An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm

Accepted Manuscript An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm

Ruiqi Wang, Huan Zhao, Yan Wu, Yufei Wang, Xiao Feng, Mengxi Liu PII:

S0360-5442(18)31170-8

DOI:

10.1016/j.energy.2018.06.105

Reference:

EGY 13147

To appear in:

Energy

Received Date:

22 January 2018

Accepted Date:

16 June 2018

Please cite this article as: Ruiqi Wang, Huan Zhao, Yan Wu, Yufei Wang, Xiao Feng, Mengxi Liu, An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm, Energy (2018), doi: 10.1016/j.energy.2018.06.105

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ACCEPTED MANUSCRIPT An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm Ruiqi Wanga, Huan Zhaoa, Yan Wub, Yufei Wanga*, Xiao Fengb, Mengxi Liua a

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249 China

b School

of Chemical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China.

[email protected]

Abstract: The facility layout design within a plant is a key step in the process of chemical engineering design. A good layout can save capital cost, energy and natural resource. The aim of this work is to determine the relative location of facilities in a large-scale industrial plant considering multi-floor structure to make the total cost minimum. The objective function consists of piping investment cost, pump power cost, land cost, and floor construction cost. Surplus rectangle fill algorithm is applied in this work, and it is combined with a genetic algorithm to obtain the optimal solution. Constraints of pump area, joint arrangement of heat exchangers, and the cross-floor facilities are also taken into consideration. In the case study, a plant from a real refinery including 217 facilities is designed with different floor number. The comparison of the three different conditions proves the important role of floor number in the trade-off among investment cost, energy consumption, and land resource. The case illustrates that, the proposed method can generate a reasonable layout design for the industrial facilities and save capital and operating cost effectively. A sensitivity analysis is also done to explore the influence of basic data on the optimal construction structure. Key words: Facility layout; multi-floor layout; surplus rectangle fill algorithm; genetic algorithm

ACCEPTED MANUSCRIPT 1. Introduction Facility layout problem (FLP) is defined as the placement of facilities in a plant area, with the aim of determining the most effective arrangement in accordance with some criteria or objectives under certain constraints [1]. Layout design can impact the economic benefit and safety performance of

the plant or industrial park significantly, just as the reactor design, process design, and heat exchanger network design do. Economy and safety are the two main factors considered in facility layout design. In terms of the economy, a good layout design can arrange the facilities properly to reduce the length of pipeline and the area of occupied land, resulting in a lower capital cost of pipeline, energy cost for material transportation, and land cost. According to statistics, 20-50% of the total operating cost is attributed to material handling, and an effective facility layout can reduce the material handling costs by 10%–30% [2]. Penteado and Ciric [3] proposed a mixed-integer nonlinear programming model (MINLP) to determine the layout of facilities within a plant. In their model, the objective function consists of piping cost, land cost, protection devices cost and financial risk. In their case study, an ethylene oxide manufacturing plant was designed and a good layout was obtained. This work is relatively early and complete compared with other research of industrial facility layout. As for safety aspect, many evaluation methods are involved. Tugnoli et al. [4] determine the facility layout considering domino effects to achieve inherent safety. The Domino Hazard Index is used to assess the safety from the perspective of domino effect. Patsiatzis et al. [5] evaluated the safety based on Dow Fire and Explosion Index system which is famous for its accuracy and is widely used worldwide. In their work, capital costs are also taken into consideration to determine the

ACCEPTED MANUSCRIPT orientations and coordinates of each facility and the safety devices to be installed. Vázquez-Román et al. [6] optimize the facility layout considering uncertainty of toxic release. The risk is calculated via probit functions and Monte Carlo simulation. Various factors impacting the diffusion of toxic gas, including wind speed, wind direction, and atmospheric stability, are carefully considered. And they found that a local optimal solution could be more acceptable since the financial risk is negligible comparing with the global optimal solution. Latif et al. [7] proposed a model to determine the layout of a plant comprehensively considering various safety risks, including fire, explosion, toxic release, and domino effects of them. The case illustrated that, despite an increase in land and piping costs, the layout obtained by the proposed method provides a great assurance of layout safety compared with the current layout. Jung [8] developed a new approach to plant layout optimization by considering consequence analysis. A risk map divided into square grids is used to indicate the distribution of hazards of the plant area, and the optimal placement and layout can be found. With the extension of plant scale, multi-floor layout becomes much more essential [9]. Patsiatzis and Papageorgiou [10] proposed a mixed integer linear programming (MILP) model considering capital and operating cost for multi-floor process plant layout. Their model can determine the number of floors and the coordinates of facilities effectively to make the cost minimum. In the work of Park et al. [11], not only multi-floor structure, but also the safety issue is involved. The TNT (trinitrotoluene) equivalent model is used to estimate the realistic equipment damage, which makes the model more practical and safe. But few works focus on the influence of cross-floor facilities in the published literature. If a facility is high enough, for example, column, it will occupy the space not only on the first floor, but also on the second and higher floor. Barbosa-Póvoa et al.

ACCEPTED MANUSCRIPT [12] proposed a MILP formulation for the layout of facilities in 3D multi-floor continuous space considering different topological characteristics, including orientation, distance, and irregular equipment shapes. As for solving algorithm, both heuristic algorithm and GAMS based algorithm are used. Caputo et al. [13] proposed a safety-based process plant layout method solved by a genetic algorithm. His work shows the process of achieving optimal facility layout, with the evolution of genetic algorithm step by step. Patsiatzis and Papageorgiou [14] proposed two efficient solution approaches, decomposition approach and iterative approach, for multi-floor process plant layout problems. The decomposition approach is generally more accurate and expensive in CPU time, while the iterative approach is opposite. Most research set the coordinates of facilities as the variables in the solving algorithm, including both heuristic algorithms, like genetic algorithm, and the solvers based on GAMS. Consequently, a lot of uncrowded layout designs will be feasible solutions, and the algorithm will spend time to try them. However, to reduce the occupied area and the length of pipeline, the facilities must be compactly arranged, which is also proved by the results of research mentioned above. The surplus rectangle fill algorithm is a kind of algorithm that can solve rectangle packing problems effectively, which is widely used in machining area for cutting stock problems. The algorithm leads to a more effective usage of raw material. Faina [15] proposed a method combining simulated annealing algorithm and surplus rectangle fill algorithm to solve the two-dimensional rectangular cutting stock problem. Lee and Lee [16] proposed a shape-based block layout (SBL) approach for solving facility layout problem, which is very similar to surplus rectangle fill algorithm. But SBL approach is based on a bay structure and leads to a low utilization rate of space.

