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Ind. Eng. Chem. Res. 1996, 35, 1354-1361
An MINLP Approach for Safe Process Plant Layout Flavio D. Penteado and Amy R. Ciric* Department of Chemical Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0171
The tragic accidents at Flixborough and Bhopal have led to the development of new legislation concerning the design and operation of chemical plants. In addition, the growing concern with safety and environmental issues places many new demands upon the designer. Process plant layout, as an important step in the design of chemical plants, is effected by these demands. This paper presents a new approach to process plant layout that integrates safety and economics. In this approach, the cost of a layout is a function of piping cost, land cost, financial risk, and protection devices cost. The financial risk term captures the risk of unsafe plants and can be expressed as the expected losses if major accidents happen (i.e., fires or explosions). The proposed approach is a mixed-integer nonlinear optimization problem (MINLP) that identifies attractive layouts by minimizing overall costs. This approach gives the coordinates of each unit, an estimate for the total piping length, the amount of land occupied, and the safety devices that have to be installed at each unit. 1. Introduction Process plant layout is usually performed during plant design. Its goal is to provide the best arrangement of process equipment in a chemical plant. A good layout strives to minimize the amount of piping used in a process and the amount of land occupied by the plant, while maintaining easy access to spaces around individual units and providing safety zones between units; a good layout will not only reduce investment costs but also avoid or minimize safety and maintenance problems. Several methods have been proposed to solve the process plant layout problem. A number of these methods are based on the facilities layout problem. This problem partitions available space into regions and then assigns departments or facilities to these spaces so as to achieve the most efficient way to manufacture a product or provide services (Rosenblatt, 1979; Urban, 1987). The facilities layout problem has been approached as a quadratic assignment problem; for example, Suzuki et al. (1991) have proposed a multigoal approach that considers piping cost, site cost, and expressed preferences about equipment arrangement in a chemical plant. Heuristic methods have been proposed that include qualitative goals, quantitative goals, or both in the objective function (Rosenblatt and Golany, 1989; Harmonsky and Tothero, 1992; Yaman et al., 1993). Expert systems have also been developed for the facilities layout problem. For example, Chen and Kengskool (1990) provide a tool that incorporates human expertise and computer graphics to solve the facilities layout problem. One of the weaknesses of the methods associated with the facilities layout problem is that they usually assume that the there are no differences between departments and that the cost of allocating departments to locations is constant. In plant layout problems, this weakness can be overcome by explicitly considering the placement of process equipment in a restricted area. This placement is constrained by codes, flow sequence, and safety requirements. Some approaches to solve this process plant layout problem have been developed in recent years. Fujita et al. (1991) proposed an approach which * Author to whom correspondence should be addressed. Email:
[email protected].
0888-5885/96/2635-1354$12.00/0
combines an artificial intelligence technique with a constraint-directed search. Jayakumar and Reklaitis (1994) presented an alternative approach based on graph partitioning. Madden et al. (1990) developed an expert system that generates 3D layouts from process flowsheets. The majority of the previous work in process plant layouts has focused upon optimizing piping costs, site costs, and qualitative preferences. Interestingly, very little work has been done on the interaction between process layout and process plant safety. Process safety has become an important issue, particularly after accidents at Flixborough (Lees, 1980) and Bhopal (Kletz, 1985). These accidents increased the public awareness of chemical hazards in the chemical process industries. As a result, new regulations were created, such as the Process Safety Management of Highly Hazardous Chemicals (1992), from the U.S. Occupational Safety and Health Association (OSHA), and the Risk Management Programs for Chemical Accidental Release Prevention, from the U.S. Environmental Protection Agency, which will become law soon. There are some basic ways to improve the safety of a chemical plant. One can install protection devices that reduce the probability or severity of an accident. Alternatively, one can reduce the chance that an accident will spread from one unit to another by installing a barrier wall or by increasing the separation between units. Clearly, there is a tradeoff between (a) the financial risk associated with an accident, which decreases as units are separated, (b) piping and land costs, which increase when units are separated, and (c) the cost of protection devices, which reduce the risk of an accident. This tradeoff can be resolved during the layout stage of process development. Process plant layout should be carefully studied during the early stages of the design of a chemical plant. Because of the large number of possibilities, process plant layouts are developed and modified several times during the design process. The use of a structured methodology for process plant layout that incorporates process safety can minimize the number of changes in the layout that result from safety studies. This paper presents a method for laying out chemical plants that explicitly considers the safe layout problem as an optimization problem. This gives a mixed-integer nonlinear programming (MINLP) problem whose objec© 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1355
