Comprehensive Review on Various Gas Hydrate Modelling Techniques: Prospects and Challenges
各种天然气水合物建模技术综述：前景与挑战

Abstract
摘要

Gas hydrates is one the most complex flow assurance problems encountered in pipelines. The gas hydrate formation in pipelines eventually leads to the blockage of pipelines interrupting pipeline operations and affects transmission safety. Over the years, many mitigation techniques are employed to resolve gas hydrate issues in pipelines. But it is equally important to predict the formation and dissociation conditions of the hydrate formation as the experimental investigation is not always viable. So, an accurate prediction modelling approach is required for it. This paper provides a detailed overview of various gas hydrate modelling techniques. Initially, the details about the thermodynamic and kinetic properties of the gas hydrates are discussed. Furthermore, the discussion on the major aspects of the thermodynamic models, Kinetic models, Statistical Models, Models developed using Computational Fluid Dynamics, and Artificial Neural Networks techniques are highlighted. Finally, shortcomings and potential prospects of gas hydrate modelling procedures are addressed.
天然气水合物是管道中遇到的最复杂的流动保障问题之一。管道中的天然气水合物形成最终会导致管道堵塞，中断管道运行并影响输送安全。多年来，许多缓解技术被采用以解决管道中的天然气水合物问题。但同样重要的是预测水合物形成的形成和分解条件，因为实验研究并不总是可行的。因此，需要一种准确的预测建模方法。本文提供了对各种天然气水合物建模技术的详细概述。首先，讨论了天然气水合物的热力学和动力学特性。此外，重点讨论了热力学模型、动力学模型、统计模型、使用计算流体动力学开发的模型以及人工神经网络技术的关键方面。最后，讨论了天然气水合物建模程序的不足之处和潜在前景。

1 Introduction
1 引言

A very relevant problem in the oil and gas industry is the flow assurance of hydrocarbon streams in subsea networks, such as pipelines. Although it includes treating multiple solid deposits from hydrocarbon fluid streams that can form in subsea flow lines, it is complex and covers many engineering disciplines. In subsea pipelines, some of the flow assurance threats include gas hydrates, slugging, degradation, wax, scales, and so on; hydrate forming in the oil and gas industry is of significant concern. Due to favourable high pressure and low-temperature environments, hydrates are major problems in the deep-water climate. Therefore, deep water flow protection has become a progressively significant issue for the oil and gas industry.
油气行业中一个非常相关的问题是海底网络（如管道）中烃类流体的流动保障。尽管它包括处理海底流动管道中可能形成的多种固体沉积物，但它非常复杂，涵盖了许多工程学科。在海底管道中，一些流动保障威胁包括天然气水合物、液块、降解、蜡、垢等；油气行业中的水合物形成问题备受关注。由于有利的 高压和低温环境，水合物是深水气候中的主要问题。因此，深水流动保护已成为油气行业日益重要的问题。

Gas hydrates are solid crystal-like substances created when guest molecules are trapped within a cage-like structure composed of water molecules [1]. Methane (CH₄), Ethane (C₂H₆), Propane (C₃H₈), Nitrogen (N₂), Carbon dioxide (CO₂), and Hydrogen Sulfide (H₂S) are the most prevalent guest molecules that create gas hydrates. Gas hydrates are members of the clathrate hydrate group, abundant in nature [2, 3]. The host molecules are water (H₂O) molecules, whereas the guest molecules are gas molecules trapped inside the host molecules. The crystals are stabilized by van der Waals force, which happens when no bonding occurs between the host and guest molecules because they may freely spin in the water cage [4]. There are significant numbers of in-situ gas hydrates in deep ocean and permafrost zones, while nearly 97 per cent can be contained in submarine hydrate sediments [5].
天然气水合物是在水分子组成的笼状结构中捕获的客体分子形成的固体晶体状物质[1]。甲烷（CH₄）、乙烷（C₂H₆）、丙烷（C₃H₈）、氮气（N₂）、二氧化碳（CO₂）和硫化氢（H₂S）是形成天然气水合物的最常见客体分子。天然气水合物是笼状水合物的成员，在自然界中丰富存在[2, 3]。主体分子是水（H₂O）分子，而客体分子是被捕获在主体分子内部的气体分子。晶体由范德华力稳定，这种力发生在主体分子和客体分子之间没有化学键形成时，因为它们可以在水笼中自由旋转[4]。在深海和多年冻土区存在大量的原位天然气水合物，而近 97%可以被包含在海底水合物沉积物中[5]。

To date, hydrate is known to form in a total of 130 gas molecules [6]. The term "clathrate" originally derives from the Greek word "Khlatron", which means shield; considering the frost, gas hydrates can be stable at temperatures greater than 273.15 K. The discovery of gas hydrates is due to Sir Humphrey Davy in 1810 [7]. He found that a solid was formed from a heterogeneous solution of chlorine gas (Cl₂) and H₂O above the ice stage. As Priestley discovered compounds that may have been clathrate hydrates in 1778, the finding may have also preceded Davy, but the absence of sufficient evidence renders this earlier discovery unclear. The initial observance of blockage of pipelines due to hydrate formation was encountered in 1934 [8].
迄今为止，已知有 130 种气体分子可以形成水合物[6]。术语"笼状化合物"最初源自希腊语"Khlatron"，意为盾牌；考虑到霜冻，气体水合物可以在高于 273.15 K 的温度下保持稳定。气体水合物的发现归功于汉弗莱·戴维爵士在 1810 年的发现[7]。他发现，在冰期以上，氯气（Cl ₂ ）和 H ₂ O 的异质溶液会形成固体。正如普里斯特利在 1778 年发现了可能是笼状水合物的化合物，这一发现可能早于戴维，但由于缺乏足够的证据，这一早期的发现并不明确。由于水合物形成的管道堵塞首次在 1934 年被遇到[8]。

For many factors, gas hydrates have received considerable interest from both academics and business. First of all, they are explicitly a possible giant energy source in the coming years, since the most optimistic calculation indicates that the volume of energy in the form of hydrate is double the total amount of all the other forms of fossil fuels on the earth [9]. Secondly, if accidental leakage of methane gas from hydrate reservoirs happens, gas hydrates pose a threat to our increasingly vulnerable atmosphere and environmental infrastructure more tacitly [10, 11]. Thirdly, there are quite a few promising engineering applications using gas hydrate as a compact technology carrier. Most of these technologies are under review. That includes the capture and storing of hydrate-based carbon [12, 13], seawater desalination [14,15,16,17], hydrogen storage [18, 19], storage and distribution of natural gas [20], and even advanced air-conditioning systems [21]. Management techniques for the inhibition and remediation of natural gas hydrates are both complex and necessary. Also, in deep-sea hydrate exploration activities, including trial production of natural gas from hydrate wells, due to the extreme subsea conditions of cooler water, higher pressure and lower temperature, we will eventually face the possibility of hydrate reformation in the production pipeline.
由于多种因素，天然气水合物已引起学术界和商界的高度关注。首先，它们明确是未来可能成为巨大能源来源，因为最乐观的计算表明，以水合物形式存在的能量体积是地球上所有其他形式化石燃料总量的两倍[9]。其次，如果水合物储层发生甲烷气体的意外泄漏，天然气水合物会对我们日益脆弱的大气和环境基础设施构成更隐晦的威胁[10,11]。第三，利用天然气水合物作为紧凑技术载体的工程应用前景广阔。这些技术大多正在审查中。包括基于水合物的碳捕获和储存[12,13]、海水淡化[14,15,16,17]、氢储存[18,19]、天然气储存和分配[20]，甚至先进的空调系统[21]。管理天然气水合物的抑制和修复技术既复杂又必要。 此外，在深海水合物勘探活动中，包括从水合物井进行天然气试生产，由于海底极端环境条件——水温较低、压力较高、温度较低，我们最终将面临生产管道中水合物再形成的可能性。

The gas hydrate research is extensive, requiring multi-scale analysis. The study of gas hydrates began at the molecular level, with researchers studying the numerous varieties of gas hydrate formations, followed by their thermodynamic and phase equilibrium features [22]. Subsequently, in order to build kinetic models to completely replicate the mechanics beneath the procedure, the study on the formation and dissociation process of gas hydrates is calculated from both microscopic and macroscopic stages [23]. Natural gas hydrate reservoir processing and the use of gas hydrate as a medium, such as flow assurance, hydrate-based seawater desalination, and energy storage, rely on a macroscopic knowledge of hydrate formation and dissociation, which also incorporates other large-scale process factors.
天然气水合物研究范围广泛，需要进行多尺度分析。对天然气水合物的研究始于分子水平，研究人员首先研究了多种天然气水合物形成的种类，随后研究了其热力学和相平衡特性[22]。随后，为了建立能够完全复制过程机理的动力学模型，对天然气水合物形成和分解过程的研究从微观和宏观阶段进行计算[23]。天然气水合物储层处理以及将天然气水合物作为介质（如流化保障、基于水合物的海水淡化和储能）依赖于对水合物形成和分解的宏观知识，这也包含了其他大规模过程因素。

Multiphase flows are fluid flow systems which consist of two or more distinct phases simultaneously flowing co-currently in a system. Multiphase system can be found in many engineering installations, especially in the oil and gas industry, such as deep-sea pipelines. Multiphase flow research is critical because the behavior of the materials is determined by the characteristics of the components in the mixture, as well as the flowrates and geometry of the system [24, 25].
多相流是指由两种或多种不同相同时在系统中并流流动的流体流动系统。多相系统在许多工程装置中都能找到，特别是在石油和天然气行业，如深海管道。多相流研究至关重要，因为材料的特性由混合物中各组分的特性、系统的流量和几何形状决定[24, 25]。

Multiphase flow pipeline systems are complicated, and design methodologies rely on an understanding of their phase behavior. In the petroleum business, multiphase flow systems can be found in wells, collecting systems, pipelines, and essential equipment in refineries [26, 27]. Multiphase flow pipelines have been causing multiple problems in the oil and gas industry, such as the formation of gas hydrates in deep sea pipelines due to the high pressure and low temperature operational conditions. This is one of the major flow assurance challenges as it leads to the blockage of pipeline affecting the transmission safety [28, 29]. During production and transportation of natural gas, the gas along with other impurities is transported through underground or underwater transmission multiphase pipelines. Because of the many fluid characteristics found in pipelines, as well as the complicated operational temperature and pressure variations, the development of gas hydrates represents a significant danger to flow assurance. The removal of natural gas hydrates in deep-water pipelines is critical because the development of gas hydrates represents a hazard to the economy and safety. Furthermore, the presence of gas hydrates in pipelines may have an impact on the environment. The study of gas hydrates is becoming increasingly intense. Hydrate characteristics, formation and dissociation circumstances, and efficient hydrate removal methods have all been widely investigated.
多相流管道系统复杂，其设计方法依赖于对其相态行为的理解。在石油行业，多相流系统存在于井、集输系统、管道以及炼油厂的关键设备中[26, 27]。多相流管道在石油和天然气行业中引发了多种问题，例如由于高压低温的运行条件导致深海管道中形成气体水合物。这是主要的流动保障挑战之一，因为它会导致管道堵塞，影响输送安全[28, 29]。在天然气生产和运输过程中，天然气与其他杂质一起通过地下或水下传输的多相流管道进行输送。由于管道中存在多种流体特性，以及复杂的运行温度和压力变化，气体水合物的形成对流动保障构成重大危险。在深水管道中清除天然气水合物至关重要，因为气体水合物的形成对经济和安全构成危害。 此外，管道中存在天然气水合物可能会对环境产生影响。对天然气水合物的研究正变得越来越激烈。水合物的特性、形成和分解条件以及高效的水合物去除方法都已被广泛研究。

Over the years, many studies have been carried out, with various inhibition techniques being proposed alongside some best prediction models to estimate the gas hydrates formation [30,31,32]. Various simulation and theoretical studies also were done using software like ASPEN HYSYS and PVTSIM but there is no clear evidence on the accuracy in prediction of gas hydrates [33, 34]. Also, many researchers have proposed various modelling techniques with theoretical approach and latest simulation techniques like Computational Fluid Dynamics (CFD) and Artificial Neural Networks (ANN). To allow flow-assurance engineers to make proper risk evaluation, say for a new pipeline flow and operating procedures with assurance, a clearer understanding of the formation of hydrates and accurate modelling and analysis tools are required.
多年来，许多研究已经开展，提出了多种抑制技术以及一些最佳预测模型来估算天然气水合物形成[30, 31, 32]。还使用 ASPEN HYSYS 和 PVTSIM 等软件进行了各种模拟和理论研究，但关于天然气水合物预测准确性的明确证据尚无[33, 34]。此外，许多研究人员提出了各种建模技术，包括理论方法和最新模拟技术，如计算流体动力学（CFD）和人工神经网络（ANN）。为了使流程保障工程师能够进行适当的风险评估，例如针对新管道流程和操作程序提供保障，需要更清晰地理解水合物形成，并需要精确的建模和分析工具。

This paper provides a detailed overview of numerous gas hydrate modelling methodologies. The major aspects of the thermodynamic models, Kinetic models, Statistical Models, Models developed using Computational Fluid Dynamics (CFD) and Artificial Neural Networks (ANN) techniques are highlighted.
本文详细概述了多种天然气水合物建模方法。重点介绍了热力学模型、动力学模型、统计模型、采用计算流体动力学（CFD）和人工神经网络（ANN）技术开发的模型的主要方面。

2 Gas Hydrates
2 天然气水合物

2.1 Formation of Gas Hydrates
2.1 甲烷水合物形成

When the hydrocarbons are flown into the pipeline, they are generally associated with water. So, 3 phases are typically present, namely liquid hydrocarbons, aqueous liquids, and gas. The models predicting the gas hydrate formation in the different flow systems are clarified into four different classifications. The oil-dominated system is the first type. The incidence of oil, in which all the water is mixed as droplets in the oil, dominates this system of gas, oil and water. The second system is a system dominated by gas, in which there are less concentrations of liquid hydrocarbon or aqueous liquid present. Hydrate blockage in the field is rarely recorded to highlight this form of multiphase system. Next type is the condensate system, in which, because of high shear, the water dissolves in the condensate or suspends as droplets in the condensate. A high water-cut system in which the water content sometimes reaches to 70 percentage of the flow volume is regarded as the last of these systems. When the blends of water and non-polar or partially polar low molecular mass gases or volatile liquids, exposed to low temperatures, hydrates formation occur. The temperature varies between 275 and 285 K, while the pressure levels are normally 3–10 MPa [4]. Gas hydrates are solid inclusion compounds that are nonstoichiometric. Figure 1 shows the typical hydrate plug that caused the subsea pipeline block. Also, some gas hydrates formed in Gas hydrate laboratory are displayed in Fig. 2.
当烃类流入管道时，它们通常与水伴生。因此，通常存在三个相，即液态烃、水相液体和气体。预测不同流系统中甲烷水合物形成的模型被划分为四种不同的分类。第一种是烃主导系统。在这种系统中，油中所有水都以液滴形式混合，主导着气、油、水的混合系统。第二种系统是气主导系统，其中液态烃或水相液体的浓度较低。该多相系统的这种形式在油田中很少记录到水合物堵塞。接下来是冷凝液系统，在这种系统中，由于剪切力较高，水溶解在冷凝液中或悬浮在冷凝液中的液滴。当水与非极性或部分极性低分子量气体或挥发性液体的混合物在低温下暴露时，会发生水合物形成。 温度在 275 至 285 K 之间变化，而压力水平通常为 3-10 MPa [4]。天然气水合物是固体非化学计量型包合物。图 1 显示了导致海底管道堵塞的典型水合物塞。此外，图 2 展示了在天然气水合物实验室形成的一些天然气水合物。

Fig. 1
图 1

Typical hydrate plug causing the subsea pipeline obstruction [35]
典型的水合物堵塞导致海底管道阻塞[35]

Fig. 2
图 2

Gas Hydrates formed in Laboratory
实验室形成的天然气水合物

2.2 Gas Hydrates structures
2.2 甲烷水合物结构

Approximately 85 mol percent water is composed of gas hydrates, and thus many of their physicochemical properties are matching to those of ice properties like density, refractive index, and physical appearance. But some properties like thermal conductivity, heat capacity and mechanical strength are different from that of the properties of the ice. Table 1 compares the physical parameters of the two most prevalent hydrate forms with water in liquid phase and water in solid phase (ice). There are 3 basic forms of gas hydrate crystal structures: structure I (sI), structure II (sII), and structure H. (sH). The various hydrate structures and their related kinds of cages are shown in Fig. 3. Structure I consists of two distinct types of cage, a small 5¹² pentagonal dodecahedral cage (containing 12 pentagonal faces on the cage) and a large 5¹²6² tetrakaidecahedral cage (contains 12 pentagonal and 2 hexagonal faces on the cage) [36]. In addition to the large hexacaidecahedral cage, denoted 5¹²6⁴, Structure II also contains the small 5¹² cages (contains 12 pentagonal and 4 hexagonal faces on the cage). Structure H consists of a small 5¹² cage, a medium 4³5⁶6³ cage (containing 3 square, 6 pentagonal and 3 hexagonal cage faces) and a wide 5¹²6⁸ icosahedral cage (contains 12 pentagonal and 8 hexagonal faces on the cage). The majority of the structure created is determined by the size of the guest molecule; for example, CH4 fits both the small and big sI cages, but C₃H₈ is too big to fit into the big sI cage but can fit into the big sII cage, and therefore sH forms [37, 38].
大约 85 摩尔百分比的物质是天然气水合物，因此它们许多的物理化学性质与冰的性质相匹配，如密度、折射率和物理外观。但有些性质，如热导率、热容和机械强度，则与冰的性质不同。表 1 比较了两种最常见的水合物形式的物理参数与液态水和固态水（冰）的物理参数。天然气水合物晶体结构有三种基本形式：结构 I（sI）、结构 II（sII）和结构 H（sH）。各种水合物结构和它们相关的笼状结构如图 3 所示。结构 I 由两种不同的笼状结构组成，一种是小型的五角十二面体笼（笼上有 12 个五边形面）和一种是大型的五十二面体笼（笼上有 12 个五边形面和 2 个六边形面）[36]。除了大型的六十二面体笼（标记为 5 ¹² 6 ⁴ ），结构 II 还包含小型笼（笼上有 12 个五边形面和 4 个六边形面）。 结构 H 由一个小 5 ¹² 笼、一个中等大小的 4 ³ 5 ⁶ 6 ³ 笼（包含 3 个正方形、6 个五边形和 3 个六边形笼面）和一个宽大的 5 ¹² 6 ⁸ 二十面体笼（笼上含有 12 个五边形和 8 个六边形面）组成。该结构的大部分由客体分子的尺寸决定；例如，CH4 可以同时进入小和大 sI 笼，但 C ₃ H ₈ 太大无法进入大 sI 笼，但可以进入大 sII 笼，因此 sH 形成[ 37, 38]。

Table 1 Physical properties of gas hydrate and their comparison with Water and Ice
表 1 气体水合物物理性质及其与水和冰的比较

Fig. 3
图 3

Various Hydrate Structures and their Related Kinds of Cages [45]
多种水合物结构及其相关类型的笼子 [45]

Conversely, since they are made of CH₄ and does not contain heavier hydrocarbons, the bulk of naturally occurring gas hydrates deposits are Structure I. Thermogenic gas hydrate accumulations containing larger hydrocarbons are outliers, forming from Structure II and, in rare cases, Structure H. Highly successful procedures for verifying or describing the composition of gas hydrates include nuclear magnetic resonance (NMR) testing, X-ray diffraction, and Raman spectroscopy. The lattice form (sI, sII, or sH) can be easily detected from powder X-ray diffraction. Raman spectroscopy can easily determine relative cage occupancies because the vibrational modes of the guest gas molecules provide evidence of their chemical surroundings.
相反，由于它们由 CH ₄ 构成且不含重质烃类，自然界中大部分天然气水合物矿藏为 I 型结构。含较大烃类的热成因天然气水合物矿藏属于例外情况，它们形成于 II 型结构，在极少数情况下会形成 H 型结构。用于验证或描述天然气水合物组成的成功方法包括核磁共振（NMR）测试、X 射线衍射和拉曼光谱。晶格形式（sI、sII 或 sH）可以通过粉末 X 射线衍射轻松检测。拉曼光谱可以轻易确定相对笼体占位情况，因为客体气体分子的振动模式提供了它们化学环境的证据。

