Coupling Layout Optimization of Key Plant and Industrial Area

Description

Read the introduction and sections 5 and 6. This article discusses a hybrid model for optimal layout planning, considering factors in plant layout design. What factors does the model not consider, and how important are these factors?

Introduction

Facility layout problem (FLP) is an important branch of industrial engineering and has a great impact on production efficiency, operating safety and construction investment of a factory. It was firstly proposed by Koopmans and Beckmann in 1957, aiming to minimize the material handling cost by arranging given facilities reasonably. The research direction of early layout problems was the single-floor layout of equal-area facilities using a discrete QAP (Quadratic Assignment Problem) model. The area was divided into grids of the same size in one-to-one correspondence with the facilities. Since the facility shape and size have an obvious impact on the overall layout area, it is unreasonable to generalize the layout problem with equal size facilities. Therefore, some works tended to convert the direction into UA-FLPs (Unequal-Area Facility Layout Problems). Due to the shortage of land resources and limited horizontal space, a multi-floor layout has become one of the research hotspots. Various methods to assign facilities into floors have been implemented. Chang et al. classified the departments into groups according to the flow relationship, and the departments of a similar category are arranged on the same floor. Wang et al. divided facilities into different floors by stochastic algorithm, and obtained an optimal solution iteratively.

Many efforts have been made to rationalize the layout results. Safety factors were implemented by the TNT (Trinitrotoluene) explosion model or domino hazard index. Limitations on the area and aspect ratio of facilities were taken into account as well. The adjacent arrangement of special plants was implemented by arranging plants with upstream and downstream relationships jointly. The same objective was also achieved by maximizing the adjacent lengths of plants with frequent flow exchanges, or the total flow rate of departments next to each other. In order to make the mathematical models more accurate, a number of works have been done. Ahmadi and Jokar established a multiple-stage model in multi-floor layout research. Facilities were assigned to each floor using mixed integer programming (MIP), and the facility location on the floor and the final layout were determined by non-linear programming (NLP). Anjos and Vieira firstly optimized the relative location of departments in the region and then determined the inner precise layout. The model solved sequentially may lead to suboptimal solutions, so Leno et al. proposed a hybrid algorithm to optimize the internal and external layout at the same time. Various algorithms were adopted, such as GA and the simulated annealing algorithm, and both of these have obtained reasonable results. To improve the performance of each algorithm, many kinds of hybrid algorithms were often applied as well.

However, through the development of layout research in recent years, there are still some aspects left to be solved or improved. In order to solve such problems, some concepts need to be clarified. There are two main types of layout - namely, plant layout and area-wide layout (general layout). A plant is defined as a collection of multiple facilities, and the industrial area usually contains various plants. Plant layout is mainly devoted to the optimal arrangement of facilities with their original sizes in the plant area. Area-wide layout studies focus on the reasonable placement of plants with fixed or flexible sizes within the industrial area. The main purpose of both layouts is to reach the reasonable use of space and meet process requirements. However, the studied land scale of the area-wide layout is much larger than the plant layout, which results in more complicated factors that need to be considered, such as geographical factors and traffic conditions. Additionally, pipeline network design plays a more important role in the area-wide layout because of the long distance, which brings more solving difficulties as well. Therefore, at present, more attention is paid to the study of plant layout, and unfortunately, only a small number of researchers have focused on the area-wide layout due to its complexity. The coupling optimization of both is even rarer. However, it is quite essential because these two layouts are indivisible. Plant layout usually has an effect on the area-wide layout to some extent, especially in the aspect of the occupied area. If it is required to reach the best of both, plant layout must be considered in the design of the area-wide layout. To the best knowledge of the authors, few previous articles consider the impact of a single plant on the overall area, or whether a better scheme can be obtained if both layouts are taken into account at the same time. In addition, in previous studies, the number of facilities or plants was generally small due to the solving difficulty of layout problems. The number of facilities considered in the optimization was less than 10 in most of works. Even in some works with a larger problem size, there were around 20 facilities in total, which is still far from the actual situation.