ACCEPTED MANUSCRIPT A number of practical constraints are considered in FLP. Lee and Lee [17] proposed a mixed integer non-linear programming (MINLP) model considering operating conditions. To mitigate danger and domino effect, and for easy maintenance and on-site repair, the safety distance and installation space are taken into account, which makes this model more practical. Original particle swarm optimization algorithm is employed. The unequal-area static and dynamic facility layout problems are dealt with in Asl and Wong’s work [18]. The static facility layout problem aims at minimizing the material handling cost, while the dynamic facility layout problem aims at minimizing the sum of material handling cost and facilities rearrangement cost. However, the works mentioned above are only appropriate for small-scale plants with up to dozens of facilities or less, due to the disordered layout design obtained from them. Moreover, a number of practical constraints are ignored in literature, which makes the new design very impractical, especially for large-scale plants. For a large-scale plant with hundreds of facilities, easy maintenance and orderly arrangement of facilities are important. For example, the heat exchangers undertaking the same heat exchange task should be arranged together for the sake of easy maintenance. In this work, a mathematical programming approach is proposed to determine the multi-floor layout of facilities in an industrial plant to make the total cost minimum. The objective function consists of piping investment cost, pump power cost, land cost, and floor construction cost. With the first consideration of constraints of pump area, joint arrangement of heat exchangers, and cross-floor facilities, this model can solve large-scale problems from real industry process. The surplus rectangle fill algorithm, working as a lower level algorithm, is firstly applied in industrial facility layout problem to obtain a better layout. A genetic algorithm is employed to solve the proposed model which works as an upper level algorithm. In terms of algorithm, a noteworthy

ACCEPTED MANUSCRIPT difference between this work and other works is that, the variables in this work are the placing sequence of facilities, rather than the coordinates of facilities. As mentioned above, setting the coordinates of facilities as variables will lead to a serious waste of time for algorithms in a lot of uncrowded layout designs. In this work, the genetic algorithm only determines the placing sequence of facilities, and the coordinates are given by surplus rectangle fill algorithm. This can promote the effectiveness of the proposed method. In the case study, a plant with numerous facilities is designed under three scenarios respectively: single-floor, double-floor, and triple-floor. The trade-off between capital investment and energy consumption is elaborately analyzed based on the optimization result. The case study illustrates the effectiveness of the proposed model and multi-floor layout, and that the combination of surplus rectangle fill algorithm and genetic algorithm is effective for large-scale industrial facility layout problems. Additionally, a resource consumption analysis is implemented to attempt to explore the significance of layout design to cleaner production from a new perspective. The natural resource consumptions under different scenarios of number of floors are counted and compared in the analysis. And a sensitivity analysis is also implemented to explore the influence of variation of basic data on the optimal construction structure. The strategy of determination of the construction structure under different scenarios of basic data is proposed in the analysis.

2. Methodology 2.1 Problem statement The problem in this paper can be described as the problem of arranging n facilities which are assumed as rectangular shapes. They can be arranged on a single floor or multiple floors. The facilities cannot overlap and the pipe length between two facilities is the Manhattan distance.

ACCEPTED MANUSCRIPT Considering practical application, some facilities need to be allocated on more than one floor, such as columns. They are tall and must be across the platforms. When they are arranged on the first floor, the same locations on other floors are occupied by columns and other facilities cannot be arranged. The pumps can only be arranged on the first floor to avoid cavitation. The facility layout problem can be stated as follows: Assumption: 

The facilities are assumed as rectangular shapes, and the dimension of a rectangle includes the safe distance and necessary installation distance, rather than the real size of facilities.



The facilities can only be laid horizontally or vertically.



The distances between every two adjacent facilities satisfy the minimum safety distance.

Given: 

A set of n facilities and their sizes.



The connection data of process material flowsheets.



The mass flow of process material flowsheets.

Determine: 

The allocation of each facility to floors and the orientation of the facility.



The number of the floors.



The land area.



The energy consumption for transporting material flow between facilities.

So as to minimize the total layout cost including land, piping, pumping and floor construction cost and reduce energy consumption. 2.2 Facility orientation constraints

ACCEPTED MANUSCRIPT The facility i can be placed in the given space horizontally or vertically. The length and width are determined by its orientation decision. ri is a binary variable. If ri=0, the facility is placed horizontally. Otherwise, it is placed vertically. The relationship between ri and the length and width of the facility i is as follows: l i  (1  ri )l i  ri w i

i  1,   , n,

(1)

w i  (1  ri )w i  ri l i

i  1,   , n.

(2)

Where li and wi are the length and width of the facility after being placed. 2.3 Non-overlapping constraints Two different facilities cannot be allocated to the same location. Each location can be occupied at most by one facility. When the relative position between the facilities i and j meet one of the following four constraints, they do not overlap: x1 j  x2 i

i  1, , n, j  1, , n,

(3)

x1i  x2 j

i  1, , n, j  1, , n,

(4)

y1i  y 2 j

i  1, , n, j  1, , n,

(5)

y1 j  y 2i

i  1, , n, j  1, , n.