More specialized (though less available) instruments, such as synchrotron X-ray diffraction and synchrotron X-ray diffraction Neutron diffraction make it possible to structurally classify gas hydrates in situ under high pressure conditions [39,40,41,42]. During phases of formation and decomposition. The ultimate instrument for structural Single-crystal X-ray crystallography is the characterization of gas hydrates. Nevertheless, as this approach involves the creation of a single crystal gas hydrate of a small scale, which is an extremely difficult task, only a few single-crystal X-ray measurements have been effectively conducted [43]. In a unique and unusual event, single crystals of naturally available gas hydrate samples were collected and studied [44].
更专业（但不太容易获得）的仪器，如同步辐射 X 射线衍射和同步辐射 X 射线衍射中子衍射，可以在高压条件下原位对气体水合物进行结构分类[39, 40, 41, 42]。在形成和分解阶段。结构表征气体水合物的终极仪器是单晶 X 射线晶体学。然而，由于这种方法涉及小规模单晶气体水合物的制备，这是一个极其困难的任务，因此只有少数单晶 X 射线测量得到了有效实施[43]。在独特且罕见的事件中，收集和研究自然界中可获得的气体水合物样品的单晶[44]。

2.3 Thermodynamic Properties
2.3 热力学性质

In all gas hydrate applications, a good knowledge of the thermodynamic properties of gas hydrate structures is important. Beginning from the estimation of the temperature and pressure levels under which a flowline would be inside the hydrate stabilization region to the evaluation of the conditions required for the dissociation of a hydrate plugs in a pipeline or reservoir of natural gas hydrate for the energy production. The stability of gas hydrate relies on temperature, pressure, composition of gas and composition of condensed phases (involving liquid hydrocarbon phase, salt content, and chemical inhibitor concentration). Figure 4 shows the profile of pressure and temperature under which fluids can be exposed within an oil or gas flowline to the platform and central processing plant from a deep-water well. The hydrate formation/stability area is the shaded envelope; any fluid inside the segment of the pipeline in this area will create gas hydrates, which may contribute to the formation of hydrate plugs.
在所有天然气水合物应用中，了解天然气水合物结构的热力学性质非常重要。从估算流动管线在水合物稳定区内的工作温度和压力水平，到评估天然气水合物管线或储层中水合物堵塞分解所需的条件以进行能源生产。天然气水合物的稳定性依赖于温度、压力、气体组成和凝聚相组成（包括液态烃相、盐含量和化学抑制剂浓度）。图 4 展示了从深水井到平台和中央处理厂的油或气流动管线中流体可能暴露的压力和温度剖面。水合物形成/稳定区域是阴影包络；该区域管线内的任何流体都会形成水合物，这可能有助于水合物堵塞的形成。

Fig. 4
图 4

Gas Hydrates stability zone in Permafrost and Ocean [62]
永久冻土和海洋中的天然气水合物稳定区[62]

As seen in Fig. 5, Adding a chemical for the inhibition of hydrate in pipeline, usually called a thermodynamic inhibitor, such as methanol (or mono ethylene glycol), can result in the hydrate stabilization region moving to cooler temperatures and/or higher pressures. The points in the Fig. 5 represents thermodynamic equilibrium conditions that are captured usually by T-cycle method. In this case, the addition of 30 wt. percent methanol, for example, will move the hydrate stability curve to the left such that the previously hydrate-prone pipeline segment seen here will no longer be inside the hydrate stability region, thereby preventing the formation of hydrates. Often known as gas hydrate inhibition, this technique of avoiding gas hydrate formation using thermodynamic inhibition. Other thermodynamic approaches to prevent the production of gas hydrate include heating/insulating the sections of the pipeline above the temperature of the formation of gas hydrate or working normally with a fluid of high salt content [7, 59].
如图 5 所示，在管道中添加用于抑制水合物的化学物质，通常称为热力学抑制剂，如甲醇（或单乙二醇），可以使水合物稳定区域移动到更低的温度和/或更高的压力。图 5 中的点表示通常由 T 循环法捕获的热力学平衡条件。在这种情况下，例如添加 30 wt.百分比的甲醇，将使水合物稳定曲线向左移动，这样之前容易形成水合物的管道段将不再位于水合物稳定区域内，从而防止水合物的形成。这种利用热力学抑制剂避免水合物形成的技术通常称为天然气水合物抑制。其他防止水合物产生热力学方法包括将管道上方温度高于水合物形成温度的段进行加热/保温，或通常使用高盐分流体工作[7, 59]。

Fig. 5
图 5

Performance of thermodynamic inhibitor and promoter
热力学抑制剂和促进剂的性能

The thermodynamic stability of gas hydrates depends on the composition of the fluid and on the composition of the gas. The addition of a bigger molecule, such as C₃H₈ to CH₄, for example, would result in the formation of mixed gas hydrate (containing guest molecules of C₃H₈ + CH₄) at a slightly lower pressure than CH₄ hydrate. That is, at 277.6 K, the formulation pressure is 0.43 MPa 4.3 for C₃H₈ hydrate (sII), 4.06 MPa for pure methane hydrate (sI) and roughly 0.8 MPa for a C₃H₈ + CH₄ hydrate (50:50 binary gas mixture). As mentioned above, C₃H₈ stabilizes sII's large cage, but is too big to fit into the big cage of Structure I (and can also form C₃H₈ hydrate). Consequently, sII hydrate can be formed by a C₃H₈ + CH₄ gas mixture (with > 0.01 mol percent C₃H₈), whereas CH₄ forms Structure I hydrate. In the case of mixtures of C₂H₆ + CH₄ gas, while each guest type forms Structure I alone, binary Structure II hydrate or binary Structure I hydrate can be formed alone at unique binary gas compositions and pressures, or Structure I and Structure II binary hydrates can coexist.
天然气水合物的热力学稳定性取决于流体和气体的组成。例如，向 CH ₄ 中添加一个较大的分子如 C ₃ H ₈ ，会导致形成混合气体水合物（含有 C ₃ H ₈ + CH ₄ 的客体分子），其形成压力略低于 CH ₄ 水合物。也就是说，在 277.6 K 时，C ₃ H ₈ 水合物（sII）的成核压力为 0.43 MPa，纯甲烷水合物（sI）为 4.06 MPa，而 C ₃ H ₈ + CH ₄ 水合物（50:50 二元气体混合物）约为 0.8 MPa。如前所述，C ₃ H ₈ 稳定 sII 的大笼，但太大而无法进入结构 I 的大笼（同时也能形成 C ₃ H ₈ 水合物）。因此，C ₃ H ₈ + CH ₄ 气体混合物（含有> 0.01 mol percent C ₃ H ₈ ）可以形成 sII 水合物，而 CH ₄ 形成结构 I 水合物。对于 C ₂ H ₆ + CH ₄ 气体混合物，虽然每种客体类型单独形成结构 I，但在独特的二元气体组成和压力下，可以单独形成二元结构 II 水合物或二元结构 I 水合物，或者结构 I 和结构 II 二元水合物可以共存。

Van der Waals-Platteeuw argued that clathrate thermodynamic characteristics may be determined from a simple model that corresponds to the three-dimensional generalization of ideal localized adsorption. [60]. Van der Waals-Platteeuw analysis is based on the following assumptions:
范德瓦尔斯-普拉特休认为，笼状物的热力学特性可以通过一个简单的模型来确定，该模型对应于理想定位吸附的三维推广。[60]。范德瓦尔斯-普拉特休的分析基于以下假设：

• (a) The contribution of the Q molecules to free energy is irrespective of the form of cavity occupancy. This eliminates clathrates in which the encaged molecules are so large that they significantly disrupt the host lattice, such as CO₂ or CH₃CN in hydroquinone.
  Q 分子对自由能的贡献与空腔占用的形式无关。这排除了那些被捕获的分子非常大以至于它们会显著破坏主体晶格的包合物，例如在氢醌中的 CO 或 CH3CN。

• (b) The encaged molecules are confined in the cavities, and a cavity can only retain one solute molecule at a time.
  被捕获的分子被限制在空腔中，并且一个空腔一次只能保留一个溶质分子。

• (c) Solute molecules' mutual interaction is ignored, i.e., the partition function for the mobility of a solute molecule in its cage is independent of the quantity and type of solute molecules present.
  溶质分子之间的相互作用被忽略，即溶质分子在其笼中的迁移配分函数与其存在的溶质分子的数量和类型无关。

• (d) Classical statistics are valid.
  经典统计有效。

In a C₃H₈ + CH₄ system, the effect of C₃H₈ is similar to the promoter molecule effect used in gas storage applications to decrease the pressure requirements for hydrate stability. The promoter molecule can, in this situation, stabilize the hydrate structures at lower pressures than the fuel gas molecule can (CH₄, natural gas, or H₂). Tetrahydrofuran (THF) (which is like C₃H₈), for example, stabilizes the large sII cage, which alone forms Structure II hydrate at temperatures below 277.5 K at atmospheric pressure. Therefore, the hydrate equilibrium pressure can be greatly decreased by applying THF to CH₄ or H₂. Today, gas hydrate thermodynamic prediction models are mainly based on the original van der Waals-Platteeuw hypothesis, which in turn is based on the core concept of calculating the hydrate's free energy as that of a water cage system that can separately and independently consume visitors. To evaluate the phase boundary, this free energy is then correlated with that of the concomitant phases [61].
在一个 C0H1 + CH2 系统中，C3H4 的作用类似于气储应用中使用的促进分子，可以降低水合物稳定所需的压力。在这种情况下，促进分子可以在比燃料气体分子（CH5、天然气或 H6）更低的压力下稳定水合物结构。例如，四氢呋喃（THF）（类似于 C7H8）可以稳定大 sII 笼，该笼在低于 277.5 K 的温度和大气压下单独形成 II 型水合物。因此，通过向 CH9 或 H10 中添加 THF，可以大大降低水合物的平衡压力。如今，气体水合物热力学预测模型主要基于原始的范德华-普拉特胡伊尔假设，该假设又基于计算水合物自由能的核心概念，即将其视为一个可以分别独立消耗访客的水笼系统。为了评估相边界，该自由能与伴随相的自由能相关联[61]。

A collection of core hypotheses about the existence of molecular interactions plus methods to approximate the parameters that describe the frequency of these interactions can be the van der Waals-Platteeuw theory. Specifically, the key assumptions widely quoted are:
关于分子相互作用存在的一组核心假设，以及近似描述这些相互作用频率参数的方法，可以是范德华-普拉特尤斯理论。具体来说，广泛引用的关键假设是：

• (a) Independence,
  独立性，

• (b) Single cage occupancy,
  单个笼位占用，

• (c) Absence of encounters between visitor and guest,
  访客与主人之间无相遇，

• (d) Lack of quantum phenomena.
  缺乏量子现象。

Recent advancements in molecular simulation have allowed the accurateness of basic assumptions of the van der Waals-Platteeuw model to be closely dissected and have further suggested that the original theory's accuracy was partially due to the dissolution of errors from individual assumptions [63]. Naturally, if the Langmuir constants are adapted to experimental results, the precision of the model increases and those semi-empirical models have the best matches, at least for temperature and strain. Several of the latest models includes numerous improvements to the vander Waals-Platteeuw principle, such as applying the model to multi component gas mixtures, allowing for lattice development due to guest occupancy, and introducing a model of Gibbs energy minimization, which is the basis for the CSMGem (CSM Gibbs energy minimization model) thermodynamic hydrate prediction model [64]. Molecular simulations have also been used to quantify hydrate thermodynamics; these simulations will test the vander Waals-Platteeuw process independently and assess the boundary of the gas hydrate process from information only of the guest and host molecules intermolecular potentials/interactions.
近年来分子模拟的进步使得范德华-普拉特尤模型的基本假设的准确性得到了深入剖析，并进一步表明原始理论的准确性部分源于各个假设中误差的消除[63]。自然地，如果将朗缪尔常数调整至实验结果，模型的精度会提高，这些半经验模型在温度和应变方面具有最佳匹配。一些最新的模型对范德华-普拉特尤原理进行了多项改进，例如将模型应用于多组分气体混合物、允许由于客体占据导致的晶格发展，并引入吉布斯能最小化模型，这是 CSMGem（CSM 吉布斯能最小化模型）热力学水合物预测模型的基础[64]。分子模拟也被用于量化水合物热力学；这些模拟将独立测试范德华-普拉特尤过程，并从客体和主体分子间分子势/相互作用的信息中评估气体水合物过程的边界。

In addition to these fundamental uses, it can be argued that the thermodynamic characteristics of gas hydrates are adequately well characterized to allow the state of the art in gas hydrate science to emphasis on enhancing our knowledge of time-dependent hydrate events.
除了这些基本用途外，可以论证天然气水合物的热力学特性已经得到了充分表征，使得天然气水合物科学的前沿能够侧重于增强我们对时间依赖性水合物事件的认识。

2.4 Kinetic Properties
2.4 动力学特性

Unlike the well-established thermodynamic features of gas hydrates, the dynamics of gas hydrate production remain a mystery. That is, projections, including amounts of the rate of gas hydrate production, are challenging and unclear due to difficulties in generating reproducible and instrument-independent kinetic results. In laboratory-scale tests, the stochastic nature of the formation of hydrates is widely found, where the induction time of nucleation can range from minutes to hours to days under equal test conditions. Usually, the time of nucleation induction is defined as the time up to the point where hydrate development occurs instinctively and is generally taken in practice as the time that induces observable changes such as decreased strain, intake of gas, increase in temperature, or visually seen crystals.
与已确立的天然气水合物热力学特征不同，天然气水合物生成的动力学仍然是一个谜。也就是说，关于天然气水合物生成速率的预测，包括生成速率的量级，都由于难以获得可重复且与仪器无关的动力学结果而具有挑战性和不确定性。在实验室规模的测试中，广泛发现水合物形成的随机性，其中成核的诱导时间在相同测试条件下可以从几分钟到几小时甚至几天不等。通常，成核诱导时间被定义为水合物自发发生发展的时间点，在实践中通常被定义为诱导可观察变化的时间，例如应变减小、气体吸收、温度升高或可见晶体的形成。

In preventing the occurrence of gas hydrate plugs during risk management techniques, the ability to track and/or forecast the kinetics of gas hydrate formation is important. Risk management is usually used where thermodynamic avoidance is inexpensive and/or practically impractical, e.g. when large quantities of methanol (> 40–60 percent vol) are needed or when the methanol content of umbilicals is restricted. Strategies for risk management include managing the kinetics of gas hydrates as well.
在风险管理技术中预防气体水合物堵塞时，跟踪和/或预测气体水合物形成动力学的能力很重要。风险管理通常用于热力学避免成本较低和/或实际不可行的情况，例如需要大量甲醇（>40-60%体积）或脐带中的甲醇含量受限时。风险管理策略也包括管理气体水合物的动力学。

For exploration field design and technologies, the capability to forecast when gas hydrates will form in a pipeline is highly useful and is the subject of a specific first of its kind instrument, CSMHyK (CSM Hydrate Kinetic model), which is united to the SPT Group's industrial standard multiphase flow simulator, OLGA. SPT group refers to an organization which holds the licence for OLGA till 2012. From 2012, Schlumberger is supplying the software. Water droplets are first entrained into the continuous oil phase due to shear in the pipeline and, in some cases, surface-active chemicals in the oil phase. The hydrate nucleates and forms a hydrate layer surrounding the droplet at the water interface (which is in touch with gas dissolved in oil) [65]. Thanks to capillary attraction and inevitably jam and plug, the hydrate particles agglomerate [66, 67].
在勘探领域设计和技术方面，预测在管道中何时会形成天然气水合物具有很高的实用价值，这也是一种首创的专用仪器 CSMHyK（CSM 水合物动力学模型）的研究对象，该仪器与 SPT 集团的工业标准多相流模拟器 OLGA 集成。SPT 集团是指持有 OLGA 许可证直至 2012 年的组织。从 2012 年起，斯伦贝谢公司开始提供该软件。由于管道中的剪切作用，水滴首先被卷入连续的油相中，在某些情况下，油相中的表面活性化学物质也会导致水滴被卷入。水合物在接触溶解在油中的气体的水界面处成核，并在水滴周围形成水合物层[ 65]。由于毛细吸引力以及不可避免的堵塞和堵塞，水合物颗粒聚集[ 66, 67]。

The subcooling (T_eq− T_system) at which hydrate begins to form, which has been empirically calculated to be 3.6 K, is a crucial input parameter in CSMHyK. Matthews and Notz [68] first proposed this benefit when assessing the subcooling needed during Texaco flow loop tests for hydrate formation and the Werner-Bolley gas condensate field test. The Werner Bolley well produced primarily gas, some condensate, and water (4 MMSCFD gas, 100 BPD condensate, and 10 BPD water). Near the wellhead, fluids from the producing well were heated, separated, metered, and then recombined for transportation. The Werner-Bolley field test remains the most regulated and recorded one for gas hydrate plug formation, considering the tremendous expenditure and efforts needed for hydrate field tests. Since this time, multiple flow loop experiments (at the flow loop facilities of ExxonMobil and Tulsa University) have been displayed. 3.6 ± 0.3 K is the subcooling temperature at which hydrates are produced.
开始形成水合物的过冷度（T _eq − T _system ），经经验计算为 3.6 K，是 CSMHyK 中的一个关键输入参数。Matthews 和 Notz [ 68] 在评估德士古流程回路试验中形成水合物所需的过冷度以及韦纳-博利气体冷凝油田试验时首次提出了这一优势。韦纳-博利井主要生产气体，还有一些冷凝油和水（4 MMSCFD 气体，100 BPD 冷凝油，和 10 BPD 水）。在井口附近，来自生产井的流体被加热、分离、计量，然后重新组合以便运输。考虑到水合物现场试验所需的巨大投入和努力，韦纳-博利油田试验仍然是记录最规范的水合物堵塞形成试验。自那时起，多个流程回路实验（在埃克森美孚和俄克拉荷马大学的流程回路设施）已被展示。3.6 ± 0.3 K 是产生水合物的过冷温度。

CSMHyK-OLGA was used in flow-loop and field experiments to predict gas hydrate formation. The scaling of 1/500 of the intrinsic kinetic rate constant for the production of methane hydrate in the ExxonMobil flow loop, highlighting the necessity to account for mass and heat transfer rate limiting factors, was derived by fitting CSMHyK estimates to one oil [69]. The same fit properly modelled hydrate formation in two separate flow loops for four distinct oils. CSMHyK anticipated the hydrate plug formation data collected in the Tommeliten Gamma field test [36]. The target of engineered kinetic regulation of hydrates in flowlines (as well as in clathrate hydrate storage materials) is to uncover the entire hydrate formation processes and to build chemical inhibitor/promoter molecules to target the primary kinetic routes. The clarification of the process of hydrate formation has been hastened in recent years due to the increase in high-performance supercomputing power.
CSMHyK-OLGA 被用于流环和现场实验以预测气体水合物形成。通过将 CSMHyK 估计值拟合到一种油[69]，推导出了埃克森美孚流环中甲烷水合物生产的固有动力学速率常数的 1/500 比例，突出了考虑质量和传热速率限制因素的重要性。相同的拟合正确地模拟了四种不同油在两个独立的流环中的水合物形成。CSMHyK 预测了 Tommeliten Gamma 现场测试中收集的水合物塞形成数据[36]。在流线（以及包合物水合物储存材料）中工程化动力学调节水合物的目标是揭示整个水合物形成过程，并构建化学抑制剂/促进剂分子以靶向主要的动力学途径。近年来，由于高性能超级计算能力的增加，水合物形成过程的阐明得到了加速。

The new knowledge gained from such large-scale computer simulations of molecular pathways to gas hydrate formation could be used in the future to encourage molecular engineering and the design of control processes and chemicals to improve gas hydrate inhibition and/or promotion, which are critical concerns in gas hydrate power applications.
从这种大规模计算机模拟分子路径到天然气水合物形成的知识，未来可用于推动分子工程和控制过程及化学品的研发，以改善天然气水合物抑制和/或促进效果，这对于天然气水合物发电应用至关重要。

