Multi-Period Operational Modelling and Optimization for Large-Scale Natural Gas Networks Considering Linepack Functions in Long-Distance Transmission Pipelines

Abstract

As a promising energy resource, offshore natural gas is primarily used for power generation. The comprehensive offshore gas-to-power system, which includes extraction, treatment, compression, pipeline transmission, and power generation, is extensive and operates within various regulatory, operational, and financial constraints. This complexity offers opportunities to optimize one or more system operations to enhance profitability while fulfilling user demands and environmental considerations. In this research, we present a model-based, computer-aided framework that intuitively connects upstream natural gas operations with downstream power generation and distribution. We develop a multi-period Mixed-Integer Nonlinear Programming (MINLP) model that integrates gas treatment, compression, and long-distance transmission with power generation. The model combines first-principle mechanistic process models with a linepack model that calculates the gas volume storable in long-distance pipelines for transmission. The linepack model facilitates gas storage and withdrawal across different periods to accommodate demand scheduling. We apply this framework using the MINLP model in three scenarios: profit maximization, cost minimization, and supply-demand balancing using linepack. The results demonstrate improved economic performance for offshore natural gas-based power generation in China under varying periodic power demands.

1. Introduction

Natural gas, unlike other fossil fuels on earth, produces less greenhouse gas emissions. It also contains less sulfide and NO_x per unit energy produced compared to other fossil fuels. It is difficult to determine the exact amount of offshore natural gas used specifically for power generation worldwide due to the lack of disaggregated data separating onshore from offshore production in global statistics. However, natural gas plays a significant role in global power generation. Global natural gas consumption is forecasted to increase by 46.3% from 2017 to 2040 [1] with electric power and industrial sectors accounting for nearly 75% of the increase [2].

According to the International Energy Agency, natural gas accounts for around a quarter of global electricity generation [3]. It is important to note that it includes both onshore and offshore natural gas. The percentage of offshore natural gas used for power generation can vary significantly by country and region. While a specific percentage is not readily available, natural gas is a commonly used fuel for power generation globally. It is safe to say that a significant portion of offshore natural gas production is utilized for this purpose. Additionally, some countries rely heavily on offshore natural gas reserves to meet their electricity needs, particularly those with limited onshore resources or environmental constraints, such as Norway, the UK, the Netherlands, Qatar, and Australia [4,5]. Until 2024, offshore natural gas projects demonstrate significant advancements and evolving trends, such as Mubadala Energy’s in offshore Indonesia, the EastMed pipeline project in the Mediterranean, the Southeast Gateway Pipeline project in North America, and the new investment in Enbridge’s offshore infrastructure to boost capacity. These initiatives collectively reflect the growing global emphasis on offshore natural gas.

Offshore natural gas, as its name implies, is extracted from below the floor of the sea. The drilling activity usually takes place on the continental shelf or the seabed, which is a long distance from the coast. For more than a hundred years, since the first offshore oil well was drilled in 1896 in California, USA [6], various methods have been employed for the “first step” in offshore natural gas utilization, which is determining how to use the extracted gas. It is an important issue to resolve because it affects the subsequent gas processing steps. The gas is usually extracted and processed on offshore processing platforms, which are built on a floating rig to remove impurities. Once processed, the natural gas is transported to shore via subsea pipelines or liquefied natural gas (LNG) carriers or consumed by other offshore facilities. Currently, pipelines are the most common method of transportation for offshore natural gas.

Long distance pipelines are one of the most cost-effective ways for natural gas transmission on a long-term basis [7,8] and widely employed all over the world. There are a total of 1308 gas pipelines in the world, and the USA is the country with the most pipelines installed [9]. A pipeline is usually long in length with large diameter. In practice, gas pipelines are not only a means of transmission, but also a storage device for safety stocks. The volume of gas that is stored in a long-distance pipeline is referred to as linepack [10]. Linepack storage depends on the compressibility of the natural gas and the length of the pipeline. Thus, by utilizing linepack, it is possible to achieve several key benefits. These include balancing supply and demand, enhancing operational flexibility, improving economic efficiency, increasing system resilience, and providing environmental benefits. These aspects are thoroughly examined in this study. Unlike onshore pipelines, which benefit from extensive networks and storage facilities, offshore pipelines rely heavily on linepack for supply continuity during downtime or limited access. These differences highlight the need for a tailored optimization model specifically designed for offshore systems. Although pipeline flow has been studied for decades, some major difficulties in the modeling still remain, such as the complex behavior of the gas in transient compressible flow inside long pipelines [11,12]. Additionally, the detection of potential pipeline wall deterioration in offshore gas pipelines is a critical issue for ensuring long-term operational integrity and can be effectively addressed using transient tests, as highlighted in recent studies by Meniconi et al. [13]. To cope with this complex behavior, rigorous dynamic pipeline models have been developed [14,15,16]. Demand, gas composition, and uncertainties in thermodynamic properties are considered in the developed models which are then applied for control-related actions. Control strategies for linepack are also developed under uncertainty [17]. However, use of a dynamic model consisting of highly nonlinear differential equations leads to non-convex constraints and greatly increases the problem complexity, resulting in frequent numerical infeasibilities and endless computational times. To improve the pipeline transportation, another option is to instead consider pipeline transmission models with a multi-period linepack feature that could provide good model fidelity while greatly reducing problem complexity.

Raw natural gas extracted from a gas well varies in different geological conditions. Generally, it contains light hydrocarbons, mainly methane (CH₄), as well as a small number of unwanted impurities such as carbon dioxide (CO₂), hydrogen sulfide (H₂S), water vapor (H₂O), nitrogen (N₂), CO₂, and H₂S. It is crucial to remove the impurities through a gas treatment unit to the extent that the extracted natural gas product meets the downstream consumers’ standards. Absorption, membrane separation, adsorption, and cryogenic technology are methods proven to be effective for natural gas treatment facilities [9]. In offshore rigs, conventional CO₂ removal from NG is mostly carried out via chemical-absorption [18], which nowadays is also the most common way for large scale productions. This process uses amine solutions to capture the sour gas. N-methyldiethanolamine (MDEA) is a popular amine solution used in a conventional amine process [19]. The gas treating unit consists of a column for sour gas absorption and a regenerator for releasing the sour gas absorbed in the rich stream. The process has been well studied and appropriate equipment has been developed along with the drastic rising demand for natural gas during the last few decades [20,21].

Efforts to optimize individual processes have been well-documented, including small-scale processing networks [10], CO₂ removal from raw natural gas or natural gas power plants [22,23], natural gas compression and energy requirement minimization for transmission [16], natural gas refining heat integration [24], and co-generation systems [25]. A previous study improved the flexibility of system facilities using offshore gas pipeline linepacks, focusing on the reliability of upstream facilities [26]. These examples demonstrate significant advancements in process optimization and industry implementation. Recent studies have made contributions to modeling and optimizing small-scale natural gas systems with different focuses. One study introduced a piecewise linearization method for improving computational performance in mixed-integer linear programming (MILP) models for gas transmission with linepack, demonstrating faster computational results compared to existing methods [27]. Similarly, another study explored how modeling and solution approaches impact the flexibility provided by gas networks to power systems [28]. A different study, focusing on the installation and expansion of oil tankers, the connection between pipelines, and FPSO was, also presented [29]. Moreover, the critical role of energy management and the integration of diverse power sources from a sustainability perspective cannot be overstated, as they are essential for achieving long-term environmental and economic objectives [30]. Nonetheless, the systematic modeling of offshore operations remains incomplete at present. That is, an optimization framework that integrates all processes that made up the system that needed to be developed. Studying the entire system enables a comprehensive and intuitive optimal solution. In large-scale systems, the optimal solution for individual processes—when combined—cannot guarantee an optimal outcome for the entire system, as it may fail to align with the system’s overall objectives. Therefore, it is essential to adopt a system-wide approach instead of focusing solely on optimizing individual processes. Additionally, while some studies focus on the economic aspects of offshore gas-to-power systems [31,32], they are rarely formulated at an operational level. These studies often lack real-world case applications that integrate actual operational parameters and equipment variables. Thus, a large-scale system needs to be optimized at a system level to ensure the optimal solution aligns with the system’s overall objectives. This underscores the necessity of adopting a system-wide approach rather than focusing solely on optimizing individual processes. Additionally, operational optimization frameworks address real engineering challenges, providing actionable insights for the maintenance, planning, and design of gas-to-power systems.

