Hella Tokos and Zorka Novak Pintarič COMPUTER AIDED PROCESS ENGINEERING FOR INTEGRATION OF INDUSTRIAL PROCESSES
Jan 17, 2016
Hella Tokos and Zorka Novak Pintarič
COMPUTER AIDED PROCESS ENGINEERING FOR INTEGRATION OF INDUSTRIAL PROCESSES
Outline
Introduction
Water network integration Basic formulation Modification of basic mathematical model Results of water network integration
Heat integration retrofit Basic formulation Modification of basic mathematical model Results of heat integration retrofit
Selection of optimal polygeneration system Mathematical model for polygeneration Results of polygeneration
Introduction In real industrial applications, mathematical models often need
several modifications in order to suit the specific industrial circumstances and to give useful results for the company.
Data collectionMeasurements
Determination of water balanceDetermination of heat balance
Consulting whit industry
INDUSTRIAL PROBLEM
Modeling OptimizationConsulting whit
industry
Incorrect balance
Correct balance
Additional constraints
PROBLEM SOLUTION
WATER NETWORK INTEGRATION
Basic formulation (Kim and Smith, 2004)
Fig 1. Superstructure for water re-use between batch processes.
Basic formulation (Kim and Smith, 2004)
0LOSSGAINOUTW n
nn
nn
nw n
n,w mmmm
Overall water mass balance:
(2) 0LOSSLOSS
GAINGAINMLOUTOPOUTPPWW
n,cn
n,cnn,cn,cnnc
nc,cn,ncw
w,cn,w
Cm
CmmCmCmCm
Mass load balance in each operation:
(1)
0LOSSGAINOUTPP,
PP,
W, nnn
ncncn
ncnnc
wnw mmmmmm
Water mass balance in each operation:
(3)
Basic formulation (Kim and Smith, 2004)
0MAXIN,OPOUTPPWW
n,cn
ncnc,cn,nc
ww,cn,w CmCmCm
Feasibility constraints on the inlet and outlet concentration:
0MAXOUT,,
OUT, ncnc CC
Upper and lower bounds for the water flow:
0W WUB,W n,wn,wn,w Ymm 0W WLB,W n,wn,wn,w Ymm
0PPPP UB,PP nc,nnc,nnc,n Ymm 0PPPP LB,PP nc,nnc,nnc,n Ymm
0OUTOUT UB,OUT nnn Ymm 0OUTOUT LB,OUT nnn Ymm
(4)
(5)
(6)-(7)
(8)-(9)
(10)-(11)
Basic formulation (Kim and Smith, 2004)
Logic constraint for existence or non-existence of a storage tank:
ESSTPP 0 nncnnc,n tt:nYY (12)
ESPPSTnnc
ncnc,nn tt:nmm
Storage tank capacity:
(13)
The objective function, is the overall cost of the water network that involves: the freshwater cost, annual investment cost for the storage tank and annual investment cost for piping.
Modification of the original model
The original model was modified over three main steps:
Water re-use between batch and (semi)continuous processes with moderate contaminant concentration.
Installation of intermediate storage tanks for collection of unused continuous wastewater streams that can be used over the subsequent time intervals.
Installation of a local (on-site) wastewater treatment unit operating in batch or in continuous mode.
Mathematical model extended with continuous streams
Fig 2. Superstructure for water re-use between batch and continuous processes.
Mathematical model extended with continuous streams
Limiting water mass of the (semi)continuous stream ww:
wwwwwwjjwwjww Jjjjttqm ,,1, 00SE,m
C,
(15)
Outlet water mass from the (semi)continuous stream ww:
SS00WCOUTC, 1 jnwwwwwwn
n,wwj,wwj,ww tt:n,J,,j,jjmmm
(14)
Mathematical model with storage tanks for continuous streams
Fig 3. Superstructure for direct and indirect water re-use between batch and continuous processes.
Mathematical model with storage tanks for continuous streams
ES00WOUT C,FOUC, 1wwJnwwwwww
nn,ww
jj,ww
Tww tt:n,J,,j,jjmmm
ESSTC,W 0wwJnwwn,ww tt:nYY
ESWST C,wwJn
nn,wwww tt:nmm
Mass of wastewater from the (semi)continuous operation ww:
(16)
Logic constraint for existence or non-existence of a storage tank for (semi)continuous operation ww:
(17)
Storage tank capacity for wastewater from (semi)continuous operation ww:
(18)
Mathematical model with local treatment units
Fig 4. Superstructure for water re-use and regeneration re-use in batch/semi-continuous processes.