(6)

Where x1i and y1i are the lower left coordinates of facility i, x1j and y1j are the lower left coordinates of facility j, x2i and y2i are the upper right coordinates of facility i, x2j and y2j are the upper right coordinates of facility j. Constraints (3)-(6) represent the facility i is on the left, right, top and bottom sides of the facility j respectively. Besides, the facility cannot be allocated out of the given space, which can be mathematically shown in constraints (7)-(10) below. The location of the facility needs to meet all of the following four constraints: x1i  0

i  1,   , n,

(7)

ACCEPTED MANUSCRIPT x2i  L

i  1,   , n,

(8)

y1i  0

i  1,   , n,

(9)

y 2i  W

i  1,   , n.

(10)

Where L and W are the length and width of the given space. 2.4 Cross-floor facility constraint Considering three-dimensional shapes of some facilities, they will occupy the space in more than one floor, such as columns. When the facility is arranged on location Ki on the first floor, the same location Ki on higher floors is also occupied. Ki=1 represents location K is occupied by facility i, otherwise, it is not occupied. The constraints are as the follows: If K1i  1

(11)

K 0 Then K 2i  1 , 2j

(12)

Where K1i is the location of i on the first floor and K2i is the same location of i on the second floor. i is the facility that needs to be allocated on more than one floor. 2.5 Pump area constraint In practice, pumps are always arranged together for the sake of convenient maintenance and orderliness, and the area pumps occupy is called pump area. In this model, pump area is arranged as a whole just as other facilities. The orientation of pumps in the pump area is fixed, while the relative locations are not. The pump area is usually long and narrow, and the short edge is parallel to the short edge of the plant. The short edge of a pump is also set to be parallel to the short edge of the pump area. The pumps are arranged by surplus rectangle fill algorithm within pump area to determine their relative locations. The real coordinates of pumps can be obtained by Eq. (13) and Eq. (14).

ACCEPTED MANUSCRIPT x pi  x p  x pri

(13)

y pi  y p  y pri

(14)

Where xpi and ypi are the real coordinates of i-th pump, xp and yp are the coordinates of pump area, xpri and ypri are the relative coordinates of i-th pump relative to the pump area. 2.6 Heat exchanger group constraint In practice, several identical heat exchangers are always organized into a group to accomplish the same heat exchange task, and they should be arranged together. In this model, each heat exchanger group is arranged as a whole. But the heat exchangers within the same group are not separately arranged because their size and connection are the same, and the change of relative location of heat exchangers will not cause any effect, which is a big difference compared with the pump area constraint. As for orientation, the heat exchangers in a same group should be arranged side by side, and the long edge of heat exchangers is set to be parallel to the short edge of the plant. 2.7 Facility floor constraint In practice, columns, reactors, and pumps should be placed in the first floor generally, and the air coolers should be placed in the top floor. In this work, the columns, reactors, and pump area are constrained to be placed in the first floor, and air coolers are constrained to be placed in the top floor. 2.8 Objective function The objective function is the total cost which considers land, pumping, piping and floor construction cost.

TC  PIC  POC  LC  FCC

(15)

ACCEPTED MANUSCRIPT Where TC is the annualized total cost, PIC is the annualized piping investment cost, POC is the annual pump operating cost for overcoming friction and gravity losses in the piping, LC is the annualized land cost and FCC is the annualized floor construction cost. n

PIC   UICmLm

m  1, , n.

m 1

(16)

Where m is the number of material flows that connect two different facilities, UICm is the annualized unit interconnection cost of different material flow piping including cost of materials and installation, and Lm is the interconnected distance of different material flow. The plant life time is assumed to be 10 years to annualize piping investment cost, land cost, and floor construction cost. The unit investment cost UIC is calculated as follows [19]: 0.48 UIC  A1wt pipe  A2Dout  A3  A4Dout

(17)

Where A1 is the pipe cost per unit weight (0.82 $/kg), wtpipe is the weight per unit length (kg/m), A2 is the installation cost (185 $/m0.48), Dout is the pipe outside diameter (m), A3 is the right-of-way cost (6.8 $/m) and A4 is the insulation cost (295 $/m). The wtpipe, Dout and Dinner are determined by Eq. (18)-(20). 2 wt pipe =644.3Dinner  72.5Dinner  0.4611

(18)

Dout  1.052Dinner  0.005251

(19)

Dinner 

4Q u

(20)

Where Dinner is the inside diameter of pipe (m), Q is the mass flow of process material flow (kg/s), ρ is the density of process material flow (kg/m3) and u is the velocity (m/s). For the distance between different facilities, it is assumed that all pipes run from the center point of a facility. The pipe length between two facilities i and j is the rectilinear distance:

Lm  x j  xi  y j  y i

i  1, , n, j  1, , n, m  1, , n.

(21)

ACCEPTED MANUSCRIPT The annual pump operating cost is n

POC  CE H  Pm

m  1, , n.

(22)

m 1

Where CE is the unit price of electric power ($/kW•h), H is the annual operating time (h/year) and Pm is the pumping power of different material flow (W). Pm 

Qhf ,m 

m  1, , n.

(23)

Where hf,m depends on energy losses caused by the on-way friction and gravity (J/kg), and η is the pump mechanical efficiency. hf ,m  

Lmum2 + m gz 2Dinner ,m

m  1, , n.

(24)

Where λ is the friction factor, g is the gravity constant, z is the altitude of vertical transportation. If a material flow is delivered from a lower floor to a higher floor, cost includes horizontal flow cost and up-ward flow cost, and αm=1, otherwise, αm=0. The land and floor construction cost are LC  UL  max( xi  0.5l i )  max( y i  0.5w i）

i  1,   , n.

(25)

FCC  UF  max( xi  0.5l i )  max( y i  0.5w i）

i  1,   , n.

