Risk Index Approach for the Optimal Layout of Chemical Processes

Article pubs.acs.org/IECR

Risk Index Approach for the Optimal Layout of Chemical Processes Minimizing Risk to Humans Kyusang Han,† Young Hun Kim,‡ Namjin Jang,† Hosoo Kim,§ Dongil Shin,¶ and En Sup Yoon*,† †

School of Chemical and Biological Engineering, Seoul National University, Seoul 151-742, Korea Hyundai Heavy Industries Co., Ltd., Yongin 446-912, Korea § Computational Science Division, National Energy Technology Laboratory, Morgantown, West Virginia 26507, United States ¶ Department of Chemical Engineering, Myongji University, Yongin 449-728, Korea ‡

ABSTRACT: Chemical processes are constructed within very compact areas in the consideration of limited resources, including land, although many of their units are dangerous and vulnerable to accidents. Even the safety among units is secured by modifying the layout of process to ensure the safety distance, this situation can get worse if the process site is near residential areas or the workspace of employees because of the risk to humans from the process. In this study, such risk to humans as well as the risk to the equipment itself are quantitatively considered to give more reliable layout of chemical processes. Modified individual risk index has been adopted, counting for the direct risk that a person near the dangerous equipment can take. With this index, optimal process layout is designed by minimization of cost and land area to consider the limitation of resources. The proposed methodology can provide a guideline to designing safe layout of a chemical process concerning the various safety distance measures including equipment−equipment distance, equipment−workspace distance, and equipment−public area distance.

1. INTRODUCTION In 2005, there was a fire and explosion at the refinery of BP Products North America in Texas City, which claimed 15 lives and caused more than 170 injuries.1 Although the direct cause of the accident was the ignition of the hydrocarbon gas released from the isomerization unit, the temporary tank trailer placed near the accident site escalated the heavy casualties. In September of 1998 in Korea, an explosion at the LPG filling station in Bucheon, Gyeonggi province, caused 1 death and 96 injuries.2 As with the previous case, the unexpected high casualty rate arose from the unclear regulations about the facility arrangement and the limitations of safety distance prescribed by law, rather than the explosion itself. The above accident cases show that guaranteeing the proper safety distance between process areas and the public or worker residence areas is crucial in the minimization of the effects of an accident and damages to humans. There has been not much research work, however, about the safe layout of hazardous facilities considering public residence or workspace of employees from the early part of designing the process. Previous research about the process layout optimization includes twodimensional layout of processes using heuristic rules3 and MILP (mixed-integer linear programming) modeling for multifloor layout optimization.4 Research considering safety factors and accident scenarios also has been carried out. The Dow Fire & Explosion Index5 was used to evaluate the effective radius and damage costs of accident and to optimize process layout by MILP,6 and scenario-based optimization using statistical methods for toxic chemical release was implemented together with disjunctive programming for layout optimization.7,8 These approaches still have limitations when it comes to risk consideration because they did not account for the risk to nearby people or dealt with it in rather indirect way. © 2013 American Chemical Society

In this study, mathematical modeling for process layout optimization is used together with the risk assessment of the process to secure safety distances, especially for humans. Optimal layout of chemical process is arranged by satisfying the safety standards for equipment in the process, calculating effective distances of an accident, and minimizing costs of land area and pipelines. To ensure the minimum effect of an accident, the following three types of distances are considered: distance between equipment and other equipment; distance between equipment and workspace (e.g., control room or worker residence building); distance between equipment and process boundary (i.e., public area). The first one is determined from previous research about the spacing between equipment. The second and third types of distances are calculated to meet the allowable limit of individual risk for workers and the public. The proposed method aims to provide more objective and direct risk consideration in process layout optimization.

2. MODIFIED INDIVIDUAL RISK A risk index is a comprehensive, integrated representation of accident frequency and consequence. Among various risk indices, individual risk (IR) is an effective measure for quantifying the risk from chemical process equipment to humans, because it is the risk to a person in the vicinity of a hazard and considers the nature, likelihood, and time period of the possible injury to the individual.9 Special Issue: PSE-2012 Received: Revised: Accepted: Published: 7274

September 16, 2012 February 10, 2013 February 11, 2013 February 25, 2013 dx.doi.org/10.1021/ie3025104 | Ind. Eng. Chem. Res. 2013, 52, 7274−7281

Industrial & Engineering Chemistry Research

Article

Figure 1. Layout optimization procedure based on the risk analysis result.

