Siting Optimization of Facility and Unit Relocation with the

Article pubs.acs.org/IECR

Siting Optimization of Facility and Unit Relocation with the Simultaneous Consideration of Economic and Safety Issues Juan Martinez-Gomez,† Fabricio Nápoles-Rivera,† José María Ponce-Ortega,*,† Medardo Serna-González,† and Mahmoud M. El-Halwagi‡,§ †

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

ABSTRACT: A general optimization model is proposed to determine the optimal plant layout with the simultaneous consideration of economic and safety aspects. An important characteristic of the proposed optimization model is that it allows the relocation of some of the existing units to reduce the risks associated with current locations. The formulation also allows the addition of new units. A multiobjective mixed-integer linear programming model (MO-MILP) is developed to determine the optimal location of new and existing units while accounting for cost and risk. The proposed model is analyzed through a case study for a hexane distillation process showing the advantages of considering the possibility of relocating units originally installed following exclusively heuristic approaches and economic criteria.

1. INTRODUCTION Improper plant layout is one of the factors contributing to risks in the chemical process industry. There are numerous examples showing the implications of plant layout on safety. One example is the explosion in a polyethylene plant in Pasadena, TX, USA (1989) which led to 23 fatalities and an economic loss of about $715 million; the inadequate distance between process equipment was identified as one of the main causes of this accident.1 In this context, several researchers have proposed ́ methodologies for the optimal facility layout. Diaz-Ovalle et al.2 proposed an approach for the optimal distribution of new units in a given location with installed facilities. In this approach, the layout was selected based on the worst-case scenario with respect to the wind speed and atmospheric conditions in the case of toxic release in the facilities (new or existing). The approach also involved trade-offs between minimum distance and minimum risk, finding that the case of minimum distance provides unsafe locations whereas the minimum risk approach provides very large distances. Jung et al.3 proposed a mixedinteger linear programming (MILP) problem for the optimal location of new units in a discrete grid terrain, where the minimization for the cost accounting for the risk in each discrete grid was considered. Vázquez-Román et al.4 incorporated stochastic parameters regarding the wind speed and atmospheric conditions in a toxic gas release, where the approach was based on a mixed-integer nonlinear programming (MINLP) problem, finding numerical complications due to the nonconvex nature of the problem. Besides the allocation of new units, another important factor to consider is the interaction among facilities. This interaction can be considered by evaluating the interconnection risk and cost. Along those lines, Han and Weng5 proposed a methodology to evaluate the risk associated with the supply chain of natural gas. Other researchers (see, for examples, Paterson et al.,6 Sanders,7 Papageorgiou and Rotstein,8 and Xu and Papageorgiou9) have solved the problem of facility layout, © 2014 American Chemical Society

where new units are added in an industrial complex in which some facilities are already installed. Han et al.10 presented an optimization approach for the facility layout including the minimization to the human risk. Furthermore, El-Halwagi et al.11 proposed an optimization approach to include safety aspects in the optimal location and supply chain of a biorefinery. Martinez-Gomez et al.12 incorporated safety issues in the optimal location of treatment units associated with industrial wastewater discharges. Given the importance of economic and safety aspects, there is a need to develop systematic methodologies that simultaneously consider risk evaluation and cost assessment in plant layout. As such, the development of optimal facility layout is not a trivial task because of the trade-offs between the two contradicting objectives. Typically, larger distances between process equipment imply higher costs (piping, pumping, and wiring, etc.) and lower risk. Furthermore, the optimal facility location is also a function of the number of units that have to be located (Armour and Buffa13). Currently, several methodologies associated with the calculus of the risk in the facility layout problem have been reported, and each methodology quantifies and includes the risk in different ways; however, there are not reported methodologies optimizing simultaneously through multiple objective functions (forming Pareto fronts) the risk and the cost, giving an explicit relation between the trade-offs of these two contradicting objectives. In the best case, the risk is included as a weighted cost in the objective function (minimizing the risk indirectly), or is calculated in the base of the layout obtained by optimizing the economic objective (only evaluating the risk without Received: Revised: Accepted: Published: 3950

July 14, 2013 January 25, 2014 February 18, 2014 February 18, 2014 dx.doi.org/10.1021/ie402242u | Ind. Eng. Chem. Res. 2014, 53, 3950−3958

