Introduction ORIGINAL PAPER. Amro A. El-Baz Æ M. Kamal T. Ewida M. Abbas Shouman Æ Mahmoud M. El-Halwagi

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1 Clean Techn Environ Policy (2005) 7: DOI /s ORIGINAL PAPER Amro A. El-Baz Æ M. Kamal T. Ewida M. Abbas Shouman Æ Mahmoud M. El-Halwagi Material flow analysis and integration of watersheds and drain systems: II. Integration and solution strategies with application to ammonium management in Bahr El-Baqar drain system Received: 27 March 2004 / Accepted: 7 September 2004 / Published online: 27 November 2004 Ó Springer-Verlag 2004 Abstract The objective of this paper is to develop a systematic methodology for mass integration in drain systems and watersheds. Mass integration is a holistic approach to the tracking, transformation, and allocation of species and streams. The watershed and drain system is first discretized into reaches. The MFA model developed in part I of this work (Simulation and Application to Ammonium Management in Bahr El-Baqar Drain System) is used to describe the environmental phenomena that affect the fate and transport of targeted species and the operators that characterize the system inputs and outputs as they relate to the surroundings. Next, we develop an integration framework which encompasses sources, sinks, and interception technologies to aid in the development for nitrogen-management strategies. The simulation model was transformed into a synthesis model by introducing optimization variables and including models for the potential management strategies. The problem of minimizing negative environmental impact subject to technical, social, economic, and regulatory constraints was posed as a nonlinear optimization program whose solution identified and synthesized the most effective solution strategies. These mathematical models and management strategies were coded into a computer-aided tool using LINGO programming platform. The program can be readily modified to address a variety of cases. Tradeoffs and sensitivity analysis were established using the devised model. The devised framework was applied to an Egyptian drain system M. M. El-Halwagi (&) Department of Chemical Engineering, Texas A&M University, College Station, TX , USA el-halwagi@tamu.edu A. A. El-Baz Æ M. K. T. Ewida Environmental Engineering Department, Faculty of Engineering, Zagazig University, Egypt M. A. Shouman College of Computers and Informatics, Zagazig University, Egypt (Bahr El-Baqar) along with the outfall to Lake Manzala. The results of the case study provide solution strategies for nitrogen management along with their technical, economic, and environmental implications. Introduction Watersheds and drains are complex environmental systems. They involve many phenomena and operators. In Part I of this work, we have introduced a material flow analysis MFA approach to provide the foundation for a mathematical model characterizing the interaction of the watersheds and drain systems with the surroundings (e.g., population centers, agricultural sector, industrial plants, etc.), the effect of transfer functions, the various transport phenomena, and the flow of water and targeted species over tributaries and reaches. Notwithstanding the usefulness of the MFA model, it is only an analysis tool. In order to develop solution strategies, MFA must be tied to a synthesis tool that can screen the alternatives and identify the optimum solutions. Towards this end, mass integration can provide an effective framework to develop solution strategies for watersheds and drain systems. Over the two decades, mass integration has developed as a comprehensive methodology for the management of pollutants and water resources in industrial plants (e.g., Dunn and El-Halwagi 2003). Because of its potential extension to management of water and pollutants in drain systems and watersheds, we review its basic aspects. Mass integration is a holistic approach to the generation, separation, and routing of species and streams throughout a system. It is a systematic methodology that provides a fundamental understanding of the global flow of mass within the process and employs this understanding in identifying performance targets and optimizing the allocation, separation, and generation of streams and species. Various process objectives such as yield enhancement, debottlenecking, resource

