A Superstructure Optimization Approach for Membrane Separation

ARTICLE pubs.acs.org/IECR

A Superstructure Optimization Approach for Membrane Separation-Based Water Regeneration Network Synthesis with Detailed Nonlinear Mechanistic Reverse Osmosis Model Cheng Seong Khor,*,†,‡ Dominic C. Y. Foo,§ Mahmoud M. El-Halwagi,^ Raymond R. Tan,z and Nilay Shah† †

Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom Chemical Engineering Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia § Department of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia ^ Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States z Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines ‡

ABSTRACT: Scarcity of freshwater resources and increasingly stringent environmental regulations on industrial effluents have motivated the process industry to identify and develop various water recovery strategies. This work proposes the use of detailed model representation for water regeneration network synthesis, in which nonlinear mechanistic models of the regeneration units are embedded within an overall mixed-integer nonlinear programming (MINLP) optimization framework. The superstructure-based MINLP framework involves both continuous variables for water flow rates and contaminant concentrations and 01 variables for selection of piping interconnections. The nonlinear regeneration model produces a rigorous cost-based relation, instead of a “black box” model, that is incorporated within the overall MINLP representing a network of numerous water sources and water sinks. Hence, such an approach enables a simultaneous evaluation of both direct water reuse/recycle and regenerationreuse/recycle opportunities. To demonstrate the proposed approach, an industrial case study is illustrated that incorporates a mechanistic model of reverse osmosis network (RON) for water regeneration for an operating refinery in Malaysia. The results indicate a potential of 58% savings in freshwater use. The capital investment for the water regeneration network is reported as $8,960,000 with a payback period of 2.1 years, thus providing economic support to pursue the RON retrofit option.

1. INTRODUCTION The optimal synthesis of water network continues to be a major problem of significant challenge in the design of process systems and its allied industries. Within the realm of the process integration philosophy for water minimization, water reuse refers to the channeling of effluent from a water-using operation to other operations except the operations where it was generated, while the latter condition is referred to as water recycle. In further reducing freshwater and wastewater flow rates after exhausting recovery opportunities via direct reuse/recycle, water regeneration will be considered, which involves performing partial treatment on the effluent by using water purification units such as membranes and steam stripping. In general, there are two major approaches for addressing the water network synthesis problem, namely the insightsbased and mathematical optimization techniques. The former typically involves water pinch analysis techniques, which offer good insights with low computational burden for process designers in network synthesis but often at the expense of requiring significant problem simplification.15 On the other hand, optimization allows rigorous treatment of large-scale complex systems by considering representative cost functions, multiple contaminants, and various topological constraints, but it frequently suffers from the high computational expense required to achieve optimality.611 Recent work in this area has increasingly witnessed the development of mathematical r 2011 American Chemical Society

models of greater rigor and complexity that employ a framework driven by optimization-based approaches, primarily mathematical programming1220 as well as soft optimization methods such as fuzzy programming2123 and artificial intelligence-based metaheuristic algorithms.24,25 Optimizationbased techniques for reuse/recycle and regeneration networks also have been developed by numerous researchers using property-integration framework.2629 In several work, the overall optimization framework is coupled with physical insights derived from water pinch analysis.27,3036 The approach typically involves the construction of a superstructurebased network representation of design alternatives for the water system, in which the corresponding optimization model formulation embeds the following two parts. First is the structural optimization problem that selects the optimal water network structure from numerous feasible alternatives, as represented by 01 decision variables. Second is the parameter optimization problem that determines the optimal performance levels of the subsystems for the selected optimal structure, as represented by continuous decision variables. However, most work does not consider incorporating Received: April 4, 2011 Accepted: October 11, 2011 Revised: September 30, 2011 Published: October 11, 2011 13444

dx.doi.org/10.1021/ie200665g | Ind. Eng. Chem. Res. 2011, 50, 13444–13456

Industrial & Engineering Chemistry Research

ARTICLE

Figure 1. General representation of the sourceregenerationsink superstructure with mixers and splitters.

Figure 2. Schematic representation of a water source.

rigorous parameter optimization models of the subsystems within an optimization framework. While research efforts have been directed toward the parameter optimization problem for the separation section of a process network,3740 relatively little work has been conducted for the water network.19,20,41 Thus, there is value in the rigorous handling of the parameter optimization problem for a water regeneration network to explore its interactions with the water-using units. This work proposes a superstructure optimization strategy for the synthesis of a water regeneration network by employing a rigorous nonlinear modeling approach for the regeneration units. We accomplish this goal by considering the use of partitioning regeneration units, specifically membrane separation-based technology for water regeneration. This type of regeneration units typically separates a water stream into a high-quality lean purified stream termed as permeate and a low-quality concentrated reject stream termed as retentate. In particular, we propose a detailed nonlinear mechanistic model for the synthesis of a reverse osmosis network (RON) regeneration unit and the allocation of water sources and sinks that are linked to this regeneration unit. This mechanistic RON model is embedded within an overall mixed-integer nonlinear programming (MINLP) superstructure framework of a water regeneration network. Clearly, the proposed framework considers the various cost components contributed by the water regeneration units.15,31,4244 Executing the overall optimization framework with respect to cost leads to a water regeneration network with minimum cost. In comparison, most previous works make use of simplified “black box” models for the water regeneration units that do not guarantee a true reflection of a minimum cost solution. In terms of problem formulation, to incorporate the concepts of regenerationreuse/recycle, this work considers fixed-flow rate water-using processes3,4 as a modeling alternative to the more traditional mass transfer-based fixed contaminant load models.1 Synthesis methods for a fixed-flow rate model consider water-using processes as sources and sinks

that generate and/or consume a fixed amount of water. Thus, such a problem formulation emphasizes flow rates as the main attribute, instead of impurity load removal (as in the fixed contaminant load formulations).5 In essence, the main contribution of this work is the development of a nonlinear modeling approach for incorporating a water regeneration system within an overall MINLP superstructure optimization framework for water network synthesis. To the best of our knowledge, while there is an appreciably rich literature on rigorous design models for wastewater treatment technologies (in the case of an RO unit operation, see for example, Saif et al.;45,46 El-Halwagi;47,48 Marcovecchio et al.;49 Maskan et al.;50 and Voros et al.51), there is a significant gap in the synthesis of a water network that simultaneously considers a rigorous representation of the regeneration units. Our work attempts to address this gap in the research literature and may be considered as an extension of Tan et al.,15 with integration of detailed modeling of the regeneration units within a water network optimization framework.

