- Email: [email protected]
An MILP model for safe multi-floor process plant layout
Anton A. Kiss, Edwin Zondervan, Richard Lakerveld, Leyla Özkan (Eds.) Proceedings of the 29th European Symposium on Computer Aided Process Engineering June 16th to 19th , 2019, Eindhoven, The Netherlands. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818634-3.50064-3
An MILP model for safe multi-floor process plant layout Jude O. Ejeha , Songsong Liub and Lazaros G. Papageorgioua,* a Centre
for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom; b School of Management, Swansea University, Bay Campus, Fabian Way, Swansea SA1 8EN, United Kingdom;
Abstract In this work, a mixed integer linear programming (MILP) model is presented to obtain the optimal layout of a multi-floor chemical process plant with minimum risk in fire and explosion scenarios. Layout decisions determine the spatial arrangement of process plant equipment on available land area considering the equipment interconnections, dimensions, costs, general operability, as well as associated structures and auxiliary units. Optimal decisions ought to strike a balance between risk and cost savings. Previous attempts to include safety considerations in the layout decision making process have been restricted to minimise connection and risk costs alone, with some unrealistic assumptions on safety distances for mostly single floor layout cases. The model presented adopts the Dow’s Fire & Explosion system to quantify risk in order to determine the optimal multi-floor plot layout simultaneously with more realistic constraints for safety distance calculations. The optimal layout design obtained minimises costs attributed to the installation of connecting pipes, pumping, area-dependent construction of floors, land purchase, as well as the risk associated with fire and explosion events by inherent and passive strategies. Keywords: multi-floor plant layout; safety; optimisation; MILP
1. Introduction Right from conceptualisation to plant decommissioning, it is quite important that safety assessments be carried out for every aspect of a chemical process plant design project (Khan and Amyotte, 2004). Improper safety considerations at each stage of design or operation can result in fatalities, injuries, disruption of production activities within the plant and its neighbouring environment. Amidst a range of factors that contribute towards the overall safety levels, a study has shown that 79% of process plant accidents were attributed to design errors, the most critical being poor layout (Kidam and Hurme, 2012). Layout design determines the spatial arrangement of chemical process plant units considering their interconnections based on pre-defined criteria. These units may be process vessels in which unit operations are carried out, storage facilities, work centres or departments, and their spatial arrangement affect capital and operating costs, efficiency of plant activities, and of particular concern to this work, the overall safety levels within the plant and the immediate environment. From an optimisation point of view, safety considerations in layout designs have been considered in the past. While a great deal of research has
380
J.O. Ejeh et al.
focused on the economic aspects alone - piping, construction and operating costs associated for a layout configuration, an ideal plant layout design ought to establish a balance between risks and costs. In a recent review, Roy et al. (2016) outlined available safety metrics for process design and their level of application. One of the key indices applicable to layout design with numerical quantification is the Dow Fire and Explosion Index (F&EI). The Dow F&EI was developed by American Dow Chemical Company (American Institute of Chemical Engineers, 1994) and is currently a widely applied method for hazard evaluation of chemical and industrial processes (Wang and Song, 2013). It estimates the hazards of a single unit based on the chemical properties of the material(s) within it, and the potential economic risk such equipment poses to itself and neighbouring structures with or without the installation of protection devices. A similar concept was adopted by Penteado and Ciric (1996) in a mixed integer non-linear programming (MINLP) model where financial risks associated with potential events from process units were modelled as cost functions with an overall objective to minimise the net present cost of a single floor layout. The choice of safety devices was also made available to reduce the associated risk levels. Patsiatzis et al. (2004) proposed a mixed integer linear programming (MILP) model solely based on the Dow F&EI to minimise the total cost associated with connecting process units by pipes, financial risks and the purchase and installation of protection devices. Other research activities have built on these to include multi-floor considerations (Park et al., 2018), human risk considerations, and in more recent times by employing the Domino Hazard Index (López-Molina et al., 2013). In this work, an MILP model is proposed to address the multi-floor process plant layout problem with safety considerations, which are quantified using the Dow F&EI. Readers may consult the Dow’s F&EI Hazard Identification guide (American Institute of Chemical Engineers, 1994) for detailed steps to calculate this metric. The proposed model will minimise the total cost attributed to pipe connections, pumping, floor construction, land purchase, installation of protection devices and financial losses in the event of an accident, which prior to this work has not been simultaneously addressed. Safety distances between equipment items are also modelled in a new way - from the opposing boundaries of equipment items as compared to the midpoints as previously done in order to better capture the actual distances between equipment for risk quantifications. Tall equipment items spanning through consecutive floors are also considered with the model determining the optimal number of floors and the equipment floor and spatial arrangements. In the rest of the paper, the problem description is outlined in section 2. In section 3 the mathematical model is proposed and its computational performance is shown with a relevant case study in section 4. Final remarks are given in section 5.