Industrial & Engineering Chemistry Research

Article

relocated to different grids that represent safer locations. There is also a set of new units that have to be located following the same economic and safety considerations as the existing units. The economic considerations include the costs of the terrain, the relocation, and interconnection among units. The risk is measured using quantitative risk assessment (QRA) which allows the estimation of the consequences of a flammable gas release. The problem consists of finding the coordinates (i,j), in a discrete grid terrain containing a set of existing units, in which a set of new or existing units must be located at a minimum cost and risk.

minimizing it). This might lead to suboptimal solutions, which follow the same paradigms of the current practices, in which only economic objectives are considered, or where they are considered in a succession of steps. On the other hand, considering only the security objective leads to increased distances between units, and sometimes to designs that are not feasible from the technical and economical points of view. The facility layout problem is not a trivial task and involves hundreds of decision variables even in small problems, and its solution requires formal mathematical programming models to systematically obtain potential attractive solutions; this is the main contribution of this work. Also, for those methodologies which consider cost and risk only, the plant layout of existing processes in which new units are to be installed has been studied, and none of the aforementioned approaches consider the important case in which the existing units need to be relocated following the same considerations as the new facilities. Thus, in this work, a new methodology for the optimal facility layout of new and existing units is proposed, where the cost and the risk are optimized simultaneously to compensate for both contradicting objectives. The risk is assessed in terms of the probability of leakage, the probability of exposition, and the consequences due to the exposition to such events and is determined using quantitative risk analysis (QRA), in which the frequency of occurrence is determined using a failure tree (see Crowl and Louvar14), allowing quantification of the magnitude of the damage caused by an accident (Jonkman et al.15). The cost is quantified in terms of the cost of installation and interconnection. The problem is modeled as a multiobjective mixed-integer linear programming (MO-MILP) problem, where the coordinates in which the location of the new and relocated units are installed are determined through a disjunctive scheme.

3. OPTIMIZATION FORMULATION Before proceeding to the optimization formulation, it is useful to define key terms and sets to be used in the model. The indices i, i′, j, and j′ (where i ≠ i′ and j ≠ j′) represent the coordinates in the center of each discrete grid, where a unit can be installed or relocated. Subscript e represents the units that can be added or relocated. The model formulation is based on the representation shown in Figure 1. For modeling purposes, the existing units are treated as new units (i.e., all of the units will be installed in new locations), but in the case of existing units the cost of installation on its current location will be zero. Considering this, the selection of the location for a given unit can be represented with the following disjunction: ⎡ ⎤ Yi , j , e ⎢ ⎥ ⎢ IntCoste = UICi , j , e ⎥ ⎥, ∨⎢ i ∈ I ⎢ LandCost = ULC e i,j,e ⎥ j∈J ⎢ ⎥ ⎢⎣ Riske = ULR i , j , e ⎥⎦

∀ e∈E (1)

The Boolean variable is Yi,j,e associated with the existence of a unit in coordinates (i,j). If it exists, then there will be an interconnection cost (IntCoste) between the new and existing units; associated with that specific location there is also associated a cost of terrain land (LandCoste) and risk (Riske). The parameter ULRi,j,e represents the number of expected fatalities per accident in coordinates i,j in the case of an accident; two types of potential accidents are considered. Boiling-liquid expanding-vapor explosion (BLEVE) and vaporcloud explosion (VCE). The parameter UICi,j,e is the interconnection cost calculated between new and existing units. And, finally, ULCi,j,e is the cost of terrain and installation. These parameters are calculated before the optimization process. The previous disjunction is reformulated as a set of algebraic equations in which the Boolean variables are converted into binary variables. This way, when the Boolean variable is true, the binary variable (yi,j,e) is equal to one, and when the Boolean variable is false the binary variable takes the value of zero. A convex hull reformulation is used (see Raman and Grossmann24 for examples of reformulations) to convert the disjunction into algebraic equations. First, the variables in the disjunction are disaggregated:

