- Email: [email protected]
Superstructure Optimisation of a WaterMinimisation Network with an Embedded Multi-Contaminant Electrodialysis Model
Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Superstructure Optimisation of a WaterMinimisation Network with an Embedded Multi-Contaminant Electrodialysis Model Chiedza D. Nezungai, Thokozani Majozi* School of Chemical and Metallurgical Engineering, University of the Witwatersrand, 1 Jan Smuts Ave, Johannesburg, 2001, South Africa [email protected]
Abstract The water-energy nexus considers the relationship between water and energy resources. The increase in environmental regulations and social pressures has made it necessary to develop processes that are conservative with respect to both these resources. This work outlines the development of an optimisation model of a water network comprised of water sources, water sinks and an electrodialysis unit for the partial purification of contaminated water. The optimisation model is based on a superstructure framework, where the objective is to minimise freshwater consumption, wastewater production, energy consumption and the operating and capital costs involved in the process integration. A comparison was done between the developed model and the more common black box model, which simplifies regeneration units to linear expressions. The results show that the black box approach can lead to inaccuracies of up to 85% in the costing of regeneration units. Furthermore, it is shown that there are significant environmental and financial benefits in the simultaneous minimisation of water and energy in water networks. Keywords: Water-energy nexus, water minimisation, mathematical modelling
1. Introduction In the realm of process integration, water minimisation involves the interaction of process units in a system with the goal of reducing the amount of freshwater consumed and/or the amount of wastewater produced by the individual units and the entire system. This can be achieved by either reusing or recycling effluent produced, in conjunction with partial treatment or regeneration of contaminated water. Partial purification can be achieved by membrane processes, such as electrodialysis, reverse osmosis, and ultrafiltration, as well as non-membrane processes, such as stream stripping or using ion exchange resins. The choice of which minimisation approach to adopt must be informed by the nature of the processes involved and the cost of regeneration. Water purification is an energy intensive process. As such, it is necessary to minimise the amount of energy required to treat effluent in a water network. The treatment process considered in this work is electrodialysis (ED). The process of ED, depicted in Figure 1, involves electromigration of ionic species across selectively permeable and alternately charged membranes. This results in the formation of a highly concentrated concentrate stream, and a diluate stream with a low contaminant concentration.
846
C.D. Nezungai, T. Majozi
Figure 1: Schematic diagram of a single stage electrodialysis unit comprised of multiple cell pairs
Different approaches to ED modelling exist, including the convective-diffusion model, and the fixed flowrate design model. The latter was adopted in this work, owing to its simplicity and ease of integration. An ED design model was developed by Lee et al (2002) for single contaminant systems, to determine the area, current and voltage involved in desalination. This model was applied by Tsiakis and Papageorgiou (2005), to optimise the capital cost and energy consumption. It was also validated against experimental work by Brauns et al., (2009). In this work, a reformulation that allows the optimisation of multi-contaminant systemsis proposed. This involves the introduction of expressions for equivalent concentration and equivalent conductivity, taking into account the complex nature of ionic mixtures. There are two major approaches adopted in water minimisation, namely, graphical and mathematical optimisation techniques. In this case, the mathematical optimisation approach was adopted, using the superstructure method. This approach allows the processing of complex systems containing multiple contaminants, as well as the capability to conveniently integrate the water network model with a regenerator model.(Khor et al., 2011). In many of the water network superstructure models to date, regeneration units are represented by a simplified linear expression of the unit performance. The disadvantage of this approach is that it does not provide an accurate representation of the cost of the water network. In most instances, the cost of purification is not considered, or a generic linear cost function is applied. This results in an offset between the actual costs of regeneration and the costs factored into the regeneration model. This work aims to highlight the adverse impact if this simplification on achieving an optimum performance index.
2. Problem statement A fixed flowrate approach was taken in the model development, i.e. a stream is described by the total flowrate of fluid and the concentration of each of the
847
Superstructure Optimisation of a Water Minimization Network with an Embedded Multi-Contaminant Electrodialysis Model
contaminants in the stream. According to this assumption,a water source is a unit that produces water or effluent while a water sink is a unit that consumes water. In short, the problem statement can be stated as follows. Given : A set of water sources, J, with known flowrates, Fj, and known contaminant concentrations, Cj,o A set of water sinks, I, with known flowrates, Fi ,and known maximum allowable concentrations, Ci,oU A set of regenerators ,R, i.e. electrodialyisis unit, with some design parameters A freshwater source, with a variable flowrate, and known contaminant concentrations A wastewater sink, with a variable flowrate and known maximum allowable contaminant concentrations It is required to synthesise the water network that minimises the amount of freshwater consumed, wastewater produced, the energy consumed in the regeneration unit and the overall cost of the water network. In addition, it is necessary to determine the optimum operating and design conditions of the electrodialysis unit (e.g. area, number of cell pairs, current and voltage).