2 79 conservation, and pollution prevention can be systematically tackled through mass integration. For an overview of the subject, the reader is referred to review literature (e.g.; El-Halwagi 1997; El-Halwagi and Spriggs 1998; Dunn and El-Halwagi 2003). Problem statement The problem to be addressed in this paper can be stated as follows: Consider a drain system with its tributaries and reaches. Point and non-point discharges to the system include several sources such as agricultural drainage, treated and untreated wastewater, industrial effluents, and precipitation. System outflows include discharge to lakes and waterways, official and unofficial use for agricultural and other purposes, seepage, and vaporization. Chemical and biochemical reactions are expected to take place within the system and will lead to species depletion or generation. The system surroundings include residential, agricultural, and industrial entities that affect the inputs and outputs to the drainage system. The system is mathematically characterized by a material flow analysis (MFA) model which tracks the flows of water and targeted chemical species in the system (described in Part I of this paper). The MFA model accounts for the relevant input, outputs, chemical/biochemical reactions, and interconnections with the surroundings. The theoretical track of this paper is aimed at the following: Development of a mathematical programming (optimization) mass integration model for system synthesis and management. The developed model will provide the right level of details and will incorporate key optimization variables. It will also involve a superstructure for the system which embeds all solution strategies of interest. Transformation of the mass integration model into a computer-aided program and numerical solution of optimization problems. Systematic screening and prioritization of the various management strategies. To demonstrate the usefulness and applicability of the developed theoretical framework, focus will be given to the simulation and management of nitrogen in Bahr El-Baqar drain system in Egypt. Theoretical development and mathematical formulation In order to develop management strategies, it is necessary to coordinate two important activities in tandem: material (mass) integration and material flow analysis and simulation. As shown in Fig. 1, simulation can only provide tracking of water and nitrogen for a prescribed system configuration. It cannot devise management strategies unless several management scenarios are MFA & Water Quality Modeling hypothesized and simulation is used to predict their consequences. Unfortunately, for a typical management problem, there are numerous (in some cases infinite) alternatives. First, there are many combinations of the management technologies (e.g., how many treatment units should be used? Where should they placed? Any hybrid systems of more than one type? In what order?). Furthermore, because of the need to optimize continuous variables (e.g., load to be removed in each management technology); there can be a tremendous number of possibilities. Finally, the need to optimize an objective function (e.g., minimize cost or environmental impact) can complicate the search process. Therefore, simulation tools are well equipped to handle the task of evolving solution strategies. The answer to the above challenges facing simulation is through mass integration and synthesis. The integration and synthesis approach does not presuppose the configuration or tasks of the management strategies. It also allows for any combination of technologies to be used simultaneously, and it searches over the infinite possibility to extract the optimum solution strategy. Mass integration techniques can handle objectives, data, and any requirements or constraints. The application of mass integration provides performance targets, solution strategies, and proposed changes to the system. As a result of these changes (e.g., in flowrate and composition), the system performance must be reassessed using analysis or simulation (such as the MFA modeling equations developed in Part I of this paper). The use of MFA model enables the update of flowrates and compositions throughout the system. By closing the information loop of integration and analysis, it is ensured that the developed insights and solution strategies activities are refined and validated. The first step in creating a mass integration model is the development of an appropriate mathematical model. Consider the MFA simulation model developed in Part I of this paper. It can be described by a set of equations that take the general form: Tracking equations: Flow & Load Propagation, input-output Relations, reach-by-reach accounting Recommended Strategies Fig. 1 Synergism between mfa and material integration Material Integration ðl u ; y u Þ ¼ w u ðl u 1 ; y u 1 ; z; s; pþ ð1þ

3 80 where L u and y u are the flowrate and ammonium concentration at any location u. These are the output variables. The vectorial function w u establishes the relation form with the flowrate and composition of the location, input variables ( z), the state variables ( s) and the intensive variables of the model ( p). MFA transfer functions (operators) The input to the water system is actually outputs from the surroundings through the transfer function given by: z ¼ Uðx v jv 2 SurroundingsÞ ð2þ where x v is the vector of input variables from the surroundings. The reader is referred to Part I of this work for a listing of the various inputs and operators. Constitutive equations These equations relate the state variables to the intensive variables p (e.g., relating equilibrium distribution of ammonia to ammonium via temperature and ph): s ¼ XðpÞ ð3þ The equations for tracking, MFA operators, and constitutive equations were described in