2. PROBLEM STATEMENT Traditionally, economic factors constituted the primary objective used for facility layout without considering safety aspects (Georgiadis and Macchietto16 and Jayakumar and Reklaitis17,18). This may lead to unsafe designs which were based on heuristic approaches (Mannan,19 Mecklenburgh,20 and Patsiatzis and Papageorgiou21). To overcome this problem, this work addresses the problem of the relocation of multiple installed units which are currently located at unsafe distances (near potentially dangerous units). Here, the cost and risk are used as optimization criteria. For modeling purposes, the terrain is divided in rectangular discrete grids with coordinates (i,j) in the center of each grid (Ozyurt and Realff22 and Penteado and Ciric23). As shown by Figure 1, there is a set of existing units that are fixed (cannot be moved) and another set of existing units that can be

∑ ∑ yi ,j ,e = 1,

∀ e∈E (2)

i∈I j∈J

IntCoste =

∑ ∑ DIntCosti ,j ,e,

∀ e∈E (3)

i∈I j∈J

LandCoste =

∑ ∑ DLandCosti ,j ,e, i∈I j∈J

Figure 1. Problem statement. 3951

∀ e∈E (4)

dx.doi.org/10.1021/ie402242u | Ind. Eng. Chem. Res. 2014, 53, 3950−3958

Industrial & Engineering Chemistry Research Riske =

∑ ∑ DRisk i ,j ,e,

Article

∀ e∈E

IIntCoste , e ′ =

i

∀ e ∈ E,

Then, the equations are written in terms of the disaggregated variables: DIntCost i , j , e = UICi , j , eyi , j , e ,

∀ i ∈ I, ∀ j ∈ J, ∀ e ∈ E

DLandCost i , j , e = ULCi , j , eyi , j , e ,

RiskInte , e ′ =

(6)

∀ e ∈ E,

∀ i ∈ I, ∀ j ∈ J, ∀ e ∈ E

DRisk i , j , e = ULR i , j , eyi , j , e ,

∀ i ∈ I, ∀ j ∈ J, ∀ e ∈ E

(8)

∀ i ∈ I,

TAC =

∀ e′ ∈ E′,

e > e′

∀ e ∈ E,

∀ j ∈ J,

(15)

∀ e′ ∈ E′,

∀ e ∈ E,

e > e′

e > e′

∑ IntCoste + ∑ LandCoste + ∑ ∑ e∈E

(17)

e∈E

IIntCoste , e ′

e ∈ E e ′∈ E ′ e>e′

(18)

where TAC is the total annual cost ($/year) and is equal to the sum of the cost of interconnection between new and existing units IntCoste, plus the cost of terrain LandCoste (this cost includes the cost of installation and terrain conditioning), and finally the cost of interconnection between new units IIntCoste,e′. The safety objective is represented by the sum of the risk of each unit in a specific location and the risk of interconnection between units:

∀ j′ ∈ j′, j ≠ j′, (11)

The first disjunction only considers the cost of interconnection between new and existing units; in order to consider the cost and risk between new units with other new units, the following disjunction is proposed: ⎡ ⎤ Zi , j , e , i ′ , j ′ , e ′ ⎢ ⎥ ∨ ⎢ IIntCoste , e ′ = UICIi , j , e , i ′ , j ′ , e ′ ⎥, i ,i′ ⎢ ⎥ j ,j ′⎢ ⎣ RiskInte , e ′ = URiskInt i , j , e , i ′ , j ′ , e ′⎥⎦

j′

It is important to mention that these objectives are contradicting each other; this happens because at longer distances the cost is increased due to the interconnection cost, but at the same time the risk is minimized. On the other hand, if the distance between facilities is decreased, the cost is also decreased but the risk increases. The economic objective for the total annual cost is expressed as follows:

(2 − yi , j , e − yi ′ , j ′ , e ′) + zi , j , e , i ′ , j ′ , e ′ ≥ 1,

∀ e′ ∈ E′, e > e′

i′

OF = {min TAC, min TRisk}

The interconnection costs between units are calculated as follows. If two units yi,j,e and yi′,j′,e′ exist and they are interconnected, then the binary variable (which indicates the existence of this interconnection) zi,j,e,i′,j′,e′ is equal to one, or otherwise is equal to zero. This relationship is modeled with the following constraint:

∀ e ∈ E,

j

The objective function is formulated as a multiobjective optimization problem in order to minimize simultaneously the total annual cost and the risk (TAC and TRisk, respectively) and is represented by the following expression:

(10)

∀ j ∈ J,

(14)