In this study, we propose an MINLP-based optimization framework that optimizes the entire offshore system from upstream gas processing to downstream power generation. This framework incorporates realistic constraints, such as actual equipment parameters and operational variables. The complex system integrates gas treatment, gas mixing, gas compression, long-distance gas transmission, and power generation is considered as a GtoP system with the objective to achieve and analyze optimal performance matrices through a model-based approach. In addition, a novel approach to optimize GtoP systems by incorporating the concept of linepack is introduced. This work is unique in its comprehensive analysis of three distinct operational strategies: profit optimization, cost minimization in rural areas, and managing power demand surges. By integrating linepack into the Mixed-Integer Nonlinear Programming (MINLP) optimization framework, a realistic and flexible solution that enhances system feasibility and performance is achieved. This approach not only improves operational efficiency but also addresses the economic and environmental impacts of GtoP systems, making it a significant contribution to the field of energy management. Figure 1 shows a simple schematic diagram of a GtoP system where the five sub-systems and their links are highlighted.

The set of process operations shown in Figure 1 is considered for operational optimization for an offshore gas to power (GtoP) system. This system originates from the upstream natural gas source and ends with the downstream power generation step, encompassing various processes in between, including gas treatment, compression, pipeline transmission and power generation. As with typical computer-aided model-based studies, the processes in the system are first modeled with appropriate model fidelity. Within these process models, Aspen Plus^® V8.8 process simulator is used to generate simulated data set to be used for data-driven process modeling. Models for the long-distance gas transport through pipelines and a multi-period linepack model for long-distance natural gas transmission has been developed. The operational optimization is then performed through a deterministic global optimization framework incorporating the developed models and employing the BARON solver [33,34] built in GAMS 24.4.6 to solve the large-scale non-convex MINLP model. This study employs three optimization frameworks: an economic optimization model aimed at maximizing profits; a cost-minimization model dedicated to a GtoP system located in rural areas, in which the linepack model is analyzed; and an operational feasibility model driven by supply-demand enhancement using linepack.

The rest of the paper includes a section on problem statement and process description (Section 2); a detailed description of the models developed for the GtoP system (Section 3); a description of the MINLP model for maximizing total profit considering all operations (Section 4); framework application of the profit-maximizing case to the model, descriptions of three case scenarios, and corresponding discussions (Section 5); and concluding statements (Section 6).

2. Problem Statement and Process Description

A GtoP system operating in the South China Sea is illustrated in Figure 2. As shown in Figure 2, it comprises a set of gas feed terminals (denoted by SNOD), splitters (denoted by SPL) and mixers (denoted by MIX), gas treating processes (denoted by CRP), compressor stations (denoted by COM), long distance pipelines (denoted by LPL), gas-fired power plants comprised by gas turbines (denoted by GTT), boilers (denoted by BOI), and steam turbines (denoted by STT), and a set of end power users (ENOD). The processes that make up the GtoP system are denoted by U (u 1, 2, …, U) and they operate in a multi-period operational mode. The periods are denoted by H (h = 1, 2, …, H). The duration of a period is 168 h. In each period, the GtoP system receives natural gas from various terminals and the composition and pressure of natural gas from each terminal vary. The components in natural gas are denoted by C (c 1, 2, …, C).

After gas is fed into the GtoP system, it is split into multiple streams. Part of the gas is sent to the gas treating plants, the rest bypass the gas treatment and is sent to the mixers, which are next in line. After a certain amount of CO₂ is removed by the amine process, natural gas streams are blended to meet the specifications given by power generation plants. Being compressed by a set of compressors, the gas is then transmitted through a set of long-distance pipelines to the power generation plants. Furthermore, the offshore facility is integrated with combustion of gas to drive the turbines, converting heat and expansion work into shaft work, driving the power generator to produce power. The flue gas from the power generation plant is recycled and sent to boilers as a heat source to generate steam. The steam turbines utilize the steam to produce additional power.

The power output is controlled by adjusting the gas flowrate supplied to the gas turbines from the pipeline outlet; the gas flowrate at the pipeline outlet is a function of inlet flow and linepack. Using the demand profile as a constraint, power production is optimized with the inlet flowrate and linepack being design variables within operational range. Hence, the potential operational profitability and feasibility that the linepack might contribute is worth exploring.

The objective is to determine the following: (1) the optimum flowrate of natural gas from each terminal at each period; (2) the linepack in consideration of downstream gas demands in each period; (3) the operational parameters and handling capacity of the processing units including MDEA gas treatment, splitters, mixers, compressors, and pipelines; and (4) the operational parameters and handling capacity in the power plant units including air provided to the gas turbines, steam generation of boilers, the operation of steam turbines and the power production of each power plant. Through optimizing the above elements, the best economic performance is obtained in a multi-period operational horizon for the GtoP system. A list of known (given) data and assumptions for the process operation are listed below.

2.1. Given

(1)

Number of natural gas terminals, flowrate bounds, compositions, and pressure of natural gas from each terminal.

(2)

Number of various processes operations in the GtoP system, minimum and maximum process loads, operating pressure and temperature bounds, and available network of processes.

(3)

Minimum and maximum demands of electricity in each period.

(4)

Economic data such as cost of natural gas, power selling price, utility cost, and other fixed costs.

(5)

Operational horizon and periods.

2.2. Assumptions

(1)

Gas in the pipelines is of turbulent flow hence perfect mixing is assumed [16].

(2)

Solubility of CH₄ in amine solvents is very low, it is thus ignored for model simplification [35].

(3)

The dynamic flow behavior is not considered at the switching points between two adjacent periods.

(4)

Constant temperature is assumed for steam from boilers.

(5)

The fixed cost is assumed to be zero.

(6)

No elevation or pipeline elbow is constructed throughout the pipeline length.

2.3. List of Decision Variables

A list of decision variables to be optimized in this study is given in

Table 1. Decision variables being optimized in the model.

Category	Decision Variable	Variable Symbol	Description
Gas Flow Variables	Gas flow rates	F, Fin, Fout	Continuous variables representing the flow rates through gas terminals, pipelines, and between processing units.
	Mole fraction	y	Continuous variables for mole fraction of a component of gas stream.
Pipeline Parameters	Inlet and outlet pressures	Pin, Pout	Continuous variables representing pressures at the start and end of each pipeline segment.
Compression Settings	Compression ratio	R	Continuous variable representing the pressure ratio across the compressor (outlet pressure/inlet pressure).
Turbine Settings	Turbine operation	P	Continuous variables for work pressure of gas turbine.
Linepack Storage	Gas storage in pipelines (Linepack)	I	Continuous variables representing the volume of gas stored in pipelines to balance supply and demand.
Air-Fuel Ratio	Air–fuel ratio for turbines	AFR	Continuous variable optimized to improve combustion efficiency and reduce operational costs.
Equipment Utilization	On/off status of compressors, turbines, and other units	Y	Binary variables determining whether specific equipment is operational during a given period.

.

3. Modeling of the GtoP System

The models representing all the process operations in the gas-to-power (GtoP) system are described in this section. An explanation of the symbols and indices is provided as follows: or processes u, u′, and u″, these are aliases of the same set U. Using Equations (1) and (2) as examples

In Equation (1), $F_{h,u}$ represents the mole flow rate of the material stream (raw gas) in process u (splitters) during period h. $F_{h,u,u^{\prime }}$ is the mole flow rate of raw gas from process u (splitters) to process u′ (the next conjunctive processes, which are mixers or CO₂ processing units) during period h.

In Equation (2), $F_{h,u^{\prime },u}$ is the mole flow rate of raw gas from process u′ (the previous conjunctive process, in this case, refer to gas terminals) to process u (splitters) during period h. $F_{h,u,u^{″},c}$ represents the mole flow rate of component c (CH₄ or CO₂) in raw gas from process u (splitters) to process u″ (mixers or CO₂ processing units) during period h. Similarly, $y_{{h,u}^{\prime },u,c}$ is the binary variable that denotes the decision to transfer component c (CH₄ or CO₂) from process gas terminal to process splitters during period h.

The symbols and indices in the remaining equations follow the same structure, describing the flow of materials and components across the different processes in the system.