Part I of this work. In order to develop management strategies, we use an optimization-based synthesis and integration framework. The general formulation for the integration program is expressed as: min (or max) f(x) ð4þ where x T =[x 1,x 2,...,x N ] is the vector of optimization variables Subject to inequality and equality constraints: g(x)60 ð5þ where g T =[g 1,g 2,...,g m ] h(x) ¼ 0 ð6þ where h T =[h 1,h 2,...,h E ] The inequality constraints will include environmental discharge limitations (or targets) as well as logical constraints for feasibility. The equality constraints will include a revised version of the model equations developed in Part I of this paper to enable the search of optimal values for input variables. Therefore, these equations will be revised to: ðl u ; y u Þ ¼ w u ðz; s; p; z; s; pþ ð7þ where z, s, p are to be optimized and z; s; p are left constant. The same is carried out for optimizing outputs from the surroundings through the MFA transfer function: ðz; zþ ¼ Uðx v ; x v jv 2 SurroundingsÞ ð8þ The building blocks for candidate management strategies include optimization of water reuse, enhancing performance of existing infrastructure, and installation of new infrastructure (e.g., WWTPs). For reuse decisions, we adopt a source-sink representation. Sources can be defined as any stream that can be reused (e.g., water for irrigation) in it and sinks are any system than can accept the source (e.g., agricultural area). Each source, q, has a flowrate denoted by L q and N components is the number of species (e.g., ions, organics, etc.) in the stream. The composition of each species is referred to as y u,comp. The overall objective of reuse via mass integration is to provide maximum utilization of water and ammonium while satisfying all system requirements and constraints. In other words, what is the best scheme to allocate the water and deal with species? As can be seen in Fig. 2, mass integration seeks to identify optimum allocation of water streams from sources to sinks. The integration strategies include segregation and mixing of streams, assignment to sinks, and adjustment of species content using interception (e.g., wastewater treatment, engineered wetland) devices that employ mass and energy separating agents. Therefore, the species interception network (SPIN) corresponds to the infrastructure (e.g., treatment, aeration, wetland, separation) that must be added to intercept tributaries and reaches and adjust their characteristics (e.g., composition). The following analysis shows how these solution strategies can be developed. Consider a number N sinks of ecological sinks that require water which are designated by the index v, where v ranges from 1 to N sinks. For the v th sink, there are two sets of constraints on flowrates and compositions: Wv min 6W v 6Wv max v ¼ 1, 2,...,N sinks ð9þ where W v is the water flowrate entering the v th sink. Y min v;comp 6Y v,comp6y max v;comp v ¼ 1,2,...,N sinks and comp ¼ 1,2,...,N components Sources Segregated Sources Species Interception Network (SPIN) Sinks #1 #2 N sinks ð10þ Sources (back to System) Fig. 2 Mass integration framework for species interception (El-Halwagi et al. 1996)

4 q th Source L q To source q+1 L q, q+1 l q, 1 l q, v l q, Nsinks Sinks v=1 v 81 interception devices to reduce the concentration of the targeted species. This situation is important when no capital investment is to be spent on new equipment. The structural representation of this no/low cost strategy is shown in Fig. 5. Each split flowrate l q,v does not have to perfectly match the sink requirement. It can be mixed with other split flows or water to match the sink requirements. This mixing (represented in Fig. 4) must satisfy the sink constraints given by Eqs. (9) and (10). The following constraints represent the material balances associated with the splitting and mixing operations: Splitting of the q th source: v=n Sinks L q ¼ L q;qþ1 þ XN sinks v¼1 ð11þ Fig. 3 Splitting of sources where Y v,comp is the composition of a certain species entering unit v. We now move to the source side. Since not all streams may be rerouted, we use the index q for the sources to be rerouted while we use the index u for all the sources. Each source, q, is split into N sink fractions that can be assigned to the various sinks (Fig. 3). The flowrate of each split is denoted by l q,v. The remaining convective flow of the source L q,q+1 proceeds to the next reach or tributary (q+1). Next, we examine the opportunities for mixing these splits and assigning them to sinks. Figure 4 shows the mixing of the split fractions into a feed to the v th sink. No/low cost strategies via direct recycle/reuse It is instructive to first consider direct recycle/reuse of wastewater streams. This refers to the allocation of wastewater streams to process units without the use of where q=1,2,..., N sources Mixing for the v th sink: N W v ¼ FreshW v þ X sources ð12þ where v=1,2,..., N sinks where FreshW v is the amount of fresh water fed to the v th sink. N W v Y comp;v ¼ X sources y q;v;comp ð13þ where v=1, 2,..., N sinks and