∑ ∑ ∑ ∑ DRiskInti ,j ,e ,i′ ,j ′ ,e ′,

∀ j ∈ J,

∀ i ∈ I,

∀ i ∈ I, ∀ j ∈ J

∀ i ∈ I , i′ ∈ I , i ≠ i′,

e > e′

DRiskInt i , j , e , i ′ , j ′ , e ′ = URiskInt i , j , e , i ′ , j ′ , e ′zi , j , e , i ′ , j ′ , e ′ ,

(9)

e

j′

(16)

The previous constraint implies that if there is a unit that cannot be moved due to practical or economic reasons, its location is fixed and the binary variable yi,j,e is equal to 1. The model on its current form does not allow the relocation of units occupying more than one grid; thus the previous constraint is enforced for all of these types of units. This is mainly due to practical reasons; usually relocating these units is not the best alternative for economical and technical issues. The nonoverlapping constraint is used to ensure that only one unit can be installed in coordinates i,j:

∑ yi ,j ,e ≤ 1,

i′

DIntCost i , j , e , i ′ , j ′ , e ′ = UICIi , j , e , i ′ , j ′ , e ′zi , j , e , i ′ , j ′ , e ′ ,

The location for those units or facilities that are not practical to relocate (due to its size or another limitation) is fixed with the following constraint: ∀ i ∈ I , ∀ j ∈ J , ∀ e ∈ FE

j

∀ e′ ∈ E′,

i

(7)

yi , j , e = 1,

∑ ∑ ∑ ∑ DIIntCosti ,j ,e ,i′ ,j ′ ,e ′,

(5)

i∈I j∈J

TRisk =

∑ Riske + ∑ ∑ e∈E

e ∈ E e ′∈ E ′ e>e′

RiskInte , e ′ (19)

where TRisk is the number of fatalities per accident and is a function of the risk associated with the allocation of new and ∀ e ∈ E,

∀ e′ ∈ E′,

e > e′

(12)

This way, if two new units are connected, the Boolean variable will be true, the associated binary variable will be equal to one, and there will be a cost of interconnection IIntCoste,e′; otherwise the cost will be equal to zero. In addition, there is a risk of interconnection RiskInte,e′. The disjunction is again reformulated using a convex hull reformulation giving the next set of equations:

∑ ∑ ∑ ∑ zi ,j ,e ,i′ ,j ′ ,e′ = 1, i

j

i′

∀ e ∈ E,

∀ e′ ∈ E′,

e > e′

j′

(13)

Figure 2. Process diagram. 3952



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see Figure 2. Table 1 shows the set of existing units in the distillation plant, the installation cost (FCe) of new units (NI1, NI2) that are going to be added to the plant, and the size of each unit. The cost parameter FCe is also associated with units for which relocation is practical. In this case, relocated units are treated as new units, and thus the cost can be modeled with the same parameter. Figure 3 shows the distribution of the units in the available terrain. The terrain was divided into 100 discrete grids, each one of 100 m2. It can be seen that the distillation column is located in the central part of the terrain and that densely populated facilities (control room and administrative building) are located at unsafe distances with respect to the distillation column and other dangerous units (TA1, TA2, and THP). Given this set of existing units, two scenarios can be identified for analyzing. First, in scenario A, existing units cannot be relocated and two new units must be added. The units to be added are a new quality control laboratory (NI1)this facility is required because it does not exist in the current processand a new control room (NI2), which is required to control the cooling tower because the existing control room is used to control the distillation tower. There are several scenarios in which an event in the hexane−heptane distillation process could end up in fire and explosion; this is because the hexane liquid and vapor phases are extremely flammable at ambient temperature when mixed with certain proportions of air or exposed to any source of ignition. Based on the worst-case scenario of a flammable gas release, two types of accident can occur, i.e., BLEVE (boiling-liquid expanding-vapor explosion)

existing units in a specific location (Risk e ) and the interconnection between units (RiskInte,e′). In order to obtain a set of optimal Pareto solutions, which consider simultaneously both objectives, the constraint method is used (see Haimes et al.25). Then, the multiobjective optimization problem is converted into a single objective limited problem. In this case, the cost is selected as the objective function and the risk is imposed as a constraint. This way, for a given risk, an optimal Pareto solution with a minimum cost can be obtained.

