an introduction to process flexibility part 1. heat exchange

8/12/2019 An Introduction to Process Flexibility Part 1. Heat Exchange

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c l a s s n d h o m e le m s

Th e o bject of th is col umn i s to e nhance o ur rea ders ' co llectio n s interes ting and n ovelproblems i n chemical e ngineering . Problem s the typ e t hat can be use d to motiva te the studentby presenting a part icular principle in class, or i n a new light , or th at ca n be a ssig ned as a novelhom e pro blem, are requested, as we ll as those tha t are m ore traditional in natur e a nd whichelucidate d ifficult co nce p ts. Pl ea se s ub mi t th em to Professor James O . Wilk es (e- mail:[email protected]) or Mark A . Burn s (e -m ail: m [email protected]) . C hemicalEngineering D epartment, Un iversity o f Mi chigan, Ann Arbor , MI 4 8109-2136.

N I N T R O D U C T I O N T O

P R O C E S S F L E X I I L IT Y art 1. eat Exchange

W .E. JON S, J.A. W L SONUni versity o f Nott in gham University Park N ottin gham N RD E ngland

Process pl ants need to be flexible to co pe w ith changesin p roduction rat es, product spec ifi ca tions, fee dstock,ca talyst dea ctivation , and h eat exc hanger fo uling . T ra

dition ally, o nce th e pro cess s tructure h as been decided, va rious operatin g cases are ev aluated and one is c hosen as th eba sis for de tailed de sign . However, se lection of th e designcase i s not straig htforward . Effectively d ealing with a ll thehighly int erre lated issues durin g design is a formidable p roblem. Hence, en gineers oft en resort to the a pplication rul e -t humb safety factor s du ring e quipment de sign e.g., adding 10% ex tra area to a heat exc hanger) in an effort to e nsureflexibilit y. Following thi s s trategy, an ex perienced engineerwo uld hope to de velop a design that is o perable a cross th eanticip ated pro cess ran ge , bu t there is no g uarantee th at th e

requir ed flexibility w i ll b e ac hieved. ': As the problem prese nted h ere cl early illu strates , di fferent plant o perating m odesca n eas ily lead to e quipment d esign situ a tio ns that are notcov ered b y a s imple safe ty fac tor.

The ab ove co mments ex plain why n o substantial coverageof fle xibility is found in any the stand ard under gradu atede sign textbooks, a part fro m a few re marks o n safe ty facto rs. D espite the se diffi culties, we feel the topic is ve ryimportant, particularl y because of the highly int egrated plant s

being bu ilt tod ay, a nd th at the basi c i deas should b e int ro

du ced to all students .So me students will encounter fl exibility probl em s as part

th eir fina l-ye ar de sign project. Th ese projects are norm ally s implif ied f rom indu strial reality, considering o nlyone f eeds tock a nd, at worst , a ca talyst dea ctivati on o r heat

Warren J ones hold s BS c a nd PhD d egrees i nc hemical e ngineering fr om the University o fNottingham and is a regi stered Ch artered Engine er . He has a wide -ranging interest in b oth fronte nd p rocesses a nd de tailed pl ant design , developed initially through nine years of experie ncewith a major e ngineering a nd construction co mpa ny. Teaching re sponsibilit ies i nclude severaldesign courses , process economics , and eng ineeri ng thermody nam ics .

Tony Wilson holds BS c and PhD deg rees inch emical e ngineering from the U niversity ofNottingham . With ind ustrial a nd consulting experience in proce ss con trol a nd ba tch pr ocesse ngineering , and with ac tive resea rch in b othfields , he coo rdinates t he department s resea rchin co mputer-aided p rocess e ngineering a nd isres ponsible f or p rocess control teaching a t theundergraduate l evel .