2. Problem Description The problem is as follows: Given a set of process plant units (i ∈ I), their dimensions length (li ), breadth (di ) and height (hi ) - and connectivity network with space and unit allocation limitations, a set of potential floors for layout with respective floor height (FH), a set of pertinent equipment item (i ∈ I pe ), a set of protection device configurations available p ) and loss control credit factor if for each pertinent item (p ∈ Pi ), with associated costs (Cip installed on an equipment item; determine the total number (NF) and area of floors (FA), the protection device configuration, p, to be installed on each pertinent equipment item, and the plot layout so as to minimise the total plant layout and safety costs.
An MILP model for safe multi-floor process plant layout
381
It is assumed that the geometries of all process plant equipment are rectangles, with horizontal connection distances taken as the rectilinear distance from the geometrical centres in the x-y plane. Vertical connection distances are taken from a design-specified height on each equipment. For safety considerations, all rectilinear distances are taken from the boundaries of equipment items to evaluate the probability, magnitude and impact of an incident. Equipment items are allowed to rotate by 90◦ and those with heights greater than the floor height can extend through consecutive floors but must start from the base of a floor.
3. Mathematical Formulation The mathematical formulation constitutes an extension of model A.1 in Ejeh et al. (2018) for the multi-process plant layout problem and by Patsiatzis et al. (2004). All constraints in model A.1 (Ejeh et al., 2018) apply with the following modifications/additions. First of all, the distance constraints written for connected equipment items ( fi j = 1) (Patsiatzis et al., 2004), are further written for pairs of items (i, j) including a pertinent item, i ∈ I pe , and any other item j, i.e., ζ = {(i, j) : i ∈ I pe , j = i}. For safety considerations, the rectilinear distances between equipment items taken from the geometrical centres no longer seem to be a valid assumption. This is especially true for process plants having large and/or tall equipment items where rectilinear distances from the geometrical centres may have a high value but the equipment items are physically close to each other. A more valid assumption will be to calculate the separation distances from the equipment boundaries as illustrated in Figure 1, as an event on a pertinent item i can emanate at any point within the item up to its boundaries.
Figure 1: Vertical and horizontal safety distances between equipment items For vertical separation distances between any two equipment items i and j (V Di j ), the distance is taken from the top of j to the bottom of i if i is on a higher floor than j, and if the reverse is the case, from the top of i to the bottom of j. However, if both i and j are on the same floor, i.e., Ni j = 1, the vertical separation distance is taken to be zero. The s is a binary variable with conditions stated above are modelled by Eqs. (1) - (3) where Sik u d a value of 1 if item i starts at floor k, and ηi j and ηi j are positive variables evaluated by Eqs. (4) - (6). Horizontal separation distances are also calculated from the item boundaries in the x and y planes as XDi j (Eqs. (7) - (11)) and Y Di j (Eqs. (12) - (16)) respectively (Figure 1). A value of zero is assigned to these distances if the opposing boundaries of an item i is not strictly to the right or left (in the x plane), or above or below (in the y plane) j. That is, items i and j overlap at any point on either the x or y plane. The binary variable Wixo j is
382
J.O. Ejeh et al.
