Chemical Engineering Feb 2001

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A SpreadsheetSo!lution page 62

A Chemical WeekM8()Ciate8 Publieation



VOLUME 108, NO, a

f:--+--+~:_;;'--!-lT he m et ho do lo gy d is -

c u ss e d h e re h e lp s e n qi -

n ee rs d ete rm in e p ip e d ia m-

e te r, t ak in g I nt o accountth e I mp a ct o f s u rf ac e

r ou g hn e ss o n i lu id flow

UM'D

White l pe d fy in g rmxe rs Iss im p le r f or l ow -v is co S it y f lu -

i ds t ha n It IS lor luqh-vecosrty0l16. mixe r spec i fi ca tion Is SlIII a

c om ple x u nd erta ln g, d ue to th e

m an y e m" r,a - s uc h a s rru xe r , pe ~d , flU Id a gita tio n

an d U nit d,m en <tons- th at m ust b e b a la nc e d t o e ll su re

the d e si re d m i xe r p e rf or m an c e. P re s en te d h e re IS a m a th e-

m ao ca l s pr ea ds he et t ha t c an b e , u se d to m an ag e t he I nt er -

r el at lO n ,f ll ps o f I he ke y v ar ia bl es , a nd s tr eam li ne t he 01/eI~

a ll m l~ r- sp ec lf ia ll io n p ro ce s s

A H A N D Y T O O L F O R S P . E C IF Y IN G M I XE R S . . . . . _. . . _ .. . . . . _. . 6 2

T he d es ir e t o t rim energy u se , m d e li mi n-

a te d ep en de nc e o n m e rc ur y h as led to

improvements Inch lo r . . . . ka ll p rocesses .

T od ay , m er cu ry -f re e p ro ce ss es to s pli t b ri ne I

i nt o c hl or in e a nd c a us n c s od a a re p o ss ib le ,

t ha n ks t o t he r ec e nt c omm e rd al iz a 1i on

o f i mp ro v ed e le ct ro de s , m em br an e s

a n d e l eC l ro l y. z er ~ g n s

M O D E R N IZ IN G C H lO R -A lK A L I T E C H N O L O G Y 3 1

IN THS ISSUE

COVER S TORY r es e ar ch p ro Je c ts . P ro d UC i ng a ll 54 C he mic als : P ow de r " ," !ln gs o ffe r

62 F e at ur e R e p< > rt : Use t h is s p re a d - fro m w oo d w as te ' N an op oro us a ' cu re ' i n m a ny a pp li ca ti on lS lm -

s he et a pp ro ac h to s im pli fy m ix er 'spooges' offered fo r lic en se ' S ne - p ro ve d c he mis tr ie s a nd n ov el c ur -

spedf icat ion By ma na gi ng t he ( em e di at lo n m a rk et (p . 23) I n g t e ch n o lo g ie s a r e. e ~ p an d in g

c om p le x I nt er re la ti on s hi ps am on g • ' No n- re g ul at or y s ol ut io n s' n o w th e use o f p ow der co atin gs m fl£'W

key v a( ja bl es . t ru s h a n~ y d e sk to p p art o f E PA policy. U . S . mercury m a rk et s, p a rt ic ul ar ly t he s e l oo k in g

t oo l c an h elp e ng in ee rs t o s tr ea m- r es ea rc h ' E PA p r o po s es m a nd at or y t o e li mi na te s ol ve n t- ba s ed p a in ts

line the t ri ck y t as k o f d e si gn in g t es ti ng o r 3 7 c h em ic a ls , v o lu n ta ryEERING

a n d s pe c if yi 'l 9 m ix e rs Flowt e st in g o f c n em ic a ls t h re a te n in g

c hil dr en · B u sh t o r ev ie w C lir rlo n 70 fe atu re R ep ort: P art 1 . P U ttin g

NEWS " o r- p ol lu t io n r u le {pp. 2 5, 2 71 li !c hn olo gy t ra ns fe r t o w or k

17 Chementator : 31 N ew sf ro nt : I mp ro ve d c hlo r- al ka li W he th ef yo u're th e buy er o r th e

" H ig h -p un ty b u ta d ie nep ro ce s se s t ri m e ne rg y c o ns u rn p- s elle r, fo llo w th es e tip s to g et th e

ti on C hlo r- al ka li p la nts a re r un - mo s t f rom yo u r t e ch r ol o gy - Ii te n s -ro ut e- N ov el v i5 Co U5 ~

n rn g m ore c le an ly to da y th an th ey m g a nd c om m er ci ali za ti on e ff or tsH u id s m IX e r' P r op yl en e

O X id e r ou te . M e th ylc ld 20 o r 3 0 y ears ago , but the y're 15 F e at ur e R e po rt : Part 2 , M i n in g

m e ti 1 ac ra la te d e al · T re a t-s ti ll p ow er h og s, R ec en t d ev el op - t he ' Fe d er al R e se rv e' o f t ec h no l-

1 1 1 9 c o ol in g w a te r w it ho u tm e nt s, i nc lu di ng b ip ola r m em o og y U .S . g o v er nmen t laboratores

ci1emicals (p. r 7)b ra ne s jl nd o th er IY P e5 o f s al t- o ff er a tr ea su r e t ro ve o f t ec hn ol -s pl it ti ng c e lt s, a re h e lp in g o gy -li ce ns ln g o pp or tu ni ne s f or t he

