Multi-objective Optimisation Using Fuzzy and Weighted Sum Approach for Natural Gas Dehydration with Consideration of Regional Climate

The majority of the existing simulation-based research works on natural gas dehydration via absorption using tri-ethylene glycol (TEG) have focused on solving single or bi-objective problems where most of the objectives are in conflict with one another. It was not until 2017 that multi-objective problems with conflicting nature have started gaining significant interest in this field, especially those involving 3 or more objectives. In this work, a multi-objective optimisation (MOO) framework was developed involving two different techniques, i.e. the fuzzy optimisation and the weighted sum approach, for handling different conflicting objectives in a natural gas dehydration process. The developed framework is straightforward, which can be applied by anyone effortlessly and can be easily extended to data from other literatures. Two different case studies, which involved bi- and tri-objectives, are given here to illustrate the efficacy of the developed framework for improving the sustainability and performance of the natural gas dehydration process. Relative to previous works without optimisation, the optimum results obtained here provide a compromised solution between different objectives. Using fuzzy optimisation in case 1, for example, increases the net profit by 0.2% and reduces the VOC emissions by 33% (i.e. better sustainability). Although the water dew point increases by 15%, it is still within the specification range and hydrate formation will not occur.


Introduction
Natural gas derived from the wellhead of the reservoir is commonly known as "wet gas" that comprises mainly methane. Some other hydrocarbons apart from methane are also present along with some impurities such as hydrogen sulphide, carbon dioxide, and water; the compositions of which differ according to various geographical locations. This "wet gas," therefore, must be subjected to a series of purification processes before it becomes a clean and dry gaseous fuel that is suitable for distribution to the end users through natural gas transporting pipeline (Anyadiegwu et al. 2014). One of these purification processes is the natural gas dehydration that removes water from natural gas. This process is essential because the presence of water vapour in the natural gas stream may cause hydrate formation in the transporting pipeline, which eventually leads to safety issues such as pipeline plugging and/or corrosion (Carroll 2014). The presence of water vapour in the natural gas stream also reduces natural gas combustion efficiency and may induce the blockage of valve fittings, process equipment, and instrumentation, especially in the presence of CO 2 and H 2 S in the natural gas stream (Gong et al. 2010;Mokhatab et al. 2006). To date, several dehydration processes are available such as absorption, adsorption, and condensation (i.e. refrigeration). Detailed comparisons between these three processes have been discussed in the work of Netusil and Ditl (2011). Among these aforementioned processes, natural gas dehydration via absorption using glycol is the most established technology, which has been widely used in the industry (Bahadori 2014). Tri-ethylene glycol (TEG) in particular is the most commonly used glycol given its superiority over other glycols such as its regeneration capability, high water affinity, high chemical stability, high hygroscopicity, low vapour pressure, low evaporation loss rate, and low thermal degradation rates in the glycol regeneration system (Bahadori et al. 2008;Rincón et al. 2016).
Literature survey on the relevant works in the past decades indicated that almost all simulation-based research studies on natural gas dehydration via absorption using TEG have centred on optimising the existing process rather than developing new processes to improve the dehydration process performance. These studies generally focus on several key areas such as (i) improving the sustainability of the dehydration process to address the environmental concern (i.e. reducing the volatile organic compound (VOC) emissions such as benzene, toluene, ethyl-benzene, and xylene (BTEX) gases) (Rouzbahani et al. 2014;Saidi et al. 2014), (ii) correlation studies that include selection and development of new thermodynamic models (Twu et al. 2005), and (iii) other simulation studies such as sensitivity analysis (Darwish and Hilal 2008), techno-economic analysis (Neagu and Cursaru 2017), and parametric studies (Ranjbar et al. 2015). A detailed summary of the studies carried out between 1991 and 2017 can be consulted for interested readers (Kong et al. 2018a). Here, several simulation-based research works of interest (categorised according to the review of Kong et al. (2018a)) are extracted and modified from this review as presented in Table 1. Ten additional works of interest published between 2018 and 2021 were additionally included. Among the 22 studies listed in Table 1, 5 studies focus on solving single objective problems, 9 studies work on solving biobjective problems, while the remaining deal with three or more objectives-containing problems. The single objective problem, for example, minimises the water content in dry product gas by analysing the effect of various manipulated variables (Isa et al. 2013) or through sensitivity analysis (Ranjbar et al. 2015). Collie et al. (1998) and Kasiri and Hormozdi (2005) illustrate a bi-objective problem, which minimises both water content and VOC emissions simultaneously. Kong et al. (2018b) elucidated a tri-objective problem, which minimised the water content, solvent loss rate (i.e. TEG loss rate), and VOC emissions, simultaneously, for improving the sustainability and performance of a natural gas dehydration process. Petropoulou et al. (2019) also worked on a tri-objective problem that minimises the water content in dry product gas, TEG loss rate, and the reboiler duty using sensitivity analysis. Other than evaluating the technical performance of the dehydration process, 9 studies in Table 1 also measure the economic performance such as revenue, capital investment, and operational cost. In terms of manipulated variables, about 78% of the studies in Table 1 select TEG flowrate (F TEG ), stripping gas flowrate (F SG ), and reboiler temperature (T Reb ) as their manipulated variables. Some other manipulated variables are also considered in a handful number of studies such as the number of absorber stages (N T ) (Chebbi et al. 2019), absorber pressure (P Abs ) (Hernandez-valencia et al. 1992), lean TEG temperature (T TEG ) (Petropoulou et al. 2019), and wet gas temperature (T Wg ) (Ranjbar et al. 2015). These manipulated variables however are categorised as "others" in Table 1 because they are not commonly selected in comparison to the TEG flowrate, stripping gas flowrate, and reboiler temperature.
