Optimal Synthesis of Refinery Property-Based Water Networks with

Research Article pubs.acs.org/journal/ascecg

Optimal Synthesis of Refinery Property-Based Water Networks with Electrocoagulation Treatment Systems Javier Tovar-Facio,† Luis F. Lira-Barragán,‡ Fabricio Nápoles-Rivera,† Hisham S. Bamufleh,§ José M. Ponce-Ortega,*,† and Mahmoud M. El-Halwagi‡,§ †

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacana 58060, México Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States § Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia ‡

S Supporting Information *

ABSTRACT: This paper presents an optimization approach to the incorporation of electrocoagulation in the design of integrated water networks for oil refineries. A disjunctive programming formulation is developed to minimize the cost of the water-management system while including the characteristics of process water streams, recycle, reuse, and treatment of wastewater streams, performance of candidate technologies, and composition and property constraints for the process units and the environmental discharges. The performance of electrocoagulation was related to temperature pH and the concentration of phenols and sodium chloride. Ancillary units including pH adjustment, reverse osmosis, and heat exchangers were used to support the electrocoagulation unit. Two case studies are presented to show the applicability of the proposed model and the feasibility of using electrocoagulation as part of an integrated water management scheme for oil refineries. KEYWORDS: Electrocoagulation, Recycle and reuse water networks, Optimization, Removal of phenolic compounds, Refinery wastewater

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conservative manner. El-Halwagi et al.7 presented a rigorous graphical targeting approach to minimize the use of fresh resources by using segregation, mixing, and direct recycle/reuse strategies. This approach was revised by Kazantzi and ElHalwagi8 and Kazantzi et al.9 to characterize streams and units based on properties through graphical techniques and by Qin et al.10 and Almutlaq and El-Halwagi11 through algebraic techniques. El-Halwagi et al.12 presented new systematic rules and visualization techniques for the identification of optimal mixing of streams and their allocation to units. Furthermore, they presented a derivation of the correspondence between clustering tools and fractional contribution of streams to minimize the usage of fresh resources. Eljack et al.13 developed property clustering techniques for the simultaneous design of molecular and process networks. Grooms et al.14 further introduced a source−interception−sink representation to embed structural configurations of interest. Foo et al.15 introduced two new tools: the property surplus diagram and the property cascade analysis technique to establish rigorous targets on the minimum usage of fresh resources, maximum direct reuse, and minimum waste

INTRODUCTION Industrial processes consume tremendous amounts of fresh water and discharge significant quantities of wastewater. Efficient mass-integration strategies that include conservation, treatment, recycle, and reuse are instrumental in reducing water usage and discharge and in abating the environmental impact associated with the discharge of pollutants to water bodies. Three massintegration approaches have been developed for the design of industrial water networks: graphical (pinch), algebraic, and optimization techniques. For recent reviews, the reader is referred to the works by El-Halwagi and Foo,1 Klemeš,2 ElHalwagi,3 Poplewski,4 and Foo.5 Pinch-based methods provide valuable visualization-based understanding of the design of recycle/reuse networks but are limited in terms of scope and size of the problem. On the other hand, mathematical programming techniques can address significantly more complex problems but require specialized knowledge to formulate and solve. A particularly important class of water networks involves the design based on a property integration framework. Property integration is a technique which is based on optimizing the allocation and manipulation of streams to units based on properties. Shelley and El-Halwagi6 proposed a property-based componentless approach to process integration and introduced the concept of property clusters that can be tracked in a © 2015 American Chemical Society

Received: August 19, 2015 Revised: October 14, 2015 Published: November 29, 2015 147

DOI: 10.1021/acssuschemeng.5b00902 ACS Sustainable Chem. Eng. 2016, 4, 147−158

Research Article

ACS Sustainable Chemistry & Engineering

Figure 1. Typical water management scheme in a refinery.41

noteworthy that the above-mentioned works have contributed significantly with the development of water networks, and these have identified the key issues to consider in their synthesis. However, very few strategies have dealt with the specific case of refinery processes, their integration opportunities, and their specific pollution problems due to phenolic compounds. Oil refineries involve significant usage and discharge of water with key opportunities for recycle and integration. Takama et al.36 presented a method for solving the planning problem of optimal water allocation and this method is applied to the allocation problem in a petroleum refinery. El-Halwagi et al.37 developed an integrated approach for managing petroleum-refinery wastewater with phenolic compounds. Bagajewicz38 presented a review of the procedures to design and retrofit water networks emphasizing results for refineries. Savelski and Bagajewicz39 presented a noniterative algorithmic procedure to design water utilization networks in refineries and process plants. Mughees et al.40 presented a research which involved property integration techniques using graphical and mathematical programming models for an oil refinery. This way, based on previous studies, this paper takes advantage of the previous knowledge about the synthesis of water networks based on properties to develop an optimization formulation for synthesizing water networks for wastewater streams in the oil-refinery industry. It should be noticed that several processes in a petroleum refinery use water with different qualities and discharge various wastewater streams (Figure 1). Hazardous compounds such as phenols are present in water process streams of several operations in the petroleum industry. Upon proper treatment, wastewater streams may be considered for recycle or reuse within the process.41 Phenolic compounds are considered as priority pollutants due to their low biodegradability and high toxicity, even at low concentrations. Therefore, they pose potential harm to the ecosystem and to human health. There are different methods for the separation of phenols such as steam-distillation, extraction, adsorption,42 and separation by membranes. Phenols may also be converted to more benign forms using wet-air oxidation, electrochemical oxidation, and biochemical treatment. The main limitations to applying these technologies are the high cost, low efficiency, and generation of toxic products.43 Recently, electrocoagulation has been proposed as an alternative to handling phenolic wastes from

