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An Layout Optimization Method For Industrial Facilities Based On Domino Hazard Index
Salvador Garcia Muñoz, Carl Laird, Matthew Realff (Eds.) Proceedings of the 9WK International Conference on Foundations of Computer-Aided Process Design July 14th to 18th , 2019, Copper Mountain, Colorado, USA. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818597-1.50015-1
AN LAYOUT OPTIMIZATION METHOD FOR INDUSTRIAL FACILITIES BASED ON DOMINO HAZARD INDEX
Ruiqi Wang1, Yan Wu2, Yufei Wang1 *, Xiao Feng2, and Mengxi Liu1 1 China University of Petroleum - Beijing Beijing, China 102249 2 Xi’an Jiaotong University - Xi’an Xi’an, Shaanxi, China 710049
Abstract Layout design is a key step in the process of chemical engineering design. In layout design, safety is the most important factor that needs to be considered. In previous work of relative research, consequence based safety evaluation method is employed to convert risk into cost for integrating safety aspect into objective function minimizing cost. However, converting risk into cost is improper due to two reasons: on the one hand, an ethical issue will be involved when converting casualties into cost; on the other hand, social effect and long-term environment effect resulting from an accident are not considered due to the difficulty of assessment. Consequently, safety should be considered as an independent indicator, rather than combined with economy. In this work, a layout method based on safety is proposed to determine the location of facilities in a plant. The Domino Hazard Index (DHI), an index that indicates the magnitude of domino effects in a plant area, is employed to evaluate the safety of a plant and guide the layout design. The sum of DHIs of facilities is set as objective function to minimize the domino effects of the plant. The proposed model is solved by genetic algorithm (GA) and implemented in a case from literature. The optimization result is analyzed and can illustrate the feasibility and advantage of the proposed method. Keywords Layout design, Risk evaluation, Domino effect, Genetic algorithm, Optimization Introduction Layout design is one of the most important aspects in the process of chemical engineering design, which has a significant impact on the performance of an enterprise, as well as heat exchanger network design and production planning & scheduling. Economy and safety are the two main factors considered in facility layout problem. Penteado and Criric (1996) proposed a mixed integer nonlinear programming (MINLP) model to determine the location of several facilities in a plant. The objective function consists of piping cost, land cost, protection
* Corresponding author: E-mail: [email protected]
devices cost, and risk cost. Their work is relatively early and comprehensive in the research filed of facility layout. Safety is extremely sensitive to layout design. Though the manufacturing technique for a single equipment is quite mature at present, it still cannot prevent accidents from occurrence obviously, because most of the accidents were aroused by human errors or systematic flaws. A large number of accidents have proved the importance of layout design in the aspect of safety of process industry. On March 23, 2005, an explosion occurred in the
An layout optimization method for industrial facilities based on domino hazard index
isomerization unit of BP Texas City refinery, resulting in 15 deaths, more than 170 injuries, and significant economic losses. It is one of the most serious U.S. workplace disasters in the past two decades. After the accident, the investigation report (2007) indicates that, the improper trailer siting is one of the four critical factors for the accident. There are two types of basic models for facility layout problems: discrete model and continuous model (1999). In discrete model, the free space is divided into many regular square girds. A facility can occupy one or more grids. Layout design method based on discrete model can work out an orderly result. However, discrete model will also lead to a coarse layout design, because the size of girds cannot always fit the size of facilities exactly. Jung (2016) proposed a method to find the optimal location of facilities for a plant by using a risk map. The plant area is divided into several grids and a risk score is estimated for each grid to generate the risk map. In continuous model, the facilities can be placed anywhere in the free space, and the facilities should have their own shapes, resulting in an involvement of non-overlapping constraint. However, continuous model is more practical and is employed in this work. As for algorithms, both General Algebraic Modeling System (GAMS) based solvers and intelligent algorithms were employed to solve industrial facility layout problems. Asl and Wong (2017) proposed a modified particle swarm algorithm for both static and dynamic facility layout problem. In their work, two local search methods and a department swapping method were introduced to prevent local optima. Additionally, some other sub-algorithms were combined to improve the solving process. Wang et al. (2018) combined the genetic algorithm (GA) and surplus rectangle fill algorithm to determine the layout of facilities. In their work, the coordinates of facilities were not set as variables any longer, and the feasible region was narrowed. By this way, the computational efficiency was improved. Many safety evaluation methods were involved in the research field of facility layout. Vázquez-Román et al. (2010) considered the uncertainty of toxic release when determine the location of facilities of a plant. The wind speed, wind direction, and atmospheric stability were incorporated to calculate the death risk for human by Monte Carlo simulation. The model was formulated as an MINLP model. Medina-Herrera et al. (2014) proposed a method based on quantitative risk analysis to determine the layout of facilities. A bowtie analysis was employed to identify possible catastrophic outcomes, which included the scenarios of fire, explosion, and toxic release. The safety evaluation methods adopted in the two works mentioned above are based on accident consequence. However, to measure human life by cost will lead to an ethical issue. On the other hand, besides casualties and property damage, the accidents will also lead to social effects and long-term environment effects. These effects are not assessed in most of previous works, and they are also difficult to be evaluated. Consequently, index based methods, an important type of safety evaluation method,