tive function minimizes piping cost, land cost, financial risk, and protection device cost. The approach determines the coordinates of each unit and the combination of protection devices that are to be installed at each unit. It can be used in the conceptual phase of the design of a chemical plant, as soon as information like preliminary dimensions of the units, their cost, material and energy balances, and a process description are available, and basic information about the probability and severity of accidents can be estimated. The information generated by this approach can be used to (a) determine whether a proposed plant could safely and economically by installed in a given area; (b) determine the types of additional safety devices to be installed; and (c) generate some low-risk layout structures that warrant further development during detailed design. The next sections describe the formulation and application of the model. 2. Problem Statement The problem addressed by this paper can be stated formally as follows: Given: (a) a set of process units, indexed i ) 1, ..., I (b) the external dimensions of the units, expressed in terms of the radius of gyration Radi and the footprint radius Fi (c) the piping connections between units, expressed as a zero-one matrix Mij, with
Mij )
{
1 0
if unit i is connected to unit j otherwise
(d) the dimensions of a rectangle of available land, Lx by Ly (e) the minimum safety distance between units i and j, Sdij (f) a collection of protection devices, indexed k ) 1, ..., K (g) the purchase and installation cost of piping Cp in $/m, the cost of land Lc in $/m2, and the purchase and installation cost of various protection devices (h) a list of the potential events at each unit, the severity of each event, measured in dollars, and the probability of each event, in yr-1 (i) an estimate of the probability of an accident spreading from one unit to another, given in terms of the distance between the units (j) the expected lifetime of the plant in years, N, and annual interest rate if expected on all investments. Determine: (a) the x and y coordinates of each unit (b) the safety devices that should be installed at each unit (c) the minimum net present cost of the layout In this work, it is assumed that the land occupied by each unit is characterized by a circular footprint. Figure 1 shows a footprint on a x-y plane. The footprint is defined here as the radius of gyration Radi of the unit plus an additional incremental radius that is required for access and maintenance. 3. Mathematical Model The process plant layout problem is an optimization problem that minimizes the cost of a layout. This cost
Figure 1. Footprint on an x-y plane.
is divided into four terms: piping cost, land cost, protection devices cost, and financial risk cost. The set of constraints to this problem includes surface area constraints, distance between units, and minimum safety distance between units. 3.1. The Objective Function. The objective is to minimize the cost associated with the layout. The cost is composed of four terms: piping costs, land costs, protection devices cost, and financial risk. 3.1.1. Piping Cost. The piping cost term is computed from:
∑i ∑j MijCp(dij - Radi - Radj)
1/2
(1)
In eq 1, dij is the distance between the center of units i and j. 3.1.2. Land Cost. The occupied land is proportional to the surface area occupied by all the equipment. This term also includes additional space occupied by a pipe rack connecting two distinct units. The land cost is given by:
Lc
(dij - Fi - Fj) ∑i πFi2 + LcWp∑i ∑ j*i
(2)
In eq 2, Wp is the width of a piperack connecting units i and j. Note that the occupied land is based upon the footprint of the units, which includes both the land occupied by the units and the land around the unit reserved for maintenance access. 3.1.3. Protection Devices Cost. Two different types of protection devices are considered in this formulation: protection systems installed at units and physical barriers installed between units. The first group includes fire relief valves, explosion suppression systems, and any other protection system that diminishes the probability or severity of accidents. The second group includes blast walls able to withstand shock waves and fire protection systems like water sprays. The protection devices that are installed on the units can function in two different ways. They can prevent an accident from occurring, or they can minimize the damage done to a unit when an accident occurs in a neighboring unit. In the second scenario, we will say that the source of the accident is the “origin” of the
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accident, and its neighboring units are the “targets” of the accident. The protection devices cost is:
∑i ∑j CbijYbij + ∑i ∑k CtarikYtarik + ∑j ∑k CpdjkYpdjk
(3)
Here, Cbij is the cost of a physical barrier installed between units i and j, and Ctarik is the cost of a protection device k installed at unit i, which is the target of the accident. Cpdjk is the cost of a protection device k installed at unit j, which is the origin of an accident. Ybij is an integer variable that equals 1 if a barrier is placed between units i and j. Ytarik is an integer variable that equals 1 if a protection device is installed at unit i, the target of an accident that occurs in another unit. Ypdjk is an integer variable that equals 1 if a protection device is installed at unit j, the origin of an accident. 3.1.4. Financial Risk. Risk is the expected financial loss associated with an accident. Expected losses are a function of both the severity and probability of the accident. The annual risk can be expressed as:
annual risk ($/yr) )
∑ severity ($/event) ×
events
probability (yr-1) This annual risk cost captures the implicit cost of an unsafe plant; this cost may represent annual insurance and liability costs. Note that this cost is a function of the distance between units because physically separating a hazardous unit diminishes the damage done to neighboring units when a fire or explosion occurs. The annual risk can be compared to the one-time costs associated with piping, land, and protection devices by computing the net present financial risk: N
net present financial risk )
annual risk × ∑ j)1 (1 + if)-j (4)
Figure 2. Example of a damange function.