discharge for property-based material reuse networks. Shoaib et al.16 extended the aforementioned water networks methods to batch systems. Ponce-Ortega et al.17 presented a mathematical programming model for the synthesis of direct recycle/reuse networks based on mass and properties such as composition, density, viscosity, pH, reflectivity, composition for hazardous materials, toxicity, chemical oxygen demand, color, and odor to satisfy environmental constrains in order to minimize the total annual cost of the system. Chen et al.18 applied the concept of property integration for resource conservation in palm oil mills. Hortua et al.19 developed a mixed-integer nonlinear programming model to synthesize resource conservation networks based on properties. Sotelo-Pichardo et al.20 presented a mathematical programming model for the reconfiguration of existing water networks based on the stream properties that impact the performance of the process units and the environment. The main limitations of these previous strategies are the property operators used, which, in some cases, are not accurate in the prediction of some properties and furthermore they do not take into account the effect of changing one property in the rest of the properties. Recently, Rojas-Torres et al.21 presented property operators with temperature dependence. Sandate-Trejo et al.22 considered the interdependence of some mixing operators; however, there are still areas of opportunity to improve the mixing rules used in these strategies. Another important aspect that has been studied is the implementation of global optimization techniques for synthesizing water network involving multiple components and multiple properties. Castro and Teles,23 Nápoles-Rivera et al.,24 Karuppiah and Grossmann,25,26 and Gabriel and El-Halwagi27 have presented different global optimization techniques for the solution of the bilinear products arising in the mass and property balances. Faria and Bagajewicz28 and Wang et al.29 have studied aspects such as the retrofitting of existing networks. Roozbahani et al.,30 Halim et al.,31 and Tudor and Lavric32 considered the inclusion of different objective functions such as social, ́ et al.33 economic, and environmental objectives. López-Diaz have studied the water integration based on properties for ecoindustrial parks, which interact with a surrounding watershed. ́ et al.34 reported the impact of using the simultaneous Martinez integration of mass and energy. Jiménez-Gutiérrez et al.35 studied the simultaneous integration of energy, mass, and properties. It is 148


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Figure 2. Proposed superstructure for water integration in an oil refinery.

tion approach is formulated in such a way that it does not involve nonconvex terms and can be solved easily to guarantee the optimal solution. This paper presents a mathematical programming model for the synthesis of recycle and reuse water networks in a petroleum refinery considering an electrocoagulation system for the removal of phenolic compounds. The model accounts for the refinery sources, sinks, extents of removal of phenols, optimization of electrocoagulation conditions, and environmental and process constrains. The model is formulated as a mixed integer nonlinear programming (MINLP) problem that minimizes the total annual cost of the system, which includes the cost for the fresh source and the capital and operating costs for the electrocoagulation treatment system.

refineries and to overcome the previous limitations. This process consists of the dissolution of sacrificial anodes upon the application of a stream between two electrodes for the treatment of wastewater containing inorganic or organic matter.44 Compared with traditional chemical coagulation, electrocoagulation has the advantage of removing the very small colloidal particles and the generation of a relatively low amount of sludge.45 In order for this emerging technology to gain industrial traction, it must be considered in the context of an overall strategy for water management and integration. As noted above, usually the synthesis of water networks has been based on conversion factors without accounting for any specific process for treating the wastewater streams. Furthermore, there are not reported approaches that consider the specific properties of wastewater streams from a petrochemical industry. It is noteworthy that these wastewater streams have specific pollutants and properties that need specific treatments before recycling these streams. In addition, when the design of the treatment processes for petrochemical wastewater streams is considered inside of the optimization model for the synthesis of water networks, several nonconvex terms appear, which yield a model for which is not possible to guarantee the optimal solution or even more it is impossible to obtain a feasible solution. Therefore, the main novelty in this paper is to proposed an optimization approach for the synthesis of petrochemical water networks considering the specific properties associated with the petrochemical wastewater streams as well as the treatment technologies for these wastewater streams, where the optimiza-

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PROBLEM STATEMENT The problem addressed in this work is stated as follows: Given is a set of wastewater streams from a petroleum refinery, which are considered as process sources to be recycled or reused. The flow rates, compositions and properties for these streams are known. Given is also a set of process units (sinks) where the process sources can be reused directly or once they receive treatment. Each sink has known requirements of flow rate and specific constraints given in terms of lower and upper limits on the properties. A set of fresh sources is available to be used as needed to satisfy the demands in the sinks with known values for the properties. Electrocoagulation is considered as a potential technology for the treatment of phenolic wastewater. The task 149