172

Copyright ChE D ivision of ASEE 997

Chemical Engine er ing Ed ucation


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(I)

(3)

(4)

(2)

(1 RB)T2 + R(B - I)T3 + (R - I)T = 0

(1 R )T4 + B(R- I)T3 + (B- I T = 0

Students are fa miliar wit h u sing heat ba lance s to c alculatethe h eat load , Q ,

to determin e hea t tran sfer a rea A , knowing the overall heattran sfer coeff icient U . Her e , (mc p)H and (mcp)c are t heprod ucts of flow rate and specif ic heat capac ity for the h otand co ld streams. Temperature s T ) to T 4 are identified inFigure I , and for t he mome nt we as sume the by-pass isclosed. But desig n to t ake into acco unt flex ibility im plies noton ly calcu latin g A , but al so lo oking at the im plications foro ther operating condition s, and thi s is wher e Eq s. ( 3) and (4)become u sefu l.P' Th ey a re deri ved for Eq s. (I ) and (2) inorder to permi t the w riting of expl icit temperature eq uations:

and th e ra te eq uation

where R = (mcp) C / rilCp H and B = exp[ UA/(IT p c R l)] .

To illu stra te , for a g iven he at exchanger (A specified) a ndkn own s tream propertie s (( ril p )C,(mcp)H' and U specif ied),we c a n ea sily calculate th e effect of a n inlet tempera ture (T)

and T 3 cha nge on both exit tempera ture s (T 2 and T4 usingEq s. (3) a nd (4). It is a ve ry simple exte nsion to a pplyseq ue nt ially th e abov e pair of eq uatio n s to a heat excha ngernetwork, t hereb y ev a luating t he n ew tem peratures th roughout th e network .

Bearing in m ind that various operating mode s are to beac commodated, it is likel y that the heat e xcha nger size d forthe mo st s evere case will be too large for t he o ther mo de s.As hinted earlier , thi s difficu lty is overcome by ope ning th eby-p ass . We assume t he heat exc hanger wi ll o perate with thesame UA (see t he Appe ndix ), but the effec tive UA fo r th eheat exc hanger plu s the par tially open by-pass (as indicatedby t he dot ted box in Figure I ) is reduce d. Increasing b y-passflow pro gressivel y reduces the e ffective UA , wher eas maximum heat tran sfer is achieved w hen the by -pass is closed .Good engineerin g practice wo uld main tain a m inimum flowrate of 5 - 10% through the by -p ass .

Eq uation s (I ) throug h (4) are wr itten for t he case of se nsib le h eating a nd sens ible co o ling of process s trea ms .Specia l cases re sult for E qs. (3) a nd (4) w he n one s ide ofth e heat exc ha nger o perates i soth erm ally. If t he co ld-sideo pera te s wit h isot h ermal vaporiza tio n at T 3 , th en E q . (3)

Fig ur 1. Heat ex hanger with b y pa ss

B y-pass I T2

CKGROUND

Mos t student s, if a sked, w ill suggest adjusting steam pre ssure or hot o il flow rate to a hea t exchanger in o rder toma intain exi t temperatur e in the f ace of proc ess flow c hange .Slightly l ess o bvio us wo uld be the sugg estio n to a lter theco ndensate l evel i n th e heat-exchanger shell, th ereby covering/ex pos ing more heat tran sfer area for s team co ndensation . Th e imp ortant point is th at stea m an d h ot oi l are ut ilities , and changing their cons umption doe s no t disturb t heprocess.

Difficult y is immediately encou ntered when co nsideringheat exc hange between two proc es s s trea ms ; c hanging theflow ra te of o ne wi ll ce rtainly affect t he exi t te mperature ofthe other. Unfortunately, int e rfe ring with a pro cess streamflow rate imm ediately up set s t he plant ma ss ba lance, whic his und esirable. Th e d ifficulty is overcome b y us ing a b y-pass(see F igure I ) th at does not aff ect the to ta l flow rat e butchanges the p roportion ac tually pa ssing thro ugh the hea texc hanger and h en ce t he h eat tran sferred. The probl em prese nted h er e is co ncerne d with heat ex changer by-pa ss arrangement s to en sure sa tisfactor y operation , in the face ofag ing cata lyst, of a reac tor at both be gin ning o f -run (BO R)and end-of-run (EO R).

exc hanger f oulin g cycle . Nevertheless , to design a n operableplant, t hought mu st be give n at an earl y stage to co ndition sunder wh ich e ach item of e quipment is expec ted to opera teand t o the process-co ntrol sc heme to be use d . Unless theprojec t s upervisor is aler t, m any stud e nts wi ll sim pl y sizeeq uipment for t he co nditions im pl ied by t he desig n m ass a nd

heat balances w ithout co nsideri ng flexibility .T his and a s ubsequent ar ticle wi ll attempt to i llu strate h ow

se lected aspects of flexi bility can be introd uced throughint eresting exa mples . In p articular , the he at-exc hang e problem deve loped h ere m ay be used direc tly in a de sig n course ,w hile th e reacto r recycle loop featu red in t he seco nd art icleco uld f orm t he b asis for project work , or for a discu ssio nq uestion in r eactor des ign, or s imply to indicate to supervisors a n area wor th d iscussing and develop ing in f uture design project s.

