A mathematical programming framework for early stage design of wastewater treatment plants

Environmental Modelling & Software 64 (2015) 164e176

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Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft

A mathematical programming framework for early stage design of wastewater treatment plants Hande Bozkurt, Alberto Quaglia, Krist V. Gernaey, Gürkan Sin* CAPEC-PROCESS, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kgs. Lyngby, Denmark

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 June 2014 Received in revised form 3 November 2014 Accepted 24 November 2014 Available online

The increasing number of alternative wastewater treatment technologies and stricter effluent requirements make the optimal treatment process selection for wastewater treatment plant design a complicated problem. This task, defined as wastewater treatment process synthesis, is currently based on expert decisions and previous experiences. This paper proposes a new approach based on mathematical programming to manage the complexity of the problem. The approach generates/identifies novel and optimal wastewater treatment process selection, and the interconnection between unit operations to create a process flow diagram. Towards this end, a superstructure approach is used to represent the treatment alternatives for reaction and separation. A generic process interval model is used to describe each alternative in terms of inputeoutput mass balances including conversion and separation factors. Next the design problem is formulated as a Mixed Integer (Non)linear Programming problem e MI(N)LP e and solved. A case study is formulated and solved to highlight the application of the framework. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Design Modeling Superstructure optimization Wastewater treatment Process flow Interconnection

1. Introduction One of the most challenging steps in wastewater treatment plant design is the selection of the treatment process defined as a combination of unit operations and processes capable of meeting effluent permit requirements (Tchobanoglous et al., 2003). We suggest to call this particular task Wastewater treatment process synthesis and define it as follows: Wastewater treatment process synthesis is the step in the design of a wastewater treatment plant where the design engineer selects unit processes (separation and/ or reaction including physical, chemical and biological processes) from numerous alternatives and interconnects them to create the process flow diagram. Hence the objective of process synthesis is to find the best process flow diagram, among numerous alternatives, for treating a given influent wastewater with its flow rate and composition to meet predefined performance criteria including effluent permit requirements as well as cost and technical requirements.

* Corresponding author. CAPEC-PROCESS Research Center, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kgs. Lyngby, Denmark. Tel.: þ45 45 25 28 06. E-mail addresses: [email protected] (H. Bozkurt), [email protected] (G. Sin). http://dx.doi.org/10.1016/j.envsoft.2014.11.023 1364-8152/© 2014 Elsevier Ltd. All rights reserved.

The number of alternative processes to choose from has been increasing steadily since the beginning of the 20th century, where many wastewater treatment processes and technologies have been developed to meet increasingly stringent performance demands (Henze et al., 2008). The current phase of development in municipal wastewater treatment technologies was initiated with the stricter effluent limit values imposed by both emission and immission based regulations. In EU, for example, the Water Framework Directive (Directive 2000/ 60/EC) regulates the ecosystems by setting quality objectives and the urban effluent wastewater quality is controlled by the Urban Wastewater Treatment Directive (91/271/EEC). A wide range of parameters were included in several different regulations covering both water and sludge disposal, i.e. organics, nutrients (total nitrogen content of the effluent wastewater should be as low as 10 mg/L while this value is 1 mg/L for total phosphorus as regulated in 91/271/EEC), pathogens, heavy metals, emerging contaminants etc. This resulted in development of new treatment technologies as well as new process flow diagrams for WWTPs. The number of available alternative technologies using physical, chemical and biological means of treatment has thus increased considerably in order to satisfy the high removal efficiencies required by the stricter regulations. The fact that the number of alternative wastewater treatment technologies is growing steadily increases the importance of early-

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

stage decision making in WWTP design and retrofitting problems. When the design procedure is divided into different stages as stated in the development funnel approach, which is shown in Fig. 1 (Quaglia, 2013), the first stage of the funnel e the early stage decision making stage e corresponds to the design stage where a variety of concepts and ideas are generated and a high number of alternatives are evaluated in a less detailed/simplified manner. The alternatives that are proven to satisfy the criteria needed by the designer can move further through the funnel to be investigated in more detail. When considering the WWTP design case, early stage decision making is mainly about: (a) Which treatment processes and unit operations to select for a particular wastewater treatment problem; and, (b) How to verify the rationale and ensure engineering optimality of the decision. Often e if not always e such decisions are multi-objective and multi-criteria based considering economics, environmental, legal and social constraints. Recently, the WWTP process selection and network design problem has evolved from being a simple technical design problem to a complex integrated decision making task, mainly because of the many aspects that are being considered in the early decision making stage (Hamouda et al., 2009). Currently, the early stage decision making for WWTP design is mainly based on expert decisions and previous experiences (Tchobanoglous et al., 2003). This approach takes values like environmental issues, water reuse, byproduct recovery (if possible) and impacts of the selected treatment technologies on the surrounding population into account and identifies the alternatives based on experience, similar existing solutions and brainstorming to come up with the most viable WWTP network (Daigger, 2005). However, with the increased complexity of the technologies for wastewater treatment and the stricter limit values for effluents, making the most feasible decision using this approach is expected to become harder and harder. An alternative approach is to cast the decision problem using mathematical programming which has been an active research area in chemical process synthesis (Grossmann, 2005), but has also seen various applications in the wastewater treatment field including Rigopoulos and Linke (2002), Vidal et al. (2002), Alasino et al. (2007, 2010). While these studies provided valuable insights and showed the promising potential of the optimization based approaches for plant design, their scope was however rather limited and focused on either optimizing a given treatment process or selecting the best candidate process from a limited number of alternatives. To realize the full potential of this approach, however, there are a number of barriers that need to be addressed and solved including representation of the increasing number of processes and unit operations in wastewater treatment processes as well as tackling the resulting multi-disciplinary complexity of the optimization problem which requires both competences and methods from optimization as well as wastewater engineering disciplines. In particular, for formulating a realistic wastewater treatment plant design problem, the complexity of the mixed integer nonlinear programming problem