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ACS Sustainable Chemistry & Engineering and design of the electrocoagulation units are to be determined through optimization. A scheme for the treatment of the process sources is proposed (Figure 2). The performance of electrocoagulation is impacted by several factors including the conditions for the inlet stream in terms of temperature, NaCl concentration, and pH.46 Hence, additional units may be needed to adjust the conditions of the stream entering to the electrocoagulation system to optimize the design. These units include the following: a unit to modify the pH (where acid or base may be added to the stream) followed by a unit to adjust the NaCl concentration (this unit employs NaCl or water), a cooler or heater to set the temperature to a desired value, and a reverse osmosis unit placed at the exit of the electrocoagulation system with the purpose of satisfying the process sink constrains and environmental discharge requirements. Figure 2 shows the superstructure that represents the problem including all the considered possibilities for integration. The process sources can be sent directly to the process sinks or to the wastewater discharged to the environment. A source may also be treated prior to reuse or discharge. The desired performance of the electrocoagulation process in terms of pH, NaCl concentration, and temperature is obtained from the experimental data reported by Abdelwahab et al.46 Thus, the treatment sets the special conditions to their corresponding desired values to carry out the electrocoagulation and reduce the phenolic compounds contained in the refinery wastewater streams. Later, the outlet stream is sent to the process sinks, to the waste discharge, or to a reverse osmosis unit. The fresh sources are sent to the process sinks as needed to meet the process sink requirements. It should be noted that the fresh sources are not sent to the waste discharge.

Fresh water (Fr) can be distributed to the different process sinks ( f r,j), avoiding the direct discharge to the environment: Fr =

i

Wi =

m

In

=m β

∑ gj + gWaste + mOut_RO j

∀i (5)

(GSink j )

The required water for the process units is equal to the fresh water ( f r,j), water directly recycled from the process streams (wi,j), treated water leaving the electrocoagulation system (gj), and the treated water processed in the reverse osmosis unit (gRO j ): GjSink =

∑ fr ,j

∑ wi ,j + gj + g jRO ,

+

r

∀j (6)

i

The wastewater discharged to the environment (Waste) is equal to the water sent from the process sources (wi,j), plus the treated water (gWaste) and the water from the reverse osmosis unit (gRO Waste) as follows: Waste =

∑ wi,Waste + gWaste + g RO Waste

(7)

i

Property Tracking. The property operator for the stream entering to the treatment unit (ψInMix (P)) is obtained by the p weighted sum of the property operators of the different process sources (ψSource (P)): p,i ψpInMix(P)mIn =

(P)hi , ∑ ψpSource ,i

∀p (8)

i

It should be noted that the property operators (ψp,i) depend on each property and these can be determined experimentally.6 The property operator for the sinks (ψSink p,j (P)) must be equal to the sum of the property operators for fresh sources (ψFresh p,r (P)), Source direct recycled sources (ψ p,i (P)), treated streams (ψOutSplit (P)), and treated water from the reverse osmosis unit p (ψOutSplit (P)): p GjSink ψpsink (P ) = ,j

∑ fr ,j ψpFresh (P) + ∑ wi , jψpSource (P ) ,r ,i r

+

gjψpOutSplit(P)

i

g jROψpRO(P),

+

∀ j , j ≠ waste, ∀ p (9)

Similarly for the wastewater stream, notice that fresh water cannot be sent to the waste discharge:

(1)

Gwasteψpwaste (P ) = ,waste

∑ wi ,wasteψpSource (P) + g wasteψpOutSplit(P) ,i i

+

RO g waste ψpRO(P),

∀p

(10)

There are specific constraints for the process sinks and for the wastewater discharged to the environment. These constraints are given in terms of lower ψSink‑Min (P) and upper ψSink‑Max (P) limits p,j p,j for the property operators for the streams entering the process sinks as follows:

(2)

Additionally, the outlet water from the treatment system (mOut) is equal to the water sent to the process sinks (gj) plus the water sent to the reverse osmosis unit (gRO j ) as follows: mOut =

∑ wi ,j + wi ,Waste + hi , j

This stream enters to all treatment units; however, during the electrocoagulation process there is a water lost. Thus, the stream leaving the electrocoagulation is related to the inlet stream through an efficiency factor (β): Out

(4)

The process sources (Wi) can be segregated and recycled to the process units wi,j, discharged to the environment (wi,Waste), or sent to the treatment system (hi):

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∑ hi

∀r

j

MODEL FORMULATION The mathematical formulation for this work includes the mass balances and property tracking to model the splitters and mixers considered in the superstructure shown in Figure 2. The formulation also includes the relationships to model the treatment units, the cost functions, and the process and environmental constraints. In the next section is presented the proposed mathematical model, and all the equations that describe the proposed disjunctions are presented in the Supporting Information. Mass Balances. The total flow rate inlet to the treatment system (mIn) is obtained from the different process sources (hi) as follows: mIn =

∑ fr ,j ,

‐Min ‐Max ψpSink (P) ≤ ψpsink (P) ≤ ψpSink (P), ,j ,j ,j

(3)

∀ P, ∀ j (11)

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ACS Sustainable Chemistry & Engineering ‐Min ‐Max ψpSink (P) ≤ ψpsink (P) ≤ ψpSink (P), ,waste ,waste ,waste

∀P

system. However, to obtain accurate correlations, high nonlinear and nonconvex relationships are obtained, which limits their implementation into an optimization formulation for synthesizing water networks and guarantying the optimal solution of even a feasible solution. Therefore, in this paper there is proposed the use of a set of experimental data identified as the best conditions for the electrocoagulation system, and these conditions can be optimized in an outer loop, yielding this way an optimization formulation that can be easily solved without numerical complications. This way, the properties for the treated wastewater stream are adjusted to the desired conditions as follows. pH Adjustment. For modeling the treatment system, first it is necessary to consider a pH adjustment unit to set the pH of the mixed stream to a desired value (It should be noticed that this value can be optimized in an outer loop). Therefore, if the pH is greater than the desired one, it is required to add an acid and if the mixed stream has a pH lower than the desired one, it is necessary to add a base. This is modeled through the following disjunction:

(12)

It should be noticed that the constrained properties depend on the requirements of the process sinks, which can be toxicity, pH, temperature, chemical oxygen demand, concentration of some pollutants, density, and viscosity, among others. Treatment Units. On the basis of previous reports,46 the electrocoagulation system has been identified as a good option for treating the wastewater streams involved in the oil refinery industry. Particularly, this systems is suited for removing phenolic compounds, which represent a severe problem in this industry. Previous studies about the electrocoagulation system to treat phenolic compounds have identified the key properties that most influence its performance; these properties correspond to the pH, sodium chloride concentration, and temperature of the treated wastewater. Therefore, there are several reports about the performance of the electrocoagulation system for different conditions of pH, sodium chloride concentration, and temperature, and these experimental data can be used to obtain correlations for the performance of the electrocoagulation

⎡ Y pH_a ⎤ ⎡ Y pH_b ⎤ ⎡ pH_c ⎤ ⎢ ⎥ ⎢ ⎥ ⎢Y ⎥ InMix InMix − pH − pH − pH − pH ⎢10 ⎥ ⎢10 ⎥ ⎢ −pHInMix −pHdesired ⎥ ≤ 10 desired ≥ 10 desired = 10 10 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ InMix −pHInMix −pHdesired In ⎥ ∨ Acid = 0 ⎢ (10−pHdesired − 10−pH )mIn ⎥ ∨ ⎢ ⎢ ⎥ − 10 (10 )m ⎢ Acid = ⎥ ⎢ Base = ⎥ ⎢ ⎥ Acid InMix Base InMix Conc ρ Conc ρ ⎢ ⎥ ⎢ ⎥ ⎢ Base = 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ pH ⎥⎦ pH Base pH Acid = cost 0 ⎦ ⎣ cost = UC Acid ⎦ ⎣ cost = UC Base

In the previous relationship, the optimization variable is InMix 10−pH , which corresponds to the property operator for the pH. The algebraic reformulation of the previous disjunction is available in the Supporting Information. Sodium Chloride Concentration Adjustment. The concentration for NaCl for the electrocoagulation treatment unit must be adjusted to a desired value46 (which can be optimized in an

outer loop).Thus, if the stream entering to the treatment unit has a concentration lower than this value, it is necessary to adjust it through the addition of NaCl. On the other hand, when the NaCl concentration of the inlet to the treatment stream is greater than the target value, it is necessary to dilute this stream by adding fresh water to adjust this concentration. This is modeled through the following disjunction:

⎡ NaCl_c ⎤ ⎤ ⎢Y ⎡ Y NaCl_a ⎤ ⎡ Y NaCl_b ⎥ ⎥ ⎢C InMix = C desired ⎥ ⎢ ⎥ ⎢ NaCl NaCl InMix desired InMix desired ⎥ ⎢ ⎢C NaCl ⎥ ⎢C NaCl ≥ C NaCl ⎥ ≤ C NaCl ⎥ ⎢ Fresh ⎢ ⎥ ⎢ ⎥ = 0 m In ⎥ ∨ ⎢ ⎛ C InMix ⎞⎥ ∨ ⎢ ⎢ NaCl ⎥ desired InMix m NaCl Fresh In InMix ⎜⎜ desired − 1⎟⎟ ⎥ ⎢ m NaCl = 0 = (C NaCl − C NaCl ) InMix ⎥ ⎢ m =m ρ ⎢m ⎥ ρ ⎝ C NaCl ⎠⎥ ⎢ ⎢ ⎥ ⎢ ⎥ H O ⎥ ⎢ cost 2 = 0 ⎢ ⎥ ⎢ ⎥ NaCl NaCl NaCl ⎣ cost ⎦ ⎢⎣ cost H2O = UCH2OmFresh ⎥⎦ ⎢ = UC m ⎥ ⎣ costNaCl ⎦

This disjunction is also reformulated in terms of algebraic equations (shown in the Supporting Information), which include three Boolean variables associated with binary variables. Then, when the stream at the inlet of this unit has a NaCl concentration lower than the desired value, the binary variable yNaCl_a is set as one; otherwise yNaCl_b is equal to one for the case when the concentration is greater than the mentioned value, and yNaCl_c is one when the concentration is equal to the desired value. Then, only one of these options must be selected.

Temperature Adjustment. The inlet temperature for the electrocoagulation system has to be adjusted to the desired value (which is optimized in an outer loop). First, if the inlet temperature is greater than this value, then a cooling utility is used to quench it. On the other hand, if the inlet temperature is lower than the desired value, steam is employed to raise its temperature. This is modeled through the following disjunction:

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Figure 3. Experimental results for modeling electrocoagulation units (on the basis of data from ref 46).

