CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 81, 2020 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Qiuwang Wang, Min Zeng, Panos Seferlis, Ting Ma, Jiří J. Klemeš 

Copyright © 2020, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-79-2; ISSN 2283-9216 

Plant Layout Optimization with Pipe Rack and Frames 

Siyu Xua, Yufei Wanga,*, Xiao Fengb 

aState Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China  
bSchool of Chemical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China  

 wangyufei@cup.edu.cn 

Layout problem is a complex task that involves plenty of aspects of engineering design. A properly designed 

layout is able to allocate resources reasonably, increase the efficiency of production and operation, and respond 

to emergencies quickly. There are various levels of layouts, and the plant layout currently attracts the most 

attention. Previous researches on the plant layout have studied a lot on the facility arrangement manner but not 

detailed the complete plant layout with special inner structures such as frames or the in-plant pipe rack. Frames 

were defined in the previous work to allocate facilities into blocks, and they are found to be suitable for the pipe 

rack design. This paper does the follow-up work to design the in-plant pipe rack on the basis of frames. To reach 

a more practical result, a detailed plant layout is figured out. The positions of departments including frames and 

high facilities are optimized in the objective of minimizing the pipeline investment cost and material handling 

cost of cross-frame connections. Material handling points of these connections are specially concerned and pre-

determined on the frames according to the frame internal layout. These points ensure the shortest length of 

internal connections. With the information above, the in-plant pipe rack can be properly designed. To ensure 

the practicality, plenty of regulations and considerations are applied. The width, floor number, and pipeline 

arrangement manner of the pipe rack are obtained. The cost of the pipelines and the pipe rack are both 

calculated. In the case study, the chemical plant used in the previous work is studied, including four frames, 

seven high facilities and 90 cross-frame connections. Preceding frame results are used subsequently for the 

plant optimization and the pipe rack design. Comparisons are made between the optimized and original layouts. 

As a result, after the optimization, there are 44,442.83 $/y reduction in the pipeline related costs and 621.75 $/y 

reduction in the pipe rack investment, which proves the effectiveness of the proposed method. 

1. Introduction 

Layout design plays an essential role in manufacturing systems. As the world is facing a serious shortage of 

resources, the well-designed layout is demanded to save materials and land resources. The facility layout 

problem (FLP) is closely related to industrial layout design and known to be NP-hard due to its complexity, 

aiming to figure out the optimal allocation of facilities in the given region (Drira et al., 2007). It was firstly proposed 

by Koopmans and Beckmann (1957), in which equal area facilities were studied and regarded as rectangles. 

Then unequal area studies (Anjos and Vieira, 2016) and multi-floor layouts (Ahmadi et al., 2017) were taken 

into account to improve layout results. Safety issues were also one of the hotspots. Fire and explosion risks 

were considered to ensure the production safety of plants (Wang et al., 2017).  

Most published layout studies generally tended to aim at minimizing material handling cost (Azadivar and Wang, 

2000). However, these material connections were often simplified as one-to-one connections to calculate piping 

costs (Caputo et al., 2015). When considering further pipeline arrangement, the pipe rack that supports multiple 

pipelines is the main aspect that should be specially considered. Previous studies focused more on the pipe 

rack among plants, however, the pipe rack within the plant was rarely mentioned in those research models, 

although it does exist in the actual industrial plants. The in-plant pipe rack in the actual situation is often simpler, 

manually designed into special shapes, such as T or L, which is hard to realize by the widely-used path-finding 

method and brings difficulties in setting mathematical models. Previous pipe rack design often took the shortest 

length or the lowest cost of the pipe rack as the objective. However, the decrease of the pipe rack length did not 

mean the decrease of the pipeline investment cost, additionally, this traditional method ignored the pumping 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET2081045 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 30/03/2020; Revised: 21/05/2020; Accepted: 26/05/2020 
Please cite this article as: Xu S., Wang Y., Feng X., 2020, Plant Layout Optimization with Pipe Rack and Frames, Chemical Engineering 
Transactions, 81, 265-270  DOI:10.3303/CET2081045 
  

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cost which may account for a larger proportion, leading to the obtained result that was not necessarily optimal 

in terms of the total cost. Besides, the conventional facility arrangement manner was to stack facilities together 

in the plant area (Wang et al., 2018), which left no space for the placement of the in-plant pipe rack. Material 

handling points are also an aspect that should be considered in the pipe rack design. In previous studies, these 

points were determined either by selecting a midpoint on a random plant edge through the optimization (Wu et 

al., 2018), or by manual decisions according to relative position of related departments (Kulturel-Konak, 2019). 