The basic calculation of risk is usually done by the product of frequency and consequence of accident that came from various quantitative risk analysis methods like Fault Tree Analysis, but IR reflects more elements. To get the IR index, HSE (Health and Safety Executive) suggest a two-step calculation.10 First, the frequency of fatality (FoF) of a person at the location of interest i, considering the accident frequency, fatality rate, weather effect, and directional effect is calculated for all the accident scenarios about the event outcome j. FoFi =

∑ feo,j pfat,i ,j pwea,i ,j pdir,i ,j j

IR i , j = feo, j (1 −

r

(1)

(2)

For some accident scenarios such as toxic release, calculation of meteorological condition including wind direction and speed has great importance for risk assessment.8,11 In this study, however, this calculation is modified to a simpler one with appropriate assumptions to deal with more general accident cases. We consider the worst-case accident scenario, which means the individual of interest is at the accident location at the time of accident. The meteorological and geographical conditions are also ignored by assuming that the effect of accident to an individual is independent to such factors. Then, individual risk for accident j at location i becomes the product of two terms. IR i , j = feo, j pfat, i , j

(4)

Since the IR consist of the accident frequency and fatality rate, the smaller the value of IR, the lower the risk. HSE’s framework for the tolerability of risk provides the criteria for the acceptable limits of IR that can be considered as safe.12 They set up the boundary values of IR between “broadly acceptable”, “tolerable”, and “unacceptable” levels of risk. For the layout optimization problem of chemical processes, we use the tolerance limits of IR between tolerable and unacceptable, which are one in a thousand (10−3) per annum for workers and 10−4 per annum for the public. The level of risk of process units varies with the distance from them, since the fatality rate is affected by distance from the hazardous equipment.13 Therefore, the IR tolerance limits mentioned above can be used to determine the minimum separation distances from equipment so the safety of both workers and the public can be secured. The distances satisfying such IR values are implemented as the distance constraint in the layout optimization problem.

Then, the fraction of time and probability of the presence of people are multiplied to FoFi to give IR for the group of people k at the location i. IR i , k = θkploc, i , k FoFi

∑ RFr )pfat,i ,j

3. PROCESS LAYOUT OPTIMIZATION BASED ON RISK ANALYSIS The optimization of process layout is carried out together with the risk boundary distance, which is the distance satisfying the risk criteria from modified IR result. Since the MILP formulation for process layout optimization is well-established, most constraints in this mathematical formulation section are based on previous research6,14 except the risk boundary distance condition for safety consideration. The proposed procedure of designing the optimal layout including quantitative risk analysis, individual risk calculation, and mathematical optimization is depicted in Figure 1. It consists of two parts: risk boundary section and layout optimization section. Risk boundary distance resulting from the first section is passed to the second section, and then, optimization is completed. The frequency of accidents can be obtained from statistical data or by using frequency modeling techniques such as FTA (fault tree analysis). The consequence of accidents can be

(3)

The effect of accident can be reduced when the protective device is installed for the equipment, and so does the fatality rate of that equipment. Assuming that the risk reduction factors (RF) of individual protective devices are independent, total fatality can be reduced as the sum of all factors. The value of risk reduction factor ranges from 0 to 1, where 1 means the perfect protection. 7275

dx.doi.org/10.1021/ie3025104 | Ind. Eng. Chem. Res. 2013, 52, 7274−7281


Article

estimated using probit analysis. The operating conditions and physical properties of materials are also considered here in order to calculate the effect of accident. These FA and CA sections are standard procedures in general quantitative risk analysis, and the bottom part of the risk boundary section (shaded blocks) has been already discussed in the previous section. Therefore, this section discusses only consisting elements of the layout optimization section. 3.1. Objective Function. For economically optimal layout satisfying the risk boundary constraint, cost minimization of a process is set as the objective. A major portion of the layout cost comes from pipeline connection and land purchase. In addition, equipment purchasing cost is included to deal with the proper division of the capacity of process units. This happens, for example, when a single storage tank of 10 ton is divided into two tanks of 5 ton in case it produces a safer process layout. Purchasing cost of protective device is also applied because it can be installed on equipment to reduce the risk. With these four types of cost to be minimized, the objective function is as follows:

yq − yp + M(2 − E1pq − E 2pq) ≥

+

q≠p

xp ≥ yp ≥

lp

∀p

2 dp

(13)