• E l e ct ro l yz e r r e co v e rs c h lo r in e o pe ra to rs tr im e le ct ric it y u se . a nd p ri va te s ec to r. T h is a rt ic le w o ll h e lpfr om H C I • T he rm op hi lic b ac te ri a p ha se o ut m erc ury u se y ou lo ca te t ec hn olo gie s o f i nl er 5t .y ie ld fe rtiliz er fro m w as te ' O n-

37 N ew sfr on t N ew d /e se l- de su lfu r- a nd m an ag e y ou r b us in es s d ea l-b oa rd d is ti ll at io n t ar ge ts v e hi cl e

i za ti on r ul es p ut re fi ne rs i n i! in gs w ith U nc le S amem iSS io n s • u cn e n- be s ed h e rb i -

q ua nd ary fa ce d w ith s tric te r 78 ~ n gi ne er in g P r ac ti ce : V a ri ed 'a p -c id es · A mm on ia fro m u re a (p , 19 )

t hr es ho ld l im it s o n s ul fu r. some re - p re ac he s fo r e lim in atin g N Ox T his• A na er ob ic p ro ce ss m ak es f il le rs a re c on si de ri ng c ut ti ng b ac k a rt ic le c om pa re s t he v ari ou s o p-m eth an e fro m w as te • A v ib ra to ry o n p ro du c1 io n o f d ie se l fu el fo r ti on s fo r N O . c on tr ol , a nd o ff er sm ix er f or rn ul np ha se re ac tio ns • o n-r oa d v eh id es . T hi s c ou ld g uid an ce fo r c ho os in g th e m os tS oil f um ig an t r ep la ce s m e th yl b ro - [ e op a ri d iz e s u p pl y c o s t. . ,H e c tr v e a p p ro a c hm lde • A hybrid a pp ro ac h to d e- 43 N ew .fro nt H ea t e xc ha ng ers 83 E ng in ee rin g P ra dic e: O ptim iz -SIfoylng wa st e • B P , K o c h s e ti le s ee k cr cs so v er a pp e al R is in g p ri ce s i ng p n eL Im a ti c- co nv e yi ng ' sy s te m sw ith E P A· F un gu s d eg ra de s fo r o il a nd g as lire g iv in g S Om e e n- N O l a ll a ir m o ve rs a re s uit ab le f orb is ph en o' A • G ua rd in g a ga in st e r gy ~ e ff io e n t p l at e -a n d -f rame de - p n e uma t ic c o n ve y in g . Read on toL e g io n n a"e 's d i se a s e (p . 211 S I g n s a n e dg e o ve r t he rr do rn tn a nt re vie w th e k ey a ite rla fo r m a1 <. in g• D OE to inv est $ 33 m illion In 80 sh e ll - a nd -t ube coumerna r t s th e best choice

CHEMICALENGINEERING WWW.CIiECOM FEBRUARY 2001 3



Cover Story

M i x l e r S e , c i f i c a l i : o nilia Sp ~ e a d s h e e l ·f r y t h is s p r e a d s h u t's l o g ic t o s im p l i f y

a n d s ;p e e d U P I m i l e r s p e c i f i c a . t i o n

Steven F. Drnry

S h ar pe M ix er s. I nc .

tewis E . GalesReyNo, Inc.

l ui il s m i lc in g has la ng b ee n c on si d-

Iered an art that ~q~:h:esthe diU-cafe ba la ndng o r 1lliIrer speed, Iluidagitation., batch dimensions, and

otlllV v l! I' ia o le s. M o r eo v er , t he s p ec if i-ca tio n o r fluid mixers for 19w-visccs i ty

app lications, wm.le simpler thM f(lr

,n ui ds o f hlgb v is cc sl ty . i s q ui te COID-

pler, dne t< > the many cri tcri !l that CllJl

be =00 to define mixer perfbnnance ..

Presented. here is .. mathsmsbical

spreadsheet Ihat can be used b o

str ea mlin e m ix er s pee i:fi ca tiD ll. T JUs

spreadsheet. cilO be ilownlb.dea di -

rectly fromwww .sbarpembnracom.

Designed for low-viscosity·fluid ap-

plications, the program illustrates the

interrelationships of mixer-perfor-

mance criteria, including bow-these cri-

teri~. va(y with sc aleu p. O nc e zu ix er

Specif iea.t iOll is understeed for low-vis-

cos i t :y l lWds , t he r ea de r W iU h e a ble to

handle the tnore-wmpficated situations

Ih.at inevitably occur wben high-eiseos-

ity fluids o r . su li ds a re e nc a uu te re d.

