Authority-enterprise Equilibrium Based Subsidy Policy for Natural Gas Hydrate Transportation Technology

. The continued rise in oil prices and environmental concerns have made natural gas (NG) one of the world’s most important energy sources. As populations and economies grow, the demand for natural gas is increasing due to the expansion of the industrial and commercial sectors, as well as increased household incomes. The potential for signiﬁcant increases in natural gas supply to meet growing demand makes decisions at all strategic, tactical and operational levels necessary in building new or restructuring existing natural gas transportation systems. In this paper, the multi-objective optimization of natural gas hydrate (NGH) transportation is proposed as a tool for supporting regulatory decisions. Three objective functions are involved in the formulation of the problem: minimization of subsidy costs, maximization of energy utilization, and maximization of proﬁt for each NGH plant. As part of the design parameters for the NGH project, the regulatory agency must consider the entrepreneur’s return on investment and the needs of current and future consumers. In the absence of an optimization tool, this problem may result in unfair gas prices or a lack of investor interest. With a continuous increase in natural gas consumption, the proposed analysis examines growing markets. The mixed subsidy mechanism was applied to a typical example in order to demonstrate the performance of the proposed approach.

neutrality by 2060." [3]. For carbon neutrality to be achieved and for peak carbon dioxide emissions to be reached, energy efficiency and emission reduction will be essential [4], as well as fundamental changes to the method of development, and energy companies must transform through active innovation in the future [5]. China's energy structure is dominated by high-carbon fossil energy, with fossil energy accounting for about 85% [6]. It is necessary to transform the energy structure based on fossil fuels to reduce carbon emissions. Among them, traditional energy companies are most directly affected. The vigorous development of low-carbon energy to replace traditional fossil energy has become the road to the business transformation of energy companies. But since the current configuration of new energy sources cannot meet sustainable development, natural gas, as the cleanest fossil energy, will be an important bridge fuel in the coming decades [7].
Projections from the U.S. Energy Information Administration indicate that the trend of natural gas playing a dominant role in the U.S. energy mix will continue for the foreseeable future [8]. The International Energy Outlook 2021 report predicts that world natural gas use will remain above 20% from 2020 to 2050. Based on the growing demand for natural gas, there is a need to reduce energy consumption by improving the energy utilization efficiency of natural gas. The increase of the utilization of natural gas requires the planning, design, and construction of an entire system to transport the gas [9]. Generally, the natural gas transportation industry is regulated by governmental agencies as a result of its natural monopoly [10]. Current commercial natural gas transportation technologies are mainly pipeline, liquefaction and compressed natural gas [11]. Natural gas hydrate technology is a promising mode of natural gas transportation due to its mild production and storage conditions and cost advantages over liquefied and compressed natural gas [12]. Pipeline natural gas (PNG), liquefied natural gas (LNG) and compressed natural gas (CNG) are already well-established modes of natural gas transportation. Adsorbed natural gas (ANG) and natural gas hydrates (NGH) have been commercially practiced or demonstrated, but are not used on a large scale.
Regarding the optimization of LNG plants, various process enhancements have been proposed by researchers [13]. In the case of PNG, most studies consider the integration with other energy systems, such as integrated electrical-gas systems (IEGSs) [14], among others. Of course, the deployment of natural gas pipelines, the installation of compressor stations [15], etc. is also considered by many researchers for optimization. The development of natural gas transportation can be promoted not only through technical aspects, but also through policies, such as coordination of electric power and natural gas transmission systems, subsidies for the construction of natural gas transportation infrastructure [16], and inventory control policy for liquefied natural gas [17]. The exploration of technical aspects of NGH enhancement is the most popular among the previous studies. There have been many technical and economic analyses of NGH as a natural gas transportation mode [18], along with cost comparisons between NGH and LNG [19], but there are few policy incentives to encourage the development of NGH technology. The development of PNG and LNG relies on sound government policies to promote them, yet governments lack incentives for emerging natural gas transportation technologies. Therefore, this paper considers the optimal policy incentives in order to promote the adoption of NGH technology in a balanced situation between natural gas companies and the government. This paper consists of four parts. In Section 2, a multi-objective bi-level model for the NGH production and transportation problem based on the hybrid mechanism is developed. Then describes the optimization method based on constraint transformation. Section 3 presents the application in the South Pars offshore gas field in the south of Iran to explore the best results. Finally, the main contributions of this paper are presented in Section 4.