• Gas Hydrates Modelling.
  天然气水合物建模。

• Thermodynamic Modelling.
  热力学建模。

In industrial applications, predicting hydrate phase equilibrium is crucial in order to successively inhibit gas hydrate formation. Statistical thermodynamic approaches are general descriptive thermodynamic models that are comparatively more precise since they combine a statistical thermodynamic approach to Gibbs energy minimization. It also takes into account the ratio of a cavity filled by molecules and phase, as well as the hydrate composition. The chemical potentials of each component in a liquid, solid (hydrate), and vapour (Lw–H–V) should be identical, according to thermodynamic equilibrium. This results in fugacities being equal, which is the requirement of an equilibrium state.
在工业应用中，预测水合物相平衡对于连续抑制天然气水合物形成至关重要。统计热力学方法是一般性描述热力学模型，因其结合了统计热力学方法来最小化吉布斯能，因此相对更精确。它还考虑了被分子填充的空腔与相的比例，以及水合物组成。根据热力学平衡，液体、固体（水合物）和蒸汽（Lw–H–V）中每种组分的化学势应相同。这导致逸度相等，这是平衡状态的要求。

The first model for calculating hydrate formation conditions is the K-Value method in 1941. The experimental determinations of equilibrium temperatures and pressures of hydrate forming up to 27.58 MPa for three natural gases are reported in this article. It was possible to calculate the equilibrium between a propane-rich fluid, a water-rich fluid, and crystalline hydrate. There is also a discussion of phase interactions and vapor–solid equilibria [70]. Later, Barrer and Stuart carried out the experiments in 1957 to determine the characteristics of gas hydrate using a mathematical thermodynamic method [71]. Van der Waals and Platteuw constructed a mathematical thermodynamic model of hydrate phase equilibria in 1959 utilizing a similar technique and knowledge of hydrate crystal structure [31]. In their analysis, using an approach similar to the adsorption of Langmuir gas, expressions of the chemical potential of water in hydrate structures sI and sII were established. As indicated in Eq. 1, the van der Waals and Platteeuw (vdWP) classic model was based on the difference between the chemical potential of water in the hydrate phase $\left({\mu }_w^H\right)$ and a hypothetical empty lattice hydrate phase (${\mu }_w^{\beta }$).
计算水合物形成条件的第一个模型是 1941 年的 K 值法。本文报道了对三种天然气水合物形成平衡温度和压力的实验测定，最高压力达到 27.58 MPa。通过该方法可以计算富含丙烷的流体、富含水的流体和结晶水合物之间的平衡。此外，还讨论了相间相互作用和气-固平衡[ 70]。后来，Barrer 和 Stuart 在 1957 年进行了实验，使用数学热力学方法来确定水合物的特性[ 71]。Van der Waals 和 Platteuw 在 1959 年利用类似的技术和水合物晶体结构知识，构建了一个水合物相平衡的数学热力学模型[ 31]。在他们的分析中，采用类似于朗缪尔气体吸附的方法，建立了水合物结构 sI 和 sII 中水的化学势表达式。如公式所示。 1, 范德华和普拉特尤（vdWP）经典模型基于水合物相中的化学势 \(\left( {\mu_{w}^{H} } \right)\) 与假设的空晶格水合物相 (\(\mu_{w}^{\beta }\)) 之间的差异。

$$\begin{array}{rl}\frac{\mathrm{\Delta }{\mu }_w^H}{RT}=& \frac{{\mu }_w^{\beta }-{\mu }_w^H}{RT}\\ =& \sum _{m=1}^2{\text{ϑ}}_m\ln \left(1+\sum _{i=1}^{nc}{C}_{mi}{f}_i\right)\end{array}$$

(1)

$C_{mi}$ is the Langmuir constant of hydrate former i in the type m cage of the crystalline structure, where ${\text{ϑ}}_m$ is the number of type m cages in the crystalline structure, and $f_i$ is the fugacity of hydrate formers. In practise, simplified methods of estimating Langmuir constants are commonly used. They vary in gas nomenclature, the number of molecules entering small and large hydrate cavities, and their statistical classification. As a consequence of the generalised determination of Langmuir constants for equivalent gases, different results are obtained, resulting in variations in the values of the measured hydrate parameters. However, because of their simplicity and ease of use, such methods are commonly used in practise achieve the most precise results when measuring hydrate parameters, it is important to choose methods of evaluating Langmuir constants. The details of the calculating Langmuir constants are discussed by various researchers over the years [72].
\(C_{mi}\) 是晶体结构中 m 型笼内第 i 种水合物形成物的朗缪尔常数，其中 \(\vartheta_{m}\) 是晶体结构中 m 型笼的数量，\(f_{i}\) 是水合物形成物的逸度。在实际应用中，通常使用简化的方法来估算朗缪尔常数。这些方法在气体命名、进入小和大水合物空腔的分子数量及其统计分类方面有所不同。由于对等效气体进行朗缪尔常数的广义测定，得到了不同的结果，导致测得的水合物参数值发生变化。然而，由于这些方法的简单性和易用性，它们在实际应用中广泛使用。在测量水合物参数时，选择评估朗缪尔常数的方法非常重要。多年来，不同研究人员讨论了计算朗缪尔常数的细节 [ 72]。

Saito et al. [73] and Parrish and Prausnitz [74] were led by the vdWP model to forecast the chemical potential of water in hydrate with that in the aqueous (or ice) process and applying an algorithm in a form appropriate for use on a device, gas hydrate equilibria. Some researchers, including Holder et al.[74] and John et al.[22], have simplified the expression of the chemical ability of water in the aqueous or ice process, as seen in Eq. 2.
斋藤等人[ 73]和帕里什与普劳斯尼茨[ 74]在 vdWP 模型的指导下，预测了水合物中水的化学势与水（或冰）过程中的化学势，并应用了一种适用于设备使用的算法形式，即气体水合物平衡。一些研究人员，包括霍尔德等人[ 74]和约翰等人[ 22]，简化了水在水或冰过程中的化学能力表达式，如式 2 所示。

$$\begin{array}{rl}\frac{\mathrm{\Delta }{\mu }_w^{\alpha }}{RT}=& \frac{{\mu }_w^{\beta }-{\mu }_w^{\alpha }}{RT}=\frac{\mathrm{\Delta }{\mu }_w^0}{RT}-\underset{T_0}{\overset{T}{\int }}\frac{\mathrm{\Delta }{h}_w}{R{T}^2}dT\\ & +\underset{P_0}{\overset{P}{\int }}\frac{\mathrm{\Delta }{v}_w}{RT}dP-RT\ln \left(a_w^{\alpha }\right)\end{array}$$

(2)

where α denotes liquid water or ice process, the reference state stands for 0 superscript/subscripts. In the alpha step, enthalpy transition and volume difference between the empty hydrate lattice and water are ∆h_w and ∆v_w.
其中α表示液态水或冰过程，参考态表示上标/下标为 0。在α步骤中，空水合物晶格与水之间的焓变和体积差分别为∆h _w 和 ∆v _w 。

Any new component added to the mixture will change the equilibrium of the phase and accordingly the fugacity of each mixture component. When fugacity was measured in the vdWP model, it was widely presumed that the volume of hydrate particles at equilibrium was quite tiny and that the system consisted mostly of two phases of vapour and liquid/solid waterAny VLE or VSE measurement with a suitable mixing rule may therefore result in fugacity, which is a reasonable prediction. Thus, the most significant aspect in fugacity measurement is the selection of an appropriate state equation and mixing law. Although EOSs such as Peng-Robinson [6] or Soave-Redlich-Kwang [75] with van der Waals mixing law may be used for hydrocarbon systems, a more sophisticated state equation, such as Valderrama-Patel–- [6], Nasrifar-Bolland [76], CPA [77], or statistical related fluid theory (SAFT) [76] equations of state, lead to improved estimation for more complicated systems, including electrolytes or very polar elements. In addition, G-excess mixing laws such as MHV1 [78] or MHV2 [30] will boost the precision of measurements of fugacity.
任何新组分加入混合物都会改变相平衡，并相应地改变混合物中每个组分的逸度。当在 vdWP 模型中测量逸度时，普遍认为平衡状态下水合物的体积非常小，系统主要由蒸汽和液态/固态水两相组成。因此，任何使用合适混合规则的 VLE 或 VSE 测量都可能得到逸度，这是一种合理的预测。因此，逸度测量的最重要方面是选择合适的状态方程和混合法则。尽管 Peng-Robinson[6]或 Soave-Redlich-Kwang[75]等使用范德华混合法则的状态方程可用于烃类系统，但更复杂的状态方程，如 Valderrama-Patel–[6]、Nasrifar-Bolland[76]、CPA[77]或统计相关流体理论（SAFT）[76]方程，能对更复杂的系统（包括电解质或极性很强的元素）进行更精确的估计。此外，G-过量混合法则，如 MHV1[78]或 MHV2[30]，将提高逸度测量的精度。

The second parameter is water activity, which is defined in Eq. 2. In the presence of additives, especially thermodynamic hydrate inhibitors, water behavior can change dramatically. Therefore, it is important to measure the water behavior very accurately to forecast the effect of these additives on the hydrate equilibrium. This is not a simple task since, under high pressure and low temperature conditions, hydrate equilibrium requires multicomponent systems, and most operation models are optimized for low pressure and dual systems. However, the combination of VLE approximation with G-excess mixing rules and the use of a model of predictive behavior such as UNIFAC or UNIQUAC may, in the liquid phase, contribute to fair precision in the calculation of water activity. For systems which contain thermodynamic promoters, the third parameter, which is the Langmuir constant, is more important. Although most thermodynamic inhibitors do not engage in gas hydrate’s crystalline structure, some of the promoters act either as hydrate formers (e.g. Tetrahydrofuran, acetone, 1–4 dioxane) [79] or as part of crystalline building blocks (e.g. tetra-n-butyl ammonium bromide) [18]. Although more complex simulation is needed to predict the state of hydrate formation in the existence of the second group, the first group, i.e. acting as hydrate formers, can be estimated by treating it as a hydrate former. For these molecules, this involves measuring fugacity, activity, and Langmuir constant.
第二个参数是水活性，其定义见式 2。在有添加剂存在时，特别是热力学型水合物抑制剂，水的行为会发生显著变化。因此，精确测量水的行为对于预测这些添加剂对水合物平衡的影响非常重要。但这并非一项简单的任务，因为在高压低温条件下，水合物平衡需要多组分系统，而大多数操作模型都是针对低压双组分系统进行优化的。然而，将 VLE 近似与 G-过量混合规则相结合，并使用预测行为模型（如 UNIFAC 或 UNIQUAC）可以在液相中为水活性的计算提供合理的精度。对于含有热力学促进剂的系统，第三个参数，即朗缪尔常数，更为重要。尽管大多数热力学抑制剂不参与水合物的晶格结构，但一些促进剂要么作为水合物形成剂（例如四氢呋喃、丙酮、1-4 二氧烷）[79]，要么作为晶格结构的一部分（例如四正丁基溴化铵）[18]。 尽管需要更复杂的模拟来预测第二组存在下水合物的形成状态，但第一组，即作为水合物形成物的物质，可以通过将其视为水合物形成物来进行估算。对于这些分子，这涉及测量逸度、活性和朗缪尔常数。

Two approaches are commonly used in literature to calculate the Langmuir constant. Parrish and Prausnitz [77] established the first and simpler form, which, as seen in Eq. 3, is a correlation acceptable for the temperature range of 260–300 K.
在文献中，通常采用两种方法来计算朗缪尔常数。Parrish 和 Prausnitz [77]建立了第一种更简单的方法，如式 3 所示，该方法适用于 260–300 K 的温度范围。

$$C_{m,i}\left(T\right)=\left(\frac{A_{m,i}}{T}\right)\exp \left(\frac{B_{m,i}}{T}\right)$$

(3)

For each hydrate former I that filled cavity type m in either structure sI or sII by Parrish and Prausnitz [77], the values for A_m,i and B_m,i parameters are given and provided in literature [31].
对于 Parrish 和 Prausnitz [77]中填充了腔体类型 m 的每种水合物形成物 I，在结构 sI 或 sII 中，A _m,i 和 B _m,i 参数的值在文献[31]中给出。

By using Lennard–Jones-Devonshire cell theory to measure the Langmuir constant, as seen in Eq. 4, the more acceptable approach is based on the intermolecular association between hydrate former and water molecules in a hydrate cavity.
通过使用 Lennard-Jones-Devonshire 细胞理论来测量朗缪尔常数，如式 4 所示，更可接受的方法是基于水合物形成物和水分子在腔体中的分子间关联。

$$C_{m,i}\left(T\right)=4\frac{\pi }{kT}\underset{0}{\overset{R_m-2_{a_i}}{\int }}\exp \left[-\frac{{\omega }_{m,i}\left(r\right)}{kT}\right]r^{2}dr$$

(4)

where k is the constant of Boltzmann, $\omega \left(r\right)$ is the spherically symmetric cell potential is the absolute temperature, which is a function of the cell radius, r, and T. R_m is the cavity radius of type m and a_i is the radius of the hydrate former I core. For the estimation of cell potential, Parrish and Prausnitz propose the Kihara principle, as seen in Eq. 5.
其中 k 是玻尔兹曼常数， 是球对称的细胞势，是绝对温度，它是细胞半径 r 和 T 的函数。R _m 是类型 m 的腔体半径，a _i 是水合物形成物 I 核心的半径。为了估算细胞势，Parrish 和 Prausnitz 提出了 Kihara 原理，如式 5 所示。

$$\begin{array}{rl}{\omega }_{m,i}\left(r\right)=& 2z_m{\in }_i[\frac{{\text{σ}}_i^{12}}{R_m^{11}r}\left({\delta }^{10}+\frac{a_i}{R_m}{\delta }^{11}\right)\\ & -\frac{{\text{σ}}_i^6}{R_m^{5}r}\left({\delta }^4+\frac{a_i}{R_m}{\delta }^5\right)\end{array}$$

(5)

where the minimum potential is ${\in }_i$, σ_{i + 2 ai} is the collision diameter, z_m is the collision diameter. The coordination number for each cavity is determined, and δN is calculated with Eq. 6 is equivalent to 4, 5, 10, and 11 for N.
在最小势能处为 ${\in }_i$ ，σ _{i + 2 ai} 是碰撞直径，z _m 是碰撞直径。每个空腔的配位数被确定，使用公式 6 计算δN 等效于 N 为 4，5，10 和 11。

$${\delta }^N\frac{\left[{\left(1-\frac{r}{R_m}-\frac{a_i}{R_m}\right)}^{-N}-{\left(1+\frac{r}{R_m}-\frac{a_i}{R_m}\right)}^{-N}\right]}{N}$$

(6)

A thorough examination of empirical similar and dissimilar equations of state in the van der Waals Platteeuw (VdW-P) thermodynamic model is performed to define the most precise technique of hydrate formation condition of methane. Furthermore, utilizing genetic programming, a new, rapid, and accurate correlation for predicting methane hydrate formation temperature is devised. Error analysis on a wide range of experimental outcomes demonstrates that the newest suggested association surpasses current associations and all VdW-P models with R² = 0.999 [71].
对范德华 Platteeuw（VdW-P）热力学模型中的经验相似和不同状态方程进行了全面研究，以确定甲烷水合物形成条件的最精确技术。此外，利用遗传编程，设计了一种新的、快速且准确的关联，用于预测甲烷水合物形成温度。对广泛实验结果进行的误差分析表明，最新建议的关联超越了当前关联和所有 VdW-P 模型，其 R² = 0.999 [71]。

The details of the various thermodynamic models applied over the years for various conditions are presented below in Table 2 for a clear understanding.
多年来应用于各种条件下的各种热力学模型的详细信息，为清晰理解，在下表中呈现。

Table 2 Thermodynamic models and their operating conditions
表 2 热力学模型及其工作条件

2.4.1 Way Forward
2.4.1 发展方向

It can be observed from the table that many modelling techniques were applied for various gases and gas mixtures. But there is no clear modelling applied for the promoters and inhibitors on various gas mixtures at high pressures. The models can be applied to various ionic liquids and amino acids effect on pure gases and gas mixtures. The models can be extended for the study on hydrate separation and storage.
从表格中可以看出，许多建模技术被应用于各种气体和气体混合物。但在高压下，针对促进剂和抑制剂在气体混合物中的建模尚无明确方法。这些模型可以应用于各种离子液体和氨基酸对纯气体和气体混合物的影响。这些模型可以扩展用于研究水合物分离和储存。

2.5 Kinetic Modelling
2.5 动力学建模

Growth of gas hydrates typically occurs after nucleation and is a dynamic phenomenon that necessitates multi-phase experiments at numerous research phases. On a macroscopical scale, the kinetics of gas hydrate formation are generally reliant on the mole consumption rate of gases. The growth of gas hydrates can be computed at the microscopic level as:
水合物的生长通常在成核之后发生，是一个动态现象，需要在多个研究阶段进行多相实验。在宏观尺度上，水合物形成的动力学通常依赖于气体的摩尔消耗速率。水合物的生长可以在微观尺度上计算为：

• 1. Mass transfer of water (H₂O) and gases to hydrate surface growth.
  水（H₂O）和气体向水合物表面的传质。

• 2. Transport of exothermic heat produced by crystals during gas growth.
  晶体在气体生长过程中产生的放热热的传输。

• 3. Intrinsic kinetics of the growth of gas hydrates.
  气体水合物生长的本征动力学。

The composition of gas hydrates has been defined depending on all these considerations. A large quantity of literature has been written and presented in Table 3.
气体水合物的组成已经根据所有这些考虑因素被定义。大量文献已被撰写并呈现在表 3 中。

Table 3 Synopsis of models of kinetic growth
表 3 动态生长模型概要

Foremost gas hydrate development models based on kinetics have been shown since 1980. The majority of these models are not established from the rules given here, and the majority of them encompass multiphase patterns. There is also a non-uniformity model that covers all of the main characteristics of gas hydrate formation kinetics.
自 1980 年以来，基于动力学的首要天然气水合物开发模型已被提出。这些模型中的大多数并非根据此处给出的规则建立，且大多数模型涵盖了多相模式。此外，还有一个非均匀模型，它涵盖了天然气水合物形成动力学的所有主要特征。

Englezos et al. [106] created an intrinsic kinetic model for the generation of methane and ethane gas hydrates with only one changeable parameter. The kinetic model is created on crystallization theory, whereas the interfacial mass transfer model is based on two-film theory. According to the findings, the rate of formation is proportional to the difference between the fugacity of the dissipated gas and the three-phase equilibrium fugacity at the experimental temperature. This distinction specifies the driving force, which includes the pressure effects. The gas consumption rate is also related to the particle size distribution's second moment. The rate constants reveal a very low temperature dependence.
Englezos 等人[106]建立了一个仅有一个可变参数的甲烷和乙烷气体水合物生成内在动力学模型。该动力学模型基于结晶理论构建，而界面质量传递模型则基于双膜理论。根据研究结果，生成速率与实验温度下逸度消散气体的逸度与三相平衡逸度之差成正比。这种差异明确了驱动力，其中包括压力效应。气体消耗速率也与颗粒尺寸分布的二阶矩有关。速率常数显示出非常低的温度依赖性。

Christianson et al. [107] show that the Gibbs free energy change for hydrate formation is a decent estimate of the driving force for hydrate growth. The rate of hydrate growth per unit area is related to the driving force. Calculations of driving forces indicate that hydrate structures other than the thermodynamically favoured structures may form.
Christianson 等人[107]表明，水合物形成的吉布斯自由能变化是水合物生长驱动力的一个合理估计。单位面积上水合物生长的速率与驱动力相关。驱动力计算表明，除了热力学上更优的结构外，还可能形成其他水合物结构。

Hussain et al. investigated the kinetics and morphology of ethane hydrate production in a batch type reactor at temperatures ranging from 270 to 280 K and pressures ranging from 0.883 to 1.667 MPa. The investigations demonstrated that the formation kinetics were affected by pressure, temperature, supercooling degree, and stirring rate [108].
Hussain 等人研究了在 270 至 280 K 温度范围和 0.883 至 1.667 MPa 压力范围内，间歇式反应器中乙烷水合物的动力学和形态。研究结果表明，形成动力学受压力、温度、过冷程度和搅拌速率的影响[108]。

