Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2009, Article I !0!"02, !0!"02, #! pages #! pages doi$#0%##&&'2009'!0!"02
Research Article Research Article
Mo de l i ngandCont l umn mn i s t i l l a t i o nCo r olofDi n e s s aPe t r o l e um Pr oc VuTr i e u Mi nh andAhma madMa Ma j diAbdulRa ni Mechanical Engineering Department, Universiti Teknologi PETRONAS , Bandar Seri skandar , !"#$% Tronoh, Perak Dar&l Rid'&an, Mala(sia Correspondence should be should be addressed to Vu (rieu Minh, )utrieuminh*+ahoo%com ecei)ed 2& -une 2009. e)ised / August 2009. Accepted 2/ eptember 2009 ecommended b+ Carlo Cattani
(his paper introduces a calculation procedure 1or modeling an and d con contro troll simu simulat lation ion o1 a )* structure% In this control, the condensate distillation column based on the energ+ balance ) re1lu3 rate ) and the boilup rate * are used as the inputs to control the outputs o1 the purit+ o1 the distillate o)erhead and the impurit+ o1 the bottom products% (he modeling simulation is important 1 or process or process d+namic anal+sis and the plant initial design% In this paper, the modeling and simulation are accomplished o)er three phases$ the basic nonlinear model o1 the plant, the 1ullorder linearised model, and the reducedorder linear model% (he reducedorder linear model is then used as the re1erence model 1or a modelre1erence adapti)e control MAC s+stem to )eri1+ the a pplicable abilit+ o1 a con)ention con)entional al adapti)e controller 1or a distillation column dealing with wi th th thee dis distu turba rbance nce an and d th thee modelplant mismatch as the in1 in1lu luenc ence e o1 the plant 1eed disturbances% Cop+right 4 2009 V% (% Minh and A% M% Abdul ani% (his is an open access article distributed under the Creati)e Commons Attribution 5icense, which permits unrestricted use, distribution, and reproduction in an+ medium, pro)ided the original wor6 is is properl+ properl+ cited%
o 1.I n t r duc t i o n istillation is the most popular and important separation method in the petroleum industries 1or puri1ication o1 1inal products% istill istillation ation columns columns are made up o1 se)eral components, each o1 which is used either to trans1er heat energ+ or to enhance mass trans1er% A t+pical distillation column contains a )ertical column where tra+s or plates are used to enhance the component separations, a reboiler to pro)ide heat 1or the necessar+ )apori7ation 1rom the bottom o1 the column, a condenser to cool and condense the )apor 1rom the top o1 the column, and a re1lu3 drum to hold the condensed )apor so that li4uid re1lu3 can be rec+cled bac6 1r om om the top o1 the column% Calculation o1 the distillation column in this paper is based based on a real petroleum real petroleum p pr r o 8ect to build a gas processing plant to raise the utilit+ )alue o1 condensate% (he nominal capacit+ o1 the plant is #/0 000 tons o1 raw condensate condensate per per +ear based on 2! operating hours per hours per da+ and
Mathematical Problems in Engineering 2
Mathematical Problems in Engineering2 Coolant 1low )al)e * #
9)erhead )apor
Table
1:
(he main str eams% eams%
e1lu3 1low )al)e * 2 N
istillate 1low )al)e * / e1lu3 drum
#
ecti1+ing
e1lu3 rate )
section
ate + :eed 1low r ate ) + , * +
Coolant 1low c
Condenser
)erhead product D product D,, - D Abo)e 1 eed eed tra+ :eed tra+
:eed concentrator c +
tripping section
;oilup rate * to the heat 1low * ! o opotional potional pr
Heater
Heat 1low )al)e * ! Heat 1low h
eboiler
;ottom 1low )al)e * &
istillation column
;ottom product product B B,, - B ;ottom li4uid
Figure 1: istillation 1lowsheet%