∀p

2

(14)

3.4. Distance between Equipment. Since a unit cannot be placed both on the right and left (above and below) of other equipment, horizontal (vertical) distance can be modeled either as Rpq or Lpq (Apq or Bpq) with the following constraints. R pq − Lpq = xp − xq ∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(5)

(16)

x R pq ≤ MW pq

The land area is set to be selected from candidates to keep the linearity of formulation, with the constraint (6) to prevent multiple selections.

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(17)

x Lpq ≤ M(1 − W pq )

∑ Qs = 1

(6)

s

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

3.2. Equipment Dimension and Orientation. All equipment is assumed to have rectangular shape and their orientation is restricted to be horizontal or vertical in a twodimensional process site. This can be represented as the following equations by using binary variable, Op. lp = apOp + bp(1 − Op)

∀p

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(8)

Dpq = R pq + Lpq + A pq + Bpq

lp + lq 2

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N xq − xp + M(1 − E1pq + E 2pq) ≥

(9)

2 (10)

dp + dq

R pq + Lpq ≥ EDp + EDq +

2

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(21)

The rectilinear distance is used instead of Euclidean distance for realistic consideration of actual piping. 3.5. Risk Boundary Distance. 3.5.1. Equipment−Equipment Distance. The minimum equipment separation distance, EDp, can be implemented as the following criteria that the distance between equipment should satisfy:

lp + lq

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

yp − yq + M(1 + E1pq − E 2pq) ≥

(20)

For example, if unit p is on the right of q (xp − xq > 0), then x is equal to 1 and the horizontal distance between Wpq equipment p and q is set to Rpq. In the same way, if equipment p is above q, then the vertical distance between them is set to Apq. Then, the rectilinear distance between the centers of equipment p and q is expressed as follows:

3.3. Nonoverlapping of Equipment. The equipment cannot be allocated to be physically overlapped to each other. To prevent this, the position of the geometric center of equipment, (xp, yp), can be modeled by using two binary variables, E1pq and E2pq, with appropriate large number, M. xp − xq + M(E1pq + E 2pq) ≥

(19)

y Bpq ≤ M(1 − Wpq )

(7)

∀p

(18)

y A pq ≤ MWpq

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

dp = ap + bp − lp

(15)

A pq − Bpq = yp − yq

s

p

(12)

Moreover, the center of equipment should be restricted as follows to avoid the equipment getting out of the process boundary:

∑ Ceq,p + ∑ Cpro,p p

2

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

minimize ∑ ∑ CNpqDpqCpipe + C land ∑ AR sQ s p

dp + dq

lp + lq 2

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(11) 7276

(22)


Industrial & Engineering Chemistry Research A pq + Bpq ≥ EDp + EDq +

Article

4.1. Problem Description. In this study, a DME filling station based on actual storage processing data of mixed DME− LPG fuel is considered. There are four main units after the loading section as in Figure 2: storage tank; compressor; pump; dispenser. Besides them, a control room is considered for workspace.

dp + dq 2

∀ p = 1, ..., N − 1, ∀ q = p + 1, ..., N

(23)

There are several research works on equipment spacing recommendations.15 In this study, we use the standard from the work of Prugh16 shown in Table 1. Table 1. Selected Equipment Spacing Recommendation for ISBL16 equipment

separation distance (m)

furnace compressor reactor pump tower/drum heat exchanger

15.3 9.6 8.9 8.8 7.7−7.2 7.5−6.6

Figure 2. Scheme of DME filling station.

