Incorporating Property-Based Water Networks and Surrounding

Article pubs.acs.org/IECR

Incorporating Property-Based Water Networks and Surrounding Watersheds in Site Selection of Industrial Facilities Luis Fernando Lira-Barragán,† José María Ponce-Ortega,† Fabricio Nápoles-Rivera,† Medardo Serna-González,† and Mahmoud M. El-Halwagi*,‡,§ †

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, 58060, México Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States § Adjunct Faculty at the Chemical and Materials Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia ‡

ABSTRACT: This paper presents a new mathematical programming approach for including water usage and discharge in the selection of installation sites for industrial facilities. Water integration within the industrial facility as well as interaction of the discharged wastewater with the environment and the surrounding watershed are considered simultaneously through a material flow analysis model. The model tracks the properties that affect the process sinks and the environment (e.g., pH, toxicity, density, color, chemical oxygen demand, etc.) as well as compositions of targeted components. The model considers all the inlets and outlets that affect the watershed as well as the interactions between the pollutants and the environment. The objective function is aimed at minimizing the total annualized cost, which includes the installation cost of the new facility, the transportation of raw materials, products, and utilities, the land cost, the wastewater treatment costs (including the piping cost), and the fresh sources cost. The proposed methodology is applied to two case studies in Egypt and Mexico.

1. INTRODUCTION The chemical and process industries are among the largest consumers of water resources and dischargers of wastewater. Recently, several techniques have been proposed to economically reduce the clean water consumption in the process industry considering the possibility to recycle, reuse, and regenerate the wastewater produced in the industrial facilities (see Figure 1). These approaches are based on different objectives (e.g., minimizing the fresh water consumption, minimizing the wastewater discharge, minimizing the regeneration costs, etc.) and using diverse techniques (e.g., graphical, algorithmic, and mathematical programming-based approaches). The heuristic approaches allow the identification of targets ahead of the design (see for example Wang and Smith,1 Dhole et al.,2 El-Halwagi and Spriggs,3 Polley and Polley,4 Hallale,5 Manan et al.,6 El-Halwagi et al.,7 Feng et al.,8 Foo9) or to solve this problem algebraically (Sorin and Bedard,10 Gomes et al.,11 Foo et al.12). Additionally, different mass integration techniques based on mathematical programming models have been proposed to obtain the optimal solution for the water integration problem inside industrial facilities (see, for example, Takama et al.,13 El-Halwagi et al.,14 Savelski and Bagajewicz,15−17 Alva-Argaez et al.,18,19 Benko et al.,20 Teles et al.,21 Gabriel and El-Halwagi,22 Kuo and Smith,23 Doyle and Smith,24 Galan and Grossmann,25 Hernandez-Suarez et al.,26 Gunaratman et al.,27 Karuppiah and Grossmann,28 Putra and Amminudin,29 Ponce-Ortega et al.,30 Nápoles-Rivera et al.,31 and Faria and Bagajewicz32−40). More recently, for addressing problems with several pollutants that are based on stream properties other than contaminant concentration, Ng et al.,41 Ponce-Ortega et al.,42−44 Nápoles-Rivera et al.,45 Kheireddine et al.,46 and Deng and Feng47 have developed techniques for water integration inside the industrial facilities © 2012 American Chemical Society

using the framework of property integration proposed by ElHalwagi and co-workers.48,49 It is worth noting that the aforementioned approaches have only considered the process activities taking place inside the industrial facilities, without taking into account the activities occurring outside the plant for the wastewater streams discharged to the environment. On the other hand, despite the increasing number of works that consider environmental aspects in the synthesis of mass exchange networks (see for example Ku-Pineda and Tan,50 Tan et al.,51 Lim and Park,52−54 Ponce-Ortega et al.44), these formulations do not take into account the interrelationships between the wastewater streams discharged to the environment and the surrounding watershed. Therefore, the physical, chemical, and biochemical interactions between the industrial discharges and other discharges and uses such as agricultural, industrial, residential, precipitation, filtration, and others have not been considered. Since the watersheds constitute an important ecological element through which the discharged industrial, residential and agricultural effluents are transported to their final disposal while undergoing physical, chemical, and biological changes, the watersheds and their surroundings are interrelated as shown in Figure 2. The discharges received by a watershed change the chemical composition and the properties of the receiving water bodies. The discharged species undergo chemical, biochemical, and physical transformations that are caused by the flora and fauna of the watersheds (see Brunner et al.,55 Baccini and Special Issue: L. T. Fan Festschrift Received: Revised: Accepted: Published: 91

February 12, 2012 April 23, 2012 May 1, 2012 May 1, 2012 dx.doi.org/10.1021/ie3003792 | Ind. Eng. Chem. Res. 2013, 52, 91−107

Industrial & Engineering Chemistry Research

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Figure 1. Recycle and reuse networks.

Figure 2. Impact of a new industrial plant in a watershed system.

Brunner,56 Lampert and Brunner,57 El-Baz et al.,58,59 and Lovelady et al.60). Recently, Lira-Barragán et al.61,62 proposed two mathematical programming approaches for the optimal water integration inside the industrial facilities considering the surroundings through an MFA model. Nonetheless, these studies were based on the composition of the wastewater streams without considering stream properties. This paper presents a mathematical model that overcomes the drawbacks of the previous plant−watershed networks by incorporating the property tracking and constraints in addition to the other environmental, technical, and economic consid-

erations. The primary focus is to include the design of water networks with multiple pollutants and properties (rather than just contaminant concentrations) in the site selection of new facilities while incorporating MFA in the surrounding watershed. In this problem, a set of sites are considered as candidates for locating a new plant in a particular watershed. Therefore, the optimum water network and, consequently, the optimum flow and quality of the wastewater discharged in a receiving water body depend on the location selected to install the plant, which depends on the interactions between the new plant and the watershed. Thus, the new plant and all sources and uses of 92

dx.doi.org/10.1021/ie3003792 | Ind. Eng. Chem. Res. 2013, 52, 91−107


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The total flow rate discharged from the new plant and its properties are optimization variables, which depend strongly on its optimal location to be determined by the optimization process. This means that the required treatment also depends on the location of the new plant. To simulate the behavior of the river, the proposed model uses the MFA technique considering all inlet and outlet streams. Then, the required treatment also depends on the constraints at the inlet of process sinks and the treatment is carried out segregating the process sources to treat them in the interceptors. One important point included in this paper is the property balances. Thus, besides the composition balances for key compounds, the model includes property balances for pH, toxicity, COD, color, viscosity, etc., which are based on the property operator functions contained in Table 1 (Shelley and El-Halwagi48).

the watershed are seen as interacting systems rather than comprising isolated components in an overall system. A material flow analysis (MFA) model is proposed for the integrated assessment of water use options in order to incorporate the sustainability of the watershed in the synthesis of property-based water networks. A superstructure is formulated with all the different alternatives for the in-plant water recovery and the plant location. The mathematical model is a disjunctive programming formulation that is reformulated as an MINLP problem considering the minimization of the total annual cost for the recycle and reuse network and the installation of the new plant to satisfy the process and environmental regulations as well as the sustainability of the watershed system in terms of properties. The model is able to consider several properties and carry out the selection of several technologies to treat the process sources. The paper is organized as follows: section 2 presents the definition of the problem addressed in this paper, section 3 presents the model formulation, section 4 presents the results and discussions of the application of the proposed model, and finally section 5 presents the conclusions of the paper.