Mathematical model with local treatment units
1. Batch local treatment units
a) Mass balance constraints
The mass balance for each operation:
Additional equations for upper and lower bounds of water mass purifiedin local treatment units are:
W PP TR PP TR OUT GAIN LOSS, , , , , , , 0w n nc n nc n tr n nc n nc tr n n n
w nc nc tr nc nc tr
m m m m m m m m
0TR,,
TR UB,,,
TR,, trnnctrnnctrnnc Ymm 0TR
,,TR LB,,,
TR,, trnnctrnnctrnnc Ymm
(19)
(21)-(22)
0MAXIN,OPTRTROUTPPWW
n,cn
nc trtr,n,ctr,n,nc
ncnc,cn,nc
ww,cn,w CmCmCmCm
Feasibility constraints on the inlet and outlet concentration:
(20)
nctrnnc
ncncctrnnc
trctrncm
Cm
rCTR
,,
OUT,
TR,,
TR,
TR,, 1
Mathematical model with local treatment units
The capacity of the local treatment unit:SSTR
,,TRC : jnc
nc ntrnnctr ttjnmm (23)
Outlet concentration from local treatment unit:
(24)
Mathematical model with local treatment unitsb) Time scheduling of batch treatment units
Fig 5. Treatment time of batch local treatment unit.
Mathematical model with local treatment units
The starting time of purification of wastewater from unit nc in local treatment unit tr :
tEnc t
S, TRnc, tr
For processes operating within the same time interval j :
The ending time of the purification is:
tE, TR
nc, tr tS
n
ΔtTR
tr
TRLBETRS, 1 tr,n,ncnctr,nc YMttt
TRUBETRS, 1 tr,n,ncnctr,nc YMttt
(25)
(26)
N,...,nc,tt,nctt ncnctr,nctr,nc 2S1
STR S,1
TR S,
TRTR S,TR E,trtr,nctr,nc ttt
(27)
(28)
The purification of wastewater from process nc in treatment unit tr has to be completed before process n starts:
Mathematical model with local treatment units
The waiting times before and after treatment are:
tEnc t
S, TRnc, tr t
E, TRnc, tr t
Sn
ΔtTR
tr
tB, TR
nc,n, tr tA, TR
nc,n, tr TRLBTR E,S 1 tr,n,nctr,ncn YMttt
TR,,
UBTR E,,
S 1 trnnctrncn YMttt
(29)
(30)
TRTR A,TRTR B,ES 1 tr,n,nctr,n,nctrtr,n,ncncn YMttttt
TRTR A,TRTR B,ES 1 tr,n,nctr,n,nctrtr,n,ncncn YMttttt
(31)
(32)
The waiting times of unselected treatment connections are forced to zeroby the following constraints:
TRTR A,tr,n,nctr,n,nc YMt
TRTR B,tr,n,nctr,n,nc YMt
(33)
(34)
Mathematical model with local treatment units
c) Storage tank after treatment unit
Constraints used to identify those processes nc that need the installation of a storage tank for purified water after treatment are:
The required storage tank capacity after purification is:
tE
nc tS, TR
nc, tr tE, TR
nc, tr tS
n
ΔtTR
tr
OUT TR, ST,UBTR A,nc,trtr,n,nc Ytt
OUT TR, ST,LBTR A,nc,trtr,n,nc Ytt
(35)
(36)
SSOUT TR, ST,,
TR,,
OUT TR, ST, : jncnc n
nctrtrnnctr ttjnYmm (37)
The required storage tank capacity before thetreatment unit is:
Mathematical model with local treatment units
The scheduling of the continuous treatment unit only differs from that of the batchtreatment unit, when defining the treatment ending time:
2. Continuous local treatment units
tE
nc tS, TRnc, tr t
E, TR
nc, tr tS
n
ΔtTR
tr
Constraints used to identify those processes nc that need the installation of a storage tank for purified water before treatment are:
d) Storage tank before treatment unit
IN TR, ST,UBTR B,nc,trtr,n,nc Ytt
IN TR, ST,LBTR B,nc,trtr,n,nc Ytt
(38)
(39)
SSIN TR, ST,,
TR,,
IN TR, ST, : jncnc n
nctrtrnnctr ttjnYmm (40)
TR S,TR E,tr,nctr,nc tt (41)
Objective function
The objective function, FObj, is the overall cost of the water network that involves the freshwater cost, annual investment costs for the storage tank, annual investment cost for piping, annual investment costs for the local treatment unit and wastewater treatment costs.