4. CASE STUDY In order to show the applicability of the proposed model, the hexane−heptane distillation process is analyzed (AIChE/CCPS26); Table 1. Size of Units unit (e)

type of unit

1 2 3 4 5

control room (CC) administrative building (EA) warehouse high-pressure storage sphere (THP) atmosphere flammable liquid storage e tank (TA1) 6 atmosphere flammable liquid storage tank (TA2) 7 cooling tower 8 process unit 9 new unit (NI1) 10 new unit (NI2)

length (m:m) 1010 1010 1010 1010 1010 1010 2010 2040 1010 1010

FCe ($) 1,000,000 300,000

3,000,000 2,000,000

Figure 3. Layout of the units already installed. 3953



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and VCE (vapor-cloud explosion). The units in which the accident is prone to occur are the hexane distillation unit and the storage tanks TA1, TA2, and THP. Second, in scenario B

two new units can be installed and two existing units can be relocated (control room and administrative building); these two facilities are selected to be moved because most of the personnel of the plant are concentrated in these buildings, and, besides, it constitutes a more practical and economical solution than moving process units. The risk associated with the installation of a unit in a given location is calculated as follows. In order to calculate the overpressure for BLEVE, the TNT equivalent model is used. The TNT equivalent mass is calculated with the following equation:

Table 2. Equivalent TNT Mass unit

mass (kg)

mass TNT (kg)

process unit atmosphere flammable liquid storage tank (TA1) atmosphere flammable liquid storage tank (TA2) high-pressure storage sphere (THP)

12000 970 970 1000

822.71 79.8 79.8 82.27

m TNT =

ηmΔHC E TNT

(20)

where mTNT is the equivalent mass of TNT, η is the empirical explosion efficiency (this term is a factor used to adjust the estimate of the TNT equivalent mass to take into account factors such as incomplete mixing of the combustible material with air and incomplete conversion of the thermal energy to mechanical energy), m is the mass of the hydrocarbon, ΔHC is the energy of explosion of the flammable gas, and ETNT is the energy of explosion of TNT. The efficiency of explosion varies in the range 1−10%; in this case a value of 10% is taken. The energy of explosion of TNT is 4686 kJ/kg, and the energy of explosion of hexane is 3855.2 kJ/mol (see Appendix B of the report by Crowl and Louvar14). Table 2 shows the equivalent TNT mass in each of the four units considered as dangerous. To assess the probability and consequence of BLEVE and VCE, the probit methodology was used. Y = −77.1 + 6.91 ln P

(21)

Figure 4. Affected percentage due to BLEVE.

Here, Y is the probit value associated with deaths from lung hemorrhage (Cui et al.27), and P is the overpressure in each grid. The probit value is converted then into an affected percentage with the next equation:

Table 3. Building Population e

unit

building population

11 12 13 14

EA CC NI1 NI2

15 10 12 6

⎡ ⎛ Y − 5 ⎞⎤ Y−5 ⎟⎥ erf⎜ P = 50⎢1 + ⎣ |Y − 5| ⎝ 2 ⎠⎦

(22)

Figure 5. Event tree (AIChE/CCPS, 2007). 3954



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the wind speed is 1.5 m/s and with F-class stability (see Crowl and Louvar14); then, the overpressure is again calculated with the TNT equivalent model. The number of fatalities is calculated as in the case of BLEVE. The total risk of installation in a given grid is considered as the sum of the fatalities caused by BLEVE and VCE and is expressed as follows:

Then, the number of fatalities caused by BLEVE are obtained as the product of the number of workers exposed and the affected percentage: fatalities from BLEVE =

no. of workers exposed affected percentage

(23)

ULR i , j , e = PBLEVE(UR i , j , e)BLEVE + PVCE(UR i , j , e)VCE

Figure 4 shows the affected percentage due to BLEVE caused for an accident in the units considered as dangerous. The parameter ULRi,j,e is calculated as follows: For example, if the administrative building (facility 11) with a population of 15 people (recommended by API 75228) is installed in coordinates (1,1), the parameter ULRi,j,e is as follows: ULR1,1,1,1 = (0.25) (0.3216)(15) = 1.206 = 2. This procedure is repeated for every new or existing unit that requires relocation in all of the grids to obtain the required parameters. Table 3 shows the population in the facilities that have working personnel. In the case of VCE, the fatalities estimation is performed by considering the worst-case scenario for the dispersion in which

