## May 2024

## Refinery And Petrochemical Integration

# A multi-objective optimization study for an integrated oil refinery-petrochemical plant—Part 1

The study of the ideal integration of an oil refinery and an ethylene production facility has regained interest due to the rising costs of crude oil and its derivatives. This study proposes a multi-objective optimization approach that maximizes the net profit and production of ethylene and propylene in an integrated plant.

The study of the ideal integration of an oil refinery and an ethylene production facility has regained interest due to the rising costs of crude oil and its derivatives. This study proposes a multi-objective optimization approach that maximizes the net profit and production of ethylene and propylene in an integrated plant. Three different ethylene and propylene production scenarios were considered and formulated as mixed-integer nonlinear programming (MINLP) problems using the general algebraic modeling system (GAMS) version 25.1.2.

In the three evaluated scenarios, the oil refinery and the ethylene production plant were integrated using their intermediate materials. The outcomes of each modeling scenario were compared in terms of their profitability, production, income, inventory costs and unit operating costs. The findings indicated that the multi-objective optimization model of an integrated plant offers better economic performance than the single-objective optimization model of an integrated plant. Modeling results also indicated that the multi-objective model for propene-prioritized optimization produces more ethylene, propylene and other petrochemical plant outputs (fuel gas, butane, butadiene, pentane and benzene) than the multi-objective model for ethylene-prioritized optimization.

Overall, this research revealed that both the oil refinery and the petrochemical plant benefit from the adoption of a multi-objective optimization model in terms of emissions reductions, cost reduction and profitability.

**Integration: An overview**** **

Advances in science and technology in the oil sector have accelerated the demand for the efficient production of crude oil and its derivatives.^{1} This efficiency is partly driven by oil companies' missions to increase their profit margin and consumers' desire to buy petroleum products at an affordable price.^{2} Significant research in literature has shown that the price of petroleum products in the global market has a strong correlation to such macroeconomic variables as industrial production, interest rates and real output.^{3,4,5} High oil prices have the potential to send shockwaves throughout the global economy, constraining consumers' purchasing power and forcing industries to reduce their output, lay off workers or terminate production altogether.^{6} With the fluctuating prices of petroleum products in the global market, more efficient techniques are required to enhance crude oil refineries' output, lower process costs, and ensure that the oil and petrochemical industries remain competitive.

The integration of refineries and petrochemical plants has been widely studied in literature due to concerns about climate change and the rising costs of crude oil in the global market.^{7} Traditionally, oil refineries' intermediate streams (e.g., ethylene, naphtha, propylene, ethane, fuel gas) are flared, blended with gasoline or sold to petrochemical companies as low-value products. Unlike traditional operating methods, the integration approach eliminates inefficiencies.^{8,9} It ensures that all intermediate products associated with oil extraction are captured and properly sent to downstream units for further processing. For example, ethane and naphtha produced from an oil refinery can be utilized as raw materials to produce ethylene and propylene through process integration.^{10} This integration strategy not only mitigates environmental pollution but also minimizes gas waste and saves costs in the long term, among other benefits.

Blending the upstream scheduling of crude oil with the downstream processes of petrochemicals production offers several benefits. Researchers are confronted with the challenge of bringing this seemingly simple idea to fruition through modeling.^{11} Several factors limit the simulation and integration of the infrastructure for both petrochemical plants and oil refineries, such as fluctuating crude oil prices, inconsistent fuel demand and different varieties of crude oil.^{12} Scholars have considered these factors (or ignored them) as shortcomings while proposing models for the integration of refineries and petrochemical plants.

The common denominator among the vast majority of contemporary studies on the integrated network of refineries and ethylene petrochemical plants is the use of the MINLP model.^{13} Eager to achieve optimal integration between a conventional UK oil refinery and a typical ethylene production plant, Ketabchi, *et al*. formulated and employed three mathematical models.^{12} MINLP models, along with relevant recent data, were used to prove that the optimal integration of both plants could generate increased financial value and deliver enhanced operability.^{14} To achieve this goal, they modeled and optimized each plant individually and then did the same for both plants. The study showed a considerable increase in profitability if the two plants were integrated.^{12}

The group asserted that the use of intermediate materials obtained from the oil refinery caused the integrated plants to earn large profits. However, since the researchers used several databases for UK refineries and petrochemical plants to define parameters for the mathematical models they used (such as price, properties, capacity, demand, supply, product specifications and process yield), it is important to proceed with caution when interpreting the results of this model-based study.