Summer / 997 / 73


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5

redu ced to

T, - BT2 + (B 1 )T3 = 0

where B = exp(VA m PH)'If the hot-side o perates with isothermal co ndensation at

T then E q. (4) reduces to

(B - l)T, - BT T4 = O (6)

w here B = exp - VA mcpc)'

Note particularly that C , mu st ha ve dimen sions con sistentwi th th e o ther variab les in Eq. (8). T he un its used here a recho se n for con venie nce in the res t of the prob lem ra ther th anto ag ree with engi neer ing p ractice; hence , the C , va lue sca nnot b e co mpare d d irectly with , say, co ntro l va lvemanuf acturer's data.

PROBLEMSTATEMENT

For th e s pecial case of mcp H= TC C i.e .. co nstant t emperatur e drivin g forc e, dT , throu ghout the heat e xchanger),it is ea sy to show that

(7)

In th e fo llowing probl em , E qs . (5) a nd (7) are m ore imm ediat ely useful than th e ge neral Eqs. (3) and (4).

Fin ally , the hydraul ic i nteraction b etween the heat exchanger and co ntrol va lve in th e by-pass lin e is i mportant.Sele ction of co ntrol-valve ty pe and size is c rucia l t o e nsure itremains o perable ove r th e ra nge of by-pass flows ex pected .Di fficulty oc curs b ecause transferring flow fro m th e heatexc hanger t o the by-pass results in a reduced pr essure dropacross th e heat exc hanger. Th e co ntrol va lve ex periences th esa me pr essure drop and so mu st acc omodate th e largestflowrat e a t the lo west pressure drop . (To achie ve s teady

state b y-pass flowrates in excess of 30 -35 %, if th e minimumis 5% , requires an unreali stically large c ontrol-valve size,and it is better to u se tw o sy nchronized valves, the sec ondbeing in se r ies with the heat ex changer and compensatingfor the de creasing pre ssure drop. )

Luyb en' summarizes th e important properti es of controlva lves. V olume flowrat e, q(m 3 I sec), throu gh a control val vedepend s o n the pr essure drop , d P( bar), co ntrol-valve size,C fluid den sity, p (kg / m 3 ) , and va lve opening , x . Th e releva nt equation, i f we ass ume dP is small co mpared t o theoperating pr essure is

q = X )(d P /p )05

Figure 2 s hows th e ba sic tlowsheet fo r th e heat exc hangerssurrounding a catalytic re actor o perating at EaR conditi ons.Th e hot r eac to r e ffluent i s co oled first by boilin g wat er at200 C and then b y prehe ating th e reactor feed. Th e proc essoperate s e ntire ly in th e gas pha se, a nd you m ay assume aco nstant specific h eat c apacity of 2.5 kJ/k gK.

At BOR , the c atalyst is mu ch mor e act ive , requir ing areactor inl et temperature of only 185 C. The corres pondingprocess flo wrate and reactor effl ue nt t emperature a re 22.5kg/sec a nd 29 6.1 0C.

a ) C alculate th e VA re quireme nts for both heat exc hangersimplied b y EaR operation . In vestigate the feas ibility ofBaR operation u sing th e VA val ues ju st determined ifno flexibil ity i s added to the flows heet.

b ) Determ ine VA re quirements for BaR o peration if thetemperature to product recovery is to be maintained at

20 0 C

Steam

BFWor, fo r m ass flowra te

where f(x) de fines th e co ntrol-valve characteristic in termsof va lve opening. F or th is problem, two va lve characteristicsare imp ortant:

To Pro ductRecovery

125C

225C

Reactor Feed 5 kg s

Interchanger

(8)

f(x) = x) Lin ear

2) Equal percentag e f(x) = 0.' (typically, a =50 ) Figure 2. EOR flows h ee t.