⎤ ⎤ ⎡ Y EXC_c ⎡ EXC_b ⎤ ⎢Y ⎡ Y EXC_a ⎥ ⎥ ⎢ InMix desired ⎥ ⎥ ⎢ InMix ⎢ ⎢T desired T = ⎥ ≤T ⎥ ⎢T ⎢T InMix ≥ T desired ⎥ ⎥ ⎢Q steam = 0 ⎥ ⎢ steam ⎢ ⎥ In InMix desired InMix ⎥ ⎢ Q m Cp T T = − ( ) cw In InMix InMix desired ⎥ ⎢ ⎢Q = m Cp ⎥ −T (T ) ⎥ ⎢Q cw = 0 ⎥ ⎢ ⎢ ⎥ steam steam steam ⎥ ⎢ cw cw cw Q = cost UC ⎥ ⎢ ⎢ cost = UC Q ⎥ ⎢ coststeam = 0 ⎥ ⎥ ⎢ ⎢ steam ⎥ cw ⎥ ⎢ cw ⎥ ∨ ⎢ AEXC2 = Q ⎢ AEXC = Q ⎥ ⎥ ∨ ⎢ cost = 0 ⎥ ⎢ ⎢ ULMTD ⎥ ULMTD ⎥ ⎢ EXC ⎥ ⎢ ⎢ ⎢A ⎥ =0 In_steam desired Out_steam In_mix ⎥ InMix Out _ cw desired In _ cw T T T T − − − ( ) ( ) ⎢ ⎢ EXC2 ⎥ −T −T (T ) − (T ) ⎥ ⎢ LMTD = ⎥ = LMTD =0 ⎥ ⎢ ⎢ ⎢A ⎥ T In_steam − T desired ⎥ T InMix − T Out_cw ln Out_steam In_mix ⎥ ⎢ ⎢ ⎥ ln desired In_cw T −T ⎥ ⎢ LMTD = 0 T − T ⎥ ⎢ ⎢ ⎢ ⎥ ⎥ ⎥ ⎢ ⎢ Cool ⎢ costHeat = 0 ⎥ Cool Heat Heat Heat EXC2 C Heat ⎥ Cool Cool EXC C =A + B (A cost ) ⎥⎦ ⎢⎣ cost =A + B (A ) ⎥ ⎥⎦ ⎢ Cool ⎢⎣ ⎣ cost ⎦ =0

(

(

)

)

⎤ ⎡ RO_b ⎡ Y RO_a ⎤ ⎥ ⎢Y ⎢ ⎥ ⎥ ⎢ Out_RO ⎢ mOut_RO ≥ mOutRO_min ⎥ m 0 = ⎥ ⎢ ⎢ ⎥ RO ⎥ ⎢C RO = C desired ⎢C NaCl = 0 ⎥ NaCl NaCl ⎥ ⎢ ⎢ ⎥ RO RO Out _ RO ⎥ ∨ ⎢ g RO + g RO = 0 ⎥ ⎢∑ g + g = αm Waste Waste ⎥ ⎢∑ j ⎢ j j ⎥ ⎥ ⎢ j ⎢ ⎥ OP _ RO RO Out _ RO ⎥ ⎢ OP_RO ⎢ cost ⎥ ) = UC (m cost 0 = ⎥ ⎢ ⎢ ⎥ RO RO ⎢ RO RO RO Out_RO C ⎥ ⎥⎦ ) ⎦ ⎢⎣ cos t = 0 ⎣ cost = A + B (m

Similar to the previous disjunctions, each Boolean variable is related to a binary variable. The binary variable yEXC_a is employed to model the case when the inlet temperature is greater than Tdesired, yEXC_b is used to model the case when the inlet temperature is lower than the desired value, and yEXC_c is used to model the case when the inlet temperature is equal to the optimal value. The algebraic reformulation of previous disjunction is presented in the Supporting Information. Reverse Osmosis. According to the proposed design for the

In the previous disjunction, YRO_a represents the Boolean variable associated with the existence of the RO unit; while YRO_b is the Boolean variable that is set as true when the unit is not required. Then, associated with each Boolean variable there is a binary variable which helps to obtain algebraic relationships, which are shown in the Supporting Information. Electrocoagulation System. For properly modeling the electrocoagulation system, in this paper it is proposed to use conditions determined experimentally (as the ones reported by

recycle and reuse network, a reverse osmosis unit is placed at the exit of the electrocoagulation process with the purpose of reducing the NaCl concentration to meet the constraints for the process sinks. In this regard, the existence for this unit is modeled through the following disjunction. 152


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ACS Sustainable Chemistry & Engineering Abdelwahab et al.46); such desired conditions for NaCl concentration, pH, processing time, c.d., and temperature are optimized in an outer loop without involving numerical complications in the optimization approach. It is noteworthy that the energy required and aluminum consumption are the key factors used to determine the electrocoagulation cost. By analyzing the experimental data of Abdelwahab et al.,46 these two aspects can be correlated with the initial phenol concentration (Figure 3). Thus, the energy and aluminum consumption are determined directly through the initial phenol concentration. As can be seen in Figure 3, the initial phenol concentration is a key factor for modeling the electrocoagulation unit and in the optimization formulation this is modeled through the following disjunction:

Figure 4. Removal efficiency for the electrocoagulation unit (on the basis of data from ref 46).