Modeling
Due to the rapid growth of natural gas demand, the optimization of natural gas pipelines in China is decided by the National Development and Reform Commission, while the optimization of non-pipeline natural gas transportation needs to be considered by researchers. Therefore, promoting the development of gas hydrate technology through subsidy policies is an effective way to optimize the natural gas transportation system. In this process, as shown in figure 1, gas hydrate plants will consider how much NGH to produce to transport natural gas. The government incentivizes NGH plants to produce more NGH through subsidies to promote more efficient use of natural gas. The transportation of natural gas will affect the stable operation of the energy system. Therefore, there is a need to ensure increased production of natural gas hydrates. However, the large-scale production of NGH also requires more investment in R&D, which cannot be ignored. Therefore, it is necessary to consider maximizing the benefits of NGH plants as much as possible. Also, the government wants to incentivize the transportation of natural gas at a lower cost, so minimizing the subsidy cost is also the goal of this paper. For the complex NGH production and transportation decision-planning problem, a hybrid mechanism based on direct production subsidy and indirect tax reduction is proposed to guide better decisionmaking and scheduling in the modelling process.

Assumptions and notations
To reduce complexity and simplify the model formulation, some simplifying assumptions are given for the NGH production transport problem: (1) the composition of the feed natural gas (mole fraction) is stable; and (2) the gas flow rate remains constant during an operating cycle [20]. Table 1 shows the mathematical notation used in the proposed model.

Upper Model
Clean energy utilization and economic benefit are two goals of the regional authority in promoting sustainable environmental-socio-economic development. Because of the high cost of the NGH process, local authorities use a hybrid mechanism combining unit extraction subsidies and tax rate reductions to incentivize NGH plants to increase their gas utilization Subsidy for a NGH unit determined by the regional authority; δ tax Tax rate for the NGH plants determined by the regional authority; Q ngh i NGH production and transportation quantity at plant i determined by the NGH plant; efficiency. Also since the government is responsible for socio-economic development, the total cost of encouraging NGH use needs to be considered.
(1) Objectives Maximize energy utilization feasibility. Natural gas is an important clean energy source due to its high demand, but the actual utilization efficiency needs to be improved due to the constraints of production and transportation. Therefore, improving the utilization feasibility of this green energy source is also a goal of local authorities. The utilization efficiency of NGH plants can be expressed as , where is the NGH capacity of NGH plant i. Indeed, an effective subsidy strategy should also maximize the minimum energy use feasibility of each NGH plant in Eq. (1), which depends on the production behaviour of each plant.
Minimize cost for NGH subsidy. Local authorities seek to promote NGH utilization by developing a hybrid subsidy policy that directly combines subsidies and tax breaks. NGH plants receive a subsidy fee from the authority and are assigned a tax rate based on the amount of NGH produced, with total tax revenue of δ tax P ngh i Q ngh i . Accordingly, NGH production subsidy costs can be expressed as the margin between the direct subsidy fee and the tax credit, as shown in Eq. (2).
(2) Constrains Direct subsidy fee assurance. The per-unit NGH subsidy fee can be considered as a special revenue for local authorities to encourage greater production volumes. Therefore, when controlling total input costs, it is also necessary that this basic subsidy be guaranteed, as shown in Eq. (3).
Tax reduction assurance of unit NGH utilization. Direct subsidy fees can relieve some pressure on NGH plants, but blended gas purification technology and transportation costs pose significant challenges in increasing NGH production. Therefore, the regional authorities need to ensure that the tax on NGH units does not exceed the maximum unit tax price that firms can afford, as shown in Eq. (4).

Lower Model
The lower-level decision-makers are NGH plants. Since NGH production and transportation decisions directly determine the amount of NGH utilized, they have a significant impact on final profits, environmental protection and socio-economic development. Based on the subsidy policies and physical constraints of local authorities, NGH plants seek to reduce their total costs and derive greater profits from their optimal transportation planning.
(1) Objectives Maximize profit for each NGH plant. Each NGH plant is independent and seeks the maximum profit possible under the subsidy and tax rate policies implemented by local authorities. Market-based NGH plants are focused on maximizing profit from NGH production and sales. From these, the profit at each NGH plant is as shown in Eq. (5).
(2) Constrains NGH production quantity limits. While companies make use of the hybrid mechanism provided by the authorities to maximize profits, NGH production is constrained by physical conditions. In order to support normal operations, each plant cannot produce less NGH than the base requirement. Since NGH production is constrained by natural gas capacity, the final seam production should not be greater than the maximum seam reserves. The NGH production is shown in the Eq. (6).
Costs constraints. During the NGH production decision process, total costs should also be considered because they directly affect profit. The cost limitations are as expressed in Eq. . 5