Hideo Tajima studied Gas Hydrate Formation Kinetics in Semi-Batch Flow Reactor Equipped with Static Mixer [109]. Sang Yeon Hong et al. performed gas uptake measurement (macroscopic point of view) and in situ Raman spectroscopic analysis (microscopic point of view) in a semi batch stirred tank reactor at constant temperature (T) and pressure (P) to completely comprehend the effect of the kinetic inhibitor poly-N-vinylcaprolactam (PVCap) on methane hydrate formation [110]. One of the most vital features of gas hydrate research is the capacity to observe the behaviour of guest molecules (big to small cavity ratio or cage change). However, the real-time characteristics of cage variation in an agitating system under constant T and P conditions have never been observed. In this work, this property (i.e., the huge to tiny cavity ratio) was analysed using in situ Raman spectra during hydrate formation in an transient system rather than a static system, which provided important information on the time-dependent hydrate kinetic behaviour. According to the findings, the existence of PVCap lowers the rate of bigger cavity encapsulation at an initial stage of hydrate formation. PVCap's impact is also explored from both a microscopic and a macroscopic standpoint.
平田英男研究了在配备静态混合器的半连续流反应器中甲烷水合物的形成动力学[109]。洪桑延等人在一个恒温（T）恒压（P）的半连续搅拌罐反应器中进行了气体摄取测量（宏观观点）和原位拉曼光谱分析（微观观点），以完全理解动力学抑制剂聚-N-戊内酯（PVCap）对甲烷水合物形成的影响[110]。气体水合物研究的一个最关键特征是观察客体分子的行为（大腔体与小腔体的比例或笼体变化）。然而，在恒定 T 和 P 条件下搅拌系统中笼体变化的实时特性从未被观察到。在这项工作中，通过在瞬态系统中而不是静态系统中进行原位拉曼光谱分析来分析这一特性（即大腔体与小腔体的比例），这为水合物形成的时间依赖性动力学行为提供了重要信息。根据研究结果，PVCap 的存在降低了水合物形成初始阶段大腔体封装的速率。 PVCap 的影响也从微观和宏观的角度进行了探讨。

Park et al. [111] evaluated the performance of kinetic hydrate inhibitors in well fluids undergoing hydrate formation. Three phases of novel experimental procedures are created in this study to model the dissociation of hydrate blockages and the conveyance of hydrate-forming well fluids. The obtained experimental results show that when the temperature of dissociated water falls within the hydrate formation region, gas hydrates immediately re-form. Following an injection of KHIs prior to conveying the well fluids, the subcooling boosted considerably, indicating the possible use of KHIs for transferring the well fluids following hydrate dissociation. Furthermore, the inhibitory effectiveness of KHIs is investigated using two distinct gases in order to assess the effect of gas composition. If the KHI is fully analyzed, our experiment indicates that KHIs are a viable solution for avoiding hydrate re-formation in hydrate-forming well fluids.
Park 等人[111]评估了在发生水合物形成的井液中，动力学抑制剂的性能。本研究创建了三种新型实验程序，用于模拟水合物堵塞的解离和水合物形成井液的输送。获得的实验结果表明，当解离水的温度处于水合物形成区域内时，水合物会立即重新形成。在输送井液之前注入 KHIs，过冷度显著提高，表明 KHIs 可用于在解离水合物后输送井液。此外，使用两种不同的气体研究了 KHIs 的抑制效果，以评估气体组成的影响。如果对 KHI 进行充分分析，我们的实验表明 KHIs 是防止水合物形成井液中水合物重新形成的可行解决方案。

Natural Gas Hydrate Particles in Oil-Free Systems with Kinetic Inhibition and Slurry Viscosity Reduction is studied by Minwei Sun and Abbas Firoozabadi [112]. In their paper, they provide a redesigned formulation that includes the surfactant, a tiny quantity of a base, and an alkane. The base balances the pH, while the alkane acts as a defoamer. The impacts of each component are methodically discussed, and a synergetic effect is discovered. In a variety of situations, the novel formulation delivers excellent anti agglomeration. Furthermore, their formulation has three additional favourable effects: kinetic inhibition, slurry viscosity reduction, and corrosion inhibition.
在无油系统中研究具有动力学抑制和浆料粘度降低的天然气水合物颗粒，由 Minwei Sun 和 Abbas Firoozabadi [112]进行。在他们的论文中，他们提供了一个重新设计的配方，包括表面活性剂、少量碱和烷烃。碱平衡 pH 值，而烷烃作为消泡剂。他们系统地讨论了每个组分的影响，并发现了一种协同效应。在各种情况下，该新型配方表现出优异的抗聚集性能。此外，他们的配方还具有三种额外的有利影响：动力学抑制、浆料粘度降低和腐蚀抑制。

Asheesh Kumar et al. [113] proposed a discussion on Role of Surfactants in Promoting Gas Hydrate Formation. The review focuses on numerous surfactants employed in gas hydrate formation studies; insights into the feasible mechanisms of action by which these surfactants modify hydrate formation kinetics are provided. According to a comprehensive analysis of the surfactant literature, enhanced rates of hydrate nucleation and growth kinetics may not be exactly connected to micelle formation. Reduced surface tension in the presence of surfactants, on the other hand, not only increases mass transfer but also influences the geometry of hydrate formation, allowing for faster hydrate growth rate.
阿什伊什·库马尔等人[113]提出了一篇关于表面活性剂在促进气体水合物形成中作用的讨论。该综述重点关注气体水合物形成研究中使用的多种表面活性剂；提供了这些表面活性剂通过可行作用机制改变水合物形成动力学的见解。根据对表面活性剂文献的全面分析，水合物成核和生长动力学的速率提高可能并不完全与胶束形成相关。另一方面，表面活性剂存在时表面张力降低，不仅增加了质量传递，还影响了水合物形成的几何形状，从而允许更快的生长速率。

Liu et al. [114] provide a new prediction model of gas hydrate formation based on kinetic model analysis and kinetic observation of the hydrate formation process. The current model research shows that the creation of gas hydrate is affected not only by the composition of the gas and the concentration of free water, but also by temperature and pressure. The expected outcome of the novel gas hydrate crystallization kinetics prediction methodology is close to the observed result, demonstrating that the prediction strategy may accurately reflect hydrate crystallization.
刘等人[114]基于动力学模型分析和水合物生成过程的动力学观测，提供了一种新的天然气水合物生成预测模型。当前模型研究表明，天然气水合物的生成不仅受气体组成和自由水浓度的影响，还受温度和压力的影响。新型天然气水合物结晶动力学预测方法预期的结果与观测结果接近，表明该预测策略能够准确反映水合物结晶过程。

Ardeshir Mali et al. [115] employed a unique multi-test tube rocking cell unit to collect vast quantities of data in order to explore the link between gas hydrate formation induction time and subcooling. The testing involved determining the induction time for a natural gas and water system at a variety of pressures and subcooling. At pressures ranging from 2 to 17 MPa, over 500 induction times were observed. The statistical analysis of the findings reveals that the start of hydrate development is logarithmically related to subcooling, and that the scatter of the start of hydrate development is bigger as subcooling increases. It was also demonstrated that the induction time for hydrate formation was shorter at greater pressures with comparable degrees of subcooling.
Ardeshir Mali 等人 [ 115] 采用了一种独特的多试管摇动单元来收集大量数据，以探索气体水合物形成诱导时间与过冷度之间的关联。该测试涉及在各种压力和过冷度下确定天然气和水的系统诱导时间。在 2 至 17 MPa 的压力范围内，观察到了超过 500 个诱导时间。对测试结果进行统计分析表明，水合物发展的开始与过冷度呈对数关系，且随着过冷度的增加，水合物发展的开始点散布范围更大。此外，研究还表明，在相似的过冷度下，较高的压力条件下水合物形成的诱导时间更短。

Yaqin Tian et al. [116] suggested a novel device for hydrate synthesis that uses a tiny nozzle to spray water into a gaseous phase. It has a large enough contact surface area for a gas–liquid interaction. At 277.15 K, methane hydrate formation studies were carried out using pure water and aqueous sodium dodecyl sulphate (SDS) solution for comparison. The trials were carried out at pressures of 7.0 and 6.0 MPa, respectively. Methane intake per mole of water and reaction rate were used to explore the kinetics of methane hydrate formation. The process of hydrate formation and the kinetics property of spraying atomization were investigated using crystal chemistry theory.
田亚琴等人[ 116]提出了一种用于合成水合物的创新装置，该装置使用微型喷嘴将水喷入气相中。它具有足够大的接触表面积，用于气-液相互作用。在 277.15 K 下，使用纯水和十二烷基硫酸钠（SDS）水溶液进行了甲烷水合物形成研究，以进行比较。试验分别在 7.0 MPa 和 6.0 MPa 的压力下进行。通过每摩尔水的甲烷摄取量和反应速率来探索甲烷水合物形成的动力学。利用晶体化学理论研究了水合物形成过程和喷雾雾化的动力学特性。

Farizhendi et al. investigated the effect of synthesized nanostructures on the kinetics of methane hydrate formation, including graphene oxide, chemically reduced graphene oxide with sodium dodecyl sulphate (SDS), chemically reduced graphene oxide with polyvinylpyrrolidone, and multi-walled carbon nanotubes [117, 118]. The presence of carbon nanostructures has no effect on the storage capacity of methane hydrate in the hydrate formation process, whereas the water conversion percent to hydrate increases significantly in the presence of carbon nanotubes, with the greatest value occurring at a carbon nanotube concentration of 90 ppm, representing a 253 percent increase in the presence of carbon nanotubes compared to that without carbon nanotubes.
Farizhendi 等人研究了合成纳米结构对甲烷水合物形成动力学的影响，包括氧化石墨烯、十二烷基硫酸钠（SDS）化学还原的氧化石墨烯、聚乙烯吡咯烷酮化学还原的氧化石墨烯和多壁碳纳米管[117, 118]。碳纳米结构的存在对水合物形成过程中甲烷水合物的储存容量没有影响，而在碳纳米管存在时，水转化为水合物的百分比显著增加，在碳纳米管浓度为 90 ppm 时达到最大值，与没有碳纳米管相比，碳纳米管的存在使转化率增加了 253%。

Modeling and experimental study of hydrate formation kinetics of natural gas water surfactant system in a multitube bubble column reactor was carried out by xin et al. [119]. To improve heat and mass transfer during the procedure of hydrate formation, an internal spiral grooved tube (ISGT) was suggested as the reaction tube in a largescale multitube bubble column reactor with external slurry circulation. Based on the solute permeation model and Kolmogorov isotropic turbulence concept, a CFD technique united with the population balance model (PBM) was used to represent the gas liquid mass transfer coefficient in such multicomponent gas (natural gas) water surfactant systems during the procedure of hydrate formation in the ISGT. The ISGT hydrate formation kinetics model was then based on the Kashchiev and Firoozabadi model. Hydrate formation experiments were done at six different pressures, temperature, and circulating flow velocities of piston pump regimes to investigate the true process of natural gas hydrate formation. The experimental data was then used to fine-tune the ideal parameters, resulting in more precise model predictions.
辛等人 [119] 在多管气泡柱反应器中对天然气水表面活性剂体系的 hydrate 形成动力学进行了建模和实验研究。为了在 hydrate 形成过程中提高传热传质效率，建议在具有外部浆料循环的大规模多管气泡柱反应器中使用内部螺旋槽管 (ISGT) 作为反应管。基于溶质渗透模型和 Kolmogorov 各向同性湍流概念，采用与群体平衡模型 (PBM) 结合的 CFD 技术来表征 ISGT 中多组分气体（天然气）水表面活性剂体系在 hydrate 形成过程中的气液传质系数。然后基于 Kashchiev 和 Firoozabadi 模型建立了 ISGT hydrate 形成动力学模型。在六个不同的压力、温度和活塞泵循环流速下进行了 hydrate 形成实验，以研究天然气 hydrate 形成的真实过程。然后利用实验数据对理想参数进行微调，从而得到更精确的模型预测。

An experimental investigation on the kinetics of integrated methane recovery and CO₂ sequestration by injection of flue gas into permafrost methane hydrate reservoirs was conducted by Aliakbar et al. [120]. The injection of flue gas into permafrost gas hydrate reservoirs was explored in this work in order to assess its use in energy recovery and CO₂ sequestration on the assumption that it might drastically lower costs compared to other technologies accessible currently. The results reveal that the kinetics of methane release from methane hydrate and CO₂ retrieved from flue gas are highly influenced by the temperature of the hydrate reservoir. The experiment at 261.2 K resulted in the capture of 81.9 percent of the CO₂ present in the injected flue gas, as well as an increase in the CH₄ concentration in the gas phase of up to 60.7 mol percent, 93.3 mol percent, and 98.2 mol percent at optimal pressures after depressurizing the system to dissociate CH₄ hydrate and after depressurizing the system to CO₂ hydrate dissociation point, respectively. This is pointedly higher than the maximum efficiency stated in the literature for both CO₂ sequestration and methane recovery via flue gas injection, demonstrating the economic feasibility of direct flue gas injection into permafrost hydrate reservoirs for methane recovery and geological CO₂ capture and storage. Finally, the thermal stability of the stored CO₂ was evaluated by heating the system, and it was discovered that the incidence of N₂ in the injection gas provides an extra safety factor for the stored CO₂ in an instance of a temperature variance.
Aliakbar 等人[120]进行了一项关于将烟气注入永冻土甲烷水合物储层进行集成甲烷回收和 CO₂封存动力学的实验研究。这项工作探讨了将烟气注入永冻土气水合物储层，旨在评估其在能源回收和 CO₂封存方面的应用，假设其成本可能比目前可用的其他技术大幅降低。结果表明，甲烷水合物释放甲烷和从烟气中回收 CO₂的动力学受水合物储层温度的影响很大。在 261.2 K 的实验条件下，捕获了注入烟气中 81.9%的 CO₂，并且在系统减压解离甲烷水合物后，气相中的 CH₄浓度分别达到了 60.7 摩尔%、93.3 摩尔%和 98.2 摩尔%，具体是在最佳压力下解离甲烷水合物后、在解离 CO₂水合物点后减压系统后。 这显著高于文献中关于 CO ₂ 封存和烟道气注入甲烷回收所声明的最高效率，表明直接将烟道气注入永久冻土甲烷水合物储层进行甲烷回收和地质 CO ₂ 捕获与封存的经济可行性。最后，通过加热系统评估了储存的 CO ₂ 的热稳定性，发现注入气体中的 N ₂ 的存在为储存的 CO ₂ 在温度变化时提供了一个额外的安全因素。

Wei Ke et al. used a chemical kinetics model to examine methane–propane hydrate formation and memory effect [121]. For three dynamic processes, the computational model consists of six pseudo-elementary reactions:
魏克等使用化学动力学模型研究了甲烷-丙烷水合物形成和记忆效应[121]。对于三种动态过程，计算模型包含六个准基元反应：

• (1) Gas dissolution into the bulk liquid,
  气体溶解到整体液体中，

• (2) A gradual accumulation of hydrate precursors for nucleation initiation.
  水合物成核前驱体的逐渐积累。

• (3) Fast and autocatalytic hydrate development upon initiation.
  成核后快速且自催化地发展水合物。

The model was written in FORTRAN, with starting parameters and rate constants computed or retrieved from data matched with experimental findings. The simulations show that the length of nucleation induction is mostly influenced by the buildup of oligomeric hydrate precursors up to a certain threshold value. The gradual buildup of precursors is the rate-limiting stage in overall hydrate synthesis, and their conversion into hydrate particles is necessary for the fast, autocatalytic process. The memory effect for hydrate nucleation was examined using this model by allocating different beginning quantities of precursor or hydrate species in simulations.
该模型使用 FORTRAN 编写，初始参数和速率常数通过计算或从与实验结果匹配的数据中获取。模拟表明，成核诱导期的长度主要受寡聚水合物前驱体积累至某一阈值的影响。前驱体的逐渐积累是整体水合物合成中的限速步骤，它们转化为水合物颗粒对于快速、自催化的过程是必要的。通过在模拟中分配不同初始数量的前驱体或水合物物种，该模型考察了水合物成核的记忆效应。

The occurrence of pre-existing precursors or hydrate particles may speed up the nucleation step while without influencing hydrate development. The computational model, together with the simulations, sheds light on the reaction kinetics and nucleation process of hydrate formation.
预先存在的前驱体或水合物颗粒的出现可能会加速成核步骤，但不会影响水合物的发展。该计算模型连同模拟，揭示了水合物形成的反应动力学和成核过程。

Xiaofang and colleagues provided a more realistic and complete bidirectional growth model of hydrate shells for a real-world pipeline system. In this model, thermodynamic phase equilibrium theory and water molecule penetration theory are used to construct a technique for predicting the concentration change of hydrate-forming guest molecules and the rate of water molecule permeation. The heat transmission model predicts the temperatures on both sides of the hydrate shell. Simultaneously, reducing the mass transfer coefficient with continuous hydrate growth is used to illustrate the problem of decreasing mass transfer efficiency with a thickening hydrate shell. The pipeline system's hydrate development kinetic parameters are then modified based on hydrate growth tests performed in a high-pressure flow loop, and the microscopic features of the particles were supplied utilizing the PVM and FBRM probes. The enhanced hydrate development model can increase the precision of hydrate formation prediction in slurry systems.
夏芳及其同事为实际管道系统提供了一种更真实、更完整的冰核壳双向生长模型。在该模型中，采用热力学相平衡理论和水分子渗透理论构建了一种预测冰核形成客体分子浓度变化和水分子渗透速率的技术。热传递模型预测了冰核壳两侧的温度。同时，通过连续冰核生长降低传质系数，以说明增厚冰核壳导致传质效率下降的问题。然后根据在高压流动回路中进行的冰核生长试验，修改了管道系统的冰核发展动力学参数，并利用 PVM 和 FBRM 探针提供了颗粒的微观特征。增强的冰核发展模型可以提高浆液系统中冰核形成预测的精度。

The details of the various kinetic models based on their mechanism of application, applied over the years for various conditions are shown in Table 3 for a clear understanding.
基于其应用机制，多年来应用于各种条件下的各种动力学模型的详细信息如表 3 所示，以便清晰地理解。

2.5.1 Way Forward
2.5.1 发展方向

It can be observed from the table that many modelling techniques were applied for various gases and gas mixtures. But there is no clear modelling applied for the promoters and inhibitors on various gas mixtures at high pressures. The models can be applied to various ionic liquids and amino acids effect on pure gases and gas mixtures. The models can be applied on desalination using hydrates, carbon separation, carbon storage.
从表格中可以看出，许多建模技术被应用于各种气体和气体混合物。但在高压下，针对各种气体混合物中的促进剂和抑制剂，没有明确的建模方法。这些模型可以应用于各种离子液体和氨基酸对纯气体和气体混合物的影响。这些模型可以应用于利用水合物进行海水淡化、碳分离和碳储存。

2.6 Statistical Modelling
2.6 统计建模

Hammerschmidt determined in 1934 that hydrates were the source of attached natural gas pipelines, thus contributing to the control of the quality of gas water and the development of advanced hydrate plug prevention strategies, including the injection into the gas stream of methanol and other inhibitors [151]. A revived interest in assessing hydrate forming conditions has been prompted by recent processing activity, which stresses intense temperature and pressure conditions [152, 153]. The proposed Hammerschmidt equation is based on the correlation between the thermodynamic temperature of gas hydrate formation in reference to that of the pipeline operating pressure. The equation is as follows:
Hammerschmidt 于 1934 年确定水合物是附着在天然气管道中的来源，从而有助于控制气水质量和发展先进的水合物堵塞性能预防策略，包括向气流中注入甲醇和其他抑制剂[151]。最近的生产活动重新引发了评估水合物形成条件的兴趣，这些活动强调了强烈的温度和压力条件[152, 153]。所提出的 Hammerschmidt 方程基于气体水合物形成的热力学温度与管道操作压力之间的相关性。该方程如下：

$$HFT=8.9\times P^{0.285}$$

(7)

where P is operating pressure.
其中 P 为操作压力。

To improve the dependability of predicting gas hydrate formation, later over the years many researchers has proposed various statistical equations and models. During this improvement of the existing models, gas gravity is found to have a major impact on the thermodynamic conditions of the gas hydrates. Based on this, Kobayashi and Sloan have presented correlation to predict HFT based on gas gravity curves [154]. The equation is as follows:
为了提高预测天然气水合物形成的可靠性，多年来许多研究人员提出了各种统计方程和模型。在改进现有模型的过程中，发现气体重度对天然气水合物的热力学条件有重大影响。基于这一点，小林和斯隆提出了基于气体重度曲线预测 HFT 的相关关系[154]。该方程如下：

$$\begin{array}{rl}HFT=& 1/[K_1+K_2(lnP)+K_3(ln{\gamma }_g)+K_5(lnP)(ln{\gamma }_g)\\ & +K_6(ln{\gamma }_g{)}^2+K_7(lnP{)}^3+K_8(lnP{)}^2(ln{\gamma }_g)\\ & +K_9(lnP)(ln{\gamma }_g{)}^2+K_{10}(ln{\gamma }_g{)}^3+K_{11}(lnP{)}^4\\ & +K_{12}(lnP{)}^3(ln{\gamma }_g)+K_{13}(lnP{)}^2(ln{\gamma }_g{)}^2\\ & +K_{14}(lnP)(ln{\gamma }_g{)}^3+K_{15}(ln{\gamma }_g{)}^4\end{array}$$