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should be introduced individually. Dow’s Fire and Explosion Index (F&EI) method (1994) is an accurate and systematic method to evaluate the safety of process industry, which is widely used in the world. The most common accident scenarios, fire and explosion, are considered in Dow’s method. Patsiatzis et al. (2004) proposed a mixed integer linear programming (MILP) model to determine the facility layout. In their work, Dow’s F&EI method was used to evaluate the safety of the plant, and different types of protection devices were alternative to be applied in the facilities to reduce the possible consequence of accident. Wang et al. (2017) proposed a model to evaluate the safety of an industrial park based on Dow’s F&EI method, and determine the layout of industrial park. Inherent safety is a key concept in process safety evaluation, and implementing inherent safety is an effective way for loss prevention and risk management. Khan and Amyotte (2005) proposed a conceptual framework named Integrated Inherent Safety Index (I2SI) to evaluate the inherent safety of a plant. I2SI is composed of several subindexes which account for hazard potential, inherent safety potential, and add-on control requirements. Domino effect was involved in many accidents with severe consequence. Domino effect will lead to an escalation of accident. Tugnoli et al. (2008) developed an index to evaluate the hazard related to potential domino effects based on I2SI. The index was called Domino Hazard Index (DHI) and was used to guide the layout design of a plant. In their case, three different layout schemes for same plant were analyzed and compared to select the best one with minimum domino effects. However, DHI evaluation method was not integrated into a systematic programming model in their work. Consequently, the method they proposed can only compare several pre-designed layout schemes manually, rather than work out a certain layout automatically. Lira-Flores et al. (2014) proposed a MINLP model to design facility layout using DHI, however, total cost was set as an objective function. In this work, DHI is set as objective function to guide the layout design and avoid the disadvantages of economy aimed method. A systematic layout design model involving non-overlapping constraint is established. The proposed model is solved by GA and implemented in a case from literature. The case shows the feasibility and advantages of the proposed model. Problem Statement The aim of this work is to determine the location of facilities in a plant to minimize the hazard of domino effects based on continuous model. The dimensions of facilities should be given to formulate non-overlapping constraints. DHI is used to evaluate the magnitude of domino effects, and the detailed information and parameters of facilities are needed, including operation
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pressure, temperature, facility type, mass of contained flammable material, and so on. Parameters that should be given and the variables to be determined are shown below: Given: The dimensions of facilities (Ri); The operation pressures and temperatures of facilities; The types of facilities (tower, vessel, and so on.) The mass and type of flammable material contained in a facility (W, ΔHc); The protection devices installed in facilities (fire wall, fire insulation, and blast wall). Determination: The coordinates of center points of facilities (xi,yi). Methodology Objective Function The DHI can score the potential of accident propagation considering possible escalation scenarios of accidents. So it is helpful for reducing subjectivity when safety and proper layout scheme are determined. The evaluation of DHI is based on I2SI method, and the effects of both inherent and passive measures on the domino escalation potential are taken into account. The first step of evaluating domino effects is to identify the facilities with significant potential of severe accident consequence. The Damage Index (DI) coming from I2SI method is used as a criterion. DI indicates the magnitude of impact of a facility to its surrounding. It is obtained by considering 4 kinds of risks: fire and explosion risk, acute toxicity risk, chronic toxicity risk, and environmental damage risk, as is shown in Equation (1). DI [( DIfe )2 (DIac )2 ( DIch )2 ( DIen )2 ]1/2 (1) The sub-indexes of DI and the detailed procedure of DI’s obtaining can be found in Khan and Amyotte’s work (2005). Then the necessity of considering the domino effect between two facilities should be confirmed. Considering a primary facility i and a secondary facility j, if Equation (2) is satisfied, the domino effect from facility i to facility j should be considered, e.i. DHSij (Domino Hazard Score) should be worked out, otherwise, DHSij should be ignored. (2) DI j (min( DI i , )) Where DIi is the DI of primary facility i; DIj is the DI of secondary facility j; § is an arbitrary threshold value that defines the lower limit of DI for facilities. If the domino effect of facility i on facility j should be considered, 4 kinds of possible accidents are evaluated respectively: fire ball, pool fire & jet fire, explosion, and fragment projection. The DHS under each kind of accident scenario should be calculated. For fireball scenario, the accident will escalate only when the flammable gas is triggered by flame directly due
R. Wang et al.
to the short duration time of fireball. Thus, if the secondary facility is contained in the fireball, the DHS=10, otherwise, DHS=0, as is shown in Equation (3).
0 DHS=
10
Dij Rfb Dij Rfb
(3)
Where Dij is the distance between primary facility i and secondary facility j; Rfb is the radius of the potential fireball. Fire insulation is a kind of effective protection measure to protect equipment. Thus, if fire insulation is equipped, the DHS = 5 in the scenario of fireball. For jet fire scenario, the worst case of horizontal fire is considered. The minimum distance between flame and secondary facility can be obtained from Equation (4). (4) d r Di ,j d f d p d s Where, df is the maximum length of flame; dp is the characteristic dimension of primary facility, i.e. the radius of primary facility; ds is the characteristic dimension of secondary facility; dr is the minimum distance between flame and secondary facility. For pool fire scenario, Eq. (4) is also used, where the df is equal to the pool radius for a non-tilted pool fire. The df can be quickly estimated from the literature of Cozzani et al. (2007). The DHS values for jet fire and pool fire scenario can be obtained from graphs of Tugnoli et al.’s work (2008) based on dr. For explosion scenario, the DHS can be obtained from the graph of Tugnoli et al.’s work (2008) according to the static peak overpressure where the secondary facility locates. The static peak overpressure is estimated by a TNT equivalent model (Lee, 2001), as is shown in Equation (5) - (8). W Hc WTNT (5) ETNT Dij z (6) 1 WTNT 3
U a b log10 z
(7)
11
log10 p0 ciU i
(8)
i 0
Where, W is the mass of flammable material in a facility (kg); ΔHc is the heat of combustion of the flammable material (kJ/kg); ETNT is the energy of explosion of TNT (kJ/kg) which is 4190-4650 kJ/kg; α is the yield factor; WTNT is the equivalent mass of TNT (kg); z is the scaled distance (m/kg1/3); U is an intermediate parameter; a, b, and ci are constant parameters and are shown in Table 1; P0 is the peak overpressure (kPa). For fragment projection, the DHS can be obtained from a graph according to the distance between primary facility and secondary facility (Dij). After determining the DHSs for all 4 potential accidents, the DHS between the primary facility i and secondary facility j can be obtained, as is shown in Equation (9).