2. PROBLEM STATEMENT The main aim of this work is to synthesize a water regeneration network with the following elements: • a set of water sources so, so ∈ SO with known flow rates Q1(so) and concentrations Cso(so,co) of contaminants co that are amenable for reuse/recycle • a set of water sinks si, si ∈ SI with fixed flow rate requirements Q2(si) and known maximum allowable concentration limit Cmax(si,co) for each of the contaminants co that are amenable for reuse/recycle • a set of water regeneration units int, int ∈ INT as technologies for the partial removal of targeted contaminants from the sources. In particular, we consider a single-stage RON to illustrate the approach of detailed model representation for the regeneration units • a freshwater source FW, FW ∈ SO with known contaminant concentrations that can be purchased to supplement the availability of water sources. The overall MINLP problem is performed in conjunction with a mechanistic model for the detailed design of a RON. The latter accounts for the important physical parameters of the membrane unit. The parameters governing the total annualized cost (TAC) of the RON include the 13445

dx.doi.org/10.1021/ie200665g |Ind. Eng. Chem. Res. 2011, 50, 13444–13456


ARTICLE

Figure 3. Schematic representation of a water regeneration unit.

following: (i) inletoutlet flow rates and concentrations; (ii) types, sizes, number, and arrangement of the membrane modules; (iii) optimal operating conditions, for example, the RO feed pressure; and (iv) types, sizes, and number of pumps and the energy-recovery device of turbine. The RON mechanistic model is incorporated into the main MINLP problem to solve for an optimal overall water regeneration network configuration that achieves minimum total cost.

the balance is modeled as an inequality. The excess water source is sent for wastewater treatment. 3.2.2. Water Balances for Regeneration Units. Figure 3 shows a schematic representation of a regeneration unit that receives a mix of water sources, which then generates permeate and retentate streams that are allocated to the sinks. The balance is formulated as

∑

so ∈ SO

3. OPTIMIZATION MODEL FORMULATION We employ total stream flow rates and compositions in terms of contaminant concentrations to formulate the MINLP optimization model for this problem.52 3.1. Superstructure Representation. The MINLP model is developed based on the superstructure representation in Figure 1. As shown, the water sources are connected to thVVe water sinks with or without being intercepted by a water regeneration unit. It is noteworthy that we exclude the operation of directly channeling a freshwater source into a regeneration unit because its contaminant concentrations are typically low enough to obviate the need for regeneration. The water regeneration unit considered in this work is a RON that may be modeled as a partitioning regeneration unit with outlets consisting of a permeate stream with low contaminant concentrations and a retentate stream with high contaminant concentrations.15,35 We consider two types of decisions in our model formulation: (1) continuous decisions as represented by the variables of water flow rates and contaminant concentrations; and (2) discrete decisions as represented by the binary 01 variables modeling the existence (or nonexistence) of the piping interconnections (a) between a source and a sink, which represents direct water reuse/recycle without regeneration; (b) between a source and a regeneration unit; (c) between a permeate or retentate stream of a regeneration unit and a sink, which represents water regenerationreuse/recycle. 3.2. Water Balances. Water balances are established on the basis of the sourceregenerationsink superstructure representation shown in Figure 1. 3.2.1. Water Balances for Sources. Figure 2 shows a schematic representation of a water source that is split into several streams for direct reuse/recycle in the sinks and/or for regeneration. The flow balance for a source is modeled as Q1 ðsoÞ g

∑ Qd ðso, intÞ þ si ∑∈ SI Qa ðso, siÞ, int ∈ INT

" so ∈ SO

ð1Þ It is noteworthy that from our computational experiments, representing this balance as an equality with the addition of an effluent term tends to cause computational difficulties. Hence,

Qd ðso, intÞ ¼

∑

si ∈ SI

Qb, perm ðint, siÞ þ

∑

si ∈ SI

Qb, rej ðint, siÞ,

" int ∈ INT

ð2Þ

The concentration balance for a regeneration unit is modeled as

∑

Qd ðso, intÞ 3 Cso ðso, coÞ ¼ Cperm ðint, coÞ 3

so ∈ SO

þ Crej ðint, coÞ 3

∑

si ∈ SI

" int ∈ INT,

∑

si ∈ SI

Qb, perm ðint, siÞ

Qb, rej ðint, siÞ,

" co ∈ CO

ð3Þ

3.2.2.1. Liquid Phase Recovery. The parameter liquid phase recovery α (where 0 < α < 1) of a regeneration unit represents a fixed fraction of its inlet flow rate that exits in the permeate stream. The complement (1α) is discharged as the retentate stream. The former is expressed as15 αðintÞ ¼

∑ Qb, perm ðint, siÞ ∑ Qd ðso, intÞ so ∈ SO

si ∈ SI

ð4Þ

It can be seen that the special case where α = 1 results in a socalled single-pass regeneration unit.35 3.2.2.2. Removal Ratio. Removal ratio (RR) refers to the fraction of mass load in a regeneration unit inlet stream that exits in its retentate stream. In this work, the RR is assumed to be a fixed value for each contaminant of a regeneration unit, modeled as follows: Crej ðint, coÞ RRðint, coÞ ¼

∑

si ∈ SI

Qb, rej ðint, siÞ

∑ Qd ðso, intÞ 3 Csoðso, coÞ so ∈ SO " int ∈ INT,

,

" co ∈ CO

ð5Þ

3.2.3. Water Balances for Sinks. Figure 4 shows the schematic representation of a water sink that receives the mixing of either the permeate or retentate stream of a regeneration unit and the source streams. The flow balance for a sink is modeled as:

∑

so ∈ SO

Qa ðso, siÞ þ

" si ∈ SI 13446

∑

int ∈ INT

ðQb, perm ðint, siÞ þ Qb, rej ðint, siÞÞ ¼ Q2 ðsiÞ,

ð6Þ



ARTICLE

Figure 4. Schematic representation of a water sink.

Figure 5. Schematic representation of an RON (after El-Halwagi48).

To forbid the mixing of permeate and retentate streams of the regeneration unit in the same sink, the constraint in eq 7 is added: Yperm ðint, siÞ þ Yrej ðint, siÞ e 1, " si ∈ SI,

" int ∈ INT

ð7Þ Since each sink can only tolerate up to a maximum allowable contaminant concentration limit Cmax(si,co), the component concentration balance for a sink is modeled as ð

∑

so ∈ SO

þ

Qa ðso, siÞ 3 Cso ðso, coÞÞ

∑

int ∈ INT

operations: pump, reverse osmosis (RO) modules, and turbine that recovers kinetic energy from the high-pressure retentate stream.46 The important variables and physical parameters of RO are incorporated to obtain a representative nonlinear function of the TAC expression for the regeneration operation, instead of a representation by a single fixed numerical value. The TAC function is subsequently fed to the main MINLP framework to obtain the optimal water regeneration network. Hence, for a given set of parameter values, the model can be solved to synthesize an optimal water regeneration network configuration. Equation 9 represents the TAC for a single-stage RON comprising annualized fixed capital costs of the RO modules, pump, and turbine as well as the operating costs for pump and pretreatment chemicals. The TAC also considers the operating revenue of the energy-recovering device of turbine and is thus formulated as 0 1 Qb, perm ðRO, siÞ B C si ∈ SI TACðcoÞ ¼ @Cmodule 3 A qP ðcoÞ