However, due to there are few works considering two levels of layouts simultaneously, it is hard to ensure that 

these points are matched with the internal layouts, which may lead to longer material transfer distance between 

internal facilities and material handling points, resulting in suboptimal results. 

To deal with the above issues, several aspects are focused on to reach a more practical result that can provide 

referential value for the industrial construction. Firstly, the in-plant pipe rack is designed on the basis of frames 

(introduced later) which can form the paths in the plant for the pipe rack arrangement. For a more detailed result, 

plenty of regulations and considerations for the pipe rack are involved. Secondly, material handling points are 

specially considered and pre-determined on the frames according to the respective internal layouts. These 

points match well with the frames and are ensured to be optimal. Lastly, a new idea for the pipe rack design is 

applied in this work. To avoid incomprehensive results, minimizing the sum of the annual pipeline investment 

and material handling cost is served as the objective to optimize the positions of departments, and then the in-

plant pipe rack can be designed. Through this approach, the lengths of pipelines and pipe rack are shortened 

and the material pumping cost can be reduced, and a comprehensive layout result can be acquired. 

2. Methodology 

A proper arrangement of frames should be figured out to provide convenience for the design of the pipe rack. 

The simplification is made that the studied departments are regarded as rectangles. To solve layout problems, 

some basic information is required, such as frame sizes and flow data of cross-frame connections. 

2.1 Considerations 

Some considerations are necessary to design a detailed and practical plant layout. Frames defined in the 

previous work (Xu et al., 2019) in the use of allocating facilities into several blocks in the plant are found to be 

suitable to leave space for the in-plant pipe rack. They have been optimized twice to ensure that their facilities 

with cross-frame connections are all close to a certain point, and due to this particularity, material handling 

points of frames can be pre-determined, and should all be covered by the pipe rack. The relative positions of 

these points in the plant will change with the frame orientation. More specific pipe rack calculations and 

considerations are involved to obtain detailed results. The in-plant pipe rack is supported by multiple pairs of 

concrete piles. The pipe rack width is determined by the total width of all the pipelines disposed on it. When the 

total pipeline width exceeds a certain limit, the multi-floor pipe rack is required. When arranging pipelines, 

various national regulations are applied, such as GB 50160, GB 50187 and SCDI 333C06, which stipulate the 

placement order, the flange and floor requirements and safety distance of pipelines. Due to the different number 

of pipelines in different position of the pipe rack, when the total width varies greatly, it is allowed to divide the 

pipe rack into several sections, and each section possesses its width and number of floors. 

2.2 Mathematical model 

Before the objective function, several constraints should be considered to complete the model and ensure the 

practicality. Boundary constraints are set to limit that the frame area should not go beyond the plant boundary. 

Non-overlapping constraints ensure that there is no cross area between frames, which guarantee the practicality 

of the plant layout. Directional constraints stipulate the frame orientation. Because the material handling points 

are fixed on the frames, the orientation has a significant effect on the position of these points. Besides, parallel 

arrangement constraints are also applied for special departments that are always adjacently arranged in the 

actual plant to fit the actual situation. 

Based on these constraints, the mathematical model can be established. In this work, the search of the in-plant 

pipe rack is shifted to minimize the investment and operating cost of cross-frame connections. As mentioned 

above, this method is eligible to not only effectively shorten the length of pipelines and the pipe rack through the 

pipeline investment cost, but also take the material handling cost into considerations at the same time, to 

minimize the total cost. The objective function can be described in Eq(1). 