(26)

Where UL is unit land cost, UF is unit floor construction cost, xi and yi are the x and y coordinates of the center of the facility i, li and wi are the length and width of the facility i. 2.9 Optimization algorithm Genetic algorithm (GA) is a kind of intelligent global optimization algorithm that mimics the process of evolution of biology in nature. Firstly, GA randomly generates a set of feasible solutions and codes them. A code of feasible solution is called individual, and the set of codes obtained is called population. Then these individuals are evaluated using the objective function. Individuals with the lowest value of the objective function can get into the next generation directly, which is

ACCEPTED MANUSCRIPT called elite selection. Then the operations of crossover and mutation are implemented in the remaining individuals to generate evolved individuals and then get into the next generation also. Now a new generation is obtained. The new individuals are evaluated using the objective function again. Repeat the steps above until the pre-set value of generation or the calculation accuracy is reached. Finally, the optimal individual in the last generation is outputted as the final result. GA has been widely used in various research fields and is generally considered as one of the most effective algorithms for global optimization. GA is adopted in this work due to its natural property of parallelism. In GA, each evaluation of the individual is independent, without any relationship between them. In this work, we employ parallel computing technology with GA. By this way, the calculation efficiency can be significantly improved. In order to obtain a better layout to reduce cost effectively, surplus rectangle fill algorithm is used as a lower level algorithm to minimize the occupied land area. GA is the upper level algorithm to determine the sequence and orientation for placement. Surplus rectangle fill algorithm is an efficient algorithm for rectangle packing problems, which is widely used in the field of machining for cutting stock problems. The algorithm places a given set of rectangles into a given area in the given sequence, so that the space occupied is minimum. In this algorithm, the free space is partitioned into several rectangles as big as possible, and they are recorded in a data set. The free space is also called remaining rectangles. When a new facility comes, the most suitable position is selected in the remaining rectangles and the facility is arranged. Then the new remaining rectangles are generated and the free space data set is updated. The remaining rectangle whose area is zero or less than the area of any unarranged facility is removed. And the remaining rectangle with a small area that is completely contained in a bigger remaining rectangle is also

ACCEPTED MANUSCRIPT removed. Then a new remaining rectangular data set is obtained for the next placement. The facilities are placed from the bottom left corner to the right. The surplus rectangle fill algorithm repeats the steps above until all facilities are arranged. In this work, genetic algorithm and surplus rectangle fill algorithm are combined to obtain a better layout. Genetic algorithm firstly randomly generates a set of feasible solutions. The feasible solutions represent the orientation, number of floor, placement sequence, and the bottom width of the plant. Every time GA is going to determine the layout of one floor, it calls surplus rectangle fill algorithm and gives data to it. Then surplus rectangle fill algorithm arranges these facilities compactly according to the sequence and orientation given by GA, and then returns the coordinates of facilities to GA. GA calculates all the costs according to the coordinates returned by surplus rectangle fill algorithm, including piping investment cost, pump operation cost, land cost, floor construction cost, and total cost. Then the operations of elite selection, crossover and mutation are implemented to this set of solutions by GA to generate a new set. Repeat the step above until a solution with low enough total cost is found. GA keeps changing the orientation, number of floor, and placement sequence of facilities, and the bottom width of the plant, and making the individuals evolve in the direction of the optimal result. Finally, a satisfying layout can be found. The flow diagram of the combined algorithm is shown in Figure 1.

ACCEPTED MANUSCRIPT

Basic data (facility type, dimension, connections) Obtain facilities dimensions and arrangement sequence from GA Generate a set of feasible solutions Establish free space (remaining rectangles) data set

Determine the floor number for each facilities (or pump area or heat exchanger group)

Prepare a facility according to the arrangement sequence Determine the arrange sequence and orientation in each floor Generate a new set of sloutions

Mutation

Find suitable rectangle from data set for the facility

Arrange facilities in each floor using surplus rectangle fill algorithm and obtain coordinates of facilities (pumps except)

Arrange the facility in the left bottom of the rectangle

Arrange pumps in pump area using surplus rectangle fill algorithm and obtain coordinates of pumps

Crossover

Selection

Calculate costs according to coordinates

Update free space data set

No If all facilities are arranged ?

No

If meet the max generation or min accuracy?

Yes Finish Return facility coordinates to GA

Yes Output the optimization solution

Surplus rectangle fill algorithm

Genetic algorithm

Figure 1 Flow diagram of the combined algorithm

3. Case study 3.1 Basic data and results In practice, the industrial plant usually contains numerous facilities. In this condition, multi-floor layout shows a great advantage. A plant with 217 facilities and 224 connections of material flow from a real refinery is designed as case, which contains 48 heat exchangers, 70 vessels, 5 reactors, 79 pumps, and 6 columns. All the data needed has been obtained, including the dimension of

ACCEPTED MANUSCRIPT facilities, manufacture process, and the viscosity, density and flow rate of material flow. The flow velocity of materials in pipes is determined according to the criterion of petrochemical engineering design [20]. After determining the flow velocity of material flow, the inner diameter of pipes can be obtained according to Eq. (20), and the unit price of pipe can also be obtained from Eq. (17)(19). The determination of flow velocity can also lead to a certain value of pump operating cost according to Eq. (22)-(24). The plant is designed under three different scenarios respectively to compare and select the best one: single-floor layout, double-floor layout, and triple-floor layout. The floor height is set as 6 m. The unit price of land is 15.15 $/ (m2·year), and the unit price of the floor is 9.09 $/ (m2·year). The pump mechanical efficiency is 0.9. The unit price of electric power is 0.121 $/kW•h. The annual operating time is 6000 h/year. Pumps are arranged as 16 row and 5 column. For circular facilities (columns, reactors, and some vessel), they are treated as squares. The side length is equal to the sum of the diameter of the circular facility and the safety distance. This case is solved by genetic algorithm in the platform of MATLAB. The generation is set as 500, and population size is set as 300. The numerical results are shown in Table 1, and the layout diagrams are shown in Figure 2, Figure 3 and Figure 4. For a better expression, the facilities are drown with real dimension and shape, without safety distance. Table 1 Numerical results under three scenarios Single-floor