protection devices at unit i, which is the target of an accident in unit j; (3) increasing the distance between units j and i; and (4) installing barriers between units i and j. The second term of the financial risk cost is given by:
RRij0(1 - SF3ijYbij)∏(1 - SF1ikYtarik)∏(1 ∑i ∑ j*i k k SF2jkYpdjk) (6) Here, RRij0 is the net present financial risk associated with accidents propagating from unit j to unit i without any barriers or protection systems. Note that this term is a function of the distance between units i and j. SF1ik and SF2jk are the risk reduction factors when protection devices k are installed at unit i (target) and unit j (origin), respectively. SF3ij is the risk reduction factor when a physical barrier is placed between units i and j. The risk RRij0 is represented by: min
Here, N is the lifetime of the plant in years, and if is the annual interest rate associated with financial investments. It should be noted that, in the rest of this work, the net present financial risk will also be referred to as the financial risk. The financial risk is constructed from two different terms. The first term corresponds to the risk reduction associated with placing a safety device k on a process unit i, when an accident occurs at i:
(1 - SF2ik)Ypdik ∑i Ri0∏ k
(5)
In eq 5, Ri0 is the initial risk of accidents at unit i without any barriers or protection systems. SF2ik is the risk reduction factor when safety protection system k is installed at unit i. Each protection system k purchased and installed at unit i attenuates the initial risk Ri0 by a factor of (1 - SF2ik). Multiple safety devices compound the risk reduction. The second term captures the risk associated with the propagation of an accident in unit j to unit i. This risk can be reduced by (1) installing protection devices at unit j, which is the origin of the accident; (2) installing
RRij0 ) Pje-Aij(dij-dij
)
(Bij(dij - dijmin) + Cij)
(7)
Here, Pj is the probability of accidents occurring at unit j. The remaining term on the right-hand side expresses the expected losses at the target. dijmin is the minimum distance between units i and j. Aij, Bij, and Cij are constants, and it can be shown that Bij ) AijCij. The constants Aij and Cij are computed by simulating the accidents and events specific to each unit. Either thermal radiation or blast pressure is calculated as a function for the distance from the unit that starts the accident. The damage at the target unit can be estimated for two points: the minimum distance between the units and any other point between them. The shape of the function of RRij0 is showed in Figure 2. Note that if units i and j are very close to each other, RRij0 is not sensibly affected by the distance between the units. That is because the target (unit i) is so close to the origin of the accident (unit j) that is essentially destroyed, and slightly moving the unit does not reduce the damage. At intermediate range, distance becomes a very important factor of risk propagation. At very large distances, the target unit is too far away from the
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1357
accident to suffer any significant damage, and RRij0 is once again unaffected by the distance between units. 3.2. Constraints. 3.2.1. Surface Area Constraints. All the equipment must be placed on the available land. This constraint can be expressed as
Fi e xi e Lx - Fi
(8)
Fi e yi e Ly - Fi
(9)
Here, xi and yi are the coordinates of the center of unit i. Lx and Ly are the boundaries of the available land. 3.2.2. Distance between Units. The distance between units is calculated by
dij2 ) (xi - xj)2 + (yi - yj)2
(10)
3.2.3. Minimum Distance between Units. The distance between units is constrained by:
dij g dijmin
(11)
where
dijmin ) max{Sdij + Radi + Radj, Fi + Fj} (12) In the above equation, Sdij is the safety distance between units i and j. Safety distances between units are usually given by codes or standards, such as NFPA (National Fire Prevention Association). 3.3. Overall Formulation. The overall formulation of the process plant layout optimization model is given by:
∑i ∑j MijCp(dij - Radi - Radj) + Lc∑i πFi2 + LcW4p∑∑(dij - Fi - Fj) + ∑∑CbijYbij + i j*i i j 0 Cpd Ypd + R (1 SF2ik)Ypdik + ∑i ∑k jk jk ∑i i ∏ k RRij0(1 - SF3ijYbij)∏(1 - SF1ikYtarik)∏(1 ∑i ∑ j*i k k