3. Mathematical model Material balances are established on the source-regenerator-sink basis.For the units involving mixing of streams, i.e. the regenerator and the sinks, a contaminant balance was conducted for each contaminant. The performance of the regeneration unit was described by the contaminant-specific removal ratio, RR, Eq. (1). This expression is often used in isolation when developing a black box model. It expresses the contaminant load in the concentrate stream, as a fraction of the contaminant load in the feed to the regenerator. Crcon ,o RRr ,o j
i
Frcon ,i
r o
R O
(1)
C j ,o F j ,r
A comprehensive electrodialysis energy minimisation model is developed and included in the water network.The driving force for electrodialysis is the electric current, I, flowing across the unit. The current is determined using a modified expression of Faraday’s law, given by Eq.(2), where zo and vorepresent the valence and stoichiometric coefficient of either the cation or the anion of any contaminant, o. Qdis the flowrate of the diluate stream, N, is the number of cell pairs in the ED unit, F, is the Faraday constant and ζ is the current efficiency.
I
F FQd C N
(2)
zo o o Δ
In order to account for the multi-contaminant nature of the ED feed, C ,the concentration flux over the unit, is given in terms of the equivalent concentration of the
848
C.D. Nezungai, T. Majozi
solution. For any given solution of salts with concentrations Co, the solution equivalent concentration, Ceq is defined according to Eq. (3).
Ceq
zo voCo o
(3)
Based on the driving force, it is then possible to determine physical characteristics of the required unit, such as the membrane area, the length and the throughput. In addition, one is able to determine the amount of energy required for desalination and for pumping purposes, and subsequently, the capital and operating costs associated with regeneration. The combination of the water network and ED model culminates in an objective function that takes into account freshwater consumption, wastewater production, and accurate capital and operating costs of ED units and necessary piping interconnections.
4. Illustrative Example The above model is applied to a pulp mill and bleached paper plant adapted from Chew et al., (2008).In the original scenario, shown in Figure 2, four separate freshwater feeds are used, with a total consumption of 8 500 tonnes per day, and 4 separate effluent streams are produced, totalling 10 500 tonnes per day.
Figure 2: Simplified PDF of Pulp mill and bleached paper plant
Two alternate process integration scenarios were compared. Firstly, the case in which a black box model is used and the costing of the actual required ED unit is performed separately; i.e. water minimisation only.The second case involves simultaneous minimisation of water and energy, using the developed model. Two contaminants were identified,namely,NaCl and MgCl2. The flowrates and contaminant concentrations of the sources and sinks are detailed in Table 1.
849
Superstructure Optimisation of a Water Minimization Network with an Embedded Multi-Contaminant Electrodialysis Model Table 1: Given data for water network
Sources
Sinks Maximum contaminant Contaminant Concentration Concentration 3 3 (Kmol/cm ) Flowrate Flowrate (Kmol/cm ) (cm3/s) (cm3/s) NaCl Source NaCl MgCl2 Sink MgCl2 Stripper 1 2.07 0 0 Washer 3.26 0.0046 0.0004 Screening 0.34 0.046 0.035 Screening 0.34 0.0125 0.0007 Stripper 2 0.24 0 0 Washer/filter 1.34 0 0 Bleaching 7.22 0.026 0.0002 Bleaching 7.22 0.0002 0.00003 Freshwater Variable Wastewater Variable 0.01 0.01 The results obtained from the optimisation are given in Table 2. In the first scenario,application of process integration results in a 36% saving in freshwater and 60% reduction of wastewater produced, in comparison with the original plant.The water minimisation black box model employs a linear cost function to determine the cost of regeneration. Such a function, however, is inaccurate as it does not account for the energy penalty associated with regenerating highly concentrated effluent. The deviation of the cost function from the actual cost of regeneration is 85%. The required ED unit has a total area of 438 m2 and requires 353 cell pairs. In the second scenario, the simultaneous minimisation of both energy and water within the water network results in a further reduction in freshwater consumption, wastewater production and cost of regeneration, as indicated in Table 2. By applying a penalty to the energy consumption, a more modest ED unit, with only 230 cell pairs and 144 m2area, is required. Subsequently there is a 53% reduction in the total cost of the water network. The modified flowsheet after energy and water minimisation is given in Figure 3. Table 2: Summary of costs in the 2 cases considered, values are given in $1000/annum
Scenario 1
Freshwater Wastewater Energy* Piping
Original 2 814.86 3 468.12 -
Water minimisation estimated ED cost 1 776.00 1 122.80 3.90 92.40
Total
6 282.98
2 995.10
*Energy associated with regeneration
Scenario 2
Water minimisation true ED cost 1 776.00 1 122.80 26.08 92.40
Water and energy minimisation 1 736.70 1 083.50 5.25 86.62
3 017.28
2 912.07
850
C.D. Nezungai, T. Majozi
Figure 3: Process flowsheet after integration with the electrodialysis unit
5. Conclusion This work explores the shortcomings of the black box model in water network optimisation by adopting an accurate representation of regeneration units. It is shown that by simultaneous minimisation of water and energy in the network, there is a significant reduction in freshwater consumption and wastewater production as well as an overall reduction in the cost of the water network. This approach also results in an 80% reduction in energy consumption in the regeneration units. Furthermore, the simultaneous approach results in more favourable design parameters for the regeneration units.