/&0 wor6ing da+s per +ear% (he 4ualit+ o1 the output products is the purit+ o1 the distillate, . D , higher than or e4ual to 9<= and the impurit+ o1 the bottoms, . B , less'e4ual than 2=% (he he basic basic 1eed stoc6 data and its actual compositions are based on # % Most o1 distillation control s+stems, either con)entional or ad)anced, assume that the control rol more column col umn oper operate atess at a constant pressure% Pressure 1luctuations ma6e the cont cult lt and reduce the per1ormanc per1ormance% e% (he )/* structure, whic difficu which h is call called ed energ+ balance structure, can be considered as the standard control structure 1or a dual composition control distillation% distilla tion% In this control structure the li4uid 1low rate ) and the )apor 1low rate * are the cont co ntro roll in inpu puts ts%% (he ob8e ob8ecti) cti)ee o1 the controller is to maintain the product outputs concentrations . B and . D despite the disturbance in the 1eed 1low + and the 1eed concentration c + :igure # % (he goals o1 this paper are two1old$ 1irst, to present to present a theoretical calculation p ocedur e pr r ocedur easibilit+ o1 a condensate column 1or simulation and anal+sis as an initial step o1 a pro8ect 1 easibilit+ stud+, and second, 1or the controller design$ a reducedorder linear model is deri)ed such that it best re1lects the d+namics o1 the distillation process and used as the re1erence model 1or a modelre1erence adapti)e control MAC s+stem to )eri1+ the abilit+ o1 a con)entional adapti)e controller 1or a distillation process dealing with the disturbance and the plantmodel mismatch as the in1luence o1 the 1eed disturbances% In this stud+, the s+stem identi1ication is not emplo+ed since e3periments r e4uiring e4uiring a real distillation column are still not implemented +et% o that a process process model based on e3perimentation on a real process cannot be done% A mathematical modeling based on ph+sical laws is per1ormed instead% :urther, the MAC controller model is not suitable 1or handling the process constraints on inputs and outputs as shown in 2 1or a coor dinator dinator
tream (emperatur e
◦
C
Pressur e atm
Condensate
5P>
aw gasoline
##<
!?
#!!
!%?
!%0
!%?
?"0
&<&
"2"
Volume 1low rate m/ 'h
22%"?
<%"<
2#%<<
Mass 1low rate 6g'h
#&!<0
&0?#
#0!0&
Plant capacit+ ton'+ear
#/0000
!/000
<"000
/
ensit+ 6g'm
model predicti predicti)e )e control MPC % In this this paper, the calculations and simulations ar e implemented b+ using MA(5A; )ersion "%0 so1tware pac6age%
2.Pr i mul a t i on oc e s sModelandS (he 1eed can be considered as a pseudobinar+ mi3ture o1 5igas isobutane, nbutane and propane and @aphtha @aphthass isopenta isopentane, ne, npentane, and higher components % (he column is designed with N #! tra+s% (he model model is simpli1ied b+ lumping some components together pseudocomponents and modeling o1 the column d+namics is based on these pseudocomponents onl+ / % :or the 1eed section, the operating pressure at the 1eed section is gi)en at !%? atm% ( he 1eed temperature 1or the preheater is the temperature at which the re4uired phase e4uilibrium is established% Consulting the e4uilibrium 1lash )apori7ation E:V cur)e at !%? atm, the re4uired 1eed temperature is selected at ##< C corresponding to the point o1 !2= o1 the )apor phase 1eed rate * + % :or the recti1+ing section, the t+pical pressure drop per tra+ is ?%"& 6Pa% (hus, the pressure at the top section is ! atm% Also consulting the Co3 chart, the top section temperatur e is determined at !? C% (hen, we can calculate the re1lu3 1low rate ) )ia the energ+ balance e4uation% :or the stripping section, the column base pressure is appro3imatel+ the pr essur essur e o1 the 1eed 1eed section section !