assigned a value of 1 if item i is strictly to the right or left of item j or 0 otherwise. The same applies for Wiyo j if item i is strictly above or below j. The relative distances between items i and j in the x plane are represented by Ri j and Li j if i is to the right of j, and if i is the left of j respectively. Ai j and Bi j represent the relative distances in the y plane if i is above j, and if i is below j respectively. E2i j is a non-overlapping binary variable and BM is a large number (Patsiatzis et al., 2004). Given these modifications, the total safety distance, T Dsi j , between equipment items i and j is then calculated by Eq. (17). s ) − hi + ηiuj + BM · Ni j V Di j ≤ FH ∑(k − 1)(Ssjk − Sik
∀ (i, j) ∈ ζ
(1)
s ) − hi + ηiuj − BM · Ni j V Di j ≥ FH ∑(k − 1)(Ssjk − Sik
∀ (i, j) ∈ ζ
(2)
V Di j ≤ BM · (1 − Ni j )
∀ (i, j) ∈ ζ
(3)
∀ (i, j) ∈ ζ
(4)
∀ (i, j) ∈ ζ
(5)
∀ (i, j) ∈ ζ
(6)
k k
ηiuj − ηidj
= 2FH ∑
s (k − 1)(Sik − Ssjk ) + hi − h j
k
ηiuj ≤ BM ·Wizj ηidj
≤
BM · (1 −Wizj )
li + l j − BM(1 −Wixo j ) 2 li + l j XDi j ≤ Ri j + Li j − + BM(1 −Wixo j ) 2 li + l j XDi j ≥ Ri j + Li j − − BM(1 −Wixo j ) 2
∀ (i, j) ∈ ζ
(7)
∀ (i, j) ∈ ζ
(8)
∀ (i, j) ∈ ζ
(9)
XDi j ≤ BM ·Wixo j
∀ (i, j) ∈ ζ
(10)
≥ 1 − E2i j | j>i −E2 ji |i> j di + d j yi − y j + 2Bi j ≥ − BM(1 −Wiyo j ) 2 di + d j Y D i j ≤ A i j + Bi j − + BM(1 −Wiyo j ) 2 di + d j Y Di j ≥ A i j + B i j − − BM(1 −Wiyo j ) 2
∀ (i, j) ∈ ζ
(11)
∀ (i, j) ∈ ζ
(12)
∀ (i, j) ∈ ζ
(13)
∀ (i, j) ∈ ζ
(14)
Y Di j ≤ BM ·Wiyo j
∀ (i, j) ∈ ζ
(15)
Wiyo j ≥ E2i j | j>i +E2 ji |i> j T Dsi j = XDi j +Y Di j +V Di j
∀ (i, j) ∈ ζ
(16)
xi − x j + 2Li j ≥
Wixo j
∀ (i, j) ∈ ζ (17) The area of exposure and maximum probable property damage cost constraints are as described in Patsiatzis et al. (2004) using the modified total distance, T Dsi j . The objective function (Eq. (18)) is the minimisation of the total cost attributed to connection, pumping, land purchase, construction, financial risk and the installation of protective devices. The financial risk is evaluated from the actual maximum probable property damage cost (Ωi ) (Patsiatzis et al., 2004) and μip is a binary variable with a value of 1 if protection device configuration p is to be purchased and installed on pertinent item i ∈ I pe . Cicj , Civj , Cihj , LC, FC1 and FC2 represent the connection cost, vertical pumping cost, horizontal pumping cost, area-dependent land purchase cost, fixed floor construction
383
An MILP model for safe multi-floor process plant layout cost and area-dependent floor construction cost respectively. min∑
∑
[Cicj T Di j +Civj Di j +Cihj (Ri j + Li j + Ai j + Bi j )] + FC1 · NF
i j=i: fi j =1
+FC2∑ARs · NQs + LC · FA + s
∑Ωi + ∑ Cipp · μip i
(18)
i,p∈Pi
4. Case study The model proposed was applied to an Ethylene oxide plant (Figure 2) (Patsiatzis et al., 2004). Six protection device configurations are made available for installation, with the first configuration having no protection device purchased or installed. Full details for the configurations, the characteristic protection devices in each, and the associated cost and loss control credit factor can be found in Patsiatzis et al. (2004). The model was solved to global optimality using GAMS modelling system v25.0.2 with the CPLEX v12.8 solver on an Intel® Xeon® E5-1650 CPU with 32GB RAM. It had 260 discrete and 386 continuous variables with 894 equations, and obtained a total cost value of 480,114.4 rmu in 33s.