3.1. Stream Splitting and Mixing Models

3.1.1. Splitting

Splitters are the first set of units the raw extracted natural gas encounters. The raw gas is split into multiple streams with the same composition. This is a typical stream divider or splitter in any process simulator. The simple model resulting from mass balance between the inlet flow and the summation of the split outlet flows is given by Equation (1). A mass balance across the composition of the streams remains the same while passing through the splitters is given in Equation (2). The structure of the symbols and indices is explained in Section 3.

$$F_{h,u}={\sum }_{u^{\prime }:\left(u,u^{\prime }\right)\in UC}{F}_{h,u,u^{\prime }} \forall u\in {SPL}_u, h\in H$$

(1)

$$F_{{h,u}^{\prime },u}{y}_{{h,u}^{\prime },u,c}=F_{h,u,u^{″},c} \forall c\in C,u\in {SPL}_u,\left(u,u″\right)\in UC,(u^{\prime },u)\in UC, h\in H$$

(2)

To decide whether a process is active or not, binary integer variable $y$ is introduced into the model equations. When the summation of stream flowrate through a process is 0, binary variable $y$ will be assigned 0 by Equation (3). Consequently, $F_{h,u}$ will be assigned 0 by Equation (4). In other cases, if the summation of flowrate through a process is not 0, binary variable $y$ will be assigned 1. $F_{h,u}$ is thus constrained in Equation (4) by its lower and upper limit.

$${\sum }_{c\in C}{y}_{h,u,u^{\prime },c}=Y_{h,u,u^{\prime }} \forall c\in C,u\in {SPL}_u,(u^{\prime },u)\in UC, h\in H$$

(3)

with

$$F_u^{min}{Y}_{h,u}\le F_{h,u}\le F_u^{max}{Y}_{h,u} \forall u, h\in H$$

(4)

The pressure of the splitters that are connected to the natural gas terminals is given by

$$P_{h,u}=P_{h,s}^{NG} \forall u\in {SPL}_u, h\in H, s\in S$$

(5)

where $F_u^{min}$, $F_u^{max}$ are the minimum and maximum flow rate of the process streams, $P_{h,u}$ and $P_{h,s}^{NG}$ are the pressure of process streams and pressure of natural gas terminals.

3.1.2. Mixing

Mixers merge streams from different processes into one stream and lead to the next process operation. The composition of the streams at the inlet may vary while the outlet stream flowrate and compositions are calculated from the conservation of mass principle at steady state. The mass and component relationships are given by

$$F_{h,u}={\sum }_{u^{\prime }:\left(u^{\prime },u\right)\in UC}{F}_{h,u^{\prime },u} \forall c\in C,u\in {MIX}_u, h\in H$$

(6)

$${\sum }_{u^{\prime }:\left(u^{\prime },u\right)\in UC}{y}_{{h,u}^{\prime },u,c}{F}_{h,u^{\prime },u}=y_{h,u,u^{″},c}{F}_{h,u,u^{″}} \forall c\in C,u\in MIX, h\in H$$

(7)

To associate the molar fraction of a component $y_{h,u,c}$ to each stream of a specific component

$$F_{h,u,c}=F_{h,u}{y}_{h,u,c} \forall c\in C,u\in MIX, h\in H$$

(8)

Similarly to Section 3.1.1, the activity of the process is decided by the existence of the associated stream. Binary variable $Y_{h,u,u^{\prime }}$ is used to establish the relationship. The flowrate is constrained by the capacity of the mixer. They are given by

$${\sum }_c{y}_{h,u,u^{\prime },c}=Y_{h,u,u^{\prime }} \forall c\in C,u\in MIX, h\in H$$

(9)

$$F_{h,u^{\prime },u}\le F_u^{max}{Y}_{h,u^{\prime },u} \forall u\in MIX,\left(u^{\prime },u\right)\in UC, h\in H$$

(10)

3.2. Pipeline Transmission and Linepack Model

The definition of the term linepack is the volume of gas that can be stored in a long-distance pipeline. It is usually not taken into consideration in pipeline transmission studies [36]. However, the massive volume of the pipeline is used as a safety stock. The linepack storage of NG rely on the compressibility of natural gas and the inner volume of the pipeline. In the multi-period model, the linepack storage needs to be continuous between two adjacent periods. In other words, the linepack storage cannot be initiated at the start of the period, its value is inherited from the end of the previous period. Furthermore, the linepack storage also needs to respond to the inlet and outlet pressure and flowrate in a single period. Thus, modeling of multi-period linepack should consider the following: (a) changes in linepack storage in a period when the inlet flowrate and outlet flowrate are not even in a single period; (b) the inheritance of linepack value between adjacent periods; (c) inlet and outlet pressures when linepack changes in different periods; and (d) pressure drop along the pipeline.

The molar flowrate, molar fraction of each component, and the pressure at the inlet equal to the ones from the previous process units (compressor), respectively. The relationships are given by Equations (11)–(13). Variables $P_{h,u}^{in}$ and $P_{h,u^{\prime }}^{out}$ are the inlet pressure of pipelines and outlet pressure of compressors, respectively.

$$F_{h,u}^{in}=F_{h,u^{\prime },u} \forall u\in LPL,\left(u^{\prime },u\right)\in UC, h\in H$$

(11)

$$y_{{h,u}^{\prime },u,c}=y_{h,u,u^{″},c} \forall c\in C,u\in LPL,\left(u,u″\right)\in UC,(u^{\prime },u)\in UC, h\in H$$

(12)

$$P_{h,u}^{in}=P_{h,u^{\prime }}^{out} \forall u\in LPL,\left(u^{\prime },u\right)\in UC, h\in H$$

(13)

The pressure drop along the pipeline is formulated and modified based on a trustworthy relation proposed by Coelho and Pinho [37]. According to this model, the pressure drop in the pipelines is associated with the average molar flowrate of gas inside the pipeline ${\overline{F}}_{h,u}$, the ambient temperature $T^{amb}$, length $L_u$ and cross-sectional area $A_u$ of the pipeline. The average molar flowrate is expressed in Equation (14). The coefficient on the right-hand side of Equation (15) is modified by units and pipe specifications used in this study.

$${\overline{F}}_{h,u}={\displaystyle \frac{F_{h,u}^{in}+F_{h,u}^{out}}{2}} \forall u\in LPL, h\in H$$

(14)

$$(P_{h,u}^{in}{)}^2-(P_{h,u}^{out}{)}^2=226.95·{\left({\overline{F}}_{h,u}\right)}^2·T^{avg}·L_u·{\displaystyle \frac{1}{A_u^5}} \forall u\in LPL, h\in H$$

(15)

Variables $P_{h,u}^{in}$ and $P_{h,u}^{out}$ are the pressure at the inlet and outlet of the pipeline, respectively.

The linepack is calculated by its initial linepack storage in addition to the accumulations in the period. In the first period, the initial linepack is approximated by the gas law under working conditions. In other periods, the initial linepack is equal to the linepack storage from the end of last period $I_{h-1,u}$. The change in accumulation in a period is calculated by the flowrate difference between inlet and outlet multiplied $\mathsf{\tau }$, the duration of the period. The relations are given below.

$$I_{h,u}={\displaystyle \frac{{\overline{p}}_{h,u}^{ini}{L}_u{A}_u}{R{T}^{amb}}}+\mathsf{\tau }·\left(F_{h,u}^{in}-F_{h,u}^{out}\right) \forall u\in LPL,h=H1$$

(16)

$$I_{h,u}=I_{h-1,u}+\mathsf{\tau }·\left(F_{h,u}^{in}-F_{h,u}^{out}\right) \forall u\in LPL,h\in H,h\ne H1$$

(17)

$${\overline{P}}_{h,u}={\displaystyle \frac{P_{h,u}^{in}+P_{h,u}^{out}}{2}} \forall u\in LPL, h\in H$$

(18)

where $A_u$ is the cross-sectional area of the pipeline, $L_u$ is the length of pipeline, $F_{h,u}^{in}$, and $F_{h,u}^{out}$ are the mass flowrate at the inlet and outlet of the pipeline, ${\overline{P}}_{h,u}$ is average pressure inside the pipeline, parameters $T^{amb}$ and ${\overline{p}}_{h,u}^{ini}$ are the ambient temperature and initial average pressure inside the pipeline.

Note that the variable linepack storage $I_{h,u}$ is the molar quantity at the end of the corresponding period. In the cases when the accumulation item is negative, it means the amount of extraction is greater than feed in this period.