comp=1, 2,..., N components In order to solve the above-mentioned assignment problem systematically, it is useful to formulate the task as an optimization problem. A theoretical model is formulated based on the structural representation of the problem to account for mass balances and assignment of sources to sinks. The objective function may take different forms. For instance, it may be desired to minimize the discharge load at the outfall. In this case, the objective function can be expressed as: l 1,v Sources Sinks y 1,v,comp Source q= 1 v=1 l q,v y q,v,comp W v Y v,comp v th Sink Source q= 2 v=2 v Source q= N sources l N sources,v y N sources,v,comp Fig. 4 Mixing of split fractions and assignment to sinks Fresh water v=n sink Fig. 5 Direct recycle/reuse source-sink assignment problem (no/ low cost solution)

5 82 Minimize the discharge load of targeted species at the outfall via direct recycle= Q outfall y outfall ð14aþ Another objective can be to maximize the reuse of water. In such case, the objective function can be mathematically represented as: Maximize the reuse of water via direct recycle= XN sinks N Sources v¼1 X ð14bþ This objective function can be readily modified to accommodate other objective functions such as maximum use of targeted species (e.g., ammonium) which implies minimum drained load. In such cases the objective function can be described as: Maximize the reused load of targeted species via direct recycle= XN sinks N Sources v¼1 X y q;v;comp ð14cþ The objective function is subject to the following constraints: Flowrate to each sink Wv min 6W v 6Wv max v ¼ 1, 2,...,N sinks ð15þ where W v is the water flowrate entering the v th sink. Y min v;comp 6Y v;comp6y max v;comp v ¼ 1,2,...,N sinks and comp ¼ 1,2,...,N components Splitting of the q th source: L q ¼ L q;qþ1 þ XN sinks v¼1 where q=1, 2, N sources Mixing for the v th sink: N W v ¼ FreshW v þ X sources ð16þ ð17þ ð18þ where v=1, 2, N sinks where FreshW v is the amount of fresh water fed to the v th sink. N W v Y comp;v ¼ X sources y q;v;comp ð19þ where v=1, 2, N sinks and comp=1, 2, N components Non-negativity of each fraction of split sources: >0 ð20þ where n =1, 2, N sources and v=1, 2, N sinks The MFA model to keep track of the changes throughout the system as a result of direct recycle/reuse: ðl u ; y u Þ ¼ w u ðl u 1 ; y u 1 ; z; s; pþu 2 Set of tributaries and reaches ð21þ The solution to this optimization program provides the optimum value of the objective function as well as details on the best allocation of sources to sinks and the revised MFA model as a result of the direct recycle/reuse strategies. Interception strategies Once the low/no cost strategies have been exhausted, additional management strategies will entail capital investment to install interception devices (e.g., wastewater treatment, engineered wetlands) to reduce the load of the targeted species. Several important design questions need to be addressed including: - Which interception technologies should be used? - Where should these interceptors be located? - What is the task of each interceptor (e.g., how much load reduction should each interceptor achieve?)? - How does the interception of one source relate to the rest of the system? The abovementioned questions are highly combinatorial in nature and require a systematic way to screen the numerous alternatives and generate the optimum solution. Furthermore, since the various sources are interconnected and will be affected when interception is undertaken, it is necessary to include a simulation model (e.g., MFA) to track the changes for the targeted species throughout the system. This is consistent with the philosophy summarized by Fig. 1. Hence, we include the MFA equations developed in Part I of this paper. We start by developing the representation of the interception system. Figure 6 is a schematic representation of the sources at different locations and the Species Interception Network int y u 1 u+1 y u 1 u+1 int y u y u Fig. 6 Representation of interception to streams Location u+1 Location u

6 83 species interception network. Each source, u, may be intercepted to adjust its composition of the targeted species from y u to the intercepted composition of yu int: Hence, the MFA model summarized by the vectorial Eq. (1) can be used to track the effect of interception as follows: ðl u ; y u Þ ¼ w u L u 1 ; y int ; z; s; p u u 1 2 Set of tributaries and reaches ð22þ For each stream u, the cost of interception technology, r, is referred to as Cost r,u. This cost is a function of flowrate, nominal (supply) composition and intercepted (target) composition. Hence, we can describe it as Cost r;u L u ; y u ; yu int : In order to determine whether or not an interceptor, r, is used for a stream u, we use the binary integer variable I r,u whose value is defined as follows: I r;u ¼ 1 if interceptor r is used for stream u ð23aþ I r;u = 0 if interceptor r is not used for stream u ð23bþ Therefore, the objective function for minimizing the cost of interception can be described as: Minimize cost of interception ¼ X X I r;u Cost r;u L u ; y