Figure 2: Flow diagram of Ethylene Oxide plant Figure 3 shows the optimal layout plot with safety considerations. With the inclusion of fire and explosion scenarios, an additional floor is required compared to the layout results without safety considerations (Ejeh et al., 2018). Out of the total cost of 480,114.4 rmu, 175,000 rmu was attributed to the installation of protection devices, 187,535.4 to financial risks and 117,579.0 rmu to connection, pumping and construction costs. The latter cost quota is much larger when compared to the case without safety considerations, 66,262 rmu (Ejeh et al., 2018), owing to additional separation distances between equipment items, a larger floor area (30m× 30m compared to 20m× 20m), as well as the cost of the additional floor constructed.
Figure 3: Optimal layout results For the case where safety was not considered and no protection device was installed, the financial risk was calculated, based on the layout results obtained in Ejeh et al. (2018), to
384
J.O. Ejeh et al.
be 935,820.9 rmu. In the optimal solution with safety considerations, protection devices were installed on all the pertinent equipment items - 1, 3 and 5 - to reduce the probability and magnitude of an incident. The total cost of purchase and installation was 175,000 rmu, with a reduced financial risk of 187,535.4 rmu. Hence, the cost of protection devices, financial risk, and other layout costs combined is much less for the case where safety is considered and protection devices are installed than if they were not. This provides for a more informed balance between cost savings and financial risks.
5. Concluding remarks An MILP model (extended from Ejeh et al., 2018 and Patsiatzis et al., 2004) was proposed for the multi-floor process plant layout problem considering connection, pumping, construction, financial risk and protection device installation costs in fire and explosion scenarios. The model successfully described tall equipment items spanning through multiple floors with more accurate safety distance calculations obtained from the boundaries of neighbouring equipment items within similar floors and on different floors. The proposed model was applied to a 7-unit case study having 3 pertinent equipment items and 6 protection device configurations. 3 floors were obtained for the optimal solution, with a larger floor area and total cost compared to the same case without safety considerations. Overall, the proposed model is proved to be able to optimise the installation of protection devices and significantly reduce the risk associated with fire and explosion, resulting in a substantial decrease in probable property damage cost, much higher than the required additional safety device purchase, installation, connection, pumping and construction costs. Future work will seek to apply the model to larger case studies with more complex connection networks.
Acknowledgement JOE acknowledges the financial support of the Petroleum Technology Development Fund (PTDF).
References American Institute of Chemical Engineers, 1994. Dow’s Fire & Explosion Index Hazard Classification Guide. Vol. 7. John Wiley & Sons, Inc., Hoboken, NJ, USA. J. O. Ejeh, S. Liu, M. M. Chalchooghi, L. G. Papageorgiou, 2018. Optimization-Based Approach for Process Plant Layout. Ind. Eng. Chem. Res. 57 (31), 10482–10490. F. I. Khan, P. R. Amyotte, 2004. Integrated Inherent Safety Index (I2SI): A Tool for Inherent Safety Evaluation. Process Saf. Prog. 23 (2), 136–148. K. Kidam, M. Hurme, 2012. Design as a Contributor to Chemical Process Accidents. J. Loss Prev. Process Ind. 25 (4), 655–666. A. López-Molina, R. Vázquez-Román, M. S. Mannan, M. G. Félix-Flores, 2013. An Approach for Domino Effect Reduction Based on Optimal Layouts. J. Loss Prev. Process Ind. 26 (5), 887–894. K. Park, D. Shin, W. Won, 2018. Risk Based 3-Dimensional and Multifloor Plant Layout Optimization for Liquefied Natural Gas (LNG) Liquefaction Process. Korean J. Chem. Eng. 35 (5), 1053–1064. D. I. Patsiatzis, G. Knight, L. G. Papageorgiou, 2004. An MILP Approach to Safe Process Plant Layout. Chem. Eng. Res. Des. 82 (5), 579–586. F. D. Penteado, A. R. Ciric, 1996. An MINLP Approach for Safe Process Plant Layout. Ind. Eng. Chem. Res. 35 (4), 1354–1361. N. Roy, F. Eljack, A. Jiménez-Gutiérrez, B. Zhang, P. Thiruvenkataswamy, M. El-Halwagi, M. S. Mannan, 2016. A Review of Safety Indices for Process Design. Curr. Opin. Chem. Eng. 14, 42–48. J. Wang, W.-H. Song, 2013. Fire and Explosion Index Calculation Method Incorporating Classified Safety Measure Credits. J. Loss Prev. Process Ind. 26 (6), 1128–1133.