54321Objmin fffffF (42)
Objective function
ALLOHY
WCW
1t
Pmmf
ww jj,ww
fw nn,fw
Freshwater cost:
(43)
Annual investment costs of storage tank installation:
ANOUT TR,IN TR,C
2 FCTCTCTCTftr
trtr
trww
wwn
n
(44)
Wastewater treatment cost:
ALLOHYLC E,
E
OUT,
TR,,
ALLOHYLB E,
E
OUT,
TR,,
ALLOHYE
E
W,
FOUT C,
E
OUT,
OUT
4
001.0
001.0
001.0001.0
tP
m
Cm
tP
m
Cm
tP
m
Cm
m
Cmf
c n nc continuoustr c
nctrncn
c n nc batchtr c
nctrncn
n c ww c c
wwcj
c
ncn
(45)
AN
OUTOUT
OUT
TR,,TR
,,
TR,,TR
,,
TR,,TRTR
,,
TR,,TR
,,
PP,PP
.
PP,PP
,
W,W
.
W,W
,
3
6003
6003
6003
6003
6003
F
Yqt
mpD
Yqt
mpD
Yqt
mpD
Yqt
mpD
Yqt
mpD
f
nnn
n
n
OUTn
trncnntrncn
trncn
n nc continuoustrtrncn
trncntrtrncn
trncn
n nc batchtrtrncn
ncnncncn
ncn
n ncncn
nwnnw
nw
w nnw
Annual investment cost for piping:
(46)
Objective function
Annual investment costs for the local treatment unit:
AN
TRTR
5
TRTR
FtJ
mKmKf
continuoustr
n
n
trtr
batchtr
ntrtr
trtr
(47)
Modifications of the original model
Multi-level design strategy
Direct water re-use betweencontinuous and batch processes
Indirect water re-use betweencontinuous and batch processes
On-site wastewater treatment unit
Identification of intra-daily connections
Identification of intra- and inter-daily connections
FINAL DESIGN
Separated integration of packaging area
Separated integration of production area
Solution strategy
Results of industrial case study
• Freshwater consumption is reduced by 21% ;
• Total investment: 167,460 EUR; Net present value : 892,811 EUR; Payback period: 1.2 a
Fig 6. Optimal water network in the production area.
Results of industrial case study
• Freshwater consumption reduced by 21,2% ;
•Total investment is 23,647 EUR; Net present value: 675, 099 EUR; Payback period: 0,25 a
Fig 7. Optimal water network in the packaging area.
Results of industrial case study
Fig 10. Water network in production and packaging area (Monday to Wednesday).
Freshwater consumption reduced by 25%
Results of industrial case study
Freshwater consumption reduced by 22%
Fig 11. Water network in production and packaging area (Thursday).
Results of industrial case study
Freshwater consumption reduced by 31 %
Fig 12. Water network in production and packaging area (Friday).
Results of industrial case study
• Freshwater consumption reduced by 26,5%
•Total investment is 828,528EUR; Net present value: 1,486,919 EUR; Payback period: 2.7 a
Packa
gin
g a
rea
Pro
ductio
n a
rea
Fig 13. Final water network in a brewery.
HEAT INTEGRATION RETROFIT
Basic formulation (Lee and Reklaitis, 1995)
LP
MILP
tP j
tI i, j
tE i, jtF i, j
tCYCLE, MIN
CP j
Tsj
Tdj
Initial operating schedule
Utility savings
Final operating schedule
Fig 14. Schematic diagram of the mathematical model.
Basic formulation (Lee and Reklaitis, 1995)
Finishing time of batch i in unit j:
(1)
Exit time of batch i from unit j:
(2)
Input time of the next batch in unit j:
(3)-(4)j,ij,itt
1 IE j,jrij,i
tt
IEOut-of-phase stage:In-phase stage:
.,,1;,,1,,
MjNitttjjiji
PIF
.,,1;,,1,,
MjNittjiji
EF
Basic formulation (Lee and Reklaitis, 1995)
Starting time of the next unit, j + 1:
Cycle time for each unit j:
.,1,,1;,,11,, IPIE JjMjNitt
jiji
.;1,,1;,,1,, IPII JjqNitt jjiji
.;,,1,1,
OPIE
CYCLE JjMjN
ttt jjN
j
.,1,1
OP
IE
CYCLE JjN
ttt
jjjrN
j
(5)
(6)
(7)
(8)
The cycle time of the production, has to be greater than or equal to the cycle time required for each unit:
.,,1 Mjttj
CYCLECYCLE (9)
Basic formulation (Lee and Reklaitis, 1995)
The repeated cyclic pattern of heat integration matches over the whole production campaign is ensured with the same operating time schedule:
.,,1;,,2,,,1,1
MjNittttjijijj
IEIE (10)
Scheduling before heat integration Scheduling after heat integration
Basic formulation (Lee and Reklaitis, 1995)
The heat exchange between two streams is possible:
HCII JkjNittYkjikji ,;,,20
,1.,, (11)
The model allows only one-to-one matches between streams:
.,;,,112 1
.,2 1
,, HCJkjMjYYN
i
M
kjki
N
i
M
kkji
(12)
Heat exchanged between the streams:
HCMAX JkjNiYΦΦ kjikjkji ,;,,20,,,,, (13)
Total utility required for the production of one batch:
ds
1pU jj
M
jj
TTCΦ
(14)
HC
Obj2U
12 , ,
,
N
i j ki j k J
F ΦΦ
Objective function: (15)
Operations without heat transfer are included One-to-two matches
Economic objective function
Modification of the original model
in-phase stage
IP1E1P1I2I 1 Jj;N,,ittttj,ijj,ij,i
(16)
in-phase stage
out-of-phase stage
Area of the heat exchanger :
, ,,
, ,lni j k
j kj k j k
AU T
(17)
Modification of the original model
Available heat transfer area of the production vessel:
(18)VESSEL,j kA A
Investment of the heat exchanger:
i
k,j,ik,jk,j YsArI (19)
Differential cash flow of retrofitted solution:
(20)
1
dHU H CU CC t , , , , t ,
, , , , , d d
1 11
1
n
i j k i j k j k ni j k i j k j k
rF r P P r I
r r
1
d dobj , C
, d
1
1 1
n
j k nj k
r rF I F
r
Objective function: (21)
Results of industrial case study
Fig 15. Schematic diagram of production in the brewhouse before heat integration
retrofit a) and after retrofit b).