%? atm because the pressure drop across this section is neglected% Consulting the E:V cur)e and the Co3 chart, the e4uilibrium temperature at this section !%? atm is determined at #!! C% (hen, we can calculate the reboiler dut+ or the the heat input B to increase the temperature o1 stripping section 1rom ##< C to #!! C% (able # summari7es the initial calculated data 1or the main streams o1 input 1eed 1low rate Condensate , output distillate o)erhead product$ 5P> and output bottom pr oduct aw gasoline % (he )apor boilup * generated b+ the heat input to the reboiler is calculated as ! $ * B − Bc B t B − t + 01 6mole'h , where B is the heat input 6-'h . B is the 1low rate o1 bottom product 6g'h . c B is the speci1ic heat capacit+ 6- 0 6g C . t + is the inlet temperatur e C . t B is the outlet temperature C . 1 is the latent heat or the heat o1 )apori7ation 6-'6g % (he latent heat at an+ temperature is described in terms o1 the latent heat at the normal boiling point & 1 2 1 B T0T B , where ees where 1 1 is the latent heat at the absolute temperature T in degr ees an6ine . 1 B is the latent heat at the absolute normal boiling normal boiling point T B in degrees an6ine . and 2 is the correction 1actor obtained 1rom the empirical chart% Ma8or design parameters to determine the li4uid holdup on tra+, column base and re1lu3 drum are calculated mainl+ based on ? < % ◦
◦
◦
◦
◦
◦
·
◦
◦
◦
◦
Velocit+ o1 )apor phase is arising in the column 3n 4 5 ) − 56 056 m 0 s , li4uid phase. wher e 5 ) 6g'm/ is the densit+ o1 li4uid phase. 56 6g'm / is the densit+ o1 )apor )apor phase. phase. 4 is the correction 1actor depending 1low rates o1 twophase 1lows% (he actual )elocit+ 3 is normall+ selected at 3 07<0 − 07<& 3n 1or 1or para paraffinic )ap or % (he diameter o1 the column is calculated on the 1ormula$ Dk !* m 0 /?0083 m , where * m 6mole'h is the mean 1low o1 )apor in the column% (he holdup in the column base is M 8 9 NB D 2k 0 ! 5 B 0 M: B 6mole , wher e column base B 9 NB m is the normal li4uid le)el in the column base. M: B is the molar weight o1 the bottom product product 6g'6mole . 5 B is the densit+ o1 the bottom product 6g'm / % imilarl+, the holdup on each tra+ is M 079&8 hT Dk 2 0 ! 5T 0 M: T 6mole , wher e hT is the a)erage depth o1 clear li4uid on a tra+ m . M: T is the molar weight o1 the li4uid holdup on a tra+ 6g'6mole . 5T is the mean densit+ o1 the li4uid holdup on a tra+ 6g'm / % And the holdup in the re1lu3 drum & ) ; * drum M M ; 0 ?0 6mole , where ) ; is the re1lu3 1low D distillate rate 6mole'h . * 1low rate 6mole'h % ; is the (he rate o1 accumulation o1 material in a s+stem is e4ual to the amount entered and generated, less the amount lea)ing and consumed within the s+stem% (he model is simpli1ied under assumptions in 9 % i Constant relati)e )olatilit+ throughout the column and the )aporli4uid e4uilib rium relation can be e3pressed b+
( n
#
<.n # , < − .n
2%#
where .n is the li4uid concentration on nth stage. ( n is the )apor concentration on where . +% )olatilit+ nth stage. < is the relati)e )olatilit ii (he o)erhead )apor is totall+ condensed% iii (he li4uid holdups on each tra+, the condenser, and the reboiler are constant and per1ectl+ mi3ed% throughoutt the s+stem i) (he holdup o1 )apor is negligible throughou ecti1+ing ) (he molar 1low rates o1 the )apor and li4uid through the stripping and r ecti1+ing sections are constant%
Bnder these assumptions, the d+namic model can be e3pressed b+ the 1ollowing e4uations$ i condenser n N 2 $ M D .C n
ii tra+ n n ;
2 to N to N M.C n 2%/
*
− ). n − D. n ,
2%2
# $ *
* + (n−#
iii tra+ abo)e abo)e the 1eed 1low n ; M .C n 2%!