Al-Qahtani also performed a detailed formulation of an oil refinery-petrochemical plant model.^{8} The investigators used an MINLP framework to model the oil refinery and petrochemical systems, with a major objective to reduce the annualized cost of refineries while maximizing the value that can be obtained from petrochemical plants. However, their work focused more on the oil refinery, ignoring the finer details of the petrochemical system. In addition to integrating a large-scale refinery network into a polyvinyl chloride (PVC) petrochemical complex, they concentrated primarily on PVC production.

Zhao developed an integrated optimization model for oil refinery production and a petrochemical platform.^{15} His work employed the Lagrangian algorithm to simplify the MINLP model, which in turn was used to optimize ethylene production through the integration of the production and utility system of an oil refinery and an ethylene production plant. This research, along with Ketabchi’s study, showed that both groups used the MINLP model to demonstrate that improved profitability can be achieved through the integration of an oil refinery and an ethylene production plant. The findings of these studies revealed that the integrated approach not only enhances the profitability of the oil refinery but also achieves an improvement in unit operations, energy savings and emissions reductions.

Apart from the MINLP model, the linear programming (LP) framework has also been used in literature to find concrete evidence that an integrated network of refineries and petrochemical plants offers substantial financial rewards to stakeholders in the oil sector.^{16} Using the LP model, Li *et al.* demonstrated the pecuniary benefits of adopting the integrated approach in their study.^{17} They optimized the raw materials fed into an ethylene cracking unit through the integration of refining and petrochemical plants and found that this approach yields greater profitability than the traditional procedure. Other research also obtained the same outcome after using the LP model to assess the economic benefits of integrative optimization in an actual refinery and ethylene cracking plant application. However, compared to the MINLP model, the LP model is less efficient in that it prioritizes profit maximization and pays little attention to uncertainty in model parameters.^{17} This limitation poses a major setback in obtaining optimal results when model parameters for oil refinery-petrochemical plant integration are nonlinearly dependent on one another.

Although research publications abound on the optimal integration between an oil refinery and a petrochemical plant, most of them have focused on oil refineries and petrochemical plants in the West, with little or no information about the feasibility and benefits of an integrated approach to plants in the Middle East.^{18} The authors’ previous study filled this research gap by proposing an optimization model that combined an oil refinery and ethylene production with the aim of maximizing profit. However, this research only concentrated on the profit maximization of ethylene and propylene rather than the profit and production maximization of the two commodities. This research gap must be filled as the world needs affordable petrochemicals production. In addition, the wide gap between Middle East countries’ oil production and consumption presents a window of opportunity for investors to save on production costs and increase revenues by integrating the operations of petrochemical plants and refineries (**FIGS. 1 **and** 2**).^{19}

Furthermore, this knowledge gap must be explored as the economies of petroleum-producing countries like Saudi Arabia have been impacted negatively by the fluctuating prices of crude oil, refining and gas products.^{20} In response to the reduction in oil prices in the international market, petroleum-producing countries have reduced their production, hoping for higher oil prices to rejuvenate their shrinking economies. However, a decline in oil production may result in shortages of ethylene and propylene, which are the major commodities produced by petrochemical companies located in this region.^{21} To mitigate this effect, petroleum-producing countries must adjust their production and marketing plans strategically and tactically based on price and demand variations. More importantly, they must adopt new technologies like artificial intelligence and machine-learning to predict future oil prices and integrate the operations of oil refineries and petrochemical plants to decrease feed costs, optimize the final product and meet market requirements. Therefore, research is needed to forecast the future price of crude oil and its derivatives and evaluate the cost-benefit of an integrated approach.^{22}

In this research, the integration of an oil refinery and an ethylene producing facility is examined using an MINLP model that prioritizes maximizing ethylene and propylene production and net profit.^{23} To the authors' knowledge, no multi-objective model that considers production-and-profit maximization of ethylene and propylene has been developed for an integrated oil refinery-petrochemical plant. The first objective of this study was to maximize the profitability and production of ethylene and propylene in the integrated plant. The second objective was to compare the results of the profit-oriented optimization obtained in previous research with those of the multi-objective optimization. This research was invaluable to the petroleum and petrochemical industries in that the results offered insights into the feasibility of using an integrated approach to lower a plant's production and operating costs, enhance the plant's feedstock and efficiency, and boost the profitability and revenues generated from refineries and petrochemical plants.