∑

ðCperm ðint, coÞ 3 Qb, perm ðint, siÞ

þ ðCpump 3 ðPOWER pump Þ0:65 Þ

þ Crej ðint, coÞ 3 Qb, rej ðint, siÞÞ e Q2 ðsiÞ 3 Cmax ðsi, coÞ, " si ∈ SI, " co ∈ CO ð8Þ Note that in Figure 4, a waste element is considered as part of the sinks in the proposed framework. This waste sink is assumed to be treated in an offsite waste treatment facility, which is not considered explicitly as part of the superstructure here, prior to discharge to the environment. It is modeled as a sink with variable flow rate. The Cmax of this sink is designated as the inlet limit for the treatment processes, which are performed to comply with the effluent standard imposed by environmental regulations. 3.3. Formulation of Rigorous Water Regeneration Network Model. This section presents a mechanistic model formulation for the detailed design of a RON. The model distinguishes this paper from previous work wherein simplified “black box” representations of partitioning regeneration units are used.4 The RON model adopted is based on El-Halwagi,47,48 in which a single-stage RON is schematically shown in Figure 5. In this work, we consider the synthesis of a hollow-fiber-type RON. We assume that the RON consists of three principal unit

þ ðCturbine 3 ðPOWER turbine Þ0:43 Þ ðPOWER pump Þ þ Celectricity 3 AOT 3 ηpump þ ðCchemicals 3 AOT 3

∑

so ∈ SO

!

Qd ðso, ROÞÞ

ðCelectricity 3 AOT 3 ðPOWER turbine Þ 3 ηturbine Þ " co ∈ CO

ð9Þ

where

!! Crej ðRO, coÞ ΔPshell πF þ PP 1 þ qP ðcoÞ ¼ Sm A PF γ 2 2 CF ðRO, coÞ

POWER pump ¼ 13447

∑

so ∈ SO

Qd ðso, ROÞðPF Patm Þð1:01325 105 Þ



ARTICLE

Table 1. Limiting Data for Water Sources water source 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

O&G (mg/L)

TSS (mg/L)

COD (mg/L)

chloride (mg/L)

phosphate (mg/L)

5.00 23.00 20.00 69.00 27.00 20.00 30.00 45.00 100.00 2.00 17.00 1.00 6.00 1.00 3.50 1.80 10.00 2.00 3.50 1.80 25.00 72.30 0.30 0.30 2.00 0.00 67.20 3.10 variable

2.000 2.000 0 24 100 0 0 1430 0 0 99.00 2.000 439.0 5.000 544.0 1.000 1.000 3.000 0 3.600 0 0 0 0 0 0 0 0 0 3.000

127.0 40.00 16.00 6774 10.00 0 1945 0 0 13.00 14.00 228.0 6081 108.0 37.00 37.00 5.000 0 1.000 0 12.00 0.129 3.000 3.000 10.00 10.00 10.00 0 10.00

167.0 52.00 86.00 178.0 22.20 0 2234 0 844.0 231.0 28.00 667.0 299.0 8610 81.00 81.00 30.00 0 48.00 0 47.00 4.974 116.0 116.0 22.20 22.20 22.20 0 22.20

0 0 0 0 0 0 0 0 0 0 0 0 0 0 152.0 152.0 108.0 0 65.83 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 18.52 18.52 19.09 0 19.34 0 0 0 0 0 0 0 0 0 0

coke run-off PSR-1 process area sulfur run-off lift station 4 users TKLE PSR-1 desalter PSR-2 desalter SWTU train PSR-2 process area PSR-1 flare knockout drum PSR-1 crude tank drain PSR-2 crude tank drain Intermediate condensate tank BD1 BW1 BD2 BW2 BD3 BW3 OWe-RG2 BDBLs2 WHB-BD1 WHB-BD2 SW2 OWg SW4-BDBL OW3b freshwater

POWER turbine ¼

and

flow rate (ton/h)

∑

si ∈ SI

Qb, rej ðRO, siÞðPR Patm Þð1:01325 105 Þ

0

1

B γ¼B @

C η C, 16Aμro LLs η A 1 þ 1:0133 105 ri 4

tanh θ ¼

e2θ 1 , e2θ þ 1

η¼

θ¼

tanh θ , θ

16Aμro 1:0133 105 ri 2

1=2

L ri

Sm = membrane area per module, ΔPshell = shell side pressure drop per module, L = fiber length, Ls = seal length, ri = inside radius of fiber, ro = outside radius of fiber, ηpump = pump efficiency, ηturbine = turbine efficiency, and πF = osmotic pressure at feed side. It is noteworthy that the formulation of the TAC expression above serves to encompass the important physical properties of the hollow fiber RO membrane to obtain a representative mechanistic model. This TAC expression for the RON is an important component of the objective function for the overall MINLP model, which will be explained in a later section. 3.3.1. Constraints on Reverse Osmosis Operating Conditions. Constraints on the RO operating conditions serve to rigorously capture the underlying characteristics, physics, and complexities

of the RO membrane in the mechanistic model. The constraint on the RO feed pressure PF is given by ΔPshell þ PP PF ¼ ΔP þ ð10Þ 2 where ΔP = (P F + P R )/2 P P , ΔP shell = P F P R , ΔP = (Nwater/(Aγ) + πF/(CF(RO,co))CS, Nwater = Nsolute/ (Cperm(RO,co)), and Nsolute = (D2M/(Kδ))CS. Next, the RO average contaminant concentration in the shell side CS is defined in order to express PF in eq 10 in terms of CF and Cperm (for the purpose of writing clarity, the indices have been omitted here): CS ¼

CF þ Crej 2QF CF Qb, perm Cperm Qb, perm CF ¼ 2 2ðQF Qb, perm Þ

ð11Þ

Combining eqs 10 and 11 yields the following expression for PF: 1 ð2QF CF Qb, perm Cperm Qb, perm CF Þ PF ¼ SFC Aγ 2Cperm ðQF Qb, perm Þ πF ð2QF CF Qb, perm Cperm Qb, perm CF Þ 2CF ðRO, coÞðQF Qb, perm Þ ΔPshell þ PP þ 2

þ

ð12Þ

where SFC = D2M/Kδ is the salt (contaminant) flux constant. 3.4. Objective Function. The objective function of the problem is to minimize the total cost of the overall water 13448



ARTICLE

Table 2. Limiting Data for Water Sinks flow rate (ton/h)

water sink

O&G (mg/L)

TSS (mg/L)

COD (mg/L)

chloride (mg/L)

phosphate (mg/L)

1.

firewater

3.00

25.00

25.00

25.00

25.00

25.00

2.

OSW-SB

144.00

50.00

20.00

20.00

25.00

25.00

3.

potable

20.00

25.00

25.00

25.00

25.00

25.00

4.

PSR-1 CT

25.60

25.00

25.00

25.00

25.00

25.00

5.

Cogen CT

54.00

25.00

25.00

25.00

25.00

25.00

6.

MG3 CT

25.00

25.00

25.00

25.00

25.00

25.00

7.

Boiler

198.50

1.00

20.00

20.00

25.00

25.00

8. 9.

HPU1 HPU2

29.70 29.70

25.00 25.00

25.00 25.00

25.00 25.00

25.00 25.00

25.00 25.00

10.

PSR-1 SW

12.39

25.00

25.00

25.00

25.00

25.00

11.