One interesting trend that can be observed from Table 1 is that limited studies have focused on solving 3 or more objectives in the last 3 decades. It was not until recently, i.e. 2017, that the research works presenting 3 or more objective problems started to appear. Another observation worth highlighting is that all the simulation studies conducted from 1991 to 2019 in Table 1 deal with several conflicting objectives but the trade-off between these conflicting objectives was not investigated. For example, Isa et al. (2013) compared the performance of the conventional dehydration process, the stripping gas dehydration process modified with Stahl column, and DRIZO process based on the water content in dry product gas. It was concluded from their simulation results that the DRIZO process provides the lowest water content in dry product gas. They further investigated the addition of potassium formate into the TEG solution and showed that such addition provides improvement for the TEG-water absorption efficiency by 2-3 times. Such improvement nevertheless was achieved at an expense of an increase in the BTEX-absorption rate. Further, the addition of potassium formate leads to an increase in the operational cost since it has to be introduced externally. At this point, they did not perform optimisation study to determine the trade-off between the improvement gain from the reduction in water content against the increase in BTEX emissions rate and operating cost. Another example is the work of Eldemerdash and Kamarudin (2016) where they conducted simulation to demonstrate the usage of chemically modified mono-ethylene glycol (mMEG) as a solvent that enables the reduction in the BTEX emissions and improved dehydration process performance. The application of mMEG requires no additional equipment and the low reboiler temperature requirement decreases the energy cost. The usage of mMEG, however, leads to a higher glycol loss rate and so far, no optimisation study has been conducted to investigate the trade-off between the reduction in BTEX emissions and the glycol loss rate. These observations reveal the presence of several conflicting objectives in a natural gas dehydration process. To address this, it is necessary to conduct MOO to determine the trade-off between these conflicting objectives in natural gas dehydration.
Other than solving the conflicting objectives using MOO, it is also worth highlighting that almost all studies listed in Table 1 only focus on benchmarking their results with the standard water content specification of 5 to 7 lb of water per million standard cubic feet of gas (lb MMSCF −1 ). Such specification is generally applicable to countries with moderate climates. Countries with colder climates (e.g. Alaska) Table 1 Summaries of selected simulation-based studies a conducted between 1991 till present a Extracted and modified from the review paper of Kong et al. (2018a)   specify a much lower water content specification of 1 to 2 lb MMSCF −1 and compliance with these lower specified limits provides assurance against hydrate formation during winter (Mokhatab et al. 2015). As such, it is also important to take into consideration the difference in regional climates when doing MOO. This work develops a MOO framework using fuzzy optimisation and weighted sum approach for solving different conflicting objectives in a natural gas dehydration via absorption using TEG, with the consideration of different regional climates. MOO is a method that deals with two or more conflicting objectives that involve trade-offs and works out the best set of solutions considering the given objectives, commonly known as "Pareto-optimal." Each solution in the set balances out each other (i.e. neither best nor worse than the other). This method was first demonstrated by Vilfredo Pareto during one of his interesting analogies which describes MOO as "In a closed society, you could not make any individual wealthier without making another individual poorer" (Aspers 2001). In the last 20 years, MOO has found numerous applications in the fields of chemical process engineering, such as retrofitting/revamping an existing process (Lee et al. 2020), process control (Vazquez-Castillo et al. 2015), sustainable supply chain management (How and Lam 2018;Yeo et al. 2020), and process improvement and design (Mei et al. 2014;Ng et al. 2014Ng et al. , 2016Sankar et al. 2019;Tarafder et al. 2005). A recent review paper by Rangaiah and co-workers had discussed the development of MOO in chemical process engineering, which can be referred to by interested readers (Rangaiah et al. 2020). To date, only a handful number of studies have demonstrated the application of MOO for natural gas dehydration. One example is the recent work of Mukherjee and Diwekar (2021) where they demonstrated an approach that relies on machine-learning algorithms, followed by optimisation with a probabilistic technique to determine an optimum combination of TEG flowrate, stripping gas flowrate, absorber pressure, and reboiler temperature, which will simultaneously provide trade-off for the VOC (i.e. BTEX gases) emissions and water content in dry product gas. They subsequently compared their optimum result against two benchmark scenarios based on the lowest water content with the highest BTEX emissions and the lowest BTEX emissions with the highest water content. Their optimum result can provide a balance between the water content in dry product gas and VOC emissions. Another MOO performed for natural gas dehydration is the work of Ani et al. (2021) that proposes the use of MOO to minimise the water content, the CO 2 emissions, and the overall energy consumption of the natural gas dehydration plant. Their MOO was carried out using non-dominated sorting genetic algorithm (NSGA-II) for attaining the Pareto fronts. They illustrated the MOO using 2 different bi-objective and 1 tri-objective as case study, i.e. minimise the CO 2 emissions and water content in the dry product gas, minimise the energy consumption and the water content in the dry product gas, and minimise the CO 2 emissions, the water content in the dry product gas, and the energy consumption of the overall dehydration plant. In all 3 cases, the optimum results obtained from the MOO facilitate better performance relative to the base case.
This paper is arranged as follows. The problem statement of this paper is described in the "Problem Statement" section. "Methodology" section then introduces the process flow diagram for the conventional and stripping gas dehydration via absorption using TEG to provide readers with a basic understanding of the processes. In addition, the "Methodology" section also explains the methodology and describes the case studies used to illustrate the developed framework. The step-by-step model formulation is also elaborated in the "Methodology" section. "Result and Discussion" section then deliberates the result and discussion while the concluding remark is presented in the "Conclusion" section.