(8)

John and Papadopoulos studied the impact of spherical asymmetry is incorporated into a version of van der Wash and Platteeuw's (1959) hydrate equilibrium model. To anticipate the divergence of Langmuir constants from ideal values, a related states correlation is applied. The Kihara parameters acquired from hydrate equilibrium data correspond well with those acquired from virial coefficient data in this model.
约翰和帕帕多普洛斯研究了球形不对称性被纳入范德瓦什和普拉特尤（1959 年）水合物平衡模型的影响。为了预测朗缪尔常数偏离理想值的趋势，应用了相关状态关联。从水合物平衡数据中获得的 Kihara 参数与该模型中从维里系数数据获得的参数吻合良好。

This is one of the most precise and dependable formulae in the gas business, and it is extensively used to predict Hydrate Formation Temperature (HFT). But, since the equation is complicated, Berge proposed a simplified version of this equation focusing on the gas gravity range [155].
这是气体行业中最为精确和可靠的公式之一，被广泛用于预测水合物形成温度（HFT）。但是，由于该方程式复杂，贝尔热提出了一个简化版本，专注于气体重力范围[155]。

For 0.555 ≤  ${\gamma \gamma }_{gg}$  < 0.58:
对于 0.555≤ ${\gamma \gamma }_{gg}$ <0.58：

$$\begin{array}{rl}HFT=& -96.03+25.37\times \ln P-0.64\times {\left(\ln P\right)}^2\\ & +\frac{{\gamma }_g-0.555}{0.025}\times [\frac{80.61\times P+1.16\times {10}^4}{\left(P+596.16\right)}\\ & -(-96.03+25.37\times \ln P-0.64\times {\left(\ln P\right)}^2\end{array}$$

(9)

For 0.58 ≤  ${\gamma \gamma }_{gg}$  < 1:
对于 0.58≤ ${\gamma \gamma }_{gg}$ <1：

$$\begin{array}{c}HFT=\frac{\left\{80.61\times P-2.1\times {10}^4-1.22\times \frac{{10}^3}{1}\left({\gamma }_g-0.535\right)-\left[1.23\times {10}^4+1.71\times \frac{{10}^3}{\left({\gamma }_g-0.509\right)}\right]\right\}}{}\\ [P-(-260.42-5.18/\left({\gamma }_g-0.535\right)\end{array}$$

(10)

With developments in the capabilities of numerical modeling and the availability of field data, from late 90’s the focus is on developing various statistical models to understand the physical and chemical properties of gas hydrates, develop accurate predictive models and for the usage of Energy conversion and management using gas hydrate technology. Among them, Motiee correlation gained a significant attention over the years for the Estimate possibility of hydrates [156]. The correlation is as follows:
随着数值建模能力的提升和现场数据的可用性，自 20 世纪 90 年代末以来，重点转向开发各种统计模型，以理解天然气水合物的物理和化学性质，开发精确的预测模型，以及利用天然气水合物技术进行能源转换和管理。其中，Motiee 关联模型多年来备受关注，可用于估算水合物的可能性[156]。该关联模型如下：

$$\begin{array}{rl}HFT=& K_1+K_2\log \left(P\right)+K_3{\left(\log P\right)}^2\\ & +K_4{\gamma }_g+K_5{\gamma }_g^2+K_6{\gamma }_g\log P\end{array}$$

(11)

After calculating the molecular descriptors from the optimized chemical structures of every investigated promoter, a linear equation is derived, which can predict or represent the desired parameter (hydrate dissociation pressure) with minimal variables and maximum accuracy. In other words, the objective is to create a subset of variables (the most statistically efficient molecular descriptor on dissociation conditions) from all presented variables (all molecular descriptors) that can predict or reflect the pressure of hydrate dissociation with the smallest possible deviation from the experimental values [157].
在计算了每个研究的促进剂的优化化学结构后，推导出一个线性方程，该方程可以用最少的变量和最大的精度预测或表示所需参数（水合物解离压力）。换句话说，目标是从所有提出的变量（所有分子描述符）中创建一个变量子集（解离条件下的最统计效率的分子描述符），该子集能够以最小的偏差预测或反映水合物解离压力的实验值[157]。

A graphical approach for estimating the hydrate formation temperature at pressures ranging from 100 psia to 4000 psia has been devised. Although most engineers have access to computer systems that use equations of state to anticipate hydrate conditions, field operations staff will find the rapid, graphical approximation technique beneficial for this purpose [158].
一种用于估算 100 磅力每平方英寸至 4000 磅力每平方英寸压力范围内水合物形成温度的图形方法已被开发出来。尽管大多数工程师能够使用状态方程来预测水合物条件，但现场操作人员会发现这种快速、图形化的近似技术对此非常有用[158]。

The Automated Lag Time Apparatus (ALTA) was originally developed to be used as an atmospheric pressure statistical analysis of ice nucleation in a glass tube. A HP-ALTA was constructed and built to achieve equivalent statistically valid data sets for the development of high gas pressure gas hydrates [159].
自动化滞后时间装置（ALTA）最初是为在玻璃管中进行大气压下冰核形成的统计分析而开发的。一个 HP-ALTA 被构建和制造出来，以实现高气压气体水合物发展所需的等效统计有效数据集[159]。

Katz devised the gas-gravity diagram (Fig. 6) to relate hydrate pressure and temperature to the specific gravity (gas molecular weight divided by air) of natural gases, excluding non-hydrocarbons [80] (Fig. 7).
卡茨设计了气-重力图（图 6），用于将水合物压力和温度与天然气的相对密度（气体分子量除以空气）相关联，排除了非烃类物质[80]（图 7）。

Fig. 6
图 6

Gas Uptake during hydrate formation
水合物形成过程中的气体摄取

Fig. 7
图 7

Initial hydrate-formation estimation for natural gases based on gas gravity [160]
基于气体比重的天然气初始水合物形成估计 [ 160]

Based on the statistical theory of gas hydrates, an improved generic methodology for determining gas hydrate formation conditions is provided. The novel approach reproduces the majority of existing experimental data acquired over a wide scale of temperatures and pressures within experimental error [161].
基于天然气水合物统计理论，提供了一种改进的通用方法来确定天然气水合物形成条件。该方法在实验误差范围内再现了大多数现有实验数据，这些数据是在广泛的温度和压力范围内获得的[161]。

Based on the homogeneity of component frugalities in all phases, a general phase equilibrium model is used to predict the hydrate suppression temperature of aqueous solution of salt and alcohol as well as the water activity. The statistical thermodynamics model uses the Cube Plus state equation for measurements of fugacity in each liquid process. The hydrate-forming conditions are based on van der Waals and Platteeuw’s solid solution theory. The van der Waals and Platteeuw statistical thermodynamic model provides a bridge between the thermodynamic macroscopic properties and the microscopic properties of the structure of the clathrate hydrate. By using the solid solution principle of van der Waals and Platteeuw as a basis, the hydrate process is modelled [74].
基于各相组分节俭性的均一性，采用通用相平衡模型预测盐醇水溶液的抑制剂温度及水活性。统计热力学模型使用立方加和状态方程测量各液相中的逸度。水合物形成条件基于范德华和普拉特尤的固溶体理论。范德华和普拉特尤统计热力学模型在热力学宏观性质与水合物结构微观性质之间建立了桥梁。以范德华和普拉特尤的固溶体原理为基础，对水合物过程进行建模[74]。

Ostergaard et al. developed A novel correlation has been created for forecasting the hydrate-free zone of reservoir fluids ranging from black oil to lean natural gas. The approach compares the hydrate dissociation pressure to the specific gravity, concentration of the hydrate-forming components in the fluid, and system temperature. The influence of nitrogen and carbon dioxide on the hydrate-free zone has also been considered. The correlation was created by generating hydrate phase boundaries for 31 fluids using a well-proven complete thermodynamic model. Hydrate phase boundaries computed by the novel correlation and the thermodynamic model for 13 separate reservoir fluids were compared, with a maximum error of 1.0 K in the projected potential hydrate-forming temperature [162].
Ostergaard 等人开发了一种新型关联式，用于预测从稠油到贫天然气的储层流体无水合物区。该方法将水合物解离压力与流体的水合物形成组分的比重、浓度和系统温度进行比较。同时考虑了氮气和二氧化碳对无水合物区的影响。该关联式通过使用一个经过充分验证的完整热力学模型，为 31 种流体生成了水合物相边界。将新型关联式和热力学模型计算的 13 种不同储层流体的水合物相边界进行了比较，预测的水合物形成温度最大误差为 1.0 K [162]。

This novel correlation can compute the pressure or temperature of hydrate formation for single components or gas combinations with or without inhibitors. These connections apply to temperatures as high as 305.372 K and pressures as high as 82.737088 MPa. The data reveal an average absolute percentage divergence of 15.93 in pressure and a 257.0222 K difference in absolute temperature [163].
这种新型关联式可以计算单一组分或含/不含抑制剂气体的水合物形成压力或温度。这些关联式适用于高达 305.372 K 的温度和高达 82.737088 MPa 的压力。数据显示压力的平均绝对百分比偏差为 15.93%，绝对温度差异为 257.0222 K[163]。

Gas hydrate saturation is measured by seismic inversion integration and rock modeling of gas hydrate-bearing structures [164].
天然气水合物饱和度通过地震反演集成和含天然气水合物结构的岩石建模来测量[164]。

• 1. Rock modeling as a function of burial depth, speed, porosity, etc. of the gas hydrate-bearing clay or sand system.
  岩石建模是作为含天然气水合物粘土或砂岩系统中的埋藏深度、速度、孔隙率等函数。

• 2. To derive IS, IP, and/or density, seismic elastic inversion.
  为获取 IS、IP 和/或密度，进行地震弹性反演。

• 3. Generation of probability distribution functions (PDF) and statistical study of rock groups with various hydrate saturations.
  生成概率分布函数（PDF），并对具有不同水合物饱和度的岩石组进行统计分析。

• 4. Using deterministic inversion or Bayesian inversion, mapping hydrate saturation.
  使用确定性反演或贝叶斯反演，绘制水合物饱和度图。

Various techniques can be used to predict hydrate formation of gases. However, every technique had some limitations in gas constituents or in temperature and pressure range. Ignoring these limitations will lead to inaccuracy [165].
有多种技术可用于预测气体水合物的形成。然而，每种技术在气体成分或温度和压力范围内都存在一些局限性。忽视这些局限性会导致不准确 [165]。

• 1. Katz method: Uses vapor-solid equilibrium constant to discover hydrate formation pressure or temperature.
  卡茨方法：利用汽-固平衡常数来发现水合物形成的压力或温度。

• 2. Gas-gravity plots established by Katz: These plots come in two forms: firstly, plots that are related to the hydrate formation temperature and pressure to gas gravity which is the apparent molecular weight of a gas mixture over the air and secondly, the charts of approved expansion that a natural gas can undergo without the risk of hydrate formation.
  卡茨建立的重力图：这些图有两种形式：首先，与水合物形成温度和压力相关的图，这些图与气体相对分子质量（即气体混合物对空气的表观分子质量）相关；其次，天然气在不形成水合物风险下可以进行的膨胀批准图表。

These methods are simple graphical methods that could be helpful for an initial estimation of conditions of hydrate formation and rough configuration of chokes and valves. These techniques have been documented to be insufficiently accurate by statistical accuracy analysis and can lead to extreme errors in the expected values for the same gas gravity with different mixtures. Empirical correlations, which are formed with an abundance of parameters in different types. This method is inspired by the approach suggested by Van der Waals and Platteeuw to statistical thermodynamics and considers the interactions between water molecules and the crystal lattice forming gas molecules.
这些方法是简单的图形方法，有助于对水合物形成条件进行初步估计和节流阀及阀门的粗略配置。通过统计精度分析，这些技术已被记录为不够准确，并且可能导致不同混合物在相同气体相对分子质量下的预期值出现极端误差。经验关联，这些关联由不同类型的众多参数形成。该方法受到范德华和普拉特尤提出的统计热力学方法的启发，并考虑了水分子与形成气体的晶格之间的相互作用。

Van der Waals-hydrate Platteeuw's phase statistical model was determined using conditions of hydrate formation, using both simple and improved state equations for the liquid and vapor phases. In the phase balance in mixtures, the cubic state equations play a critical role [166].
范德华-水合物 Platteeuw 相统计模型是根据水合物形成的条件，使用适用于液相和气相的简单和改进状态方程确定的。在混合物的相平衡中，立方状态方程起着关键作用[166]。

The cage occupancy of each guest molecule in the large and small cages of the C₃H₈ + CH₄ hydrate can be extracted by linking a statistical thermodynamics equation with the intensity ratios of guest molecules. However, the cage occupancies of CH₄ and C₃H₈ could not be calculated with a statistical model after the replacement because of the complete separation of CH₄ and C₃H₈ in every cage as well as the lack of ability to detect N₂ and CO₂ accurately by MAS NMR analysis [167].
C ₃ H ₈ + CH ₄ 水合物的大笼和小笼中每个客体分子的笼占位情况可以通过将统计热力学方程与客体分子的强度比联系起来来提取。然而，由于 CH ₄ 和 C ₃ H ₈ 在每个笼中完全分离，以及无法通过 MAS NMR 分析准确检测 N ₂ 和 CO ₂ ，所以在替换后无法用统计模型计算 CH ₄ 和 C ₃ H ₈ 的笼占位情况 [ 167]。

Bahadori et al. developed a unique empirical correlation for predicting the hydrate formation condition of sweet natural gases in a timely manner. The discovered correlation is valid for a wide range of temperatures (265–298 K), pressures (1200–40,000 kPa), and molecular weights (16–29). The newly suggested equation yields constantly correct findings over the recommended pressure, temperature, and molecular weight ranges [168].
Bahadori 等人开发了一种独特的经验关联式，能够及时预测甜天然气水合物形成的条件。所发现的关联式适用于广泛的温度范围（265–298 K）、压力范围（1200–40,000 kPa）和分子量范围（16–29）。所提出的方程在推荐的压力、温度和分子量范围内始终能给出正确的结果[168]。

In previous publications, it has been demonstrated that highly accurate state reference equations for fluid phases comprising water and carbon dioxide can be combined with solid phase state equations to obtain a coherent explanation of Carbon Capture and Storage (CCS)-related thermodynamic systems. The famous model derived from Ballard and Sloan, based on the statistical model of van der Waals and Platteeuww, can be modelled on gas hydrates (vdWP) [169].
在之前的出版物中，已经证明由水和二氧化碳组成的流体相的高精度状态参考方程可以与固相状态方程相结合，以获得对碳捕获与封存（CCS）相关热力学系统的连贯解释。基于范德华和 Platteeuww 的统计模型而得出的著名模型（vdWP）[ 169] 可以用于模拟气体水合物。

Two broad correlations have been proposed by Zahedi et al. for HFT. One correlation contains 11 parameters, whereas the other has 18 parameters. To get constants for the proposed equations, 203 experimental data points were collected from the literature. For statistical analysis, the Engineering Equation Solver (EES) and Statistical Package for the Social Sciences (SPSS) software packages were used. The resulting correlations' accuracy has also been certified by comparison with experimental data and certain recently commonly utilized correlations [170].
Zahedi 等人提出了两种用于 HFT 的广泛关联。一种关联包含 11 个参数，而另一种包含 18 个参数。为了获取所提出方程的常数，从文献中收集了 203 个实验数据点。对于统计分析，使用了工程方程求解器（EES）和社会科学统计软件包（SPSS）。通过将实验数据与某些最近常用的关联进行比较，验证了所得关联的准确性 [ 170]。

Some interesting conclusions are made possible by the Clapeyron equation applied to three-phase hydrate formation lines of binary mixtures. The Clapeyron equation relates enthalpy and volume transition to the slope of phase equilibrium lines. With regard to the retrograde behavior shown at high pressures by some hydrate formers, it can be concluded that the density of the hydrate phase is the same precisely at the maximum temperature of the three-phase hydrate formation lines as the total density of the two other phases in equilibrium with hydrates. Therefore, since the state equations used to model the fluid phases are highly accurate in density, especially compared to the cubic state equations that are still commonly used in hydrate modeling, the accuracy of the hydrate phase density obtained benefits from the accuracy of the fluid phase models [171].
通过将克拉珀龙方程应用于二元混合物的三相水合物生成线，可以得出一些有趣的结论。克拉珀龙方程将焓和体积转变与相平衡线的斜率联系起来。对于某些水合物形成物在高压下表现出的逆行行为，可以得出结论：水合物相的密度在三相水合物生成线的最高温度处，与与水合物处于平衡状态的其他两相的总密度完全相同。因此，由于用于模拟流体相的状态方程在密度方面非常精确，特别是与仍然常用于水合物建模的立方状态方程相比，所获得的水合物相密度的准确性受益于流体相模型的准确性[171]。

For mixture-gas hydrates, modeling phase equilibrium requires the appropriate mixing rule to find the mixture parameters that depend on the individual component property. The most typically used mixing rule for gas hydrates systems in the van der Waals one-fluid type mixing rule. This is widely used for non-polar mixtures but fails to precisely find the properties of asymmetric and polar component mixtures. Another category of mixing rules, with a purpose of capturing polar mixture properties, use excess Gibbs free energy (GE) as a base and is known as GE-type mixing rules. This includes but is not limited to Huran-Vidal, modified Huran-Vidal, Kurihara, Wong-Sandler (WS) and a linear combination of Vidal and Michelson (LCVM) [172]. Out of all of these, the WS mixing rule has received notoriety for its accuracy in predicting phase equilibrium for strongly nonideal mixtures. The Helmholtz free energy accounted in the WS mixing rule makes sure of the quadratic reliance of second virial coefficient on the composition of gas components as required by statistical thermodynamics. Besides that, the Helmholtz free energy at infinite pressure as assumes as Gibbs free energy at zero pressure. However, GE-type mixing rules are not typically used for predicting gas hydrate formation conditions, but often used in VLE calculation. The classic thermodynamic model was derived by van der Waals and Platteuw, which makes use of statistical thermodynamics to determine the hydrate phase model [173].
对于混合气体水合物，建模相平衡需要采用适当的混合规则来找到依赖于各组分性质的混合参数。范德华单流体型混合规则是气体水合物系统中最常用的混合规则。该规则广泛用于非极性混合物，但无法精确确定非对称和极性组分混合物的性质。另一类旨在捕捉极性混合物性质的混合规则以过量吉布斯自由能（GE）为基础，被称为 GE 型混合规则。这包括但不限于 Huran-Vidal、改进型 Huran-Vidal、Kurihara、Wong-Sandler（WS）以及 Vidal 和 Michelson 的线性组合（LCVM）[172]。在这些规则中，WS 混合规则因其对强非理想混合物相平衡预测的准确性而闻名。WS 混合规则中包含的 Helmholtz 自由能确保了第二维里系数对气体组分组成的二次依赖关系，符合统计热力学的要求。 除此之外，无限压力下的亥姆霍兹自由能被视为零压力下的吉布斯自由能。然而，GE 型混合规则通常不用于预测气体水合物形成条件，而常用于 VLE 计算。经典的热力学模型由范德华和普拉图依推导，该模型利用统计热力学来确定水合物相模型[173]。