The remainder of this article is structured as follows; Section 2 provides a description of the challenge; the mathematical representation of the multi-objective model is presented in Section 3; the methodology of the case studies is discussed in Section 4; the results of the multi-objective model are analyzed and discussed in Section 5; and conclusions are provided in Section 6.

**SECTION 2: CHALLENGE STATEMENT**

The impetus for combining refinery operations and an ethylene production plant is driven by profit maximization. The implementation of the proposed integration ensures that the oil refinery minimizes natural gas flaring and channels more intermediate petrochemical streams for productive use. Simultaneously, the ethylene production plant receives high-grade raw feedstocks from the refinery at a competitive price.

To achieve the objectives of this study, the two plants were modeled and optimized individually, and then optimization was done for the final integrated plant—three mathematical models were employed to perform the simulation using the MINLP framework. **TABLE 1** illustrates the meaning of the abbreviations used in **FIGS. 3–5.**

The oil refinery flowchart is shown in **FIG. 3.** The crude oil in the CDU is heated to temperatures between 350°C and 380°C, and then separated into seven segments: residues, vacuum gasoil (VGO), atmospheric gasoil (AGO), light gasoil (LGO), raw kerosene, heavy straight-run naphtha (HSRN) and light SRN (LSRN). The catalytic reforming unit (CRU) produces reformer gasoline and naphtha. HSRN and LSRN are mixed with reformer gasoline and then blended with methyl tert-butyl ether (MTBE) to produce gasoline in the gasoline blender. Raw kerosene and hydrogen (H_{2}) are mixed in the HDS unit and later sent to the DS unit to produce fuel gas. Part of the raw kerosene in the HDS unit is also used to produce kerosene in the kerosene tank. LGO is transferred directly to the diesel blender, where it is blended with kerosene. AGO and VGO are channeled to the FCC unit (FCCU) to enhance the yield of cracked gasoil, cracked gasoline, diesel and fuel oil. The ethane and propane from the FCCU are flared or stored in a reservoir.

**FIG. 4** illustrates the flowchart of the ethylene production plant. This plant is comprised of a cracking furnace, a quench tower, a DM, a DE, a DE, a DB, a DP, a PFR and an EFR. Feedstocks (ethane, HVGO, AGO and naphtha) obtained from the oil refinery are heated to about 1,050 K–1,150 K in the cracking furnace. The propane and methane obtained from the cracking furnace are channeled to the DM, DE, DE, DP, DB, DPE, PFR and EFR for further processing. Ethylene is produced from the EFR, while other products are obtained indirectly from other reactors, such as the PFR (propylene), the DB (butane) and the DPE (pentane and benzene). The H_{2 }from the DM is more useful to the oil refinery than to the ethylene production plant. This gas is instrumental in the production of gasoline, naphtha and reformer gasoline. As shown in **FIG. 4,** these units work together through a series of processes to produce refined products.

The oil refinery and the ethylene production plant work in unison as a single system, as shown in **FIG. 5.** This integration benefits both plants. The ethylene production plant receives fuel gas, naphtha, AGO, NVGO and ethane directly from the oil refinery, while the oil refinery collects H_{2 }from and supplies propane to the ethylene production plant. This arrangement minimizes waste and air pollution and ensures that all feedstocks and by-products from the process units are utilized effectively and efficiently.

**SECTION 3: OPTIMIZATION MODEL OF THE INTEGRATED PLANT**

In accordance with the preceding process description, a multi-objective optimization model was formulated by combining the refinery model with the ethylene plant model. This section is divided into four steps. First, the oil refinery mathematical expression is presented. The mathematical formulation includes the material and energy balances of the intermediate products of the oil refinery, as well as the relationship between market demand and sold materials. Second, a description of the ethylene production plant's mathematical formulation is given. The relationship between the raw material inventory balance and the total amount of materials generated in the ethylene production facility is included in the description. Third, the mathematical formulation for the segment that connects the ethylene producing plant and the oil refinery is presented. Finally, details about the integrated plant's profit maximization are given.

