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 collection Measurements Determination of water balance Determination 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) Overall water mass balance: (2) Mass load balance in each operation: (1) Water mass balance in each operation: (3)

Basic formulation (Kim and Smith, 2004) Feasibility constraints on the inlet and outlet concentration: Upper and lower bounds for the water flow: (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: (12) 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 : (15) Outlet water mass from the (semi)continuous stream ww : (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 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 purified in local treatment units are: (19) (21)-(22) Feasibility constraints on the inlet and outlet concentration: (20)

Mathematical model with local treatment units The capacity of the local treatment unit: (23) Outlet concentration from local treatment unit: (24)

Mathematical model with local treatment units b) 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 : t E nc t S, TR nc, tr For processes operating within the same time interval j : The ending time of the purification is: t E, TR nc, tr t S n ΔtΔt TR tr (25) (26) (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: t E nc t S, TR nc, tr t E, TR nc, tr t S n ΔtΔt TR tr t B, TR nc,n, tr t A, TR nc,n, tr (29) (30) (31) (32) The waiting times of unselected treatment connections are forced to zero by the following constraints: (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: t E nc t S, TR nc, tr t E, TR nc, tr t S n ΔtΔt TR tr (35) (36) (37)

The required storage tank capacity before the treatment unit is: Mathematical model with local treatment units The scheduling of the continuous treatment unit only differs from that of the batch treatment unit, when defining the treatment ending time: 2. Continuous local treatment units t E nc t S, TR nc, tr t E, TR nc, tr t S n ΔtΔt TR 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 (38) (39) (40) (41)

Objective function  The objective function, F Obj, 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. (42)

Objective function Freshwater cost: (43) Annual investment costs of storage tank installation: (44) Wastewater treatment cost: (45)

Annual investment cost for piping: (46) Objective function Annual investment costs for the local treatment unit: (47)

Modifications of the original model Multi-level design strategy Direct water re-use between continuous and batch processes Indirect water re-use between continuous 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 Packaging area Production area Fig 13. Final water network in a brewery.

HEAT INTEGRATION RETROFIT

Basic formulation (Lee and Reklaitis, 1995) LP MILP t P j t I i, j t E i, j t F i, j t CYCLE, MIN C P j TsjTsj TdjTdj 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) Out-of-phase stage:In-phase stage:

Basic formulation (Lee and Reklaitis, 1995) Starting time of the next unit, j + 1: Cycle time for each unit 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: (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: (10) Scheduling before heat integrationScheduling after heat integration

Basic formulation (Lee and Reklaitis, 1995) The heat exchange between two streams is possible: (11) The model allows only one-to-one matches between streams: (12) Heat exchanged between the streams: (13) Total utility required for the production of one batch: (14) Objective function:(15)

 Operations without heat transfer are included  One-to-two matches  Economic objective function Modification of the original model in-phase stage (16) in-phase stage out-of-phase stage

Area of the heat exchanger : (17) Modification of the original model Available heat transfer area of the production vessel: (18) Investment of the heat exchanger: (19) Differential cash flow of retrofitted solution: (20) 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: (1) Annual electricity production: (2) Increase in fuel consumption: (3) Tax relief on the reduced carbon dioxide emission: (4)

Mathematical model for polygeneration The cash flow: (5) Investment in polygeneration system: (6) Cogeneration system with back-pressure steam turbine - increased heat production during heating season (7)

Mathematical model for polygeneration (8) Upper bound of heat production increase: The cash flow: (9) Investment in the polygeneration system: (10)

Mathematical model for polygeneration Cogeneration system with open-cycle gas turbine The produced “green energy” : (11) The cash flow: (12) Trigeneration system with back-pressure steam turbine

Logical constraint for the selection of optimal polygeneration system: (13) Mathematical model for polygeneration 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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