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An layout optimization method for industrial facilities based on domino hazard index
Table 1 Parameters of TNT equivalent model Parameter a c0 c2 c4 c6 c8 c10
Value -0.21436 2.78077 -0.15416 0.09885 -0.02681 0.00163 0.00015
Parameter b c1 c3 c5 c7 c9 c11
Value 1.35034 -1.69590 0.51406 -0.29391 0.10910 -0.02146 0.00168
DHSi, j max k ( DHS i , j ,k )
(9)
Where, DHSi,j,k is the DHS of accident k originating from facility i to facility j. The DHI can be obtained for facility i: n
DHIi = DHSi , j
(10)
j 1
The sum of DHIs of facilities is set as an objective function to minimize the domino hazard in the plant area, as is shown in Equation (11)
them: above/below, and right/left. A binary variable can be used to describe the relative location of two facilities, and the non-overlapping constraint can be mathematically shown as Equation (12) . zoverlapping ,i , j 1 zoverlapping ,i , j L L L L y y y ,i y , j d x x x ,i x , j d i j i j 2 2 2 2 (12) Where, zoverlapping,i,j is a binary variable representing the relative location of facility i and facility j. When zoverlapping,i,j=1, facility j is forced to be in the up or down side of facility i, as shown in Figure 1 (a). When zoverlapping,i,j=0, facility j is forced to be in the right or left side of facility i, as shown in Figure 1 (b). xi, yi, xj, and yj are the coordinates of facility i and j. Lx,i, Lx,j, Ly,i, and Ly,j are the length of facility i and j paralleling to x axis and y axis respectively. d/2 is the distance between two facilities reserved for installation and maintenance, and the facilities should also keep distance of d/2 from the boundary of plant area.
Plant j
m
Min DHI
DHIi
d 2
Plant j
(11)
i 1
Plant i
Plant i
d 2
Non-overlapping Constraint This work is based on continuous model and the shapes of facilities are considered. Consequently, the nonoverlapping constraint should be involved. Considering two facilities, there are two kinds of relative location for
(a)
(b)
Figure 1 Two kinds of relative location of facility i and j
Table 2 Detailed information of facilities No.
Name
Abbr eviati on
R (m)
DI
Operation temperature (℃)
Operation pressure (atm)
1 2 3 4 5 6 7
Air compressor Feed mixer Quench tower Reactor Absorber Solvent splitter Acid extraction tower Distillation column 1 Distillation column 2 Distillation column 3 Solvent mixer
CM FM QC RT AB SP EX
1 1.25 1.4 1.65 1.25 1.55 1.25
7 29 25 47 30 21 30
200 100 280 100 100 90
D1
1.5
22
D2
0.9
D3 SM
8 9 10 11
4 5 5 3 3 2.4
Mass of flammable material (W/kg) 0 100 230 520 410 210 390
150
3
21
150
1.25
27
1.1
20
Whether install firewall 0 0 0 1 0 0 0
Whether install fire insulation 0 0 0 0 0 0 1
Whether install blast wall 1 1 1 1 1 1 1
430
0
0
1
3
280
0
0
1
150
3
120
0
0
1
100
3
150
0
0
1
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R. Wang et al.
4
CONTROLLERS
Solving Algorithm In this work, Genetic Algorithm is employed to solve the proposed model. GA is considered as one of the most effective algorithms and is widely used in various research fields. It imitates the process of evolution of biology in nature. The coordinates and binary variables of relative locations of facilities are set as variables in this work to minimize the objective function. Case Study A case from Lira-Flores et al.’s work (2014) is used here for demonstration. The case is an acrylic acid production process containing 11 facilities and 13 material connections. The detailed parameters and information of
facilities are shown in Table 2, including radii, operation conditions, and the installed protection devices. In this case, the air compressor is square with a side length of 2m. Most of facilities are columns. They are treated as squares, and the side lengths are diameters (2hRi) of the columns. The masses and types of flammable material are estimated due to the absence of them in references. The assumptions of a firewall in reactor and a blast wall in acid extraction tower is set. Fire insulations are installed in all facilities. The boundary of plant area is set as 30 mh40 m. In the method of I2SI, the DHSs of different accident scenarios should be obtained from curves in graphs according to dr, static over pressure (p), and distance between facility i and j (Dij). To evaluate DHSs automatically in the algorithm, the curves are converted into formulas with a coefficient of correlation (R2).
Table 3 The value of DHIs Primary unit CM FM QC RT AB SP EX D1 D2 D3 SM
CM n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a
FM 2.5 2.2 10.0 2.0 2.2 10.0 2.3 4.0 2.4 2.4
QC 7.0 6.3 6.1 10.0 10.0 6.5 10.0 7.0 8.5 10.0
RT 4.5 10.0 3.7 3.4 4.0 5.2 3.9 4.5 4.5 4.5
AB 6.9 5.9 10.0 5.6 10.0 6.5 10.0 7.0 7.0 7.0
Secondary unit SP EX 4.5 1.0 n.a 1.9 n.a 1.0 n.a 1.6 n.a 1.0 1.0 n.a n.a 1.3 4.5 3.5 4.5 1.8 n.a 1.0
D1 10.0 n.a. n.a. n.a. n.a. n.a. n.a. 10.0 10.0 n.a.
D2 7.0 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
D3 10.0 n.a. n.a. n.a. n.a. n.a. n.a. n.a. 10.0 n.a.