* + (n−#
* (n−#
− (n
− (n
) .n
# − .n
,
# $
) .n
# − .n
* + ( +
− (n
,
Mathematical Problems in Engineering & Table
tage .n
(n tage .n (n
2:
Mathematical Problems in Engineering &
(he stead+ state )alues o1 concentrations concentrations . .n and (n on each tra+%
;ottom
(ra+ #
(ra+ 2
(ra+ /
(ra+ !
(ra+ &
(ra+ ?
(ra+ "
0.0375
0%0920
0%#&&9
0%2#20
0%2!?#
0%2?2<
0%2"0#
0%2"/#
0%#<#2
0%/?&/
0%
0%?0!!
0%?!9?
0%??9!
0%?""?
0%?<09
(ra+ <
(ra+ 9
(ra+ #0
(ra+ ##
(ra+ #2
(ra+ #/
(ra+ #!
istillate
0%2<##
0%/#""
0%/9?/
0%&//?
0%"0!#
0%
0%9/?9
0%?<9&
0%"2&?
0%"<<&
0%
0%9/##
0%9?<"
0%9<
Table
3:
0.9654
0%99/"
Product 4ualit+ depending on the change o1 the 1eed rates% Purit+ o1 the distillate Impurit+ o1 the bottoms oduct . D = oduct . B = pr p r oduct pr p r oduct
@ormal 1eed rate
9?%&!
/%"&
educed 1eed rate #0=
90%2/
0%??
Increased 1eed rate #0=
9"%/0
##%??
i) tra+ below the 1eed 1low n ; $ * (n−#
M .C n 2%&
) tra+ n n
2 to ; to ;
−
) .n
# − .n
) + . +
− .n
,
# $
M .C n 2%?
)i reboiler n
− (n
* (n−#
− (n
) ) + .n
# − .n
,
# $ M B .C #
) ) + .2
−
* (#
− B. # 7
2%"
Although the model is simpli1ied, the representation o1 the distillation s+stem is still nonlinear due to the )aporli4uid e4uilibrium relationship between (n and .n in 2%# % (he distillation process simulation is done using Matlab imulin6 as shown in :igure 2% 2% (he d+namic model is represented b+ a set o1 #? no nonl nliine nea ar di diff erential e4uations$ .# . B is the li4uid concentration in bottom. .2 is the li4uid concentration in the #st tra+, ./ is the li4uid concentration in the 2nd tra+. 7 7 7 . .#& is the li4uid concentration in the #!th tra+. and .#? . D is the li4uid concentration in the distillate% I1 there are no disturbance in the operating conditions as shown in :igure /, /, the s+stem is to reach the stead+ state such that the purit+ o1 the distillat distillate e product . D e4uals 0%9?&! and the impurit+ o1 the bottoms product . B e4uals 0%0/"&% (able 2 indicates the stead+state )alues o1 concentration o1 .n and ( n on each tra+% ince the 1eed stream depends on the upstream processes, the changes o1 the 1 eed eed stream can be considered as disturbances including the changing in 1eed 1low rates and 1 eed eed compositions% imulations with these disturbances indicate that the 4ualit+ o1 the output products gets worse i1 the disturbances e3ceed some certain ranges as shown in (able /% /% (he designed s+stem does not achie)e the operational ob8ecti)e o1 the product 4ualit+ . D ≥ 079< and . B ≤ 0702 and the product 4ualit+ 4 ualit+ will get worse dealing with disturbances%