(24)

where PBLEVE and PVCE are the probabilities of occurrence of each event, in this case 0.25 and 0.34, respectively; see Figure 5 (AIChE/CCPS, 2007). It is noteworthy to mention that for the case study the interconnection risk was considered zero; this is due to the small diameter of the pipelines used in the hexane distillation process (see Jung et al.3). The cost of interconnection for piping and wiring is assumed as $0.1/m (taken from Jung et al.29 for this specific case) for the interconnection between all facilities. The parameter ULCi,j,e is calculated as follows: ULCi , j , e = FCe + Cland + A

(25)

where FCe is the installation cost (if the unit already exists, it is equal to zero), Cland is the cost of terrain assumed as $5/m2, and A represents the cost for terrain conditioning. It should be noted that the proposed model cannot relocate units which expand over more than one grid (additional constraints would be required); however, to model a fixed unit that expands over more than one grid, such as the cooling tower, the appropriate variables y are fixed to 1. The model for this case study consists of 773,489 binary variables, 2,337,597 continuous variables, and 5,801,239

Figure 6. Pareto curve for scenario A.

Figure 7. Final layout for the solution i of Scenario A. 3955



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5. RESULTS Scenario A. This scenario considers only the addition of two new units and existing units cannot be moved. The Pareto curve (see Figure 6) shows the solutions obtained for this scenario. From this curve, point i offers a good compromise between cost and risk, due to the change in slope between the points h and i. For this point i, the TAC is $705.365/year with an expected number of fatalities of 14. The final distribution of the facilities is shown in Figure 7. Unit NI1 is located 35.35 m away from the distillation column in the grid with coordinates (9,5) showing a low danger percentage, while unit NI2 is located in grid (9,2) away from any dangerous unit. Scenario B. This scenario corresponds to the addition of two new units and the relocation of two existing facilities. Figure 8 shows a set of Pareto optimal solutions in which the contradictory behavior of both objectives can be seen. For the higher cost (solution a) of $2,011,190/year, the number of fatalities is equal to zero. This result is a consequence of the fact that the units (new and relocated) are installed in grids in which the percentage of affectation is equal to zero. This way, the number of fatalities is also zero. However, this option represents the higher cost of interconnection because of the longer distances between facilities. This solution in particular is the best if the safety is considered as outweighing criterion; however, plant layout must consider equilibrium between cost and risk (AIChE-CCPS31). In this sense, solution b might be more attractive because this particular point presents a considerable reduction in the cost, representing savings for $1,210/year with respect to solution a. This solution yields a TAC of $2,009,980/ year and 1 fatality. Figure 9 shows the final location (obtained in

constraints. The model was coded in the software GAMS, and the resulting MILP was solved using the solver CPLEX (Brooke et al.30); each point of the Pareto curves was solved in an average CPU time of 6.77 min in a workstation with two processors Intel core i7 at 3.2 GHz with 100 GB of RAM. Furthermore, because the proposed model is linear, there were not observed numerical complications during the solution step. Moreover, an analysis for the scalability indicates that if the number of new units increases to double using the same number of grids; then the number of binary variables, continuous variables, and constraints increase 53% with respect to the base case, and the CPU time increases 55%. For the case of the number of units, if the number of grids increases to double, then the number of binary variables, continuous variables, constraints, and CPU time increases 300%, 300%, 300%, and 367%, respectively. It should be noticed that the effect of the increment in the number of grids is more significant than the number of new units.

Figure 8. Pareto curve for scenario B.

Figure 9. Final layout for solution b of scenario B. 3956



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for the different optimal solutions identified; however, for different processes this might not be the case and the Pareto front helps to devise the trade-offs between the considered objectives.

solution b) of the four units; it can be seen that the existing units were reallocated; the administrative building was completely displaced from the area of affectation reducing the number of fatalities from 11 to 0. Its final location was in coordinates (9,2). The control room also was reallocated to a safer location (grid (9,5)), where the number of expected fatalities was reduced from 15 to 1. Regarding the new units, these were located in grids out of the reach of any potential accident where the total number of fatalities for solution b is equal to one; NI2 was located in grid (5,2) and facility NI2 in grid (6,2). Table 4 shows the results obtained in both Pareto sets. A significant difference between both scenarios is the number of

■

Corresponding Author

*E-mail: [email protected]. Tel.: +52 443 3223500 ext. 1277. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Scientific Research Council of the Universidad Michoacana de San Nicolás de Hidalgo.