165

can grow exponentially, which needs an effective formulation and analysis method, which is the focus of this study. Moreover, the knowledge-based decision support systems developed for conceptual WWTP design have been presented in the literature covering many different aspects of early stage design including technical, economical, environmental and social considerations; however, these approaches do not cover the optimization step for the process synthesis (Comas et al., 2003; Garrido-Baserba et al., 2012). In this study, we propose a superstructure based optimization framework based on mathematical programming to manage the complexity of the problem and generate/identify novel and optimal process selection and interconnection to create a process flow diagram for design of WWTPs. The purpose of the framework is to support the WWTP design specialists in the process of making early stage design decisions by allowing them to compare several different treatment technologies with respect to many different criteria. The framework contains a superstructure method for representing the design space, and a systematic method for modeling and data collection which enables effective formulation of a mixed integer nonlinear programming problem using a template approach. The framework is explained in more detail in Section 2, and is then applied to a case study for retrofitting the Benchmark Simulation Model no. 2 (BSM2) plant as described in Section 3. The framework is evaluated under a number of scenarios and the results are critically analyzed and discussed in Section 3.5. 2. Framework for synthesis and design of WWTP networks A superstructure based optimization framework was developed and evaluated successfully for various network design problems including soybean oil processing, biorefinery, oil refinery wastewater treatment etc. (Quaglia et al., 2012). The framework, modified and adapted in the context of the WWTP design problem is given in Fig. 2. Each of the steps mentioned in Fig. 2 will now be explained in more detail: Step 1: In the first step the scope of the problem (wastewater characterization, effluent limit definitions etc.) is defined together with the objective function. The problem is defined as the treatment of domestic wastewater where a set of pollutants such as organic nitrogen need to be removed. The characterization of the wastewater source and the sink limitations for different water, solids and gas streams leaving the plant (for example effluent restrictions) are defined here. The objective function, which represents the total annualized cost (TAC), is formulated together with different scenario definitions. In the below equation, TAC is defined as the summation of operational (OPEX) and capital cost (CAPEX).

TAC ¼ OPEX þ

CAPEX t

Fig. 1. Illustration of the development funnel approach, where the number of feasible process options is gradually reduced from left to right (Quaglia, 2013).

(1)

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Fig. 2. The superstructure based optimization methodology adapted for design of optimal WWT systems (Quaglia et al., 2012).

Step 2: The second step comprises a superstructure definition consisting of different water sources, different tasks for water and sludge treatment together with sinks and process alternatives for the defined tasks. A superstructure, for example shown in Fig. 3, is a compact representation of different process alternatives (i.e. treatment technologies in the wastewater treatment case). Process steps, which are the columns, represent wastewater sources and sinks for the effluent streams (effluent water, sludge, by-products etc.) as well as different tasks to be carried out throughout the network in order to connect sources and sinks. In each step, in the rows, alternative treatment process intervals (e.g. separation (primary clarifier, secondary clarifier, membrane reactor, etc.) or reaction (activated sludge for C, N or P removal together, nitritation, anammox etc.) and their different configurations) responsible for a specific task are placed. There are three different ways of constructing a superstructure. One of the methods is alternative collection, in which all known WWTP network configurations are arranged in a superstructure representation. The resulting superstructure includes the known configurations and enables only to screen among the known candidates, which does not allow the selection of innovative technologies or configurations. The second approach is the method of combinatorial synthesis. In this approach, the superstructure is composed of all treatment technologies placed under the relevant task connected to the others in every possible connection way (Fig. 3 is an example of a full combinatorial superstructure). This approach results in a very large

Fig. 3. A representative superstructure for wastewater treatment networks.

search space and redundant configurations. A third approach is called the insight-based approach, which is used in this study. The latter approach takes into account expert knowledge to include the well-known configurations together with the innovative technologies and configurations in the superstructure, as well as eliminating the unfeasible and non-convenient alternatives and connections (Quaglia et al., 2014a). At this point, the selection of technologies to be placed in the superstructure and the connections between the alternatives are defined by design experts with a prior screening procedure. A representative superstructure example is given in Fig. 3, where a treatment plant is defined as a sequence of different treatment tasks in addition to wastewater sources and sinks. Under each treatment task, a number of alternative technologies are listed. The superstructure is then formulated by defining the feasible connection streams between treatment tasks. In this example, a full-combinatorial connection between different source/sink/process intervals is defined. Step 3: In this step, a systematic data collection procedure is used to design the treatment technologies placed in the superstructure, which is illustrated in Fig. 4. In this context, we used the commonly accepted design procedures given by the ATV design standards (2000), Tchobanoglous et al. (2003), WEF manuals (2010) and Henze et al. (2008) for the design of a treatment process alternative for a given wastewater source. A particular treatment process design is made by using system specific design criteria like SRT and HRT together with temperature dependent biokinetic constants, settling tank data and internal/external recycle ratios. Here, the treatment technologies are designed at their optimality by fixing the SRT and HRT values rather than optimizing them and in a second step more rigorous models can be used for optimization once the number of alternatives is reduced. This two-tiered approach for optimization is chosen on purpose to manage the complexity of the optimization problem which becomes otherwise intractable (Quaglia et al., 2014b). The output from the design includes volumes, utility consumption (electricity, chemicals, aeration), and sludge production data which are used to calculate the capital and operational costs as well. The algorithms for the design were implemented in a Matlab script to automate this step and ensure consistency and reproducibility. The system design parameters, e.g. SRT and HRT, are selected from a given range that is obtained from engineering practice (Tchobanoglous et al., 2003) so that they satisfy the effluent requirements with

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

167

Fig. 4. Illustration of the systematic data collection procedure.

minimum required capital and operational cost. The procedure is iterative; i.e. the SRT and HRT are modified until converging to a solution satisfying all the constraints. Each process interval in the superstructure is structured using a generic model which is illustrated in Fig. 5. The intervals are composed of a number of phenomena namely: mixing of all the flows entering the interval and the utilities added, reaction, separation of flow for internal recycle and sludge wastage, waste separation, flow separation for external recycle and sending the flow to the process intervals of the next step. The mathematical equations defining the intervals are given in Table 1. Using the generic model (Fig. 5, Table 1), the treatment alternatives are described by inputeoutput mass balances. In the mixing equation, all different influent flows containing the same component originating from the previous process intervals to the process interval of interest (from k to kk) are mixed together by using the first equation (1.1) and then the flow after mixing is obtained in equation (1.2) by mixing the flow resulting from equation (1.1) with the utility flow (where 0  ai,kk  1). The utility flow is calculated by the third equation (1.3) (where mi,ii,kk is given as daily mass of utility added/flow of corresponding component). The reaction in the generic interval is defined so that the key reactant is converted to the other components with a given conversion efficiency by using

Fig. 5. Generic process interval structure: mass inputeoutput model.