Therefore, to deal with the above issues, a new idea to design an area-wide layout is put forward. The main contribution of this work lies in the development of the conventional single-layout studies, which means that the coupling optimization of the two layouts mentioned above is realized by several steps of optimization. The impact of plant layout on the area-wide layout is emphasized. This work focuses on improving the practicality of the layout optimization method and explores the internal relationships of different levels of layouts. The plant layout and area-wide layout are concerned at the same time and the coupling relationships between them are especially considered. The main purpose of this work is to figure out the impact of a special plant on the overall industrial area and the coupling relationships between a plant and the industrial area, so that some new construction ideas can be provided. This area has significant research value but has rarely been mentioned in previous studies. It is very beneficial if the cost of the industrial area can be greatly reduced by only modifying one certain plant. To achieve the above objectives, a method with multiple steps is proposed to solve the problem sequentially. Firstly, the key plant with the greatest impact on the overall layout is figured out and modified. It is then coupled with the industrial area. The whole layout with all the plants is optimized and compared with the original one to study the impact of changes in the key plant on the overall layout. Through the above steps, plant layout is well related to the area-wide layout. In addition, based on previous research, safety distance, multi-floor model and joint arrangement of special facilities are applied. A case with practical size is studied. A combined algorithm of the genetic algorithm (GA) and surplus rectangle fill algorithm (SRFA) is adopted to give rules for facility placement and optimize layout results effectively. As a conclusion, the point of this work is that a common problem which has not been studied before is raised and a set of approaches to address it is put forward. Through the case study, a better solution than the original one is certainly obtained due to the more comprehensive approach.

Source: Yan Wu, Siyu Xu, Huan Zhao, Yufei Wang, and Xiao Feng, https://www.mdpi.com/2227-9717/8/2/1Fhtm
This work is licensed under a Creative Commons Attribution 4.0 License.

Case Study and Result Discussion

In order to prove the effectiveness of the optimization process and the proposed methodology, a refinery was taken as an example. There were 20 plants in total, e.g., a power station (PS), crude oil fractionation plant (COF), gas separation (GS), hydrogenation union (HU), residual and wax oil hydrodesulfurization (RWH), fluidized catalytic cracking (FCC), light hydrocarbon recovery (LHR), LPG desulfurization and demercaptan (LPGDD), sulfur recovery (SR), aromatics combine plant (AC), hydrogen production (HP), continuous catalytic reforming (CR), naphtha hydrofining (NH), polypropylene and polyester (PP), delayed coking (DC), air separation and compressor (ASC), central control room (CCR), railway transportation department (RTD), tank field (TF), and sewage treatment area (STA). The initial sizes of the plants are shown in Table 1. It should be noted that the lengths and widths include both the original plant sizes and the safety distances.

Table 1. Sizes and area of each plant.

Number	Name	Length (m)	Width (m)	Area (m²)
1	PS	205	234	47,970
2	COF	95	190	18,050
3	GS	37	59	2183
4	HU	176	190	33,440
5	RWH	165	190	31,350
6	FCC	74	186	13,764
7	LHR	59	44	2596
8	LPGDD	59	146	8614
9	SR	80	190	15,200
10	AC	196	88	17,248
11	HP	91	190	17,290
12	CR	88	146	12,848
13	NH	88	59	5192
14	PP	73	146	10,658
15	DC	124	205	25,420
16	ACS	99	80	7920
17	CCR	92	69	6348
18	RTD	117	439	51,363
19	TF	731	434	317,254
20	STA	176	322	56,672

Process of Finding the Key Plant

In this section, the key plant with the greatest impact was found based on our methodology. Because the changes of the area and aspect ratio theoretically affect the overall industrial area, the two aspects were both studied. The area and aspect ratio of each plant were adjusted one by one while the sizes of other plants remained unchanged. The aim of this action is to study the influence on the area-wide layout of each plant. Two scenarios were used for the study. One scenario only changed the area of a certain plant, and the other adjusted the area and aspect ratio simultaneously.

When studying the area change of a plant, it was assumed that the area of the modified plant is 20%, 40%, 60% and 80% of the original one. The minimum of the occupied industrial area was set to be the optimization objective, and the e value of each plant was calculated one by one. When the area and aspect ratio were simultaneously changed, the area was still calculated as above, and the aspect ratio was regarded as a random variable with a certain upper and lower bound according to the inner structure of the plant. The aspect ratio was calculated with other variables in GA to obtain the modified plant layout and calculate the e value of the plant. The values of e of each plant with different areas and aspect ratios are listed in Table 2. Since GS and LHR are too small compared with other plants and have little impact on the overall layout, they are excluded from the selection of the key plant. RTD is not eligible to be the key plant because its size is fixed.

Table 2. e value of each plant.