Global Model
The global model shown in Eq. (8) can be obtained by sorting Eq. (1)-Eq. (7). This paper summarizes the three objectives of maximizing energy utilization, minimizing costs and maximizing benefits. However, these three objectives are not necessarily extreme at the same time, so this model is based on the equilibrium principle to balance these two objectives. A compromise can be found for the conflict between regional authorities and NGH plants by adjusting the performance of decision-makers in both layers. The authorities strive to develop a suitable hybrid funding mechanism to achieve both the energy use objective Eq. (1) and the financial cost minimization objective Eq. (2). For the local authorities, the realistic limitations of Eqs. (3)-(4) and the production and transportation options identified by the NGH plant are introduced into the final blended subsidy policy. Then, based on this predetermined strategy, the NGH plant designs a feasible NGH production and transportation plan. Thus, there is an interaction between the local authorities and the NGH plant, with the latter trying to achieve the profit maximization Eq. (5) by increasing revenues, seeking additional subsidies from the authorities, or reducing costs. The practical constraints in Eqs. (6)- (7) should also be considered when developing a suitable production program. In summary, the global model is presented as follows:

Model Solving Approach
The global model Eq. (8) established in Eq. (1)-Eq. (7) is a complex, multi-objective, bilevel programming problem that reflects the inherent relationship between local authorities and NGH plants in the NGH production and transportation process. As highlighted in many past studies, the multi-objective problem is difficult to solve due to the different dimensions of the objective function [22]. To ensure sustainable economic and energy use, local governments can adjust the NGH utilization rate to the appropriate range. As in the study by Zeng et al. [23], this paper will be set to the attitude of regional authorities towards improving energy utilization; thus, the objective Eq. (1) can be converted to the the constraint min Although this is a single-objective planning problem and the equation is complex. Using existing mathematical algorithms, the KKT-approach is introduced to solve the equation [24].

Case Study
In this section, the South Pars offshore gas field in the south of Iran is used to verify the validity and operability of the proposed model.

Case Representation and Data Collection
In this paper, four markets from Iran are selected and four NGH plants are considered [20]. Table 2 shows the natural gas systems and their hydrate structures of each NGH plant [25]. Table 3 shows the distances between these NGH plants and markets. The cost are shown in table 4.

Results and Discussion
Increasing NGH productivity significantly affects the performance of local governments, which in turn affects the decision on the hybrid subsidy mechanism. In order to improve the validity and reliability of the results, different situations in which the parameters change were analyzed. The optimization results associated with different decision makers' attitudes (strategy parameter β) were identified as follows. Table 5 shows the optimal response of each NGH plant and the optimal decision β of the local authorities when the β changes. to control financial costs, the local authorities tend to lower the tax rate first to promote greater production at each NGH plant. In turn, plants try to adjust their operating plans to influence the performance of the local authorities and to obtain greater financial incentives to achieve their profit maximization goals. When β= 0, the local authorities have a very lenient energy use policy, which means that the subsidy intensity is also small. In this case, the operating costs of the four NGH plants are very high, which directly leads to lower profits. As the energy utilization target increases (β from 0 to 0.05, 0.1, 0.15 and 0.2), the authorities need to increase the NGH unit production subsidy and reduce the tax rate as NGH plant decision-makers are constrained by the cost; that is, the total cost to the authorities increases in order to increase NGH production rates and each plant struggles to adjust its operating plan to maximize profits. Overall, plant 2 and 4 expanded production, plant 1 and 3 hydrate production increased slightly. Based on the above calculation results and analysis, there are several basic conclusions. First, the integrated consideration of multiple stakeholders can improve NGH utilization. Second, under a strict energy utilization policy, the marginal energy efficiency benefits outweigh the government costs.

Conclusion
A hybrid subsidy mechanism for NGH production and transportation based on a governmentfirm equilibrium is proposed to achieve greater clean energy use. The study finds that a hybrid subsidy mechanism combining direct production subsidies and indirect tax reduction subsidies can significantly alleviate the pressure of high investment and operating costs of NGH plants. The study also shows that the hybrid subsidy mechanism determined by local governments can increase the profits of NGH plants and the production of NGH. This paper addresses the energy waste problem of natural gas transportation and attempts to apply the hybrid subsidy mechanism to the NGH production and transportation process to achieve sustainable development of the natural gas industry.
It can be concluded from the study that a hybrid subsidy mechanism is necessary for natural gas-stranded areas. In the absence of a hybrid subsidy mechanism, NGH production is limited due to cost issues, and a large amount of stranded natural gas reservoirs are abandoned, resulting in energy waste. Using the proposed optimization method, a hybrid subsidy mechanism can be established. It is shown that the hybrid mechanism can be used to guide the environmentally friendly production of NGH plants. By transforming energy use targets into constraints and changing the subjective attitude of authorities, efficient energy use and sustainable socio-economic development can be achieved.