+TAC = MHC PIC  (1) 

TAC includes two aspects, which are material handling cost (MHC) and pipeline investment cost (PIC). MHC is 

related to the pump power in the use of material handling. It can be calculated by electricity price and energy 

consumption due to the friction resistance. PIC is related to the pipeline materials and is shown in Eq(2). 

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=

 
1

n

i i

i

PIC = Af UPC MD  (2) 

where, Af is the annualized factor, which can be calculated by Eq(3). UPC is the unit price of the pipeline 

investment ($/m) which is obtained according to the approach by Stijepovic and Linke (2011). It is presented in 

Eq(4)-(5). MD is the Manhattan distance between material handling points of departments. 

 +

+ −

(1 )

(1 ) 1

T

T

IR IR
Af =

IR
 (3) 

= + + +0.82 185 6.8 295
pipe out out

UPC wt D D  (4) 

= + +
2

644.3 72.5 0.4611
pipe inner inner

wt D D  (5) 

where, IR is the interest rate and T is the plant life. wtpipe represents unit quality of the pipeline (kg/m). Dout and 

Dinner are the outer and inner diameter of the pipeline (m). 

Beside the objective function, some other formulas are also required for the calculation of the pipe rack cost, so 

as to design a detailed plant layout. It is necessary to verify the rationality of the pipe rack through its cost, and 

this cost (PRC) is calculated with empirical formulas, represented in Eq(6)-(7). 

=   +  11.50 3300
rack

space

s
PRC Af wt V

s
 (6) 

=   80
rack f rack

wt n wd s  (7) 

where, wtrack is the weight (kg) and s is the length of the pipe rack section (m). sspace is the distance between 

every two pairs of concrete piles (m), and V is the volume of a single concrete pile (m3). nf is the number of 

floors, and wdrack is the width of the pipe rack section (m). 

2.3 Algorithms 

To solve this mathematical model, a hybrid algorithm is applied combining genetic algorithm (GA) and surplus 

rectangle fill algorithm (SRFA). The construction of the algorithm is not the research focus of this work, so only 

a brief introduction is made. SRFA is eligible to arrange rectangular frames closely in the rectangular plant. GA 

forms the framework of the whole algorithm, and is used to minimize TAC through the iteration. GA decides the 

frame orientation and placement order, and sends the information to SRFA. SRFA allocates frames and returns 

the coordinates to GA for the optimization, to minimize the total cost. These two algorithms work together to 

ensure their functions. The optimization process is carried out in MATLAB, and the operators of GA are default. 

3. Case study 

To verify the effectiveness of the methodology, as mentioned above, the catalytic cracking plant used in the 

previous work is subsequently studied, and the previously obtained frame data is used in this work. On the basis 

of frames, further explorations are carried out to reach detailed and practical plant layout results. 

3.1 Data acquisition 

There are 11 target departments including four frames named A, B, C and D and seven high facilities involving 

5 towers and 2 reactors, which ought to be placed outside the frames. These high facilities are named to be 

absorption-desorption tower (ADT), fractionating tower (FT), stripping tower (ST), reabsorption tower (RT), 

stabilization tower (STA), settler-regenerator (SR) and riser reactor (RR). The sizes of frames and high facilities 

are listed in Table 1. It should be noted that FT and ST are always arranged adjacently because of their close 

relationships, and in the calculating process, they satisfy parallel arrangement constraints and can be named 

as parallel facilities. The same condition is also suitable for RR and SR. 

Table 1: Sizes of the studied departments 

 Name A B C D ADT FT ST RT STA SR RR 

Length (m) 23.66 20.03 20 32.88 2.8 6 1.2 1.8 2.8 12 3.4 

Width (m) 42.4 26.5 22.1 24.6 2.8 6 1.2 1.8 2.8 12 3.4 

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3.2 Frame arrangement 

Among all the material connections existed in the plant, 90 of them transport materials between frames or high 

facilities. They are regarded as cross-frame connections, and are studied in this case. Material handling points 

of frames are pre-determined, and match well with the frame internal layout. To adapt to different situations, 

different from other frames, two material handling points are set for frame C due to its more connections. The 

layout is optimized with the objective function, considering material handling points and safety distance. As a 

result, the final TAC is calculated to be 57,600.63 $/y, and the plant layout diagram is shown in Figure 1a. 