Table 1. Mixing Property Operators property

2. PROBLEM STATEMENT Given is a set of alternatives to place a new industrial plant (L = {l|l = 1, 2, ..., Nl}). Each site has associated an installation cost, (Clandl). Also is given a set of process sources (process streams), (I = {i|i = 1, 2, ..., Ni}). Each process source has a set of given properties (P = {p|p = 1, 2, ..., Np}), which may include composition, density, pH, toxicity, viscosity, etc. These streams can be segregated to be recycled and/or reused in the process sinks, and the process determines the values for the flow rate and the properties for each process source given by Wi and PInSource , respectively. Besides, given is a set of process sinks i,p (process units), J = {j|j = 1, 2, ..., Nj}. Each process sink requires a given flow rate (Gj), with specific limits for the inlet properties (PInSink ). In addition, there is available a set of fresh j,p sources (K = {k|k = 1,2,...,Nk}) that can be sent to the process sinks (Fk), each one with given properties (PFresh k,p ). As can be seen in Figure 4, for each property to be treated there is a set of interceptors in the proposed superstructure to treat each of the properties individually. Therefore, there is a set of interceptors to treat the first property (INT1), then for the second property exists a second set of interceptors (INT2), and for the N property to be treated there is the last set of interceptors (INTN). Finally, there is a set of environmental regulations (PWaste,max ) for the wastewater discharged to the environment p (Waste). This new stream will be discharged to a river or watershed, which is divided in several reaches (R = {r|r = 1, 2, ..., Nr}) and each reach can receive several effluents (T = {t|t = 1, 2, ..., Nt}). Thus, a set of sustainability constraints is imposed for the properties of the stream discharged to the final disposal. The problem consists in determining simultaneously the recycle and reuse network based on properties and the optimal location for the new plant that discharges wastewater to the surrounded watershed avoiding the accumulation of pollutants and maintaining under control the water discharged at the final disposal (considering the properties of the streams in the watershed) and, at the same time, satisfying the environmental constraints for the pollutants through the watershed system. The objective function is the minimization of the total annual cost (TAC) that includes the installation costs for the new plant, the treatment costs for the process sources, the costs of fresh sources and the piping costs.

operator

composition

ψz(z) = z

toxicity

ψTox(Tox) = Tox

chemical oxygen demand

ψCOD(COD) = COD

pH

ψpH(pH) = 10 pH

density

ψρ(ρ) =

1 ρ

viscosity

ψμ(μ) = log(μ)

Reid vapor pressure

ψRVP(RVP) = RVP1.44

electric resistivity

ψR(R ) =

1 R

paper reflectivity

5.92 ψR (R ∞) = R ∞

color

ψColor(Color) = Color 0.606

odor

ψOdor(Odor) = Odor

∞

On the other hand, the main stream of the river is fed by several streams called tributaries (FTr,t). As it can be seen in Figure 3, the watershed system exchanges water during its trajectory (i.e., water for agricultural use, wastewater discharged to the river with and without treatment, industrial and residential effluents, etc.) and, finally, discharges a total stream to the final disposal. In addition, natural phenomena like precipitation, filtration, and vaporization are taken into account in the model. Since all these processes can modify significantly the characteristics of the river, for tracking adequately the mean properties, the river is sectioned in parts where the properties can be considered constant (these sections are represented in Figure 3 with ovals). These parts or sections are called reaches, which represent zones where no big intermediate effluents are discharged and/or extracted. Also, the model accounts for the main effluents discharged in each reach, which are called tributaries. The tributaries can be channels or branches of the river, which may contain discharges with/without treatment, industrial discharges, etc. The flow rates (FTr,t) and properties (PTrib p,r,t ) of the tributaries affect the reaches where they are discharged. It should be noted that the discharges to the watershed contain compounds that interact chemically and biochemically with the system through the flora and fauna established in the watershed. 93



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Figure 3. Alternatives to locate the new industrial plant in a watershed system. 1

To ensure the sustainability of the surrounding watershed system, it is required to carry out an analysis based on properties before the optimization to determine the capacity of the final disposal to decompose chemically and biochemically the pollutants. The analysis yields the sustainability constraints, which ensure that the pollutants will not be accumulated in the system and maintain the properties of the watershed under adequate limits. Figure 4 shows the proposed superstructure to treat the properties of the process streams. In this superstructure, process sources are segregated to treat the first property, without mixing different process sources. At the exit of the first treatment, process sources are segregated again and sent to the following interceptors to treat the second property. The same sequence is used to treat all required properties in the property interception network, where the mixing of different process sources is avoided in all the steps of the treatment. Each process source that leaves the treatment units is segregated to be sent to each process sink or to the wastewater stream. The available fresh sources can be used in the process sinks when they are required. To adjust the streams properties, a set of interceptors can be used. Different units can be used for these purposes, including separation units to recover some hazardous materials, neutralization units to modify the pH, and aeration units to modify the chemical oxygen demand, among others. Therefore, a given adjustment factor is used to characterize the performance of each available interceptor, and these adjustment 1