3.5.2. Equipment−Workspace Distance. From the result of IR calculation, the risk boundary distance of equipment for a worker, RDwork,p, can be obtained and applied to the criteria for equipment−workspace distance. R pq + Lpq ≥ RDwork, q +

The basic information of those units is shown in Table 2. Using these data and the other information including operation conditions, layout optimization has been carried out in order to minimize the cost while securing the safety for workers and the public. Here, the layout of a DME filling station was optimized for three scenarios: (1) various capacities of storage tank; (2) storage tanks with the same total capacity but different combinations; (3) installation of protective devices. The following assumptions are made for this case study: • The process site is square-shaped, and the smallest one among discrete candidates should be selected. • The equipment is simplified to rectangles, and the accident occurs from the geometrical center of them. • Pipeline connections between equipment are rectilinear. • The effect of protective devices is not considered in frequency/consequence analysis. 4.2. Risk Boundary Calculation. The risk index for DME filling station is evaluated by analyzing the historical accident database of LPG filling stations which is a similar process to this case. Accident records from 1987 to 2003 in Korea18 are investigated, and three major types of accident are identified: flash fire, BLEVE (boiling liquid expanding vapor explosion), and VCE (vapor cloud explosion). Flash fire and VCE are modeled for all four major pieces of equipment in the DME filling station while BLEVE is modeled only for the storage tank. With these types of accident scenarios and operation conditions of equipment, a probit model for accident effect evaluation is built to be used for individual risk calculation. Figure 3 shows how the equipment’s risk boundary was determined from the IR value. The dashed line represents the IR limit for workers (10−3). Since the fatality rate terms of IR calculation varies with the distance from the equipment, the minimum distance that meets the IR tolerance limit can be obtained by using this chart. For example, the dispenser should be placed 25 m or more away from workspace because that is the minimum distance below the IR limit for workers (only the integer numbers for distance are taken). The risk boundary distances and the IR values at those distances are listed in Table 3 for the equipment in the DME filling station. Equipment spacing values of storage tank, pump, and compressor are brought from that of tower/drum, pump,

lp + lq 2

∀ p = workspace, ∀ q = 1, ..., N ( ≠ p) A pq + Bpq ≥ RDwork, q +

(24)

dp + dq 2

∀ p = workspace, ∀ q = 1, ..., N ( ≠ p)

(25)

3.5.3. Equipment−Process Boundary Distance. Risk boundary distance of equipment for public, RDpub,p, can also be calculated from the IR. Using this, the distance between the center of equipment and four sides of the process boundary can be modeled as follows: xb , u − xp ≥ RDpub, p + xp − xb , l ≥ RDpub, p + yb , u − yp ≥ RDpub, p +

yp − yb , l ≥ RDpub, p +

lp 2 lp 2 dp 2

dp 2

∀ p = 1, ..., N ∀ p = 1, ..., N ∀ p = 1, ..., N

∀ p = 1, ..., N

(26)

(27)

(28)

(29)

4. CASE STUDY In this section, the proposed methodology is applied to a DME (dimethyl ether) filling station which is a part of the blending process of DME, LPG, and butane designed by Korean Gas Corporation (KOGAS). DME is the simplest ether which is considered as the next generation fuel for the future. Since it is clean and the physical properties are similar to LPG (liquefied petroleum gas), DME has caught attention as a substitute for petroleum-based fuels.17 DME filling stations are to be located near the public area like a gas station, and therefore, safe layout within the limited investment and land area is important. 7277



Article

Table 2. Equipment Information of DME Filling Station no.

a

equipment

1

storage tank

2 3 4 5

pump compressor dispenser control room

width (m)

depth (m)

connection

pipeline costa ($)

capital costa ($1,000)

1.8 2.5 2.5 2.5 0.8 0.8 0.82 15

2.6 4.1 6.36 8.76 0.6 0.6 0.44 20

2, 3

13.6 13.6 13.6 13.6 13.6 13.6 13.6

16 21 26 31 7 87 11

5 ton 10 ton 15 ton 20 ton

1, 4 1 2

Cost values in this work were converted from KRW, with an exchange rate of $1 = 1,100 KRW.