According to the positions of the departments, the cross-frame connections in the plant can be figured out for 

the subsequent steps, and are drawn in Figure 1b to link the related departments. For a clearer presentation of 

these material connections, the diagram is simplified. Only the relative positions of departments are preserved, 

and the parallel facilities such as FT, ST and RR, SR are drawn as a whole. 

 

 

Figure 1: (a) Optimized plant layout diagram and (b) schematic diagram of cross-frame connections  

As Figure 1a shows, departments are properly arranged in the plant area. Material handling points of frames 

are noted. Specially, frame C is properly arranged, which proves that if a case with a two-point frame can be 

solved, other cases with multi-point frames can be dealt with as well. Through the diagram it can also be seen 

that the parallel arrangement constraints are well achieved. The close positions of material handling points and 

the existence of frames bring convenience for the design of the in-plant pipe rack.  

3.3 Pipe rack design 

To calculate the precise data of the pipe rack, cross-frame connections should be studied. The cross-frame 

connections that are presented in Figure 1b should be properly arranged on the pipe rack, and for a more 

precise result, plenty of regulations are referenced. Space between various pipelines, the sizes of flanges and 

the safety distance are stipulated. For the pipelines of high temperature, the insulation layers are required, and 

their thickness is acquired according to GB/T 8175. The placement order is also specified, such as pipelines 

with flammable media should be far enough from the high temperature ones, and heavy and large pipelines are 

required to be placed close to the support column.  

 

 

Figure 2: In-plant pipe rack of the optimized layout 

The in-plant pipe rack width is set to be less than 6 m, and when the total pipeline width is larger than 6 m, the 

multi-floor structure is allowed. Pipelines higher than 250 °C ought to be arranged on the upper floor. The 

268



spacing between two floors is set to be 1.2 m. The pipe rack is supported by multiple pairs of concrete piles that 

are spaced 6 m apart. When calculating the pipe rack, 20 % of the width is reserved for the convenience of 

future expansion. Different sections of the pipe rack can be set to be of different length, width or floor number 

depending on the pipelines. In the design process, the usual shape T or L for in-plant pipe rack is also strived 

to achieve, and the connecting point to the external pipe rack of the plant is also considered. With these 

parameters and considerations, the in-plant pipe rack is designed and shown in Figure 2. 

Table 2: Numerical results of the in-plant pipe rack 

 Length (m) Width (m) Floor number Section cost ($/y) Total cost ($/y) 

Section E-F 23.8 5.12 3 2,058.3 

6,425.96 Section F-H 46.1 5.04 2 3,208.97 

Section F-G 21 4.89 1 1,158.69 

 

The pipe rack in this case is designed to be of T shape according to the arrangement manner of departments 

and is eligible to cover all the material handling points. A point H for the material exchanges outside the plant is 

also concerned to connect the in-plant pipe rack with that outside the plant. To reduce the construction difficulty 

and save the materials of the pipe rack, three sections of different sizes are determined. For each section, the 

size, floor number and construction cost are calculated. The total annual cost of the whole pipe rack is 6,425.96 

$/y. The detailed numerical results are listed in Table 2. 

3.4 Result comparison and discussion 

In this work, the positions of departments are optimized considering the optimal material handling points, and 

then a proper in-plant pipe rack is designed. In order to prove the effectiveness of this approach, a comparison 

is required to verify if the optimized arrangement manner of frames and the pipe rack is reasonable. In the 

previous work, departments are manually arranged on the basis of preliminary estimation of the closeness of 

the material exchange, which considers only the rough pipeline length and may lead to suboptimal solutions. In 

this work, the previous layout is named as the original layout, and a pipe rack that covers all the departments is 

also designed under the same condition for a reasonable comparison. The same considerations are applied.  