N

1

N

,...,int ψp(PiOutPIN,int ) = γpint ,...,int ψp(PiInSource ), ,p ,p

i ∈ I , p ∈ P , int1 ∈ INT1, ..., intN ∈ INT N

3. MODEL FORMULATION The model is a combination of the material flow analysis technique, a disjunctive model to place in the optimal position the new industrial plant, and the superstructure model for the water integration inside the plant. The next sections explain these models. 3.1. Material Flow Analysis for the Watershed Based on Properties. Recently Lira-Barragán et al.61,62 proposed an MFA model for watersheds based on the composition of the streams. This model is extended in this paper to consider property balances that are suited for wastewater streams constituted by several compounds. In addition, the environmental constraints are given in terms of limits for specific properties that affect the environment. The balances required to model the watersheds in terms of properties are based in Figure 3 and these are stated as follows. Overall Balance for Each Reach. The exit flow rate (Qr) from each reach r is equal to the inlet flow rate (Qr−1) plus precipitation (Pr), direct industrial discharges (Dr), residential discharges (Hr), the sum of all effluents entering to the reach (FTr,t) and the possible discharge from the new plant if this is installed near the reach r of the l allowable (QPNEWr(l)), minus the extractions due to natural phenomena such as filtration and evaporation (Lr) as well as used water (Ur) in the r section of the river. Therefore, the overall balance for each reach can be written as follows:

N

,...,int factors (γint ) can be calculated prior to the optimization p process. This approach leads to linear models for the interceptors. The adjustment factor depends on several variables such as the value of the property at the inlet conditions of the interceptor, design and operating parameters as well as the flow rate. The available treatment technologies considered in the property interception network can be simulated (i.e., using process simulators) to get their adjustment factors. It should be noted that the property operators values for the inlet condition of the process sources are also ). Thereknown prior to the optimization process, ψp(PInSource i,p fore, the property values at the exit conditions of the property interception network can be calculated before optimization as follows:

Nt(r)

Q r = Q r − 1 + Pr + Dr + Hr +

∑ FTr ,t + QPNEWr(l) t=1

− Lr − Ur ,

∀r∈R

(1)

where Nt(r) refers to the total number of tributaries that are discharged to the reach r. Property Balances for Each Reach. The product of the property operator times the flow rate (ψp(PReach p,r )Qr)) for each reach r is equal to the property operator times the flow rate at the inlet (ψp(PInReach p,r−1 )Qr−1)), adding the property operator Prec contained in the precipitation (ψp(Pp,r )Pr)), industrial 94



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Figure 4. Superstructure for the recycle and reuse network. Resid discharges (ψp(PInd p,r )Dr), residential discharges (ψp(Pp,r )Hr), Nt(r) Trib the sum of tributaries (∑t = 1 ψp(Pp,r,t )FTr,t) and the property operator from the new plant in the case that the new plant is PNEW )QPNEWr(l)), subtracting the located in this reach (ψp(Pp,r(l) Loses Uses loses (ψp(Pp,r )Lr), uses (ψp(Pp,r )Ur) and taking into account

the change in the property operator associated to the chemical reactions that are carried out in that section of the river (∫ V V=r 0rp,r dV). The reactive term considers the chemical and biochemical reactions that take place in the river because of the interaction between the pollutants and the system. Therefore, 95



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the property balance for each section of the river r is stated as follows:

affecting the properties of the streams. The effect of the chemical or biochemical reactions over the properties for reaches (eq 5) and tributaries (eq 6) can be represented as follows:

InReach Prec ψp(PpReach , r )Q r = ψp(P p , r − 1 )Q r − 1 + ψp(P p , r )Pr Nt(r)

+

ψp(PpInd , r )Dr

+

ψp(PpResid , r )Hr

+

∑ ψp(PpTrib , r , t )FTr , t

∫V

t=1

V =0

σp rp , r dVr = kp[ψp(PpReach , r )] Vr ,

∀ p ∈ P, r ∈ R

r

(5)

Loses Uses + ψp(PpPNEW , r(l) )QPNEWr(l) − ψp(P p , r )Lr − ψp(Pp , r )Ur

−

∫V

V =0

rp , r dVr ,

∀ p ∈ P, r ∈ R

r

∫V

(2)

∀ p ∈ P, r ∈ R, t ∈ T

(3)

The total flow rate discharged from the tributary t to the reach r (FTr,t) is the sum of discharges without treatment (SUntreated ), r,t discharges with treatment (STreated ), industrial discharges (Ir,t), r,t pluvial discharges (Pr,t), direct discharges (Dr,t), and the new discharge if the new facility is located on this tributary (QPNEWr,t(p)), subtracting the losses (Lr,t) and use (Ur,t) of water. Property balances for each tributary. The next balance that includes the reaction term is used to calculate the property operator discharged from the tributary t to the reach r.

Prec Direct + ψp(PpInd , r , t )Ir , t + ψp(P p , r , t )Pr , t + ψp(P p , r , t )Dr , t Loses + ψp(PpPNEW , r , t (l))QPNEWr , t (l) − ψp(P p , r , t )Lr , t

∫V

V =0

rp , r , t dVr , t ,

r ,t

∀ p ∈ P, r ∈ R, t ∈ T

Dr , t = αr , t A r , t ,

∀ r ∈ R, t ∈ T

Ur , t = βr , t A r , t ,

∀ r ∈ R, t ∈ T

αr,t is the water required per area and its units are m3/ha·s, while βr,t is the discharged flow rate per area and its units also are m3/ha·s. 3.2. Location of the New Plant. This work considers a set of alternatives to locate the new industrial facility (L), which are specified before the optimization process. Then, for each alternative, it is necessary to consider the possible discharge of the new wastewater flow rate (QPNEWl) and its property )). If the new industrial plant is located on operators (ψp(PPNEW p,l the alternative 1, the wastewater flow rate and the property operators associated to this site must be greater than zero; otherwise, if the new plant is not located on the position 1, the wastewater flow rate and the property operators discharged would be zero. This is included in the following disjunction:

Untreat Untreat Treat + ψp(PpTreat ψp(PpTrib , r , t )FTr , t = ψp(Pp , r , t )Sr , t , r , t )Sr , t

− ψp(PpUses , r , t )Ur , t −

(6)

where kp is the kinetic constant of degradation for each property p measured experimentally, σp is the reaction order for each property, ψp(PReach p,r ) is the property operator at the reach r, while ψp(PTrib p,r,t ) is the property operator at the tributary t, and Vr and Vr,t are the volumes for the reach and tributary, respectively. Agricultural Discharges and Uses. Experimental information is used to compute the agricultural discharges (Dr,t) as well as the agricultural uses (Ur,t) through a pair of experimental parameters that depend on the agricultural area (Ar,t).