The operating pressure of the pipeline is subjected to lower and upper bounds of pipeline configuration:

$${\overline{P}}_{h,u}^{min}\le {\overline{P}}_{h,u}\le {\overline{P}}_{h,u}^{max} \forall u\in LPL, h\in H$$

(19)

3.3. Natural Gas Treatment Model

The CO₂ in natural gas is removed to a certain level according to specifications from the fuel specifications of the downstream power plant. Removal of CO₂ is achieved using N-methyldiethanolamine (MDEA) as a solvent in an absorption column, as shown in Figure 2 (CO₂ removing process). MDEA is a tertiary amine which can absorb CO₂ by bicarbonate formation and can be easily regenerated [38]. After absorption, the purified gas is obtained, and the CO₂-rich solvent is transported into the regenerator for CO₂ stripping. The lean solvent gathered at the bottom of the column is then pumped back to the absorber [39]. A mass balance across the absorber, that is, the natural gas entering the absorber, equals the sum of purified gas and the CO₂ removed is given by Equation (20). The composition balance in an absorber is expressed in Equations (21) and (22). Binary variable $Y_{h,u,c}$ is used to indicate if the corresponding process is proceeding.

$$F_{h,u}=F_{h,u,u^{\prime }}+F_{h,u,c} \forall c={\mathrm{C}\mathrm{O}}_2,\forall u\in CRP, h\in H$$

(20)

$$y_{{h,u}^{\prime },u,c}{F}_{h,u}=F_{h,{u,u}^{\prime },c} \forall c={\mathrm{C}\mathrm{H}}_4,u\in CRP, h\in H$$

(21)

$$y_{h,u,u^{\prime },c}=Y_{h,u,c} \forall c={\mathrm{C}\mathrm{O}}_2,u\in CRP, h\in H$$

(22)

The CO₂ treatment process requires two forms of energy: electricity and heat. Electricity is consumed by the pumps to transport the regenerated solvent back into the absorber. Heat, provided by low-pressure steam, is consumed by the reboiler from the regenerator.

For electricity consumption, the relationship proposed by Mofarahi et al. [40] is used:

$$E_{h,u}={\displaystyle \frac{{∆p}_u{F}_{h,u}^{sol}}{3600{\gamma }^{sol}{\eta }_u}} \forall u\in CRP, h\in H$$

(23)

where parameter ${∆p}_u$, ${\gamma }^{sol}$, ${\eta }_u$ are the pressure drop from the regenerator to the absorber, molar density of the solvent, and pump efficiency, respectively. Variable $F_{h,u}^{sol}$, denoting the throughput of lean solvent is calculated in Equation (24). It is positively related to the amount of CO₂ removal $F_{h,u,\mathrm{c}\mathrm{o}2}$ and the absorbability of the solvent $\kappa$ [41].

$$F_{h,u}^{sol}=\kappa F_{h,u,c} \forall c={\mathrm{C}\mathrm{O}}_2,\forall u\in CRP, h\in H$$

(24)

The consumed heat $Q_{h,u}$ provided by low-pressure steam is made up of 3 parts, as given in Equation (25): the heat that raises the solvent temperature in the column $Q_{h,u}^{so}$, the heat of CO₂ absorbing reaction $Q_{h,u}^{ab}$, and the heat removed from the condenser $Q_{h,u}^{cd}$. Each of the 3 items on the right-hand side is given by Equations (26)–(28), respectively.

$$Q_{h,u}=Q_{h,u}^{cd}+Q_{h,u}^{ab}+Q_{h,u}^{so} \forall u\in CRP, h\in H$$

(25)

$$Q_{h,u}^{cd}={ϵ}^{reg}{\iota }^{reg}{F}_{h,u,c} \forall c={\mathrm{C}\mathrm{O}}_2,\forall u\in CRP, h\in H$$

(26)

$$Q_{h,u}^{ab}={\delta }^{reg}{F}_{h,u}^{\mathrm{C}\mathrm{O}2} \forall u\in CRP, h\in H$$

(27)

$$Q_{h,u}^{so}={\epsilon }^{sol}∆{\tau }^{reg}{F}_{h,u}^{sol} \forall u\in CRP, h\in H$$

(28)

where parameters ${ϵ}^{reg}$, ${\iota }^{reg}$, ${\delta }^{reg}$, ${\epsilon }^{sol}$, and $∆{\tau }^{reg}$ are the specific latent heat of the reflux stream from the condenser, the reflux ratio of the regenerator, the specific reaction heat of CO₂ desorption, the specific heat capacity of the solvent, and the solvent temperature that rose in the regenerator, respectively.

3.4. Compression Model

To offset the pressure-drop in pipeline transport and meet the pressure specifications of the downstream power plant, natural gas is compressed by a set of compressors. A set of mass balances and component constraints given by Equations (29) and (30) indicates that molar flowrate and composition of the streams do not change in the compression process.

$$F_{h,u}=F_{h,u,u^{\prime }} \forall u\in COM,\left(u,u^{\prime }\right)\in UC, h\in H$$

(29)

$$y_{{h,u}^{\prime },u,c}=y_{h,u,u^{″},c} \forall c\in C,u\in COM,\left(u,u″\right)\in UC,(u^{\prime },u)\in UC, h\in H$$

(30)

The pressure at the inlet of the compressors is given by Equation (31). The pressure at the outlet of the compressors presented in Equation (32) is calculated using compression ratio.

$$P_{h,u}^{in}=P_{h,u^{\prime }} \forall u\in COM,\left(u^{\prime },u\right)\in UC, h\in H$$

(31)

$$P_{h,u}^{in}{R}_{h,u}=P_{h,u}^{out} \forall u\in COM, h\in H$$

(32)

where $P_{h,u}^{in}$, $P_{h,u}^{out}$, and $R_{h,u}$ are the inlet and outlet pressure, and compression ratio, respectively.

For isentropic compression, isentropic efficiency is defined to calculate the practical enthalpy change. Hence, the required power is computed using Equation (33). A correlation developed by Moshfeghian [42], Equation (34), is used to calculate the isentropic exponent ${\theta }_u$ based on empirical correlations with parameter ${\phi }_u$ given. In Equation (33), ${\mathsf{\epsilon }}_c$ is the specific heat capacity of the individual components in the gas.

$$E_{h,u}={\displaystyle \frac{1}{{\eta }_{h,u}}}{\sum }_{c\in C}\left({\epsilon }_c{y}_{{h,u}^{\prime },u,c}{F}_{h,u}\right)\left[{\left(R_{h,u}\right)}^{{\displaystyle \frac{{\theta }_u-1}{{\theta }_u}}}-1\right] \forall u\in COM,(u^{\prime },u)\in UC, h\in H$$

(33)

$${\theta }_u=1.3-0.31\left({\phi }_u-0.55\right) \forall u\in COM$$

(34)

3.5. Power Plant Model

3.5.1. Gas Turbines

In a power plant, gas turbines are the essential equipment used to generate electric power. A gas turbine is a combustion engine that convert fuels to mechanical energy, which then drives a generator that produces the target product: electrical power. Gas turbine models have been formulated [43] in different aspects by a previous study, yet difficult to adapt to large-scale, multi period models. In this section, a hybrid gas turbine model is proposed to facilitate the adaptability while keeping a good degree of accuracy.

The hybrid gas turbine model is made up of first principal-based mass balance equations incorporated with process simulation-based data-driven equations. The mass balance equations are employed to cover the mass balance and composition control of flue gas, whereas the data-driven equations are employed to reveal the relationships between fuel consumption, the molar ratio of air to fuel, combustion pressure and output power.

Methane and air are drawn into the combustion chamber where full combustion occur. The molar mass balance is made across gas turbines. The mass balance of related substances, nitrogen, oxygen, water, and carbon dioxide at the process outlet are given in Equations (35)–(38).

$$F_{h,u,u^{\prime },c}=0.79F_{h,u}^{air} \forall c=N_2,u\in GTT,(u,u^{\prime })\in UC, h\in H$$

(35)

$$F_{h,u,u^{\prime },c}=0.21F_{h,u}^{air}-2y_{h,u}^{{CH}_4}{F}_{h,u^{\prime },u}, \forall c={\mathrm{O}}_2,\forall u\in GTT,\left(u^{\prime },u\right)\in UC,(u,u^{\prime })\in UC, h\in H$$

(36)

$$F_{h,u,u^{\prime },c}=2y_{h,u}^{{\mathrm{C}\mathrm{H}}_4}{F}_{h,u^{\prime },u} \forall c={\mathrm{H}}_2\mathrm{O},u\in GTT,\left(u^{\prime },u\right)\in UC,(u,u^{\prime })\in UC, h\in H$$

(37)

$$F_{h,u,u^{\prime },c}=F_{h,u^{\prime },u} \forall c={\mathrm{C}\mathrm{O}}_2\forall u\in GTT,\left(u^{\prime },u\right)\in UC,(u,u^{\prime })\in UC, h\in H$$

(38)

The composition of natural gas entering gas turbines is constrained in Equation (39) representing a gas specification made by power plants. This constraint has an impact on the middle stream gas treatment processes, that is, the level of CO₂ removal in the natural gas streams. The govern equation of workload of gas turbines is given in Equation (40).