the utilities added, while maintaining the overall mass balance within the system boundaries of the process interval. The reaction equation (1.4) calculates the flow after reaction; the key reactant is removed with specified conversion efficiency and the other components are produced or removed according to the defined stoichiometry. As shown in Fig. 6, the stoichiometry matrix (gi,kk,rr) is defined by expressing the reactions occurring in a treatment technology. After the design of the treatment technology, the flows of the components after the reaction are known; therefore, the resulting design data are converted into a matrix which the MI(N) LP routine can use by applying equation (2). The next equation (1.5) calculates the flow after waste separation, where any waste stream which is separated from the main flow is defined by a waste split factor. According to our design assumptions, the sludge is wasted out3 ) is from the reaction tank; therefore, the corresponding flow (Fi;kk separated from the main stream before any composition change occurs. The amount of wastage is defined by the ratio SW. The flow is then separated to different outflows with their respective compositions as it happens in the secondary sedimentation tank as well, with a separate thickening factor applied for soluble and out1 ) is particulate components (Spliti,kk). The first outlet stream (Fi;kk the effluent water stream and follows the water stream line, whereas the concentrated stream is separated into two other rec ) and the secondary streams which are the sludge recycle flow (Fi;kk out2 ). The ratio between these two streams is deteroutlet flow (Fi;kk mined by the external recycle ratio. The outlet streams (FXi;k;kk ) are then directed to the other intervals and the direction of the flow leaving the process interval is determined by the binary variable which contains superstructure information (Sk,kk). Its value is equal to 1 if the connection is present and 0 if there is no connection between two intervals. If a process interval is selected by the optimization tool, then the binary variable assigned to it (ykk) is equal to 1, otherwise it is 0. This is only possible by expressing relations between binary and continuous variables, which is done with the activation constraints. Logical cuts, represented by equation (1.12), are included to ensure the selection of only one process interval from a process step, which thus prevents the selection of undesired or infeasible solutions. The last equation (1.13) ensures that the effluent limits are satisfied in the sink intervals for defined

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Table 1 Mathematical equations representing the generic process model in each interval of the superstructure. Phenomena

Equation

Mixing in Fi;kk ¼

Explanations

X

Fi;k;kk

i,ii: Component index k,kk: Process interval index in : Inflow to the process interval Fi;kk Fi;k;kk : Inflow of component i to process kk coming from k mix : Flow after mixing Fi;kk Ri;kk : Utility flow ai;kk : Fraction of utility consumed mi;ii;kk : Specific consumption of utility reac : Flow after reaction Fi;kk gi;kk;rr : matrix representing reaction stoichiometry qreact;kk;rr : Conversion efficiency of the key reactant react w : Flow after waste separation Fi;kk Wi;kk : Waste split factor out1 , F out2 , F out3 : Outlet streams from interval Fi;kk i;kk i;kk Spliti;kk : Flow split factor SWkk : Sludge wastage flow rate ratio rec : External recycle flow rate Fi;kk reckk : External recycle ratio X: 1,2,3 (representing three different outlet flow streams) Sk;kk : Binary variables containing superstructure information ykk : Binary variable describing the process interval xk : Variable bounded by xLO and xUP k k Limi;kk : Effluent limit value of component i

(1.1)

f

mix in ¼ Fi;kk þ ai;kk *Ri;kk Fi;kk

(1.2)

X  mi;ii;kk *Fii;kk

(1.3)

Utility addition Ri;kk ¼

ii

Reaction reac mix Fi;kk ¼ Fi;kk þ

X   gi;kk;rr *qreact;kk;rr *Freact;kk

(1.4)

rr;react

Waste separation

  w reac ¼ Fi;kk * 1  Wi;kk Fi;kk

(1.5)

out1 w Fi;kk ¼ Fi;kk *Spliti;kk

(1.6)

out2 w out1 rec Fi;kk ¼ Fi;kk  Fi;kk  Fi;kk

(1.7)

out3 reac Fi;kk ¼ Fi;kk *SWkk

(1.8)

  rec w out1 ¼ Fi;kk  Fi;kk *reckk Fi;kk

(1.9)

Flow separation

outX *Sk;kk FXi;k;kk  Fi;kk

(1.10)

UP ykk *xLO k  xk  ykk *xk

(1.11)

Activation

Logical cuts

X

ykk  1

(1.12)

kk

Effluent limits Limi;kk 

X

in Fi;kk

(1.13)

f

components. Once the design data of the treatment technologies are converted into model parameters, the generic process interval model is run and validated by using the design data.

gi;kk;rr ¼ 

mix  F reac Fi;kk i;kk mix reac Freact;kk  Freact;kk

! (2)

Step 4: The formulation of the MI(N)LP and its solution take place in the fourth step of the synthesis and design framework, and results in the optimal network, fate of pollutants throughout the

treatment network and the value of the objective function. With respect to the nature of the problem, the optimization problem can result in a linear or non-linear formulation. In this step the MI(N)LP problem is formulated and solved. The models represent the mass inputeoutput model for each process interval, process constraints, structural constraints, effluent limit constraints, cost models together with the objective function. The adapted MI(N)LP formulation for the specific case of a WWTP design/retrofit study is described below. The detailed model is given elsewhere in Table 1.

Min OBJ ¼

X

OPEXkk þ

kk

CAPEXkk t

(3)

subject to; Process model

  h ai;kk ; mi;ii;kk ; gi;kk;rr ; qreact;kk;rr ; Wi;kk ; Spliti;kk ; SWkk ; reckk ¼ 0 Fig. 6. Illustration of the reaction occurring in the process interval and its stoichiometry.

(4)

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

3.1. Problem formulation

Process constraints

  g Sk;kk  0

(5)

Structural constraints

X

ykk  1

169

where y2f0; 1gn

(6)

kk

The optimal wastewater network design problem is then formulated as an MI(N)LP in GAMS (GAMS Development Corporation, 2011) and solved for different scenarios. The optimization model in GAMS consists of an objective function covering both operational (utility cost in terms of aeration, chemical addition and electricity use, landfill cost together with mixing and pumping cost, and income from biogas use) and capital costs (with regard to the size of the units), logical constraints defining the process flow diagram of the solution and process constraints describing the process models of each treatment technology in the superstructure. The formulated MI(N)LP problem was solved by using the DICOPT solver for the non-linear case and the CPLEX solver for the linear case in GAMS software. Step 5: Uncertainty and sensitivity analysis are performed in order to generate robust solutions. It is also important to show that the network is feasible over the whole uncertain domain defined with respect to the uncertain input parameters. For instance, in the wastewater treatment case, the composition of the wastewater is highly uncertain over time and this uncertainty has to be taken into account during design studies. Therefore, in this step the design problem is solved under uncertainty. For the selected parameters, in their defined uncertain domain, Monte Carlo sampling is performed and the stochastic programming problem is reformulated and solved for the different combinations of uncertain parameters resulting from the Monte Carlo sampling (Quaglia et al., 2013). The results are then used for a reliability and robustness analysis of the optimal solution for the treatment process and the resulting process flow diagram.