FTr , t = SrUntreat + SrTreat + Ir , t + Pr , t + Dr , t + QPNEWr , t(l) ,t ,t ∀ r ∈ R, t ∈ T

σp rp , r , t dVr , t = kp[ψp(PpTrib , r , t )] Vr , t ,

r ,t

Overall Balance for Each Tributary. For the tributary t that discharges to the reach r, the overall balance is written as follows:

− Lr , t − Ur , t ,

V =0

(4)

Reactive Terms. The chemical reactions that are carried out in the rivers have strong effects over the properties of the streams in the watershed. Several components can be degraded

⎤ ⎡ ⎤ ⎤ ⎡ ⎡ Yl Y1 Y2 ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎢ ψ (P pPNEW ⎢ ψ (P pPNEW ) ≥ 0, QPNEW1 ≥ 0 ⎥ ⎢ ψp(P pPNEW ) = 0, QPNEW1 = 0 ⎥ ) = 0, QPNEW1 = 0 ⎥ ,1 ,1 ,1 p p ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎢ ψ (P PNEW ) = 0, QPNEW = 0 ⎥ ∨ ⎢ ψ (P PNEW ) ≥ 0, QPNEW ≥ 0 ⎥ ∨ ··· ∨ ⎢ ψ (P PNEW ) = 0, QPNEW = 0 ⎥ , 2 2 2 ⎥ ⎢ p p ,2 ⎥ ⎥ ⎢ p p ,2 ⎢ p p ,2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋮ ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎢ ψ (P PNEW ) ≥ 0, QPNEW ≥ 0 ⎥ ⎢ ψ (P PNEW ) = 0, QPNEW = 0 ⎥ ⎢ ψ (P PNEW ) = 0, QPNEW = 0 ⎥ l l l ⎦ ⎦ ⎣ p p,l ⎣ p p,l ⎦ ⎣ p p,l

∀p∈P

(Yl) must be false and the ψp(PPNEW ) and QPNEWl associated p,l to such locations must be set as zero. A similar situation occurs for the case when the selected location is 2, 3, and so on for the l possible locations. It is important to remark that the value for the flow rate of the wastewater and the property operators of the new plant are strongly influenced by the location through the material flow analysis model, satisfying the environmental regulations given to maintain under control the properties and the desired constraints in intermediate reaches, as well as the sustainability

In this disjunction, the Boolean variable associated to the ) is the property location l of the new plant is Yl, while ψp(PPNEW p,l operator for the property p from the wastewater stream of the new industrial facility (QPNEWl). As it can be seen, these variables depend on the final location of the new plant. In this sense, the disjunctive model establishes that if the optimal location for the new plant is on alternative 1, then the Boolean variable Y1 is set as true; therefore, ψp(PPNEW ) and QPNEW1 p,l must be greater than zero, while all the others Boolean variables 96



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constraints at the final disposal. Notice that these variables also depend on the mass integration inside the plant where there are sinks constraints to be met at the inlet to process units. Previous disjunction is reformulated using the convex hull technique (see Raman and Grossmann63 and Ponce-Ortega et al.64). The reformulation includes the transformation of the Boolean variables (Yl) into a set of binary variables (yl). When the Boolean variables are true, the associated binary variables must be set as 1; otherwise, when the Boolean variables are false, the associated binary variables are zero. Therefore, the following relationship is used to select only one location to install the plant:

∑ yl

where Fk is the total flow rate for the fresh source k and f k,j is the segregated flow rate from the fresh source k sent to process sink j. Notice in Figure 4 that the fresh sources only are sent to the process sinks. Splitting of Process Sources to the Property Interceptors. The interception network is segregated avoiding the mixing of different process sources. If a process source does not require any treatment, it is sent to a fictitious unit (located at the end of the set of property interceptors) with effectiveness and cost equal to zero. Next equation represents the segregation of each process source to treat the first property on the first set of available interceptors.

=1 (7)

QPNEWl ≤ QPNEW Upyl ,

∀l∈L

ψp(PpPNEW ) ≤ ψp(P PNEW )Up yl , ,l

∀ p ∈ P, l ∈ L

(8)

1

wiint =

∑ QPNEWl = Waste ) = ψp(Ppdisc), ∑ ψp(PpPNEW ,l l∈L

2

∀ i ∈ I , int1 ∈ INT1 (14)

int2 ∈ INT2

Notice that this approach does not allow the mixing of different process streams. This approach eliminates the nonlinearities involved in the property balances, although the problem size increases exponentially. Following the same sequence for N properties to be intercepted, the next equations model the segregations. 1

2

wiint ,int

,...,intN − 1

1

2

wiint ,int

∑

=

intN ∈ INT N

,...,intN

,

∀ i ∈ I , int1 ∈ INT1, ..., intN − 1 ∈ INT N − 1

(15)

Splitting of Sources at the Exit of the Interception Network. After the treatment network, the process sources are segregated and directed to the process sinks and to the wastewater stream discharged to the environment.

(10)

l∈L

1

wiint ,int ,

∑

(9)

where QPNEWUp and ψp(PPNEW )Up are the upper limits for p,l PNEW QPNEWl and ψp(Pp,l ), respectively. Notice that ψp(PPNEW )Up p,l is an upper bound for all properties p. These constraints are required to ensure that QPNEWl and ψp(PPNEW ) take values p,l greater than zero only when the new plant is located in a particular position l. Equations to Interconnect the Models. The following relationships are required to interconnect the material flow analysis model with the superstructure model for the mass integration inside the plant:

∀l∈L (11)

1

N

wiint ,...,int =

where “Waste” is the flow rate discharged to the environment by the new industrial plant and ψp(Pdisk p ) is the property operator for each property of this stream. In this regard, eq 7 assures that only one location is selected, then just one of the l variables for QPNEWl and ψp(PPNEW ) can be greater than zero, p,l and eqs 8 and 9 are satisfied. 3.3. Superstructure Modeling for in-Plant Treatment. The proposed superstructure for the in-plant treatment is shown in Figure 4, which is based on the ones reported by Ponce-Ortega et al.43 and Gabriel and El-Halwagi.22 The size for this formulation increases exponentially as a function of the number of treated properties (N); however, the model obtained for this superstructure has a linear behavior, which is the main advantage of this formulation because it avoids the mixing of different streams and, thus, it is very useful for the optimization process. As can be seen in Figure 4, for each property to be treated there is a set of treatments units; therefore, it generates N treatment units for each stream. Splitting Fresh Sources. Each fresh source is segregated and sent to any process sinks. j∈J

(13)

Then, to treat the second property, the flow rates at the exit of the first line of interceptors are segregated, avoiding the mixing of streams, and again these are fed to the second set of interceptors.

The next upper limits for the variables QPNEWl and ψp(PPNEW ) p,l complete the reformulation.