$$y_{h,u,c}^{min}\le y_{h,u,c}\le 1 u\in GTT,\forall c={\mathrm{C}\mathrm{H}}_4, h\in H$$

(39)

$$F_{h,u}^{in,min}\le F_{h,u}^{in}\le F_{h,u}^{in,max} \forall u\in GTT, h\in H$$

(40)

The data-driven gas turbine model, as shown in Equation (41), is made to reflect the relationship between the output power $W_{h,u}$ and a set of variables including the inlet fuel flowrate ($F_{h,u}^{in}$), the molar ratio of air to fuel ($R^{air}$), percentage composition of CH₄ (denoted by $y^{\mathrm{C}\mathrm{H}4}$), and the pressure in the air compressor or the combustion chamber (denoted by $P^{ac}$). To obtain the explicit form of such a relationship, a rigorous model is built in Aspen Plus V8.8. The input data sets are imported within reasonable range for obtaining the desired output data sets. Then, all the data sets are used for fitting of the explicit gas turbine equation.

$$W_{h,u}=f\left(F_{h,u}^{in},R^{\mathrm{a}\mathrm{i}\mathrm{r}},y^{\mathrm{C}\mathrm{H}4},P^{ac}\right) \forall u\in GTT, h\in H$$

(41)

The process flowsheet diagram is shown in Figure 3. The fuel stream consists of CH₄ and CO₂ and is substituted with a mixture of pure CH₄ and CO₂. Air is drawn into the combustion chamber by the compressor, together with the natural gas stream, and is fed into a combustion chamber which is simulated with a Gibbs Reactor. The high temperature flue gas expands in a turbine, driving the turbine blade to work. In the rigorous model, the flow rate of CH₄ varies from 1230 to 1600 kmol/h. The discharge pressure from the compressor is 1.57 to 2.67 MPa, and the molar ratio of air to fuel is between 21.5 and 45 to the handling capacity. These boundary conditions can be adjusted according to the practical applications and gas turbine configurations. The efficiency of the compressors and gas turbines can be adapted according to specific operations and engine configurations. The air compressor and the turbine share the same shaft, so the net output power is the turbine output power subtracted by the compressor power consumption.

For the rigorous gas turbine model, the sensitivity analysis tool provided by Aspen Plus V8.8 is utilized to obtain data for model regression. The sensitivity analysis tool allows iteration of its calculation sequence through a range of values provided for one or more independent variables to obtain a specified result for a dependent variable. Therefore, $F_{h,u}^{in},R^{air},P^{ac}$ are chosen as independent variables, and $W_{h,u}$ as the dependent variable. The percentage of composition of methane $y^{\mathrm{C}\mathrm{H}4}$ is not introduced into the analysis because it can be controlled by varying the inlet molar flow of CH₄ and CO₂ individually. In the sensitivity analysis, the operational range for each independent variable is divided evenly by a number of points, thus specifying the iteration step length. The purpose is to solve all the combinations of each point from each individual variable. After a successful run of the simulation in Aspen Plus V8.8, 1166 entries of results data are acquired. We applied multivariate regression on data and obtained the explicit form of gas turbine model shown in Equation (42). To obtain a good prediction, a high-dimensional model is used to replace the linear regression. The difference between the simulation results and the predicted results is shown in Figure 4. It can be seen that the two value levels fit very well. Similarly, the heat rate of flue gas at the outlet of the gas turbine $V_{h,u}^{ex}$ is regressed and expressed in Equation (43).

$$W_{h,u}=11.591+0.101F_{h,u}^{in}{y}^{\mathrm{C}\mathrm{H}4}+0.250R^{air}+3.534{P^{ac}}^2-0.013F_{h,u}^{in}{y}^{\mathrm{C}\mathrm{H}4}{P}^{ac}-0.580R^{air}{P}^{ac} \forall u\in GTT, h\in H$$

(42)

$$V_{h,u}^{ex}=3600·\left(-53.2822+0.136F_{h,u}^{in}{y}^{CH4}+0.3208R^{air}+14.132P^{ac}\right) \forall u\in GTT, h\in H$$

(43)

3.5.2. Boilers

The boiler in a power plant absorbs heat from gas turbine flue gas to generate steam. The absorbed heat $Q_{h,u}$ is calculated by

$$Q_{h,u}=F_{h,u}{V}_{h,u\prime }^{ex} \forall u\in BOI,(u^{\prime },u)\in UC, h\in H$$

(44)

The modified boiler model from Shang and Kokossis [44] is represented in Equation (45). It reflects the relationship between the heat from gas turbine flue gas and the flowrate of evaporated steam.

$$\left[{\sigma }_u{F}_{h,u}^{steam,max}{Y}_{h,u}+\left(1+{\beta }_u\right)F_{h,u}^{steam}\right]\left[\left(1+{\lambda }_u\right){\epsilon }^{wat}\left({\tau }^{shs}-{\tau }^{wat}\right)+{ϵ}^{shs}+{\epsilon }^{ste}\left({\tau }^{ohs}-{\tau }^{shs}\right)\right]=Q_{h,u}-Q_{h,u}^{exh} \forall u\in BOI, h\in H$$

(45)

where parameters ${\sigma }_u$ and ${\beta }_u$ are regressed operational parameters, ${\lambda }_u$ is blowdown ratio of boiler, parameters ${\tau }^{wat}$, ${\tau }^{shs}$ and ${\tau }^{ohs}$ are temperatures of boiler feed water, saturated water and overheated high-pressure steam. Parameters ${\epsilon }^{wat}$, ${ϵ}^{shs}$, ${\epsilon }^{ste}$ are specific latent heat of water, specific heat capacity of high-pressure steam, specific heat capacity of water, respectively.

Along with evaporation, the exhaust heat from the boiler that is emitted to the surroundings is expressed by Equation (46).

$$Q_{h,u}^{exh}=\sum _c{F}_{h,u,c}{Cp}_{u,c}(T^{flu}-T^{amb}) \forall u\in BOI,c\in C, h\in H$$

(46)

To monitor the carbon emission accounting for greenhouse effect, CO₂ in the flue gas is brought up by

$$F_{h,u,c}=F_{h,u^{\prime },u} \forall c={\mathrm{C}\mathrm{O}}_2,\forall u\in BOI,\left(u^{\prime },u\right)\in UC, h\in H$$

(47)

The boiler operation load constraint is given by

$$F_{h,u}^{steam,min}{Y}_{h,u}\le F_{h,u}^{steam}\le F_{h,u}^{steam,max}{Y}_{h,u} \forall u\in BOI, h\in H$$

(48)

3.5.3. Steam Turbines

A steam turbine that utilizes the steam from the boiler is included in the optimization framework. A typical steam turbine model that is presented by Mavromatis and Kokossis [45] is widely used with a satisfactory performance. The relationship between power output and flowrate of steam input is expressed by Equation (49). The turbine load constraints are shown in Equation (50).

$${3600E}_{h,u}={\displaystyle \frac{6}{5}}{\displaystyle \frac{1}{{\beta }_u}}\left({ϵ}_u^{ise}-{\displaystyle \frac{{\sigma }_u}{F_u^{steam,max}}}\right)\left(F_{h,u}^{steam}-{\displaystyle \frac{1}{6}}{F}_u^{steam,max}{Y}_{h,u}\right) \forall u\in STT, h\in H$$

(49)

$$E_{h,u}^{min}{Y}_{h,u}\le E_{h,u}\le E_{h,u}^{max}{Y}_{h,u} \forall u\in STT, h\in H$$

(50)

where $E_{h,u}$ is the electricity produced from the stream turbine, ${ϵ}_u^{ise}$ is the specific isentropic enthalpy change in steam, $E_{h,u}^{min}$ and $E_{h,u}^{max}$ are the minimum and maximum load of the steam turbine, $Y_{h,u}$ is a binary variable denoting the operating status of the steam turbine, and ${\sigma }_u$ and ${\beta }_u$ are regression parameters.