u ; y int u ð24þ r u In the case of a hybrid system (more than one interception technology applied to the same source), the reader is referred to El-Halwagi et al. (1996) for the synthesis of an interception network. In addition to the aforementioned constraints, it also necessary to include a constraint specifying the desired discharge load or concentration of the targeted species at the outfall, i.e. y outfall 6youtfall desired ð25þ The solution to this mixed integer nonlinear program (MINLP) provides the minimum cost management solution which meets the desired discharge limits. It also determines which interception technologies should be used, where they should be applied, and what their tasks should be. Targeting of minimum discharge load It is beneficial to benchmark the performance of the system aside from cost constraints. In this context, an important question is for a given set of interception technologies applied to specific streams, what is the minimum discharge load of the targeted species at the outfall? This question can be readily answered by modifying the developed mathematical formulation. First, we use the concept of minimum interceptable composition, yu int;min : It corresponds to the maximum possible performance of the interception technology to reduce the intercepted composition of the targeted species in stream u. By revising the MFA model with minimum interception composition and defining the objective function as minimum load at the outfall, we get: Minimize discharge load at the outfall ¼ Q outfall y outfall;comp ð26þ Subject to the revised MFA model: ðl u ; y u Þ ¼ w u L u 1 ; y int;min ; z; s; p u u 1 2 Set of tributaries and reaches ð27þ The solution to this optimization program provides the minimum discharge load that can be achieved regardless of cost. It also described the revised MFA as a result of maximum interception using specific interceptors applied to specific streams. This targeting exercise is important in setting insightful benchmarks for the achievable discharge loads. Case study: Bahr El-Baqar drain system leading to Lake Manzala As mentioned in the problem statement, the management of ammonium ions in Bahr El-Baqar drain system and watershed associated with Lake Manzala will be used to illustrate the applicability of the developed mathematical procedures. Bahr El-Baqar drain in Egypt is one of the largest drain systems east of the Nile delta contributing almost 45% of the total discharge of Lake Manzala. In turn, Lake Manzala discharges into the Mediterranean Sea. Lake Manzala, northeast Nile delta, Egypt, has an area of about 1,000 km 2, an average depth of 1 m, and yields about 35% of Egypt s aqua cultural production (40,000 metric t). The data for the case study as well as results of simulation are given in Part I of this paper. In applying the developed management procedures to Bahr El-Baqar case study, two interception technologies will be considered: wastewater treatment and engineered wetland. Both are considered because of the commercial maturity. Other technologies can be easily added once their techno-economic aspects become well documented and competitive. Three streams are targeted for interception based on their loads: the combined discharge from El-Gabal El-Asfar and El-Berka, the stream from Balaqs treatment unit, and the cumulative stream preceding the outfall. The following data and assumptions are used: 1. The removal efficiency of the wetland for the ammonium was considered 58% (VKI 1995). 2. The cost function for the wetland was based on the pilot project for the wetland near Lake Manzala

7 84 (25,000 m 3 /day for $4 million). Hence, the cost of wetland was taken as a function of the flowrate as follows: Cost Wetland ¼ 13.8 Q Wetland where the cost of wetland is given in millions of US dollars and the flowrate to the wetland is in m 3 /s. This expression is based on extrapolating cost data of a current pilot project by the Egyptian Environmental Affairs Agency (EEAA). (El-Saadany 2003). 3. The capital cost (in US dollars of treated wastewater) of the additional wastewater treatment units for the is taken as 300*Q Treated *N Treatment where Q Treated is the volumetric flowrate (m 3 /s) of the treated wastewater and N Treatment is the number of treatment stages to be added in series. This expression is based on the data of Bixio et al. (2001) for retrofitting projects. The cost function compares well with the reported cost of the expansion project for El-Gabal El-Asfar WWTP which cost $400 million to process 0.5 million m 3 /day. It is assumed that about a third of that cost is allocated to denitrification. The combined flowrate of the total stream from El-Gabal El-Asfar and El-Berka is about 1.5 million m 3 /day. Hence, the cost of an additional unit to treat the combined flow of El- Gabal El-Asfar and El-Berka is about $400 million. Additional treatment units are assumed to be placed in series with the nitrification reaction taking place in a CSTR whose residence time and reaction kinetics match the one in El-Gabal El-Asfar. For the CSTR with first-order