PSR-2 SW

36.96

25.00

25.00

25.00

25.00

25.00

12.

BDBLu

56.33

25.00

25.00

25.00

25.00

25.00

13.

waste

variable

24200

6800

8650

200.0

200.0

Table 3. Data on Manhattan Distance D (m) for Case Study (Note: Numerals Are as Indicated in Table 1 for Sources and Table 2 for Sinks) Sink source

1

2

3

4

5

6

7

8

9

10

11

12

13

regeneration Unit RO

1 2 3 4 5

50 60 50 60 50

50 50 50 50 50

50 60 50 60 50

60 70 60 70 60

70 80 70 80 70

80 90 80 90 80

90 100 90 100 90

100 110 100 110 100

110 130 110 130 110

130 140 130 140 130

140 150 140 150 140

110 120 110 120 110

150 150 150 150 150

50 40 65 100 40

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

40 60 90 100 90 60 70 110 80 50 50 60 60 70 70 80

50 50 80 90 80 50 60 100 70 50 50 50 50 60 60 70

50 60 70 80 70 60 70 90 80 50 50 60 60 50 50 60

50 70 80 70 80 70 80 80 90 60 60 70 70 60 60 50

60 80 90 80 90 80 90 70 100 70 70 80 80 70 70 60

70 90 100 90 100 90 100 80 110 80 80 90 90 80 80 70

80 100 110 100 110 100 110 90 130 90 90 100 100 90 90 80

90 110 130 110 130 110 130 100 140 100 100 110 110 100 100 90

100 130 140 130 140 130 140 110 150 110 110 130 130 110 110 100

110 140 150 140 150 140 150 130 120 130 130 140 140 130 130 110

130 150 120 150 120 150 120 140 150 140 140 140 140 140 140 130

140 120 150 120 150 120 150 150 160 140 140 150 150 140 140 140

140 150 180 150 180 150 160 120 170 150 150 130 130 150 150 140

50 50 120 50 30 50 100 150 35 40 50 30 50 50 45 150

22

70

60

50

60

70

80

90

100

110

130

140

140

130

40

23

80

70

60

50

60

70

80

90

100

110

130

140

140

50

24

90

80

70

80

90

100

110

130

140

150

120

150

150

30

25

100

90

80

70

80

100

90

80

70

80

140

150

130

45

26

110

60

70

80

90

100

110

90

100

110

130

140

140

130

27

80

70

60

50

60

70

80

90

100

110

130

140

140

35

28

70

60

50

60

70

80

90

100

110

130

140

140

130

40

29

100

110

100

90

80

70

60

50

60

70

80

90

170

30

70

60

70

60

50

60

70

50

60

70

80

130

regeneration unit RO

80

regeneration network that consists of the following cost components on an annualized basis: (i) cost of freshwater use; (ii) treatment cost of wastewater; (iii) TAC of the

regeneration units (i.e., RON), as described in the previous section; and (iv) capital and operating costs of the piping interconnections. 13449



ARTICLE

Table 4. Economic Data and Model Parameters for Case Study parameter

value

parameter

value

annual operating time (AOT)

8760 h

unit cost for freshwater Cwater

$1.00/ton

liquid phase recovery factor α

0.7

unit cost for effluent treatment Cwaste

$1.00/ton

0.4 atm

interest rate per year m

5%

shell side pressure drop per module ΔPshell

number of years n

5 years

pump efficiency ηpump

0.7

7200

turbine efficiency ηturbine

0.7

osmotic pressure coefficient OS

0.006 psi/(mg/L)

parameter p for carbon steel piping a

cost based on CEPCI value of 318.3

a

Table 6. Process and Economic Data for Detailed Design of RON48

parameter q for carbon steel piping cost based on CEPCI value of 318.3

250

velocity v

1 m/s

solute (contaminant) flux constant D2M/Kδ

0.750 m

TSS

0.975

seal length Ls

0.075 m

COD chloride

0.9 0.94

permeate pressure of

1 atm

phosphate

0.97

TACðcoÞ ∑ Qa ðfreshwater, siÞ þ Cwaste 3 Q2 ðwasteÞÞAOT þco ∑ si ∈ SI ∈ CO

regeneration unit Pp inside radius of fiber ri outside radius of fiber ro

21 106 m 42 106 m

membrane area per module Sm

180 m2 per module

cost of pretreatment chemicals Cchemicals

$0.03/ton

cost of electricity Celectricity

$0.06/kW 3 h

cost per module of HFRO membrane Cmodule

$2300/year 3 module

cost coefficient for pump Cpump cost coefficient for turbine Cturbine

$6.5/year 3 W0.65

$18.4/year 3 W0.43

Table 7. Summary of Main Results of Optimal Solution for the Case Study parameter

value

TAC of RON

$96,291/year

TAC of overall water regeneration network

$2,738,000/year

total freshwater use without water regeneration (FW1) total freshwater use with water regeneration (FW2)

705 ton/h 295.9 ton/h

∑ ∑

percentage of freshwater saving =

58%

∑ ∑

number of RON modules

!

p Qa ðso, siÞ mð1 þ mÞ þ q 3 Ya ðso, siÞ Da ðso, siÞ 3 n n 3600v ð1 þ mÞ 1 so ∈ SO si ∈ SI ! p Qb, perm ðint, siÞ þ q 3 Yb, perm ðint, siÞ Db, perm ðint, siÞ 3 3600v int ∈ INT si ∈ SI ! p Qb, rej ðint, siÞ þ q 3 Yb, rej ðint, siÞ Db, rej ðint, siÞ 3 3600v int ∈ INT si ∈ SI p Qd ðso, intÞ Dd ðso, intÞ 3 þ q 3 Yd ðso, intÞ ð13Þ 3600v so ∈ SO int ∈ INT n

þ

1.82 108 m/s

fiber length L

The formulation of the piping cost component assumes a linear fixed-charge cost model whose structure allows the following behavior or property to prevail: with fixed costs and 01 variables, each time a pipeline segment is used, the associated fixed charge is incurred. Thus if a particular flow rate falls below a threshold value, the executed optimization procedure is inclined to set it to zero to avoid a fixed charge. Hence, adopting the linear fixed-charge cost model affords the attractive behavior of reducing the number of piping interconnections required, particularly those with small flow rates (see later section). The details of the formulation of the objective function are as follows:53

þ

0.001 kg/m 3 s 5.573 108 m/s 3 atm

RR

contaminant

þ

permeability coefficient KC water viscosity μ water permeability coefficient A

Table 5. RR for Contaminants in the RON

þ

1.82 108 m/s

solute (contaminant)

Chemical Engineering Plant Cost Index.

minðCwater

= 4.0828 104 atm

∑

∑ ∑

∑

It is assumed that all the pipelines share the same properties of the parameters p and q, the 1-norm Manhattan distance D, and stream velocity v. Here, we observe that the expression for TAC as represented in eq 9 is dependent on the type of contaminant. This is computationally undesirable because for multicomponent problems, the TAC needs to be accounted for a summation over the contributions of all contaminants involved in order to obtain a truly representative objective function value. Such an enumeration is bound to be computationally expensive, particularly considering the complex expression that TAC entails. Thus, in the next section, the expression for TAC is reformulated in such a way so as to eliminate its dependence on contaminant type.