Double-floor

Triple-floor

Piping investment cost (PIC) ($/year)

54,678

42,132

40,513

Pump operating cost (POC) ($/year)

38,231

34,973

39,371

Energy consumed for material

315,403

288,524

324,810

ACCEPTED MANUSCRIPT transportation ( kW•h/year) PIC+POC ($/year)

92,908

77,104

79,884

Land cost (LC) ($/year)

77,679

48,476

40,294

Floor construction cost (FCC) ($/year)

0

29,086

48,353

LC+FCC ($/year)

77,679

77,562

88,647

Total cost ($/year)

170,588

154,666

168,531

Legend Pump Reactor Vessel Heat exchanger Tower Air cooler

Figure 2 The layout diagram of single-floor structure

ACCEPTED MANUSCRIPT Legend Pump Air cooler Vessel Heat exchanger Tower in the first floor Reactor in the first floor Tower occupied space in higher floor Reactor occupied space in higher floor

(a) The first floor of double-floor structure

(b) The second floor of double-floor structure

Figure 3 The layout diagram of double-floor structure

Legend:

Pump Heat exchanger

Air cooler

Vessel

Tower in the first floor

Tower occupied space in higher floor

Reactor in the first floor

Reactor occupied space in higher floor

(a) The first floor of triple-

(b) The second floor of triple-

(c) The third floor of triple-

floor structure

floor structure

floor structure

Figure 4 The layout diagram of triple-floor structure

3.2 Analysis of the optimization results It can be seen from Table 1 that the optimal layout of double-floor structure has the lowest total

ACCEPTED MANUSCRIPT cost, which is approximately 10% lower compared with the optimal layout of single-floor structure and triple-floor structure. To analyze the variation and trend, the cost of every sub-item is drawn in Figure 5. 100,000

120,000

90,000 100,000

80,000 70,000

80,000

60,000 50,000

60,000

40,000 40,000

30,000 20,000

20,000

10,000 0

0 PIC

Sing-floor

POC

PIC+POC

Double-floor

Triple-floor

(a) PIC and POC of three scenarios

LC Sing-floor

FCC

LC+FCC

Double-floor

Triple-floor

(b) LC and FCC of three scenarios

Figure 5 the costs of sub-items of three scenarios In terms of piping investment cost, as is shown in Figure 5 (a), the optimal layout with single-floor structure has the highest cost, while the costs of double-floor and triple-floor structure are relatively low. This phenomenon can be explained this way: in the condition of single-floor, the space near a certain facility is limited, and other facilities can only be placed around it horizontally, resulting in that some facilities having material exchange with it will be forced to be placed far away. This leads to a long connection of pipe and a high piping investment cost. As for the scenario of double-floor or triple-floor, besides the horizontal space, the vertical space can also be used to place facilities, resulting in the reduction of pipe length and piping investment cost. In the aspect of pump operating cost, as is shown in Figure 5 (a), the optimal layout with doublefloor structure has the lowest cost, while the costs of single-floor and triple-floor structure are relatively high. This phenomenon can be explained this way: as is mentioned in the last paragraph, the single-floor structure has long pipelines, leading to a high on-way resistance and a high

ACCEPTED MANUSCRIPT consumption of pump power, but no vertical transportation exists. The triple-floor structure can lead to the increase of quantity and altitude of vertical transportation of material, and the vertical transportation of material consumes lots of energy and is extremely expensive compared to the horizontal transportation. So the single-floor and triple-floor structure are relatively expensive in pump operating cost. The double-floor structure has a reduced pipeline length and a limited increase of vertical transportation compared to single-floor structure, making a good balance between pipeline length and vertical transportation. Consequently, the cost of the double-floor structure is relatively low. Summarising the two points mentioned above, the determination of floor number is the trade-off between piping investment cost and pump operating cost. If we add up the piping investment cost and pump operating cost, as is shown in Figure 5 (a), it can be seen that the lowest sum comes from the optimal layout with double-floor structure. This phenomenon indicates that the doublefloor structure makes a balance between piping investment cost and pump operating cost. For the land cost, as is shown in Figure 5 (b), there is no doubt that the layout with single-floor structure has the highest cost. The cost of the double-floor structure is approximately half of singfloor structure, and the triple-floor structure has the lowest cost. But it does not mean the land cost will be 1/n, when the number of floors is n. With the increase in floor number, the land cost decreases less and less. The land cost of the optimal layout with triple-floor structure is far from one-third of single-floor structure. There are two reasons for this: (1) Because the influence of cross-floor facilities (columns and reactors) has been taken into consideration in this proposed method, these facilities will occupy space in every floor, resulting in that the more the number of floors is, the more total area occupied by these

ACCEPTED MANUSCRIPT facilities is (the area is equal to n × projected area of cross-floor facilities, n is the number of floors). Thus with the increase in floor number, the land area decreases less and less. (2) The constraints that the pumps must be placed in the first floor and the air coolers must be placed in the top floor have been taken into consideration, which leads to the existence of lower bound of the occupied land area. If this lower bound is reached or approached, it will be useless to increase the number of floors and the land cost will not decrease obviously. If the floor number keeps increasing, the land area occupied will decrease less and less to become a constant finally. In this condition that the floor number reaches an unnecessary value, much free space may appear in some floors. This trend can be found in Figure 4(c). In the figure, It can be seen that a number of free space apeared in the third floor. As for floor construction cost, as is shown in Figure 5 (b), there is no doubt that the more the number of floors is, the higher the floor construction cost is. Summarizing the two points mentioned above, the determination of floor number is not only the trade-off between piping investment cost and pump operating cost, but also the trade-off between land cost and floor construction cost. Because the floor construction cost of unit area is lower than the land purchase cost of unit area, it is economical to use a multi-floor building as much as possible. However, because of the existence of the lower bound of the occupied land area, increasing the floor number would be useless when the lower bound has already been approached. Adding the land and construction costs up, as is shown in Figure 5 (b), it can be seen that, for this case, the lowest sum also comes from the optimal layout with double-floor structure. The phenomenon indicates that the double-floor structure can also make a balance between land cost and floor construction cost.