The problem is defined as treatment of domestic wastewater comprising mainly COD, nitrogen and solids as pollutants. The wastewater composition is shown in Table 2. The objective is to design the WWTP network against the lowest operational (aeration cost, sludge disposal cost, pumping and mixing cost as well as biogas price) and capital cost possible while satisfying the effluent limitations for organic material and nitrogen.

3.2. Superstructure development The superstructure developed for this problem is shown in Fig. 7. It consists of a domestic wastewater source interval (WW) in the source column, and sinks for water, sludge and biogas in the last column. Treatment technologies are located in between the source and the sinks, and include primary treatment, secondary treatment, tertiary treatment, disinfection and sludge treatment as the tasks. The primary treatment consists of a primary sedimentation tank (PC) and a by-pass interval (BP1). In the biological treatment task, there are three technologies (Modified Ludzack e Ettinger e MLE, Oxidation ditch e OxD, and upflow anaerobic sludge blanket e UASB) and a by-pass interval (BP2). The tertiary treatment is mainly responsible for nitrogen rich wastewater treatment and includes the following technologies: partial nitrification (Sharon), partial nitrification and anaerobic ammonium oxidation (SharoneAnammox) and a by-pass interval (BP3). Disinfection technologies comprise different treatments: UV, O3, chlorine and by-pass (BP4). The sludge treatment line on the other hand, consists of sludge stabilization options (AnD-Anaerobic digester, AeD e Aerobic digester) receiving the sludge from a Thickener.

3.3. Data collection 3. Case study: Benchmark wastewater treatment plant To highlight the presentation and application of the superstructure based optimization methodology, a simple yet representative wastewater treatment network problem was defined, with focus on a domestic WWTP layout design. The activated sludge plant defined in the Benchmark Simulation Model no. 2 (Gernaey et al., 2014) was selected, since this plant layout is generally known in the wastewater treatment modeling community.

Table 2 Influent wastewater characterization, average composition (Gernaey et al., 2014). Description

Component

Value

Unit

Soluble inert organic matter Readily biodegradable substrate Particulate inert organic matter Slowly biodegradable substrate Active heterotrophic biomass Active autotrophic biomass Particulate products arising from biomass decay Oxygen Nitrate and nitrite nitrogen NHþ 4 þ NH3 nitrogen Soluble biodegradable organic nitrogen Particulate biodegradable organic nitrogen Alkalinity Flow rate

SI SS XI XS XB,H XB,A XP

27.23 58.18 92.49 363.94 50.68 0 0

g g g g g g g

SO SNO SNH SND XND SALK Q

0 0 23.85 5.65 16.13 7 20,648

g -COD/m3 g N/m3 g N/m3 g N/m3 g N/m3 mol/m3 m3/d

COD/m3 COD/m3 COD/m3 COD/m3 COD/m3 COD/m3 COD/m3

The development of the database for the represented superstructure was done by following the steps of the systematic data collection procedure given in Fig. 4. For illustration purposes, the detailed calculations for a selected process interval (MLE) are given below. Moreover, the calculation steps for all other process intervals can be found in Appendix 1. Data Step 1: The characterization of the wastewater source is taken from the Benchmark Simulation Model no.2 (BSM2) definition (Gernaey et al., 2014) and given in Table 2. The pollutants are represented by Activated Sludge Model no.1 (ASM1) components (Henze et al., 2000). The effluent limits given in the Urban Wastewater Treatment Directive (91/271/EEC) are taken as a reference for the sink intervals. Data Step 2: The technology to be designed is selected as a Predenitrification activated sludge system with low SRT and the configuration is specified as MLE technology. Data Step 3: The SRT and HRT of the system are selected as 14 days and 12 h respectively, whereas the anoxic to aerobic volume ratio is set to 0.6 (Tchobanoglous et al., 2003). All the temperature dependent biokinetic constants needed in the design procedure are taken from the BSM2 (Gernaey et al., 2014) for a temperature of 15  C and given in Table 3. The external recycle ratio is fixed to be 100% of the influent flow rate. Data Step 4: The design is done as follows (ATV design standards, 2000; Tchobanoglous et al., 2003; WEF, 2010; Henze et al., 2008):

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Fig. 7. Benchmark WWTP superstructure.

 The volume of the tanks is calculated by using the aerobic and anoxic HRT values and the influent flow rate Q. Accordingly Vae is calculated to be 5764 m3 and Van is 3459 m3.

Vae ¼ HRTae *Q

(7)

Van ¼ HRTan *Q

(8)

 The amount of solids produced is found by using the following equations, where S0 represents the influent total COD concentration and CN represents the NH4eN to be oxidized in in out (CN ¼ Sin NH þ SND þ XND  SNH  NS with NS being the nitrogen content of biomass). (XBH ¼ 961 g COD/m3, XBA ¼ 182 g N/m3, XP ¼ 833 g COD/m3, XI ¼ 1434 g COD/m3 and XT ¼ 3410 g/m3)

The effluent COD (denoted as S) and ammonia (denoted as NH) are calculated by using the following equations where S ¼ 3.29 g COD/m3 and NH ¼ 0.64 g NH4eN/m3.

XBH ¼

 SRT Yh ðS0  SÞ HRT 1 þ bh *SRT

(11)

Ks *ð1 þ bh *SRTÞ     S¼ an SRT* mh VVtot  bh  1

XBA ¼

 SRT Ya *CN HRT 1 þ ba *SRT

(12)

(9)

XP ¼ NH ¼

KNH *ð1 þ ba *SRTÞ     ae  ba  1 SRT* ma VVtot

(10)

Table 3 Biokinetic parameters (Gernaey et al., 2014). Parameter

Unit

Value

Ya Yh fp KS bh

g cell COD/g N g cell COD/g COD dimensionless g COD/m3 1/d 1/d g NH3eN/m3 1/d 1/d

0.24 0.67 0.2 10 0.3 4 1 0.05 0.5

mh KNH ba

ma

h

  i fp *bh *XBH þ fp *ba *XBA *SRT

(13)

SRT XI ¼ XI0 * HRT

(14)

XT ¼ XBH þ XBA þ XP þ XI

(15)

 Calculations of the amount of oxygen consumed for cell decay (ROb) and nitrification (ROn) are shown below. The variables MXBH and MXBA refer to the total mass of microorganisms in the reaction tank. As a result the oxygen consumption was calculated as 1372 and 3883 kg/d for cell decay and nitrification, respectively.

