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Introduction

Petroleum; a major natural resource occurs as a mixture of different hydrocarbons mainly in the liquid phase (Al-jamimi et al., 2021). The composition and properties of crude oil varies, hence there are usually large spectra and dissimilarities in the properties and structures of various products produced from crude oil (Lu et al., 2019). This also shows in the way it behaves during refining. A large proportion of the global supply of petroleum emanates from the Middle East and some major parts of Africa (Zhijun et al., 2018). Petroleum needs to be transformed into various essential products, because it can not be utilized in its original state (Coker, 2018).  Liquefied Petroleum Gas (LPG), gasoline, kerosene, Light Cycle Oil (LCO), fuel oils, and diesel are a majority of these products among many others (Leffler, 2020).

Petroleum undergoes various physical and chemical transformations (Davudov and Moghanloo, 2017). These transformations usually occur in various process with each process taking place in a distinct process unit (Bukhtoyarov et al., 2018). Fractional distillation is usually among the first processes carried out during petroleum refining, then other processes follow which are usually phase separation, hydro-treating, further cracking among many others (Locatelli et al., 2017).

Global economic growth and development has been largely dependent on the petroleum sector in many parts of the world, with the petroleum sector sustaining various nations’ economy (Hassani et al., 2017). In order to maintain this sustenance, the refining capacity of those economies has to be sufficient to meet up eith both the domestic and global demands (Kaiser et al., 2019).

Conventional petroleum refineries are large industrial structures comprising many different crude-processing units, with each refinery having its own distinct configuration based on the desired products, economic constraints, type of crude being processed, and the refinery’s location (Haoruo, 2019). Refineries, based on their configurations, range from small topping and reforming refineries to complex refineries (Idris et al., 2018). Based on their operating capacities, refineries can be classified into modular and conventional complex conversion refineries, the former having capacities in the range of 500 to 50,000 bpsd and the latter having operating capacities above 100,000 bpsd (Ogbon, et al., 2018).

A modular refinery is a low capacity refinery with a refining capacity within the range of 500 to 50,000 bpsd (Ogbon, et al., 2018). It is a refinery that can be transported quickly and easily as its parts are constructed in modules, with a low refining capacity ranging from 500 to 30,000 bpsd (Ogbon, et al., 2018). Modular refineries offer the advantages of flexibility, low deployment time, low capital requirement, reduced construction time, cost-effectiveness in remote areas, and production of one product at a time (Khor and Varvarezos, 2017). In various parts of the world, in particular, the construction and operation of modular refineries will provide employment opportunities, especially in the oil-rich regions, reducing pipeline vandalisms, and the running of illegal refineries in the region (Angela et al., 2019). In addition, the establishment of modular refineries will lead to a reduction in environmental pollution, as waste by-products, which are usually poured into streams, can be used in some other process plants for processing into valuable products (Mamudu et al., 2019). The establishment of modular refineries may also solve the problem of refined crude oil to meet domestic consumption, and maybe, for export (Gbakon, 2017).

All refineries perform three basic functions, which are; separation (fractional distillation), conversion (cracking and rearranging the molecules), and treatment, in spite of the size (Ruble, 2019).

This work will be based primarily on the crude oil distillation processes, carried out in the atmospheric and vacuum distillation columns (Raheel, 2019). A modular refinery will also be considered for this work (Ogundari et al., 2017).

Currently, there is a struggle to meet both the domestic and global demands for petroleum products due to a number of reasons among which is the global refining capacity (Nkazi and Ngwanza, 2019). A solution to this problem could be the establishment of more refineries to increase the global refining capacity (Udonne and Akinyemi, 2018). Modular refineries, in particular, have been identified as a true solution ensure the achievement of this goal (Baldea et al., 2017).

Since the approval of the establishment and operation of privately owned refineries in the global industry, the need to optimize refineries has arisen to enable the refineries maximize profit and productivity among others (Nwozor et al., 2020). This work is to carry just that out, that is, optimize the distillation of crude oil in the various units of a modular (small-scale) refinery (Tijani et al., 2020).

Problem Statement

The current global refining capacity for crude oil is inadequate to meet both the local and global demands for petroleum products, leading to the need for its importation, and outsourcing to other alternatives to meet the global energy demand (Shah, 2019).

The challenges faced by the existing global refineries include; insufficient government policies, lack of turnaround maintenance in the refineries (turnaround maintenance is recommended to be conducted every two years, with a maximum of three years) and the vandalism of pipelines which supply these refineries with crude oil, leading to a loss of revenue, among others (Praise et al., 2019). This pipeline vandalism has a prominent effect on the government revenues, as due to the constant attacks on pipelines, frequent replacements and repairs are carried out on these pipelines leading to huge amounts being wasted annually on pipeline maintenance (Olujobi, 2021).

Aim and Objectives

The aim of this work is to describe, theoretically, the optimisation of crude oil distillation in the various units of a modular (small-scale) refinery. This research is to focus on two units, the atmospheric and vacuum distillation units.

The objectives of this work are:

• Objective 1:  Development of  an objective function that provides a scalar quantitative performance measure that needs to be minimized or maximized.
• Objective 2:  Development of a predictive model that describes the behaviour of the system (Starzyk, 2019).
• Objective 3:  Defining and describing the variables that appear in the predictive models that must be varied to satisfy the constraints.

Research Questions

The identified research questions for this project are provided below:

• What variables are considered while developing the objective function(s)?
• What constraints are considered while developing the objective function(s)?
• Are there government policies that cannot be accounted for in the development of the objective function(s) (IEA, 2013)?
• If political constraints are considered, how would they affect the accuracy of the obtained results?
• How sensitive are the considered variables?

Deliverables

The deliverables of this project are; a project report, mathematical models and simulated results. The models should be able to consistently represent the relationship between the  objective function(s) and the proposed variables. Also, the report should contain a complete documentation of how the mathematical models were arrived at.

Relevance

This work is important because due to a number of reasons; the current refining capacity of the existing global refineries is inadequate to meet both the global and domestic demands for petroleum products, hence the need for the establishment of modular refineries (Ogbon et al., 2018).

Modular refineries offer the advantages of flexibility, low deployment time, low capital requirement, reduced construction time, cost effectiveness in remote areas, and production of one product at a time. As such, the establishment of modular refineries at strategically planned locations would curb the issue of pipeline vandalism as the construction and operation of modular refineries will provide employment opportunities, especially in harsh regions, reducing the constant pipelines vandalism, and the running of illegal refineries in the various global regions.

The optimization of crude oil distillation would allow for the efficient use of resources, in the form of crude oil and the required utilities, which prevents wastage of these resources, while maximising profit from the refinery (Raheel, 2019).

Methodology

This project focuses on secondary research, development of an optimization problem and obtaining results, and they are discussed below:

Secondary research

The secondary research in this project will utilize a systematic approach (Johnson et al., 2016) to review the works of literature. The steps involved in the systematic review of the literature are provided below:

• Step 1: Identify the research questions that can be used for the project.
• Step 2: Identify the keywords that should be used to research the works of literature.
• Step 3: Extract the journals and books that are appropriate for this project.
• Step 4: Write the literature review chapter.

Development of an optimization problem

 The development of the optimization problem are in stages:

• Stage 1:  Development of the needed variables.
• Stage 2: Development of a multi-linear objective function.
• Stage 3:  Developing the appropriate constraints.
• Stage 4: Testing the objective function

Obtaining results

The developed optimization problem would be solved using an appropriate software/method(s); and the results would be evaluated.

Evaluation

The risk assessment conducted for this project is provided in the table below:

Table 1:  Risk assessment