As a result, four sections are determined. All kinds of costs are calculated, and are compared in Table 3. 

 

 

Figure 3: In-plant pipe rack of the original layout 

Table 3: Cost comparison of the optimized layout and the original layout 

Cost ($/y) In-plant pipe rack MHC PIC TAC 

Optimized layout 6,425.96 36,306.51 21,294.12 57,600.63 

Original layout 7,047.71 84,792.01 17,251.45 102,043.46 

 

It can be figured out from Figure 3 that due to the arrangement manner of departments, the pipe rack of the 

original layout is a little longer compared with the optimized layout. More branches are required to cover all the 

departments and the shape T is hard to achieve. In the case that the same calculation method is used for the 

two scenarios, the pipe rack cost of the original layout is 7,047.71 $/y, which is 621.75 $/y more than the 

optimized one. The optimized pipe rack is proved to be better and reduces around 9% of the pipe rack cost. 

The effectiveness of the placement manner of departments can also be well reflected. Original plant layout is 

manually determined according to the relationships between frames and high facilities. Departments with more 

connections are positioned as close as possible to reduce the total pipeline length, so as to reduce the length 

and cost of the pipe rack. Due to PIC is the cost that are directly related to the pipeline length, PIC of the original 

layout is less than that of the optimized layout because the original one focus only on manually decreasing the 

269



pipeline length. However, with the extension of the operation time of the factory, MHC will take more and more 

proportion and possess a greater impact on the total cost, which cannot be ignored in the design process. The 

optimized layout considers PIC and MHC at the same time to reach a final layout. According to Table 3, although 

PIC of the optimized layout is 4,042.67 $/y higher, MHC is 48,485.5 $/y less than the original layout, more than 

ten times the increase of PIC, which turns out to be a greater reduce, so it is not comprehensive enough to 

consider only the reduction in the length. When considering MHC and PIC together, there is 44,442.83 $/y 

reduction totally, which is an around 40 % drop and proves the advantages of the proposed method compared 

with the widely-used path-finding method that only shortens the pipe rack length, especially when the material 

handling cost is higher. As a conclusion, the plant layout considering both PIC and MHC is proved to be better. 

As a follow-up work, this work designs the pipe rack by means of optimizing material connections, considers the 

arrangement manner of departments and the detailed in-plant pipe rack design, and forms a complete 

methodology for the plant layout together with the previous work, which is demonstrated to be an effective and 

detailed plant layout study. 

4. Conclusions 

This work expends the content of plant layout studies and achieves a detailed industrial layout by optimizing the 

positions of departments in the plant and designing the in-plant pipe rack, and the material handling points are 

also considered. The department positions are optimized in the objective of minimizing the material handling 

cost and pipeline investment cost of cross-frame connections, and the pipe rack is determined according to the 

positions of departments and material handling points. Plenty of regulations and considerations are involved. In 

the case study, the layout of a chemical plant based on frames is optimized and its in-plant pipe rack is designed. 

To verify the effectiveness of the proposed method, costs of the original layout are calculated for comparison. 

Numerically, through the optimization, there are 44,442.83 $/y reduction in the costs related to cross-frame 

connections and 621.75 $/y reduction in the pipe rack construction cost compared with the original plant layout. 

Data shows that there are advantages in the plant and pipe rack design by considering the pumping and pipeline 

investment simultaneously. On the basis that all the material handling points are covered, the chosen objective, 

on the one hand, shortens pipeline and pipe rack length through pipeline investment cost, and on the other, 

considers the material handling cost as well to ensure the minimum of the total cost. As a result, the optimized 

layout saves 9 % of the pipe rack cost and 40 % of the pipeline related costs, and is proved to be better. 

Efforts have been made in the plant layout studies to reach a more practical and detailed result of referential 

value to the actual industries. However, due to the particularity of the shape of the in-plant pipe rack, it is hard 

to directly added into the model, so the cost of which has not yet been involved in the objective function. This 

issue is planned to be solved in the future work. 

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