∑ fk ,j ,

∀i∈I

int1 ∈ INT1

l∈L

Fk =

1

wiint ,

∑

Wi =

1

N

∑ giint,j ,...,int

N

1

,...,int + giint , ,Waste

j∈J

∀ i ∈ I , int1 ∈ INT1, ..., intN ∈ INT N

(16)

Overall Balance at the Mixing Point Prior to Any Sink. The total flow rate at the inlet of any sink (Gj) must be completed by the sum of the flow rates from process sources intercepted, as well as the flow rates from the fresh sources. Gj =

∑ ∑

···

i ∈ I int1 ∈ INT1

N

1

∑ intN ∈ INT N

,...,int giint + ,j

∑ fk ,j , k∈K

∀j∈J

(17)

Property Balances at the Mixing Point Prior to Any Sink. These balances are required to calculate the properties at the inlet to any process sink. k ψp(P jInsin )Gj = ,p

∑ intN ∈ INT N

∀k∈K

+ (12)

···

i ∈ I int1 ∈ INT1 1

N

1

N

,...,int ,...,int [ψp(PiOutPIN,int )giint ] ,p ,j

∑ [ψp(PkFresh , p )fk , j ], k∈K

97

∑ ∑

∀ j ∈ J, p ∈ P (18)



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Overall Balance for the Waste Stream. The total flow rate of the wastewater stream discharged to the environment is given by the sum of the process sources after the treatment units that are sent to the waste.

∑ ∑

Waste =

intN ∈ INT N

i ∈ I int1 ∈ INT1

N

1

∑

···

different purposes, it becomes necessary to impose a set of property constraints on corresponding reaches to guarantee the quality of the water extracted. The proposed model is able to consider these constraints through the following relationship:

,...,int giint ,Waste

Desiredmax ψp(P pDesiredmin ) ≤ ψp(PpReach ), , m(r ) , m(r )) ≤ ψp(P p , m(r )

(19)

∀ p ∈ P , m ( r ) ∈ M (R )

Property Balances for the Waste Stream. Next equation is used to calculate the properties for the waste stream discharged to the environment. ψp(PpWaste)Waste =

∑ intN ∈ INT N

∑ ∑

where M(R) represents a subset of reaches of all the reaches r ) and that require a specific water quality, while ψp(PDesiredMAX p,m(r) ψp(PDesiredMIN ) are the limits for the property operators with p,m(r) desired properties in specified reaches to maintain the water quality in them. Sustainability Constraints. To ensure the sustainability of the watershed and its surroundings, and to avoid putting at risk the final disposal (lake, sea, or ocean), the next constraints must be met because the environmental regulations imposed on the plant discharge could not be enough:

···

i ∈ I int1 ∈ INT1 N

1

N

1

,...,int ,...,int (ψp(PiOutPIN,int )giint ), ,p ,Waste

∀p∈P (20)

Sink Constraints. The process sinks impose a set of constraints to work properly that usually are given in terms of specific properties like the composition of specific compounds, density, pH, viscosity, thermal conductivity, etc. In this work, these constraints are stated in terms of the property operators as follows: k,min ψp(P jInsin ) ,p

≤

k ψp(P jInsin ) ,p

Sustainablemax ψp(P pSustainablemin) ≤ ψp(PpReach ), ,final) ≤ ψp(P p

∀p∈P

k,max ψp(P jInsin ), ,p

≤

j ∈ J, P ∈ P

Environmental Constraints. The environmental regulations impose a set of constraints on the industrial plant in terms of properties as follows: ∀p∈P (22)

This set of constraints includes upper and lower limits for specific properties in the wastewater discharged to the environment like pH, COD, toxicity, color, etc. Constraints for the Quality of Specific Reaches. Because the water in some specific zones of the rivers can be used for min TAC =

∑ Clandlyl l∈L

+ HY ∑ [ i∈I

+ kf

k∈K int 1 int 1 VarCcap wi

∑

i∈I

i∈I

1

intN ∈ INT N

1

int int FixCcap zi + ···

int1∈ INT1

+ WaPipC ∑

∑ 1

i ∈ I int ∈ INT

N

int ∈ INT

N

1

intN ∈ INT N

1

1

int ∈ INT

N

∑ N

int ∈ INT

N

N

1

int int ,...,int wi (VarCop )]

intN int1 ,...,intN wi (VarCcap )] N

∑ 1

∑

··· 1

∑

+ ···

int1∈ INT1

∑[ ∑

1

int int VarCop wi + ···

∑ FreCkFk + HY ∑ [ ∑

+ HY

(24)

where ψp(PReach p,final ) is the property operator in the final disposal ) after installing the new industrial facility, while ψp(PSustainableMIN p and ψp(PSustainableMAX ) are the set of sustainability constraints for p property p. Notice that the sustainability constraints are generated making a sustainability analysis for the final disposal prior to the optimization process. Satisfying these constraints ensures that the natural degradation of the pollutants in the final disposal will maintain the properties under sustainable limits. Objective Function. Finally, the objective function consists in minimizing the total annual cost (TAC), which comprises the annualized installation costs for the new plant, the fresh sources costs, the treatment cost (including operational cost, variable and fixed capital cost), and the piping costs.

(21)

ψp(PpWaste,min) ≤ ψp(PpWaste) ≤ ψp(PpWaste,max ),

(23)

N

1

int int ,...,int zi (FixCcap )] + HY [TrPipC ∑ ( i∈I

N

,...,int giint + EqPipC ∑ ,Waste

∑ 1

i ∈ I int ∈ INT

where HY is the hours per year that operates the new industrial plant and kf is the factor used to annualize the inversion. The annualized installation cost (Clandl) takes into account the land cost and the transportation costs for raw materials, products and services. Notice that this annualized installation cost takes into account simultaneously capital and operational costs, and that the factor used to annualized the capital costs is used to provide the associated cost per year. Fresh sources cost (FreCk) is caused by the required amount of fresh sources to satisfy the water requirements of the process sinks as well as the properties constraints imposed on them. Also, process sources need to be treated prior to be sent to the process sinks, as well as prior to

N

int ∈ INT

N

1

wiint + ···

int ∈ INT 1

∑

··· 1

∑

N

∑ giint,j ,...,int j∈J

∑ intN ∈ INT N

+ FrPipC

1

∑ ∑ fk ,j ] k∈K j∈J

N

wiint ,...,int )

(25)

being discharged to the environment. A set of technologies must be selected to treat the process sources yielding capital and operational costs for each one of the interceptors required. N The operational cost (Varint op ) for the interceptors depend on the treated flow rate, while the capital cost contains a variable N cost (Varint cap ) that also depends on the treated flow rate and a N

fixed component (Fixint cap ). Finally, the piping costs for the four sections showed in the superstructure are considered. The first section involves the pipes required when the process sources are sent to treatment (TrPipC); then, once the process sources are treated they can be sent to the wastewater stream 98