ACCEPTED MANUSCRIPT For this case, the double-floor structure is the optimal structure and the cost is the lowest. But it does not mean double-floor structure is optimal for all plants. When designing the layout of a certain plant, it is essential to try several different structures with different number of floors, find the optimal layout of each of them, and make an elaborate trade-off among investment cost, energy consumption, and land resource. It can be seen from Figure 2, Figure 3, and Figure 4 that, the obtained layout is orderly and can meet the requirements of large-scale plants, which illustrates the necessity of considering crossfloor facilities constraint, pump area constraint, heat exchanger group constraint, and facility floor constraint.

4. Discussion 4.1 Resource consumption analysis In “3.2 Analysis of optimization results”, the influence of the number of floors on various costs is analyzed. However, the environment impact is a more important point that should be considered in the process of industrial design, and the cost cannot reflect the environment impact of an industrial design. In this part, an exploration of the influence of facilities layout on environment impact is implemented from the view of natural resource consumption. Based on the case study, the exploration compares the consumption of natural resource under three different scenarios of the single, double and triple floor. The consumption of building material for double and triple floor structures is calculated based on the “criterion of multistory frame structure” and “seismic intensity seven area”, that is, to build 1 m2 building, 40 kg rebar, 0.34 m3 concrete, and 0.2 m3 standard brick are needed. The total steel

ACCEPTED MANUSCRIPT is the sum of steel for pipeline and rebar, and the total building material is the sum of concrete and brick. The consumption of natural resource and costs under the three scenarios in the case study are shown in Table 2. Table 2 Natural resource consumption and costs Single-floor

Double-floor

Triple-floor

Length of pipeline (m)

7,997

6,174

5,878

Weight of pipeline steel (kg)

40,912

31,823

30,891

Electrical energy (kW·h/year)

315,405

288,524

324,810

Land (m2)

5,127

3,199

2,659

Weight of rebar (kg)

0

127,977

212,752

Concrete (m3)

0

1,088

1,808

Standard brick (m3)

0

640

1,064

Total building material (m3)

0

1,728

2,872

Total steel weight (kg)

40,912

159,800

243,644

Total cost ($/year)

170,588

154,666

168,531

Group 1

Group 2

Total

These resource can be divided into two groups, group 1 and group 2. Group 1 involves the resource that are attributed to the layout apparently, including steel for pipeline, electrical energy and land. Group 2 involves the resource that are consumed by the building, including rebar, concrete and standard brick. The consumption of the Group 1 and Group 2 are shown in Figure 6 and Figure 7

ACCEPTED MANUSCRIPT respectively.

Weight of pipeline (kg)

Pipeline length (m) Electrical energy (102kW·h/year) Land area (m2)

54000

9000

48000

8000

42000

7000

36000

6000

30000

5000

24000

4000

18000

3000

12000

2000

6000

1000

0

0 Single-floor Double-floor Triple-floor Electrical energy Weight of pipeline steel Pipeline length

Figure 6 Resource consumption of Group 1 Weight of rebar (kg)

Concrete (m3) Standard brick (m3)

250000

2500

200000

2000

150000

1500

100000

1000

50000

500

0

0 Single-floor

Weight of rebar

Double-floor Concrete

Triple-floor Standard brick

Figure 7 Resource consumption of Group 2 Figure 6 indicates the reduction of pipeline length, weight of pipeline steel and land resource with the increase of floor number, which is attributed to the use of vertical space, as is analyzed in “3.2 Analysis of optimization result”. And double-floor structure requires the lowest electrical energy which is also analyzed in 3.2. In Figure 7, the requirement of all three kinds of resource increases

ACCEPTED MANUSCRIPT with the growth of floor number. The consumption of resource can be evaluated from 4 aspects, that is, steel resource (steel for pipeline and rebar), electrical energy, land resource and building material (concrete and brick). These 4 aspects are drawn in Figure 8 Land area (m2) Total building material (m3)

Electrical energy (kW·h/year) Total steel weight (kg) 350000

6300

300000

5400

250000

4500

200000

3600

150000

2700

100000

1800

50000

900

0

0 Single-floor

Double-floor

Triple-floor

Electrical energy

Total steel weight

Land area

Total building material

Figure 8 Resource consumption from the view of 4 aspects As is shown in Figure 8, the significant increase of total steel weight with the growth of floor number indicates that, the reduction of steel usage for pipeline attributed to the growth of floor number is just a drop in the bucket compared with the increase of steel usage for building. The land resource can be significantly saved if a higher structure is employed. Taking the total cost into consideration, the 3 different scenarios can be evaluated by the 5 indicators. The 5 indicators are nondimensionalized based on the largest value of each indicator and are drawn in Figure 9.