kinetics, C out ¼ 1 ð28þ C in 1 þ ks Hence, for N Asfar stages in series the outlet ammonium concentration can be calculated as 1 ð1 þ ksþ N ð29þ Asfar It is worth noting that for the current operation of El- Gabal El-Asfar, the values of C out and C in are 10 and 40 ppm of ammonium, respectively. Hence, the removal efficiency is 75%. Targeting for the case study As mentioned earlier, it is useful to benchmark the performance of the system by identifying the minimum discharge load of the targeted species at the outfall. If we choose low/no cost strategies, WWTP technologies that can be applied to El-Gabal El-Asfar and El-Berka wastewater as well as Balaqs s wastewater, and engineered wetland before the outfall of Lake Manzala, we use the concept of minimum interceptable composition, y int;min u for each technology and designate it to be full removal for the WWTP and the wetland operating at maximum allowable flowrate of 15 m 3 /s with removal efficiency of 58% (VKI 1995). By revising the MFA model with minimum interception composition and defining the objective function as minimum ammonium concentration at the outfall, we get the solution to be 1.95 ppm of ammonium at the outfall to Lake Manzala. Since before the management strategies, the concentration at the outfall is 4.25 ppm, the target indicates a potential reduction of 54% in the ammonium concentration at the outfall. Low/no cost strategies and maximum utilization of existing infrastructure Prior to spending capital on new infrastructure, it is necessary to maximize the performance of existing infrastructure so as to develop no/low cost strategies. Until recently, the wastewater treatment plant of Shoubra El Kheima (Balaqs) was working only as a primary treatment only but the secondary stage was under construction. Moreover the operation of secondary stage will result in an effluent of ammonium concentration of 10 mg/l rather than 35 mg/l as primary effluent. Hence, using this facility to its maximum capability will reduce ammonium discharge. Additionally, there are reuses pumping stations on the last reaches of Bahr El-Baqar drains. Maximizing the reuse out of these stations while using the current infrastructure will decrease the ammonium load to the Lake. Finally, the Egyptian Ministry of Housing has established several new facilities for wastewater treatment plants along the drain and up to Lake Manzala. Maximizing the use of these facilities will reduce the ammonium discharge. It was assumed that these facilities can treat wastewater down to 17 ppm. The aforementioned strategies were fed as inputs to the MFA simulation model to simulate the discharge at the outfall as a result of these strategies. The result showed that by applying these strategies the concentration of the outfall will decrease from 4.25 to 3.09 ppm of ammonium at the outfall to Lake Manzala. Interception strategies As mentioned before, we will consider commercially available technologies for the interception of wastewater streams to reduce ammonium concentration. In this regards, we consider WWTP for the wastewater streams of El-Gabal El-Asfar and El-Berka as well as the wastewater stream from Balaqs. Additionally, we consider an engineered wetland before the outfall to Lake Manzala. For each targeted level of discharge, we can solve the cost minimization program described earlier using LINGO to determine the minimum interception cost needed to achieve the designated discharge level. The results of the optimization study are shown in

8 85 Cost in dollars 1.20E E E E E E E Ammonium concentration at the outfall Fig. 7 Cost of reduction in ammonium concentration at the outfall Fig. 7. As can be seen, the existing infrastructure for pumping stations, reuse, and WWTP can reduce the concentration at the outfall from 4.25 to 3.09 without additional investment. However, in order to reduce the ammonium at the outfall, the cost increases as a function of the discharge concentration until it reaches $1,078 million to reach 2.0 ppm of ammonium at the outfall. Figures 8 and 9 provide additional insights on the load to be removed using each interception strategies versus the outfall concentration and reduction in discharge load of ammonium at the outfall. It is interesting to note that because of the complex nature of the system, the load removed at the different interception devices is not equal to the load reduction at the outfall. Reactive transformations of ammonium to other nitrogenous forms throughout the system contribute to such differences. As mentioned earlier, the developed framework is of general nature and the cost and performance data for the interception technologies can be easily changed or expanded to explore other scenarios and technologies. Conclusions Mass integration techniques were developed to provide a holistic basis for the screening and optimization of the various management strategies. A superstructure was developed to represent all plausible strategies of interest. The strategies include combinations of reuse, operation of current wastewater plants under construction, advanced