(FW1 FW2)/FW1 100 20

3.5. Reformulation of the TAC Expression Independent of Contaminant Type. El-Halwagi48 defines the osmotic pressure of

the RO on the feed side πF as a function of the contaminant concentration. Since the contaminant concentration of the permeate is significantly lower than that of the feed side, the RO osmotic pressure on the permeate side can be neglected. In this work, we adopt the relation by Saif et al.46 for the osmotic pressure on the retentate side ΔπRO, which seeks to cover a representative range possibly encountered in the optimization procedure: ΔπRO ¼ OS 3

∑co CF, average ðRO, coÞ

ð14Þ

where OS is a proportionality constant between the osmotic pressure and average solute concentration on the feed side,46 with its value in the range of 0.0060.011 psi/(mg/L).54 The average concentration for a contaminant on the feed side CF,average(RO,co) is rewritten in terms of its concentration on the 13450



ARTICLE

Saif et al.46 proposes the following relation for the permeate flow rate from RO QP:

permeate side as follows:

∑ Cperm ðRO, coÞ 3 AðΔP ΔπRO Þγ co ∈ CO CF, average ðRO, coÞ ¼ ∑ Kc ðcoÞ co ∈ CO

ð15Þ

QP ¼ ðnumberofmodulesÞ 3 A 3 Sm 3 γðΔP ΔπRO Þ

where Kc is the contaminant permeability coefficient.

QP ¼ qP

thus, the number of modules is derived accordingly as

∑

si ∈ SI

0 B ΔPshell B A 3 Sm 3 γBPF þ PP @ 2

OS 3

ð16Þ

Qb, perm ðRO, siÞ

1 ΔPshell þ PP ΔπRO γC Cperm ðRO, coÞ 3 A PF 2 C co ∈ CO C A Kc

∑

ð17Þ

where ΔP = PF (ΔPshell/2+PP). For the purpose of completeness, reformulation of the TAC expression independent of contaminant type is as follows: 1

0 B B B B B B 0 TAC ¼ Cmodule B B B OS 3 B B ΔPshell B B þ PP BA 3 Sm 3 γBPF @ @ 2

∑

si ∈ SI

Qb, perm ðRO, siÞ

ΔPshell Cperm ðRO, coÞ 3 A PF 2 co ∈ CO Kc

∑

C C C C C C 1C C þ PP ΔπRO γCC C CC CC AA

Qd ðso, ROÞÞðPF Patm ÞÞ0:65 þ Cturbine ðð ∑ Qb, rej ðRO, siÞÞððPF ΔPshell Þ Patm ÞÞ0:43 ∑ so ∈ SO si ∈ SI

þ Cpump ðð ð þ ð

∑

so ∈ SO

∑

si ∈ SI

Qd ðso, ROÞÞðPF Patm ÞCelectricity 3 AOT ηpump

þ ð

∑

so ∈ SO

Qd ðso, ROÞÞCchemicals 3 AOT ð18Þ

Qb, rej ðRO, siÞÞððPF ΔPshell Þ Patm Þηturbine 3 Celectricity 3 AOT

3.6. Big-M Logical Constraints. Logical constraints and discrete binary variables are adopted to determine the existence of a stream piping interconnection. Logical constraints are imposed such that, if a 01 variable is zero (or one), the associated continuous flow rate variable(s) must also be zero (correspondingly, nonzero), but this is provided that there is a fixed cost charge penalized in the objective function for the 01 variable. These relationships can be enforced by formulating logical constraints using the big-M parameters, in which M is a valid upper (or lower) bound, denoted by the subscripts “L” (or “U”) respectively, that can be taken as equivalent to the maximum (minimum) capacity of the corresponding pipeline. Thus, these logical constraints also ensure that the maximum (minimum) flow rates that can be operated are not exceeded for the respective piping interconnections. In this work, the lower bounds on the flow rates are set to a value of zero, unless casespecific thresholds can be specified. To maintain practicality with real-world situations, a flow rate value that is smaller than 0.500 ton/h is taken to be zero in the computational experiments. Formulations of the big-M logical constraints for various piping

interconnections are presented (in a compact representation form):55 MaL ðso, siÞ 3 Ya ðso, siÞ e Qa ðso, siÞ e MaU ðso, siÞ 3 Ya ðso, siÞ

ð19Þ

Mb,L perm ðso, siÞ 3 Yb, perm ðso, siÞ e Qb, perm ðint, siÞ e Mb,U perm ðso, siÞ 3 Yb, perm ðso, siÞ

ð20Þ

Mb,L rej ðso, siÞ 3 Yb, rej ðso, siÞ e Qb, rej ðint, siÞ e Mb,U rej ðso, siÞ 3 Yb, rej ðso, siÞ

ð21Þ

MdL ðso, intÞ 3 Yd ðso, intÞ e Qd ðso, intÞ e MdU ðso, intÞ 3 Yd ðso, intÞ

ð22Þ 3.7. Variable Bounds. Constraints on the lower and upper bounds for the following variables are enforced for a complete representation of the problem: total feed flow rate into the RO 13451


Qb,perm(int,si) regeneration unit

Qa(so,si)

23.20

2.405

PSR-1 CT

1.800

4.698

cogen CT

8.033

MG3 CT

boiler

28.81

18.11

100.0 2.000

30.00

69.00

4.769

5.000

waste

13452

RO

100.0

freshwater

2.998

29.59

14.74

28.00

32.10

67.20 3.100

SW4-BDBL

OW3b

2.000

SW2 OWg

1.769

25.00

17.51

21.79

23.27

0.300

17.42

0.300

6.354

WHB-BD2

1.800

3.500

WHB-BD1

BDBLs2

OWe-RG2

BW3

BD3

BD2 BW2

BW1

BD1

1.000

11.88

14.58

BDBLu

6.000

9.543

PSR-2 SW

intermediate condensate tank

1.038

0.962

PSR-1 SW

1.000

5.370

HPU2

PSR-2 crude tank drain 3.500

14.70

HPU1

PSR-1 crude tank drain

PSR-1 flare knockout drum

SWTU train PSR-2 process

PSR-2 desalter

PSR-1 desalter

14.76

4.630 0.962

5.057

potable

TKLE 30.30

OSW-SB

19.77

0.964

firewater

users

lift station 4

sulfur run-off

coke run-off PSR-1 process area

water source

Water Sink

Table 8. Optimal solution on flow rates (in ton/h) and piping interconnections for the case study (note: values are shown only for optimally selected interconnections)

Industrial & Engineering Chemistry Research ARTICLE



17.00

5.239

7.229

10.53

regeneration unit RO

0.378 3.296

COD

feed concentration CF (mg/L)

13.56

47.90

0

0

permeate concentration Cperm (mg/L)