4. MINLP Model Optimization of GtoP System Operation

This study employs three optimization frameworks: an economic optimization model aimed at maximizing profits; a cost-minimization model dedicated to a GtoP system located in rural areas, in which the linepack model is analyzed; and an operational feasibility model driven by supply-demand enhancement using linepack. The optimization framework is designed as a Mixed-Integer Nonlinear Programming (MINLP) model, which aims to find the optimal operational parameters for the gas-to-power (GtoP) system while considering various processes. The objective of maximizing profit is expressed in Equation (51). The first item inside the brackets on the right-hand side of Equation (51) is product income, the second item is the cost of raw natural gas, the third item is the cost of electricity purchased for the compressors and MDEA solvent transmission in CO₂ treatment processes, and the fourth item is the steam consumption costs for the CO₂ treatment processes. Parameter ζ is the unit price of power, gas, or steam. Parameter $\pi$ is other fixed costs.

$$Profit={\sum }_h\left[{\sum }_{u\in GTT\cup STT}\left({\zeta }^{pwr}{E}_{h,u}\right)-{\sum }_s\left({\zeta }^{NG}{F}_{h,s}^{NG}\right)-{\sum }_{u\in COM\cup CRP}\left({\zeta }^{pwr}{E}_{h,u}\right)-{\sum }_{u\in CRP}{\zeta }^{stm}{Q}_{h,u}\right]-\pi$$

(51)

The model includes the following sets of constraints to ensure the feasibility and accuracy of the solution:

• Gas Splitting, Processing, and Mixing Constraints (Equations (1)–(19)): these constraints ensure mass balance and proper flow rates for gas splitting, absorption, and mixing units in the upstream processes.
• Compression Process Constraints (Equations (20)–(25)): these constraints account for the pressure increase and energy consumption in the compression units. They include the isentropic efficiency of the compressors and pressure limits at the inlet and outlet.
• Pipeline Transmission and Linepack Process Constraints (Equations (26)–(34)): these constraints handle the flow of gas through the pipeline, pressure drops, and linepack. Linepack is treated as a periodical storage mechanism, allowing the system to balance supply and demand across different periods.
• Gas Turbine Process Constraints (Equations (35)–(40), (42) and (43)): these constraints define the operation of the gas turbines, ensuring that the generated power meets demand while respecting operational limits such as fuel consumption and turbine efficiency.
• Boiler and Steam Turbine Process Constraints (Equations (44)–(50)): these constraints cover the usage of steam in the power generation through steam turbines.

By incorporating these constraints, the MINLP model ensures that all critical processes in the GtoP system are represented accurately, enabling the determination of globally optimal operational variables. Thus, the optimal operational model can be summarized as a standard MINLP model with the following structure:

Max Objective function, Equation (51);

S.t. Constraints for gas splitting, processing, mixing processes, Equations (1)–(19);

Constraints for compression process, Equations (20)–(25);

Constraints for pipeline transmission and linepack process, Equations (26)–(34);

Constraints for gas turbine process, Equations (35)–(40), (42) and (43);

Constraints for boiler and steam turbine processes, Equations (44)–(50).

5. Case Study

In this section, three cases are studied to illustrate the performance of different operational strategies and their impacts on the GtoP system. The first case focuses on profit optimization, where the generated power can be uploaded to the grid and monetized, maximizing profit. The second case examines cost minimization in a rural GtoP system, where excess power is not favorable and cannot be monetized, emphasizing efficient resource use and minimal waste. The third case addresses a scenario with a surge in power demand, resulting in a shortfall in gas supply, demonstrating how linepack enhances feasibility by providing a buffer to manage supply and demand fluctuations effectively. These cases provide comprehensive insights into the versatility and effectiveness of linepack in various operational contexts.

5.1. Case Description

An industrial GtoP system located in Hainan Island, South China, is considered for application of the MINLP model and its solution approach. The flowsheet setup is a typical GtoP system, identical to the one shown in Figure 2. The system receives natural gas from two sources, each providing gas with different levels of methane content. The power plant is connected to the external grid, allowing the generated power to be output for profit. The downstream power demands must be sufficiently met in all periods. The objective is to optimize the total profit of the GtoP system. The conditions of gas from the two sources are listed in

Table 2. Condition of natural gas from gas sources.

Items		Source 1			Source 2
		H1	H2	H3	H1	H2	H3
Upper bound (kmol/h)		4500	4500	4500	3000	3000	3000
Composition	CH4	0.74	0.74	0.74	0.68	0.68	0.68
	CO2	0.26	0.26	0.26	0.32	0.32	0.32
Pressure (MPa)		1.48	1.52	1.43	1.48	1.52	1.43
Price of natural gas (USD/kmol)		4.50	4.50	4.50	3.82	3.82	3.82

. The gas is transmitted through three long pipelines to three individual power plants. The configuration details of the pipelines are provided in

Table 3. Pipeline configuration.

	Pipeline 1	Pipeline 2	Pipeline 3
Diameter of pipeline (m)	0.35	0.37	0.39
Length of pipeline (km)	120	100	80

. Each power plant is contracted to a customer with specific power demands. Note that the power price changes over time, and the minimum power demands also vary in different periods. The upper bounds of power generation in the power plants are constrained by the limited gas feed available to the system.

Table 4. Price and minimum power demand for downstream customers.

Items	H1	H2	H3
Power price (USD/MW·h)	120	132	144
Customer 1 (MW)	105	152	110
Customer 2 (MW)	100	152	115
Customer 3 (MW)	100	142	112

gives the specific power demands of customers and the price plan of market electricity. The price of natural gas and electricity in the example is extracted from the energy market of South China. Additionally, in the power plants, the overheated high-pressure steam operates at a temperature of 425 °C and a pressure of 4.5 MPa. The fixed cost is adjusted as necessary to reflect any changes in operational requirements or market conditions.

5.2. Optimization Framework Application

The workflow for solving the MINLP model is illustrated in Figure 5, consisting of seven steps. Data collection includes market data and process parameters, either provided or extracted from online documents or simulations. The MINLP model, formulated to handle both discrete and continuous decision variables, is coded in GAMS 24.4.6, a versatile algebraic modeling platform for mathematical programming [46]. The computational capabilities and challenges of solving MINLP models are addressed using insights from Bussieck and Pruessner [47]. The global solver BARON [34], known for its polyhedral branch-and-cut algorithm, is employed to solve the MINLP model and obtain optimal results related to the specific objectives [33]. The framework builds on the foundational principles of MINLP described by Floudas [48]. Finally, the solution results are analyzed for decision-making and provide actionable insights.

According to the power demand listed in Table 4, a constraint has been placed for each of the three power plants. To insert these constraints into the model, the first item in objective function Equation (51) is adjusted as follows. To define the power production in each power plant by ${E1}_h$, ${E2}_h$, and ${E3}_h$, a set of constraints for power production in each plant are listed:

$$a_h\ge {E1}_h\ge b_h \forall h\in H$$

(52)

$$a_h\ge {E2}_h\ge b_h \forall h\in H$$

(53)

$$a_h\ge {E3}_h\ge b_h \forall h\in H$$

(54)

In which,

$${E1}_h={\sum }_{u\in GTT1\cup STT1}\left(E_{h,u}\right) \forall h\in H$$

(55)

$${E2}_h={\sum }_{u\in GTT2\cup STT2}\left(E_{h,u}\right) \forall h\in H$$

(56)

$${E3}_h={\sum }_{u\in GTT3\cup STT3}\left(E_{h,u}\right) \forall h\in H$$

(57)

Parameters $a_h$ and $b_h$ are the lower and upper bounds of power demand.

The objective function for this case is presented as follows:

$$Profit=\sum _h\left[{\zeta }^{sale}({E1}_h+{E2}_h{+E3}_h)-{\sum }_s\left({\zeta }^{NG}{F}_{h,s}^{NG}\right)-\sum _{u\in COM\cup CRP}\left({\zeta }^{prch}{E}_{h,u}\right)-\sum _{u\in CRP}{\zeta }^{stm}{Q}_{h,u}\right]$$

(58)

By adapting this case to the developed model, the objective function has been reformulated as Equation (58), while the rest of the constraints remain unchanged. Thus, the MINLP model is summarized as

max Objective function, Equation (58);

s.t. Equations (1)–(40), (42)–(50) and (52)–(57).

The MINLP model is solved using the global optimization solver BARON 16.3.4 [33] in GAMS 24.4.6 [46] on a Dell XPS desktop PC (Dell Inc., Round Rock, TX, USA) equipped with an Intel^® Core (TM) i7-7700CPU 3.60 GHz Desktop PC with 64 bit/MS Windows 10 environment. The computational time is 274.85 s wall clock time, and the global optimization result is obtained.

5.3. Computational Results and Discussion

5.3.1. Profit Maximization

As described in Section 5.1, a profit-driven scenario is examined in this analysis. The aim is to determine the power generation for each period at each power plant and to assess the difference in profit between the original and optimized operations. Importantly, the original operation does not account for the proposed linepack model, which is integrated into the optimized operation. The other conditions for both operations remain the same.

The results of the economic optimization are presented in

Table 5. Economic optimization result.