Average,bulk.tluid velocityi t . . wgnificant percentage of fluid-mix-

ing applications in the ebemleal

p ro ce ea in du tr ia s (C P O d ea l w it h le w-viscasit y f luids. where mild, medium

or violent miring: 81'S the only materia

specified. Since these mixing .regimes

haee no standard ilefinition, illiorpre.

t anol l is usual ly left: !o the user; Here,

the authol1l a:i :bit rini ly define mild.

m ed iU J n a nd mlent mixing ' !IS th e"qui.va len. t of average bulk-f la ld ve-

locities ( V O l of 19, 3 6 and 54 ftlmin,

TABlE5IJMMARY

'TABLE t. Mild ! 1 'I l >< , in g ;

TABLE 2. M~dmi.i"9

T:ABLE 3. Med i.m m ixi ng;

T.A.BLE 4. ~;um m;"i"9:TABLIE 5,. Vialenl mi.ing:

TABL'E 6. Violenl mixing:

Bvlk-~u i .d - e l O : c i l y

Bv l k- nu id " " Io c ll r

B u l k- " ui d v el oc it y

au l~-Aui" ""Iooi]y

Bolk-Auid ".,Joeil)'

Bvlk-Auid "ebdly

I B f t/ m in , D/,18 ft/m in. ];)/T

.3 6 ft lm in . I i) IT

3 6 f t/ mi n, o/r5 4 f t/ mi n, D iT54 h/m /n . O jT

0.25

0.35

6.15

0.35

0.250.35

INOMENCLAl iURE·

respectively. The bulk-fluid vel<lcity

in the mixed tank is defined in Eq)1n .lion: (l) as the pri:tqary pumping ca-

pac ity of the mrpel le r in ftSlmin (Q),

divided by the tank'. horizontal

crcss-aectienal area. in ft2 fA). All

terms are defined in the. ncmencla-

ture box, above.

v,=g mA

Quantified values for mild,

medium and violent mixing have

been cited.in the literature and arenecessary in this exercise as 8 start-

i ng point for other calcula tions . How-

ever, f u . i . s artiCle demonstrates toot,regardless ofthe characteris tic chosen

as the basis :For mixer spec:l :l icat iOll

and scal eup, other design parameters

will vary in 'W a ys tha t are n ot n eees-

6 :1 C HE MIC Al. E NGlN5 'E RIN G W W W .C HE .C OM FE BR UA RY 2D D1



sar ily imuit ive to the engineer. No one

characteristic can be singled out for

selection and scaleup in all cases .

Defining m.Ud .ng inten i~yWhen cansulting WW l an equipment

desiCJler, the end user should describe

the mixing requirements in his OTher

own wards. It i during this recitalthat the designer forms judgments

about the intensi ty of mixing reqru,.e,j

to SlltislY process need . In addttt on,

because an accurat e and complet e def·

inition o r mixing requirements is

vital , the designer and use, should

jointly fill out a mixing-data sheet

that methodically def ines a ll t he im-

portant aspects ofmixer performance.

This step in the design and pecifi-

cati.on proce mWil not be rushed or

oversimplified. Once a mixer is manu-

factured and installed, itis difficult for

changes to be made to the uni t without

re_roav ing ita n d r et um in g it to t he l ac -

Wry• .fu some instances, components

..,thin th e mix.eT may limi t cerl :Jti n

change . For in stance, a larger motor

may exceed tbe capabilit y ofthe drive

(also known" th e gear redueerl or the

mixer shaft , which drives the impel ler.

If that is the ca e. then a completely

new mixer would be requi red. To fur-

ther complicate matters, 0 new mixer

migh t bes ig n i .5 c an tl y heavier, thereby

exceeding L h . e cIIpaci.ty of the process

vessel or the building structure.

Shalt

Balf!e

Z Impeller

c

t-----T----i

FIGURE·1. The basic mixer dimensions,

shown (B, C, 0, T,Bnd Z) a re def ined In

lila nomencl<!lIJre box ( 1 ' . 62). Thespreadsheets (Tables 1-{j) emplov or rratles. '010.25 .nd 0.3510 demonstra te the

Imp.~. on mixer operal in s pa rameters of

varying this ·rallo

Complicating factor

Viscosi~:Tables 1-6 (pp. 63-68) were

generated using' a Microaofl. Excel

preadsheet uuderthe pretense thatmost f luid applications involve low-vis-

cosity liquids. '!'bis assumptio» is neces-

sary in order fur the data generated by

the t ab l to be accurate, If i1 ui d vi .

i 1 ;y is greater than 100 cP, then the se-

lection charts sbould be used with great

eantio or not at all, Ai l viscositiea in-

crease, thelikelibood thatIluids will ex-

hibit non-Newtonian behavior also in-

creases. The design or mixers fur

bigh-viscosity applications or for non-

N ew to ru a n f lu id s r eq u ir es c o ns id er ab leexpertise an d should be avoided by

those with limited experience:·

Solids': Tile presence of solids .in. 0

process fluid : complicates mixer de-

sign, and ruay hamper the ur efulnes

of !.be selection tables. Fluids with

rapidly sett ling aHde may requiremere that are m O D Y t imes la rger

than those suggest ed by the tables.

01) the othor band, aile may use the

tables to design mixers that contain

sol ids with. s low set il il lg Tate.

G",ses: lujected or formed in situ,

gases tlutt are present i . 1 I a liquidmedium pose a major problem in

mixer specification. If gases are pre-

sent in .nrore than miniscule concen-

tr a tions, the selection tables shou ld

Dot be used.

Equipment description

The basie mixer eonfiguratton recom-

mended for simple applications is

shown in Figure 1 (above, le ft) . As il-

lustrated in t his sketch, the bat ch has

a Iiquid-depth-to-tank-diameter rat io

CHfMICAl ENGINEffiING WWW.CHECOM FEBRUARV 200 I 6.3



(defined as ZITI of approximately 1.[1.

A batch. of this shape 'is easy to mix

using a single hydrofoil impel le r, . 1 0 -

e aW i a pp l' O' <i Jn at el y 1 13 0 1 t h e l iquid

depth (Z) from the bo t tOm Qftbe tank.