ACCEPTED MANUSCRIPT

Electricity

Building material

Steel Single-floor

Land

Cost Double-floor

Triple-floor

Figure 9 The comparison of resource consumption trends of 3 construction structures In terms of electrical energy and cost, no significant gap exists among the three scenarios. However, single-floor structure consumes the most land source and saves the most steel resource and building material, while the triple-floor structure is opposite. The double-floor structure is a balance between them. Consequently, the determination of the number of floors signifies the trend of natural resource consumption, that is, the designer wants to consume more land resource or more steel resource and building material. However, the consumption trend is not always between land resource and steel & building material. The trend will be different in different cases. 4.2 Sensitivity analysis The analysis in section 3.2 is valid only when the electricity price, land price, floor construction price and pipeline price are fixed. However, these basic data varies in different countries and regions. And actually, the designer is more concerned about the influence of variation of these basic data on the optimal number of floors, so that the most suitable construction structure can be determined under the condition of a given country or region, or a given set of basic data. The sensitivity analysis shown below is also based on the case study. The facility sizes and material connections are fixed, and the electricity price, land price, floor construction price and pipeline price are changed to explore the influence of unit price on the optimal number of floors.

ACCEPTED MANUSCRIPT 4.2.1 Electricity price The values of 0.03, 0.09, 0.12, 0.15, and 0.24 $/kW·h are adopted for unit price of electricity. The optimal total costs under different structure are shown in Table 3, and these data are visualized in Figure 10. In Figure 10, the sizes of bubbles represent the costs. The optimal structures under different electricity unit price are highlighted, and the highlighted line shows the variation of the optimal structure resulting from the variation of electricity unit price. Table 3 The optimal total costs under different electricity price and structure Optimal total cost

Optimal total cost

Optimal total cost

Electricity price

Optimal with single-floor

with double-floor

with triple-floor

structure ($/year)

structure ($/year)

structure ($/year)

0.03

134,379

126,458

148,632

Double-floor

0.09

152,538

148,032

158,308

Double-floor

0.12

170,588

154,666

168,531

Double-floor

0.15

171,509

162,258

175,068

Double-floor

202,707

188,415

198,688

Double-floor

($/kW·h)

structure

Optimal structure

0.24

4 Triple-floor 3 Double-floor 2 Single-floor1 0 0

0.03 1

20.09

3 0.12 4

0.15 5

0.24 6

Electricity price7($/kW·h)

Figure 10 Visualized optimal total costs under different electricity price

ACCEPTED MANUSCRIPT Figure 10 indicates that, for this case, the variation of unit price of electricity has almost no impact on the optimal number of floors at least in the range of 0.03 to 0.24 $/kW·h. The double-floor structure is always the optimal one. The policy of time-of-use electricity price may be implemented in some area. This kind of fluctuation of electricity price may impact the production schedule of an enterprise. However, Figure 10 indicates that, this kind of fluctuation or the variation in different areas of electricity price has no impact on the optimal construction structure of a plant. 4.2.2 Land price The values of 12.12, 15.15, 18.18, 22.73, and 27.27 $/ (m2·year) are adopted for the unit price of land. The optimal costs with different structure and unit price of land are shown in Table 4, and these data are visualized in Figure 11. In Figure 11, the sizes of bubbles represent the costs; the optimal structures under each unit price of land are highlighted; the highlighted line shows the variation of the optimal structure resulting from the variation of land unit price. Table 4 The optimal costs under different land price and structure Optimal total cost

Optimal total cost

Optimal total cost

with single-floor

with double-floor

with triple-floor

Land price

Optimal

($/ (m2·year))

structure structure ($/year)

structure ($/year)

structure ($/year)

12.12

140,464

141,175

161,759

Single-floor

15.15

170,588

154,666

168,531

Double-floor

18.18

182,591

167,737

176,154

Double-floor

22.73

196,308

183,437

185,156

Double-floor

27.27

228,033

204,068

200,260

Triple-floor

ACCEPTED MANUSCRIPT Optimal structure

4 Triple-floor 3 Double-floor 2 Single-floor 1 0 0

12.12 1

15.15 2

3

18.18

4

22.73 5

27.27 6

Land price ($/ (m2·year)) 7

Figure 11 Visualized optimal total costs under different land price As is discussed in section 3.2, the less the number of floors is, the more land the layout design will need. Consequently, the low land unit price is in favor of single-floor structure, while the high land unit price is in favor of triple-floor structure. A detailed comparison of costs of the two optimal layouts under different land price at 15.15 and 12.12 $/ (m2·year) is shown in Table 5. The Condition A will be explained later. Table 5 Detailed comparison of optimal structures under different land price The difference of costs Land price 15.15 ($/

12.12

between the two scenarios

Condition A

(m2·year)) of land price ($/year)

The optimal Double-floor

Single-floor

PIC ($/year)

42,132

44,610

2,478

42,132

POC ($/year)

34,973

34,531

-441

34,973

LC ($/year)

48,476

61,323

12,847

38,781

FCC ($/year)

29,086

0

-29,086

29,086

structure

ACCEPTED MANUSCRIPT Total Cost ($/year)

154,666

140,464

Land area (m2)

3,199

5,059

-14,202

144,971 3,199

Table 5 indicates that, when the unit price of land dropped from 15.15 to 12.12 $/ (m2·year), the strategy of purchasing more land (increased from 3199 m2 to 5059 m2) is adopted by the proposed model to reduce the total cost. Specifically, the model increased the investment for land to obtain more land area, accompanied by some little increase or fluctuate of pipeline investment cost (PIC) and pump operation cost (POC). In return, the high floor construction cost (FCC) is completely avoided. The reduction of FCC (29,086 $/year) is more than the increase of the sum of PIC, POC, and LC (14,884 $/year). So it can be found that the optimal structure of plant building is sensitive to land price. However, because of the reduction in land price, the total cost will reduce accordingly, even if the layout design remains in the optimal layout under the land price of 15.15 $/ (m2·year). Consequently, Condition A is used to illustrate the effectivity of the proposed model. In Condition A, the layout design is the same as the optimal layout in the condition of 15.15 $/ (m2·year), while the land price is counted as 12.12 $/ (m2·year). It can be seen that the total cost is reduced from 154,666 to 144,971 $/year due to the drop in land price. However, the optimal solutions found by the proposed model under the scenarios of double-floor and single-floor structure (141,175 and 140,464 respectively from Table 4) are both better than Condition A, which illustrates that, the proposed model makes full use of the advantage of cheap land and reduced more total cost. The comparison here proves the validity of the analysis above. 4.2.3 Floor construction price The values of 3.03, 6.06, 9.09 and 12.12 $/ (m2·year) are adopted for the unit price for floor