Thermodynamics predictions are vital in case of gas mixture caused by hydrate structure transition. More accurate predictions for gas mixtures via the bridge of statistical thermodynamics was enabled by the modern spectroscopy. The van der Waals mixing as well as its modified forms have been proven successful in applicability in highly nonideal mixtures. This is not the case for low density limits where the models are inconsistent. Additionally, these rules of mixing have failed to have a quadratic dependence of second virial coefficient as required by the statistical mechanics. To combat these issues, the Wong-Sandler mixing rule was proposed. Using the vdW model as a base, the WS mixing rule can be ignored in a small range of pressure and temperature but not near the high- and low-density limits of fluids. At the lower limit, the fluid phase can be assumed to be a perfect gas and the molecular interactions can be ignored, while the same properties resemble the liquid at the higher limit. These factors are accounted in the WS mixing rule and the model reduces to the virial equation of state for the former case and to an activity coefficient model for the latter. Contrastingly, the linear mixing rule fails to capture these phenomena. The presence of simple fluid phases is another issue. The rare characteristic of the model is that it can be applied the same way in both cases with accuracy where other models are restricted in that they perform well only for which they are designed.
在由水合物结构转变引起的气体混合物情况下，热力学预测至关重要。现代光谱学通过统计热力学的桥梁实现了对气体混合物更准确的预测。范德华混合及其修正形式已被证明在高度非理想混合物中具有成功的适用性。然而，在低密度极限下，这些模型存在不一致性。此外，这些混合规则未能满足统计力学所要求的第二维里系数的二次依赖关系。为了解决这些问题，提出了 Wong-Sandler 混合规则。以 vdW 模型为基础，WS 混合规则在小范围的压强和温度下可以忽略，但在流体的高、低密度极限附近则不能忽略。在低密度极限下，流体相可以假设为理想气体，分子间相互作用可以忽略，而在高密度极限下，具有相同的性质，类似于液体。WS 混合规则考虑了这些因素，对于前一种情况，该模型简化为维里状态方程，而对于后一种情况，则简化为活度系数模型。 相比之下，线性混合规则无法捕捉这些现象。简单流体相的存在是另一个问题。该模型的独特之处在于，它可以用相同的方式在两种情况下都保持准确性，而其他模型则受限，它们只在设计用途上表现良好。

In order to estimate the hydrate phase equilibria, van der Waals and Platteeuw (vdWP) developed the most promising model. An ideal solid solution derived from classical statistical thermodynamics is the vdWP model. Using an anology for the Langmuir isotherm, this thermodynamic model for gas hydrates was derived, whereby different adsorption sites exist for many hydrate former species [77]. Several attempts have been done to modify and improve the vdWP hydrate model to eliminate nearly all of the hypotheses done in the basic vdWP model. To take into account the different clusters of smaller molecules present within the hydrate cavities and guest-guest interactions inside a cavity, the statistical thermodynamic model has been updated. There is no basic model, however, to take the guest-guest relationship into account in nearby cavities. In most hydrate-forming systems that include high concentrations of inhibitors, which include salts, the dire limitations of the fluid phase model, which does not take into account the effect of hydrogen bonding as well as electrolyte contributions, can lead to dire errors. The molecules can be assumed to be spherically symmetrical during measurements, to prevent ambiguity.
为了估算水合物相平衡，范德华和普拉特尤（vdWP）开发了最有前景的模型。vdWP 模型源于经典统计热力学推导的理想固溶体。通过借鉴朗缪尔等温线的类比，推导出这个用于气体水合物的热力学模型，其中许多水合物形成物种存在不同的吸附位点[77]。人们已经做了多次尝试来修改和改进 vdWP 水合物模型，以消除基本 vdWP 模型中几乎所有的假设。为了考虑水合物空腔内较小分子的不同簇和空腔内客体-客体相互作用，统计热力学模型已经更新。然而，目前还没有基本模型能够考虑邻近空腔中的客体-客体关系。在大多数包含高浓度抑制剂（包括盐类）的水合物形成体系中，由于流体相模型忽略了氢键效应以及电解质贡献，其严重的局限性可能导致严重的误差。 在测量过程中，可以假设分子是球对称的，以避免歧义。

In this analysis, the suggested hydrate model is derived from the large van der Waals and Platteeuw-type (vdWP) models family. Alas, none of the existing models of hydrate is paired with the most reliable state multiparameter equations available for phases other than hydrate, causing the latest model to be derived. A model of natural gas hydrates is Ballard and Sloan's gas hydrate model. While Ballard and Sloan accounted in their model for several components related to natural gas, they did not take into account oxygen, argon and carbon monoxide, which are essential components in the creation of a CCS model. The model of Ballard and Sloan was regarded as the basis for the derivation of the upgraded model for mixed hydrates. In order to minimize the number of adjustable parameters directly related to the measurement of the reference properties and the molar volume of mixed hydrates, a few changes and improvements have to be made [174]. Ternary mixtures of water and three hydrate formers have been measured for phase equilibria of several different phases, including fluid phases, gas hydrates, solid water and solid carbon dioxide. Different models were employed for each point. According to prior works, which focused on accurate modeling of gas hydrates from pure gases, the current model for mixed hydrates was derived [175]. From the Ballard and Sloan model, the mixed hydrates model was developed, which can be deemed as a state-of-the-art model for the mixed hydrates of basic natural gas mixtures.
在这项分析中，所建议的水合物模型源自大型范德华和 Platteeuw 型（vdWP）模型家族。然而，现有的水合物模型均未与适用于除水合物外其他相态的最可靠的状态多参数方程相匹配，因此需要推导出最新的模型。天然气水合物的模型是 Ballard 和 Sloan 的水合物模型。虽然 Ballard 和 Sloan 在其模型中考虑了与天然气相关的多个组分，但他们并未考虑氧气、氩气和一氧化碳，这些是构建 CCS 模型所必需的组分。Ballard 和 Sloan 的模型被视为混合水合物升级模型的推导基础。为了最小化与参考性质和混合水合物摩尔体积测量直接相关的可调参数数量，必须进行一些变更和改进[174]。已测量了水和三种水合物形成物的三元混合物的相平衡，包括流体相、气体水合物、固态水和固态二氧化碳。每个点采用了不同的模型。 根据先前的研究，这些研究专注于纯气体中气水合物的精确建模，当前的混合水合物模型被推导出来[175]。从 Ballard 和 Sloan 模型中，混合水合物模型被开发出来，这可以被视为基本天然气混合物混合水合物的一种最先进模型。

Based on recent studies, results comparable to statistical model results can be extracted from the extended Walton model by inserting the coordination number as a function of pressure or porosity. Statistical modelling shows that "the average strain assumption offers a pretty excellent approximation to the bulk modulus but a rather poor approximation to the shear modulus." On this basis, it can be concluded that, when applied to oblique compression, the Hertz-Mindlin model, established for standard compression, is not as accurate as originally assumed [176].
根据近期研究，通过将配位数作为压力或孔隙率的函数插入扩展沃尔顿模型，可以提取出与统计模型结果相当的结果。统计建模表明，“平均应变假设对体积模量提供了相当好的近似，但对剪切模量的近似则相当差。”基于此，可以得出结论，当应用于斜向压缩时，为标准压缩建立的赫兹-明德尔模型，其准确性并不像最初假设的那样高[176]。

Several groups have researched double cage occupancy. According to statistical mechanics, a vdWP model was built to ensure that large cavities can be double occupied. A term for a double occupied wide cavity broadened the formulation for the chemical potential. This method inspired other groups and was used as a reference for the usage in models for phase equilibrium calculations and molecular simulations. It was successfully used to calculate hydrate compositions where double cage occupancy occurs at high pressures. Experimental occupancy data can be related to calculated values of the proposed model [177]. In relation to the quantified occupancy data, there is a slight offset between the experimental data and the calculated values. Typically, the estimated rates are greater than the observed data. The use of heavy water in the experimental setup may cause this. Since the occupancy data was considered to match the parameters and, according to statistical vdWP assumptions, all calculations were performed with a consistent model, the occupancy values can be considered satisfying.
已有多个研究小组研究了双笼占位问题。根据统计力学，建立了一个 vdWP 模型以确保大笼可以被双占位。一个用于双占位宽笼的项扩展了化学势的公式。这种方法启发了其他研究小组，并被用作相平衡计算和分子模拟模型中的参考。它成功用于计算在高压下发生双笼占位的水合物组成。实验占位数据可以与所提出模型的计算值相关联[177]。关于量化占位数据，实验数据与计算值之间存在轻微偏差。通常，估计的速率大于观测数据。实验装置中使用重水可能是造成这种现象的原因。由于占位数据被认为与参数匹配，并且根据统计 vdWP 假设，所有计算都是使用一致的模型进行的，因此占位值可以被认为是令人满意的。

Analytical investigations of the conditions for gas hydrate production utilize basic classical thermodynamics equations. The investigations took use of Van der Waals' general statistical model for the interpretation of clathrate compound characteristics and its advancements in later works of scientists who subsequently used it on gas hydrates, explained and supplemented it. The behavior of gas hydrates under pressure will also vary according to the Clausius–Clapeyron equation, ranging from hydrates destabilization of the sII structure to considerable hydrates stabilization of the KS-I structure. The presence of numerous voids in the solid phase of gas hydrates was investigated, with the equilibrium concentration varying and being governed by the formation energy value. To investigate the effect of phase transition conditions on excess in non-equilibrium defects, two scenarios were considered: phase 1 was solid (ice + gas) and phase 2 was liquid (water + gas). In addition, a novel Classius-Clapeyron equation is employed for the circumstances of gas hydrate formation, which takes into account the presence of an excess in non-equilibrium defects through a series of mathematical transformations. To this day, statistical thermodynamics approaches have allowed for a thorough explanation of the chemical and physical characteristics of gas hydrates, as well as data on the nature of the interaction of forces among molecules in a gas hydrate crystal and the specifics of the gas hydrates structure. Van der Waals developed the statistical model for describing the features of hydroquinone clathrate molecules [178]. As a consequence, this model has been utilized globally for gas hydrates and has been researched further in scientific publications. Thanks to the equations derived, it was possible to define the degree of filling of the gas hydrate crystal lattice, the circumstances of production, and the composition. These equations may be found by determining the temperature-dependent ratio of the water vapour pressure over pure water, an aqueous solution, or ice that are in equilibrium with the gas hydrate to the water vapour pressure over an empty gas hydrate lattice. the difference in the chemical potentials of water, an aqueous solution, or ice in equilibrium with the gas hydrate, and the chemical potential of water in an empty gas hydrate lattice as a temperature and pressure function, as well as the Langmuir constant as a temperature function.
气体生成条件的解析研究利用了基本的经典热力学方程。这些研究采用了范德华的一般统计模型来解释笼状化合物的特性，以及后来科学家们在此基础上对气体水合物进行应用、解释和补充的进展。气体水合物在压力下的行为也将根据克劳修斯-克拉佩龙方程而变化，从 sII 结构的分解到 KS-I 结构的显著稳定。研究了气体水合物固相中存在大量空隙的情况，平衡浓度会变化，并受形成能值控制。为了研究相变条件对非平衡缺陷的影响，考虑了两种情况：第一阶段为固态（冰+气体），第二阶段为液态（水+气体）。 此外，还采用了一种新型克拉珀龙方程来描述气体水合物形成的条件，该方程通过一系列数学变换考虑了非平衡缺陷的存在。迄今为止，统计热力学方法已经能够全面解释气体水合物的化学和物理特性，以及关于气体水合物晶体中分子间相互作用力的性质和气体水合物结构的细节。范德华提出了统计模型来描述氢醌水合物的特性[178]。因此，该模型已被全球用于气体水合物研究，并在科学出版物中得到了进一步研究。借助所推导的方程，可以确定气体水合物晶格的填充程度、生成条件和组成。 这些方程可以通过确定与气水合物处于平衡状态的纯水、水溶液或冰的水蒸气压与空气水合物晶格上的水蒸气压的比值来获得。同时，需要考虑与气水合物处于平衡状态的纯水、水溶液或冰的水化学势与空气水合物晶格中水的化学势之间的差异，将其作为温度和压力的函数，以及朗缪尔常数作为温度的函数。

The principal for phase equilibrium was developed by Gibbs over 100 years ago. This principle state that:
相平衡的基本原理由吉布斯在一百多年前提出。该原理表明：

• 1. The temperature and pressure of the phases are identical.
  各相的温度和压力相同。

• 2. Each component's chemical potential is equal in every point.
  每个组分的化学势在每一点都相等。

• 3. A minimal Global Gibbs free energy.
  一个最小的全球吉布斯自由能。

This can be applied to phase equilibrium conditions involving Gas hydrate and are very useful for the formation of the models for performing hydrate equilibrium calculations [1].
这可以应用于涉及气体水合物的相平衡条件，并且对于形成进行水合物平衡计算的模型非常有用[1]。

Three common models have been derived or used as a base for development of any model to estimate formation of hydrates:
已经推导出三种常见的模型，或者作为任何估计水合物形成的模型开发的基础：

• 1. Statistical Model
  统计模型

  
  

  Statistical model was first proposed by Van der Waals and Platteuw in 1959 for estimating rate of formation of hydrates. The non-H₂O species concentration served as the process of adsorption of gas onto solid in gas hydrates.
  统计模型最早由范德华和普拉特于 1959 年提出，用于估算水合物的生成速率。非水物种浓度在气体水合物中充当气体在固体上的吸附过程。

• 2. Multi component statistical model
  多组分统计模型

  
  

  The first statistical model method was used as a base for formation of gas hydrates calculations but was not accepted due to lack of accuracy. Hence, a modified statistical model was derived by Parrish and Prausnitz in 1972 to make accurate calculations for gas hydrate formation easier. This model differs from the previous statistical model because it includes the multi component mixtures that forms gas hydrates and is involved over all components.
  最初的统计模型方法被用作气体水合物生成的计算基础，但由于缺乏准确性而未被接受。因此，帕里斯和普拉乌斯尼茨于 1972 年推导出一种改进的统计模型，以简化气体水合物生成的精确计算。该模型与之前的统计模型不同，因为它包括形成气体水合物的多组分混合物，并涉及所有组分。

• 3. Equilibrium model
  平衡模型

  
  

  A vital improvement was made by the model derived by Peng and Robinson in 1977. This model is used to predict the formation of gas hydrates when hydrocarbon exists at equilibria. Change in enthalpy and volumetric change must first be evaluated. An equivalent equation of the perms can also be used.
  彭和罗宾逊于 1977 年提出的模型做出了关键改进。该模型用于预测当烃类处于平衡状态时气态水合物的形成。首先需要评估焓变和体积变化。也可以使用渗透率的等效方程。

The calculation for potential of water in the hydrate phase is based on the Van der Waals and Platteeuw model which is developed from statistical thermodynamics [179].
水合物相中水的势能计算基于范德华和普拉特尤模型，该模型源自统计热力学[179]。

Salufu et al. suggested empirical connection utilising gravity technique and statistical analysis software to demonstrate the mathematical equation that correlates hydrate-formation temperature, pressure, water vapour pressure, and specific gravity of hydrocarbon systems. 300 data points from the literature were used to create the connection. The correlation was confirmed by comparing it to some of the existing correlations using 26 data points that were not involved in the optimization [180].
Salufu 等人建议利用重力技术和统计分析软件建立经验关联，以展示与水合物形成温度、压力、水蒸气压和烃类系统比重相关的数学方程。他们使用文献中的 300 个数据点创建了这种关联。通过使用 26 个未参与优化的数据点将其与一些现有关联进行比较，验证了该关联[180]。

Based on the three-phase theory relating to gas hydrate saturation and velocity, a three phase Biot form theory was proposed. This hypothesis has been updated further. Water, grain, and gas hydrates in the isostrain state are taken into account in the condensed version of this theory. The velocity of the gas hydrates containing sediments was modelled using the STPBE, assuming isotropic conditions. The bulk (k) and shear (μ) modules of the gas hydrate bearing sediments were further formed where the gas hydrate occupies the pore space [181].
基于与天然气水合物饱和度和速度相关的三相理论，提出了一个三相 Biot 形式理论。该假设已被进一步更新。在该理论的精简版本中，考虑了在等应变状态下水、颗粒和天然气水合物。使用 STPBE 对含沉积物的天然气水合物速度进行了建模，假设条件为各向同性。当天然气水合物占据孔隙空间时，进一步形成了天然气水合物承载沉积物的体积（k）和剪切（μ）模量[ 181]。

The formation of hydrate happens during the vapour-liquid interface in which water film is in abundance in dissolved guest gas. Classical thermodynamics like the euqtion of state model can define the nonideality of the vapour phase. On the other hand, for the hydrate phase, van der Waals and Platteeuw's statistical thermodynamics based model is used to show the change in the chemical potential of water for an empty and filled hydrate by using the Boltzmann weighted guest's volume integration; host potential function over the cavity radius [182].
水合物的形成发生在蒸汽-液相界面，其中水膜富含溶解的客体气体。经典热力学如状态方程模型可以定义蒸汽相的非理想性。另一方面，对于水合物相，使用基于 van der Waals 和 Platteeuw 的统计热力学模型，通过使用 Boltzmann 加权客体体积积分和主体势函数在空腔半径上的积分，展示了空置和充满水合物的水化学势的变化[ 182]。

To predict hydrate formation temperature (HFT) at a given pressure state, accurate statistical regression analysis can theoretically be carried out. The optimization algorithm will build a validation model to help predict the HFT. Theoretically, accurate statistical regression analysis to predict hydrate formation temperature (HFT) can also be performed for the multiphase system at a given pressure state. To estimate the error between the expected and actual results, ANOVA statistical analysis can be performed. Theoretically, accurate statistical regression analysis to predict hydrate formation temperature (HFT) can also be performed for the multiphase system at a given pressure state. A linear regression is shown in the plot, indicating that temperature and pressure are directly proportional to each other. Data used for the development of the prediction model is limited because for each experiment, gas hydrate thermodynamic experiments can take up to 48 h.
要预测给定压力状态下的水合物形成温度（HFT），理论上可以开展精确的统计回归分析。优化算法将构建一个验证模型以帮助预测 HFT。理论上，对于给定压力状态下的多相系统，也可以进行精确的统计回归分析来预测水合物形成温度（HFT）。为了估计预期结果与实际结果之间的误差，可以进行 ANOVA 统计分析。理论上，对于给定压力状态下的多相系统，也可以进行精确的统计回归分析来预测水合物形成温度（HFT）。图中显示了一个线性回归，表明温度与压力成正比。由于每次实验中，气体水合物热力学实验可能需要长达 48 小时，因此用于开发预测模型的数据有限。

The experimental results are used to predict the conditions of gas hydrate formation. Initially, a data solver tool was used to tabulate the experimental results. A correlation is then established between the components of X and Y. At a given pressure state, this equation is used to predict the gas HFT [183].
实验结果用于预测气体水合物形成的条件。最初，使用数据求解工具将实验结果制成表格。然后，在 X 和 Y 的成分之间建立关联。在给定的压力状态下，使用该方程预测气体 HFT [183]。

The details of the various statistical models applied over the years for various conditions are tabulated below for a clear understanding.
为清晰理解，下表列出了多年来针对各种条件应用的各类统计模型的详细信息。

As it can be observed from the table, most of the correlations are limited to a certain gas gravity range. None of the correlations can accurately predict the CO₂ rich gases.
从表格中可以看出，大多数关联式仅限于特定的气体相对密度范围。没有任何关联式能够准确预测富甲烷气体。

2.6.1 Way Forward
2.6.1 前进方向

As discussed, and shown in Table 4, there is a need for an accurate prediction equation that can be applied for higher gas gravity gases. Also, a need for the equation that can be applied for various multiphase systems is visible.
如前所述，如表 4 所示，需要一种适用于高气相对密度的准确预测方程。此外，需要一种适用于各种多相系统的方程也很明显。

Table 4 Synopsis of various prominent statistical models applied on gas hydrates studies
表 4 气水合物研究中应用的各类主要统计模型概要

2.7 Computational Fluid Dynamics (CFD)
2.7 计算流体动力学（CFD）

With the advancements in simulation capabilities, the application of computational fluid dynamics has brought a great impact on the study of gas hydrates.
随着模拟能力的进步，计算流体动力学的应用对气体水合物的研究产生了重大影响。

A novel experimental setup is used, which allows for in-situ determinations of the population density function of methane hydrate particles during crystallization in a pressurized reactor. New results can be obtained using this equipment, especially regarding the granular aspects of crystallization processes and the effect of the stirring rate. Mean particle size is also expected to be at least attributable to breakage, whereas aggregation-dominated are the quiet regions. These findings are explored within the context of a model that takes into account gas absorption, primary and secondary nucleation, crystal formation, agglomeration, and breakage. The relevant processes and parameters of methane hydrate crystallization can be calculated and quantified based on this discussion [144].
使用了一种新型实验装置，该装置允许在高压反应器中结晶过程中原位测定甲烷水合物颗粒的种群密度函数。使用该设备可以获得新结果，特别是在结晶过程的颗粒方面和搅拌速率的影响方面。平均颗粒尺寸也至少可以归因于破碎，而安静区域以聚集为主。这些发现是在一个考虑了气体吸收、初级和次级成核、晶体形成、聚集和破碎的模型背景下进行探讨的。基于此讨论，可以计算和量化甲烷水合物结晶的相关过程和参数[144]。