SM 2.4 2.4 10.0 10.0 10.0 10.0 2.1 6.0 2.4 2.4 -
Table 4 Optimization result of Facility coordinates Facility No. 1 2 3 4 5 6 7 8 9 10 11 ;
x-axis coordinate 10.0 3.0 3.2 3.2 37.1 9.4 27.3 36.5 31.9 18.6 37.2
y-axis coordinate 26.6 3.1 15.3 26.3 3.1 3.7 16.0 15.8 2.9 27.2 27.2
Figure 2 Optimization results of plant layout The pipe cost is also studied to compare with LiraFlores et al.’s work (2014). The pipe cost can be obtained according to Equation (13): n
C pipe Lpipe ,i U pipe i 1
(13)
An layout optimization method for industrial facilities based on domino hazard index
Where, Cpipe is the cost of pipe ($); Lpipe,i is the length of material connection i (m); Upipe is the unit price of pipe, which is 166.13$/m according to Lira-Flores et al.’s work (2014). The case is solved by GA in the platform of MATLAB with a Xeon E5-2690 2.9GHz CPU and Windows 10 operation system. The generation and population size are set as 1000 and 500 respectively. The optimization results are shown in Figure 2 and Table 4. The total DHI of objective function is 414.9. Table 4 is the DHIs of facilities in the condition of optimization result, and the “n.a.” means the Eq. (2) is not satisfied for the pair of primary and secondary facilities. In Figure 2, the red box means a fire wall is installed in the facility, and the blue box means a blast wall is installed in the facility. In Figure 2, the reactor, the facility with highest temperature, pressure, and the most mass of flammable material, is placed in the corner of the plant area. Reactor is also the facility with highest DI indicating that it has the highest risk as a primary facility in the plant area. Putting reactor in the corner can reduce its impact of domino hazard on the other facilities. The location of compressor is also noteworthy. Due to the low DI of compressor (DI = 7), the Equation (2) is not satisfied when compressor is assumed as a secondary facility for any primary facility. Consequently, the accident consequence of compressor as a secondary facility is weak, so that it is located near the reactor. However, the pipe cost of the proposed method is 45,609$, while it is 37.944$ in Lira-Flores et al.’s work (2014). The capital cost will increase if only safety issue is considered. In a word, the proposed method based on DHI can arrange the facilities in a plant area and design layout properly based on an accurate analysis of risk of domino effects. By employing index based safety evaluation method, the disadvantages of consequence based evaluation methods are avoided. Conclusion In this work, a method based on DHI is proposed to determine the location of facilities in a plant. DHI is set as the objective function. The proposed method is implemented in a case from the work of Lira-Flores et al. (2014). From the results of the obtained layout, the proposed model can arrange facilities properly by identifying dangerous primary facilities and secondary facilities. The proposed method can ensure the safety and reasonability of the obtained layout design. The implementation of index based safety evaluation method can avoid converting risk to economy and the accompanied ethic issue and difficulty of social effect evaluation. However, the proposed layout design method based on safety only may lead to an increase of capital cost. More works are needed to achieve a compromise between safety and economy.
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Acknowledge Finical support from the National Natural Science Foundation of China (No. 21576286) should be greatly acknowledged. References AIChE, (1994). Dow's Fire and Explosion Index Hazard Classification Guide (7th Ed.). Asl, A. D., Wong, K. Y. (2017). Solving unequal-area static and dynamic facility layout problems using modified particle swarm optimization. J Intell Manuf, 28, (6), 1317-1336 Baker, J. A., Bowman, F. L., Erwin, G., Gorton, S., Hendershot, D., Leveson, N., Priest, S., Rosenthal, I., Tebo, P. V., Wiegmann, D. A., Wilson, L. D. (2007). The report of the BP U.S. refineries independent safety review panel. Cozzani, V., Tugnoli, A., Salzano, E. (2007). Prevention of domino effect: From active and passive strategies to inherently safer design. J Hazard Mater, 139, (2), 209219 Jung, S. (2016). Facility siting and plant layout optimization for chemical process safety. Korean J Chem Eng, 33, (1), 17 Khan, F. I., Amyotte, P. R. (2005). I2SI: A comprehensive quantitative tool for inherent safety and cost evaluation. J Loss Prevent Proc, 18, (4-6), 310-326 Lees, F. P. (2001). Loss Prevention In The Process Industries: Hazard Indentification, Assessment and Control. Lira-Flores, J., Vázquez-Román, R., López-Molina, A., Mannan, M. S. (2014). A MINLP approach for layout designs based on the domino hazard index. J Loss Prevent Proc, 30, 219-227 Medina-Herrera, N., Jiménez-Gutiérrez, A., Grossmann, I. E. (2014). A mathematical programming model for optimal layout considering quantitative risk analysis. Comput Chem Eng, 68, 165-181 Ozyurt, D. B., Realff, M. J. (1999). Geographic and process information for chemical plant layout problems. Process System Engineering, 45, (10), 2161 Patsiatzis, D. I., Knight, G., Papageorgiou, L. G. (2004). An MILP approach to safe process plant layout. Chemical Engineering Research and Design, A5, (82), 579–586 Penteado, F. D., Ciric, A. R. (1996). An MINLP Approach for Safe Process Plant Layout. Ind Eng Chem Res, 35, (4), 1354 - 1361 Tugnoli, A., Khan, F., Amyotte, P., Cozzani, V. (2008). Safety assessment in plant layout design using indexing approach: Implementing inherent safety perspective Part2—Domino Hazard Index and case study. J Hazard Mater, 160, (1), 110-121 Vázquez-Román, R., Lee, J., Jung, S., Mannan, M. S. (2010). Optimal facility layout under toxic release in process facilities: A stochastic approach. Comput Chem Eng, 34, (1), 122-133 Wang, R., Wu, Y., Wang, Y., Feng, X. (2017). An industrial area layout optimization method based on dow's Fire & Explosion Index Method. Chemical Engineering Transactions, 61, 493-498 Wang, R., Zhao, H., Wu, Y., Wang, Y., Feng, X., Liu, M. (2018). An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm. Energy, 158, 1038-1051
AN LAYOUT OPTIMIZATION METHOD FOR INDUSTRIAL FACILITIES BASED ON DOMINO HAZARD INDEX
Ruiqi Wang1, Yan Wu2, Yufei Wang1 *, Xiao Feng2, and Mengxi Liu1 1 China University of Petroleum - Beijing Beijing, China 102249 2 Xi’an Jiaotong University - Xi’an Xi’an, Shaanxi, China 710049