Table 4. Protective Devices no.

protective device

risk reduction factor

installation cost ($)

r-1 r-2 r-3

cooling water system overpressure relief device fire relief device

0.1 0.24 0.25

5,000 20,000 25,000

Table 5. Protective Device Installation for DME Filling Station equipment

installed device

overall risk reduction factor

storage tank pump compressor dispenser

r-1, r-2, r-3 r-1, r-2 r-1, r-2 r-1

0.59 0.34 0.34 0.1

Table 6. Risk Boundaries with Protective Devices

Figure 3. Individual risks against the distances from equipment.

and compressor in Table 1, respectively. For the dispenser, we assumed it to have the spacing value between that of the storage tank and pump. To account for the risk reduction by additional protection to process equipment, three types of protective devices are considered. We assumed that the effect of each protective device on IR is independent so that the total risk reduction factor is the sum of each reduction factor which is installed to that equipment. Some protective devices are selected from previous research19 as in Table 4. Tables 5 and 6 show their installation and the reduced risk boundary distances. 4.3. Process Layout Result. The optimization problem is formulated as MILP and solved in GAMS20 with ILOG CPLEX solver to minimize the total cost of layout of DME filling station. As an illustration, the facility layout was optimized for DME filling stations with different storage tanks. The capacity of storage tanks are varied while that of other units is fixed. As can be seen in Figure 4, the required area of a process site gets larger as the capacity increases. The more important

equipment storage tank

for workers

for the public

RDwork,p (m)

RDpub,p (m)

11 13 15 16 10 12 23

16 20 23 25 12 13 26


pump compressor dispenser

observation is about the position of units. Storage tanks are allocated near the center of the process site, the farthest point from the public area (process boundary) because they cause the highest individual risk. On the other hand, the control rooms, which are assumed as the space for workers, are placed on the corner of the site because they do no harm to the public but only take the risk from other equipment. Figure 5 shows the risk contours of process equipment for the case of c in Figure 4. Dashed and solid circles represent the risk contours for workers

Table 3. Risk Boundary Calculation Result for worker equipment storage tank

pump compressor dispenser


for the public

equipment spacing

RDwork,p (m)

IR

RDpub,p (m)

IR

EDp (m)

26 31 37 40 15 18 25

0.00094 0.00097 0.00096 0.00099 0.00066 0.00042 0.00088

39 49 56 62 17 19 29

0.000072 0.000093 0.000096 0.000083 0.000042 0.000042 0.000086

7.7

7278

8.8 9.6 8



Article

Figure 4. Optimal facility layout of DME filling station with various storage capacities.

20 ton tank. Figure 6 shows the layout result of three cases among these combinations. Table 7 and Figure 7 are the cost comparison of all five combinations. For all the cases, the land cost affects the total cost much more than the cost of equipment and pipeline, and therefore, case 4 which requires the smallest land area shows the lowest total cost. The risk contours for case 4 are illustrated in Figure 8, also showing that all risk boundaries are within the process site. In contrast, the control room and some public areas can suffer from higher individual risk when the proposed IR-based constraints are not considered. Figure 9 shows such a case: the risk contours for 10−3 and 10−4 per annum are not contained within the process boundary for the same combination as case 4. In this case, the total cost of layout can be lowered due to the smaller required land area, but the workers and public should take a higher individual risk than 10−3 per annum. Since the land cost in total layout cost is of great importance, it is desirable to minimize the land area by reducing the risk from process equipment. Installation of additional protective devices is a solution for risk reduction. The effect of protective devices is considered and compared only for case 4 because it was the most economic layout option without protection. Figure 10 depicts the arrangement of a fully protected DME filling station with two 10 ton storage tanks, and the cost difference from the unprotected case is shown in Table 8.