0.48

6.84

0

0

0

0

HPU2

0.890

HPU1

2.648

model type computing platform

MINLP Windows XP on Acer laptop with Intel Pentium M processor

solver

1.40 GHz and 496 MB of RAM GAMS/BARON57

number of continuous

926

variables

2.229

number of binary variables

432

number of constraints

573

number of nodes explored

1801

in branch-and-bound scheme 0.489

CPU time

1000.08 s

regeneration unit QF(int), the RO feed pressure PF, and RO osmotic pressure on the retentate side ΔπRO, as shown below, respectively: QFL ðintÞ e QF ðintÞ e QFU ðintÞ, whereQF ðintÞ ¼

1.803

potable

PSR-1 flare knockout drum

TKLE

Users

sulfur run-off

Qd(so,int) water source

RO regeneration unit

Qb,rej(int,si)

∑

so ∈ SO

Qd ðso, intÞ,

" int ∈ INT

ð23Þ

PFL e PF e PFU

ð24Þ

ΔπLRO e ΔπRO e ΔπURO

ð25Þ

Hence, the complete model formulation consists of the objective function given by eq 13 subject to the constraints 1 8, 10 12, and 14 25. The model gives rise to a nonconvex MINLP due to the presence of nonlinear functions involving bilinear terms in the regeneration unit concentration balance (eq 3) as well as linear fractional terms, exponential terms, and power terms in the objective function (eq 13). These nonlinear nonconvex terms can result in multiple local optimal solutions, which calls for the implementation of global optimization techniques to guarantee a reliable solution.

0.268

OSW-SB firewater

143.7

phosphate

Table 10. Problem Size and Computational Statistics

water source

Table 8. Continued

44.06

chloride

(mg/L)

boiler MG3 CT

TSS

retentate concentration Crej

PSR-1 SW

PSR-2 SW

BDBLu

waste

Table 9. Optimal Contaminant Concentrations for Feed and Product Streams of RON in the Case Study

PSR-1 CT

cogen CT

Water Sink

ARTICLE

4. CASE STUDY—WATER NETWORK IN A PETROLEUM REFINERY The proposed model is implemented in GAMS 23.2.1 using the general purpose global optimization solver BARON that executes a branch-and-reduce algorithm.56 An industrial case study based on data obtained from a petroleum refinery in Malaysia is considered here to illustrate the proposed approach. The refinery water network involves 29 water sources and 13 water sinks, with limiting water data displayed in Table 1 and Table 2. Table 3 gives data on the Manhattan distance D between any two elements in the network. Table 4 presents the economic data and model parameters for the case study. A RON is used as a water 13453


Industrial & Engineering Chemistry Research regeneration unit in this case study. Table 5 and Table 6 provide the RR and process and economic data for the detailed design of the RON. Note that water sources with oil and grease content are not sent for regeneration in the RON in this case study. Optimal solution of the refinery case study is reported in Table 7, Table 8, and Table 9. The optimal design suggests an installation of 20 RO membrane modules, amounting to a total surface area of 3780 m2. The annualized RON investment and operating costs is $96,291/year. TAC of the overall water regeneration network is determined as $2,738,000/year. With a capital investment of $8,960,000 and savings of $4,267,000/year in freshwater use and wastewater generation, the project has a payback period of 2.1 years. A 58% savings in freshwater use is achieved as compared to the existing base case operations. Hence, it is economically attractive to pursue the retrofit alternative of installing and operating the RON. The nontrivial computational expense (approximately 17 min as reported in Table 10) is due mainly to the large-scale size of the problem and correspondingly, the large number of 01 variables involved, which is a reflection of the industrial relevance of the case study. Our computational experience reveals that a loose upper bound (i.e., a larger value) on a freshwater flow rate tends to lead to its higher consumption. Some further observations from our computational experience pertain to the fact that the variable RO feed flow rate tends to assume its lower bound in order to achieve minimum total network cost; hence, a tight lower bound value is specified. It is also noteworthy that the constraint on PF, as enforced by eq 12, tends to cause numerical difficulties arising from division with a zero value. Although this issue appears to be able to be overcome by specifying a nonzero lower bound value for Qb,perm, the solution could still be infeasible. Therefore, the lower and upper bounds of variable PF ought to be enforced, for example, by adopting the common range specified in El-Halwagi.48 In addition, the osmotic pressure ΔπRO tends to return an unreasonable value (of greater than 1000 atm), thus tight lower and upper bound values are incorporated, particularly the latter since our computational experience reveals that the variable is inclined to reach its maximum value.

5. CONCLUSIONS This paper has addressed the synthesis of a water regeneration network by proposing a MINLP optimization framework that considers a detailed representation of the regeneration unit using nonlinear mechanistic models. The approach is demonstrated on membrane separation-based partitioning regeneration unit by investigating the interactions of a single-stage reverse osmosis network with of the water sources and sinks in a water network. The MINLP is solved to global optimality by using GAMS/BARON. It is noteworthy that the proposed approach for the mechanistic model is not limited to only one regeneration unit or a specific water treatment technology, thus offering scope for future work. In other words, it is certainly possible to apply the proposed formulation for the case of multiple treatment technologies in series or parallel, for instance, one that involves a sequence of an ultrafiltration unit and an RO unit, which is typically found in industrial practice. However, the complexity involved arises from the arrangement of these two technologies and the determination of intermediate compositions. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

ARTICLE

’ NOTATION Sets and Indices

SO = sources so SI = sinks si INT = regeneration units (or interceptors) int CO = contaminants co Parameters

A = water permeability coefficient AOT = annual operating time Cmax(si,co) = maximum allowable contaminant concentration co in sink si Cso(so,co) = contaminant concentration co in source stream so Cchemicals = unit cost of pretreatment chemicals Cwaste = unit cost for waste treatment Celectricity = unit cost of electricity Cmodule = unit cost of HFRO membrane module Cpump = cost coefficient for pump Cturbine = cost coefficient for turbine D2M/Kδ = solute (contaminant) flux constant Kc = solute (contaminant) permeability coefficient m = fractional interest rate per year Ma(so,si) = big-M constant for interconnection between source so to sink si Mb,perm(int,si) = big-M constant for interconnection between regeneration unit int to sink si Mb,rej(int,si) = big-M constant for interconnection between regeneration unit int to sink si Md(so,int) = big-M constant for interconnection between source so to regeneration unit int n = number of years OS = osmotic pressure coefficient at HFRO PF = feed pressure of regeneration unit Pp = permeate pressure of regeneration unit p, q = parameter for carbon steel piping cost based on Chemical Engineering Plant Cost Index (CEPCI) POWERpump = pump power POWERturbine = turbine power Q1(so) = flow rate of source so Q2(si) = flow rate of sink si RR = removal ratio Sm = membrane area per module α = liquid phase recovery μ = viscosity of water Continuous Variables

CF(int,co) = concentration of contaminant co in feed stream of regeneration unit int Cperm(int,co) = concentration of contaminant co in permeate stream of regeneration unit int Crej(int,co) = concentration of contaminant co in retentate stream of regeneration unit int CS(int,co) = concentration of contaminant co in shell side of regeneration unit int Qa(so,si) = allocated flow rate between source so and sink si Qb,perm(int,si) = allocated flow rate between permeate stream of regeneration unit int and sink si Qb,rej(int,si) = allocated flow rate between retentate stream of regeneration unit int and sink si Qd(so,int) = allocated flow rate between source so and regeneration unit int 13454