Abstract Layout design is a key step in the process of chemical engineering design. In layout design, safety is the most important factor that needs to be considered. In previous work of relative research, consequence based safety evaluation method is employed to convert risk into cost for integrating safety aspect into objective function minimizing cost. However, converting risk into cost is improper due to two reasons: on the one hand, an ethical issue will be involved when converting casualties into cost; on the other hand, social effect and long-term environment effect resulting from an accident are not considered due to the difficulty of assessment. Consequently, safety should be considered as an independent indicator, rather than combined with economy. In this work, a layout method based on safety is proposed to determine the location of facilities in a plant. The Domino Hazard Index (DHI), an index that indicates the magnitude of domino effects in a plant area, is employed to evaluate the safety of a plant and guide the layout design. The sum of DHIs of facilities is set as objective function to minimize the domino effects of the plant. The proposed model is solved by genetic algorithm (GA) and implemented in a case from literature. The optimization result is analyzed and can illustrate the feasibility and advantage of the proposed method. Keywords Layout design, Risk evaluation, Domino effect, Genetic algorithm, Optimization Introduction Layout design is one of the most important aspects in the process of chemical engineering design, which has a significant impact on the performance of an enterprise, as well as heat exchanger network design and production planning & scheduling. Economy and safety are the two main factors considered in facility layout problem. Penteado and Criric (1996) proposed a mixed integer nonlinear programming (MINLP) model to determine the location of several facilities in a plant. The objective function consists of piping cost, land cost, protection
* Corresponding author: E-mail: [email protected]
devices cost, and risk cost. Their work is relatively early and comprehensive in the research filed of facility layout. Safety is extremely sensitive to layout design. Though the manufacturing technique for a single equipment is quite mature at present, it still cannot prevent accidents from occurrence obviously, because most of the accidents were aroused by human errors or systematic flaws. A large number of accidents have proved the importance of layout design in the aspect of safety of process industry. On March 23, 2005, an explosion occurred in the
An layout optimization method for industrial facilities based on domino hazard index
isomerization unit of BP Texas City refinery, resulting in 15 deaths, more than 170 injuries, and significant economic losses. It is one of the most serious U.S. workplace disasters in the past two decades. After the accident, the investigation report (2007) indicates that, the improper trailer siting is one of the four critical factors for the accident. There are two types of basic models for facility layout problems: discrete model and continuous model (1999). In discrete model, the free space is divided into many regular square girds. A facility can occupy one or more grids. Layout design method based on discrete model can work out an orderly result. However, discrete model will also lead to a coarse layout design, because the size of girds cannot always fit the size of facilities exactly. Jung (2016) proposed a method to find the optimal location of facilities for a plant by using a risk map. The plant area is divided into several grids and a risk score is estimated for each grid to generate the risk map. In continuous model, the facilities can be placed anywhere in the free space, and the facilities should have their own shapes, resulting in an involvement of non-overlapping constraint. However, continuous model is more practical and is employed in this work. As for algorithms, both General Algebraic Modeling System (GAMS) based solvers and intelligent algorithms were employed to solve industrial facility layout problems. Asl and Wong (2017) proposed a modified particle swarm algorithm for both static and dynamic facility layout problem. In their work, two local search methods and a department swapping method were introduced to prevent local optima. Additionally, some other sub-algorithms were combined to improve the solving process. Wang et al. (2018) combined the genetic algorithm (GA) and surplus rectangle fill algorithm to determine the layout of facilities. In their work, the coordinates of facilities were not set as variables any longer, and the feasible region was narrowed. By this way, the computational efficiency was improved. Many safety evaluation methods were involved in the research field of facility layout. Vázquez-Román et al. (2010) considered the uncertainty of toxic release when determine the location of facilities of a plant. The wind speed, wind direction, and atmospheric stability were incorporated to calculate the death risk for human by Monte Carlo simulation. The model was formulated as an MINLP model. Medina-Herrera et al. (2014) proposed a method based on quantitative risk analysis to determine the layout of facilities. A bowtie analysis was employed to identify possible catastrophic outcomes, which included the scenarios of fire, explosion, and toxic release. The safety evaluation methods adopted in the two works mentioned above are based on accident consequence. However, to measure human life by cost will lead to an ethical issue. On the other hand, besides casualties and property damage, the accidents will also lead to social effects and long-term environment effects. These effects are not assessed in most of previous works, and they are also difficult to be evaluated. Consequently, index based methods, an important type of safety evaluation method,
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should be introduced individually. Dow’s Fire and Explosion Index (F&EI) method (1994) is an accurate and systematic method to evaluate the safety of process industry, which is widely used in the world. The most common accident scenarios, fire and explosion, are considered in Dow’s method. Patsiatzis et al. (2004) proposed a mixed integer linear programming (MILP) model to determine the facility layout. In their work, Dow’s F&EI method was used to evaluate the safety of the plant, and different types of protection devices were alternative to be applied in the facilities to reduce the possible consequence of accident. Wang et al. (2017) proposed a model to evaluate the safety of an industrial park based on Dow’s F&EI method, and determine the layout of industrial park. Inherent safety is a key concept in process safety evaluation, and implementing inherent safety is an effective way for loss prevention and risk management. Khan and Amyotte (2005) proposed a conceptual framework named Integrated Inherent Safety Index (I2SI) to