Figure 5. Risk contours for the case of a single 20 ton storage tank.

and the public, respectively. It can be easily checked that the risk contours for the public (IR < 10−4) do not cross the process boundary. A second layout optimization problem is to determine the optimal configurations of storage tanks with the same total capacity. The required land area, which causes cost, can be enlarged by a bunch of units with relatively low risk as well as a single unit with high risk. Thus, there should be an optimal case with the lowest cost when the storage tank is divided into many. Here, we consider a DME filling station with 20 ton of storage capacity that can be made up by five combinations of storage tanks: four 5 ton tanks; two 5 ton tanks, and a 10 ton tank; a 5 ton and a 15 ton tank; two 10 ton tanks; and a single

5. CONCLUSION In this work, facility layout optimization of a chemical process for safe and effective land use has been proposed. Due to the economic restriction, most of chemical processes have compact configurations in spite of the risk from hazardous materials and equipment, and this may cause heavy casualties and property damage when an accident occurs. We have addressed this issue

Figure 6. Optimal facility layout of DME filling station with various storage configurations. 7279



Article

Table 7. Cost Comparison of Optimization Results combination land area (m2) land cost ($) equipment and pipeline cost ($) total cost ($)

case 1

case 2

case 3

case 4

case 5

5 ton × 4 22500 9,343,636 181,273 9,524,909

5 ton × 2 + 10 ton 21025 8,731,109 166,127 8,897,236

5 ton + 15 ton 16900 7,018,109 151,873 7,169,982

10 ton × 2 15625 6,488,636 151,873 6,640,509

20 ton 18225 7,568,345 138,291 7,706,636

Figure 7. Cost comparison of layout cases. Figure 10. Optimal facility layout of DME filling station with protective devices.

Table 8. Effect of Protection in Layout Cost 2

land area (m ) total cost ($)

no protection

full protection

difference (%)

15625 6,640,509

13225 5,643,718

−15.4 −15.0

form of modified individual risk (IR) to workers and the public. Then, this has been converted to a safety distance constraint which satisfies the tolerance limit of IR for different groups of people. We have implemented this constraint into MILP formulation of layout optimization problem and solved for minimum cost. As a case study, facility layout of a DME filling station has been optimized using the proposed method. The optimal configurations of process equipment have been found and compared for the cases of the storage capacity variation, the total capacity division, and the protective device installation. The proposed method provides the economically efficient layout of a chemical process and enhances the inherent safety of the process by reducing the risk to humans at the same time. It is desired to apply this method in the early stage of process design to ensure the feasibility and reliability of the layout result.

Figure 8. Risk contours for the case of two 10 ton storage tanks.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-2-880-1581. Fax: +82-2-872-1581. E-mail: esyoon@ pslab.snu.ac.kr. Notes

The authors declare no competing financial interest.

■

Figure 9. Risk contours for the case of two 10 ton storage tanks without IR consideration.

ACKNOWLEDGMENTS This work was supported by Man-made Disaster Prevention Research Center of NEMA of Korea, and the authors are also grateful to Institute of Chemical Processes, Automation and

by layout optimization using the risk index approach. First, the risk of process equipment to humans has been assessed in the 7280



Article

(8) Center for Chemical Process Safety. Guidelines for Chemical Process Quantitative Risk Analysis; 2nd ed.; Wiley-AIChE: New York, 1999. (9) Amey VECTRA Limited. A Simplified Approach to Estimating Individual Risk; Health and Safety Executive: Merseyside, U.K., 2007. (10) Vázquez-Román, R.; Lee, J.-H.; Jung, S.; Mannan, M. S. Optimal facility layout under toxic release in process facilities: A stochastic approach. Comput. Chem. Eng. 2010, 34, 122−133. (11) Jung, S.; Ng, D.; Lee, J.-H.; Vazquez-Roman, R.; Mannan, M. S. An approach for risk reduction (methodology) based on optimizing the facility layout and siting in toxic gas release scenarios. J. Loss Prev. Process Ind. 2010, 23, 139−148. (12) Health and Safety Executive Reducing risks, protecting people; HSE Books: Merseyside, U.K., 2001. (13) Jo, Y.-D.; Crowl, D. A. Individual risk analysis of high-pressure natural gas pipelines. J. Loss Prev. Process Ind. 2008, 21, 589−595. (14) Papageorgiou, L. G.; Rotstein, G. E. Continuous-Domain Mathematical Models for Optimal Process Plant Layout. Ind. Eng. Chem. Res. 1998, 37, 3631−3639. (15) Heikkilä, A.-M. Inherent safety in process plant design An indexbased approach. Helsinki University of Technology: Espoo, Finland, 1999. (16) Prugh, R. W. Plant Safety. In Kirk-Othmer Encyclopedia of Chemical Technology; John Wiley: New York, 1982; Vol. 18. (17) Kim, H.; Han, K.; Yoon, E. S. Development of Dimethyl Ether Production Process Based on Biomass Gasification by Using MixedInteger Nonlinear Programming. J. Chem. Eng. Jpn. 2010, 43, 671− 681. (18) Korea Gas Safety Corporation (KGS) Yearbook of Gas-related Accident; Korea Gas Safety Corporation: Gyeonggi-do, Korea, 1987− 2003. (19) Penteado, F. D.; Ciric, A. R. An MINLP Approach for Safe Process Plant Layout. Ind. Eng. Chem. Res. 1996, 35, 1354−1361. (20) Rosenthal, R. E. GAMS - A User’s Guide; GAMS Development Corporation: Washington, D.C., 2008.