ROb ¼



       Vae Vae þ 1fp *ba *MXBA * 1fp *bh *MXBH * Vt Vt (16)

ROn ¼ 4:57*Q *CN

(17)

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176 Table 4 Process information for secondary treatment task process intervals. Properties

 DP3 ¼

Process interval

Oxidation Upflow Modified Anaerobic LudzackeEttinger ditch Sludge (MLE) Blanket (UASB)  Temperature ( C) 15 15 15 SRT (days) 14 28 120 HRT (h) 12 24 14 Reactor volume (m3) 9223 18,446 12,956 Settler volume (m3) 3774 3411 e Anoxic/Aerobic volume ratio 0.6 0.6 e 3 3410 3032 18,590 MLSS (g/m ) Wastage flowrate (% influent flow) 3.5 3.5 e Sludge recycle flow (% influent flow) 100 100 e COD removal efficiency (%) 88.4 87.78 68.5 Total N removal efficiency (%) 77.2 78.48 e

   1  fp *ba *MXBH * VVant

Corresponding technology

 The wastage flow rate, which is assumed to be wasted from the reaction tank, (Qw ¼ 658 m3/d) is calculated as follows.

Qw ¼

V SRT

(18)

 In order to find the effluent nitrate concentration, the denitrification potential (DP) is calculated by using the following equations where K2 refers to denitrification rate and was taken as 0.07 g NO3/(g cell COD*d) (Henze et al., 2008). Accordingly DP1 ¼ 8.02, DP2 ¼ 12.78 and DP3 ¼ 15.13 g N/m3 which gives a total denitrification potential (DP) of 35.93 g N/m3 and a nitrate effluent concentration of 10.14 g N/m3. DP1, DP2 and DP3 represent the denitrification potential for readily biodegradable COD, slowly biodegradable COD and biomass respiration, respectively.

  DP1 ¼ DP2 ¼

Ssi *

1 Yh

(19)

2:86 K2 *ðXS  SÞ*Yh *SRTan 1 þ ðbh *SRTÞ

(20)

171

(21)

2:86*Q

DP ¼ DP1 þ DP2 þ DP3

(22)

Seff NO ¼ CN  DP

(23)

Data Step 5: The separation step is designed by defining a thickening factor for the sedimentation part of the separation. These values differ for soluble components and particulate components. Accordingly, 48% of the soluble and 0.2% of particulates by mass leave with the water stream, while the rest is assumed to settle in the sludge zone. The flow equal to the influent flow rate is directed to the influent of the same process interval as the sludge recycle, and the rest is sent to the water effluent line. Moreover, the volume of the sedimentation basin is calculated by assuming specific surface overflow rate (SOR) and solids loading rate (SLR) values as well as a certain depth of the tank from a range given for circular clarifiers (WEF, 2010). In this respect, SOR and SLR values for the system are selected as 1.6 m/h and 130 kg/m2*d, respectively whereas the depth of the clarifier was 4 m. The resulting volume of the sedimentation basin then became 3774 m3. Secondary treatment process alternatives were designed and the features of the processes are summarized in Table 4. For the purpose of validating the systematic data collection procedure used in the case study, the design parameters and performance values of the pre-denitrification activated sludge type of treatment units obtained using the steady-state design model (Eqs. (7)e(23)) are compared with the steady state results obtained from a simulation carried out using a rigorous model, i.e., Activated Sludge Model 1 (ASM1). The simulation with the rigorous ASM1 model was performed in Matlab/Simulink®. The results are presented in Table 5 which indicates that the differences between the estimated removal efficiencies for COD, TN and TSS by the rigorous model (ASM1) and the steady-state design model used in this study were quite small, i.e. the average relative error is less than 1.5%, 5% and 1.5%, respectively. Therefore it is concluded that with the same design values selected (temperature, SRT and HRT), the estimated

Table 5 Validation of systematic data collection procedure. Parameter

Rigorous model (ASM1)

Steady-state design model (this study)

Rigorous model (ASM1)

Steady-state design model (this study)

Corresponding technology Temperature ( C) HRT (h) SRT (days) Anoxic/Aerobic volume ratio

Pre-denitrification activated sludge 15 12 14 0.6

Pre-denitrification activated sludge 15 12 14 0.6

Pre-denitrification activated sludge 15 24 28 0.6

Pre-denitrification activated sludge 15 24 28 0.6

COD (g COD/m3) Influent Effluent Reduction (%)

381.19 47.50 87.54

381.19 44.16 88.42

381.19 46.56 87.78

381.19 42.59 88.83

Nitrogen (g N/m3) Total N influent SNO effluent SNH effluent Total-N effluent Total-N reduction (%)

54.14 11.41 0.17 12.80 76.36

54.14 10.14 0.64 12.32 77.24

54.14 9.95 0.07 11.65 78.48

54.14 7.77 0.39 9.51 82.43

Suspended Solids (g COD/m3) Influent Effluent Reduction (%)

211.27 12.95 93.87

211.27 10.62 94.97

211.27 11.97 94.33

211.27 9.44 95.53

172

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Table 6 Cost information for operational and capital cost items. Cost item

Unit

Value/range

Description/assumption

Electricity consumption of oxygen transfera Typical chlorine demandb Sodium hypochlorite costc Typical ozone demandd Energy requirement for ozonee

kg O2/kwh mg/L euro/kg mg/L kwh/kg O3

1.9e3.2 10e25 0.12 10e15 21e35.2

Electricity costf Landfill costg Biogas priceh

euro/kwh euro/t eurocent/m3 methane

0.0978 107 40.3

US$/m3 US$/m3 US$/m3 US$/m3 US$/m3 US$/m3

425 175 290 375 400 350

Coarse bubble diffusor For activated sludge type plant effluents e e Sum of ozone generation (air feed), ozone contacting and all other uses (on the average) In Denmark for industry In Denmark, on the average In Denmark (assumptions: 1 mol of methane is 24 L and 1 mol of methane accounts for 64 g of COD) Based on the price level of 2006, for 100,000 PE Based on the price level of 2006, for 100,000 PE Based on the price level of 2006, for 100,000 PE Based on the price level of 2006, for 100,000 PE Based on the price level of 2006, for 100,000 PE Based on the price level of 2006, for 100,000 PE

Capital Capital Capital Capital Capital Capital a b c d e f g h i

cost cost cost cost cost cost

e e e e e e

UASBi Aeration tanki Secondary settleri Primary settleri Sludge thickeneri Anaerobic digesteri