This distance is d ef in ed ~ C!Z~ll4.

8hooo batches, Dr those With ZI'rTa~tios signifi=Uy less than 1 .0, ar emum diff icult 10mix because th e nor-

mal f lnw patt erns produead by tit " im-

peller c a nn o t f o rm in th e batch apace .On the othe. rlmnd. bat ches withZ,rrapos sig:n:lfi=tly fI' t ' Iate, than 1.0

may requtre multiple impellers,

Ratios of impelle r diameter to tank

diameter (D/Tl n orm ally ra ng e fro m0.25 to 0.4, with OJ¥.!being idea l. Fig·

me 1 depicts one of four ant iswirl lmf·

fl.es posi t ioned at a 90·deg angles re -speeti.n' to the taJlk cil'll1lmt<).nm.~.

These baffles preveat low·vi.sj1Q~[Lylu-

ids f rom swirling du e In t he i 'm p e l1 e r

ro tefum. Tbe ratio of bafile width l'O

tank diameter, or BIT, should beE'l'JaI to 1112. Baffles designed tn thisratio are ",,,,,epted as ""' industry s t a n -derd fo r low.";scos.ity·fll,lid applica-

t io n s .1 wg e1 ' b a il le ' d t) n o tn e c es s ar il yi,m p ro v e .Q!iXer performance ""c ; l may,

in fact, interfennoith it.

Criticll11designpueametersHorsepower and shail: .spaed are tb.

t",o mosL-criticalparameters involved

in de. fi ni:Qg the mixer' s capabili ty to

d ~l i" er a certain l ev el o f l l e; r li J rmaace ,such as a specified buls-fluid velocity.

U n fo rtu na te ly , t he y a re m o re d if li cu ltto specify than a mixer', gen,,~al di-

mensions. Motor borsepower an.d

mtser shaf t s p ee d d e £i o e the <lgit .abion

inten"sity impmed by the mixer andalso cO .n JmuWl l aW t he m L "" r's s i" ,. La

a manufacturer,

T<>furtber explain the spoci:f icat i l1I1.

o f m ix er size, c on sid e r tw o different

lO·hp misers with respect ive shaft

speeda or 1,750 rpm and S4 rpm. Th.

first mixer runs at the actual motor

speed and does not nflj!{) a gear re- ,

ducer . Howe",>.c,: in o rd er f o. t th e s ec -

o nd .m :i:x er to o pera te a t IIl ow er s ha ft

speed, it will require a gear reducer ,

whiob. is II! ,'ery heavy, "astly piece of

machinery. Thas, the Br . t mixer

might ",.,fgh 600 lb and cost $5 ,000,

while the second mixer n:t ight weigh

1 ,5 00 l b a nd c os t $ lO ',O O 0- -2 Q,O O O .

Th e eomplete des.igu of a wi'el' from

a mechanical standpcini m an Impor-

tant but compl i c a t ed task, Most fluid

mixers use a c!lll~il' ' ' 'j}' ' ' ' iI. ,holt ( a shaft ,with DO bottom bearing) to drive aDD

support Lb. impelLer. ''rhe sh.aft IIIU~t

be o f s u il ic ie n t d iam et er 1Q keep i . 1 1 e

st resses p:roduoed by terque, es well as

the bending momenta, witlrln accept·

able limits. Bending moments occur

when the impelle r exper iences f lnctn-

ating horizontal forees that piISl i it to -

wards the vessel! ! wails. 'lil,ese forres

.xtend evsr the lenglih of the lll i, ", r

shaft tp the lowost bilaring ill. the gear

reducer , thereby producing II bending

,;wment that adds to the tcrque-In-

duced Shall. stresses.

Furthermore, the designer mhet de-

termine the natural frequencies of vi-

bratitm of tile drive, $haft and im-

peUe'r system Iall measured in rpm}.

an d ensure that they dliJ IJ1 ' from the

' O pe ra ti ng s pe ed . o f t he s y st em . If th efrequencies coincide, the resultant vi,

b ra tir m w ill 'lu i. k1 }1 fat igue tho mixer -

shaft to r other major componeuts ), re -

ducing its 1if00ycle to min utes.

O ne w ay to a v o id ' th is seeoario is toselect t a n k s with aZI Taraboot 1.0. At

this m tio . the canliilevered·shaft lel lgtb

and reqWJ:ed tank diameter are opti·

mized, A design ratio of ztr » 1 usu-

ally danntas lONg, slender vessels unix-

ers ""til long, cansilevered shaftslwhiilh are e:"I;>eDsl~·e. ecmplicated me -

chan i ca l C!lIlfigll",tioos.

Dlscusslen of ealeulatdonsTables 1--6 were generated uaing the

equat ions and calculations t llat foUow.

Six "ebi; of conditions, ~hOWJl in 111.

tahl~ summary(ilQx,

p, (2) were choselJto delllOrulLr.W hf)'w jhe bulk mIld ve-

loci ty (V') and DIT rat io impact mixer

5.pecifioatimru;. When these va lues a reiIlput at the top (If th e spreadsheet , as

shown. in the table insert (p. 62, top

right) tb. prog ram c",hihte. ih, in fer-

mation Iis ted in ColumnsB thr.ough It.for each ofthe batch volumes input into

Co IUDU I A. W rt. bio p ra ctic al limits.these tables can be gnnerllted for n

wid . . range or parameters, by &peci( '~c.

ing finer graduations ofDIT and Y'.