Problem Statement
As briefly described in the "Introduction" section, several conflicting objectives exist in the natural gas dehydration processes. One common example is the conflicting nature between the water content in the dry product gas, VOC (i.e. BTEX gas) emissions, and TEG loss rate, with increasing TEG flowrate (Braek et al. 2001;Eldemerdash and Kamarudin 2016). Here, a higher TEG flowrate is needed to attain a lower water content in dry product gas. This however was achieved at an expense of an increase in the VOC emissions and TEG loss rate. Although this issue has been addressed previously by graphically plotting all the 3 objectives in 1 graph on the y-axis with the TEG flowrate on the x-axis ( Fig. 1) (Kong et al. 2018b), it has resulted in two optimum points (i.e. TEG flowrate), which provides trade-off between either the water content in dry product gas and TEG loss rate or the water content in dry product gas and VOC (i.e. BTEX gases) emission (Fig. 1). The TEG flowrate in between optimum point 1 and point 2 was treated as an optimum range that provides trade-off between all the three objectives (i.e. water content in the dry product gas, VOC emissions, and TEG loss rate). To obtain a more specific optimum TEG flowrate that takes into consideration all three objectives simultaneously, a better alternative is to address this as a MOO problem. Another example is the consumption of a portion of dry product gas (i.e. sale gas) as stripping gas in the stripping gas dehydration process. Although the consumption of stripping gas reduces the water content in dry product gas, it also decreases the revenue for the dehydration process since less amount of dry product gas becomes available for sale.
Therefore, this paper aims to develop a MOO framework that provides trade-off between the different contradicting objectives for improving the sustainability and performance of a natural gas dehydration via absorption using TEG. Two different case studies will be used to illustrate the proposed framework for solving different objectives i (e.g. minimise water content in dry product gas while maximise the net profit margin), at different manipulated variables j (e.g. TEG flowrate, stripping gas flowrate, and reboiler temperature). For each case study, two different MOO techniques are employed, i.e. fuzzy optimisation and weighted sum approach. The fuzzy optimisation provides the best compromised solution considering all different objectives while the weighted sum approach takes the overall degree of satisfaction by allocating different weightage to each objective. The optimum results obtained from both MOO techiques are compared against published literature without optimisation to demonstrate its potential for providing the best compromised solution between different objectives.

Methodology
This section describes the process flow diagram for the natural gas dehydration process and explains the MOO framework developed for handling different objectives for improving the sustainability and performance of a natural gas dehydration via absorption using TEG. The process flow diagram for the natural gas dehydration is described in the "Process Description" section while framework development and the details of each MOO technique are discussed in the "Framework Development" section and "Multi-objective Optimisation Techniques" section. The description of the two different case studies with different scenarios is presented in the "Case Studies" section while the model development and limitations are made available in the "Model Development" section. Figure 1 depicts the superimposed process flow diagram for the conventional and stripping gas dehydration process via absorption using TEG. In the conventional dehydration process, excessive liquid component present in the wet gas (e.g. water) is first removed by using a two-phase separator prior to the absorption process. Then, the wet gas enters the absorption tower from the bottom and flows up in a countercurrent manner to contact with the fresh (i.e. regenerated) TEG that enters from the top of the tower. During their contact, the regenerated TEG (i.e. water lean TEG) absorbs the water vapour from the wet gas and the dry product gas (i.e. dehydrated natural gas) leaves from the top of the tower. The water-rich TEG, on the other hand, leaves through the bottom of the tower and is directed through an expansion valve to reduce its pressure. After that, the water-rich TEG is sent to the flash separator where low pressure and high temperature facilitate the removal of light and soluble gas components such as carbon dioxide. After leaving the flash tank, the water-rich TEG is then pre-heated using a heat exchanger with the hot regenerated TEG that comes out from the regeneration tower before entering the regenerator. In the regenerator, the regenerated TEG flows downward while water vapour, hydrocarbon, and traces of TEG are removed from the regenerator overhead. The regenerated TEG that leaves from the bottom of the regenerator is recycled back to the top of the absorption tower via the circulation pump. Minor portion of TEG that was lost during the absorption, flash, and regeneration processes is compensated via an additional make-up flow. Before entering the absorption tower, the regenerated TEG is cooled by heat exchange with the sale gas that exits from the top of the absorber.

Process Description
The process flow diagram for the stripping gas dehydration process is analogous to the conventional dehydration process, except for the injection of a portion of dry product gas as stripping gas. Therefore, the process flow diagram for the stripping gas dehydration process is shown in Fig. 2, with the injection of stripping gas reflected by the dashed line. Here, a few additional equipment are required such as an expansion valve and a heater to adjust the pressure and temperature of the stripping gas so that it matches the operating condition of the regenerator. Figure 3 shows the overview of the developed framework, which comprises 5 steps. In the first step, the objectives are defined such as minimising the water content in dry product Fig. 1 Trade-off between water content in dry product gas, VOC (BTEX gases) emission, and TEG loss rate at different TEG flowrate modified from the work of Kong et al. (2018b) gas and maximising the net profit of the dehydration process. In the second step, the key manipulated variables are selected such as the TEG flowrate and reboiler temperature. Using these pre-defined objectives and manipulated variables, the natural gas dehydration process is simulated using commercial simulation software (e.g. Aspen Hysys V8.8). From the simulation, the results (i.e. objectives such as water content) are recorded while varying the different manipulating variables (e.g. varying TEG flowrate). The number of data to be recorded depends on the number of manipulated variables, the range of each manipulating variable, and the set interval. For instance, varying the TEG flowrate from 880 to 1340 kg h −1 at an interval of 20 kg h −1 will provide 24 different results (e.g. water content). Then, these recorded results are converted into correlations by means of regression analysis using mathematical software, Design Expert V6, so that global optimal solution can be obtained during the MOO. The response surface reduced quadratic method using historical data was chosen for the regression analysis with no transformation involved. The model selection for each correlation was conducted manually to identify the correlation that yields the highest R 2 value. The detailed examples of the correlation development will be further outlined in the "Model Development" section. Herein, it is worth mentioning that decision-maker can choose to skip this step if they have limited knowledge of regression analysis because the MOO can still be performed merely based on the simulated results. Without using the correlation function, however, implies that the obtained solution for the manipulated variables will lie on the pre-determined value and there are chances where the global optimum solution lies in between these pre-determined values. The last step of the framework involved the application of MOO technique to obtain the optimum solution. Here, two different MOO techniques are employed: fuzzy optimisation via max-min aggregation and the weighted sum approach coupled with entropy method, and the details of each technique are given in the "Multi-objective Optimisation Techniques" section.