evaluate the inherent safety of a plant. I2SI is composed of several subindexes which account for hazard potential, inherent safety potential, and add-on control requirements. Domino effect was involved in many accidents with severe consequence. Domino effect will lead to an escalation of accident. Tugnoli et al. (2008) developed an index to evaluate the hazard related to potential domino effects based on I2SI. The index was called Domino Hazard Index (DHI) and was used to guide the layout design of a plant. In their case, three different layout schemes for same plant were analyzed and compared to select the best one with minimum domino effects. However, DHI evaluation method was not integrated into a systematic programming model in their work. Consequently, the method they proposed can only compare several pre-designed layout schemes manually, rather than work out a certain layout automatically. Lira-Flores et al. (2014) proposed a MINLP model to design facility layout using DHI, however, total cost was set as an objective function. In this work, DHI is set as objective function to guide the layout design and avoid the disadvantages of economy aimed method. A systematic layout design model involving non-overlapping constraint is established. The proposed model is solved by GA and implemented in a case from literature. The case shows the feasibility and advantages of the proposed model. Problem Statement The aim of this work is to determine the location of facilities in a plant to minimize the hazard of domino effects based on continuous model. The dimensions of facilities should be given to formulate non-overlapping constraints. DHI is used to evaluate the magnitude of domino effects, and the detailed information and parameters of facilities are needed, including operation
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pressure, temperature, facility type, mass of contained flammable material, and so on. Parameters that should be given and the variables to be determined are shown below: Given: The dimensions of facilities (Ri); The operation pressures and temperatures of facilities; The types of facilities (tower, vessel, and so on.) The mass and type of flammable material contained in a facility (W, ΔHc); The protection devices installed in facilities (fire wall, fire insulation, and blast wall). Determination: The coordinates of center points of facilities (xi,yi). Methodology Objective Function The DHI can score the potential of accident propagation considering possible escalation scenarios of accidents. So it is helpful for reducing subjectivity when safety and proper layout scheme are determined. The evaluation of DHI is based on I2SI method, and the effects of both inherent and passive measures on the domino escalation potential are taken into account. The first step of evaluating domino effects is to identify the facilities with significant potential of severe accident consequence. The Damage Index (DI) coming from I2SI method is used as a criterion. DI indicates the magnitude of impact of a facility to its surrounding. It is obtained by considering 4 kinds of risks: fire and explosion risk, acute toxicity risk, chronic toxicity risk, and environmental damage risk, as is shown in Equation (1). DI [( DIfe )2 (DIac )2 ( DIch )2 ( DIen )2 ]1/2 (1) The sub-indexes of DI and the detailed procedure of DI’s obtaining can be found in Khan and Amyotte’s work (2005). Then the necessity of considering the domino effect between two facilities should be confirmed. Considering a primary facility i and a secondary facility j, if Equation (2) is satisfied, the domino effect from facility i to facility j should be considered, e.i. DHSij (Domino Hazard Score) should be worked out, otherwise, DHSij should be ignored. (2) DI j (min( DI i , )) Where DIi is the DI of primary facility i; DIj is the DI of secondary facility j; § is an arbitrary threshold value that defines the lower limit of DI for facilities. If the domino effect of facility i on facility j should be considered, 4 kinds of possible accidents are evaluated respectively: fire ball, pool fire & jet fire, explosion, and fragment projection. The DHS under each kind of accident scenario should be calculated. For fireball scenario, the accident will escalate only when the flammable gas is triggered by flame directly due
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to the short duration time of fireball. Thus, if the secondary facility is contained in the fireball, the DHS=10, otherwise, DHS=0, as is shown in Equation (3).
0 DHS=
10
Dij Rfb Dij Rfb
(3)
Where Dij is the distance between primary facility i and secondary facility j; Rfb is the radius of the potential fireball. Fire insulation is a kind of effective protection measure to protect equipment. Thus, if fire insulation is equipped, the DHS = 5 in the scenario of fireball. For jet fire scenario, the worst case of horizontal fire is considered. The minimum distance between flame and secondary facility can be obtained from Equation (4). (4) d r Di ,j d f d p d s Where, df is the maximum length of flame; dp is the characteristic dimension of primary facility, i.e. the radius of primary facility; ds is the characteristic dimension of secondary facility; dr is the minimum distance between flame and secondary facility. For pool fire scenario, Eq. (4) is also used, where the df is equal to the pool radius for a non-tilted pool fire. The df can be quickly estimated from the literature of Cozzani et al. (2007). The DHS values for jet fire and pool fire scenario can be obtained from graphs of Tugnoli et al.’s work (2008) based on dr. For explosion scenario, the DHS can be obtained from the graph of Tugnoli et al.’s work (2008) according to the static peak overpressure where the secondary facility locates. The static peak overpressure is estimated by a TNT equivalent model (Lee, 2001), as is shown in Equation (5) - (8). W Hc WTNT (5) ETNT Dij z (6) 1 WTNT 3
U a b log10 z
(7)
11
log10 p0 ciU i
(8)
i 0
Where, W is the mass of flammable material in a facility (kg); ΔHc is the heat of combustion of the flammable material (kJ/kg); ETNT is the energy of explosion of TNT (kJ/kg) which is 4190-4650 kJ/kg; α is the yield factor; WTNT is the equivalent mass of TNT (kg); z is the scaled distance (m/kg1/3); U is an intermediate parameter; a, b, and ci are constant parameters and are shown in Table 1; P0 is the peak overpressure (kPa). For fragment projection, the DHS can be obtained from a graph according to the distance between primary facility and secondary facility (Dij). After determining the DHSs for all 4 potential accidents, the DHS between the primary facility i and secondary facility j can be obtained, as is shown in Equation (9).