Out 1
I n 1
Condens erandrefluxdrum I n1 I n2
Out 1 Out 2
4 Tray1 I n1 I n2
5P> purit+
Out 1 Out 2
0
3 Tray1
Module o1 recti1+ing section
I n1 I n2
Out 1 Out 2
9utput #
2 Tray1 I n1 I n2
Out 1 Out 2
1 Tray1
I n1 I n2
Out 1 Out 2
0 Tray1 I n1 I n2
Out 1 Out 2
Tray9
##77//!/ ##
I n1 I n2 I n3
(+ ∗ * +
Out 1 Out 2
Tray8
:eed rate
I@ !7?90/
.+ ∗ )+
I n1
Out 1
I n2
Out 2 Tray7
I n3
Out 1 Out 2 I n1 6 T r a y I n2 Out 1 Out 2 I n1 I n2 Tray5 Out 1 Out 2 I n1 I n2 Tray4 Out 1 I n1
Module o1 stripping section
I n2 Tray3Out 2
>asoline impurit+ 0
I n1 Out 1 I n2 Tray2Out 2
9utput 2 I n1Tray1Out 1 I n2 Out 2
I n 1
Out 1 Out 2
Col umn mnbaseandreboi l er
Figure 2: Model simulation with Matlab imulin6%
Hence we will use an adapti)e controllerDMACDto ta6e the s+stem 1rom these stead+ gets% state outputs o1 . D 079?&! and . B 070/"& to the desired output tar gets%
o c e s s 3.Li ne a r i z at i onoft heDi s t i l l a t i onPr In order to obtain a linear control model 1or this nonlinear s+stem, we assume that the )ariables de)iate onl+ slightl+ 1rom some operating conditions #0 % (hen (hen the nonlinear e4uation in 2%# can be e3panded into a (a+lor s series% I1 the )ariation )ariation . .n − . n is small,
. t c u d o r p e t a l 079 l i t s i d 07< e h t 1 o
. D
07"
+ t i 07? r u P 07&
07! 07/ 072
. B
07# 00
&0
#00
#&0
200
2&0
/00
/&0
(ime
Figure 3: (he stead+state )alues o1 concentrations concentrations . .n on each tra+%
we can neglect the higherorder terms in .n − .n % (he lineari7ation o1 the distillation column leads to a #?thorder linear model in the state space 1orm$ ' C t
A' t ,
B& t
/%#
4' t ,
( t
wher e .# t
' t ' t
⎡⎢ ⎢ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦
− . # tead+ tate
⎤ ⎥
⎥ ⎡
,
% %
⎤ ⎣ ⎦
& t * t
.#? t
.#? tead+
−
−
* tead+
tate
tate
.# t ( t
) t − )tead+ tate , /%2
.#? t
− .# tead+ tate
. #? tead+
−
tate
7
(he matri3 A elements n 1or each stage ar e i r eboiler$ eboiler$
= # * B 1or n
# ,
a# , ,##
−
M B
,
a# ,2
) M B
5: ,
/%/
ii stripping section, tra+ #
?$
÷
= n− # * 1or n
2
÷
M
an,n −#
" ,
iii 1eeding section, tra+ "
= n * ,
÷
an7n
−
M
a< ,"
< ,
a9 ,<
9 ,
an,n
,
M
#
) ) +
= < * ,
a<7<
−
M
,
/%!
,
M
a979
) ,
M
= 9 * )
= < * 1or n
) ) +
<$
= " * 1or n
) ) +
−
M
a< , ,99
a9 ,#0
,
/%&
M ,
) M ,
i) recti1+ing section, tra+ 9
÷
= n 1or n
# −
an,n −#
#0 ÷ #& ,
#!$ *
= *
* +
M
,
an7n
n
−
)
* +
,
M
/%?
) an,n
#
M
) condenser$
= #& #& * 1or n
a#? ,#&
#? ,
) D
* +
,
a#? , ,#? #?