6. References E.Brauns, W. De Wilde, B. Van de Bosch, P. Lens, L. Pinoy, M.Empsten, 2009, On the experimental verification of an electrodialysis simulation model for optimal stack configuration design through solver software. Desalination, 249, 1030-1038 I.M.L. Chew, R. Tan, D.K.S. Ng, D.C.Y. Foo, T. Majozi, J. Gouws, 2008, Synthesis of Direct and Indirect Interplant Water Network. Ind. Eng. Chem. Res. 47, 9485–9496. H.J Lee, F. Sarfert, H. Strathmann, S.H.Moon, 2002, Designing of an electrodialysis desalination plant. Desalination 142, 267–286. P. Tsiakis, L.G.Papageorgiou, 2005, Optimal design of an electrodialysis brackish water desalination plant. Desalination 173, 173–186. S.C. Khor, D.C.Y. Foo, M. El-Halwagi, R. Tan, N. Shah, 2011, A Superstructure Optimization Approach for Membrane Separation-Based Water Regeneration Network Synthesis with Detailed Nonlinear Mechanistic Reverse Osmosis Model. Ind. Eng. Chem. Res. 50, 13444– 13456.
Superstructure Optimisation of a WaterMinimisation Network with an Embedded Multi-Contaminant Electrodialysis Model Chiedza D. Nezungai, Thokozani Majozi* School of Chemical and Metallurgical Engineering, University of the Witwatersrand, 1 Jan Smuts Ave, Johannesburg, 2001, South Africa [email protected]
Abstract The water-energy nexus considers the relationship between water and energy resources. The increase in environmental regulations and social pressures has made it necessary to develop processes that are conservative with respect to both these resources. This work outlines the development of an optimisation model of a water network comprised of water sources, water sinks and an electrodialysis unit for the partial purification of contaminated water. The optimisation model is based on a superstructure framework, where the objective is to minimise freshwater consumption, wastewater production, energy consumption and the operating and capital costs involved in the process integration. A comparison was done between the developed model and the more common black box model, which simplifies regeneration units to linear expressions. The results show that the black box approach can lead to inaccuracies of up to 85% in the costing of regeneration units. Furthermore, it is shown that there are significant environmental and financial benefits in the simultaneous minimisation of water and energy in water networks. Keywords: Water-energy nexus, water minimisation, mathematical modelling
1. Introduction In the realm of process integration, water minimisation involves the interaction of process units in a system with the goal of reducing the amount of freshwater consumed and/or the amount of wastewater produced by the individual units and the entire system. This can be achieved by either reusing or recycling effluent produced, in conjunction with partial treatment or regeneration of contaminated water. Partial purification can be achieved by membrane processes, such as electrodialysis, reverse osmosis, and ultrafiltration, as well as non-membrane processes, such as stream stripping or using ion exchange resins. The choice of which minimisation approach to adopt must be informed by the nature of the processes involved and the cost of regeneration. Water purification is an energy intensive process. As such, it is necessary to minimise the amount of energy required to treat effluent in a water network. The treatment process considered in this work is electrodialysis (ED). The process of ED, depicted in Figure 1, involves electromigration of ionic species across selectively permeable and alternately charged membranes. This results in the formation of a highly concentrated concentrate stream, and a diluate stream with a low contaminant concentration.