Two matches were predicted by the optimization model: heating the adjunct mash by the waste vapour produced during boiling and heating the mash by the heat released during wort clarification in whirlpool
The heat exchange of the first match can be accomplished
by a half-pipe coil jacket on the adjunct mash tun. Utility savings: 434,690 EUR/a. Required heat exchange area: 59 m². Investment: 12,590 EUR. The net present value is positive at discount rate of 10 %. The payback period: around 11 days.
The second match was rejected by the company, it can not satisfy the total heat demand of the mashing stage
Results of industrial case study
POLYGENERATION
Mathematical model for polygeneration
Fig 16. Superstructure of mathematical model for selecting the optimal polygeneration system.
Mathematical model for polygeneration
Cogeneration system with back-pressure steam turbine
Monthly electricity production:
;321;1221P ,,i,,jYcQE iijj,i (1)
Annual electricity production:12
P, a P,
1
1,2,3;i i jj
E E i
(2)
Increase in fuel consumption:
P,a a
ADDa
1,2,3;i i i
i i
f E Y q FF F Y i
q
(3)
Tax relief on the reduced carbon dioxide emission:
2,
C a CG P,aCO 1,2,3;i ii
m u Y q u E i (4)
Mathematical model for polygeneration
The cash flow:
2,
P,a E EN P,a M ADD FC t CO
1
dt
d d
1
1 11, 2, 3;
1
i i i i
n
i n
iF r E P m P E P F P
rr I i
r r
(5)
Investment in polygeneration system:
;3,2,1MAX iYcΦKI iiii (6)
P ADD, HEAT, 4,5,6; 1, 2,10,11,12;j i i i j j i iQ c Y E Q c f i j JH
Cogeneration system with back-pressure steam turbine - increased heat production during heating season
(7)
Mathematical model for polygeneration
;654 UPHEAT, ADD,HEAT ADD, ,,ifYf iii (8)
Upper bound of heat production increase:
The cash flow:
2,
P,a E H ADD,HEAT
C tEN P,a M ADD F
CO
1
dt
d d
1
1 14, 5, 6;
1
i i i jj jH
i
i i
n
i n
i
E P P f Y qF r
m P E P F P
rr I i
r r
(9)
Investment in the polygeneration system:
;6,5,4HEATADD,MAX iYcfΦKI iiiii(10)
Mathematical model for polygeneration
Cogeneration system with open-cycle gas turbine
12
S P D,
1
7;i i i j jj
E Y E E i
The produced “green energy” :
(11)
;7
1
11
11
dd
dt
FADDMaP,GESEDtC
irr
rIr
PFPEPEPErF
n
n
i
iiiii
The cash flow:
(12)
Trigeneration system with back-pressure steam turbine
Logical constraint for the selection of optimal polygeneration system:
10
1
1ii
Y
(13)
Mathematical model for polygeneration
10
obj NP1
ii
F V
Objective function:
(14)
Results of industrial case study The optimal polygeneration system is:
Cogeneration system whit a back-pressure steam turbine at a pressure level of 42.2 bar
The heat production would be increased during the heating season by 50 %. The electricity production would cover 42.5 % of the current brewery’s
consumption. The net present value is positive and the payback period is 3.2 a. The disadvantage of this solution is that the plant would become dependent
on external consumers of surplus heat energy.
Fig 17. Cogeneration system with back-pressure steam turbine.
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