−
M D
M D
,
/%"
where = where = n is the lineari7ed Vapor5i4uid E4uilibria V5E constant$ = n
d( n d. n
< 2
< − # . n
#
7
&7?<
!7?< .n
#
/%<
2
(he matri3 B elements ar e .2
1or n
# ,
># ,#
. n 1or n
2
÷
>n,#
#& ,
1or n
#? ,
M B
#? , ,# #
),
# − . n
M
>
(#
−
b# , ,22 ),
.#? ), M D
−
>n,2
>#? , ,22
*, M B (n − ( n−# −
( #& M D
M
*7
*,
/%9
(he output matri3 4 is
4
# 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 #
7
/%#0
(he 1ullorder linear model which represents a two inputstwo outputs plant outputs plant in e4uation in /%/ can be e3pressed as a reduced order linear model as in ##, ##, #2 $ .
#
6 0
? c s
#
. B
/%##
, ) *
−# −4A B where 6 0 is the stead+state gain$ 6 0 B,, ? c is the time constant$ M M D # − . D M B # − . B . B . D ? c , s ln S s s
/%#2
where M where M 6mole is the total holdup o1 li4uid inside the column. M D 6mole is the li4uid holdup in the condenser. M B 6mole is the li4uid holdup in the reboiler. s is the Fimpurit+ sumG. S is the separation 1actor % As the result o1 calculation, the reducedorder linear model o1 the plant is a 1irstor der der s+stem with a time constant o1 ? c #79&<< h $ .
. B
#
#
#79&<< s
0700!2
−0700?2
−0700&2
0700"2
)
7
/%#/
*
E4uation /%#/ is e4ui)alent to the 1ollowing linear model in state s pace$ − 07�&
' C r t
0 −07�&
0 07002#
' r r t
# 0 0 #
& t t , , /%#!
−0700/#
(r t
' r t t , , −07002?
her e ' r r
' r # r # ' r 2 r 2
are state )ariable, &
0700/"
are two manipulated inputs, and (r
d)
d. B
ar e
d. D
d*
two outputs o1 5P> and and gasoline p pr r oduct% Sta>ilit( test % (he s+stem is as+mptoticall+ stable since all eigen)alues o1 the state matri3 ar e in the le1t hal1 o1 the comple3 plane −07�& , −07�& %
4.MRAC Bui dS i mul a t i on l di ngandS Adapti)e control s+stem is the abilit+ o1 a controller which can ad8ust its parameters its parameters in such a wa+ as to compensate 1or the )ariations in the characteristics o1 the process% Adapti)e contr ol ol
e1erence model
B
@ C m t
m
e1erence state @ m t
(m t
S 0 S
e1erence output
Am
5MC
M
&c t
−
& t
@ C t
B
Contr ol signal
e1erence signal
−
isturbances
Plant
Plant state @ t 0 S S
e t tate err or or
( t
4 Controlled output
A
) ) t
M t
Ad8ustment mechanism
Figure 4: MAC bloc6 diagram%
is widel+ applied in petroleum industries because o1 the two main reasons$ 1irstl+, most o1 processes proces ses are nonlinear and the lineari7ed models are used to design the controllers, so that secondl+, most o1 the the controller must change and adapt to the modelplant mismatch. secondl+, processes proces ses are nonstationar+ or their characteristics are changed with time, and this leads again to adapt the changing control parameters parameters%% ence (he general 1orm o1 an MAC is based on an innerloop 5inear Model e1er ence Controller 5MC and an outer adapti)e loop shown in :igure !% !% In order to eliminate err ors ors between betwee n the model and the plant and the controller is as+mptoticall+ stable, MAC will calculate online the ad8ustment parameters in gains ) and M b+ ) t and M t as detected state error e t when changing A, B in the process plant% imulation program is constructed using Maltab imulin6 with the 1ollowing data%
# Process Plant ' C A' B& noise , (
wher e A
<# 0
0 <2
, B
C # 0
, 4 0 C 2
dependent on the process d+namics%
!%#
4' ,
0700! −07 00##
, and <# , <2 , C # , C 2 are changing and
−0700"
0700#"
Mathematical Problems in Engineering ##
Mathematical Problems in Engineering ##
2 Re;erence Model ' C m Am ' m Bm &c ,
(m
−
072?#?
where A where Am
, B
0
m
−072?#?