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(WaPipC) or process sinks (EqPipC). The final section covers the pipes to connect the fresh sources with process sinks (FrPipC). Remarks. (a) The model presented considers simultaneously the water integration inside the industrial facility and the sustainability of the surrounding watershed. (b) The model presented in this paper is based on the properties of the streams, considering property balances, as well as process and environmental constraints given in terms of limits for the properties. This situation is very useful for streams constituted by several pollutants, where the component balances are not suited to characterize them. (c) The effect of the chemical and biochemical reactions over the properties can be represented by a simple kinetic model. The kinetic constants can be measured experimentally. (d) The annualized installation costs (Clandl) include different costs: transportation cost of raw materials, transportation cost of products, services, and the land cost for the alternative l. These costs depend directly on the location 1 ,...,intN selected for the new plant. (e) Adjustment factors (γint ) p are parameters known for each unit to treat each property, which can be determined experimentally or estimated by simulation. Therefore, the property balances in the superstructure for the treatment systems are not required in the optimization model. Also, to determine the outlet property from the interception network only the following relationship is 1 ,...,intN OutPIN,int1,...,intN used: ψp(Pi,p ) = γint ψp(PinSource ). p i,p

4. RESULTS AND DISCUSSION The model presented was coded in the general algebraic modeling system (GAMS).65 Two examples are presented to show the implementation of the proposed formulation, one N from Egypt and the other one from Mexico. Fixint cap are fixed as zero for both examples. 4.1. Example 1. Bahr El-Baqar System. The Bahr ElBaqar system is in Egypt and its description was given by Lovelady et al.60 The system receives several types of discharges (i.e., agricultural, industrial, municipal effluents) and the properties restricted in the environment are the toxicity, COD, odor, color, and the composition of a dangerous pollutant. The properties restricted in the process sinks are the composition and the toxicity. Four candidate sites are identified to install a new industrial plant, where each one has an associated installation cost (see Table 2). Figure 5 shows the

Figure 5. Bahr El-Baqar system.

The natural degradation of pollutants along the system helps to improve the properties like toxicity, COD, color, etc. Specifically, in this system the kinetic constants in terms of properties are: kComp = 9.041909 × 10−6/s, kTox = 5.208473 × 10−7/s, kCOD = 4.08396 × 10−6/s, kOdor = 2.083389 × 10−6/s and kColor = 3.645931 × 10−6/s, which correspond to a kinetics of first order. In addition, the new plant operates 8000 h/year and kf = 0.1. Table 3 shows the characteristics for the fresh Table 3. Fresh and Process Sources for Example 1 sources 1 2 3

Table 2. Installation Cost for the Different Sites to Locate the New Plant for Example 1 site

annualized installation cost, $/year

1 2 3 4

14,000,000 12,500,000 11,000,000 10,000,000

1 2

flow rate, m3/s 0.316 0.435 0.402

composition, ppm 88.7 77.2 52.4 0 10

toxicity, %

Process 0.14 0.22 0.16 Fresh 0 0.005

COD, mgO2/L

odor

color

139 93 128

6 7 5.5

150 262 290

sources and the process sources; notice that the flow rates for the fresh sources are optimization variables and the specifications of COD, odor, and color are not presented because fresh sources can only be sent to process sinks, which do not contain constraints in terms of these properties for this example. The flow rate required for each process sink as well as the maximum composition and toxicity allowed are presented in Table 4, while Table 5 shows the available interceptors to treat the properties considered.

Bahr El-Baqar system, and the four available locations as well as the properties considered and the constraints imposed over the system. The set of constraints is explained by considering the reach 6. Before installing the new plant, it has a composition and toxicity of 1.312 ppm and 0.0076, and the maximum composition and toxicity allowed after the installation of the plant are 1.34 ppm and 0.0078, respectively. A similar explanation applies to the constraints imposed on the remaining reaches of Figure 5. 99



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installation cost, $4.816 × 106/yr of treatment cost, $573,330/ yr of fresh source cost and $827,532/yr of piping cost. The results obtained for the solution of the proposed model shows that the new plant must be installed in the site 3 with the mass integration based on properties showed in Figure 6. Notice that some properties for the stream discharged to the environment are limited by the environmental constraints, whereas others are lower than the environmental constraint. Specifically, the composition, the toxicity, as well as the color require a larger reduction to satisfy the constraints imposed on the river or the final disposal to maintain the quality of the water around the system (see Figure 7). Therefore, the results show that if the new plant only satisfies the environmental regulations imposed by the legislation on the wastewater, the sustainability requirements of the system are not fulfilled since the associated environmental impact of the wastewater discharged from the new plant is not in line with the estimated degradation capacity of the watershed. On the other hand, this example was solved previously by Lira-Barragán et al.62 while only considering the compositions of chemical compounds and without taking into account the properties. Lira-Barragán et al.62 found that the optimal location of the new plant is site 4 with a total annualized cost of $12.121 × 106/yr. When the constraints based on properties for the in-plant sinks and the wastewater discharged to the environment are not included, some constraints may be violated. For example, the properties in reach 6 (toxicity of 0.0088, COD, odor, and color of 42.808, 2.936, and 134.69, respectively) represent a risk for the water extracted for human activities, and this problem is avoided in the solution given by the formulation proposed in this paper. 4.2. Example 2. Balsas Watershed. This case considers the Balsas watershed that is one of the largest systems in Mexico. This system transports several types of discharges until the Pacific Ocean, and CONAGUA 67,68 reported the information for it shown in Figure 8. In this case, the properties considered were the composition, toxicity, density, COD, odor, and color, and the properties restricted for the stream discharged to the environment are composition, toxicity, COD, odor, and color, while the process sinks limit only the composition and density. The system offers 20 possible