Industrial & Engineering Chemistry Research QF(int) = total feed flow rate into regeneration unit int Nsolute = solute flux through the HFRO membrane Nwater = water flux through the HFRO membrane PR = retentate pressure from regeneration unit qP = permeate flow rate per HFRO module TAC = total annualized cost ΔπRO = osmotic pressure on HFRO retentate side Binary 01 Variables for Existence of Stream Piping Interconnections

Ya(so,si) = between source so and sink si Yb,perm(int,si) = between permeate stream of regeneration unit int and sink si Yb,rej(int,si) = between retentate stream of regeneration unit int and sink si Yd(so,int) = between source so and regeneration unit int

’ REFERENCES (1) Wang, Y. P.; Smith, R. Wastewater Minimization. Chem. Eng. Sci. 1994, 49 (20), 3533–3533. (2) Bagajewicz, M. A Review of Recent Design Procedures for Water Networks in Refineries and Process Plants. Comput. Chem. Eng. 2000, 24 (910), 2093–2113. (3) El-Halwagi, M. M.; Gabriel, F.; Harell, D. Rigorous Graphical Targeting for Resource Conservation via Material Recycle/Reuse Networks. Ind. Eng. Chem. Res. 2003, 42 (19), 4319–4328. (4) Manan, Z. A.; Foo, D. C. Y.; Tan, Y. L. Targeting the Minimum Water Flow Rate Using Water Cascade Analysis Technique. AIChE J. 2004, 50 (12), 3169–3183. (5) Foo, D. C. Y. State-of-the-Art Review of Pinch Analysis Techniques for Water Network Synthesis. Ind. Eng. Chem. Res. 2009, 48 (11), 5125–5159. (6) Takama, N.; Kuriyama, T.; Shiroko, K.; Umeda, T. Optimal Planning of Water Allocation in Industry. J. Chem. Eng. Jpn. 1980, 13 (6), 478–483. (7) Savelski, M. J.; Bagajewicz, M. J. On the Optimality Conditions of Water Utilization Systems in Process Plants with Single Contaminants. Chem. Eng. Sci. 2000, 55 (21), 5035–5048. (8) Savelski, M.; Bagajewicz, M. Design of Water Utilization Systems in Process Plants with a Single Contaminant. Waste Manage. 2000, 20 (8), 659–664. (9) Bagajewicz, M.; Savelski, M. On the Use of Linear Models for the Design of Water Utilization Systems in Process Plants with a Single Contaminant. Chem. Eng. Res. Des. 2001, 79 (A5), 600–610. (10) Grossmann, I. E.; Lee, S. Global Optimization of Nonlinear Generalized Disjunctive Programming with Bilinear Equality Constraints: Applications to Process Networks. Comput. Chem. Eng. 2003, 27 (11), 1557–1575. (11) Gunaratnam, M.; Alva-Argaez, A.; Kokossis, A.; Kim, J. K.; Smith, R. Automated Design of Total Water Systems. Ind. Eng. Chem. Res. 2005, 44 (3), 588–599. (12) Faria, D. C.; Bagajewicz, M. J. On the Appropriate Modeling of Process Plant Water Systems. AIChE J. 2010, 56 (3), 668–689. (13) Faria, D. C.; Bagajewicz, M. J. On the Degeneracy of the Water/ Wastewater Allocation Problem in Process Plants. Ind. Eng. Chem. Res. 2010, 49 (9), 4340–4351. (14) Faria, D. C.; Bagajewicz, M. J. Profit-Based Grassroots Design and Retrofit of Water Networks in Process Plants. Comput. Chem. Eng. 2009, 33 (2), 436–453. (15) Tan, R. R.; Ng, D. K. S.; Foo, D. C. Y.; Aviso, K. B. A Superstructure Model for the Synthesis of Single-Contaminant Water Networks with Partitioning Regenerators. Process Saf. Environ. 2009, 87 (3), 197–205. (16) Karuppiah, R.; Grossmann, I. E. Global Optimization of Multiscenario Mixed Integer Nonlinear Programming Models Arising in the

ARTICLE

Synthesis of Integrated Water Networks under Uncertainty. Comput. Chem. Eng. 2008, 32 (12), 145–160. (17) Karuppiah, R.; Grossmann, I. E. Global Optimization for the Synthesis of Integrated Water Systems in Chemical Processes. Comput. Chem. Eng. 2006, 30 (4), 650–673. (18) Tan, R. R.; Foo, D. C. Y.; Ng, D. K. S.; Chiang, C. L.; Hu, S.; KuPineda, V. An Approximate Mixed Integer Linear Programming (MILP) Model for the Design of Water Reuse/Recycle Networks with Minimum Emergy. Asia-Pac. J. Chem. Eng. 2007, 2 (6), 566–574. (19) Bringas, E.; Karuppiah, R.; Roman, M. F. S.; Ortiz, I.; Grossmann, I. E. Optimal Groundwater Remediation Network Design Using Selective Membranes. Ind. Eng. Chem. Res. 2007, 46 (17), 5555–5569. (20) San Roman, M. F.; Bringas, E.; Ortiz, I.; Grossmann, I. E. Optimal Synthesis of an Emulsion Pertraction Process for the Removal of Pollutant Anions in Industrial Wastewater Systems. Comput. Chem. Eng. 2007, 31 (56), 456–465. (21) Tan, R. R.; Cruz, D. E. Synthesis of Robust Water Reuse Networks for Single-Component Retrofit Problems Using Symmetric Fuzzy Linear Programming. Comput. Chem. Eng. 2004, 28 (12), 2547–2551. (22) Aviso, K. B.; Tan, R. R.; Culaba, A. B. Designing Eco-industrial Water Exchange Networks Using Fuzzy Mathematical Programming. Clean Technol. Environ. 2010, 12 (4), 353–363. (23) Aviso, K. B.; Tan, R. R.; Culaba, A. B.; Cruz, J. B. Bi-level Fuzzy Optimization Approach for Water Exchange in Eco-industrial Parks. Process Saf. Environ. 2010, 88 (1), 31–40. (24) Je_zowski, J.; Bochenek, R.; Poplewski, G. On Application of Stochastic Optimization Techniques to Designing Heat Exchanger- and Water Networks. Chem. Eng. Process 2007, 46 (11), 1160–1174. (25) Hul, S.; Tan, R. R.; Auresenia, J.; Fuchino, T.; Foo, D. C. Y. Water Network Synthesis Using Mutation-Enhanced Particle Swarm Optimization. Process Saf. Environ. 2007, 85 (B6), 507–514. (26) Napoles-Rivera, F.; Ponce-Ortega, J. M.; El-Halwagi, M. M.; Jimenez-Gutierrez, A. Global Optimization of Mass and Property Integration Networks with in-Plant Property Interceptors. Chem. Eng. Sci. 2010, 65 (15), 4363–4377. (27) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; El-Halwagi, M. Automated Targeting Technique for Concentration- and PropertyBased Total Resource Conservation Network. Comput. Chem. Eng. 2010, 34 (5), 825–845. (28) Ponce-Ortega, J. M.; El-Halwagi, M. M.; Jimenez-Gutierrez, A. Global Optimization for the Synthesis of Property-Based Recycle and Reuse Networks Including Environmental Constraints. Comput. Chem. Eng. 2010, 34 (3), 318–330. (29) Ponce-Ortega, J. M.; Hortua, A. C.; El-Halwagi, M.; JimenezGutierrez, A.; Property-Based, A Optimization of Direct Recycle Networks and Wastewater Treatment Processes. AIChE J. 2009, 55 (9), 2329–2344. (30) Alva-Argaez, A.; Kokossis, A. C.; Smith, R. Wastewater Minimization of Industrial System Using an Integrated Approach. Comput. Chem. Eng. 1998, 22 (Suppl.), S741–744. (31) Alva-Argaez, A.; Kokossis, A. C.; Smith, R. A Conceptual Decomposition of MINLP Models for the Design of Water-Using Systems. Int. J. Environ. Pollut. 2007b, 29 (13), 177–205. (32) Alva-Argaez, A.; Kokossis, A. C.; Smith, R. The Design of Water-Using Systems in Petroleum Refining Using a Water-Pinch Decomposition. Chem. Eng. J. 2007a, 128 (1), 33–46. (33) Alva-Argaez, A.; Vallianatos, A.; Kokossis, A. A Multicontaminant Trans-shipment Model for Mass Exchange Networks and Wastewater Minimisation Problems. Comput. Chem. Eng. 1999, 23 (10), 1439–1453. (34) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R. Automated Targeting Technique for Single-Impurity Resource Conservation Networks. Part 1: Direct Reuse/Recycle. Ind. Eng. Chem. Res. 2009, 48 (16), 7637–7646. (35) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R. Automated Targeting Technique for Single-Impurity Resource Conservation Networks. Part 2: Single-Pass and Partitioning Waste-Interception Systems. Ind. Eng. Chem. Res. 2009, 48 (16), 7647–7661. 13455