Fuzzy Optimisation (Max-Min Aggregation)
Fuzzy optimisation can be used for both maximisation and minimisation of the individual objective function as illustrated in Fig. 4 (Bellman and Zadeh 1970;Zadeh 1965). Herein, a degree of satisfaction, λ, is introduced to balance the targeted objective functions. In Fig. 4, the value "1" indicates that the solution is at full satisfactory while a value of "0" represents a total dissatisfactory. For example, if the objective is to  Multi-objective framework for natural gas dehydration via absorption using TEG minimise the water content in dry product gas, the minimisation model should be used as represented by Fig. 4b or vice versa (Zimmermann 1978). In the case where more than one objectives are considered simultaneously, fuzzy optimisation via max-min aggregation should be implemented because it is difficult to obtain a single solution that provides the best performance in all objectives, especially when the objectives contradict each other in nature (e.g. lower water content in dry product gas generally requires a higher TEG flowrate, which translates to a higher operating cost).
The max-min aggregation maximises the least satisfied objective to prevent over-prioritising one objective over another. As mentioned in the "Introduction" section, the literature survey has indicated that no existing studies had employed the max-min aggregation method for optimising natural gas dehydration via absorption using TEG. Following this approach, the degree of satisfaction for the least satisfying objective, λ Least , is maximised, given as: The least satisfying objective is obtained using the lowest value among the degree of satisfaction for different objectives, λ Ojb i , given as: Equations 3 and Eq. 4 describe the maximisation (Fig. 4a) and minimisation models (Fig. 4b), respectively.
where i represents different targeted objectives and the λ Obj i is bounded between 0 and 1. The x i L and x i U represent the lower and upper bound that can be achieved by the individual objective function, respectively.

Weighted Sum Approach
The weighted sum approach converts multiple objectives into a single objective by assigning different weightage to each objective (see Eq. 2) and takes the overall degree of satisfaction, λ Overall , given as: where ω i refers to the weightage assigned to each objective. As a note, the weightage can be determined by using various prioritisation methods such as the analytical hierarchy process (AHP) (Saaty 1987), entropy method (Shannon 1948), and fuzzy technique for order preference by similarity to ideal solution (Fuzzy-TOPSIS) (Hwang and Yoon 1981). In this study, the entropy method is employed for assigning weightage to different objectives. The entropy method utilises the probability theory to compute the uncertain information and determines the importance of every response without input from the decision-maker, translating to a non-biased solution. It is frequently used in the field of process system design, particularly for material selection (Hafezalkotob and Hafezalkotob 2016) and optimisation of machine operation (Kumar et al. 2013). It is calculated as follows: where e i represents the individual entropy value for objective i. The e i is determined using the following equation: where r ji is the normalised value of the jth manipulated variables in the ith objectives (i.e. normalise the individual objective obtained at different manipulated variables) calculated using Eq. 8, while m is the total number of data sets in a given problem.
To note, the sample calculations for the entropy of water dew point for case 1 scenario 1 are made available in the Supporting Information (Table A1).

Case Studies
This section describes the two case studies used to illustrate the application of the developed framework. The first case study is based on the work of Kong et al. (2018b, c) with two different climate scenarios while the second case study is based on the work of Mukherjee and Diwekar (2021).