	Original Operation (105 USD)	Optimized Operation (105 USD)
Total profit	137.51	149.37
Power income	304.77	328.18
Cost
Raw gas cost	148.65	159.82
Power cost	14.44	14.96
Steam cost	4.17	4.03
Total cost	167.26	178.81

. The optimized operation yields an 8.62% increase in total profit. This improvement is primarily due to increased power income. However, the optimization also results in higher gas consumption, leading to increased operational costs. These costs include power consumption for compression, steam, and power costs for CO₂ removal process.

The solution results are depicted in Figure 6 and Figure 7a,b, highlighting the status of power generation and the material flow pattern. Figure 6 shows that both the original and optimized operations sufficiently provided power for the downstream users. In the meantime, the power generation varies between the original and optimized operations across the three power plants during each period. In the optimized operation, during the third period, Plants 2 and 3 generated more power due to higher power sale prices, resulting in increased profit. Consequently, more gas was consumed in Plants 2 and 3, leading to reduced gas availability for Plant 1 and resulting in lower power generation.

Figure 7a,b illustrates the material flow pattern in each system, demonstrating that increased production correlates with a larger material feed. The cost differences include a larger gas feed (by 7.03%), increased water usage (by 7.70%), and higher flue gas generation (by 7.35%). Conversely, CO₂ removal decreased (by 2.80%) because the optimized operation directs the gas to unit CRP2, which has higher energy efficiency. In this scenario, the optimized operation achieves better profitability and improved power supply performance at a slightly higher cost. This enhanced profitability and efficiency make the optimized operation more attractive for profit-driven scenarios.

5.3.2. Cost Minimization Model

In regions with less developed infrastructure, particularly rural areas, excess power generated cannot be uploaded to the grid and therefore cannot be monetized, emphasizing efficient use of resources. In this scenario, the objective is to minimize costs including costs of natural gas consumption, costs of power for compressors and solvent pump, costs for steam consumption, and fixed cost, while fulfilling the power demand from users. Thus, the objective of minimizing cost is expressed in Equation (59).

$$Cost={\sum }_h\left[{\sum }_s\left({\zeta }^{NG}{F}_{h,s}^{NG}\right)+{\sum }_{u\in COM\cup CRP}\left({\zeta }^{pwr}{E}_{h,u}\right)+{\sum }_{u\in CRP}{\zeta }^{stm}{Q}_{h,u}\right]+\pi$$

(59)

The optimal operational model is formulated as a minimization problem, subjected to the following constraints:

min Objective function, Equation (59);

s.t. Constraints for gas splitting, processing, mixing processes, Equations (1)–(19);

Constraints for compression process, Equations (20)–(25);

Constraints for pipeline transmission and linepack process, Equations (26)–(34);

Constraints for gas turbine process, Equations (35)–(40), (42) and (43);

Constraints for boiler and steam turbine processes, Equations (44)–(50);

Constraints for power generation capacity in each power plant, Equations (52)–(57).

The methodology for solving this model adapts the constraints from the first case while maintaining consistent system parameters. The optimization results, compared to the original operational parameters derived from the gas-to-power (GtoP) system in the South China Sea, are detailed in

Table 6. Computational results comparison for original and optimized operation.

Case Types	Original Operation				Optimized Operation
Periods	H1	H2	H3	Sum	H1	H2	H3	Sum
Total cost (106 USD)	5.8667	5.859	5.8887	17.6146	3.3353	5.2449	3.7749	12.3552
NG cost 106 USD	5.2416	5.2416	5.2416	15.7248	3.0198	4.6929	3.3919	11.1047
Power cost 106 USD	0.4798	0.4721	0.5018	1.4538	0.1901	0.3950	0.2468	0.8320
Steam cost	0.1453	0.1453	0.1453	0.4360	0.1254	0.1570	0.1362	0.4185
Power output MW	333	448	358	1139	305	446	337	1088
Stream flowrate
Terminal1 kmol/h	3500	3500	3500	10,500		1963	242	2205
Terminal2 kmol/h	4000	4000	4000	12,000	4706	5000	5000	14,706
Sum				22,500				16,911
CO2 emission	759	759	759	2278	655	820	712	2187
De-C heat demand MW	3.01	3.01	3.01	9.04	2.60	3.25	2.82	8.68
De-C lean solvent flow t/h	9114	9114	9114	27,342	7862	9845	8538	26,246
Compressor power MWh	17.25	16.87	18.34	52.45	3.78	12.51	6.10	22.40
Linepack1 kmol	9634	9634	9634	28,901	7996	9792	8175	25,963
Linepack2 kmol	8972	8972	8972	26,915	6685	8050	7057	21,792
Linepack3 kmol	7974	7974	7974	23,923	5546	6233	5733	17,512
Pipeline1 pressure in	2.59	2.92	2.59		2.12	2.87	2.19
Pipeline2 pressure in	2.59	2.56	2.59		1.78	2.39	1.95
Pipeline3 pressure in	2.59	2.44	2.59		1.58	1.93	1.68
Pipeline1 pressure out	1.41	1.08	1.41		1.20	1.20	1.20
Pipeline2 pressure out	1.41	1.44	1.41		1.20	1.20	1.20
Pipeline3 pressure out	1.41	1.56	1.41		1.20	1.20	1.20
Air into Gas turbine1	41,344	51,803	41,344	134,490	26,082	38,601	27,414	92,096
Air into Gas turbine2	52,040	50,761	52,040	154,840	24,744	38,595	28,739	92,078
Air into Gas turbine3	66,366	57,187	66,366	189,919	24,748	35,935	27,944	88,627
NG into GT1 kmol/h	1744	2186	1744	5675	1411	2088	1483	4982
NG into GT2 kmol/h	2196	2142	2196	6533	1339	2088	1555	4981
NG into GT3 kmol/h	2800	2413	2800	8013	1339	1944	1512	4794
Sum				20,222				14,757
GT1 exhaust heat MW	188	210	182	581	135	201	142	479
GT2 exhaust heat MW	246	202	229	677	128	201	149	479
GT3 exhaust heat MW	314	233	309	856	128	187	145	460
Sum				2114				1418
Air fuel ratio for GT	30	30	30		23.4	23.4	23.4
Boiler1 steam exit MW	29	36	29	93	18	27	19	65
Boiler2 steam exit MW	239	35	223	497	17	27	20	65
Boiler3 steam exit MW	307	226	302	836	17	25	20	62
Sum				1426				192
Steam into ST1 kmol/h	8116	8882	7777	24,776	5847	8865	6168	20,881
Steam into ST2 kmol/h	30	8490	30	8550	5524	8864	6488	20,876
Steam into ST3 kmol/h	37	37	37	111	5525	8223	6296	20,044

. The optimization result shows that the total annual cost (TAC) for total-site operation was reduced by 29.8%, primarily due to significant savings in natural gas feed and energy consumption, which includes both power and steam. It is important to note, however, that the power output was also decreased. This adjustment was intentional within the optimization framework, designed to ensure an adequate power supply for downstream users. Nonetheless, the total profit from the optimized operation was lower compared to the original setup. This discrepancy arises because surplus power generation contributed additional profit when fed back into the grid. Such profits are contingent on the presence of advanced energy infrastructure capable of accommodating grid uploads, which, in this case, is neither feasible nor profitable.

As detailed in Table 6, the optimized operation opted for the utilization of less expensive gas from Terminal 2 over the pricier option from Terminal 1. This decision is directly influenced by the current price differential between the two gas grades, indicating that processing lower-grade gas incurs lower costs than utilizing higher-grade alternatives. However, this strategy is highly dependent on the fluctuating gas price landscape and can only be effectively determined through this simulation model, which aids in informed decision-making.

The reduced consumption of natural gas not only lowers the cost associated with the gas itself but also leads to decreased power consumption of compressors and operational pressures in pipelines. Consequently, the air–fuel ratio (AFR) was adjusted to match the Gas Turbine’s (GT) nominal parameters. From an energy perspective, there was a notable reduction in the heat content of the exhaust from the GT. Despite the hot exhaust being routed to a boiler and subsequently to a steam turbine, the steam produced by the boiler is limited. Consequently, the exiting steam from the gas turbine still retains high temperatures, representing a loss of potential energy without further utilization.

Overall, in the cost minimization model, the optimized operation facilitates a substantial cost saving of up to 29.8% of the total operational costs, reducing 24.8% of the total natural gas feed. This optimization not only contributes to a 4.0% reduction in carbon emissions but also promotes more efficient energy use and minimizes energy wastage, all while satisfying the requirements of downstream customers.