**Oil refinery mathematical formulation**** **

Market demand and the sold materials are assumed to be equal. This relationship is expressed in Eq. 1:

Regarding the final products, the material inventory balance—which is the total amount of materials produced in the refinery units considering the used commodities—is presented in Eq. 2:

The inventory balance is the difference between the inventory balance for final products and the number of production materials sold. Eq. 3 is used to express this relationship:

Eq. 4 indicates that the materials produced in the blending headers equal the materials used in blending. The inequalities in the blending process are represented in Eqs. 5 and 6:

The flowrate of the unit (*u*) is described in Eq. 7, where *u*, *m* and *Bm* refer to the operation mode, unit capacity [flowrate in unit (*u*) processing units in the oil refinery] and a binary variable showing whether the unit is active with operation mode (*m*):

Eq. 8 denotes that for each time (*t*), only operation of the unit (*u*) is permissible:

For all operation modes, the flowrate of each processing unit is assumed to be equal to the total flowrates. This relationship is expressed in Eq. 9:

Eq. 10 denotes that the flowrate of the processing unit equals the total used materials in the refinery, while Eq. 11 represents the equivalence relation between the fraction of flowrate and the materials produced in refinery processing:

**Ethylene production plant mathematical formulation **

To produce the appropriate products, the ethylene manufacturing system utilizes several reactors. The inventory balance for raw materials in the ethylene manufacturing facility is: Total goods produced in the plant + the raw materials delivered to the plant minus the total goods consumed in the furnace. This relation is expressed in Eq. 12:

Eq. 13 depicts the demand limitations and inventory balance for the final products. The inventory is the total amount of produced materials minus the volume of materials sold and the volume of fuel used by the boiler:

Eqs. 14 and 15 represent the economic penalty, *PEN (c, t)* which is an important factor to consider in the plant’s inventory when the material inventory is more than the security integrity level (SIL). The loss in the overall profit is the result of security level exceedance. As presented in Eq. 16, the security level should not be exceeded to avoid a loss in the total profit, and the material inventory should be less than the inventory capacity:

It is also necessary to consider the fuel gas/oil material balance. The material balance of the entire fuel gas/fuel oil purchased is represented in Eq. 17. According to this mathematical formula, the amount of fuel/fuel oil that is produced and purchased is ≥ the total amount of fuel/fuel oil that is utilized in the boiler and cracking furnaces:

Another assumption considered was that the amount of propane and methane produced equals the fuel oil generated from the furnace. This assumption is demonstrated in Eq. 18:

Developed by Berreni and Wang,^{24} Eqs. 19 and 20 are used to compute the coke formation reaction rate:

An equivalence relation exists between the product yield model and the total fixed yield, fractions of the furnace outlet temperature and coke thickness. This association is depicted in Eq. 21:

The association between the flowrate in the furnace and commodities produced/consumed in the furnace is presented with the material balance in Eqs. 22 and 23:

For a constraint with a yield fraction < 1, Eq. 24 should be used. Eq. 25 denotes that the materials consumed in the cracking furnace equal the flowrate:

It is assumed in Eq. 26 that only one commodity can be processed in each furnace at a particular time. *B(u, c, t)* is the binary variable for the ethylene production plant, where *u* is the operating unit, *r* is the used material and *t* is the period:

Eq. 27 indicates that the changeover condition *z* is equal or greater than the binary variable at period *t* + 1 – the binary variable at period *t*:

The production of each commodity *FP1 (u,c,t)*, which is a direct function of the flowrate, is expressed in Eq. 28. The maximum pressure of the separation column and the unit separation factor (SF) are associated with each other using the operating condition (*T*_{p} (*u, t*),):

Finally, Eq. 29 reveals that the fuel consumption in the boiler or furnace equals the sum of three parameters: the linear flowrate function, the furnace’s outlet temperature and dilution steam:

**Mathematical formulation for the interconnection section between plants: Inventory balance for the ethylene production plant**** **

In this section, the material balance of materials moved from the oil refinery to the ethylene manufacturing plant is explained. While Eq. 31 shows the chemical inventory balance from the ethylene production plant to the oil refinery, Eq. 30 shows the raw material inventory balance from the oil refinery to the ethylene production plant, as illustrated in **FIG. 4:**