min 1/2
SF2jkYpdjk) (P) Subject to
Fi e xi e Lx - Fi Fi e yi e Ly - Fi dij2 ) (xi - xj)2 + (yi - yj)2 dij g dijmin min
RRij0 ) Pje-Aij(dij-dij
)
(Bij(dij - dijmin) + Cij)
of the process units; consequently, the initial positions or layout of the process units must be carefully selected. It should be noted that the integer variables appear in nonlinear terms; consequently, problem (P) cannot be solved with standard MINLP techniques, such as Generalized Benders Decomposition (Geoffrion, 1974) or the Outer Approximation Method (Duran and Grossmann, 1987). However, problem (P) does have two special properties that can be exploited in a solution procedure. Property One. The integer variables do not appear within the constraint set. The integer variables only appear in the device cost and risk reduction terms of the objective function. Property Two. The objective function is polylinear with respect to the integer variables. When all variables except one integer variable Yi are held constant, the objective function takes the form R + βYi. If β is positive, Yi will be driven to zero; if β is negative, Yi will be driven to 1. These properties imply that problem (P) can often be solved as a relaxed mixed-integer nonlinear programming problem (RMINLP) where the integer variables are treated as continuous variables that are bounded between zero and 1. At the solution, these variables will naturally equal zero or 1. However, unlike linear assignment problems that can also be solved as relaxed integer problems (Garfinkel and Nemhauser, 1990), there may be some rare applications of problem (P) where one or more of the integer variables do not equal zero or 1 at the optimal solution of the RMINLP. A nonlinear branch and bound method is recommended for these cases. The model uses a circular footprint for each processing unit. This assumption may be unrealistic for cylindrical and rectangular units with large aspect ratios. In these cases, an elliptical footprint with variable orientation can be used. This modification is particularly important if problem (P) is to be extended to three-dimensional problems, since spherical processing units are not common. With additional integer variables, these units can also be forced to follow specified lines of orientation, if desired. Problem (P) assumes a straight-line pipe connection between units. This assumption is somewhat unrealistic: pipes will more likely follow pipe racks that lie on a rectangular grid. One can adjust the pipe length used in problem (P) by using the Manhattan metric (dij ) |xi - xj| + |yi - yj|). However, it is more difficult to force numerous pipe sections to follow one pipe rack. Last, it should be noted that problem (P) can also be used to develop layout when an existing process is to be expanded by adding new units. In this case, the existing units are placed at fixed coordinates. Protection devices can be installed at existing units in order to minimize the propagation of risks. 4. Case Study
3.4. Discussion. Problem (P) is a mixed-integer nonlinear programming problem (MINLP), since it contains both continuous and integer variables, and the objective function and some of the constraints contain nonlinear terms. Problem (P) is also a nonconvex optimization problem: the financial risk term in the objective function is nonconvex, and the minimum distance constraint creates a reverse convex feasible region. Most of the nonconvexities involve the location
The proposed approach is demonstrated with a case study that develops the layout for an ethylene oxide manufacturing plant. The process flow diagram is shown in Figure 3. In this process, ethylene and oxygen are converted to ethylene oxide in a plug flow reactor. The exiting stream, containing carbon dioxide, water, unreacted ethylene, and ethylene oxide, is cooled in a shell and
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 Table 3. Severity and Financial Risk for Individual Units
unit
severity ($)
annual net present probability risk financial (events/year) ($/year) risk ($)
reactor (1) 2,680,000 EtO absorber (3) 856,000 650,400 CO2 absorber (5)
0.008 0.008 0.008
21,440 6,850 5,200
202,000 64,400 49,200
Table 4. Parameter Aij in the Expression for Net Financial Risk of Propagation target
Figure 3. Process flow diagram for ethylene oxide.