5.3.3. Linepack Analysis

The linepack in a pipeline, which represents the accumulation of gas within the system, is determined by the inlet and outlet flow rates during a given period. Specifically, when the inlet flow exceeds the outlet flow over a particular period, there is an increase in the stored gas volume. Conversely, if the inlet flow is less than the outlet flow, gas is withdrawn from the linepack, resulting in a reduction in the stored volume compared to its initial state. In this section, the linepack status are compared between models “with-” and “without-linepack” from the case in Section 5.3.2. The linepack data are extracted from the optimization result and shown in

Table 7. Model results for case study.

Items		With Linepack			Without Linepack
		Period 1	Period 2	Period 3	Period 1	Period 2	Period 3
Pipeline 1	Start linepack [kmol]	9634	7996	9792	9634	9634	9634
	End linepack [kmol]	7996 (−)	9792 (+)	8175 (−)	9634 (=)	9634 (=)	9634 (=)
	Flow in [kmol/h]	1401	2099	1473	1744	2186	1744
	Flow out [kmol/h]	1411	2088	1483	1744	2186	1744
Pipeline 2	Start linepack [kmol]	8972	6685	8050	8972	8972	8972
	End linepack [kmol]	6685 (−)	8050 (+)	7057 (−)	8972 (=)	8972 (=)	8972 (=)
	Flow in [kmol/h]	1325	2096	1549	2196	2142	2196
	Flow out [kmol/h]	1339	2088	1555	2196	2142	2196
Pipeline 3	Start linepack [kmol]	7974	5546	6233	7974	7974	7974
	End linepack [kmol]	5546 (−)	6233 (+)	5733 (−)	7974 (=)	7974 (=)	7974 (=)
	Flow in [kmol/h]	1324	1948	1509	2800	2413	2800
	Flow out [kmol/h]	1339	1944	1512	2800	2413	2800
Sum of start linepack in 3 pipelines [kmol]		26,580	20,227	24,075
Sum of end linepack in 3 piples [kmol]		20,227 (−)	24,075 (+)	20,965 (−)
Natural gas cost (106 USD)			11.10			15.72
Gas treating cost (105 USD)			7.99			8.32
Compression cost (105 USD)			4.51			10.57
Total cost (106 USD)			12.35			17.61

. The resultant linepack for each period is annotated with the symbols (‘+’), (‘−’), or (‘=’), indicating whether the linepack has increased, decreased, or remained constant, respectively. This notation provides a clear, at-a-glance indication of changes in linepack across different periods. For models that do not incorporate linepack dynamics, the linepack data refers simply to the quantity of gas that the pipelines contain, which remains unchanged across different periods. In contrast, for models that do consider linepack, changes in the linepack are clearly marked. An increase (‘+’) in the linepack indicates that more gas was stored during the period, reflecting a scenario where the inlet flow rate was greater than the outlet flow rate, and vice versa. During the first period, all three pipelines report increased linepacks. The second and third periods show a decrease (‘−’) followed by an increase (‘+’) in linepacks, respectively. This fluctuation suggests strategic gas storage during the first and third periods when gas prices were lower, and a release of gas during the second period when prices peaked. According to the “Sum of End Linepack” presented in Table 6, the three pipelines exhibit a consistent pattern of storing and releasing gas in response to price fluctuations, aiming at minimizing total cost in operational strategies. This behavior underscores the utility of adjusting linepack levels to enhance financial outcomes by capitalizing on variations in gas prices.

The introduced linepack modeling feature facilitates reduced costs by synchronizing gas throughput to power plants with fluctuating market gas prices. This is particularly advantageous in profit-driven scenarios in rural areas lacking a power grid connection for uploading.

5.3.4. Supply–Demand-Driven Scenario: Operational Feasibility Enhanced by Linepack

Compared to onshore operations, offshore gas production presents enhanced stability challenges. This instability stems primarily from the complex maintenance requirements of floating rigs and other essential platforms, demanding work shifts, and stringent material supply constraints. Nonetheless, it is imperative to ensure a reliable power supply to maintain uninterrupted operations for power users. One potential solution to address these challenges is the strategic utilization of extensive pipeline storage. In this scenario, consider an announced increase in power demand from downstream power users, while gas feed conditions remain constant. The focus of this analysis is to assess whether the linepack—the amount of gas stored within the pipeline under pressure—can contribute to operational feasibility while ensuring a stable power supply. Typically, when faced with increased demand, deficiencies might be mitigated through alternative sources such as LNG transported by cargo ships or natural gas from other terminals. However, these alternatives do not diminish the critical role of linepack in demand regulation. Therefore, this study exclusively investigates the impact of linepack on maintaining supply stability. The objective function used is the same as that for profit maximization, as maximizing profit under strict power demand constraints inherently ensures the feasibility of the operation.

Table 8. Original gas feed and increased power demand.

Items	H1	H2	H3
Maximum gas feed in terminal 1 (kmol/h)	3500	3500	3500
Maximum gas feed in terminal 2 (kmol/h)	2500	2500	2500
Power price (USD/MW·h)	139	105	182
Customer 1 (MW)	155~183	132~155	170~181
Customer 2 (MW)	162~175	130~155	170~188
Customer 3 (MW)	162~180	135~163	172~188

outlines the revised power demands for the three plants involved.

The results show that the “with-linepack” MINLP model is solved, but the without-linepack model quickly returned infeasible. The economic results are extracted and shown in Figure 8. The linepack results are presented in Figure 9, where the linepacks in all the pipelines are summed up and denoted as “gas inventory” to reveal the overall trend in the whole system. As the power demand is higher in the first and third periods, and lower in the second period, the gas inventory shows an opposite trend in response. In other words, gas is stored in low-demand periods and released in high-demand periods. Meanwhile, in the model without linepack, the high-power demand constraint in the second period rendered the model infeasible due to insufficient gas feed.

This scenario highlighted the potential of linepack to address supply–demand challenges in the GtoP system.

Linepack offers a less complex solution compared to alternatives such as LNG cargo ships and trucks. Within the adjustable range, linepack scheduling can be considered a primary strategy for managing gas shortages or surges in power demand, providing more flexible and resilient operational planning. The use of linepack as a primary strategy in GtoP systems not only simplifies logistical operations but also reduces the dependency on external gas storage and transportation infrastructure. By utilizing the existing pipeline network, linepack enhances the system’s ability to quickly respond to fluctuations in gas supply and power demand. This adaptability is crucial for maintaining operational efficiency and meeting regulatory requirements in dynamic energy markets.

6. Conclusions

A framework for an offshore gas to power (GtoP) system is developed to establish an intuitive connection between the upstream gas source and the downstream power users. This framework is designed to mitigate the challenges in offshore operations under regulatory aspects, as well as providing insights for future offshore power sector planning. The proposed non-convex MINLP optimization framework integrates gas treatment, compression, pipeline transmission, and power generation. The mathematical model is implemented and solved in GAMS environment.

This study provides a detailed analysis of three scenarios, showcasing how the presented model can enhance system resilience, economic efficiency, and environmental sustainability. In addition, a novel approach to optimize GtoP systems by incorporating the concept of linepack is introduced. In addition, it is shown that linepack can effectively manage supply and demand fluctuations, particularly in scenarios with variable power demands and limited gas supply, highlighting the importance of considering linepack in the design and operation of GtoP systems, offering valuable insights for future research and practical applications.

The optimization framework proposed in this study effectively addresses the systematic challenges of gas-to-power systems by integrating gas mixing, processing, transportation, and power generation into a unified model. Its modular and flexible design ensures broad applicability to offshore natural gas systems. By adjusting parameters such as pipeline length, diameter, and gas composition, the framework can be scaled to accommodate networks of different sizes. The inclusion of binary variables in the superstructure allows for flexible configurations, enabling the selection or exclusion of processes based on specific network layouts. Furthermore, the objective function can be tailored to prioritize diverse operational goals, such as minimizing emissions, reducing costs, or maximizing economic returns, as demonstrated in the case studies.

This adaptability extends the framework’s relevance beyond the specific case study presented, allowing it to optimize operations across various scenarios. The incorporation of Linepack dynamics provides a distinctive advantage in managing supply–demand fluctuations, ensuring both operational stability and economic efficiency. These features establish the framework as a valuable tool for advancing energy system design, planning, and sustainability.

The GtoP system model represents an improvement in the integration of processes and networks. Developing new offshore energy and infrastructure projects requires a systematic framework that can contribute to their operability and feasibility, including sizing and optimizing offshore pipeline networks, and evaluating potential profitability. For existing systems, the GtoP model can be employed to minimize inconsistencies among individual unit operations and transmission networks. With the growing potential of offshore gas, a systematic operational GtoP model serves as a flexible and robust optimization tool to improve overall performance.