The dissociation of methane hydrate in a porous core sample is investigated, as well as the production of methane gas and water, as well as the thermal and multiphase flow conditions. During the hydrate dissociation process, the corresponding multiphase gas–liquid flows were studied. Time evolutions of gas and water generations during hydrate dissociation were tested for different surrounding temperatures and outlet valve pressures, and differences in temperature, heat, and flow conditions in the core were simulated. It was found that the rate of hydrate dissociation is affected by the physical and thermal conditions of the core sample, as well as the heat source from the atmosphere and the outlet valve strain. Porosity and relative permeability are significant considerations in the processes of hydrate dissociation and gas production. The temperature at the dissociation front decreases due to hydrate dissociation and then increases due to thermal convection in the centre tested. The rate of gas and water generation increases as the surrounding temperature rises due to a higher rate of hydrate dissociation. Reduced outlet valve pressure raises the rate of hydrate dissociation and, as a result, the rate of gas and water supply [187].
研究了多孔核心样品中甲烷水合物的分解，以及甲烷气体和水的产生，以及热和多相流条件。在水合物分解过程中，研究了相应的多相气液流。在不同周围温度和出口阀门压力下，测试了水合物分解过程中气体和水的生成随时间的变化，并模拟了核心中温度、热和流条件的变化。研究发现，水合物分解速率受核心样品的物理和热条件、大气热源和出口阀门应变的影响。孔隙率和相对渗透率在水合物分解和气体产生过程中是重要的考虑因素。由于水合物分解，分解前沿的温度降低，然后由于中心测试的热对流而升高。由于水合物分解速率加快，气体和水的生成速率随着周围温度的升高而增加。 降低出口阀门压力会提高水合物的分解速率，进而提高气体和水的供应速率[187]。

Jassim et al. suggested and applied the principle of particle deposition to the hydrate that has formed in a gas/vapor flow [188]. CFD was used in configuring the carrier gas (methane) behavior by solving the Navier-Stoke equation for turbulent flow to obtain gas velocity and other properties in different areas. As a consequence of the Brownian effect, very small particles that are less than one micrometer settle, whereas gravitational and inertial settling regulates the deposition of comparatively larger particles. In the Brownian regime, the collection deposition is strong for very tiny particles and decreases as particles expand, while the collection efficiency increases with particle size inertia regime. The particles velocity profile is similar to the profile of the carrier fluid.
Jassim 等人提出并应用于气/蒸汽流中形成的天然气水合物沉积原理[188]。通过求解湍流 Navier-Stoke 方程，CFD 被用于配置载体气体（甲烷）的行为，以获得不同区域的气体速度和其他特性。由于布朗效应，小于一微米的微小颗粒沉降，而重力和惯性沉降则调节较大颗粒的沉积。在布朗区域，收集沉积对非常微小的颗粒作用强烈，随着颗粒增大而减弱，而收集效率在颗粒惯性区域随颗粒尺寸惯性而增加。颗粒速度分布与载体流体的分布相似。

The combined CFD-PBM model for gas hydrate aggregation in the turbulent flow loop was developed by Balakin et al. in STAR-CD [189, 190]. The model involves one-moment approach for the hydrate PSD evolution. The results of population balance simulation are calibrated with the off-line two-compartmental PBM-code which was validated with the results of sampling done in experiments. The size distribution (PSD) of flocculated hydrate particles was determined in this work by sampling from the water-hydrate slurry for distinct volume fractions of particles in the system. The system is aggregation-dominated with particles increase their size in flow direction as the mean flow velocity is relatively small and the inlet hydrate particle size is low, so their collisions are more effective. The system is breakage-dominated with the decrease of particle size in flow direction. The most intensive aggregation goes in the vicinity of the wall as the shear rate there is at maximum and the breakage is weaker than to aggregation.
Balakin 等人基于 STAR-CD 开发了用于湍流循环中气体水合物聚集的 CFD-PBM 模型[189, 190]。该模型采用单矩方法描述水合物粒径分布（PSD）的演变。人口平衡模拟的结果通过与离线两室 PBM 代码校准，该代码已通过实验采样结果验证。本研究通过从水合物浆料中采样，确定了絮凝水合物粒子的粒径分布（PSD），系统内不同体积分数的粒子采样分析。该系统以聚集为主导，随着平均流速相对较小且入口水合物粒子尺寸较低，粒子在流动方向上尺寸增加，其碰撞更为有效。系统以破碎为主导，粒子尺寸在流动方向上减小。最剧烈的聚集发生在壁面附近，因为该处剪切率最大，而破碎作用弱于聚集作用。

Hydrate ResDim, methane production simulator was first built for the National Energy Technology Laboratory NETL by Lawrence Berkeley National Laboratory (LBNL) [191]. It explains the mathematical model that regulates methane hydrate dissociation via system depressurization or thermal stimulation, as well as the transport of numerous temperature-dependent components in several stages via a porous media. The model equations are constructed by integrating multiphase Darcy's law for gas and liquid into mass variable balances and energy consumption equations. Two sub models for hydrate dissociation are also explored in Hydrate ResSim: a kinetic model and a pure thermodynamic model. On average, the kinetic model demonstrated a lower dissociation rate than the equilibrium model. The hydrate dissociation patterns altered dramatically when the thermal boundary state was changed from adiabatic to constant temperature. The surface area component of the kinetic model was shown to have a substantial influence on the rate of hydrate dissociation. As the surface area component dropped, the disparity between the kinetic and equilibrium models increased.
水合物 ResDim 是一种甲烷生产模拟器，最初由劳伦斯伯克利国家实验室（LBNL）为美国国家能源技术实验室（NETL）构建[191]。它解释了通过系统降压或热刺激来调控甲烷水合物解离的数学模型，以及通过多孔介质在不同阶段传输多种温度依赖性组分的过程。该模型的方程式通过将气相和液相的多相达西定律整合到质量变量平衡和能量消耗方程中来构建。Hydrate ResSim 中还探讨了两种水合物解离的子模型：动力学模型和纯热力学模型。平均而言，动力学模型的解离速率低于平衡模型。当热边界状态从绝热改变为恒温时，水合物解离模式发生了显著变化。动力学模型的表面积分量被证明对水合物解离速率有重要影响。随着表面积分量的降低，动力学模型与平衡模型之间的差异增大。

A study of the Freon R11 hydrate that exist in a turbulent flow. CFD which can be used to simulate static systems is also primarily used to study this phenomenon. A loop experiment was conducted to compare the results between the experiment and the CFD model. A CFD numerical simulation was constructed using 66 363 polyhedral control volumes in STAR-design. The dimensions and mesh were designed in accordance to simulate the real time hydrate formation process. Boundary conditions were assessed to increase accuracy [192]. The model did validate the experiment with less than 8% of discrepancy. Gas hydrate plugs can form in pipelines and has negative effects. CFD has been used to model this phenomenon. Fluid properties were determined numerically by using Fluent software. Boundaries are also simulated with the FLUENT software. The basic occurrence of growth and nucleation of hydrate particles are simulated using the FLUENT software [3].
一项关于湍流中存在的 Freon R11 水合物的研究。可用于模拟静态系统的计算流体动力学（CFD）也被主要用于研究这一现象。进行了一项回路实验，以比较实验结果与 CFD 模型的结果。在 STAR-design 中构建了一个包含 66,363 个多面体控制体积的 CFD 数值模拟。尺寸和网格设计是根据模拟实时水合物形成过程而设计的。边界条件被评估以提高精度[192]。该模型验证了实验，偏差小于 8%。水合物栓塞可以在管道中形成，并产生负面影响。CFD 已被用于模拟这一现象。流体特性通过使用 Fluent 软件进行数值确定。边界也通过 FLUENT 软件进行模拟。水合物颗粒的生长和成核的基本现象使用 FLUENT 软件进行模拟[3]。

Jassim et al. suggested the theory of particle deposition to model the deposition of hydrate particles produced in the turbulent area in a gas/vapor driven flow and direction of particle motion. In order to understand the near wall effects, the model incorporates the power of the bouncing principle for particles with sizes greater than the sublayer thickness. The apparatus used to verify model findings using water-saturated air and propane was also discussed in this report. Fluid properties were obtained using CFD software by solving Navier–Stokes equation for turbulent flow. Tiny particles are affected by the main fluid velocity in the turbulent region, but the effect reduces because of high particle inertia for relatively large particles. The deposition distance reduces as the size of the particle increases. The deposition distance is in linear proportion to the amount and height of the Reynolds tubing.
Jassim 等人提出了颗粒沉积理论，用于模拟在气/蒸汽驱动流动和方向中湍流区域产生的水合物颗粒的沉积和运动方向。为了理解近壁面效应，该模型结合了对于尺寸大于亚层厚度的颗粒的弹跳原理的功率。报告中还讨论了使用饱和水空气和丙烷验证模型结果的设备。流体特性是通过求解湍流 Navier-Stokes 方程使用 CFD 软件获得的。在湍流区域，微小颗粒受主流体速度的影响，但对于相对较大的颗粒，由于颗粒惯性高，这种影响会减小。沉积距离随着颗粒尺寸的增加而减小。沉积距离与 Reynolds 管的数量和高度成线性比例。

Centered on the Eulerian multiphase flow modelling approach, a three-dimensional Computational Fluid Dynamics (CFD) model for hydrate formation in oil-dominated flows is derived [193, 194]. The author believed that the gas bubbles and water droplets were held as scattered stages in the liquid. The gas dissolved into the oil reaches the water droplets and when the situation is right, hydrate is formed. An example of a job used to illustrate the model's functioning. At the no-slip walls, it indicates the speeds drop to zero and rise to the highest value at the middle of the tube.
以欧拉多相流建模方法为基础，推导出了一种适用于油主导流中水合物形成的三维计算流体动力学（CFD）模型[193, 194]。作者认为气体气泡和水滴以分散相态存在于液体中。气体溶解到油中后到达水滴，当条件合适时，水合物便形成。通过一个实例来说明模型的运行机制。在无滑移壁面上，模型显示速度降为零，并在管道中部达到最高值。

A three-dimensional, transient Eulerian CFD model was created by Balakin et al. [195] for hydrate deposition in a turbulent flow of a pulp containing low-pressure hydrate particles to correctly reflect the experimental findings. It was visually discovered during the tests in the homogeneous regime that the flow in the bends showed higher speeds locally than in the straight sections. For the same method parameters, but marginally higher than the experimental ones, the model projected frictional pressure drops. With the aid of an in-house subroutine, the CFD model predicted the spatial distribution of particle sizes determined using the equation below: As the agglomerate breakage increases with increasing velocity gradients in the flow, the mean particle size in the entire domain is inversely proportional to the mean flow velocity, a phenomenon that has also been seen among the experimental findings. An incorrect quantitative result would result from using a mean particle size that is independent of the mean velocity of the flow.
Balakin 等人[195]创建了一个三维瞬态欧拉 CFD 模型，用于模拟含有低压水合物颗粒的浆料湍流中的水合物沉积，以正确反映实验结果。在均匀流态测试中，通过视觉观察发现，弯道处的流动速度局部高于直管段。对于相同的方法参数（但略高于实验参数），该模型预测了摩擦压降。借助内部子程序，CFD 模型预测了粒子尺寸的空间分布，其计算公式如下：随着流动中速度梯度的增加，聚集体破碎加剧，整个域内的平均粒子尺寸与平均流动速度成反比，这一现象也出现在实验结果中。如果使用与流动平均速度无关的平均粒子尺寸，将导致定量结果错误。

The processes of hydrate production in natural gas pipelines was highlighted by Naseer et al. [196] Computational Fluid Dynamics (CFD) was used to further understand the processes of water vapor condensation and subsequent water deposition in lowered portions of a gas pipeline. User specified functions (UDF) embedded into the CFD-software Fluent were used to model the pipeline temperature profile, condensation of water vapor at walls, hydrate forming, and hydrate slurry rheology. The uphill portions of gas pipelines were discovered to be natural sites for water absorption and hydrate formation. CFD has seen to be a helpful instrument for understanding dynamic physical processes that arise in multiphase flow problems.
Naseer 等人[196]强调了天然气管道中水合物生成的过程。计算流体动力学（CFD）被用于进一步理解气体管道低处水蒸气冷凝和随后的水沉积过程。嵌入到 CFD 软件 Fluent 中的用户指定函数（UDF）被用于模拟管道温度分布、壁面水蒸气冷凝、水合物形成和水合物浆液的流变学。研究发现，气体管道的上坡部分是天然的水吸收和水合物形成的场所。CFD 已被证明是理解多相流问题中出现的动态物理过程的得力工具。

A study of the flow behaviors and the possibility of hydrate formation risks due to pipeline leakage in subsea natural gas (NG) pipeline with water depths more than 2,000 m was conducted by Zhai et al. The pipeline system flowing characteristics during water ingress scenarios distinguish from gas egress scenario [197, 198]. For water ingress, the gas outlet flowrate at higher pressure difference decreases first before it recovers and stabilizes; similarly, the outlet gas temperature demonstrates in a contrast trend. The CFD results match well with the water leak rate and the liquid holdup predicted from the OLGA simulations. It should be highlighted that if there is a large difference between the pipeline internal and external pressures, water jet velocity is very high (up to 130 m/s), which can cause erosional issues in the vicinity of the leak, but pipeline rupture a likely event.
由 Zhai 等人进行了一项研究，探讨了水深超过 2,000 米的深海天然气（NG）管道因泄漏导致流动行为和 hydrate 形成风险的可能性。在进水场景下，管道系统的流动特性与气体逸出场景有所不同 [197, 198]。对于进水情况，高压差下的气体出口流量会先降低，然后恢复并稳定；同样，出口气体温度也呈现出相反的趋势。CFD 结果与 OLGA 模拟预测的水泄漏速率和液相持率吻合良好。需要强调的是，如果管道内部和外部压力存在较大差异，水射流速度会非常高（高达 130 m/s），这可能导致泄漏附近发生侵蚀问题，但管道破裂是一个可能发生的事件。

Gharaibah et al. [199] presented a description of multiphase flow simulation tools current state-of-the-art, as well as their new development and adaptation for subsea applications. The focus is on multiphase flow modelling using Computational Fluid Dynamics (CFD) simulation techniques, specifically on their strengths and limitations as used to simulate the action of hydrocarbons as they move from the reservoir to the processing plant. Applications of multiphase CFD instruments to facilitate the design, operation, and monitoring of SPS are also presented and explored, as are the innovations and validations needed to replace expensive laboratory tests, component certification, and field tests.
Gharaibah 等人[199]介绍了多相流模拟工具的当前最先进技术状态，以及它们在海底应用中的新开发与适应性。重点在于使用计算流体动力学（CFD）模拟技术进行多相流建模，特别是它们在模拟从储层到处理厂流动的烃类行为时的优势与局限性。文中还介绍了和探讨了多相 CFD 工具在促进 SPS 设计、操作和监测中的应用，以及所需的创新和验证，以替代昂贵的实验室测试、部件认证和现场测试。

Li et al. [200] used the Euler model and CFD-PBM model to simulate the gas–solid-liquid three-phase flow of underwater gas hydrate pipe transport. The CFD-PBM model simulation results indicate that gas phase and solid phase both concentrate in the pipe to the core, but not explicitly as an Euler model. The gradient of velocity in the radial direction is therefore smaller than in the Euler model. The bubble’s key behaviour is that tiny bubbles coalesce into big ones. The CFD-PBM model for flow state distribution simulation is more homogeneous than the Euler model. So, to explain the three-phase flow condition, the CFD-PBM model is stronger than the Euler model.
李等人[200]使用欧拉模型和 CFD-PBM 模型模拟了水下天然气水合物管道运输中的气-固-液三相流。CFD-PBM 模型的模拟结果表明，气相和固相都集中在管道中心，但不如欧拉模型那样明显。因此，径向方向上的速度梯度比欧拉模型要小。气泡的主要行为是微小气泡合并成大气泡。用于流态分布模拟的 CFD-PBM 模型比欧拉模型更均匀。因此，为了解释三相流条件，CFD-PBM 模型比欧拉模型更有效。

A mechanistic CFD model was proposed in order to understand the mechanisms controlling the hydrate formation in offshore pipelines. Two case scenarios considering inlet pure water volume fractions of 20% (low) and 40% (high) were simulated so that the effects of mass transfer of methane from the gas to liquid phase and the conversion of the dissolved methane due to reaction could be analyzed. It can be observed that water tends to have higher volume fraction values at the bottom of the pipe for both case scenarios, which maximum values achieved were 97.53% and 99.33% for low and high inlet water volume fractions, respectively [201]. The subcooling values non-zero at positions near the wall at which values of rate of hydrate formation and mass fraction of hydrate in water phase were found to be high as well.
提出了一种基于机理的计算流体动力学（CFD）模型，旨在理解控制海上管道中水合物形成的机制。模拟了两种案例情景，考虑了入口纯水体积分数为 20%（低）和 40%（高）的情况，以便分析甲烷从气相到液相的质量传递效应以及由于反应导致的溶解甲烷的转化效应。可以观察到，在两种案例情景中，水在管道底部倾向于具有更高的体积分数，低和高入口水体积分数分别达到的最大值是 97.53%和 99.33% [201]。在靠近壁面的位置，过冷度值非零，在这些位置发现水合物形成速率和水相中水合物质量分数都很高。

Deep sea petroleum pipelines for which is used for transport of gas often can have formation of crystalline compounds called gas hydrates. Computational fluid dynamic methods can be used to study the formation of gas hydrates in these pipelines. The CFD-PBM method was tested to verify the sub-model balance occurrence. The CFD-PBM method is capable of studying and validating the accumulation and deposition of gas hydrates in petroleum pipelines [202]. The rheological model uses a set of equations to determine the viscosity concept of the flow in the vessel. Eular- CFD is used to model the flow of hydrate-water–oil suspension.
用于运输天然气的深海石油管道中，经常会出现称为天然气水合物的结晶化合物。计算流体动力学方法可用于研究这些管道中天然气水合物的形成。CFD-PBM 方法被测试以验证子模型的平衡发生。CFD-PBM 方法能够研究和验证石油管道中天然气水合物的积累和沉积[202]。流变模型使用一组方程来确定容器中流动的粘度概念。Eular-CFD 用于模拟水合物-水-油悬浮液的流动。

Ibrahim et al. studied the behaviour of a multiphase flow and prediction of the future position and state of hydrate formation within the multiphase pipeline structure using the simulation method of Computational Fluid Dynamics (CFD) for complete flow assurance accountability. The simulation was carried out by imitating a system that is subject to a system dominated by gas rather than a system dominated by liquid [203]. The region that is heavily embedded with the turbulence is at the end of the bending section, depending on the simulation outcome. The presence of hydrate formation in the pipeline system would have a considerable effect on the difference in pressure between the pipeline parts. The theory of Bernoulli matched the phenomenon and, as defined, velocity and pressure are inversely proportional to each other.
Ibrahim 等人研究了多相流的特性，并利用计算流体动力学（CFD）的模拟方法，对完整流动安全负责地预测了多相管道结构中水合物形成的未来位置和状态。该模拟通过模仿一个以气体为主导而非以液体为主导的系统进行[203]。根据模拟结果，湍流强烈嵌入的区域位于弯曲部分的末端。管道系统中水合物的存在会对管道各部分之间的压力差产生相当大的影响。伯努利理论与此现象相符，并定义了速度和压力之间呈反比关系。