Number	Name	Area Changes Aspect Ratio Stays the Same				Area Changes Aspect Ratio Changes
Number	Name	20%	40%	60%	80%	20%	40%	60%	80%
1	PS	1.10	1.46	1.76	1.89	1.20	1.18	1.76	1.71
2	COF	2.13	1.80	2.13	1.14	1.56	1.80	2.13	1.14
3	HU	1.26	1.53	2.22	2.15	1.26	1.69	1.41	2.45
4	RWH	1.35	1.14	1.55	2.94	1.27	1.36	1.55	2.94
5	FCC	2.70	3.23	4.28	5.21	2.70	3.48	4.84	7.07
6	LPGDD	2.68	3.17	4.16	2.38	2.08	2.38	3.57	2.38
7	SR	2.19	1.80	2.19	2.70	1.35	1.80	2.28	3.62
8	AC	1.41	1.88	2.23	4.46	2.08	1.58	2.23	2.08
9	HP	1.93	1.38	1.63	2.98	1.41	1.78	2.22	4.15
10	CR	2.69	3.06	2.79	3.19	2.59	3.06	3.19	3.44
11	NH	2.96	3.95	1.97	3.95	4.44	3.29	1.97	3.95
12	PP	3.25	3.05	1.90	1.92	3.13	3.05	4.33	5.29
13	DC	1.66	1.55	1.81	2.82	1.86	1.95	2.82	3.63
14	ACS	3.07	2.59	2.59	2.59	3.07	4.10	4.53	4.53
15	CCR	4.24	3.77	2.83	3.23	3.63	3.77	3.63	3.23
16	TF	1.05	1.10	1.15	1.16	1.03	1.07	1.05	1.11
17	STA	1.06	1.24	1.49	1.72	1.29	1.18	1.49	1.27

In order to display the results more intuitively, the average value of e under the two different conditions was calculated and is drawn in Figure 2.

Figure 2. Average of e of each plant in two scenarios.

As mentioned above, the larger the value of e, the greater the influence of the plant on the area-wide layout. Combined with Table 2 and Figure 2, it can be seen that when only the area of a plant changes, the average e value of the FCC plant is higher than other plants. When both the aspect ratio and area are changed, the e value of the FCC plant is still larger in each area condition and is the largest in average. In particular, when the area is 80% of the original one, e reaches 7.07. This shows that the FCC plant has a much greater impact on the area-wide layout than other plants. When the area of the FCC plant is modified, the overall area can be significantly reduced. Therefore, the FCC plant was selected as the key plant in this case.

Internal Layout Optimization of the Key Plant

Through the efforts above, FCC was selected to be the key plant with 217 facilities in total, including 48 heat exchangers, 70 vessels, five reactors, six towers and 79 pumps, and 224 material connections. Since it was proved to be an effective way of modifying the key plant, the changes in the area and aspect ratio of the FCC plant were carried out at the same time by building a double-floor structure and modifying the inner layout of each floor.

For the internal layout of the FCC plant, the bottom length of the plant was set as a variable with 20 m lower bound and 60 m upper bound. The floor height was set as 6 m. Pumps were centrally arranged in a pump area with 16 rows and five columns on the first floor. Air coolers were placed on the second floor. Towers and reactors were placed across floors. Their shapes in a two-dimensional plane were circles and were treated as rectangles with sides equal to their diameters for the convenience of arrangement. Parallel heat exchangers were placed as groups with other facilities. The algorithm combining GA and SRFA was applied to solve the mathematical model by using parallel computation on MATLAB with the objective of minimizing the total cost. Figure 3 shows the plant layout plan after the modification, and Table 3 shows the comparison of the sizes and costs of the original and modified plant layout. Figure 4 shows the convergence curve of the hybrid algorithm. Due to the adoption of parallel computing, the calculation speed was greatly increased, and the computing time for the optimization of the layout inside the FCC plant was around 300 s.

Figure 3. Floor layout of modified FCC layout.

Figure 4. Convergence curve of the hybrid algorithm.

Table 3. Results comparison of original and modified FCC layout.

	Original Layout	Reconstruction Layout
Length (m)	34	42
Width (m)	146	76
LC (10⁴ ¥/a)	49.57	32.15
PIC (10⁴ ¥/a)	30.26	34.99
POC (10⁴ ¥/a)	22.28	29.82
FC (10⁴ ¥/a)	0	19.29
TC (10⁴ ¥/a)	102.11	116.25

It can be seen from Table 3 that, after the modification, the area of the FCC plant is 64.89% of the original one. However, in terms of costs, the original layout is superior. After the modification, the total cost is higher. In order to facilitate comparative analysis, the comparison of five kinds of cost of the key plant is drawn in Figure 5.

Figure 5. The cost comparison of original and reconstruction layout.

Combined with Figure 3 and Figure 5 and Table 3, it can be seen that the modified layout satisfies the constraints established in the model; however, its total cost is higher than the original layout, which is 1.1625 million yuan per year.