origin
Table 1. Equipment Purchase Cost unit
equipment type
purchase cost ($)
1 2 3 4 5 6 7
reactor heat exchanger A ethylene oxide absorber heat exchanger B CO2 absorber flash tank pump
335,000 11,000 107,000 4,000 81,300 5,000 1,500
Table 2. Dimensions of the Units unit
dimensions: diameter or length and width (m)
radius (m)
footprint (m)
1 2 3 4 5 6 7
0.61 3.66 × 0.91 0.84 2.78 × 0.91 0.84 0.3 0.7 × 1.68a
0.61 2.05 0.84 1.46 0.84 0.3 0.91
2.61 5.71 3.84 4.24 3.84 1.3 1.2
a Floor area for pumps with a capacity between 200 and 300 gpm (Kern, 1977).
tube heat exchanger. Ethylene oxide is then stripped out of the gas stream by water. The unabsorbed gas is cooled in a heat exchanger and then sent to the carbon dioxide absorber. CO2 is scrubbed out of the gas. The remaining gases are recycled to the reactor. The CO2/ water stream is separated, and the solvent is recycled back to the carbon dioxide absorber. Table 1 shows the purchase cost of each unit in the process. The approximate size of each unit is given in Table 2, including both the radius of gyration and the footprint. In the case of circular equipment, like the reactor and absorption columns, the radius of gyration is simply the external diameter of the unit, while the footprint is the radius of gyration plus an additional increment that varies according to the unit. An increase of 3.0 m in the radius of gyration was used in the case of the absorption columns, while an increment of 2.0 m was used for the ethylene oxide reactor. For units with a rectangular shape like the heat exchangers, it was assumed that additional area is needed around the heat exchangers so that they can be periodically disassembled and cleaned. The footprint is more than twice the radius of gyration. This case study considers three possible accidents: an explosion at the reactor, an explosion at the ethylene oxide absorber, and an explosion at the CO2 absorber.
reactor EtO absorber CO2 absorber
unit 1 unit 2 unit 3 unit 4 unit 5 unit 6 unit 7 0.246 0.273
0.231 0.323 0.327
0.485 0.225
0.205 0.345 0.354
0.485 0.286
0.442 0.314 0.470
0.489 0.223 0.279
For each of these three units, it was assumed that the severity of the accident is 800% of the purchase cost of the unit. This is the purchase and installation cost of the original equipment and its ancillary instrumentation, wiring, etc., and the cost to purchase and install new equipment, instrumentation, wiring, etc. The probability of the accident at each one of these units is 0.008 yr-1 (Clemens, 1993). Table 3 shows the annual risk, which is the product of severity and probability, and the net present financial risk Ri0 associated with the destruction of each one of these units. The net present financial risk was calculated assuming a lifetime of 25 years and an annual interest rate of 10%. It is important to note that this example has only considered the risk to capital investments within the oxide plant. The damage function showed in eq 7 is introduced to measure the expected losses at neighboring units when an explosion happens at any of the three major units. The constants A, B, and C from eq 7 were determined through the simulation of explosions at each of the three major units. This was carried out using the equivalent TNT method (Lees, 1980; AIChE, 1989), which calculates the pressure wave of the explosion as a function of the distance. The constants A and C are given in Tables 4 and 5. Constant B is equal to AC. It is assumed here that mandatory protection devices are already installed at the units, such as safety relief valves, minimum wall thickness, etc., and that optional or redundant devices are available that may further reduce the risk of the plant. The optional protection devices to be installed were selected from the list of safety features and preventive measures from the Mond Index (1985). These safety features and preventive measures can reduce the probability of events, their severity, or both. The optional protection devices are to be installed at the ethylene oxide reactor, the ethylene oxide absorber, or the carbon dioxide absorber. Table 6 lists the additional safety devices that could be installed on these units. Table 7 gives the cost of these devices and the risk reduction factors. Additional data are given in Table 8. Figure 4 shows the initial position of the units. This is a compact rectangular initial layout with the units
Table 5. Parameter Cij in the Expression for Net Financial Risk of Propagation target origin reactor EtO absorber CO2 absorber
unit 1
unit 2
16,427,020 16,427,020
82,984 414,920 539,396
unit 3 807,528 6,054,060
unit 4
unit 5
unit 6
unit 7
30,176 181,056 196,144
613,480 4,601,084
37,720 377,200 377,200
2,828 113,160 113,160
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1359 Table 6. Additional Protection Devices k-1 additional cooling water at 150% of flowsheet requirement is available for at least 10 min k-2 equipment fitted with additional overpressure relief devices k-3 process vessel contains additional fire relief devices k-4 second skin on reactor to protect against pressure k-5 explosion protection system on reactor k-6 duplicated control shutdown system on absorption towers k-7 duplicated control system with interlocking flow control on reactor Table 7. Protection Device Data cost
SF2
device
unit 1
unit 3
unit 5
unit 1
unit 3
unit 5
k-1 k-2 k-3 k-4 k-5 k-6 k-7
5,000 30,000 15,000 65,000 20,000
5,000 20,000 25,000
5,000 20,000 25,000
0.1 0.24 0.25 0.6 0.2
0.1 0.24 0.25
0.1 0.24 0.25
30,000
30,000
0.32
0.32
20,000
0.46
Figure 5. Optimal layout.