846
C.D. Nezungai, T. Majozi
Figure 1: Schematic diagram of a single stage electrodialysis unit comprised of multiple cell pairs
Different approaches to ED modelling exist, including the convective-diffusion model, and the fixed flowrate design model. The latter was adopted in this work, owing to its simplicity and ease of integration. An ED design model was developed by Lee et al (2002) for single contaminant systems, to determine the area, current and voltage involved in desalination. This model was applied by Tsiakis and Papageorgiou (2005), to optimise the capital cost and energy consumption. It was also validated against experimental work by Brauns et al., (2009). In this work, a reformulation that allows the optimisation of multi-contaminant systemsis proposed. This involves the introduction of expressions for equivalent concentration and equivalent conductivity, taking into account the complex nature of ionic mixtures. There are two major approaches adopted in water minimisation, namely, graphical and mathematical optimisation techniques. In this case, the mathematical optimisation approach was adopted, using the superstructure method. This approach allows the processing of complex systems containing multiple contaminants, as well as the capability to conveniently integrate the water network model with a regenerator model.(Khor et al., 2011). In many of the water network superstructure models to date, regeneration units are represented by a simplified linear expression of the unit performance. The disadvantage of this approach is that it does not provide an accurate representation of the cost of the water network. In most instances, the cost of purification is not considered, or a generic linear cost function is applied. This results in an offset between the actual costs of regeneration and the costs factored into the regeneration model. This work aims to highlight the adverse impact if this simplification on achieving an optimum performance index.
2. Problem statement A fixed flowrate approach was taken in the model development, i.e. a stream is described by the total flowrate of fluid and the concentration of each of the
847
Superstructure Optimisation of a Water Minimization Network with an Embedded Multi-Contaminant Electrodialysis Model
contaminants in the stream. According to this assumption,a water source is a unit that produces water or effluent while a water sink is a unit that consumes water. In short, the problem statement can be stated as follows. Given : A set of water sources, J, with known flowrates, Fj, and known contaminant concentrations, Cj,o A set of water sinks, I, with known flowrates, Fi ,and known maximum allowable concentrations, Ci,oU A set of regenerators ,R, i.e. electrodialyisis unit, with some design parameters A freshwater source, with a variable flowrate, and known contaminant concentrations A wastewater sink, with a variable flowrate and known maximum allowable contaminant concentrations It is required to synthesise the water network that minimises the amount of freshwater consumed, wastewater produced, the energy consumed in the regeneration unit and the overall cost of the water network. In addition, it is necessary to determine the optimum operating and design conditions of the electrodialysis unit (e.g. area, number of cell pairs, current and voltage).
3. Mathematical model Material balances are established on the source-regenerator-sink basis.For the units involving mixing of streams, i.e. the regenerator and the sinks, a contaminant balance was conducted for each contaminant. The performance of the regeneration unit was described by the contaminant-specific removal ratio, RR, Eq. (1). This expression is often used in isolation when developing a black box model. It expresses the contaminant load in the concentrate stream, as a fraction of the contaminant load in the feed to the regenerator. Crcon ,o RRr ,o j
i
Frcon ,i
r o
R O
(1)
C j ,o F j ,r
A comprehensive electrodialysis energy minimisation model is developed and included in the water network.The driving force for electrodialysis is the electric current, I, flowing across the unit. The current is determined using a modified expression of Faraday’s law, given by Eq.(2), where zo and vorepresent the valence and stoichiometric coefficient of either the cation or the anion of any contaminant, o. Qdis the flowrate of the diluate stream, N, is the number of cell pairs in the ED unit, F, is the Faraday constant and ζ is the current efficiency.
I
F FQd C N
(2)
zo o o Δ
In order to account for the multi-contaminant nature of the ED feed, C ,the concentration flux over the unit, is given in terms of the equivalent concentration of the
848
C.D. Nezungai, T. Majozi
solution. For any given solution of salts with concentrations Co, the solution equivalent concentration, Ceq is defined according to Eq. (3).
Ceq
zo voCo o
(3)
Based on the driving force, it is then possible to determine physical characteristics of the required unit, such as the membrane area, the length and the throughput. In addition, one is able to determine the amount of energy required for desalination and for pumping purposes, and subsequently, the capital and operating costs associated with regeneration. The combination of the water network and ED model culminates in an objective function that takes into account freshwater consumption, wastewater production, and accurate capital and operating costs of ED units and necessary piping interconnections.
4. Illustrative Example The above model is applied to a pulp mill and bleached paper plant adapted from Chew et al., (2008).In the original scenario, shown in Figure 2, four separate freshwater feeds are used, with a total consumption of 8 500 tonnes per day, and 4 separate effluent streams are produced, totalling 10 500 tonnes per day.