0
# 0
4 m ' m ,
, 4
m
0 #
!%2
0700!
−0700"
−0700##
0700#"
/ State +eed>ack
& M& c
where ) where )
# 0
/ 0
and M
0 2
0 !
!%/
− )',
%
! 4losed )oop
' C
' Bc &c A − B) ' BM &c Ac '
!%!
& Error E&ation E&ation ors, is a )ector )ector o1 state err ors,
e#
e ' − ' m
e2
eC ' C − ' C m A' B& − Am ' m − Bm &c Am e
Ac
− Am
'
Bc
−
!%&
Bm &c Am e
wher e I
− C # ' #
0
−
0
− C 2 ' 2
0
,
C # &c#
0
C 2 &c2
0
%
? )(ap&nov +&nction # 2 e T P e 2
* e,
−
0
T −
0
,
!%?
matri3% where 2 is an adapti)e gain and P is a chosen positi)e matri3%
" Derivative 4alc&lation o; o; )(ap&nov +&nction d* dt
where
T
− Am P − P Am
%
−
2 eT e 2
−
0 T
d P e dt 2
T
,
!%"
MAC
etpoint
Pr ocess ocess
PI
9utput
−
@oise
Figure 5: Adapti)e controller with MAC and PI%
0
T
:or the stabilit+ o1 the s+stem, d*0dt 0, we can assign the second item − 0 or d 0 t 2 T P e t −2 T P e% (hen we alwa+s ha)e d*0dt − 2 0 2 eT e % 0 d t 0 d t d 0 # 0
T
I1 we select a positi)e matri3 matri3 P P F 0, 1or instance, P , then we ha)e − A m P − PmA 0 2 07&2/2 0 % ince matri3 is ob)iousl+ positi)e de1inite, then we alwa+s ha)e d*0 t d t d 0
−
#70!?&
plantmodel el mismatches% s +stem is stable with an+ plantmod 2 0 2 eT e 0 and the s+stem
< Parameters Parameters AdG&stment AdG&stment
2 2 C ' − d ⎢
⎡ − C # ' # ⎤ ⎥ ⎢
−2 ⎢ ⎥ ⎢ ⎢ Cc# ⎣
dt e
0
&
#
⎡
0
⎡
d # 0
⎤
d t t
0
0
#
⎥ ⎢ P ⎥ ⎥ ⎥ ⎢ ⎦ ⎦ ⎣ e
C 2 &2c
⎢ ⎥2
⎢
⎢ ⎢⎥ ⎢ 0 d t d t ⎣
⎥ ⎢ ⎢
d 0 ⎥ t d t ⎢ 2
/
t d ! 0d t
⎤
2 C # ' # e#
2 2 2 22 C ' e⎥
−2 C
⎥
!%<⎥
⎥
7
& e⎥
# c# #
−22 C 2 &c2
⎦
e2
Anal(sis is 9 Sim&lation Res<s and Anal(s e assume that the reducedorder linear model in /%#! can also maintain the similar stead+ state outputs as the basic nonlinear model% @ow we use this model as an MAC to ta6e the process plant 1rom these stead+state outputs . D 079?&! and . B 070/"& to the desir ed ed targets 079< ≤ . D ≤ # and 0 ≤ . B ≤ 0702 amid the disturbances and the plantmodel mismatches as the in1luence o1 the 1eed stoc6 disturbances% (he design o1 a new adapti)e controller is shown in :igure & where we install an MAC and a closedloop PI Proportional, Integral, eri)ati)e controller to eliminate the errors between the re1erence setpoints and the outputs% e run this controller s+stem with diff erent plantmodel mismatches, 1or instance, a 07&0
−
0
#7& 0
plant with A , B and an adapti)e gain 2 2&% (he operating setpoints 0 −07"& 0 27& 1or the real outputs are . DR 0799 and . BR 070#% (hen, the re1erence setpoints 1or the PI controller are r D 0702?# and r B −0702"& since the real stead+stat stead+state e outputs are . D 079?&! and . B 070/"&% imulation in :igure ? shows that the controlled outputs . outputs . D and . B ar e alwa+s stable and trac6ing to the model outputs and the re1erence setpoints the dotted lines, r D and r B amid the disturbances and the plantm plantmodel odel mismatches% mismatches%
. t c u d o r p e t a l l i t s i d e h t 1 o
+ t i r u P
070/
r
.