Case Study 1: Maximise Net Profit and Minimise Water Content and VOC Emissions
The first case study is a tri-objective MOO problem that provides trade-off between the economics, sustainability, and performance of a stripping gas dehydration process, represented in terms of net profit, VOC emissions, and water content in dry product gas, respectively. As indicated in the "Introduction" section and the "Problem Statement" section, there is a conflicting nature between the water content in the dry product gas and VOC emissions, with increasing TEG flowrate (Kong et al. 2018b). A higher TEG flowrate is required to achieve a lower water content in dry product gas but this was achieved at an expense of an increase in the VOC emissions and the operating cost of the dehydration plant. Notably, the revenue of the dehydration plant also increases since a lower water content in dry product gas translates to an increase in higher heating value (HHV) of the sale gas, and the revenue is often calculated using HHV (Kidnay et al. 2011). Two manipulating variables are considered in this case, i.e. the TEG flowrate and the stripping gas flowrate. The stripping gas flowrate here is represented in terms of a portion of dry product gas (i.e. % of sale gas), y SG . This is because the previous study was conducted at a fixed TEG flowrate (e.g. 1059 kg h −1 ) while manipulating the stripping gas flowrate (e.g. y SG = 0.2 to 1% of the total sale gas flowrate) (Neagu and Cursaru 2017). As highlighted earlier in the "Introduction" section and the "Problem Statement" section, another possible alternative is to consume more TEG instead of the dry product gas as stripping gas. Hypothetically, this may increase the net profit of the dehydration process since the increase in solvent cost (i.e. operating cost) due to the increase in TEG flowrate is traded-off against the decrease in stripping gas consumption (i.e. a lower stripping gas consumption represents an increase in revenue due to more product gas available for sale). Therefore, the present case aims to determine an optimum combination between TEG flowrate and stripping gas flowrate that provides a balance between net profit margin, VOC emissions, and water content in dry product gas, which represents the economic, sustainability, and technical aspects of a stripping gas dehydration process.
Two different scenarios are illustrated in the present case to further exemplify the framework. The first scenario targets countries with moderate climate where the water content specification is generally higher, between 5 and 7 lb MMSCF −1 . This translates to a water dew point range of approximately − 3 to − 7 °C. Herein, Malaysia was chosen as a specific example, which stipulates water dew point specification range between + 5 and − 25 °C. The second scenario targets countries with colder climate (e.g. Alaska), which specify a lower water content specification of 1 to 2 lb MMSCF −1 (Mokhatab et al. 2015). This translates to a water dew point specification of approximately − 19 to − 28 °C. Since the water dew point for scenario 1 was specified at a range between + 5 and − 25 °C, the water dew point specification for scenario 2 was thus set to a lower value of at least − 25 °C and below. The simulation specification is listed in Table 2.

Case Study 2: Minimise VOC Emissions and Water Content
Case 2 aims to demonstrate the generic application of the developed MOO framework to other literature data. This case study was adapted from the work of Mukherjee and Diwekar (2021), which aims to minimise the VOC emissions and water content in dry product gas. Relative to case 1, more manipulated variables are considered here, which include the TEG flowrate, stripping gas flowrate, absorber pressure, and reboiler temperature. As described in the "Introduction" section, Mukherjee and Diwekar (2021) demonstrated an entirely different approach that relies on machine-learning algorithms, followed by optimisation with a probabilistic technique to perform MOO. They aimed to determine an optimum combination of TEG flowrate, stripping gas flowrate, absorber pressure, and reboiler temperature, which simultaneously provides the lowest VOC emissions and water content in dry product gas. They employed the least absolute shrinkage and selection operator (lasso) method for their variable selection followed by support vector regression (SVR) for metamodeling. Then, they optimised the problem using a novel metaheuristic optimisation algorithm, known as the efficient ant colony optimisation (EACO). The process simulation method employed by Mukherjee and Diwekar (2021) is similar to the present developed framework, although it was carried out using different commercial software (ProMax) instead of Aspen Hysys, which is used in this work. Table 3 summarises the simulation specifications for case 2.

Model Development
Case Study 1 Step 1: Define Objectives The main objective in case 1 is to optimise the dehydration process with the consideration of three aspects, i.e. water content in dry product gas (performance), VOC emissions (sustainability), and net profit margin (economic). Note that the water content is represented in terms of water dew point (i.e. the temperature at which water begins to condense) in this case. The VOC emissions, on the other hand, account for hydrocarbons that encompass more than 5 carbon molecules (e.g. pentane C5 +). On the other hand, the net profit (C NP ) is defined as the difference between revenue (C Revenue ) and variable cost of production (C VCOP ) (see Eq. 9).
The C Revenue is estimated using Eq. 10 following the same calculation as the work of Kong et al. (2018c). On the other (9) C NP = C Revenue − C VCOP (11) C VCOP = (Q Reb × C Steam ) + (F TEG × C TEG ) + (F TEG,m × C TEG ) + (Q Cond × C Elec ) Step 2: Define Process Variables Two manipulating variables are considered in case 1, i.e. F TEG and y SG . First, the F TEG was varied from 880 to 1340 kg h −1 (i.e. ± 20% from the work of Kong et al. (2018c)) with an increment of 20 kg h −1 . This was followed by varying the y SG at 10 different levels, which ranges from 0.1 to 1% of the total sale gas produced, for every increment of the F TEG . Altogether, this requires a total of 240 simulation runs during the subsequent process simulation in step 3 (i.e. 24 different intervals of F TEG × 10 different intervals of y SG ).
Step 3: Process Simulation Using the pre-defined objectives and manipulating variables in step 1 and step 2, a total of 240 simulation runs were carried out using Aspen HYSYS V8.8. The parameters used for the simulation and the representative flowsheet are made available in the Supporting Information (Table A2 and Figure A1). The overall simulation results are plotted based on three objectives ( Figure A2 in Supporting Information) and the numerical results are tabulated in Table A3 in the  Supporting Information while the result summaries for the  3 different objectives are given in Table 4.
Earlier in the "Case Study 1: Maximise Net Profit and Minimise Water Content and VOC Emissions" section, two different scenarios were described based on different climate requirements that are represented using the water dew point specification. The water dew point for the first scenario was specified between + 5 and − 25 °C. Nevertheless, it is clear from Table 4 that the highest (i.e. maximum) water dew point that can be obtained from the simulation is − 12.37 °C. This value is already far below the highest water dew point specification of + 5 °C set by the local authority in Malaysia. Therefore, the water dew point for scenario 1 is kept at between − 12.37 and − 25 °C. The water dew point for the second scenario, on the other hand, remains the same as previously described in the "Case Study 1: Maximise Net Profit and Minimise Water Content and VOC Emissions" section of at least − 25 °C and below.
The water dew point (WDP), VOC emissions, HHV, reboiler duty, and condenser duty obtained from Aspen Hysys in step 3 can be converted into the form of correlations by means of regression analysis using Design Expert software version 6.0, given by Eqs. 12-16. The economic calculations of TEG make-up cost and the revenue (Eq. 10) are also correlated using the identical method, given by Eq. 17 and Eq. 18, respectively. As explained in the "Framework Development" section, these correlations help to determine the global optimal solution during the MOO (step 5). The R 2 values for the developed correlations are mostly above 0.99 (see Supporting Information (Table A4)), which highlights the accuracy and reliability of the developed correlation. These developed correlations were additionally validated against literature (Kong et al. 2018c(Kong et al. , 2020Neagu and Cursaru 2017) where average errors of 1%, 0.44%, and 26% were obtained, respectively, which highlights the accuracy of the developed correlations (see Supporting Information (Table A5)).
Step 5: Multi-objective Optimisation In the last step, the pre-defined objectives (e.g. water content in dry product gas, VOC emissions, and net profit margin), manipulated variables (e.g. F TEG and y SG ), constraints (e.g. minimum water dew point specification), and the developed correlations (e.g. Eq. 1 to Eq. 5 and Eq. 12 to Eq. 18) are loaded into the mathematical software for solving MOO using two different techniques (i.e. fuzzy optimisation and weighted sum approach). Here, the MOO model is solved through non-linear programming (NLP) with global solver by using LINDO V18.0 (note that for more details on the LINDO formulation, please refer to the coding attached in Supporting Information).