Cokrrm. .A . batch "oJ",,,",e (V): A

r an ge o fu sr u" -s :~ 'f .i ed " ,. ..I nl ll @; ,i ll U . S .

gal, i :input 'into Cells Al3 through

A S 3 . T h es e v ol um e s, w hil e arbitrary,

a ret yp ic al o Fm oa t miring applicat ions .

For the examples ' provided, B . range of

25()....:lO.OijO ge l has heen.seleeted. AB aprecauti.onazy measure, the spread -

shee t logic should not be ,,!led for ""I·

UlD"S great ar than 10,000 gal

Columns Band C, diooU!ter ( '1:)

and liquid depth (Z),A s previously

s tat ed, aba tch shape with UT=l.1'1 it;

i dea l for mix:ing and. agita ti<m. With

this asswnptiOf,l, the t !U)k diameteriT). cal culat ed 'i n inches using til.

vo lume. in C o lu m n A . , E ql Ja ti <l .. ( 2) c an

be s o lv e< ! f o r R 1;0 yield the radius o f aeylinderin .It. '!'be liquid depth (Zl if!

equal to twioe the diameter (2ft), as

repm;;ented below:

Vgo1 =( i l E ~ ) '(2R) (7.4.l!~~ ) [2}

The spreadshee t automatiepJly con-

ver ts the radius to diameter, by multi-

plying by 2, and inches to feet, by mul-

tiplying by 12. T he re&u:lts are

generaeed in Column B and copied

into Column C, where they 9.1$0repre-

eDt ]jquid depth.

C(l lumn D, ' impeller diameter r D J :T he :im p elle r d ia m et er C D ) is c alc ula te d

ininches , by m ul tip ly in g th o diameter

oCthemi> : . , d batch t T l f r om ' C o lu J D I lB ,

by th e ratio of impellar diameter to tank

diameter (D' I.TJ, whic.b i$ lnputinto Cell

E6, W J : re n designing the spreadsheet

equations, oneIll"!I.' tJopi>E6 as $E$6to

. f i x the value, iIItbat eell for relative cal-e ula tio ns d on e ill sn bs eq ue nt ro ws.

Columll.F, ea1"uiateci.halhpeed (N):

T h e s p ro a .d S h e et Ill","" d e C c r r o . m e the.haIts p ee d b e fo re itcan ca l eul a te shalt pow" , "

rsBp]:in C olo ;J W lj!;.B utt o c a]c u]a teN , ~

required pumpingrate, Q, must first befuund in fi ll pe r minute, T o do this, the

sl'~ U5IlS bulk-fluid velocity (lI'}

from Cell 1 2 I input .as C e l l $ 1 $ 2 ], c a lc u la te s

tim b a tc h bm iw n J: al crcss-scetinnal !Im!l

1 A l li nm the tank diam' l t i l r (T) listed in

ColumnB ria Equatioll (3) ,

(3)

and then sol...es Equaeion (1) for Q .

Once Q ismolVn, the basis for the cal-

eulafions in. c ol um n . F becomes the di -mensionless pumping number IVII a s

$ bawn in Equation (4):



O HE MIC Alo NG IN EE RIN G W VO "< 'I. CH E. CO M F EB R UA RY 2 00 1 65



Cover Story

The. -preadsheel then ealeulates the

shaft speed t N J , in rpm, required 'to

produce the pumping rate (Q), given

th e impeller diameter mH i:o m C o lu m nD, and the dimensionles pumping

number uVqi from Cell $E$8.

Column E, calcula.ted .haft power

(SHp): The shaf t horsepower i shown

in Column E. The basis for the calcu-

lation ofSHp i tho power number, a

sbown inEqu~tion (5) below.

This equation must be. rearranged to!!OI". for P. In this equat ion, P is ac-

tua l ly a form o f H I' whose' UIUI.$

have been "fixed" to render N dimen-

sionless . When th e :SllreaiL,beet cal-culates S Hp. it incorporates this cor-

rection factor. A ll other terms are

knO\\1I1: Np j dsfined inCell $E$7,

liquid density (p) is calculated u ing'

the specific gravity from Cell sess,impeller diameter (D) is known from

Column D, and aha:! '! .speed, N, has

just been generated in Oelunm Fusing Equal:ion (41.

Columll G. minimum. horsepower

of the motor (Hpj: The minimum

molor horsepower is cal¢ul<>ted by di-

viding the haft power in Column E

hy O . 5 . T Ili i the value used to

specify mixer performance because itaccounts for' vari ati ons in f luid prop-

erties, as well a for power losses

through gears , bearings and seal .

tendard motors do no~ come in the

ratings calculated in thiS column.

The user hould purchase the next-

larger standard motor, to minimize

the purehase cost over that of" non-

standard motor.

For example, motors come in stan-

dard sizes, uch as 1, 1.5, 2, and 3 hp.

[fYOI l order II motor with a L23·hp

rat ing, which i not available off the

.helf, you would b. char g ed a high

price ror eustomieation of the non-

standard motor, for the sake of mini-

mizing operating costs. Rather, a

manufacturer may rightly encourage

you to purcha e a. Lb-hp motor,

which would probably be in stock.

(4)

Column J, potoer per volume

(H_pIV): To build this column, divide

the minimum motor horsepower

from Column G by the mixed volume

from Column A divided by 1,000.