An MILP model for safe multi-floor process plant layout Jude O. Ejeha , Songsong Liub and Lazaros G. Papageorgioua,* a Centre
for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom; b School of Management, Swansea University, Bay Campus, Fabian Way, Swansea SA1 8EN, United Kingdom;
Abstract In this work, a mixed integer linear programming (MILP) model is presented to obtain the optimal layout of a multi-floor chemical process plant with minimum risk in fire and explosion scenarios. Layout decisions determine the spatial arrangement of process plant equipment on available land area considering the equipment interconnections, dimensions, costs, general operability, as well as associated structures and auxiliary units. Optimal decisions ought to strike a balance between risk and cost savings. Previous attempts to include safety considerations in the layout decision making process have been restricted to minimise connection and risk costs alone, with some unrealistic assumptions on safety distances for mostly single floor layout cases. The model presented adopts the Dow’s Fire & Explosion system to quantify risk in order to determine the optimal multi-floor plot layout simultaneously with more realistic constraints for safety distance calculations. The optimal layout design obtained minimises costs attributed to the installation of connecting pipes, pumping, area-dependent construction of floors, land purchase, as well as the risk associated with fire and explosion events by inherent and passive strategies. Keywords: multi-floor plant layout; safety; optimisation; MILP
1. Introduction Right from conceptualisation to plant decommissioning, it is quite important that safety assessments be carried out for every aspect of a chemical process plant design project (Khan and Amyotte, 2004). Improper safety considerations at each stage of design or operation can result in fatalities, injuries, disruption of production activities within the plant and its neighbouring environment. Amidst a range of factors that contribute towards the overall safety levels, a study has shown that 79% of process plant accidents were attributed to design errors, the most critical being poor layout (Kidam and Hurme, 2012). Layout design determines the spatial arrangement of chemical process plant units considering their interconnections based on pre-defined criteria. These units may be process vessels in which unit operations are carried out, storage facilities, work centres or departments, and their spatial arrangement affect capital and operating costs, efficiency of plant activities, and of particular concern to this work, the overall safety levels within the plant and the immediate environment. From an optimisation point of view, safety considerations in layout designs have been considered in the past. While a great deal of research has
380
J.O. Ejeh et al.
focused on the economic aspects alone - piping, construction and operating costs associated for a layout configuration, an ideal plant layout design ought to establish a balance between risks and costs. In a recent review, Roy et al. (2016) outlined available safety metrics for process design and their level of application. One of the key indices applicable to layout design with numerical quantification is the Dow Fire and Explosion Index (F&EI). The Dow F&EI was developed by American Dow Chemical Company (American Institute of Chemical Engineers, 1994) and is currently a widely applied method for hazard evaluation of chemical and industrial processes (Wang and Song, 2013). It estimates the hazards of a single unit based on the chemical properties of the material(s) within it, and the potential economic risk such equipment poses to itself and neighbouring structures with or without the installation of protection devices. A similar concept was adopted by Penteado and Ciric (1996) in a mixed integer non-linear programming (MINLP) model where financial risks associated with potential events from process units were modelled as cost functions with an overall objective to minimise the net present cost of a single floor layout. The choice of safety devices was also made available to reduce the associated risk levels. Patsiatzis et al. (2004) proposed a mixed integer linear programming (MILP) model solely based on the Dow F&EI to minimise the total cost associated with connecting process units by pipes, financial risks and the purchase and installation of protection devices. Other research activities have built on these to include multi-floor considerations (Park et al., 2018), human risk considerations, and in more recent times by employing the Domino Hazard Index (López-Molina et al., 2013). In this work, an MILP model is proposed to address the multi-floor process plant layout problem with safety considerations, which are quantified using the Dow F&EI. Readers may consult the Dow’s F&EI Hazard Identification guide (American Institute of Chemical Engineers, 1994) for detailed steps to calculate this metric. The proposed model will minimise the total cost attributed to pipe connections, pumping, floor construction, land purchase, installation of protection devices and financial losses in the event of an accident, which prior to this work has not been simultaneously addressed. Safety distances between equipment items are also modelled in a new way - from the opposing boundaries of equipment items as compared to the midpoints as previously done in order to better capture the actual distances between equipment for risk quantifications. Tall equipment items spanning through consecutive floors are also considered with the model determining the optimal number of floors and the equipment floor and spatial arrangements. In the rest of the paper, the problem description is outlined in section 2. In section 3 the mathematical model is proposed and its computational performance is shown with a relevant case study in section 4. Final remarks are given in section 5.