Table 4. Requirements for the Process Sinks for Example 1 process sink

flow rate, m3/s

compositionmax

toxicitymax

1 2 3

0.365 0.290 0.335

55.5 36.2 30

0.013 0.011 0.010

Table 5. Characteristics of the Available Interceptors for Example 1 interceptor Rec1 Rec2 Tox1 Tox2 Aer1 Aer2 Ads1 Ads2 Dec1 Dec2

adjustment factor Composition 0.05 0.22 Toxicity 0.08 0.17 COD 0.06 0.23 Odor 0.02 0.16 Color 0.10 0.20

cost, $/m3 0.090 0.072 0.105 0.075 0.055 0.032 0.065 0.047 0.070 0.051

The costs for the fresh sources 1 and 2 are $0.190/m3 and $0.142/m3, respectively. On the other hand, the environmental constraints for the wastewater stream in terms of properties are: PSustainable = 50, PSustainable = 0.1, PSustainable = 75, PSustainable = 2.7, Comp Tox COD Odor Sustainable and PColor = 100. Then, to satisfy these constraints the model considers a set of interceptors with different efficiencies to remove the pollutants and to improve the properties. Finally, the piping costs for each section in the superstructure are TrPipC = 0.003 $/m3, WaPipC = 0.006 $/m3, EqPipC = 0.010 $/m3, and FrPipC = 0.008 $/m3. The problem for this case study was implemented in the software GAMS (Brooke et al.65), and it was solved using the solver DICOPT (Viswanathan and Grossmann66). The optimal solution requires a total annual cost of $17.317 × 106/yr, which is constituted by the next cost components: $11.1 × 106/yr of

Figure 6. Mass integration based on properties for Example 1. 100



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Table 6. Installation Costs for Example 2 site

annualized installation cost, $/year

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8,000,000 8,500,000 9,000,000 10,500,000 9,500,000 9,000,000 15,500,000 14,500,000 17,700,000 22,000,000 18,000,000 17,500,000 24,000,000 28,000,000 23,500,000 17,000,000 20,000,000 19,000,000 16,000,000 17,000,000

the new plant is working. The property odor discharged to Pacific Ocean is 0.654 and once the new plant is operating must be lower or equal to 0.68. This explanation has to be followed to understand all the constraints imposed on the river. It is important to note that in the restricted reaches, toxicity is strictly regulated. To model the reactive effects, the kinetic constants in terms of properties for first order kinetics are as follows: kComp = 3.2376 × 10−6/s, kTox = 4.5205 × 10−7/s, kCOD = 1.9273 × 10−6/s, kOdor = 8.315 × 10−7/s and kColor = 1.1423 × 10−6/s. Remember that the density is not restricted in the environment. Furthermore, the new plant will operate 8000 h/year with a kf = 0.1. Table 7 shows the characteristics for the fresh and process sources; notice that for fresh sources only the specifications of composition and density are presented because they cannot be

Figure 7. Impact of the new wastewater stream over Bahr El-Baqar system.

locations to install the new industrial facility, and their installation costs are presented in Table 6. Figure 8 shows the properties before installing the new facility as well as the set of constraints imposed on the system. For example, the composition discharged on the Pacific Ocean prior to the installation of the new plant is 1.466 ppm, and it is desired that this concentration does not exceed 1.47 ppm when

Figure 8. Balsas watershed system (possible locations and the constraints on the river). 101



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Table 7. Fresh and Process Sources for Example 2 sources 1 2 3 4 5 6 7 8 9 10 11

flow rate, m3/s

composition, ppm

0.363 0.241 0.046 0.447 0.196 0.204 0.281 0.329 0.282 0.266 0.215

toxicity, % Process 0.11 0.04 0 0.13 0.21 0.25 0 0.13 0.09 0.7 0.3 Fresh

64.6 58 45.3 60 52 62 54.5 47.8 46 82.1 26.4

1 2 3

0 1 2

process sink

flow rate, m3/s

compositionmax

densitymin

densitymax

1 2 3 4 5 6 7

0.348 0.428 0.406 0.312 0.336 0.294 0.196

16 19.4 23.3 28.5 18 14 22.5

2.2 1.95 2.35 1.7 2.2 1.8 2.45

2.4 2.1 2.55 1.9 2.3 2 2.55

density for each process sink. The unitary cost for fresh source 1 is $0.128/m3, for fresh source 2 is $0.113/m3, and for fresh source 3 is $0.097/m3. Table 9 shows the characteristics (efficiency and variable cost) for the property interceptors. For this case, the variables costs are included in just one term. The environmental legislation imposes the next constraints on the wastewater stream: PSustainable = 50, PSustainable = 0.1, Comp Tox Sustainable Sustainable PSustainable = 75, P = 2.7, and P = 100. While the COD Odor Color Table 9. Available Interceptors for Example 2

Rec1 Rec2 Tox1 Tox2 Aer1 Aer2 Ads1 Ads2 Dec1 Dec2

Composition 0.11 0.23 Toxicity 0.00 0.08 COD 0.18 0.43 Odor 0.14 0.39 Color 0.10 0.20

color

density, g/mL

149 88 108 185 120 76 243 164 297 326 146

6.3 7.7 5.1 4.8 7.6 8.2 3.7 7.4 4.8 8.5 5.7

250 234 298 202 194 164 179 346 264 394 195

0.94 2.41 1.14 1.20 2.70 1.64 1.85 1.75 2.45 0.89 2.15

piping costs for each section in the superstructure are TrPipC = 0.001 $/m3, WaPipC = 0.002 $/m3, EqPipC = 0.005 $/m3, and FrPipC = 0.003 $/m3. Then, the proposed model was applied for this case study yielding an optimal solution where the new facility must be placed in alternative 6 with a total annual cost of $14.9 × 106/ yr, composed by $9 × 106/yr of installation cost, $3.6 × 106/yr of treatment cost, $1.5203 × 106/yr of fresh source cost, and $779,040/yr of piping cost. Figure 9 shows the water network based on properties for this example; notice that the value of toxicity in the wastewater stream is zero, satisfying the constraint in reach 8, where it is rquired to be zero (see Figure 10). Also, it is worth noting that most of the properties in the wastewater streams almost take the upper limits of the environmental constraints. Nonetheless, the composition requires a greater reduction to satisfy the constraints imposed on reach 8 to meet the quality of the water extracted for human activities. On the other hand, if the proposed model by LiraBarragán et al.62 is applied to this example (i.e., if the properties are not taken into account), the optimal solution to install the new plant is alternative 1, obtaining a total annualized cost of $10.214 × 106/yr. However, in that solution, some of the properties have values greater than the maximum allowed, yielding not sustainable solutions. Finally, Table 10 shows the computation time for the problems presented in this work, using a computer with an i5 processor at 2.3 GHz with 4 GB of RAM.