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An layout optimization method for industrial facilities based on domino hazard index
Table 1 Parameters of TNT equivalent model Parameter a c0 c2 c4 c6 c8 c10
Value -0.21436 2.78077 -0.15416 0.09885 -0.02681 0.00163 0.00015
Parameter b c1 c3 c5 c7 c9 c11
Value 1.35034 -1.69590 0.51406 -0.29391 0.10910 -0.02146 0.00168
DHSi, j max k ( DHS i , j ,k )
(9)
Where, DHSi,j,k is the DHS of accident k originating from facility i to facility j. The DHI can be obtained for facility i: n
DHIi = DHSi , j
(10)
j 1
The sum of DHIs of facilities is set as an objective function to minimize the domino hazard in the plant area, as is shown in Equation (11)
them: above/below, and right/left. A binary variable can be used to describe the relative location of two facilities, and the non-overlapping constraint can be mathematically shown as Equation (12) . zoverlapping ,i , j 1 zoverlapping ,i , j L L L L y y y ,i y , j d x x x ,i x , j d i j i j 2 2 2 2 (12) Where, zoverlapping,i,j is a binary variable representing the relative location of facility i and facility j. When zoverlapping,i,j=1, facility j is forced to be in the up or down side of facility i, as shown in Figure 1 (a). When zoverlapping,i,j=0, facility j is forced to be in the right or left side of facility i, as shown in Figure 1 (b). xi, yi, xj, and yj are the coordinates of facility i and j. Lx,i, Lx,j, Ly,i, and Ly,j are the length of facility i and j paralleling to x axis and y axis respectively. d/2 is the distance between two facilities reserved for installation and maintenance, and the facilities should also keep distance of d/2 from the boundary of plant area.
Plant j
m
Min DHI
DHIi
d 2
Plant j
(11)
i 1
Plant i
Plant i
d 2
Non-overlapping Constraint This work is based on continuous model and the shapes of facilities are considered. Consequently, the nonoverlapping constraint should be involved. Considering two facilities, there are two kinds of relative location for
(a)
(b)
Figure 1 Two kinds of relative location of facility i and j
Table 2 Detailed information of facilities No.
Name
Abbr eviati on
R (m)
DI
Operation temperature (℃)
Operation pressure (atm)
1 2 3 4 5 6 7
Air compressor Feed mixer Quench tower Reactor Absorber Solvent splitter Acid extraction tower Distillation column 1 Distillation column 2 Distillation column 3 Solvent mixer
CM FM QC RT AB SP EX
1 1.25 1.4 1.65 1.25 1.55 1.25
7 29 25 47 30 21 30
200 100 280 100 100 90
D1
1.5
22
D2
0.9
D3 SM
8 9 10 11
4 5 5 3 3 2.4
Mass of flammable material (W/kg) 0 100 230 520 410 210 390
150
3
21
150
1.25
27
1.1
20
Whether install firewall 0 0 0 1 0 0 0
Whether install fire insulation 0 0 0 0 0 0 1
Whether install blast wall 1 1 1 1 1 1 1
430
0
0
1
3
280
0
0
1
150
3
120
0
0
1
100
3
150
0
0
1
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R. Wang et al.
4
CONTROLLERS
Solving Algorithm In this work, Genetic Algorithm is employed to solve the proposed model. GA is considered as one of the most effective algorithms and is widely used in various research fields. It imitates the process of evolution of biology in nature. The coordinates and binary variables of relative locations of facilities are set as variables in this work to minimize the objective function. Case Study A case from Lira-Flores et al.’s work (2014) is used here for demonstration. The case is an acrylic acid production process containing 11 facilities and 13 material connections. The detailed parameters and information of
facilities are shown in Table 2, including radii, operation conditions, and the installed protection devices. In this case, the air compressor is square with a side length of 2m. Most of facilities are columns. They are treated as squares, and the side lengths are diameters (2hRi) of the columns. The masses and types of flammable material are estimated due to the absence of them in references. The assumptions of a firewall in reactor and a blast wall in acid extraction tower is set. Fire insulations are installed in all facilities. The boundary of plant area is set as 30 mh40 m. In the method of I2SI, the DHSs of different accident scenarios should be obtained from curves in graphs according to dr, static over pressure (p), and distance between facility i and j (Dij). To evaluate DHSs automatically in the algorithm, the curves are converted into formulas with a coefficient of correlation (R2).
Table 3 The value of DHIs Primary unit CM FM QC RT AB SP EX D1 D2 D3 SM
CM n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a
FM 2.5 2.2 10.0 2.0 2.2 10.0 2.3 4.0 2.4 2.4
QC 7.0 6.3 6.1 10.0 10.0 6.5 10.0 7.0 8.5 10.0
RT 4.5 10.0 3.7 3.4 4.0 5.2 3.9 4.5 4.5 4.5
AB 6.9 5.9 10.0 5.6 10.0 6.5 10.0 7.0 7.0 7.0
Secondary unit SP EX 4.5 1.0 n.a 1.9 n.a 1.0 n.a 1.6 n.a 1.0 1.0 n.a n.a 1.3 4.5 3.5 4.5 1.8 n.a 1.0
D1 10.0 n.a. n.a. n.a. n.a. n.a. n.a. 10.0 10.0 n.a.
D2 7.0 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
D3 10.0 n.a. n.a. n.a. n.a. n.a. n.a. n.a. 10.0 n.a.