This gives units of hp per thousands

of gall')ns, and Is used mora fre-

queatly than, say, torque per vol·

ume, wben analyzing mixer perfor-

manee, 'otic" that the required

horsepower per volume decrease

with volume for mixers that del iver B

constant bulk-fluid velocity.

Column H, torque (T qi : Torque is •

significant characteris tic or property

used to specify a mixer, and is calcu-lat ed using Equation [6).

53,025·Hp

TQ=--N-.--

' In this equnt iou, l : / p is ~he 11I1m-

mUD) horsepower obta ined from Col-

um n G, an d N is obtained from Col-

umn F. As hewn in Column R, ilie

lprque required for mixers providing a

constant bulk-fluid velocity increase

with volume.

(5)

Cotumn 1, torque per noiume

IT l tV ) ; Torque: per volume can. be

used to scale up a mixer, provided

OM wants to maintain a similar bulk-

fluid velocity in the lat'gAr tank a in

the smaller 00e. The valuesjn Col-

umn I are generated b y dividing

torque (Column Hl by the batch vel-"me (VI. The latter, expressed in

units of rhcusanda of galion'S, is cal-

culated by dividing the value in Co l -wnn.A b y 1,000 gal when writing the

equaticn in Cell 113. Notice that theT Q I V reQuJred fo r mixers delivering

" const ant bulk-f luid velQcity ;8 tha

same for any volume listed in atabl e.

Cul.wIl. J{, R'ey"old$ number

(NR.): The Reynolds number is cal cu-

lated in Equation (7) using tbe im-

pel ler diameter from Co lumn D, shall

peed from Column F, the density as

specific gravi1.), from Cell $E$5, and

fluid viscosi ty from Cell 5E$<l ..A con-

stant 10.;is required on the right

hand side of the equa tion to make the

units dimensionless.

N " . :D"Np!'

1> 6 CH EM ICA l E NGJN~R lNG W WW .CHE .COM Fa lA UA AY 2001

(6l

Column ll~ lurn.ouers per minu ..-e ;

Batch turnovers per minute is a com-

mon cbaracteriatle considered by mixer

designers . Turnover iscalculated by di-

The Reynold number i~ a ratio. of

inertial to viscous forces. lL is well

known that as the Reynolds Dumberincreases, t he f lo w regime i s becon r i n .gmore turbulent. Ln order {or the equa-

tions in the spreadsheet to be valid,

the mixed Ilow must be turbulent (in

other words, NR. must be above

10, (100). Column K serves to "er i fythat t urbulent conditi ons exist, and to

illu stra te the e ff ec t o r s ca le 00 N!W.

inee the user of !:bese selection

charts is usual ly more concern ed with

th e overall magnitude of NR<' rather

than Its exact valne, Co111.= K is ex-

pressed iu sc ientifi c nota tion. Notice

lha.t N!W increases w ith v olu me for a

fixed bulk-fluid velocity.

Colu-mnr. Froude number (N~:The Fronde number, calculated via

EqUll tion (8), expresses the rat io of' in-

arbial to grm,;t.lltiotull Inrces impartedby an impel.ler to the process fluid.

(8)

In order (or NI'r to be dimensionless,

Nmust be converted to revls by divid-

mg b y 6 0 B lo lin , D m ust be conver ted to

f!. bydividing by 12 injJt and ilia accel -

eration of gravity mllst be input as 32

IlIs2. The higher the Froude number,

the greate r the surface deformat ion of

the mixed fluid. Nl'r decreases with in-

creasing volume. Therefore, the user

cane.~ calmer surface condi tions as

the volume iaereasea, while the bulk-

fluid veloci ty remains r ,on.smnt .

Baflle!linhibiHheformation ofa sur-

f a c e v o r tex ( in oilie r words, a V· haped

surface .with tbe bottom tip of the V at

th mixer shall) because they prevent

the fluid from rotat ing horizontally and

centr ifugnlly towards the outer edge of

th e tank. B u t b aJ lle s d o n o t p re ve nt t he

surface of the fluid from surging, or

f rom oilie r types o r motion. Bl!(lause

this art icle eonsiders only ful ly baIDed

a pp llc at io ns ( wh er e a s ur fa ce v or te x is

not produced), the Froude number is

not signif icant. i n the correlat ions dis-

cussed. However, it Js helpful La see

bow it varia with volume.

(7)



C;H~MIC;ALENGINEERING WWW.Ct!~.COM FEBRUARY2001 67



viding tho pumping capacity of the im-

pel ler lQ) in galIroin by the botch vol-

ume in gaUOIlS from Column. A. 'Ihe re -sult is lImin or turnovers per minute ,

In this instance, Q is calculated using

EqyBt ion (4). The pumping number

f rom Ccl lES7, t he s ha ft s pe ed in rpmtfro m C olu mn FI , a nd . impeller diame-

ter (from Column DI are multipl ied. D

is first divided by12 to convert-to It, and

then raised to th e third pow er. T he en -

tire resul t is multiplied by 7.4S to <an-

vert from f t 3 /mi n to galI~

A l th o ug h t h es e v a lu es o fQ a rs s ho w ni n Column 0, the mathemabioal equa-

tion is fneorpcrated directly into Col-

umn M , wbich bo" that the number of

tumevers per minute decreases with

vo lume, for a f ix ed bulk·fluid veloci ty .