As for LC, the land cost of the double-floor modified layout is lower, which is 64.89% of that of the original single-floor layout. However, in the ideal case where all the facilities can be arranged without constraints, the land cost should be 50% of the original one when an additional floor is added. The reason is that, firstly, the practical constraints must be satisfied. Secondly, towers and reactors occupy the same position on the two floors at the same time. Additionally, pumps must be placed on the first floor as a pump area, which limits the area of the first floor and may lead to the loose layout of other floors. Therefore, the land cost is 64.89% of the original one, instead of 50%. The pipe investment cost PIC and pumping operating cost POC after the modification are both higher. This is because the materials are transformed horizontally in the single-floor layout and only needs to overcome friction resistance. When it becomes a multi-floor structure, cross-floor connections are added, and the more connections in the vertical direction there are, the longer the vertical conveying distance will be. In addition to overcoming the friction resistance, the materials need to overcome gravity, which increases the energy consumption and leads to the increase in the operational cost. After the modification, due to the addition of floors, the floor construction cost FC needs to be taken into account. As for the total cost, after the modification, it is 141,400 CNY/a higher than the original cost.

Coupling of the Key Plant and Industrial Area

In this section, the key plant and other plants are optimized through coupling to figure out the effectiveness of the proposed methodology. With the initial sizes of all the plants and the sizes of the modified FCC plant, the industrial area is optimized with the objective of minimizing the total land cost. The original and modified industrial layout are, respectively, drawn in Figure 6 and Figure 7. The comparison of numerical results is represented in Table 4, which shows the respective and coupling results of the key plant and industrial area.

Figure 6. Layout diagram with original fluidized catalytic cracking (FCC).

Figure 7. Layout diagram with modified FCC.

Table 4. Results comparison of original and reconstruction FCC and industrial layout.

	Original Layout	Modified Layout	Difference between the Modified and Original Layout	Coupling Result
FCC plant total annual cost (10⁴ ¥/a)	102.11	116.25	14.14	−180.61
Industrial annual cost (10⁴ ¥/a)	7492.75	7298.00	−194.75	−180.61

The modified key FCC plant with a new area and aspect ratio was coupled with the whole industrial layout, and the e of the FCC plant was calculated to be 4.58, indicating that the change in the key plant can effectively reduce the industrial area. Combined with Figure 6 and Figure 7 and Table 4, it can be seen that, for the key plant itself, the total annual cost after the reconstruction is 141,400 CNY/a higher than before. However, when the key plant is coupled with other plants to reach an area-wide layout, there is a significant reduction in the overall total industrial cost. The coupling cost after the modification is 1,947,500 CNY/a less than before, which is around 17 times the increased cost of the key plant itself. Combined with the two costs, the overall total cost of the industrial layout reduces by 1,806,100 CNY/a. Even though the key plant cost is higher after the modification due to the increase in PIC, POC, and FC, the total cost of the industrial area is still much lower. This is because after the modification, the changes of the area and aspect ratio lead to a better coupling of the key plant and other plants. A more compact area-wide layout is acquired and the land is used more efficiently, which greatly reduces the occupied area and saves the land cost. Compared with the increased cost of the key plant itself, the reduced cost of the whole industrial land is far greater and, therefore, the modified layout is obviously better. This indicates that the key plant surely has a significant impact on the area-wide layout. The plant modification and the slight increase in costs in the key plant may lead to a substantial reduction in the total costs of the area-wide layout, which can provide an idea for the design of an industrial park.

Conclusions

This paper proposes a new idea and a method regarding the layout problem. In previous studies, the correlation between the industrial area and a single plant has rarely been considered. To fill this gap, the coupling relationship of these two layout scales are focused on in this work, which will certainly lead to a better result. To reach a coupling layout planning, three steps of the optimization are carried out in sequence. The key plant with the greatest impact is selected according to the variable e. It is then modified in a multi-floor structure with plenty of constraints and the objective function, which is the total cost, including piping investment cost, pumping operating cost, land cost and floor construction cost. Both the cross-floor placement of towers and reactors and the constraints for the placement of specific facilities are considered. Finally, the original and modified key plant are separately optimized with other plants. The land cost is the objective function in the optimization of area-wide layout. Diagram and numerical comparisons are reached for the analysis of the coupling optimization. A refinery served as an example to verify the proposed methodology. A better solution was achieved. Case results show that even though the plant cost after the modification is 141,400 CNY/a higher, there is a 1,947,500 CNY/a reduction in the area-wide layout cost. When the key plant is coupled with the industrial area, the final total cost is reduced by 1,806,100 CNY/a, which turns out to be a significant improvement.

When studying the area-wide layout in the future, this method can be used to figure out the plant that has a greatest influence on the whole layout. The time value of money will be involved as well to reach a more valuable result. The internal modification of the key plant itself can bring great benefits to the whole industrial layout transformation, which saves resources and capital costs to a great extent. This method provides reference and a new direction for the retrofitting of a plant or a whole industrial area.

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Date:	Thursday, 3 April 2025, 10:05 PM