ARTICLE

(36) Ng, D. K. S.; Foo, D. C. Y.; Tan, R. R.; Pau, C. H.; Tan, Y. L. Automated Targeting for Conventional and Bilateral Property-Based Resource Conservation Network. Chem. Eng. J. 2009, 149 (13), 87–101. (37) Kraemer, K.; Kossack, S.; Marquardt, W. Efficient Optimization-Based Design of Distillation Processes for Homogeneous Azeotropic Mixtures. Ind. Eng. Chem. Res. 2009, 48 (14), 6749–6764. (38) Caballero, J. A.; Grossmann, I. E. An Algorithm for the Use of Surrogate Models in Modular Flowsheet Optimization. AIChE J. 2008, 54 (10), 2633–2650. (39) Caballero, J. A.; Grossmann, I. E.; Keyvani, M.; Lenz, E. S. Design of Hybrid DistillationVapor Membrane Separation Systems. Ind. Eng. Chem. Res. 2009, 48 (20), 9151–9162. (40) Lima, R. M.; Grossmann, I. E. Optimal Synthesis of p-Xylene Separation Processes Based on Crystallization Technology. AIChE J. 2009, 55 (2), 354–373. (41) Dzhygyrey, I.; Je_zowski, J.; Kvitka, O.; Statyukha, G. Distributed Wastewater Treatment Network Design with Detailed Models of Processes. In Computer-Aided Chemical Engineering; Jezowski, J., Thullie, T., Eds.; Elsevier: Atlanta Ga., 2009; Vol. 26, pp 853-858. (42) Bandyopadhyay, S.; Cormos, C. C. Water Management in Process Industries Incorporating Regeneration and Recycle through a Single Treatment Unit. Ind. Eng. Chem. Res. 2008, 47 (4), 1111–1119. (43) Gabriel, F. B.; El-Halwagi, M. M. Simultaneous Synthesis of Waste Interception and Material Reuse Networks: Problem Reformulation for Global Optimization. Environ. Prog. 2005, 24 (2), 171–180. (44) Kuo, W. C. J.; Smith, R. Design of Water-Using Systems Involving Regeneration. Process Saf. Environ. 1998, 76 (B2), 94–114. (45) Saif, Y.; Elkamel, A.; Pritzker, M. Optimal Design of ReverseOsmosis Networks for Wastewater Treatment. Chem. Eng. Process 2008, 47 (12), 2163–2174. (46) Saif, Y.; Elkamel, A.; Pritzker, M. Global Optimization of Reverse Osmosis Network for Wastewater Treatment and Minimization. Ind. Eng. Chem. Res. 2008, 47 (9), 3060–3070. (47) El-Halwagi, M. M. Synthesis of Reverse-Osmosis Networks for Waste Reduction. AIChE J. 1992, 38 (8), 1185–1198. (48) El-Halwagi, M. M., Pollution Prevention through Process Integration; Academic Press: San Diego, CA, 1997. (49) Marcovecchio, M. G.; Aguirre, P. A.; Scenna, N. J. Global Optimal Design of Reverse Osmosis Networks for Seawater Desalination: Modeling and Algorithm. Desalination 2005, 184 (13), 259–271. (50) Maskan, F.; Wiley, D. E.; Johnston, L. P. M.; Clements, D. J. Optimal Design of Reverse Osmosis Module Networks. AIChE J. 2000, 46 (5), 946–954. (51) Voros, N. G.; Maroulis, Z. B.; MarinosKouris, D. Short-Cut Structural Design of Reverse Osmosis Desalination Plants. J. Membr. Sci. 1997, 127 (1), 47–68. (52) Quesada, I.; Grossmann, I. E. Global Optimization of Bilinear Process Networks with Multicomponent Flows. Comput. Chem. Eng. 1995, 19 (12), 1219–1242. (53) Chew, I. M. L.; Tan, R.; Ng, D. K. S.; Foo, D. C. Y.; Majozi, T.; Gouws, J. Synthesis of Direct and Indirect Interplant Water Network. Ind. Eng. Chem. Res. 2008, 47 (23), 9485–9496. (54) Parekh, B. S., Reverse Osmosis Technology; Marcel Dekker: New York, 1988. (55) Biegler, L. T.; Grossmann, I. E.; Westerberg, A. W. Systematic Methods of Chemical Process Design; Prentice Hall: Upper Saddle River, NJ, 1997. (56) Tawarmalani, M.; Sahinidis, N. V. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications; Kluwer Academic Publishers: Dordrecht, Germany, 2002; Vol. 65, p 504. (57) Sahinidis, N. V.; Tawarmalani, M. Baron 7.2.5: Global Optimization of Mixed-Integer Nonlinear Programs, User’s Manual. 2005. http://www.andrew.cmu.edu/user/ns1b/baron/bibliography.html (accessed May 29, 2011).

13456


A Superstructure Optimization Approach for Membrane Separation

Recommend Documents