Table 8. Additional Data
Table 9. Coordinates of the Units
symbol
description
value
Cp Lc Wp Lx Ly
piping cost land cost width of a piperack maximum length in x direction maximum length in y direction
196.8 $/ma 67 $/m2 1m 100 m 100 m
a Purchase cost of a 4 in. diameter stainless steel pipe (Peters and Timmerhaus, 1990).
optimum layout
no protection devices
all protection devices
unit
x (m)
y (m)
x (m)
y (m)
x (m)
y (m)
1 2 3 4 5 6 7
2.61 10.31 32.80 18.31 13.90 13.59 12.89
29.98 25.83 27.67 19.91 3.84 17.02 19.42
2.61 10.2 33.28 18.35 14.05 13.67 12.94
29.41 26.17 28.14 20.37 3.84 17.4 19.79
2.61 10.54 28.42 18.03 13.02 13.09 12.59
24.93 22.41 23.27 15.87 3.84 13.36 15.81
Table 10. Additional Safety Devices reactor
EtO absorber
CO2 absorber
additional cooling water additional fire relief devices duplicate control system
additional cooling water
additional cooling water
Table 11. Cost Breakdown for Optimum Layout net present cost ($)
% of total
piping protection devices land financial risk from individual units financial risk from propagation
10,440 50,000 45,550 175,870 8960
3.6 17.2 15.7 60.5 3
total
290,820
element
Figure 4. Initial layout.
1-7 in sequence. The process plant layout optimization problem was solved with GAMS (Brooke et al., 1988). The solution takes from 10 to 30 s of CPU time on a SPARC 2 workstation. Figure 5 shows the final process layout, and the coordinates of each unit are given in Table 9. Notice that the high-risk equipmentsthe reactor (unit 1), the ethylene oxide absorber (unit 3), and the CO2 absorber (unit 5)sare located far from each other. These long distances minimize the propagation of accidents from these units to the other units. The heat exchangers (units 2 and 4), flash tank (unit 6), and recycle pump (unit 7) do not offer any risk, and so they can be located close to each other in order to minimize piping and land costs. Notice that these units are placed in the center of a triangle, while the hazardous units are placed at the vertices of the triangle. This formation reduces the distance from hazardous units to nonhazardous units, while increasing the separation between hazardous units. This layout requires 53.5 m of pipe and 680 m2 of land. The protection devices for each unit are shown in Table 10. Three additional protection devices are purchased for the ethylene oxide reactor: process cool-
ing water at 150% of the flowsheet capacity for 10 min, an on-line control system capable of shutdown of the unit, and additional fire protection devices at the reactor. An additional process cooling system is to be purchased for each of the absorbers. The total net present cost is $290,820. The breakdown of these costs is given in Table 11. It should be noted that the costs are dominated by the financial risk. It is interesting to compare these results with two additional cases. The first case is when no protection devices are installed at any unit. The results are shown in Tables 9 and 12. Note that the piping and land costs are very similar to those from the optimal case. The total piping length is now 54.84 m, and 689.7 m2 of land is occupied. The total cost is $381,900. The financial risk associated with this layout, $315,600, is more than 80% of the total cost. The layout is given in Figure 6. The second case is when all the protection devices are installed at each unit in an attempt to reduce the
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Figure 6. Layoutsno protection systems.
Figure 7. Layoutsall protection systems.