Case Study 2
The model development for case 2 is analogous to that for case 1 except for a few minor differences, which is elaborated in this section. Unlike in case 1, the water content here is represented in terms of lb MMSCF −1 while the VOC emissions are represented in terms of BTEX emissions. Here, 4 manipulated variables are considered, which include  TEG flowrate, absorber pressure, reboiler temperature, and stripping gas flowrate (Table 3). It is worth noting that the process simulation and correlation development (step 3 and step 4) are omitted in the present case since sufficient data has been provided by Mukherjee and Diwekar (2021) whose work was adapted in the present case.

Model Limitations
The result validation for the developed correlations in case 1 ("Case Study 1" section) shows good agreement only with the literature of Kong et al. (2018cKong et al. ( , 2020) whose operating data is similar to those adopted in case 1. The result validation nonetheless did not fit well with other literature (e.g. the work of Neagu and Cursaru (2017)), indicating the limitation of the developed correlations. Therefore, the process simulation and correlation development in step 3 and step 4 must be repeated for different operating data, which is time-consuming. Another limitation worth noting is that the present framework employed the entropy method for the weighted sum approach, which depends highly on the number of data set(s) and does not involve any input from the decision-makers (i.e. expert judgement). In the case where one objective has to be prioritised over another and expert judgement is required, other alternative weightage methods should be considered, e.g. AHP that relies on expert judgement, which will result in different optimum solutions.

Case 1
Case 1 determines the combination of TEG flowrate and stripping gas flowrate that provides a balance between the economic, sustainability, and performance of a stripping gas dehydration process, represented in terms of water dew point, VOC emissions, and net profit, respectively. Two different scenarios are presented based on countries with different climate requirements.