The fuel gas supply is the accumulation of the commodities bought from the market, oil refinery and ethylene production plant. This relation is represented in Eq. 32:

The association between fuel oil, cracked gasoline and H_{2} flow streams is expressed in Eq. 33:

**Mathematical formulation for the interconnection section between plants: Inventory balance for the oil refinery**** **

The material balance of materials transferred to the oil refinery from the ethylene production plant is described in this section. Eq. 34 represents the product inventory balance of the ethylene production plant. This section details the material flow of materials from the ethylene-producing facility to the oil refinery. The ethylene-producing plant's product inventory balance is represented in Eq. 34 by the number zero:

The intermediate product from the ethylene production plant to the refinery is the cracked gasoline, and the inventory balance of that material is depicted in Eq. 35:

As expressed in Eq. 36, the inventory balance of the fuel oil is the difference between the amount of oil produced in the refinery and ethylene production plant and the amount sold, as shown in Eq. 36:

Similarly, Eq. 37 indicates the inventory balance for fuel gas:

Eq. 38 shows the inventory balance of the H_{2} generated in the ethylene production plant and used in the H_{2 }treating units of the oil refinery. The flow stream mixing relationship is shown in Eqs. 39–41:

**Objective function mathematical formulation**** **

The objective function is a mathematical expression used to achieve the best financial outcome in an integrated model. The proposed model has two objectives. The first objective is profitability maximization, as stated in Eq. 42. The ethylene manufacturing facility and refinery's revenue, the expense of inventories, equipment, upkeep and raw materials for both plants are all given numerical values by this cost function. The objective function is mathematically expressed in Eq. 42, where *SC (c, t)* denotes the quantity of material sold and *p(c)* denotes the substance's price. The revenue from the output of the ethylene plant is the second term, and the revenue from the intermediate goods is the third. Raw materials, inventory costs and processing costs are also included, along with *PRI (c, t)* (the quantity of materials purchased), *IN (c, t)* (the amount of material inventory), *(c)* (the cost of inventory), *FU (u, t)* (the flowrate) and *pi(u)* (the cost of the unit operation). Other variables in the equation include the cost of ethylene production plant supply, material change costs, operating costs of separation columns and penalty costs:

The second objective is to maximize the production of the petrochemical plant's key products, which are ethylene and propylene, as expressed in Eq. 43 or Eq. 44. Two scenarios are considered to achieve the second objective. The first scenario focuses on maximizing the production of ethylene in the EFR unit. The second scenario concentrates on the propylene produced from the PFR unit and the propylene transferred from the oil refinery. MRE (propylene) is maximized, along with profitability, to implement the multi-objective optimization model:

**Multi-objective solution method**** **

An MINLP model was developed in the previous section. A multi-objective model's optimal solution maximizes both objective functions simultaneously. No optimal solution was obtained due to the conflict between the objective functions. Considering this limitation, we need to find a compromise between the two objectives. The best way to solve such models is to adopt multi-objective methods. Hence, this study used a hybrid approach, the weighted metric method. By optimizing each objective function individually, the weighted metric method minimizes the digression between objective functions and their ideal solutions. The weighted metric method is expressed in Eq. 45:

where:

*n* is the number of objectives

*f _{i}* is the objective function of

*i*

*f _{i}*

^{*}is the ideal solution of the objective function

*i*obtained by the individual optimization method

*r* is the norm of the equation.

However, in the weighted sum method, a positive weight is assigned to each objective function. The weight assigned to objective functions must satisfy this condition: *∑ _{i}^{n} w_{i} = 1* constraints. The goal is to transform the problem, ensuring that it turns into a mono-objective optimization problem by minimizing the combined objective function, which is the weighted sum of the objective functions, as shown in Eq. 46:

Where *n* is the number of objective functions, and *w _{i}* and

*f*are the weight and the objective function

_{i}*i*, respectively.

Based on the approaches presented to solve multi-objective models, the authors adopted a hybrid method—as depicted in Eq. 47—to maximize the profitability (*Prof*) and production (*Prod*) of ethylene or propylene in an integrated plant:

**Part 2**** **

Part 2—to be published in the June issue of *Hydrocarbon Processing*—will present two case studies of a multi-objective optimization model that aims to maximize the profitability and production of ethylene and propylene in an integrated plant. **HP**

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