Table 12. Cost Breakdown for Layout with No Protection Devices
increasing the distance between units, installing protection devices at the origin of accidents, installing protection devices at the target of accidents, and placing physical barriers between units. The methodology presented in this paper explicitly considers these four possibilities. The process plant layout optimization problem was formulated as a mixed-integer nonlinear programming problem (MINLP) where the integer variables define the existence of protection devices installed at units or physical barriers between units. This MINLP has some special properties that allows it to be solved as a relaxed MINLP, where the integer variables become continuous variables that are naturally bounded between zero and 1. This significantly simplifies the solution procedure. A case study of a layout for an ethylene oxide production plant was completed. This case study showed that piping and land costs are the least important cost terms associated with the optimal layout. The tradeoff is between the cost of additional protection devices and the reduction in financial risk associated with accidents and their propagation. The selection of the additional protection devices is a function of the combination of cost and risk reduction for each protection device. The financial risk associated with accidents and their propagation is the dominant cost of the final process layout. Future work will address the possibility of the orientation of rectangular units within the circular footprint. In addition, units with shapes other than circles will be represented more realistically, allowing the possibility of more compact layouts. Future work will also include other cost terms, such as downtime and business interruption costs, maintenance costs, etc. Improvements can be done to allow the representation of the real diameter and material of piping. Last, the ability to solve three-dimensional layouts would certainly enhance the flexibility of this methodology.
net present cost ($)
% of total
piping protection devices land financial risk from individual units financial risk from propagation
10,790 0 46,280 315,600 9310
2.8 0 12.1 82.6 2.5
total
381,980
element
Table 13. Cost Breakdown for Layout with All Protection Devices net present cost ($)
% of total
piping protection devices land financial risk from individual units financial risk from propagation
8250 315,000 39,440 57,530 8880
1.9 73.4 9.2 13.4 2.1
total
429,100
element
financial risk. The results are shown in Tables 9 and 13. Piping and land costs are still less important than protection devices cost and financial risk. The total cost is $429,110. The financial risk is drastically reduced to $66,420 by the adoption of protection devices. The total piping length is 42 m, and the total occupied land is 587 m2. The final process layout is given in Figure 7. Notice that the final shape of the layout is the same but that the use of more safety devices has compacted the structure. 5. Conclusions An optimization problem has been presented that can develop safe and economical layouts for chemical plants. This methodology accounts for the financial risk associated with accidents and their propagation to neighboring units, as well as other cost terms associated with a layout, such as piping cost, land cost, and protection devices cost. The financial risk associated with accidents is divided into two categories: financial risk associated with accidents at the units where they happen, and financial risk associated with risk propagation from the units where the accidents happen to neighboring units. There are four possible ways to minimize risk propagation:
Acknowledgment This work has been supported by the Fulbright Commission, Encyclopedia Britannica, and American Chamber of Commerce in Sao Paulo, Brazil, whose cooperation is gratefully appreciated. The work of Kendra Bell, Mick Hundley, Sean Madigan, Rich Rogers, and Paul Sagel in the development of the process flow diagram is also acknowledged.
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1361
Nomenclature Aij ) constant in eq 7 Bij ) constant in eq 7 Cij ) constant in eq 7 Cp ) piping cost Cbij ) cost of a physical barrier installed between units i and j Cpdjk ) cost of a protection device k installed at unit j, origin of an accident Ctarik ) cost of a protection device k installed at unit i, the target of an accident dij ) distance between units i and j dijmin ) minimum distance between units i and j Fi ) footprint of unit i Lx ) maximum length in the x direction Ly ) maximum length in the y direction Lc ) land cost Mij ) parameter which defines if units i and j are connected by piping Pj ) probability of accidents at unit j Ri0 ) initial risk of accidents at unit i without any protection systems or physical barriers Radi ) radius of unit i RRij0 ) initial risk of accidents propagating from unit j to unit i without any protection systems or physical barriers Sdij ) safety distance between units i and j SF1ik ) risk reduction factor when protection device k is installed at unit i, the target of an accident SF2ik ) risk reduction factor when protection device k is installed at unit i, the origin of an accident SF3ij ) risk reduction factor when a physical barrier is installed between units i and j Wp ) width of a piperack connecting different units xi ) X coordinate of unit i yi ) Y coordinate of unit i Ybij ) integer variable defining the existence of a physical barrier between units i and j Ypdjk ) integer variable defining the existence of a protection device k at unit j, the origin of an accident Ytarik ) integer variable defining the existence of a protection device k at unit i, the target of an accident
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Received for review April 19, 1995 Revised manuscript received December 21, 1995 Accepted January 13, 1996X IE9502547
X Abstract published in Advance ACS Abstracts, March 1, 1996.