ColURm ,impeller tip speed (U,):

The impel ler t ip speed is calculated by

E qu at io n 1 91 :

U, =rJ)12

Impelle r diameter and shaft. peed

are obta ined from Columns D and F,

'Cl!pectively, U, is f ixed under condi-

t i ons of increasing batch vul ume and

constant bulk-fluid velocity.

Column 0,pIlmping capacity (Q):

T!)e impel ler pumping capac ity (gal-

l o n s per m in u te ). w hic h i s u se d t o c a l-

(9)

Column Q , Prandtl nwnber (Np);

The Prandtl number is a function of

fluid properties such all v iscosi ty ,heat eepacity, and thermal conduct iv-

ity. as defined in Cell. $E$4, $L 5

and $LS6, respectively. The values

have b e en c e rr ee te d to render NPr di -mensienle s , I is calculated inCol-

umn Q to facil itate subsequent calcu-

culata turnovers per minute in. Col-um n 1 1 1 , is listed in C o 1w :n n 0 t o i llu s-trate its variation with volume at a

f ixed bulk-fluid valoeity.

Coll.lm"P, blend.time (9): Blend t ime

lin minutes) can be calculated using

Equation 1101, where No is the blend

numberfmm CeUSE$9andNis thecal-

eulated shaft speed from COlumn F:

N.=N9

HGWe\'eT,Equation [lllisthe basis for

caloula t ing blend time as shown in Col -

um n "P . T his rn ore -c or np le x fo rm o f the

b l en d n umb er i n cl u de s t he e f fe c t o fD I 'l '.

o~ N._

!··(~tThis correlation predicts that the

blend time for a batch increases with

volume for 8 fixed bulk-fluid velooity

- constant velocit ies take longer tot raverse the la rger tanks.

6.8 Cf-{EMICALfi.NG1N~RING WWW.CIiE.CQM fEBRUARY 2Q01

nOI

h T = K . [ D " N e ) a ( G p I J ) ~ ( J 1 _ ) ' (13)

k p /, p",

In Column R, 'ii.calculated using

tank diameter (T) Irom Column.8,

t he rm a l c o n du c ti vi ty (k) fro m C ellSL86, th e heat-transfer-equat ion eon-

stanf ( k " J from Cell $L$7, NRr from

Column K, N Pr tl-om C01= Q , the

ral:io o r fluid v is co $ it ie s f rt lm c el lsE$4 and Cell $L$4, and lhe expo.

Den t s 11, b and c from Cells ,$I. 8, $L 9

and S1$10, respectively. 'I'hls correla-

tion predicts that the agitated-film

la tions of the bea t transfer coef fici ent

lid in Co l umn R.

(11)

Column R, agitated-film heat-

transfer coefficient (h): The ngi-

tat ed-fi lm beat- transfe r coeff ic ient is

required to estimate the ability to add

or remove heat from a IlI'OC~SS ve el,with the given heat-exchange S\lJ"·

fa ces . B elo w is th e standard cor re l a-tion from which the heat-transfer co-

efficient i~ calculated:

NN. ~ N ; . N ~ , ( J : ! . . ) ' (12)P~II

Th i s dimensionless ccrre lar iee can

be expanded a shewu in Equation

(13). where the agitated film heal-

transfer coefficient emerges as k on

the lett hand side:



Cover Story

TABI.E 7. Motor t lo"epowar SpeelffcaHonac hieve a \ r 0

mixer, If on

V0

Mol,,, H pN Tumovers V' A

h horsepower togal In, hp rpm per min it/min m'in 1!tuJ(h)(ft2j('f)standard CO

IMOO 35 .S 2.52 117 1 . · 5 11 1.2 SIling til" speed

10,000 SO . 1 0.66 42 1.5 18 1. 6 401'torque will1,946.9 in.-lb

TABLE 8. Scalaup Using a 3 -h pV MoforH N

InT~bV' a mos t eertainl

gal hp rpm tl/m;n min I ),O O O. ca 1 B P P

Table 4 InformaHon 1 . 0 00 1.13 183 J89.4 36 0.4 duces a torqu

fxlsllng appnCOf iOA 1.000 1 190 332 i sc los enoug

Tabl .. 4lntormoHon 5,000 3.31 107 1.946.9 36 0.6 ommended by

Possible recommenc:loHon 5,000 5 100 3 ,150 .3 E

Recommended 5.000 3 10 0 1,a90.S'Olber Readinp

heat- transfer coeJI ic ient decreases dri ve. The user should se Jec l a ge ar re-t. D k k i !, Y . D a v id

' C u d agitAtion

with increasing volume. for a constant. dueer tha t y ie lds the nex t- lower ava il - F"m"w:)' 197

bulk-Iluid velocity. In practice, 8 de- able shaft speed. 2. Ssr;e!l";, RJ. . .~uLh

signer must provide additional surface lflhe motor is larger than specified P ce:Gb.3.JI

area o r larger ternperature-driving by th.e table, and the gear reducer ae- 3. Bc r J inslc i , D n,rithm.~l:la-.r':l)

[0""_ to get the required heat transfer leeled gives a shaft speed lower than,. B rodltey. I

in larger vessels, the one in Table 7, the mixer manu- '"I"nI.n.porl

facturer should adjust ilie impeller pro:u:b." Mc C

Compnrfsen among tables diamete r so tha t it tha t ful ly u ti li . .e s3S!l-$9.