Siemens (2009). Tchobanoglous et al. (2003). AWWA Michigan Section (2006). Takahara et al. (2006). Tchobanoglous et al. (2003). URL1 (2013). URL2 (2013). Hahn et al. (2010). Van Haandel and van der Lubbe (2012).

system performance results in terms of removal efficiencies were in agreement with each other and therefore the systematic data collection and design for treatment alternatives is considered to be validated against the more rigorous model. Data Step 6: The objective function represents the total annualized cost (TAC) as shown in Eq. (1) and the optimization problem is formulated to minimize the TAC. OPEX corresponds to the operational cost and is composed of aeration, electricity, chemical addition, pumping, mixing and landfill cost as well as biogas price as an income. CAPEX, on the other hand represents the capital cost and t is the lifetime of the treatment plant. All the cost data are collected from information available in the open literature and summarized in Table 6. Pumping (PE ¼ 0:004Qa þ 0:008Qr þ 0:05Qw Þ and mixing cost (ME ¼ 24*0:005Vi Þ in kWh/d are defined as a function of flow (return sludge e Qr , internal recycle e Qa and sludge wastage e Qw ) and tank volumes e Vi , respectively (Copp, 2002).

3.4. Generic process interval model and MILP formulation One of the most challenging steps in optimization based approaches is the resulting mathematical complexity of formulating and solving the optimization problem. To manage this complexity and facilitate the effective formulation and analysis of the problem, a separation principle was used that separates the database needed for model parameters from MINLP formulation and solution in GAMS. The procedure is explained as follows. Once the data have been collected for all the process intervals, they are stored as matrices in an MS Excel based structure. The data in the matrices are sent to GAMS by using GDX (GAMS Data Exchange) utilities. GDXXRW is used in this respect, which is the utility responsible for reading from and writing to an MS Excel spreadsheet. Once the data are transferred to GAMS, the formulated MILP problem, consisting of the generic equations defined in Table 1, is solved. Note that when a new problem is defined, only the database needs to be changed, while the generic MINLP model can still be used. The data flow and problem formulation (partly as a screenshot) can be seen in Fig. A.1. In Table 7, a summary of the

parameters used in the MILP problem formulation is presented. The maintenance of the database will be ensured by the user by selecting and using the updated model parameters in the model generation step. The optimization methodology allows also including expert knowledge about technology selection by means of logical cuts in the superstructure definition. In this particular case study, since it is known from expert knowledge that selection of a high SRT activated sludge technology (in this case oxidation ditch) together with the anaerobic digestion is not meaningful, this combination is eliminated from the search space by simply inserting a constraint in the problem formulation as y(OxD) þ y(AnD)  1.

3.5. Results and discussion 3.5.1. Optimal process selection The objective of the optimization problem is to select among the treatment alternatives so that the resulting treatment process flow diagram has the minimum TAC and at the same time satisfies the effluent limits given in the Urban Wastewater Treatment Directive (91/271/EEC). The formulated optimization problem is solved by using GAMS (GAMS Development Corporation, 2011) using the solver CPLEX. The details of the solution will be analyzed and discussed in this section for three scenarios corresponding to different objective function formulations. The optimal process selection and the process flow diagram after solution of the model are given in Table 8 for three different scenarios, and the process flow diagram for scenario 1 is illustrated in Fig. A.2. The first scenario takes only the OPEX into account while the other scenarios are based on TAC. In the third scenario a more stringent total N limit is defined for the sink interval. Under the conditions of the first scenario, tertiary treatment and disinfection tasks are by-passed and the water stream is sent to the water sink interval after being treated by the primary clarifier and low SRT MLE system whereas the sludge is stabilized in the anaerobic digester and sent to the sink interval. When the capital cost is also added into the formulation of the objective function (i.e. scenario 2), the network selection does not change; however an

Table 7 Summary table for the data collection. Mixing

ai,kk

mi,ii,kk

Key reactant(s) (react)

Reaction stoichiometry (gi,kk,rr)

Reaction efficiency (qreact,kk,rr)

Sludge wastage (SWkk)

Waste separation (Wi,kk)

Sludge recycle (reckk)

Flow separation (Spliti,kk)

PC

e

e

e

e

e

e

e

e

e

MLE

SO to SS ratio

1

4.09

SS, SNH, XS

100% SS removal 96% SNH removal 97% XS removal

3.5% of incoming flow

e

100% of incoming flow

OxD

SO to SS ratio

1

4.29

SS, SNH, XS

100% SS removal 98% SNH removal 97% XS removal

3.5% of incoming flow

e

100% of incoming flow

48% for solubles and water 0.2% for particulates

UASB

e

e

e

SS

100% SS removal

e

1 for CH4

e

e

SHARON

eSO to SNH ratio eNaOH to SNH ratio SO to SNH ratio

1 1 1

3.14 2.85 1.78

SNH

With respect to SS SS ¼ 1, So ¼ 4.07, XI ¼ 0.77, XBH ¼ 0.6, XBA ¼ 0.19, XP ¼ 0.87 With respect to SNH SNH ¼ 1, SNO ¼ 0.25, XND ¼ 0.03 With respect to XS: XS ¼ 1 With respect to SS: SS ¼ 1, So ¼ 4.27, XI ¼ 0.77, XBH ¼ 0.15, XBA ¼ 0.14, XP ¼ 0.97 With respect to SNH: SNH ¼ 1, SNO ¼ 0.20, XND ¼ 0.03 With respect to XS: XS ¼ 1 SS ¼ 1, SNH ¼ 0.05, XI ¼ 0.002, XS ¼ 2.91, XBH ¼ 0.41, XP ¼ 0.36, XND ¼ 0.15, CH4 ¼ 0.94 SNH ¼ 1, SNO ¼ 0.99, SO ¼ 6.18

99.3% for solubles and water50% for particulates 48% for solubles and water 0.2% for particulates

50% SNH removal

e

e

e

e

SNH

80% SNH removal

e

1 for N2

e

e

Electricity to water ratio

0

15.87

Pathogens

SNH ¼ 1, SNO ¼ 0.137, SO ¼ 2.16, N2 ¼ 1.08 Pathogens ¼ 1

e

e

e

e

Ozone

Ozone to water ratio

0

12.5

Pathogens

Pathogens ¼ 1

e

e

e

e

Chlorine

0 1 e

2.12e17.5

Pathogens

Pathogens ¼ 1

e

e

e

e

AnD

eElectricity to water ratio eChlorine to water ratio e

e

XBH, XBA, XS

e

1 for CH4

e

50% for solubles and 0.7% for particulates

AeD

SO to XBH ratio

1

0.99

XBH, XBA

With respect to XBH: XBH ¼ 1, SNH ¼ 0.07, XP ¼ 0.02, CH4 ¼ 0.81 With respect to XBA: XBA ¼ 1, With respect to XS: XS ¼ 1 With respect to XBH: XBH ¼ 1, SO ¼ 1.35, SNO ¼ 0.07, XP ¼ 0.27 With respect to XBA: XBA ¼ 1