2. Problem Description The problem is as follows: Given a set of process plant units (i ∈ I), their dimensions length (li ), breadth (di ) and height (hi ) - and connectivity network with space and unit allocation limitations, a set of potential floors for layout with respective floor height (FH), a set of pertinent equipment item (i ∈ I pe ), a set of protection device configurations available p ) and loss control credit factor if for each pertinent item (p ∈ Pi ), with associated costs (Cip installed on an equipment item; determine the total number (NF) and area of floors (FA), the protection device configuration, p, to be installed on each pertinent equipment item, and the plot layout so as to minimise the total plant layout and safety costs.
An MILP model for safe multi-floor process plant layout
381
It is assumed that the geometries of all process plant equipment are rectangles, with horizontal connection distances taken as the rectilinear distance from the geometrical centres in the x-y plane. Vertical connection distances are taken from a design-specified height on each equipment. For safety considerations, all rectilinear distances are taken from the boundaries of equipment items to evaluate the probability, magnitude and impact of an incident. Equipment items are allowed to rotate by 90◦ and those with heights greater than the floor height can extend through consecutive floors but must start from the base of a floor.
3. Mathematical Formulation The mathematical formulation constitutes an extension of model A.1 in Ejeh et al. (2018) for the multi-process plant layout problem and by Patsiatzis et al. (2004). All constraints in model A.1 (Ejeh et al., 2018) apply with the following modifications/additions. First of all, the distance constraints written for connected equipment items ( fi j = 1) (Patsiatzis et al., 2004), are further written for pairs of items (i, j) including a pertinent item, i ∈ I pe , and any other item j, i.e., ζ = {(i, j) : i ∈ I pe , j = i}. For safety considerations, the rectilinear distances between equipment items taken from the geometrical centres no longer seem to be a valid assumption. This is especially true for process plants having large and/or tall equipment items where rectilinear distances from the geometrical centres may have a high value but the equipment items are physically close to each other. A more valid assumption will be to calculate the separation distances from the equipment boundaries as illustrated in Figure 1, as an event on a pertinent item i can emanate at any point within the item up to its boundaries.
Figure 1: Vertical and horizontal safety distances between equipment items For vertical separation distances between any two equipment items i and j (V Di j ), the distance is taken from the top of j to the bottom of i if i is on a higher floor than j, and if the reverse is the case, from the top of i to the bottom of j. However, if both i and j are on the same floor, i.e., Ni j = 1, the vertical separation distance is taken to be zero. The s is a binary variable with conditions stated above are modelled by Eqs. (1) - (3) where Sik u d a value of 1 if item i starts at floor k, and ηi j and ηi j are positive variables evaluated by Eqs. (4) - (6). Horizontal separation distances are also calculated from the item boundaries in the x and y planes as XDi j (Eqs. (7) - (11)) and Y Di j (Eqs. (12) - (16)) respectively (Figure 1). A value of zero is assigned to these distances if the opposing boundaries of an item i is not strictly to the right or left (in the x plane), or above or below (in the y plane) j. That is, items i and j overlap at any point on either the x or y plane. The binary variable Wixo j is
382
J.O. Ejeh et al.