In_Ph ⎤ ⎡ Y C _c ⎥ ⎢ ⎡ C In_Ph_ _a ⎤ ⎡ ⎤ ⎢ C In_Ph _b In_Ph In_Ph_Min ⎥ Y ≥C C ⎢Y ⎥ ⎢ ⎥ ⎢ ⎥ ⎢C In_Ph ≤ C In_Ph_Min ⎥ ⎢C In_Ph ≥ C In_Ph_Max ⎥ ⎢ In_Ph In_Ph_Max ⎥ ≤ C C ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ In In ⎢m = 0 ⎥ ⎢ ⎥ ⎢ m =0 ⎥ mIn ≥ 0 ∨ ∨ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ EC = 0 ⎢ EC = 0 ⎥ ⎢ ⎥ ⎢ ⎥ EC = f1 (C In_Ph) ⎢ AlC = 0 ⎥ ⎢ ⎥ ⎢ ⎥ AlC = 0 ⎢ ⎥ ⎢ ⎥ ⎢ In_Ph ⎥ = AlC ( ) f C _ _ OP Treatm OP Treatm ⎣ cost 2 =0 ⎦ ⎢ = 0 ⎦ ⎣ cost ⎥ ⎢⎣ costOP_Treatm = UCKWhEC +UC AlCAlC ⎥⎦

In the previous disjunction, three options are considered. The first one (associated with the Boolean variable YCIn_Ph_a) represents the case when the initial phenol concentration is lower than the minimum allowed (CIn_Ph_Min), the second option (associated with the Boolean variable YCIn_Ph_b) represents the case when the initial phenol concentration is greater than the maximum allowed (CIn_Ph_Max). In these two options, the electrocoagulation unit is not used and the associated operating cost must be zero. In the third scenario (associated with the Boolean variable YCIn_Ph_c), the electrocoagulation unit is required, and the corresponding energy (EC) and aluminum (AlC) consumed are calculated to determine the associated operating cost (costOP_Treatm). Again, the disjunction was reformulated as a set of algebraic constraints, which are shown in the Supporting Information. It is worth noting that there are two important differences of the considered process and the conditions of the experiments by Abdelwahab et al.,46 the first one is that the considered process is continuous (whereas in Abdelwahab et al.46 it was batch), and the difference in the scales. However, the proposed optimization formulation is general, and this can be used with different and more accurate experimental data for the electrocoagulation system. It should be noted that the removal efficiency for the electrocoagulation system, γ, is determined experimentally and depends on the following functionality: γ = f (pH, I , C In_Ph , C NaCl , T )

γ=

−0.3005C In_Ph + 108.74 100

(14)

The outlet phenol concentration from the electrocoagulation unit is determined as follows: In P COut Ph = P Ph(1 − γ ) C

(15)

Objective Function. The total annualized cost is the sum of the total operating costs including the fresh water cost (FrUCFresh) and the costs associated with operate each unit required plus the annualized capital costs for the units involved in the treatment. TAC = HY[Fr UCFresh + (cost pH + costNaCl + cost H2O + costcw + coststeam + costOP_RO + costOP_Treatm)] + kF(costCool + costHeat + costTreatm + costRO) (16)

In the previous equation, HY represents the operating hours (8000 h/y) and kF corresponds to the annualization factor for the depreciation of capital cost. It should be noted that the corresponding optimization formulation is a mixed-integer nonlinear programming (MINLP) problem, which was coded in the GAMS software.47

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RESULTS AND DISCUSSION To show the applicability and advantages of the proposed methodology, two case studies are presented as follows. Case 1. This example was adapted from Ponce-Ortega et al.48 Eight process sources are available, and their characteristics are given in Table 1. Four sinks are considered. The constraints for the maximum and minimum capacities, and also the allowed properties in sinks and waste, are given in Table S1 (available in

(13)

Notice that the desired conditions determined experimentally for the electrocoagulation system were considered; however, the initial phenol concentration is the only optimization variable in the formulation in the inner loop. This is modeled employing the correlation shown in Figure 4. 153


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in terms of properties are the following: the phenol concentration must be lower or equal to 1 mg/L, a range of 6−8 for the pH, the upper value for the NaCl concentration is 2 kg/m3, and an interval for the temperature must be in the range from 293 to 303 K. Figure 5 shows the optimal network for the proposed case study and additional information is given in Table S2 (available in the Supporting Information). Notice that all the sinks and environmental constraints are satisfied (Table S3) by mixing process sources, treated water, and fresh water. This way, almost all the process sources are reused, and the fresh water consumption is reduced to only 13.79% of the original value without integration. Also, the waste generated is reduced by 324.79 m3/h. The flow rates and characteristics of the streams entering the adjustment train previous to the electrocoagulation system are shown in Table S4 (available in the Supporting Information). It can be seen that it is a slightly basic stream, with a NaCl concentration equal to the optimal concentration and

Table 1. Flow Rates and Properties of Process Sources for Case Study 1 Wi

flow (m3/ h)

phenol (mg/L)

pH

NaCl (kg/ m3)

temperature (K)

1 2 3 4 5 6 7 8

6.31 3.15 157.73 3.15 39.43 11.04 50.47 283.91

15 30 1.2 30 12 8.5 2 42

5.5 7.3 8.0 6.4 7.5 6.8 6.6 7

0.3 0.2 1.0 1.5 2.5 3.0 1.0 2.0

305 295 310 325 318 298 313 307

the Supporting Information). Additionally, there is a fresh source to be used in the process sinks. This fresh source is available with a phenol concentration of zero, a pH of 7, NaCl concentration of zero, and temperature of 295 K. On the other hand, the environmental constraints imposed over the wastewater stream