wastewater treatment facilities and engineering wetland. A source-interception-sink representation was adopted to provide a mathematical basis for tracking mass while incorporating the effect of the candidate strategies. In addition to the structural representation constraints, the MFA simulation model was transformed into a synthesis model by introducing optimization variables and including models for the potential management strategies. Other constraints included technical limitation, regulatory mandates, and socioeconomic aspects. The result was a mixed-integer nonlinear programming formulation that can be solved to address a variety of objectives (e.g., environmental impact, cost, etc.) while identifying the most effective management strategies. The integration model can also be used to identify environmental global targets without commitment to specific solution strategies. Mass integration techniques were developed for the system. Mass tracking, allocation, and interception were included. Fig. 8 Total load removed from the interception units at the via different concentrations at the outfall Load removed from interception units (gm/sec) Ammonium concentration at the outfall (mg/l) Load removed from interception el Gabal Load removed from interception Balaqs Load removed from Wetlands Total load Fig. 9 Total load removed from the outfall with the load removed from the interception units load removed from the interception units (gm/sec) Load removed from the outfall (gm/sec) Load removed from interception el Gabal Load removed from interception Balaqs Load removed from Wetlands Total load

9 86 Also, management strategies along with their associated costs were incorporated into the superstructure. A nonlinear programming formulation was coded into LINGO platform. The integration model was used to develop management strategies to control the discharge of ammonium into Lake Manzala. The solution strategies were ranked in order of cost. The solution starts by effective utilization of existing infrastructure such as the operation of the secondary stage at Balaqs, the operation of the WWTP in cities along the drain, and the maximization of reuse from the existing reuse pump stations. Next, the solution strategies include the construction of advanced wastewater treatment units for Balaqs and El-Gabal El-Asfar. Finally, engineered wetlands are used to provide additional residence time and biochemical depletion of ammonium prior to discharge into Lake Manzala. The discharge concentration of ammonium at the outfall was reduced from 4.25 ppm to 3.09 ppm by maximizing the use of existing infrastructure. Subsequently, a combination of interception technologies using wastewater treatment and engineered wetland were added to reduce the concentration to 2.00 ppm. Cost and discharge tradeoffs have been identified. The solution also quantifies the role of the various entities in solving the problem and provides a cost-benefit analysis for the proposed strategies. List of symbols FreshW v I r,u L u p q s u v W v x v y u the amount of fresh water fed to the v th sink (m 3 /sec) binary integer variable of interceptor and stream flow rate at location u (m 3 /sec) intensive variable in the model index for sources a state variables index for location index for sinks water flowrate entering the v th sink (m 3 /s) vector of input variables from the surroundings composition of the targeted species at location u (gm/m 3 ) y int u :intercepted composition at location u (gm/ m 3 ) Y u concentration at location u (gm/m 3 ) Y v,comp: z Greek symbols the composition of a certain species entering unit v (gm/m 3 ) an input variable w u MFA vectorial function at location u F MFA operator function relating output of the surroundings to input of water system W Constitutive equation relating the state variables to the intensive variables Acknowledgements The authors gratefully acknowledge the financial support of the NSF (project # OISE ) and Zagazig University. References Bixio DG, Parmentier D, Rousseau F, Verdonck J, Meirlaen PA, Vanrolleghem, Thoeye C (2001) Integrating risk analysis in the design/simulation of activated sludge sytesms. Proceedings of the Water Environment Federation s Technical and Educational Conference (WEFTEC) Dunn RF, El-Halwagi MM (2003) Process integration technology review: background and applications in the chemical process industry. J Chem Tech Biotech 78: El-Halwagi MM, Spriggs HD (1998) Solve design puzzles with mass integration. Chem Eng Prog 94(8):25 44 El-Halwagi MM (1997) Pollution prevention through process integration: systematic design tools. Academic Press, San Diego El-Halwagi MM, Hamad AA Garrison GW (1996) Synthesis of waste interception and allocation networks. AIChE J 42(11): El-Saadany H (2003) Assistant director of the project of the engineering wetland of Lake Manzala. Egyptian Environmental Affairs Agency (EEAA), Cairo, Egypt, (personal communication) VKI (water quality institute in Denmark) (1995) Feasibility study review report: engineered wetland at Lake Manzala. DANIDA Publication, Copenhagen, Denmark