Table 8. Requirements for the Process Sinks for Example 2

adjustment factor

odor

2.3 2.45 1.8

sent to the wastewater stream discharged to the environment where the other properties are restricted. Table 8 shows the requirements for the flow rate and maximum composition, as well as the minimum and maximum

interceptor

COD, mgO2/L

variable cost, $/m3

5. CONCLUSIONS This paper has introduced a water integration approach to consider simultaneously the integration inside the plant and the sustainability of the surrounded watershed during the selection of a construction site of a new industrial facility. A material flow analysis is developed and coupled with an optimization formulation to track, manipulate, and assign properties and compositions while considering water integration alternatives and the impact on the surrounding watershed. The model also considers the integration of the wastewater discharged from the industrial facility with the other discharges in the regions that impact the watershed (e.g., agricultural, domestic, other industrial discharges, evaporation, filtration, etc.). Phenomena occurring within the watershed are accounted for from the natural degradation of the pollutants through the watershed

0.026 0.021 0.054 0.049 0.022 0.018 0.013 0.011 0.019 0.015 102



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Figure 9. Mass integration for Example 2.

Figure 10. Impact of the new wastewater stream over Balsas system.

103



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r = reach Sink = sink Source = source t = tributary Treat = treated Trib = tributary Untreat = untreated Waste = waste discharged to the environment

Table 10. Size and Computation Time for the Problems Considered concept

example 1

example 2

number of constraints number of continuous variables number of binary variables CPU time (s)

1,415 5,030 4 4.36

9,527 30,876 20 19.96

Sets

and their effect on the specific properties that are constrained in the system. Economic and environmental issues are included in the optimization formulation. The devised model has been applied to two case studies, one from Egypt and the other one from Mexico. The results show that the traditional water integration schemes that do not consider the surrounding watershed may not be sufficient to ensure the sustainability of the watershed. To satisfy the sustainability requirements, the interaction of the wastewater streams discharged to the environment with other discharges and uses through the watershed must be considered in conjunction with the physical, chemical, and biological phenomena occurring in the watershed. The results also show that the property-based approach proposed in this paper is suited for problems with several pollutants that are difficult to quantify in terms of the composition of the streams. Finally, when only the composition is considered, several property requirements may not be satisfied.

■

I = set for the process sources, {i|i = 1,...,Ni} INTN = set for property interceptor N, {int|int =1,...,NintN} J = set for the sinks, {j|j = 1,...,Nj} K = set for the fresh sources, {k|k = 1,...,Nk} M(R) = subset for the specific reaches that require properties constraints L = set for the sites to locate the new plant, {l|l = 1,...,Nl} P = set for the properties, {p|p = 1,...,Np} R = set for the reaches, {r|r = 1,...,Nr} T = set for the tributaries, {t|t = 1,...,Nt} Parameters

Ar,t = area cover by effluent t in reach r, acre or ha Clandp = annualized installation cost for the new plant in site p, $/year Dr,t = agricultural discharges from tributary t to reach r, m3/s Dr = direct discharges to the reach r, m3/s EqPipC = piping cost to send process sources to process sinks, $/m3 N N FixCint cap = fixed part of the capital cost for interceptor int , $/year FreCk = unit cost for fresh utility k, $/m3 FrPipC = piping cost to send fresh sources to process sinks, $/m3 Gj = total flow rate for process sink j, m3/s HY = operation time per year, hr/year Hr = total discharge (i.e., industrial + sanitary) to the reach r, m3/s Ir,t = industrial discharge from the tributary t to the reach r, m3/s kf = factor used to annualize the capital costs kp = kinetic constant for the degradation for property p Lr,t = total losses (filtration and evaporation) from tributary t of the reach r, m3/s Lr = total losses (filtration and evaporation) from the reach r, m3/s Ni = total number of process sources NintN = total number of interceptors Nj = total number of sinks Nk = total number of fresh sources Nl = total number of sites allowable to locate the new plant Np = total number of properties Nr = total number of reaches Nt = total number of tributaries Pr,t = precipitation discharged for the tributary t to the reach r, m3/s Pr = precipitation discharged to the reach r, m3/s PDesired p,m(r) = desired properties in some reaches PWaste,max = environmental regulation for the property to be p discharged by the new plant PSustainable = sustainability constraints at the final disposal p Suntreated = residual wastewater discharged without treatment r,t to the reach r for tributary t, m3/s

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 979 845-3484. Fax: 979 845-6446. Notes

The authors declare no competing financial interest.

■ ■ ■

ACKNOWLEDGMENTS Authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACYT). DEDICATION To Professor L. T. Fan with deep gratitude for his inspiration and seminal contributions in process systems engineering NOMENCLATURE

Indexes

Direct = direct Ind = industrial i = process source int = interceptor In = inlet j = sink k = fresh source l = site to locate the new plant m(r) = specific reaches that require property constraints max = maximum min = minimum N = number of properties to be treated Out = out PNEW = new industrial plant Prec = precipitation p = property Resid = residential 104



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Streated = residual treated wastewater discharged to the reach r r,t for tributary t, m3/s TrPipC = treatment piping cost, $/m3 Ur,t = water used from tributary t discharged to reach r, m3/s Ur = water used from reach r, m3/s N VarCint cap = variable part for the capital cost for interceptor intN, $/m3 N VarCint op = variable cost associated to operation of the interceptor intN, $/m3 Vr,t = volume for tributary t from reach r, m3 Vr = volume for reach r, m3 Wi = total flow rate for the process sources i, m3/s WaPipC = waste piping cost, $/m3 αr,t = agricultural flow rate per area, m3/ha*s βr,t = agricultural use of water from tributary t, m3/ha s 1 ,...,intN γint = efficiency factor to improve the property p for the p interceptor intN ρ = density σp = reaction order for property p ψp = property operator for the mixing rule for property p

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Variables

Fk = total flow rate for fresh source k, m3/s f k,j = segregated flow rate from fresh source k to sink j, m3/s FTr,t = flow rate discharged by the tributary t to the reach r, m3/s N gint1,...,int = segregated flow rate from interceptors intN to i,j process sink j for process source i, m3/s 1 ,...,intN gint = segregated flow rate from interceptors intN to i,Waste waste for process source i, m3/s Pdisk p = property for the final discharge of the new plant to the river PNEW Pp,r(l) = property of the waste stream, to be discharged for the new plant installed on site l PReach p,final = property discharged to the final disposal Qr = flow rate exit from the reach r, m3/s Qr−1 = flow rate inlet to the reach r, m3/s QPNEWl = flow rate discharged for the new plant for the location p rp,r = reaction carried out in the reach r in terms of property p rp,r,t = reaction carried out in the tributary t that discharges to the reach r in terms of property p TAC = total annual cost, $/year 1 ,...,intN wint = segregated flow rate from process source i to i interceptor intN, m3/s Waste = total flow rate for the waste stream discharged to the environment, m3/s Yl = Boolean variable for the location of the new plant yl = binary variable for the location of the new plant

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