assigned a value of 1 if item i is strictly to the right or left of item j or 0 otherwise. The same applies for Wiyo j if item i is strictly above or below j. The relative distances between items i and j in the x plane are represented by Ri j and Li j if i is to the right of j, and if i is the left of j respectively. Ai j and Bi j represent the relative distances in the y plane if i is above j, and if i is below j respectively. E2i j is a non-overlapping binary variable and BM is a large number (Patsiatzis et al., 2004). Given these modifications, the total safety distance, T Dsi j , between equipment items i and j is then calculated by Eq. (17). s ) − hi + ηiuj + BM · Ni j V Di j ≤ FH ∑(k − 1)(Ssjk − Sik
∀ (i, j) ∈ ζ
(1)
s ) − hi + ηiuj − BM · Ni j V Di j ≥ FH ∑(k − 1)(Ssjk − Sik
∀ (i, j) ∈ ζ
(2)
V Di j ≤ BM · (1 − Ni j )
∀ (i, j) ∈ ζ
(3)
∀ (i, j) ∈ ζ
(4)
∀ (i, j) ∈ ζ
(5)
∀ (i, j) ∈ ζ
(6)
k k
ηiuj − ηidj
= 2FH ∑
s (k − 1)(Sik − Ssjk ) + hi − h j
k
ηiuj ≤ BM ·Wizj ηidj
≤
BM · (1 −Wizj )
li + l j − BM(1 −Wixo j ) 2 li + l j XDi j ≤ Ri j + Li j − + BM(1 −Wixo j ) 2 li + l j XDi j ≥ Ri j + Li j − − BM(1 −Wixo j ) 2
∀ (i, j) ∈ ζ
(7)
∀ (i, j) ∈ ζ
(8)
∀ (i, j) ∈ ζ
(9)
XDi j ≤ BM ·Wixo j
∀ (i, j) ∈ ζ
(10)
≥ 1 − E2i j | j>i −E2 ji |i> j di + d j yi − y j + 2Bi j ≥ − BM(1 −Wiyo j ) 2 di + d j Y D i j ≤ A i j + Bi j − + BM(1 −Wiyo j ) 2 di + d j Y Di j ≥ A i j + B i j − − BM(1 −Wiyo j ) 2
∀ (i, j) ∈ ζ
(11)
∀ (i, j) ∈ ζ
(12)
∀ (i, j) ∈ ζ
(13)
∀ (i, j) ∈ ζ
(14)
Y Di j ≤ BM ·Wiyo j
∀ (i, j) ∈ ζ
(15)
Wiyo j ≥ E2i j | j>i +E2 ji |i> j T Dsi j = XDi j +Y Di j +V Di j
∀ (i, j) ∈ ζ
(16)
xi − x j + 2Li j ≥
Wixo j
∀ (i, j) ∈ ζ (17) The area of exposure and maximum probable property damage cost constraints are as described in Patsiatzis et al. (2004) using the modified total distance, T Dsi j . The objective function (Eq. (18)) is the minimisation of the total cost attributed to connection, pumping, land purchase, construction, financial risk and the installation of protective devices. The financial risk is evaluated from the actual maximum probable property damage cost (Ωi ) (Patsiatzis et al., 2004) and μip is a binary variable with a value of 1 if protection device configuration p is to be purchased and installed on pertinent item i ∈ I pe . Cicj , Civj , Cihj , LC, FC1 and FC2 represent the connection cost, vertical pumping cost, horizontal pumping cost, area-dependent land purchase cost, fixed floor construction
383
An MILP model for safe multi-floor process plant layout cost and area-dependent floor construction cost respectively. min∑
∑
[Cicj T Di j +Civj Di j +Cihj (Ri j + Li j + Ai j + Bi j )] + FC1 · NF
i j=i: fi j =1
+FC2∑ARs · NQs + LC · FA + s
∑Ωi + ∑ Cipp · μip i
(18)
i,p∈Pi
4. Case study The model proposed was applied to an Ethylene oxide plant (Figure 2) (Patsiatzis et al., 2004). Six protection device configurations are made available for installation, with the first configuration having no protection device purchased or installed. Full details for the configurations, the characteristic protection devices in each, and the associated cost and loss control credit factor can be found in Patsiatzis et al. (2004). The model was solved to global optimality using GAMS modelling system v25.0.2 with the CPLEX v12.8 solver on an Intel® Xeon® E5-1650 CPU with 32GB RAM. It had 260 discrete and 386 continuous variables with 894 equations, and obtained a total cost value of 480,114.4 rmu in 33s.