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125 C. Wh ich o pe rating m ode se ts th e design for

I ) the int erchanger?

2) the bo iler? SOLUT ON

To investiga te the feasi bility of aR operation with t heabove UA va lue s, it is prob abl y best to s tart with t heboiler. Us ing Eq. (5) ,

B=exp (86 .65/(22 . 5 x 2.5 = 4.667

and the process exi t temperature

b ) T o determine the UA re qu i re ments f or aR , it is advisable t o redraw the flowsheet to reflect a R operatio n, asshown in Figure 3. Th e rea ctor feed mu st be he ated from100 C to 185 C, hence the c ros s-ove r tempera tur e o f thereactor effl uent from the boi ler to the intercha nge r is210 C to maint ain a te mperature of 125C to prod uctrecove ry.

= 296 .1 + (4 .667 - I) 200 = 220 .6 4 .667

We can now calc ulate th e two ex it temperat ures fro m t heint erchanger. Us ing Eq. 7 ,

VA mcp = 250/ 22 .5 x 2.5) = 4.444and th e temperature d ifference is

=2 5 x 2 .5 x 100 = 6250 k W

= 25 K

= 6250 /25 = 250 kW /K

= 25 x 2 .5 x 75 = 4687 .5 kW

= 54 .1 K

= 4687 .5/54 .1 = 86 .65 kW/ K

(220.6 - 100 / 4 444 + I) = 22 .15 K

Hence t he p reheated reac to r feed wi ll be a t

(220 .6 - 22. 15) = 198.4 5 C

and the s tream t o pro duct recovery is s lightly t oo co ld at

122 .l 5C (but m ay be accep table ). Th e pr eheated reacto r fee d , however , is ce rtainly far too ho t at 198 .45 C.Co nclu sion hea t exc hangers size d fo r Ea R operationwi ll no t function sa tisfactori ly at aR

a ) Int erchanger dut y

Te m peratur e diff erence

Int erchan ge r UA

Boiler d uty

Log mean tem p . d ifferenc e

Boi ler UA

Stearn

BFW

f T he boi ler has a hot-side pressure dro p of 0.4 bar ca lculate d for E a R flowra te with no by-passing. Wh y wo uldan e qu al perce ntage va lve with a =50 be more s uitablefo r thi s se rvice th an a linea r one ?

185C

c, = 1.0 , 1.75 , 2. 5In stead y-s tat e o peration , a co ntrol va lve should operatewi th an opening b etween 0.2 a nd 0 .8 . Yo u ma y ass ume aco nstant gas densi ty o f 20 kg / and neglect pipin gfriction losses .

d ) Add the by-passes to the fl owsheet and ind icate how yo uwould co nfig ure the t emperature con tro l loops. Howwo ul d th e plant be operated wi th yo ur co ntrol scheme?

e) Th e interchanger has a co ld-side p ressure drop of 0.6 barca lcula ted f or E a R flowrate a nd n o by-passing . Se lect asuita ble control va lve from t he fo llowing range of va lveswit h linear c harac teristics:

c) If the mi nimum flowra te th rough the by- pa ss is 5 ofthe main flowrate , determine t he des ign UA req uirements fo r both h eat exc hanger s. Wh at percen tage of themain fl owrate s hould pass throu gh the by-pass to permitthe al tern ative o perati ng mode ?

Figure 3 . BOR flows he e t

which is 23 .5 less than th e UA req uire d for Ea R;hence, E a R ope ration wi ll set the design o f th isitem of e quipment.

Boiler d ut y = 22 .5 x 2.5 x 86 . 1 = 4843. 1 kW

Log mean tem p . diff erence = 38 .05 K

Bo iler UA = 484 3.1/38 .05 = 127.28 kW / K

Interchanger

Rea ctor Feed22 .5 kg/s

210C

125C

To Pro ductRecov ery

Int erchanger d utyT emperat ure di ffere nce

Int erchanger UA

= 22 .5 x 2 .5 x 85 = 4 781 .3 kW=2 5 K

=4781.3/25 = 191.25 kW /K

SlIlIIlIIer / 997 / 75


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an introduction to process flexibility part 1. heat exchange

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