100% pathogen removal 100% pathogen removal 100% pathogen removal 100% XBH and XBA removal 80% XS removal

e

e

e

50% for solubles and 0.7% for particulates

SHARONAnammox UV

100% XBH and XBA removal

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

Treatment process

173

174

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

Table 8 Summary of results for different scenarios. Scenario Objective Total N Selected process flow diagram function limit (mg/L)

Value of objective function (unit cost)

1

OPEX

15

219.051

2

TAC

15

3

TAC

10

WW-PC1-MLE-BP3-BP4Thickener-AnD-DischargeSludge-Biogas WW-PC-MLE-BP3-BP4Thickener-AnD-DischargeSludge-Biogas WW-PC-MLE-BP3-BP4Thickener-AnD-DischargeSludge-Biogas

912.080

912.080

Table 9 Cost summary and performance evaluation for the different scenarios.

Objective function

Unit

Scenario 1

Scenario 2

Scenario 3

e

OPEX & Total N limit of 15 mg/L 229.187 614.191 695.058 e 43.687 27.044 e 219.051 39.16 9.82

TAC & Total N limit of 15 mg/L 229.187 614.191 695.058 e 43.687 27.044 693.029 912.080 39.16 9.82

TAC & Total N limit of 10 mg/L 229.187 614.191 695.058 e 43.687 27.044 693.029 912.080 39.16 9.82

Aeration cost unit cost Landfill cost unit cost Biogas price unit cost Electricity cost unit cost Pumping cost unit cost Mixing cost unit cost Capital cost unit cost Objective function value unit cost Effluent COD g COD/m3 Effluent Total N g N/m3

expected increase in the objective function is observed due to capital cost. In the third scenario, when the effluent nitrogen limit value is lowered down to 10 mg N/L, the optimizer once again selects the MLE technology coupled with primary clarifier to treat the wastewater and anaerobic digester for sludge stabilization purposes. Although the anaerobic treatment alternative of the UASB coupled with the nitrogen rich wastewater treatment alternatives of the tertiary treatment task can satisfy the effluent total nitrogen limit, the UASB alone cannot generate an effluent stream complying with the COD effluent limit criteria when operated at such low temperatures. Experimental work also showed the decrease in the efficiency of the UASB reactor with the decreasing temperature (Lew et al., 2004). Although anaerobic treatment of domestic wastewater has been successfully demonstrated in full scale all over the world, the conclusion here, however, is that in order to comply with the regulations the system should either be operated

at higher temperatures or it should be integrated with effluent polishing steps which are not included in the current superstructure (i.e. facultative ponds, sand filtration, constructed wetlands, trickling filters, physico-chemical treatment and activated sludge treatment) (Henze et al., 2008). Therefore this treatment alternative has not been selected by the optimizer under either of the scenarios as expected from the above-mentioned process engineering expertise. The cost summary and the performance evaluation for the scenarios are presented in Table 9. MLE is favored both for its low operational cost (low utility requirement and high sludge production resulting in high biogas production) and capital cost. The optimizer also gives the flow of components through the selected process flow diagram. The stream table of the components for the solution of Scenario 1 is shown in Table 10, where the flows are given as the flows after reaction in each process interval. By using this information the selected process flow diagram is evaluated in terms of its performance, which is presented also in the summary of the results in Table 9. It can be seen that both COD and total nitrogen concentrations are below the limits set by the regulations (limits for COD and total nitrogen are 100 g COD/m3 and 15 g N/m3, respectively). This analysis shows that the selected process flow diagram is capable of decreasing the concentrations of the key pollutants below the effluent discharge limits while using the minimum amount of utilities. 3.5.2. Solution statistics The model and solution statistics of the problem are given in Table 11. Accordingly, the solution time required for the problem containing 44,445 equations is 0.172 s. 3.5.3. Uncertainty analysis To perform the uncertainty analysis in the context of a process synthesis problem, the following three step procedure is used: uncertainty characterization, uncertainty mapping and decision making under uncertainty. In the first step, the uncertain parameters are identified and a uniform probability distribution is assigned to characterize the

Table 11 Model and solution statistics. Number of variables Number of binary variables Number of equations Objective function Execution time (s) Solver

42,319 20 44,445 1 0.172 CPLEX

Table 10 Scenario 1 stream table.

Q SI SS SO SNO SND SNH XI XS XBH XBA XP XND CH4

Unit

WW1

PC

MLE

BP3

BP4

Thickener

AnD

Discharge

Sludge

m3/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d kg/d

20,648 562 1201 e e 117 492 1909 7514 1046 e e 333

20,648 562 1201 e e 117 492 1.909 7514 1046 e e 333

42,633 1160.382 e 2305.431 341.204 e 22.055 52,521.861 116.229 34,557.848 6344.526 29,234.094 5167.206

20,553 559.420 e 1111.448 164.494 e 10.633 105.044 0.232 69.116 12.689 58.468 10.334

20,553 559.420 e 1111.448 164.494 e 10.633 105.044 0.232 69.116 12.689 58.468 10.334

763 20.771 e 41.267 6.108 e 0.395 1811.664 4.009 1192.022 218.845 1008.387 178.235

190 5.159 8.407 2.435 0.360 e 126.268 2743.809 752.192 e e 1031.705 342.536 4599.228

20,553 559.420 e 1111.448 164.494 e 10.633 105.044 0.232 69.116 12.689 58.468 10.334