6. ,Il!iliy. D.,'ldA general observatien of Ibe selection the higber horsepower and lower iogpn>l.olo>nO

cllartsreveals several dynamiQll oc- shatt peed. 6. Di c :u , . .Davideurring a lll ong the table s. Table s 1 1I..tpc. ro r

and 2 . which ref le ct 11 constant bulk- ealeupi impIifiedMJm:h 1994.

fluid veloc ity of 1 ll NOlin , have DIT Another use for the se se lec tion table s~. FManD, Julia.

va:ncei ;l £mpell

r at ios of 0 .25 and 0 .35, r espect ively. i s to fac il itate mixer sca leup . Assume, i:atiom, Ch.r.m.

When D IT inc reases , be value s c fHp, for instance, that an operator bas II S.Napta.S ..

N,TQ.Tif"', BplV. R " NEr , u, an d 1.000-gal.li'luid·pbase mixing appliea- tiOti," H . 8 .

W"lIey.New'ih dec rease. The same observa tions tiau in whieh the mixer i s pe rfo rming

9. Olrlah ue, J .Y.hold t rue when comparing Table 3 sa t israc tor iJy . This: mixer has a l-hp McGraw-Hill

with Ta ble 4 (whe re V' = 36 ftJminJ motor and a ahaft peed of' 190 rpm.

and Table 5 with T a ble 6 rwhere V = The ope rata r wants to spe cify a mixe rAuthors

54fiJminJ. that will perform just a well in 8

5,OOO·galapplication. ,

Predicttng proce re ults The first step involves examination of

lee

he tables presented prove to b~ in- the six. selection tables tolind opemting

valuable during' seiactlon o r mbiars. rendition- that d~y 'res~mble those of

Suppose a mixer is re quire d for a Jiq- the LOOCl-ga l~ng applica ticn , th. ..- eby

~J iid-phase proce ss in a lO,OOO'gal b e d di n g l ig h t on the mixing jn~

tank, and thai the term "mild blend- predueed by this mixer-motor duo. A s-ing" i 8 uitab le descr ip tion of the urns- that one ident ifies the ccndi ticns. in ,\mil]1rm;Ylw

mi ring inte nsity required, Using the th.llrst row aCTable 4, lo r medium mix-of CatUnr:nw Ul

A1QbE, and is •

two tables for mild mixing a t 10,000 ing and a DIT !If 0 .35. a s shown sspa- inth». '~~Q.fW

gal, one extracts the following data, ra~y inTableS (abovel.

~

recapitulated in Table 7 (a bove). The The tmljue delivered by the existing

most-important data are the motor l,QOO..galmi= is s l ight ly less than thathorsepower ( Hp l and he mixer ~h1'l:1t s.peciliedbyTaWe 4 fur prod ue ing a bulk-

speed. ince one: e annob rea dily pur- fluid velocity QF36 flImin. It is safe to as-

chase a 2.52- or O.66-hp motor off the 5umetlwt a 5.QOO..galmixerwbose torque

shelf, th. next-latger available motor is sIigjilly less than that speci fied by

- in this case a 3·bp or a 314-hp, Ta ble 4 will perform similarly to the ex-bolhBS.""" ~

should be selected. isting llliNerin the l"OOO-galapp l iea t ien , mte U.a. iy . Os

Furlherlllore. it m a y ! lo t b e p o sa ib le Notice th.at Table 4 recommends a ~["{ [QdSIm:rp<.1 \II'lt.Gale:Si:iatn

to purchase a ll?-rpm or 42·rpm 3.31·hp motor ope ra ting aL107 rpm to P">~

f 36 f t lmin in 8 5.OOCl-gal.

e vinere se the motor

5 hp (the next -h ighe r,ufigurabion), while .redue-

to 100 rpm, the resul ting

be much higher than the

specified in Table 4.

m oto r a t 100 rpm will al·

) ' be adequ ate fo r the

licahlon because it pro-

e of 1 ,890 .8 in- lb , which

h to th e 1,946.9 in.-Ib rec-

the table. •

ditedbyRil.a.L.D'.4quirro

S.• aruI Ricks. Rl.bard w" L U t ·

refresbee eedee. C lu !m . EDI ! • •

6.

C:d~i:~~,~~~~r id . " T .h e Ad.""nL t~ rthe Algo-

urt. N ew Y o rk . . ' 20 0 0.

toOOrt "and H~"l)(ty, H.o..rryC_Phenomena, A Unified Ap-ruw-Hill. New York~ 19~ pp.

"Facing tb.e~h91Ien~ ormix.·uidi. eliml. E'lg .•~ltsy201)0.

S. and Heinr~an.il RamI!!Sh.Duid arWc,g, elrl 'm.. 1i"8"

n ' 8. R 'D d B(IIkker, Andre. Ader geomet;ry l~lIIliquid agi..

E :n g: .A Ug 'll aL 1 99 11

~c: . PriDcip~eB"and Appllcabled Press, Ko dac sb e, T ok yv an d

ork, L975.

I "j-r111id 1 ' 1 ' 1 0 0 0 8 T"' lthnolom-:N l! .W 'Y o r: k . 1 9 S3 .

CHEMICAL ENGlN.,ERING WWW.CHE.COM FEBRUARY 200; 69

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Chemical Engineering Feb 2001