Scenario 1
Prior to the MOO, three different combinations of TEG flowrate and stripping gas that provide the lowest VOC emissions (i.e. greatest sustainability performance), the highest net profit margin, and the lowest water content of − 25 °C are specified (Table 5). These three combinations will be used as a benchmark for subsequent comparison against the optimal result obtained from the MOO. Table 5 reveals that the combination for the TEG flowrate and stripping gas flowrate for the lowest VOC emissions and the highest net profit margin is identical, which consumed 880 kg h −1 of TEG with 0.1% of sale gas as stripping gas. Using such combination provides a net profit of $32.55 million with VOC emissions of 38.26 kg year −1 . It also provides the highest water dew point specification of − 12.37 °C. The benchmark for the lowest water dew point of − 25 °C, on the other hand, was obtained using 880 kg h −1 of TEG flowrate with a higher stripping gas flowrate of 0.9% of the sale gas. Such combination produces a lower annual net profit of $32.28 million with higher VOC emissions of 312.67 kg year −1 .
Relative to the three benchmarks, a trade-off combination was first determined using fuzzy optimisation. The optimal performance is obtained when the λ Least is maximised at 0.624, which corresponds to a TEG flowrate of 880 kg h −1 coupled with 0.4% of the sale gas as stripping gas. Such optimum combination provides a higher water dew point of − 21.20 °C, slightly above the lowest water dew point specification of − 25 °C. On the other hand, the VOC emissions have been reduced significantly by about 54% to 141 kg year −1 . In comparison to the lowest VOC emissions benchmark, however, such VOC emissions are higher by about 3.7 times. The net profit for such optimum combination was found to be $32.45 million per annum, which is higher than the lowest water dew point benchmark by about $170,000 per annum (or 0.52%). Nonetheless, such net profit is lower by about $100,000 per annum (or 0.3%) relative to the highest net profit benchmark. Here, it is clear that the optimum combination of TEG flowrate and stripping gas flowrate obtained at the maximum λ Least of 0.624 provides the highest satisfaction value among the three objectives. It represents the best compromised solution that balances the water dew point specification, VOC emissions, and the net profit margin, without over-prioritising any of these individual objective functions. The above was repeated using the weighted sum approach. The calculated entropy weightages for the water dew point, VOC emissions, and net profit in scenario 1 are given as 0.16359, 0.83639, and 0.00005, respectively. The overall degree of satisfaction, λ Overall , using the weighted sum approach was found to be 0.889 and the corresponding optimum combination was found to be the same as the one found in the lowest VOC emissions case and the highest net profit benchmark case. Here, since both the fuzzy optimisation and weighted sum approach provide a water dew point that is below the highest water dew point specification of + 5 °C, hydrate formation will not occur. The weighted sum approach however provides lower VOC emissions (i.e. better sustainability performance) and a higher net profit margin relative to the fuzzy optimisation in the present case. Nevertheless, one should note that the weighted sum approach is highly dependent on the weightage (i.e. the optimum result varies according to different weightage) as described in the "Model Limitations" section. Moreover, the weighted sum approach in the present study employed the entropy weightage, which is highly dependent on the number of samples (i.e. number of simulation run). Different numbers of samples will result in different weightage, which translates to a different optimum result. Therefore, it is inappropriate to assume that the weighted sum approach will always provide a better result in comparison to the fuzzy optimisation method. As such, the optimum result obtained from both methods is used as a subsequent comparison against literature without any optimisation Kong et al. (2018c).
Relative to the literature (Kong et al. 2018c), the optimum result using fuzzy optimisation resulted in a higher net profit margin by about $69,000 per annum (or 0.2%) while the VOC emissions are reduced drastically by about 33% from 211.11 to 141.17 kg year −1 . This indicates that fuzzy optimisation is capable of providing solutions with better economic and sustainability performances in comparison to previous work. The water dew point however increases by about 15% from − 25 to − 21.20 °C. The optimum result using weighted sum approach provides analogous results where the net profit margin is higher by about $167,000 per annum (0.51%) and the VOC emissions have been reduced drastically by about 173 kg year −1 (82%) relative to the literature, which reflects its economic and sustainable superiority. Although the water dew point increases by almost 50% from − 25 to − 12.37 °C, it is still within the specification range where the hydrate formation will unlikely occur. Overall, the optimum results obtained using both MOO technique provide better economic and sustainable performance relative to the literature, albeit to a different extent. Further, the water dew point obtained from both optimum results can meet the desired water dew point specification.
In a nutshell, it can be deduced from the simulation results (Supporting Information Table A3 and Table 5) that the water dew point can only be reduced at an expense of a lower net profit margin or a higher VOC emissions rate. In contrast, a higher net profit margin or lower VOC emissions is always traded-off by an increase in water dew point. Such findings are in agreement with the previous study (Braek et al. 2001). With the implementation of the proposed MOO framework, an optimum combination of TEG flowrate and stripping gas flowrate that provides a balance between water dew point, net profit, and VOC emissions can be obtained.

Scenario 2
Scenario 2 repeats the same methodology as scenario 1 but targets countries with colder climates (e.g. Alaska). Table 6 displays three different combinations of TEG flowrate and stripping gas flowrate that provide the lowest VOC emissions, highest net profit margin, and the lowest water dew point specification of − 28.40 °C. These two combinations are used as the benchmark for subsequent comparison against the optimum result obtained from MOO. In comparison to the benchmarks, the trade-off combination using fuzzy optimisation was determined and the TEG flowrate was found to be 1100 kg h −1 coupled with 0.8% of the sale gas as stripping gas. Such combination coincides with the maximum λ Least of 0.506, which provides a water dew point of − 27.23 °C, VOC emissions of 279.80 kg year −1 , and net profit of $32.315 million per annum. Compared to the lowest water dew point case, the VOC emissions had reduced by about 20% from 350 to 279.8 kg year −1 but it is still higher than the lowest VOC benchmark by about 68 kg year −1 (or 32%). The net profit, on the other hand, is higher than the lowest water dew point case by about $72,000 per annum (or 0.22%). Nevertheless, it is about $67,000 per annum (equivalent to 0.2%) lower than that of the highest net profit case.
Using the weighted sum approach, the λ Overall was found to be 0.950, which translates to an optimum TEG flowrate of 1340 kg h −1 combined with 0.57% of the sale gas as stripping gas. This optimum setting provides identical performance relative to the lowest VOC emissions or the highest net profit case, with a small average variance of about 0.4% in all 3 objectives.
Analogous to scenario 1, the optimum result obtained from the MOO provides a balance between water dew point, net profit, and VOC emissions. Both the fuzzy optimisation and weighted sum approach provide a water dew point that is within the specification range. Similarly, the weighted sum approach also provides lower VOC emissions and a higher net profit margin relative to the fuzzy optimisation. However, it is worth reiterating that the weighted sum approach depends highly on the weightage and it does not always provide a better result in comparison to the fuzzy optimisation method. In contrast, fuzzy optimisation which does not depend on the weightage can provide the most compromised result without over-prioritising any of the individual objectives.

