hella tokos and zorka novak pintarič

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 Optimization Consulting 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.


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)


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

,mC

,

(15)

Outlet water mass from the (semi)continuous stream ww:SS00WCOUTC, 1 jnwwwwww

nn,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.


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

trctrnc m

CmrC TR

,,

OUT,

TR,,

TR,

TR,, 1

Mathematical model with local treatment unitsThe capacity of the local treatment unit:

SSTR,,

TRC : jncnc n

trnnctr 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.


The starting time of purification of wastewater from unit nc in local treatment unit tr :

tEnc tS, TRnc, tr

For processes operating within the same time interval j :

The ending time of the purification is:

tE, TRnc, tr t

Sn

ΔtTRtr

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:


The waiting times before and after treatment are:

tEnc tS, TR

nc, tr tE, TRnc, tr tSn

ΔtTRtr

tB, TRnc,n, tr t

A, TRnc,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)


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:

tEnc t

S, TRnc, tr t

E, TRnc, tr t

Sn

ΔtTRtr

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:


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

tEnc tS, TR

nc, tr tE, TRnc, tr t

Sn

ΔtTRtr

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

1 tP

mmfww j

j,wwfw n

n,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

mCm

tP

mCm

tP

mCm

mCm

f

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

5TRTR

FtJ

mKmKfcontinuoustr

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.


• 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.


Fig 10. Water network in production and packaging area (Monday to Wednesday).

Freshwater consumption reduced by 25%


Freshwater consumption reduced by 22%

Fig 11. Water network in production and packaging area (Thursday).


Freshwater consumption reduced by 31 %

Fig 12. Water network in production and packaging area (Friday).


• Freshwater consumption reduced by 26,5% •Total investment is 828,528EUR; Net present value: 1,486,919 EUR; Payback period: 2.7 a

Packaging areaProduction area

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 savingsFinal 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


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,OP

IECYCLE JjMj

N

ttt jjN

j

.,1,1

OPIE

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)


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


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

1 2 , ,,

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


in-phase stage

IP1E1P1I2I 1 Jj;N,,ittttj,ijj,ij,i

(16)

in-phase stage

out-of-phase stage

Area of the heat exchanger :, ,

,, ,ln

i j kj k

j k j k

AU T

(17)


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)


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


POLYGENERATION

Mathematical model for polygeneration

Fig 16. Superstructure of mathematical model for selecting the optimal polygeneration system.


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 aADD

a 1,2,3;i i ii 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 polygenerationThe 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)


;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 polygenerationCogeneration 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

111

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)


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.

Thank you for your Attention!

[email protected]

hella tokos and zorka novak pintarič

Documents

outlet water mass

water flow

overall water mass balance

indirect water reuse

semicontinuous processes

batch processes

batchsemicontinuous

semicontinuous operation