Figure 5. Optimal network for case study 1. 154


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The optimal results are shown in Figure 6 and Table S7 (available in the Supporting Information); it should be noted that no wastewater is generated and all the sinks constrains are satisfied (Table S6) by mixing process sources, treated water, and fresh water as it is shown in Table S8 (available in the Supporting Information). This way, all the process sources are reused, and the fresh water consumption is reduced up to 45.14% of the value with respect to the case when no integration is used and the waste generated is reduced in 122.50 m3/h. This means that all process water from different sources is reused when the electrocoagulation process is used in the water network. Table S9 (available in the Supporting Information) shows the flow rates and properties of the segregated streams from process sources to the adjustment train previous to the electrocoagulation system, it can be seen that there is a slightly basic stream, with a NaCl concentration equal to the optimal concentration and with a temperature higher than the required one. Table S10 (available in the Supporting Information) shows the flow rate and properties for the stream leaving and inlet to the electrocoagulation treatment unit. Notice that the phenol concentration has a reduction of 99.96%. This removal efficiency allows satisfying the sink constraints as well as a reduction in the fresh water consumption. Here, the electrocoagulation process eliminates wastewater discharge and all the water from process sources is reused in the sinks. Finally, Table 3 shows the main results obtained for the case studies presented. It should be noted that the treatment allows reducing the fresh water consumption by 86.22% and 54.86% for case studies 1 and 2, respectively; whereas the capital costs are $109,869.6 and $46,195/y, respectively. Finally, the implementation of the proposed approach allows reducing the total annual cost by 79.99% and 52.79% for the case with the treatment system for case studies 1 and 2, respectively.

with a temperature higher than the required one. Table S5 (available in the Supporting Information) shows the characteristics of the stream leaving the electrocoagulation system and the characteristics of the inlet stream that is processed in the electrocoagulation unit. Notice that the phenol concentration has a reduction of 97.40%. The high value for the removal efficiency allows satisfying the sink and waste constraints as well as a reduction in the fresh water consumption. Case 2. This example was taken and adapted from Al Zarooni and Elshorbagy.49 Six process sources where selected, and their characteristics are given in Table 2. Four sinks are considered, Table 2. Flow Rates and Properties of Process Sources for Case Study 2 Wi crude tank hydroskimmer condensate flare sour water hydrocracker flare hydroskimmer flare

flow (m3/h)

phenol (mg/L)

pH

NaCl (kg/m3)

temperature (K)

3.00 22.50 6.00 30.00 3.00

2 15 50 10 35

6.3 7.6 8.2 5.8 7.8

0.03 0.4 3.2 0.5 3.0

300 298 303 301 308

3.00

30

7.4

0.3

318

and the constraints for maximum and minimum capacities and allowed properties in sinks and waste are given in Table S6 (available in the Supporting Information). As it was presented in case study 1, there is a fresh source to be used in the process sinks. This fresh source is available without phenol, a pH of 7, NaCl concentration of zero, and temperature of 295 K. The environmental constraints imposed over the wastewater stream in terms of properties are the same as in case study 1.

Figure 6. Optimal network for case study 2. 155


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ACS Sustainable Chemistry & Engineering Table 3. Flow Rate at the Exit of Electrocoagulation Treatment case study

fresh water (m3/y) fresh water cost ($/y)

case study 1 without treatment case study 1 with treatment case study 2 without treatment case study 2 with treatment

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2,960,000.0 408,040.0 980,000.0 442,408.0

operating costs ($/y)

electrocoagulation capital cost ($/y)

total annual cost ($/y)

0.0 347,632.0 0.0 7,224.0

0.0 109,869.6 0.0 46,195.3

7,340,800.0 1,469,449.6 2,430,400.0 1,150,596.3

7,340,800.0 1,011,948.0 2,430,400.0 1,097,177.0

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CONCLUSIONS

This paper has presented an optimization approach for incorporating electrocoagulation in the system design and integration of water networks in oil refineries. A proper superstructure has been developed and the corresponding model was formulated as a disjunctive programming model which seeks to optimize the system and minimize the cost while accounting for the stream properties, the performance of electrocoagulation and ancillary units, and the process and environmental constraints. Due to the characteristics of the refinery wastewater streams, a treatment system was included in the superstructure which allows the adjustment of the properties and concentrations of the involved streams. Several factor (i.e., pH, temperature, and NaCl concentration) were considered for the design of the electrocoagulation system. Energy and aluminum consumption and phenol removal were modeled through correlations that were developed based on experimental data. Furthermore, the proposed optimization problem is formulated such that the highly nonlinear and nonconvex terms are eliminated, and this way the problem can be solved without numerical complications. The proposed model has been applied to two case studies. The results have shown that the implementation of the proposed scheme (which includes the use of properly designed electrocoagulation systems along with ancillary units) improves the cost and performance of the water management system. This is because the proposed scheme allows adjusting the properties through the water network and optimizing the performance of the treatment system. Furthermore, the identified solutions significantly reduce the fresh water consumption and the wastewater discharge.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +52-443-3223500. Ext. 1277. Fax: +52-443-3273584. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT). Also this project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant No. 263/135/ 1433. Therefore, the authors acknowledge with thanks DSR technical and financial support.