Figure 2: Flow diagram of Ethylene Oxide plant Figure 3 shows the optimal layout plot with safety considerations. With the inclusion of fire and explosion scenarios, an additional floor is required compared to the layout results without safety considerations (Ejeh et al., 2018). Out of the total cost of 480,114.4 rmu, 175,000 rmu was attributed to the installation of protection devices, 187,535.4 to financial risks and 117,579.0 rmu to connection, pumping and construction costs. The latter cost quota is much larger when compared to the case without safety considerations, 66,262 rmu (Ejeh et al., 2018), owing to additional separation distances between equipment items, a larger floor area (30m× 30m compared to 20m× 20m), as well as the cost of the additional floor constructed.
Figure 3: Optimal layout results For the case where safety was not considered and no protection device was installed, the financial risk was calculated, based on the layout results obtained in Ejeh et al. (2018), to
384
J.O. Ejeh et al.
be 935,820.9 rmu. In the optimal solution with safety considerations, protection devices were installed on all the pertinent equipment items - 1, 3 and 5 - to reduce the probability and magnitude of an incident. The total cost of purchase and installation was 175,000 rmu, with a reduced financial risk of 187,535.4 rmu. Hence, the cost of protection devices, financial risk, and other layout costs combined is much less for the case where safety is considered and protection devices are installed than if they were not. This provides for a more informed balance between cost savings and financial risks.
5. Concluding remarks An MILP model (extended from Ejeh et al., 2018 and Patsiatzis et al., 2004) was proposed for the multi-floor process plant layout problem considering connection, pumping, construction, financial risk and protection device installation costs in fire and explosion scenarios. The model successfully described tall equipment items spanning through multiple floors with more accurate safety distance calculations obtained from the boundaries of neighbouring equipment items within similar floors and on different floors. The proposed model was applied to a 7-unit case study having 3 pertinent equipment items and 6 protection device configurations. 3 floors were obtained for the optimal solution, with a larger floor area and total cost compared to the same case without safety considerations. Overall, the proposed model is proved to be able to optimise the installation of protection devices and significantly reduce the risk associated with fire and explosion, resulting in a substantial decrease in probable property damage cost, much higher than the required additional safety device purchase, installation, connection, pumping and construction costs. Future work will seek to apply the model to larger case studies with more complex connection networks.
Acknowledgement JOE acknowledges the financial support of the Petroleum Technology Development Fund (PTDF).
References American Institute of Chemical Engineers, 1994. Dow’s Fire & Explosion Index Hazard Classification Guide. Vol. 7. John Wiley & Sons, Inc., Hoboken, NJ, USA. J. O. Ejeh, S. Liu, M. M. Chalchooghi, L. G. Papageorgiou, 2018. Optimization-Based Approach for Process Plant Layout. Ind. Eng. Chem. Res. 57 (31), 10482–10490. F. I. Khan, P. R. Amyotte, 2004. Integrated Inherent Safety Index (I2SI): A Tool for Inherent Safety Evaluation. Process Saf. Prog. 23 (2), 136–148. K. Kidam, M. Hurme, 2012. Design as a Contributor to Chemical Process Accidents. J. Loss Prev. Process Ind. 25 (4), 655–666. A. López-Molina, R. Vázquez-Román, M. S. Mannan, M. G. Félix-Flores, 2013. An Approach for Domino Effect Reduction Based on Optimal Layouts. J. Loss Prev. Process Ind. 26 (5), 887–894. K. Park, D. Shin, W. Won, 2018. Risk Based 3-Dimensional and Multifloor Plant Layout Optimization for Liquefied Natural Gas (LNG) Liquefaction Process. Korean J. Chem. Eng. 35 (5), 1053–1064. D. I. Patsiatzis, G. Knight, L. G. Papageorgiou, 2004. An MILP Approach to Safe Process Plant Layout. Chem. Eng. Res. Des. 82 (5), 579–586. F. D. Penteado, A. R. Ciric, 1996. An MINLP Approach for Safe Process Plant Layout. Ind. Eng. Chem. Res. 35 (4), 1354–1361. N. Roy, F. Eljack, A. Jiménez-Gutiérrez, B. Zhang, P. Thiruvenkataswamy, M. El-Halwagi, M. S. Mannan, 2016. A Review of Safety Indices for Process Design. Curr. Opin. Chem. Eng. 14, 42–48. J. Wang, W.-H. Song, 2013. Fire and Explosion Index Calculation Method Incorporating Classified Safety Measure Credits. J. Loss Prev. Process Ind. 26 (6), 1128–1133.