Case 2
Case 2 elucidates an example where the developed framework is extended to other literature whose operating data is not in the same range as those employed in case 1. Here, the MOO was performed using the operating data from the work of Mukherjee and Diwekar (2021) for finding the lowest VOC emissions and lowest water content in the dry product gas, the sub-optimal (non-Pareto optimal) and optimal (Pareto optimal) solutions of which are plotted in Fig. 5, with the Pareto front optimisation indicated in the same figure.
The optimal results obtained from both fuzzy optimisation and weighted sum approach are also plotted in Fig. 5 while the numerical results are further summarised in Table 7. The VOC emissions in the present case are expressed in terms of BTEX gas emissions while the water content is given in lb MMSCF −1 . Mukherjee and Diwekar (2021) provided two different benchmarks that offer the lowest BTEX emissions and lowest water content in dry product gas, which are also listed in Table 7, similar to what has been performed for case 1. These benchmarks are used as subsequent comparison against the optimum solution obtained from MOO. Note that, the reduction in BTEX emissions is always traded-off by a marginal increase in the water content, similar to what was observed in case 1.
Using the fuzzy optimisation, the optimum water content in dry product gas and the BTEX emissions were found to be 5.11 lb MMSCF −1 and 368.92 ton year −1 , respectively. This was achieved by using 3.08 standard gallon per minute (i.e. SGPM) of TEG flowrate with 94.92 million standard cubic feet per day (i.e. MMSCFD) of sale gas as stripping gas at an absorber pressure of 520.12 psig and reboiler temperature of 386.98 °F. As compared to the work of Mukherjee and Diwekar (2021), the optimum result obtained using fuzzy optimisation in the present case utilised a lower absorber pressure and reboiler temperature, which translates to savings in operational cost. Such potential savings nonetheless were traded-off by the marginal increase in TEG flowrate. Other than that, the stripping gas consumption has also been reduced by about 5% (i.e. less dry product gas is consumed), which brings about an increase in the revenue for the dehydration process.
In comparison to the benchmark that provides either the lowest water content in dry product gas (i.e. good) with the highest BTEX emissions (i.e. worst) or the lowest BTEX emissions (i.e. good) with the highest water content (i.e. worst), the optimum results obtained using Pareto optimal solution, Pareto front, fuzzy optimisation, and weighted sum for case 2 fuzzy optimisation provide the best compromised solution between the water content in dry product gas and BTEX emissions, without over-prioritising any of the objectives. For example, the optimum water content of 5.11 lb MMSCF −1 falls in between the lower and upper limits of the water content specification benchmark of 2.41 lb MMSCF −1 and 13.89 lb MMSCF −1 (Table 7). Similarly, the BTEX emissions of 368.92 ton year −1 also fall in between the lower and upper limits of the BTEX emissions benchmark of 65.58 ton year −1 and 1238.21 ton year −1 (Table 7). With this, one does not need to increase the risk of forming hydrate in pipelines by sacrificing the water content in dry product gas for lower BTEX emissions to comply with the environmental regulations, and vice versa.
The above MOO using fuzzy optimisation was repeated using weighted sum approach and the optimum results are also given in Table 7. Using weighted sum approach, the water content in dry product gas increases to 6.19 lb MMSCF −1 while the BTEX emissions were reduced further to 272.40 ton year −1 . This was obtained by using 2.79 SGPM of TEG flowrate with 99.18 MMSCFD of sale gas as stripping gas at an absorber pressure of 599.50 psig and reboiler temperature of 392.36 °F. Relative to the literature (Mukherjee and Diwekar 2021), the optimum result using weighted sum approach consumed lower TEG flowrate and stripping gas flowrate. It also utilised a slightly lower absorber pressure and reboiler temperature. Altogether, this leads to better economic performance for the dehydration process.
Based on the results obtained in this work, it appears that using weighted sum approach provides a better result because it consumed a lower utility and raw material relative to fuzzy optimisation. Further, the BTEX emissions were reduced significantly by about 26% (equivalent to 96.52 ton year −1 ). Although the water content in dry product gas is higher by about 21%, it is still within the standard specification range of 5 to 7 lb MMSCF −1 . However, it should be noted that the weighted sum approach depends strongly on the weightage (i.e. data set(s)) and does not always provide a better result in comparison to the fuzzy optimisation, analogous to both scenarios in case 1. The fuzzy optimisation, however, provides the most compromised result without over-prioritising any of the individual objectives.

Conclusion
In conclusion, a MOO framework was developed in this study for handling different conflicting objectives for improving the sustainability and performance of a natural gas dehydration process via absorption using TEG. The framework consists of 5 steps that are relatively easy to follow, which can be employed by anyone effortlessly with minimum modelling skills. Two different MOO techniques were employed, i.e. the fuzzy optimisation method and the weighted sum approach, which were illustrated using two different case studies. The first case study determines an optimum combination of TEG flowrate and stripping gas flowrate that provides trade-off between economic, sustainability, and performance which are represented in terms of net profit, VOC emissions, and water content in dry product gas, respectively, for two different climate scenarios. In both climate scenarios, the optimum TEG flowrate and stripping gas flowrate were found to give balance between all the three objectives, without neglience of any objective. The optimum results obtained from the MOO were additionally compared against the literature result without any optimisation. The results showed that both MOO techniques produce a higher net profit margin and lower VOC emissions by about 0.4 and 58% on average, respectively. Although the water content in both scenarios increases by about 33% on average relative to literature, it is still within the desired specification and hydrate formation will not occur. The second case study aims to demonstrate the generic applicability of the developed framework where it employed an entirely different set of operating data obtained from the literature. In case 2, both the water content in dry product gas and the BTEX emissions were minimised with more manipulated variables. Relative to the literature, the optimum result obtained from case 2 utilised a lower utility and lesser raw material, which translates to a better economic performance for the dehydration process. Overall, the MOO framework developed in this work helps to balance the different conflicting objectives for improving the sustainability and performance of a natural gas dehydration process. For future work, the developed framework can potentially be extended to solve the multi-objective optimisation problem of an integrated system, which encompasses both natural gas sweetening and natural gas dehydration processes. Future studies can also explore the possibility of performing MOO using the direct optimiser function in Aspen Hysys and compare the result against that obtained from the MOO framework in this work. Lastly, future research can also be directed towards developing a generic visualisation tool (e.g. Piper diagram (Teng et al. 2016)), which is useful for decisionmakers from non-technical backgrounds (e.g. management level) or with minimum computational background, further closing the knowledge gap between technical and non-technical workforces.