Systems Research Institute, and Engineering Research Institute of Seoul National University.

■

NOMENCLATURE

Sets

i = location or equipment of interest j = event outcome k = group of people p, q = process equipment r = protective device s = candidate of process site Parameters/Variables

ap, bp = length of each side of p Apq (Bpq) = vertical distance between the center of p and q ARs = land area of s Ceq,p = purchase cost of p Cpipe (Cland) = unit cost of pipeline (land) Cpro,p = cost of protective device installed on p CNpq = connectivity between p and q Dpq = rectilinear distance between p and q E1pq, E2pq = binary variables for nonoverlapping constraints EDp (EDq) = equipment spacing distance of p (q) feo,j = frequency of j FoFi = frequency of fatality at i IRi,j = individual risk of fatality to i from j IRi,k = individual risk of fatality to k at i lp (dp) = horizontal (vertical) length of p N = total number of equipment Op = binary variable for orientation of p pdir,i,j = probability of j being directed at i pfat,i,j = probability of fatality at i produced by j ploc,i,k = probability of k is at i pwea,i,j = probability of the weather condition required to produce j at i RFr = risk reduction factor of r Qs = selection of s Rpq (Lpq) = horizontal distance between the center of p and q RDpub,p = risk boudary distance for the public from p RDwork,q = risk boudary distance for workspace from q Wxpq, Wypq = binary variables for relative position of p and q xp (xq) = x-coordinate of center of p (q) yp (yq) = y-coordinate of center of p (q) θk = fraction of time that k spends in the area of interest

■

REFERENCES

(1) Khan, F. I.; Amyotte, P. R. Modeling of BP Texas City refinery incident. J. Loss Prev. Process Ind. 2007, 20, 387−395. (2) Park, K.; Sam Mannan, M.; Jo, Y.-D.; Kim, J.-Y.; Keren, N.; Wang, Y. Incident analysis of Bucheon LPG filling station pool fire and BLEVE. J. Hazard. Mater. 2006, 137, 62−67. (3) Suzuki, A.; Fuchino, T.; Muraki, M.; Hayakawa, T. An Evolutionary Method of Arranging the Plot Plan for Process Plant Layout. J. Chem. Eng. Jpn. 1991, 24, 226−231. (4) Patsiatzis, D. I.; Papageorgiou, L. G. Optimal multi-floor process plant layout. Comput. Chem. Eng. 2002, 26, 575−583. (5) American Institute of Chemical Engineers. Dow’s Fire & Explosion Index Hazard Classification Guide; 7th ed.; Wiley-AIChE: New York, 1994. (6) Patsiatzis, D. I.; Knight, G.; Papageorgiou, L. G. An MILP Approach to Safe Process Plant Layout. Chem. Eng. Res. Des. 2004, 82, 579−586. (7) Díaz-Ovalle, C.; Vázquez-Román, R.; Sam Mannan, M. An approach to solve the facility layout problem based on the worst-case scenario. J. Loss Prev. Process Ind. 2010, 23, 385−392. 7281


Risk Index Approach for the Optimal Layout of Chemical Processes

Recommend Documents