SM 2.4 2.4 10.0 10.0 10.0 10.0 2.1 6.0 2.4 2.4 -
Table 4 Optimization result of Facility coordinates Facility No. 1 2 3 4 5 6 7 8 9 10 11 ;
x-axis coordinate 10.0 3.0 3.2 3.2 37.1 9.4 27.3 36.5 31.9 18.6 37.2
y-axis coordinate 26.6 3.1 15.3 26.3 3.1 3.7 16.0 15.8 2.9 27.2 27.2
Figure 2 Optimization results of plant layout The pipe cost is also studied to compare with LiraFlores et al.’s work (2014). The pipe cost can be obtained according to Equation (13): n
C pipe Lpipe ,i U pipe i 1
(13)
An layout optimization method for industrial facilities based on domino hazard index
Where, Cpipe is the cost of pipe ($); Lpipe,i is the length of material connection i (m); Upipe is the unit price of pipe, which is 166.13$/m according to Lira-Flores et al.’s work (2014). The case is solved by GA in the platform of MATLAB with a Xeon E5-2690 2.9GHz CPU and Windows 10 operation system. The generation and population size are set as 1000 and 500 respectively. The optimization results are shown in Figure 2 and Table 4. The total DHI of objective function is 414.9. Table 4 is the DHIs of facilities in the condition of optimization result, and the “n.a.” means the Eq. (2) is not satisfied for the pair of primary and secondary facilities. In Figure 2, the red box means a fire wall is installed in the facility, and the blue box means a blast wall is installed in the facility. In Figure 2, the reactor, the facility with highest temperature, pressure, and the most mass of flammable material, is placed in the corner of the plant area. Reactor is also the facility with highest DI indicating that it has the highest risk as a primary facility in the plant area. Putting reactor in the corner can reduce its impact of domino hazard on the other facilities. The location of compressor is also noteworthy. Due to the low DI of compressor (DI = 7), the Equation (2) is not satisfied when compressor is assumed as a secondary facility for any primary facility. Consequently, the accident consequence of compressor as a secondary facility is weak, so that it is located near the reactor. However, the pipe cost of the proposed method is 45,609$, while it is 37.944$ in Lira-Flores et al.’s work (2014). The capital cost will increase if only safety issue is considered. In a word, the proposed method based on DHI can arrange the facilities in a plant area and design layout properly based on an accurate analysis of risk of domino effects. By employing index based safety evaluation method, the disadvantages of consequence based evaluation methods are avoided. Conclusion In this work, a method based on DHI is proposed to determine the location of facilities in a plant. DHI is set as the objective function. The proposed method is implemented in a case from the work of Lira-Flores et al. (2014). From the results of the obtained layout, the proposed model can arrange facilities properly by identifying dangerous primary facilities and secondary facilities. The proposed method can ensure the safety and reasonability of the obtained layout design. The implementation of index based safety evaluation method can avoid converting risk to economy and the accompanied ethic issue and difficulty of social effect evaluation. However, the proposed layout design method based on safety only may lead to an increase of capital cost. More works are needed to achieve a compromise between safety and economy.
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Acknowledge Finical support from the National Natural Science Foundation of China (No. 21576286) should be greatly acknowledged. References AIChE, (1994). Dow's Fire and Explosion Index Hazard Classification Guide (7th Ed.). Asl, A. D., Wong, K. Y. (2017). Solving unequal-area static and dynamic facility layout problems using modified particle swarm optimization. J Intell Manuf, 28, (6), 1317-1336 Baker, J. A., Bowman, F. L., Erwin, G., Gorton, S., Hendershot, D., Leveson, N., Priest, S., Rosenthal, I., Tebo, P. V., Wiegmann, D. A., Wilson, L. D. (2007). The report of the BP U.S. refineries independent safety review panel. Cozzani, V., Tugnoli, A., Salzano, E. (2007). Prevention of domino effect: From active and passive strategies to inherently safer design. J Hazard Mater, 139, (2), 209219 Jung, S. (2016). Facility siting and plant layout optimization for chemical process safety. Korean J Chem Eng, 33, (1), 17 Khan, F. I., Amyotte, P. R. (2005). I2SI: A comprehensive quantitative tool for inherent safety and cost evaluation. J Loss Prevent Proc, 18, (4-6), 310-326 Lees, F. P. (2001). Loss Prevention In The Process Industries: Hazard Indentification, Assessment and Control. Lira-Flores, J., Vázquez-Román, R., López-Molina, A., Mannan, M. S. (2014). A MINLP approach for layout designs based on the domino hazard index. J Loss Prevent Proc, 30, 219-227 Medina-Herrera, N., Jiménez-Gutiérrez, A., Grossmann, I. E. (2014). A mathematical programming model for optimal layout considering quantitative risk analysis. Comput Chem Eng, 68, 165-181 Ozyurt, D. B., Realff, M. J. (1999). Geographic and process information for chemical plant layout problems. Process System Engineering, 45, (10), 2161 Patsiatzis, D. I., Knight, G., Papageorgiou, L. G. (2004). An MILP approach to safe process plant layout. Chemical Engineering Research and Design, A5, (82), 579–586 Penteado, F. D., Ciric, A. R. (1996). An MINLP Approach for Safe Process Plant Layout. Ind Eng Chem Res, 35, (4), 1354 - 1361 Tugnoli, A., Khan, F., Amyotte, P., Cozzani, V. (2008). Safety assessment in plant layout design using indexing approach: Implementing inherent safety perspective Part2—Domino Hazard Index and case study. J Hazard Mater, 160, (1), 110-121 Vázquez-Román, R., Lee, J., Jung, S., Mannan, M. S. (2010). Optimal facility layout under toxic release in process facilities: A stochastic approach. Comput Chem Eng, 34, (1), 122-133 Wang, R., Wu, Y., Wang, Y., Feng, X. (2017). An industrial area layout optimization method based on dow's Fire & Explosion Index Method. Chemical Engineering Transactions, 61, 493-498 Wang, R., Zhao, H., Wu, Y., Wang, Y., Feng, X., Liu, M. (2018). An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm. Energy, 158, 1038-1051