ACCEPTED MANUSCRIPT construction. The optimal total costs under the scenarios of different unit prices for floor construction are shown in Table 6 and Figure 12. Table 6 The optimal costs under different floor construction price and structure Floor construction

Optimal total cost

Optimal total cost

Optimal total cost

price ($/

with single-floor

with double-floor

with triple-floor

Optimal structure (m2·year))

structure ($/year)

structure ($/year)

structure ($/year)

3.03

170,588

135,120

126,871

Triple-floor

6.06

170,588

143,121

147,964

Double-floor

9.09

170,588

154,666

168,531

Double-floor

Optimal structure 170,588 12.12

187,507

192,465

Single-floor

4 Triple-floor3 Double-floor2 Single-floor1

0 0

3.03 1

6.06 2

9.09 3

12.12 4

Floor construction 5 price ($/ (m2·year))

Figure 12 Visualized optimal total costs under different floor construction price

ACCEPTED MANUSCRIPT Table 7 Detailed comparison of optimal structure under different floor construction price The difference of costs Floor construction price 9.09 ($/

3.03

between the two

Condition B

(m2·year)) scenarios ($/year)

The optimal structure

Double-floor

Triple-floor

PIC ($/year)

42,132

33,660

-8,471

42,132

POC ($/year)

34,973

33,729

-1,244

34,973

LC ($/year)

48,476

42,487

-5,989

48,476

FCC ($/year)

29,086

16,995

-12,091

9,695

Total Cost ($/year)

154,666

126,871

-27,795

135,276

Floor construction area (m2)

3,199

5,608

3,199

The low floor construction price is in favor of multi-floor structure. Very similar to the variation of land price, the proposed model constructed higher plant building to take full advantage of cheap floor construction, and the total cost is reduced. A detailed comparison of costs of optimal structures under different floor construction price at 9.09 and 3.03 $/ (m2·year) is shown in Table 7. Same with land price, because of the reduction in land price, the total cost will reduce accordingly, even if the layout design remains in the optimal layout under the floor construction price of 9.09 $/ (m2·year). Consequently, Condition B is also used to illustrate the effectiveness of the proposed model. Like land price, the same conclusion can be found. 4.2.4 Pipeline price Based on the pipeline price in the case study, the variations of pipeline price of 50% reduction,

ACCEPTED MANUSCRIPT 30% reduction, 0% reduction, 30% increase, 50% increase, and 400% increase are adopted. The results are shown in Table 8 and Figure 13. Table 8 The optimal costs under different pipeline price and structure Optimal total

Optimal total Optimal total cost

Variation of

cost with single-

pipeline price (%)

floor structure

cost with triple-

Optimal

floor structure

structure

with double-floor structure ($/year) ($/year)

($/year)

-50.00%

130,757

133,463

142,570

Single-floor

-30.00%

146,331

149,742

150,593

Single-floor Double-

0.00%

170,588

154,666

168,531 floor Double-

30.00%

177,910

171,218

176,695 floor Double-

50.00%

199,869

173,915

178,339 floor

Optimal structure

400.00%

324,238

323,761

289,313

Triple-floor

4 Triple-floor3 Double-floor2 Single-floor1 0 0

-50% 1

-30% 2

3

0%

4

+30% 5

+50% 6

+400% Pipeline price 7 8

(%)

Figure 13 Visualized optimal total costs under different pipeline price

ACCEPTED MANUSCRIPT As is shown in Figure 6, single-structure has the longest pipeline. The length of pipeline drops significantly with the structural change from single-floor to double-floor, while drops slightly with the structural change from double-floor to triple-floor. Consequently, a lower pipeline price is in favor of single-floor structure. For this case, when the pipeline price reduces 30%, the single-floor structure becomes the optimal structure. However, when the pipeline price increases, the doublefloor structure will be the optimal structure. Only in the condition of a sharp increase of 400% of pipeline price, triple-floor structure is better.

5. Conclusion This work aims to determine the locations of facilities in a large scale industrial plant considering multi-floor structure and a number of constraints. The case study with 217 facilities illustrates the effectiveness of the combination of surplus rectangle fill algorithm and genetic algorithm for the industrial facility layout problems. The results also illustrate the necessity of considering practical constraints to meet the requirements of plants. In this work it is found that, the number of floors is the most critical variable that has great impact on investment cost, energy consumption, and land resource. When the number of floors is high, land resource is saved but more investment on floor construction is required. When the floor number is low, large area and long piping are required, but floor construction cost is lower. According to the resource consumption analysis, the layout with lower floors consumes more land resource and the layout with higher floor consume more steel and building material. In the sensitivity analysis, it is found that the fluctuation of electricity price have almost no impact on the optimal construction structure, while the optimal structure of a plant is sensitive to land price, floor construction price, and pipeline price.

ACCEPTED MANUSCRIPT Acknowledgement Financial supports from the National Natural Science Foundation of China (No. 21576286) and Science Foundation of China University of Petroleum, Beijing (No. 2462017BJB03 and 2462018BJC004) are gratefully acknowledged.

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ACCEPTED MANUSCRIPT

Highlights 1. Trade-off between capital investment and energy consumption are considered in layout

design. 2. The surplus rectangle fill algorithm is firstly employed to solve facility layout problem. 3. The model can solve industrial scale problem. 4. The influence of cross-floor facility is firstly taken into account.