Figure 2: Simplified PDF of Pulp mill and bleached paper plant
Two alternate process integration scenarios were compared. Firstly, the case in which a black box model is used and the costing of the actual required ED unit is performed separately; i.e. water minimisation only.The second case involves simultaneous minimisation of water and energy, using the developed model. Two contaminants were identified,namely,NaCl and MgCl2. The flowrates and contaminant concentrations of the sources and sinks are detailed in Table 1.
849
Superstructure Optimisation of a Water Minimization Network with an Embedded Multi-Contaminant Electrodialysis Model Table 1: Given data for water network
Sources
Sinks Maximum contaminant Contaminant Concentration Concentration 3 3 (Kmol/cm ) Flowrate Flowrate (Kmol/cm ) (cm3/s) (cm3/s) NaCl Source NaCl MgCl2 Sink MgCl2 Stripper 1 2.07 0 0 Washer 3.26 0.0046 0.0004 Screening 0.34 0.046 0.035 Screening 0.34 0.0125 0.0007 Stripper 2 0.24 0 0 Washer/filter 1.34 0 0 Bleaching 7.22 0.026 0.0002 Bleaching 7.22 0.0002 0.00003 Freshwater Variable Wastewater Variable 0.01 0.01 The results obtained from the optimisation are given in Table 2. In the first scenario,application of process integration results in a 36% saving in freshwater and 60% reduction of wastewater produced, in comparison with the original plant.The water minimisation black box model employs a linear cost function to determine the cost of regeneration. Such a function, however, is inaccurate as it does not account for the energy penalty associated with regenerating highly concentrated effluent. The deviation of the cost function from the actual cost of regeneration is 85%. The required ED unit has a total area of 438 m2 and requires 353 cell pairs. In the second scenario, the simultaneous minimisation of both energy and water within the water network results in a further reduction in freshwater consumption, wastewater production and cost of regeneration, as indicated in Table 2. By applying a penalty to the energy consumption, a more modest ED unit, with only 230 cell pairs and 144 m2area, is required. Subsequently there is a 53% reduction in the total cost of the water network. The modified flowsheet after energy and water minimisation is given in Figure 3. Table 2: Summary of costs in the 2 cases considered, values are given in $1000/annum
Scenario 1
Freshwater Wastewater Energy* Piping
Original 2 814.86 3 468.12 -
Water minimisation estimated ED cost 1 776.00 1 122.80 3.90 92.40
Total
6 282.98
2 995.10
*Energy associated with regeneration
Scenario 2
Water minimisation true ED cost 1 776.00 1 122.80 26.08 92.40
Water and energy minimisation 1 736.70 1 083.50 5.25 86.62
3 017.28
2 912.07
850
C.D. Nezungai, T. Majozi
Figure 3: Process flowsheet after integration with the electrodialysis unit
5. Conclusion This work explores the shortcomings of the black box model in water network optimisation by adopting an accurate representation of regeneration units. It is shown that by simultaneous minimisation of water and energy in the network, there is a significant reduction in freshwater consumption and wastewater production as well as an overall reduction in the cost of the water network. This approach also results in an 80% reduction in energy consumption in the regeneration units. Furthermore, the simultaneous approach results in more favourable design parameters for the regeneration units.
6. References E.Brauns, W. De Wilde, B. Van de Bosch, P. Lens, L. Pinoy, M.Empsten, 2009, On the experimental verification of an electrodialysis simulation model for optimal stack configuration design through solver software. Desalination, 249, 1030-1038 I.M.L. Chew, R. Tan, D.K.S. Ng, D.C.Y. Foo, T. Majozi, J. Gouws, 2008, Synthesis of Direct and Indirect Interplant Water Network. Ind. Eng. Chem. Res. 47, 9485–9496. H.J Lee, F. Sarfert, H. Strathmann, S.H.Moon, 2002, Designing of an electrodialysis desalination plant. Desalination 142, 267–286. P. Tsiakis, L.G.Papageorgiou, 2005, Optimal design of an electrodialysis brackish water desalination plant. Desalination 173, 173–186. S.C. Khor, D.C.Y. Foo, M. El-Halwagi, R. Tan, N. Shah, 2011, A Superstructure Optimization Approach for Membrane Separation-Based Water Regeneration Network Synthesis with Detailed Nonlinear Mechanistic Reverse Osmosis Model. Ind. Eng. Chem. Res. 50, 13444– 13456.