Table 4. Results Comparison for the Different Scenarios scenario

solution

TAC ($/year)

TRisk (fatalities)

IntCost

ULCi,j,e

A

h i j k a b c d e f g

706,064 705,365 705,286 705,285 2,011,190 2,009,980 2,009,900 2,009,820 2,009,880 2,009,730 2,009,260

13 14 15 22 0 1 2 5 8 9 11

4164 3265 3186 3185 7190 5680 5600 5520 5480 5430 5060

701,900 702,100 702,100 702,100 2,004,000 2,004,300 2,004,300 2,004,300 2,004,400 2,004,300 2,004,200

B

AUTHOR INFORMATION

■

NOMENCLATURE

Scripts

i,i′ coordinate of each grid center (m), i′ ≠ i j,j′ coordinate of each grid center (m), j′ ≠ j e,e′ new unit e′ ≠ e Sets

I,I′ J,J′ E,E′ FE

fatalities; this difference is due to the fact that in scenario A the control room and the administrative building are located in unsafe locations and cannot be reallocated. This causes that the effect of an accident (number of fatalities) is constant for these two facilities, and the total damage is the sum of these fatalities and the number of fatalities caused for the installation of the new facilities. On the other hand, the advantage of not moving the existing units resides in the lower costs obtained for all of the points in the Pareto set obtained for scenario A. Finally, it should be noted that the economic objective does not change significantly for the different optimal solutions identified; this is mainly for the high installation costs for the units involved for all of the places considered (i.e., these installation costs are high independently of the place where the unit is installed). Thus, the difference in the total annual cost is not too high, but this may be considered important for the industry.

set set set set

of components i,i′ of components j,j′ of components e,e′ for fixed units

Parameters

δi,j ΔHC

η mTNT m ETNT PBLEVE PVCE P r UICi,j,e

6. CONCLUSION This work has presented a new optimization-based approach for the optimal facility layout. A multiobjective approach has been proposed to consider simultaneously the cost and the risk associated with the plant layout. The proposed approach overcomes the limitations of previous methodologies in which the addition of new units and the relocation of existing units have not been considered simultaneously. The developed mixedinteger linear programming model is general and can be applied to problems of practical interest. The results show the importance of proper plant layout and unit addition originally designed based on heuristic rules and following exclusively economic criteria. The results also show the importance of considering unit relocation in reconciling economic and safety objectives. For the presented case study, the economic objective does not change significantly

ULCi,j,e UIRi,j,e UICIi,j,e,i′,j′,e′ URiskInti,j,e,i′,j′,e′ Y Ze

minimum separation distance (m) energy of explosion of flammable gas (energy/ mass) empirical explosion efficiency equivalent TNT mass mass of hydrocarbon (mass) energy of explosion TNT probability of occurrence of BLEVE due to releases probability of occurrence of VCE due to releases affected percentage due to BLEVE and VCE distance from the dangerous facility to the center of each grid interconnection cost between new and existing units ($) land cost ($) installation risk (fatalities) interconnection cost between new units ($) interconnection risk (fatalities) probit value associated with death from lung hemorrhage scaled distance

Variables

DIntCosti,j,e DIIntCosti,j,e,i′,j′,e′ DLandCosti,j,e DRiski,j,e 3957

disaggregated variable associated with interconnection cost for the new units ($) disaggregated variable associated with the interconnection cost between new units ($) disaggregated variable associated with the land cost ($) disaggregated variable associated with the risk of installation (fatalities)


Industrial & Engineering Chemistry Research DRiskInti,j,e IntCoste IIntCoste,e′ LandCoste Riske RiskInte,e′ TAC TRisk Yi,j,e Yi,j,e Zi,j,e,i′,j′,e′ zi,j,e,i′,j′,e′

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Article

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disaggregated variable associated to the risk of interconnection (fatalities) installation cost for the new units ($) interconnection cost of new units ($) land cost ($) installation risk (fatalities) interconnection risk (fatalities) total annual cost ($/year) overall risk associated with the installation and interconnection of new units (fatalities) Boolean variable associated to the existence of new units binary variable associated to the existence of new units Boolean variable associated with the existence of interconnection between the new units binary variable associated with the existence of interconnection between the new units

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