95 2.580 4.203 1.217 0.180 e 63.134 2724.602 746.927 e e 1024.483 340.138

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

uncertainty range. The resulting distribution parameters such as the minimum, the maximum and the mean values are recorded in the database. The uncertain domain is then sampled using the Latin Hypercube Sampling technique. In the Benchmark WWTP case study, the uncertain parameters are chosen as the cost related parameters (oxygen transfer efficiency, electricity price and landfill price), effluent total nitrogen limits and influent wastewater characterization. The details of the uncertain domain definition and sampling can be found elsewhere (Bozkurt et al., 2014) and the table showing uncertain parameters and their domain is shown in Appendix 2. In the second step, the optimization problem was solved for 50 scenarios generated in the preceding sampling step. The analysis of the optimization results indicated that two different WWTP networks were identified as optimal with different frequencies (see details in Table 12). The cumulative distribution of the objective function is illustrated in Fig. 8 where the x-axis shows the objective function value, which represents operational and capital cost, and the y-axis represents the probability that the value of the objective function will be lower than the stated value on the x-axis. This indicates that there is a significant uncertainty on the treatment cost (the objective function) which ranges from 693 to 1606 unit cost. Compared with the deterministic solution case given in Table 9, it can be seen that 78% of the scenarios result in higher objective function values and in 16% of the scenarios, a different network configuration is selected. Although the output from the uncertainty analysis very much depends on the defined domain of input uncertainties (step 1), this comparative analysis already indicates the significance of considering uncertainty analysis for better informed decision making, at least compared to one-point analysis (the case of the deterministic solution). In the last step of the uncertainty analysis, the optimization problem is formulated as a stochastic programming problem and solved using the sample average approximation (SAA) technique (Birge and Louveaux, 1999). The selected WWTP network and the cost breakdown for the solution under uncertainty are given in Table 13. In order to summarize the results of the uncertainty analysis, several indicators are defined (Quaglia, 2013): Expected value of perfect information (EVPI), value of stochastic solution (VSS) and uncertainty price (UP). The EVPI represents the expected increase in the objective function resulting from uncertainty. When EVPI is large (as compared to the value of the objective function), the designer is expected to work more on the design phase; a low EVPI, on the other hand, indicates that the current design can further go through the development funnel (Fig. 1). In the particular case study the EVPI is calculated as 39.833 (4.36% of the deterministic value of TAC).

EVPI ¼ minðEq ðf ðx; y; qÞÞÞ  Eq ðminðf ðx; y; qÞÞÞ

(24)

In the VSS calculation, the difference between the performance of the selected network (in the deterministic solution) under uncertainty conditions and the solution of the problem under uncertainty is calculated. The calculated VSS value for the Benchmark Table 12 Uncertainty mapping results. Network

Probability of realization

Selected intervals

1

84%

2

16%

WW-BP1-MLE-BP3-BP4-Thickener-AnDDischarge-Sludge-Biogas WW-BP1-UASB-Shar-An-BP4-BP5-DischargeSludge-Biogas

175

Fig. 8. Cumulative distribution of the objective function.

Wastewater Treatment Plant case study is 0 because the network selection did not change under uncertain conditions (solution under uncertainty).

VSS ¼ Eq ðf ðxdet ; ydet ; qÞÞ  minðEq ðf ðx; y; qÞÞÞ

(25)

Finally, the UP indicates the cost of uncertainty by calculating the difference between the objective function values of the solution under uncertainty and the deterministic solution. It was calculated as 229.246 for the case study under consideration.

UP ¼ minðEq ðf ðx; y; qÞÞÞ  minðf ðx; yÞÞ

(26)

The calculated EVPI value is very low as compared to the objective function value of the deterministic solution which indicates that the optimizer did not identify a better solution in the design space. Hence this means that the current network selection is mature to go further through the project development stages (Fig. 1). The VSS value is found to be 0; since both stochastic and deterministic formulation ended up in the same network solution, the performance is the same and therefore the difference is 0. The UP on the other hand, is relatively high, 25% of the deterministic objective function value itself, which indicates that the uncertainties inherent in the operation of the plant namely wastewater composition and load will likely increase the operation cost of the project by that much within the project lifetime. Therefore, by considering all these indicators, and especially the UP indicator, the user can conclude that the uncertainty in the model parameters affects the performance of the selected process network significantly and the uncertainty should be reduced in order to achieve a more optimal design decision. If uncertainties affecting the system

Table 13 Summary of SAA results. Network Aeration cost Landfill cost Biogas price Electricity cost Pumping cost Mixing cost Effluent penalty Capital cost Objective function value

WW-PC-MLE-BP3-BP4-Thickener-AnDDischarge-Sludge-Biogas 461.773 615.289 699.496 e 43.687 27.044 e 693.029 1141.326

176

H. Bozkurt et al. / Environmental Modelling & Software 64 (2015) 164e176

cannot be decreased, e.g. by improving the available wastewater characterization through a long term measurement campaign, then one can consider designing a flexible network which is a solution that is addressed elsewhere (Quaglia et al., 2013). 3.5.4. Future perspectives of the mathematical programming framework Current work focused on presenting the underlying foundations, theory and practical implementation of the methodology using an illustrative example. Future work will consider (a) expanding and updating the superstructure database of technologies; (b) including resource recovery technologies for the WWTP; (c) adding greenhouse gas emissions estimations in addition to the energy consumption and production for sustainability analysis etc.; and, (d) consideration of technical uncertainties such as key performance parameters (yield, conversion, etc.) to make decision making more robust (Sin et al., 2011; Quaglia et al., 2013). Therefore as well, the expanded tool is expected to be an enabling technology for design engineers for early stage idea generation and comparison of the treatment technologies at their optimality, and for selection of the best among the alternatives with respect to the desired criteria from the WWTP network (i.e. low cost, low energy consumption, nutrient recovery, complying with the effluent limitations, robustness etc.). 4. Conclusions A superstructure based optimization methodology has been developed to support optimal treatment process selection which is a critical and challenging step in the early stage of wastewater treatment plant design. A novel framework to help effective formulation and management of the complexity of the optimization problem is developed. The underlying theory and mathematical concepts, the required methods for its solution and analysis and its practical implementation as a tool is presented, using the BSM1 as an illustrative case study. For the design space, the superstructure method is used representing several process alternatives, which are mathematically described using a generic process model, to enable the user to compare them in an optimization context. The database consisting of all the necessary parameters for the generic process models is developed for each alternative in the superstructure and validated against a more rigorous model (ASM1). The deterministic solution resulted in different objective function values for different scenario definitions; however, when the data uncertainty is taken into account considerable variations in the network performance and objective function value were observed. The tool is expected to support and facilitate generation and evaluation of ideas for identifying optimal solutions to design and retrofitting of WWTPs. Future work will focus on further expansion of the superstructure and its database (with MBR, SBR, sludge reject water stream treatment alternatives, etc.), as well as on treatment of uncertainties in the optimization based design of wastewater treatment plants. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.envsoft.2014.11.023. References Alasino, N., Mussati, M.C., Scenna, N., 2007. Wastewater treatment plant synthesis and design. Indust. Eng. Chem. Res. 46, 7497e7512. Alasino, N., Mussati, M.C., Scenna, N., Aguirre, P., 2010. Wastewater treatment plant synthesis and design: combined biological nitrogen and phosphorus removal. Indust. Eng. Chem. Res. 49, 8601e8612.

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