0702
070#
0 −070# −0702
r B −070/
. B
20
!0
?0
<0
#00
#20
#!0
(ime
Figure 6: Correlation o1 o1 plant plant outputs, model outputs, outputs, and re1erence setpoints%
5.Co nc l us i o n e ha)e introduced a procedure to build up a mathematical model and simulation 1or a condensate distillation column based on the energ+ balance )/* structure% (he mathematical modeling simulation is accomplished o)er three phases$ the basic nonlinear model, the 1ullorder lineari7ed model and the reducedorder linear model% esults 1rom the simulations and anal+sis are help1ul 1or initial steps o1 a petroleum petroleum pro8ect pro8ect 1easibilit+ stud+ and design% (he reducedorder linear model is used as the re1erence model 1or an MAC MAC oller % (he controller o1 MAC and PI theoreticall+ allows the plant outputs trac6ing contr oller the re1erence setpoints to achie)e the desired product 4ualit+ amid the disturbances and the modelplant mismatches as the in1luence o1 the 1eed stoc6 disturbances% In this paper, the calculation o1 the mathematical model building and the r educed educed order linear adapti)e controller is onl+ based on the ph+sical laws 1rom the pr ocess% ocess% identi1ications including (he real s+stem the e3perimental production 1actors, speci1ic designed structures, parameters estimation, and the s+stem )alidation are not mentioned here% :urther, the MAC controller is not suitable 1or the online handling o1 the pr ocess ocess constraints%
Re f e r e nc e s # PetroVietn Petro Vietnam am >as Compan+, FCondensate processing plant pro8ectDprocess description,G (ech% ep% <20/?02;M0#, PetroVietnam, ashington, C, BA, #999% 2 E% Marie, % trand, and % 6ogestad, FCoordinator MPC 1or ma3imi7ing plant thr oughput,G 4omp&ters H 4hemical Engineering , )ol% /2, no% #2, pp% #9&20!, 200<% / H% Jehlen and M% at7sch, FComple3 FComple3 multicomponent distillation calculations b+ continuous thermod+namics,G 4hemical Engineering Engineering Science Science,, )ol% )ol% ! 2, no% 2, pp% 22#2/2, #9<"% ! % >% E% :ran6s, :ran6s, Modeling Modeling and Sim&lation in 4hemical Engineering , ile+Intersc ile+Interscience, ience, @ew Kor6, @K, BA, #9"2% Auc6land, @ew Lealand, #9<2% & % 5% 5% @elson, @elson, Petrole&m Petrole&m Re;iner( Engineering , Mc>rawHill, Auc6land, ? M% V% -oshi, Process E&ipment Design Design,, Macmillan Compan+ o1 India, @ew el elhi, hi, India, #9"9%
" % 5% McCabe and -% C% mith, Unit Operations o; 4hemical 4hemical Engineering , Mc>rawHill, @ew Kor6, @K, BA, #9"?% < P% uithier, uithier, )e )e Petrole Ra ffinage et 6enie 4himi&e, 4himi&e , Paris Publications de lInstitut :rancaise du Petr ole, ole, Paris, :rance, #9"2% 9 >% 0tephanopoulos, 4hemical Process 4ontrol , PrenticeHall, Englewood Cliff s, @-, BA, #9