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NOMENCLATURE

Variables

Acid = acid added in treatment AEXC = cooler’s area AEXC2 = heater’s area AlC = aluminum consumed Base = base added in treatment CIn_Mix NaCl = NaCl concentration inlet to MIX-1 CNaCl = NaCl concentration CpIn_Mix = heat capacity CIn_Ph = phenol concentration costOP_Treatm = operating treatment cost costTreatm = treatment cost coststeam = steam cost costcw = cooling cost costHeat = heater cost costNaCl = NaCl cost costH2O = fresh water cost costpH = pH adjust cost costcool = cooler cost costOP_RO = operating cost for reverse osmosis costRO = reverse osmosis unit cost EC = energy consumed Fr = total flow rate of fresh sources r f r,j = segregated flow rate from fresh source r to sink j gWaste = segregated flow rate from treatment to waste gRO Waste = segregated flow rate from RO to waste gj = segregated flow rate from treatment to sink j gRO j = segregated flow rate from RO to sink j hi = segregated flow rate from sources to treatment LMTD = logarithmic mean temperature difference mIn = total flow rate from sources to treatment mOut = total flow rate from treatment to sinks mNaCl = total flow rate of NaCl added in treatment mFresh = total flow rate of fresh water added in treatment mOut_RO = total flow rate from RO to sinks mOutRO_Min = minimum total flow rate from RO to sinks mOutRO_Max = maximum total flow rate from RO to sinks pHIn_Mix = pH inlet to MIX-1

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.5b00902. Thorough explanation for the reformulation of the used disjunctions as well as the description of the used nomenclature for variables, parameters, Greek symbols, Boolean variables, and indices; flow rate and property constrains for the sinks for the case studies (Tables S1 and S6); segregated flow rates from sources, fresh water, treatment unit, and RO to the sinks and waste for the case studies (Tables S2 and S7); sink and waste properties for the case studies (Tables S3 and S8); flow rate from sources to treatment for the case studies (Tables S4 and S9); flow rate in the electrocoagulation treatment system for the case studies (Tables S5 and S10); and the parameters used in the case studies (Table S11) (PDF) 156


Research Article

ACS Sustainable Chemistry & Engineering Qcw = heat removed Qsteam = heat added TIn_Mix = temperature inlet to MIX-1 wi,j = segregated flow rate from souses to sinks wi,waste = segregated flow rate from sources to waste Waste = Total flow rate for the waste stream discharged to the environment TAC = total annual cost

YNaCl_a = logic variable for case a for NaCl concentration adjustment YNaCl_b = logic variable for case b for NaCl concentration adjustment YNaCl_c = logic variable for case b for NaCl concentration adjustment YEXC_a = logic variable for case a for temperature adjustment YEXC_b = logic variable for case b for temperature adjustment YEXC_c = logic variable for case c for temperature adjustment YRO_a = logic variable for case a for reverse osmosis process YRO_b = logic variable for case b for reverse osmosis process YIn_Ph_a = logic variable for case a for electrocoagulation process YIn_Ph_b = logic variable for case b for electrocoagulation process YIn_Ph_c = logic variable for case c for electrocoagulation process

Parameters

A = constant for the cost estimation B = constant for the cost estimation C = constant for the cost estimation ConcAcid = acid concentration ConcBase = base concentration Cdesired NaCl = desired NaCl concentration for electrocoagulation process CIn_Ph_Max = maximum concentration of phenol CIn_Ph_Min = minimum concentration of phenol GSink = total flow rate inlet to sink j j HY = time of operation of the plant in hours year kF = factor used to annualize the inversion pHdesired = desired pH for electrocoagulation process U = global heat transfer coefficient UCAcid = unit cost for acid in treatment UCAlC = unit cost for aluminum anode UCBase = unit cost for base in treatment UCcw = unit cost for coolant in treatment UCFresh = unit cost for fresh water UCH2O = unit cost for fresh water in treatment UCKWh = unit cost for electricity UCNaCl = unit cost for sodium chloride UCRO = unit cost for treating wastewater in reverse osmosis UCsteam = unit cost for the steam Tdesired = desired temperature for the electrocoagulation process Wi = total flow rate for the process source i

Subscripts and Superscripts

Max = maximum Min = minimum In = inlet Out = outlet Cool = cooler Heat = heater RO = reverse osmosis Treat = treatment Indices

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i = process source j = sink p = property r = fresh source Waste = waste stream

REFERENCES

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Greek Symbols

α = efficiency factor for the reverse osmosis process β = efficiency factor for the electrocoagulation process γ = efficiency factor for phenol removal in electrocoagulation process ρIn_Mix = inlet treatment density ψInMix (P) = properties for the streams inlet to the treatment p unit ψSource (P) = properties of the streams from the different p,i process sources ψSink p,j (P) = property operator for the sinks ψSink_Max (P) = maximum for the property operator for the p,j sinks ψSink_Min (P) = minimum for the property operator for the p,j sinks ψSink_Max p,waste (P) = maximum for the property operator for the waste ψSink_Min p,waste (P) = minimum for the property operator for the waste ψFresh p,r (P) = property operator for fresh sources ψOutSplit (P) = property operator for treated wastewater p ψRO p (P) = property operator for reverse osmosis outlet stream Boolean Variables

YpH_a = logic variable for case a for pH adjustment YpH_b = logic variable for case b for pH adjustment YpH_c = logic variable for case c for pH adjustment 157


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Optimal Synthesis of Refinery Property-Based Water Networks with

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