNFUw/DdIf9DJ6jTJcywsiJ7ZaisUjwimaJdLdehTi/2W0E7WA1/LMK1aLH1nMb+dTTSokgxI6HA2kEY5DQswZAUChfNqLCYg7iECQ6czMDdOCxXPSz4W0dGfKyNOxnxFf07UUJq7TxN3GYKNLUPvQr+zxsUNO4NS5nlBWEm6ovGheKkeVUqH0mDgtTcCRBGurdyMQUDglz1TVdC+PDLj8VZ1Vu786nbOn6/rmObvWZv2AEL2RE7ZifslPWZYF/Zd3bLfnrfvB/enXdfrza8dWaf/TMN7xePbq3/</latexit>
Nmin = {ln[0.9962/(1 0.9962)]/[0.0308/(1 0.0308)]}/ln(2.28) = 10.9
<latexit sha1_base64="8oNSSofXdqd1lpfcWqv6LV2+Pog=">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</latexit>
R<latexit sha1_base64="SVMEVoJcedBDisFohnO4jPMdMDE=">AAACEXicbZDLTgIxFIY7eEO8oS7dNBITWDhMR1AWmpC4cYlGLgkQ0ikFGjqdSdsxIRNewY2v4saFxrh15863sVwWCp6kyZf/Pyen5/dCzpR2nG8rsbK6tr6R3Extbe/s7qX3D2oqiCShVRLwQDY8rChnglY105w2Qkmx73Fa94bXE7/+QKVigbjXo5C2fdwXrMcI1kbqpLN3nbjlMzGGVzCLCq7t5pFTtM9z+azh0inKGQPZTrGTzji2My24DGgOGTCvSif91eoGJPKp0IRjpZrICXU7xlIzwuk41YoUDTEZ4j5tGhTYp6odTy8awxOjdGEvkOYJDafq74kY+0qNfM90+lgP1KI3Ef/zmpHuldoxE2GkqSCzRb2IQx3ASTywyyQlmo8MYCKZ+SskAywx0SbElAkBLZ68DDXXRme2e1vIlC/ncSTBETgGWYDABSiDG1ABVUDAI3gGr+DNerJerHfrY9aasOYzh+BPWZ8/8suXWQ==</latexit> min = (142.2/105.6)/(2.28 1) = 1.05
stream 15
1.26 ≤ R ≤ 1.58
N
theory= 2 x 10.9 = 21.8 N
actual= (21.8 / ε (=0.6) ) x 1.1 = 43 trays Vapor flowrate (Str. 13) = 22,700 kg/h
⇢v = 6.1 kg/m3<latexit sha1_base64="LtdvlZgrGSeWdMvZn5EXEWEbvNc=">AAACAnicbVDLSsNAFJ34rPUVdSVuBovgKiatqAuFghuXFewDmhgm00k7dCYJM5NCCdWNv+LGhSJu/Qp3/o3TNgttPXDhcM693HtPkDAqlW1/GwuLS8srq4W14vrG5ta2ubPbkHEqMKnjmMWiFSBJGI1IXVHFSCsRBPGAkWbQvx77zQERksbRnRomxOOoG9GQYqS05Jv7rujF/gBewTPLechcwWG/e8LvKyPfLNmWPQGcJ05OSiBHzTe/3E6MU04ihRmSsu3YifIyJBTFjIyKbipJgnAfdUlb0whxIr1s8sIIHmmlA8NY6IoUnKi/JzLEpRzyQHdypHpy1huL/3ntVIUXXkajJFUkwtNFYcqgiuE4D9ihgmDFhpogLKi+FeIeEggrnVpRh+DMvjxPGmXLqVjl29NS9TKPowAOwCE4Bg44B1VwA2qgDjB4BM/gFbwZT8aL8W58TFsXjHxmD/yB8fkDMNSV/w==</latexit>
u = (1.2 1.5)/6.10.5 = (0.49 0.60) m/s
<latexit sha1_base64="EWGJzeR217BL+JPNeLbdte9nuus=">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</latexit>
Heuristics 11
Vapor flowrate (Str. 13) = 22,700 kg/h
22,700kg
h ⇥ 1 h
3,600 s ⇥ m3
6.1 kg = 1.03m3
s =v
<latexit sha1_base64="OWB0XLcDh2Mu94bUt8PRVc/rACE=">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</latexit>
Dtower = [4v/⇡u]0.5 = [(4)(1.03)/(3.142)/(0.49 ⇠ 0.60)]0.5 = 1.64 ⇠ 1.48 m
<latexit sha1_base64="AAna9mg8ujLZFErp6Ywc0BNKra8=">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</latexit>
Ptower = (Nactual)( Ptray) = (43)(0.007) = 0.30 bar
<latexit sha1_base64="T5A2kPyg4rsFXnFK430YLIRyjec=">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</latexit>
Tables 1.5 and 1.7 and F 1.5 From Heuristics
Tower diameter 1.5 m 1.48 - 1.64 m
Reflux ratio, R 1.75 1.26 - 1.58
Number of trays 42 43