Pei-Yi Yu et al. [204] investigated preliminary cases of porosities of 0.74, 0.66, and 0.49, each of which is called a representative cubic unit of an MH collection. The initial temperature of the MH pellets within the cubic unit, 253.15 (K), dissociated due to the driving force of fugacity difference, ex. 0.56 and 0.54 (MPa), while warm water of 282.15 and 276.15 (K) flowed in. Periodic conditions are applied at surfaces of the inlet/right/front sides in the calculation, which are modified at each time level. The methane flux at the surface is assumed to be absorbed into the water in this high-pressure state and compared to Kim et al. (1987)'s association at a Reynolds number of around 50. The dissociation flux results in cases 5 and 6 with porosity 0.49 agree well with Kim's association. Nevertheless, as porosity rises, flux increases due to quick transport in bulk flow, as seen in cases 1–4 of this report. In this work, if the transport phase in bulk flow is faster than the dissociation rate, the surface flux becomes saturated as Reynolds no. exceeds 100.
Pei-Yi Yu 等人 [204] 研究了孔隙率为 0.74、0.66 和 0.49 的初步案例，每个案例被称为 MH 集合的一个代表性立方单元。在立方单元内的 MH 小球初始温度为 253.15 (K)，由于逸度差的驱动力，例如 0.56 和 0.54 (MPa)，发生了分解，同时 282.15 和 276.15 (K) 的温水流过。在计算中，对入口/右/前侧表面施加周期性条件，这些条件在每个时间级别被修改。假设表面处的甲烷通量在这种高压状态下被吸收到水中，并与 Kim 等人 (1987) 在雷诺数约为 50 时的关联进行比较。分解通量在孔隙率为 0.49 的案例 5 和 6 中与 Kim 的关联吻合良好。然而，随着孔隙率的增加，由于主体流动中的快速传输，通量增加，如本报告中的案例 1–4 所示。在这项工作中，如果主体流动中的传输阶段比分解速率快，则当雷诺数超过 100 时，表面通量会达到饱和。

Dynamic modelling of hydrate agglomeration in pipe was conducted. The main aspects in this model are collision frequency, agglomeration efficiency, breakage frequency and size distribution. CFD software 14.5 was used here. A curvilinear model was used to determine agglomeration frequency. Flow shear was utilized in calculating breakage frequency of hydrate particles. Size of particle distribution was determined by utilizing binary distribution [205].
对管道中水合物聚集体进行了动态建模。该模型的主要方面包括碰撞频率、聚集体效率、破碎频率和尺寸分布。这里使用了 CFD 软件 14.5。采用曲线模型来确定聚集体频率。利用流动剪切力来计算水合物颗粒的破碎频率。颗粒尺寸分布由二元分布[205]确定。

Jujuly et al. offer a computational fluid dynamics (CFD) model to investigate the influence of hydrate flow in pipelines using ANSYS FLUENT multiphase flow modelling techniques in this work. The CFD model is validated and expanded to a sophisticated M-shaped jumper configuration. The pipeline is subjected to a finite element study based on fluid–structure interaction [206, 207]. The structural model's sensitivity is evaluated using hydrate volume fractions and velocities. The sensitivity analysis may be used to build an optimal underwater pipeline jumper design, resulting in a safer (lower deformation) and more cost-effective (less pipeline material) offshore pipeline. A bigger hydration volume percent has a stronger influence on the jumper structure, resulting in stress development in the jumper. Because of the heavy impact by the hydrate particles, when there is hydrate flow in the jumper, stress develops and deformation happens.
Jujuly 等人在这项工作中提供了一个计算流体动力学（CFD）模型，利用 ANSYS FLUENT 多相流建模技术来研究 hydrate 流在管道中的影响。该 CFD 模型经过验证并扩展到复杂的 M 形跳接器配置。管道基于流-结构相互作用进行了有限元研究[206, 207]。使用 hydrate 体积分数和速度评估了结构模型的敏感性。敏感性分析可用于构建优化的水下管道跳接器设计，从而实现更安全（变形更小）和更具成本效益（管道材料更少）的海上管道。更大的 hydrate 体积百分比对跳接器结构的影响更强，导致在跳接器中产生应力。由于 hydrate 颗粒的重度影响，当跳接器中有 hydrate 流动时，会产生应力并发生变形。

A 3D CFD model containing three phases (gas-vapour-hydrate) developed by to ascertain the position and time of gas hydrate formation in a gas transfer pipeline including a 90° elbows [208]. In this model, gas hydrate formation predicted utilizing Piecewise-linear mechanism at 0.01 s time intervals as the model developed is optimized for the best skewness and has less number of mesh elements. For this purpose, a typical system comprising three phases of methane, liquid water and gas hydrate considered and consequent equations solved through application of an appropriate mixing rule model. Moreover, the PISO method used to solve simultaneously the energy and momentum balance equations. The K-ɛ-RNG model along with Standard Wall Functions used to determine gas turbulence. Ultimately, a first order up-winding method utilized to discretize the momentum balance equations. Through CFD the authors were able to identify the location and amount of hydrate formed. This information helped to prevent hydrate formation through injecting of inhibitors at the right spot.
一个包含三种相（气-蒸汽-水合物）的三维 CFD 模型，用于确定气输管道（包括 90°弯头）中水合物形成的位置和时间[208]。在该模型中，利用分段线性机制在 0.01 秒的时间间隔内预测水合物形成，因为该模型针对最佳倾斜度进行了优化，并且网格单元数量较少。为此，考虑了一个典型的三相系统，包括甲烷、液态水和水合物，并通过应用适当的混合规则模型求解相应的方程。此外，使用 PISO 方法同时求解能量和动量平衡方程。K-ɛ-RNG 模型与标准壁函数用于确定气体湍流。最终，采用一阶迎风法对动量平衡方程进行离散化。通过 CFD，作者能够确定水合物形成的位置和数量。这些信息有助于通过在正确位置注入抑制剂来防止水合物形成。

Modelling was used to identify the flow of hydrate behavior. Main key parameters which were calculated were the collision frequency, agglomeration frequency, breakage frequency and size distribution. CFD software of FLUENT 14.5 was used. By observing log-normal distribution, hydrate particle size distribution can be determined. Flow rate affects pressure gradients in simulation [209].
建模用于识别水合物行为流动。计算的主要关键参数包括碰撞频率、聚集频率、破碎频率和尺寸分布。使用了 FLUENT 14.5 的 CFD 软件。通过观察对数正态分布，可以确定水合物颗粒尺寸分布。流量影响模拟中的压力梯度[209]。

High pressure and low temperatures can cause formation of gas hydrates. Increased pressure drops, reduced flow rate, and increase in temperature difference can be caused by the gas hydrate formation. CFD simulation using ANSYS workbench in Design Modeler and Mesh Modeler was used to generate the geometry and mesh of the pipes. Pyramidal cells with progressive mesh were used. Orthogonal quality was also used. Based on CFD simulation, blockage diameter and length have high impact on pressure drop [210].
高压和低温会导致气体水合物形成。气体水合物形成会导致压降增加、流速降低和温差增大。在 Design Modeler 和 Mesh Modeler 中使用 ANSYS Workbench 进行 CFD 模拟，用于生成管道的几何形状和网格。使用了具有渐进式网格的金字塔单元，并使用了正交质量。基于 CFD 模拟，阻塞直径和长度对压降有显著影响[210]。

Ibrahim et al. studied the behaviour of a multiphase flow and prediction of the future position and state of hydrate formation within the multiphase pipeline structure using the simulation method of Computational Fluid Dynamics (CFD) for complete flow assurance accountability. The simulation was carried out by imitating a system that is subject to a system dominated by gas rather than a system dominated by liquid [203]. The region that is heavily embedded with the turbulence is at the end of the bending section, depending on the simulation outcome. The presence of hydrate formation in the pipeline system would have a considerable effect on the difference in pressure between the pipeline parts. The theory of Bernoulli matched the phenomenon and, as defined, velocity and pressure are inversely proportional to each other.
Ibrahim 等人研究了多相流的特性，并利用计算流体动力学（CFD）的模拟方法，对完整流动安全负责地预测了多相管道结构中水合物形成的未来位置和状态。该模拟通过模仿一个以气体为主导而非以液体为主导的系统进行[203]。根据模拟结果，湍流强烈嵌入的区域位于弯曲部分的末端。管道系统中水合物的存在会对管道各部分之间的压力差产生相当大的影响。伯努利理论与此现象相符，并定义了速度和压力之间呈反比关系。

CFD modelling was carried out to simulate the hydrate formation in pipelines. Data used were from Ilam refinery in Iran. Simulated data is compared with modelling data. Mathematical flow equations were implemented to determine fluid properties like heat coefficients etc. Simulation by COMSOL and HYSIS were used. Numerical and simulated results complied with each other [211].
进行了 CFD 建模以模拟管道中的水合物形成。所使用的数据来自伊朗的 Ilam 炼油厂。模拟数据与建模数据进行了比较。实施了数学流动方程以确定流体特性，如热系数等。使用了 COMSOL 和 HYSIS 进行模拟。数值和模拟结果相互符合[211]。

Mathematical modelling was utilised to model hydrate formation in pipelines. Main fluid characteristics like pressure and temperature was taken into consideration during the modelling. Experiment was also carried out to study the hydrate formation in pipes to ensure definite comparison is conducted. It was found that increase in pressure causes hydrate to shift up and reduces decomposition. When inlet flow is low, reflow occurs [212].
数学建模被用于模拟管道中的水合物形成。建模过程中考虑了主要的流体特性，如压力和温度。同时进行了实验来研究管道中的水合物形成，以确保进行明确的比较。研究发现，压力的增加会导致水合物向上移动并减少分解。当入口流量较低时，会发生回流[212]。

Wang et al. conducted research about the Study on the characteristics of natural gas hydrate crystal structures during decomposition process [213]. The higher the heating temperature and initial pressure, the more the particle number fluctuates. The physical model of hydrate particle decomposition is developed based on the microscopic changes of hydrate particles in the decomposition phase obtained by high-speed digital camera and other instruments, and on the separate physical models of two forms of hydrate particles.
王等人研究了天然气水合物在分解过程中的晶体结构特征[213]。加热温度和初始压力越高，颗粒数量波动越大。水合物颗粒分解的物理模型是基于高速数字相机等仪器获得的分解阶段水合物颗粒的微观变化，以及两种形式水合物颗粒的单独物理模型而开发的。

Hydrate risks are also presenting a significant danger to deep water flow assurance in offshore activities. The distribution of hydrate particle size in pipelines is closely related to hydrate slurry viscosity, flow pressure drops, and interface heat and mass transfer. Hydrate particle bedding may cause hydrate plugging in pipelines. As a result, hydrate particle size distribution and hydrate particle bedding have a large effect on pipeline hydrate flow assurance. A new hydrate agglomeration model was used to predict hydrate particle size distribution and hydrate particle bedding in pipeline flowing structures, which was then solved by the program FLUENT 14.5 along with several CFD models. The simulations based on the type and characteristics of hydrate particle size distribution, as well as the characteristics of flowline hydrate particle bedding. Furthermore, the effects of hydrate particle size, initial distribution form, hydrate volume fraction, flow rate, and initial hydrate particle diameter were studied. The findings of this study can be used to guide the implementation of deep-water flow assurance [214].
水合物风险也对海上作业中的深水输运保障构成重大威胁。管道中水合物颗粒大小的分布与水合物浆液粘度、流动压降以及界面传热传质密切相关。水合物颗粒沉积可能导致管道堵塞。因此，水合物颗粒大小分布和水合物颗粒沉积对管道水合物输运保障具有显著影响。采用一种新的水合物聚集体模型来预测管道流动结构中的水合物颗粒大小分布和水合物颗粒沉积，并通过 FLUENT 14.5 程序结合多种计算流体动力学模型进行求解。基于水合物颗粒大小分布的类型和特征，以及流动管线水合物颗粒沉积的特性进行模拟。此外，研究了水合物颗粒大小、初始分布形态、水合物体积分数、流速和初始水合物颗粒直径的影响。本研究结果可用于指导深水输运保障的实施[214]。

Berrouk et al. used an Eulerian–Eulerian multiphase technique to create a 3D computational fluid dynamics model of hydrates slurry flow in a pipeline [215]. A Reynolds averaged numerical simulation based on the Reynolds stress model was used to represent the turbulence. Particle size and shear viscosity models for hydrates were built and implemented into the CFD model. The model's predictions on pressure gradients at different input velocities and hydrate volume percentages were compared to the experimental data. Hydrate deposition properties were examined, and hydrate deposition bed heights were obtained at low inflow velocities. This study might provide helpful information on hydrate-laden flow in pipes and assist in redesigning them for enhanced flow assurance.
Berrouk 等人采用欧拉-欧拉多相流技术，创建了一个用于管道中水合物浆料流动的三维计算流体动力学模型[215]。基于雷诺应力模型的雷诺平均数值模拟被用于表征湍流。建立了水合物的粒径和剪切粘度模型，并将其应用于计算流体动力学模型中。模型对不同输入速度和水合物体积百分比的压降预测与实验数据进行了比较。研究了水合物沉积特性，并在低入口流速下获得了水合物沉积床层高度。这项研究可能为管道中的水合物载流提供有益信息，并有助于重新设计管道以增强流动保障。

Song et al. used computational fluid dynamics (CFD) techniques to create a new simulator for NGH formation in core-scale sandy sediments [216]. The kinetic reaction model of hydrate formation, the NGH permeability reduction model, and the heat and mass transport model in porous media serve as the foundation for the mathematical model. The hydrate forming model is developed in C and used as a subroutine for Fluent software, which is used to solve the governing equations of multiphase flow. By comparing it to published experiments and numerical simulations, the simulator system is validated. Furthermore, for the first time, this analysis reproduces the experiment's fluctuant temperature trend during the 1.0–2.0 h time span. The created algorithms put several response surface models of NGH formation/dissociation to the test. The simulation and investigation of the impacts of the RSH model and the initial fluid distribution on the hydrate forming phase. The variation of the RSH in NGH formation/dissociation should be taken into account while modelling hydrate re-formation in the utilization of NGH. The initial distribution of water and gas in the enclosed reactor has a considerable impact on the production of hydrates. Furthermore, when water and methane are mixed uniformly in a homogeneous porous medium, the hydrate distribution is non-uniform. This study contributes to the parametric evaluation of the RSH model in hydrate formation and dissociation modelling.
宋等人利用计算流体动力学（CFD）技术创建了一个新的适用于核心尺度砂质沉积物中天然气水合物（NGH）形成的模拟器[216]。水合物形成的动力学反应模型、NGH 渗透率降低模型以及多孔介质中的热量和质量传递模型构成了数学模型的基础。水合物形成模型是用 C 语言开发的，并作为 Fluent 软件的子程序，用于求解多相流的控制方程。通过与已发表的实验和数值模拟进行比较，验证了模拟器系统。此外，该分析首次重现了实验在 1.0-2.0 小时时间跨度内的波动温度趋势。创建的算法测试了 NGH 形成/解离的多个响应面模型。模拟和研究了 RSH 模型和初始流体分布对水合物形成阶段的影响。在利用 NGH 时，建模水合物再形成时应考虑 NGH 形成/解离过程中 RSH 的变化。 封闭反应器中水和气的初始分布对水合物的生成有显著影响。此外，当水和甲烷在均匀多孔介质中均匀混合时，水合物的分布是不均匀的。本研究有助于对 RSH 模型在水合物生成和分解建模中的参数进行评估。

The details of the various prominent models devloped by CFD are tabulated in Table 5.
由 CFD 开发的各类突出模型的详细信息已列于表 5 中。

Table 5 Synopsis of Various CFD models applied on gas hydrates studies
表 5 应用于天然气水合物研究的各种 CFD 模型概览

2.7.1 Way Forward
2.7.1 前进方向

It can be observed from the table that many CFD modelling techniques were applied for various gases and gas mixtures. But there is no clear modelling applied for the promoters and inhibitors on various gas mixtures at high pressures. The models can be applied to various chemicals applied on hydrate research. The models can be applied on desalination using hydrates, carbon separation, carbon storage.
从表格中可以看出，许多计算流体动力学（CFD）建模技术被应用于各种气体和气体混合物。但在高压下，针对促进剂和抑制剂在各种气体混合物中的建模尚无明确应用。这些模型可应用于 hydrate 研究中使用的各种化学品。这些模型可应用于使用 hydrate 进行海水淡化、碳分离和碳储存。

2.8 Artificial Neural Networks (ANN)
2.8 人工神经网络 (ANN)

A major shift in computing has been brought on by the advent of high-speed modelling machines and large data processing applications. Dependence on the rough manual measurements for the measurement of the formation of gas hydrate is considerably decreased. In comparison, the well-known manual measurement techniques provide a wider variety of further calculations in nature. Since these simulation models are mainly thermodynamic models suggested by experts, the improvement and advancement of new applications is thus highly important. One of the pressing issues concerning the analysis of gas hydrates, as mentioned before, is that they are by nature non-stochiometric. In addition, there is a need for debate regarding the formation of various forms of gas hydrates. The use of rigorous models may have distinguished many types of gas hydrates.
随着高速建模机器和大型数据处理应用的兴起，计算领域发生了重大转变。对粗略手动测量气体水合物形成过程的依赖性已大大降低。相比之下，众所周知的传统手动测量技术提供了更广泛的进一步计算。由于这些模拟模型主要是专家建议的热力学模型，因此改进和开发新应用至关重要。正如之前提到的，气体水合物分析的一个紧迫问题是它们本质上是非化学计量的。此外，还需要就不同形式的气体水合物的形成进行讨论。使用严格模型可能已经区分了多种类型的气体水合物。

Hydrates have previously taken a substantial turn on the basis of the calculations introduced by researchers reporting studies on Natural Gas Prediction and Regulation. Various strategies began to emerge to reduce the flow impact of hydrates. Any recent advances have centered on the avoidance and management of gas hydrate formation in both offshore wells and onshore structures [220].
水合物之前基于天然气预测和调控研究报告中研究人员提出的计算方法发生了重大转变。开始出现各种策略来减少水合物对流动的影响。最近的进展主要集中在海上油井和陆上结构中水合物形成的避免和管理上[220]。

Commonly used in this field, major control procedures include variants on currently adapted methods, such as:
在该领域常用的重要控制程序包括对当前采用方法的变体，例如：

• 1. Reduction of device strain by the application of heat
  通过应用热量减少设备应变

• 2. Dehydrating some volumes of gas/liquid phases to minimize the supply of hydrate forming materials.
  将部分气体/液体相脱水，以减少水合物形成物质的供应。

• 3. Effective method of inhibition
  有效的抑制方法

• 4. Causing hydrate formation to be eventually treated by the discharge of H₂O, trapping and decomposing hydrates.
  通过排放 H ₂ O 最终处理水合物形成，捕获并分解水合物。

Inhibition analysis has improved as it decreases the possible impact of hydrates on the flow mechanism. In recent times, anti-agglomerants have been shown to be more efficient and highly suitable for regulating hydrate formation, especially in oil production systems operating under offshore conditions. During the deep-water applications, significant problems including Gas hydrates, emulsions, foam, water quality issues were not found during service. Methanol inhibition use was substantially limited, but anti-agglomerate use would have potential benefits, such as a smaller storage plant and lower pumping requirements, in addition to less availability and lower umbilical requirements. The early use of MULTIFLASH hydrate modelling tools was documented during this analysis.
抑制分析已经得到改进，因为它减少了水合物对流动机制的可能影响。近年来，抗絮凝剂已被证明更有效，并且非常适合调节水合物形成，特别是在海上作业的石油生产系统中。在深水应用中，服务期间未发现水合物、乳化液、泡沫、水质问题等重大问题。甲醇抑制的使用受到很大限制，但抗絮凝剂的使用具有潜在效益，例如储存设施更小、泵送要求更低，以及可用性减少和脐带要求降低。在此分析中记录了早期使用 MULTIFLASH 水合物建模工具的情况。

Later, further focus came from experiments on phase activity and multiphase transient lines. Most transient multiphase models available are based either on the Two-Fluid Model (TFM) that includes one momentum preservation equation for each phase or on the Drift-Flux Model (DFM) based on one overall momentum preservation equation plus some algebraic slip relationships [221]. However, to further improve the phase activity approach to understanding formation hydrates in multiphase systems, a zero-pressure wave model based on a one-dimensional approach has been developed. This led to the creation of models to establish the mechanisms of evolution of hydrates from nucleation to dynamic growth as the basis. For the understanding of hydrate behavior over the flow, the use of numerical methods became very important. In addition to major developments in soft computing methods such as ANN, GA, large data processing tools came into application and altered the whole image of the research. In order to figure out which technique provides more detailed results, various estimation approaches for hydrate formation temperature (HFT) have been checked [222].
后来，研究进一步集中在相活性实验和多相瞬态线上。目前大多数可用的瞬态多相模型要么基于包含每个相的动量守恒方程的双流体模型（TFM），要么基于一个总体动量守恒方程加上一些代数滑移关系的漂移通量模型（DFM）[221]。然而，为了进一步改进相活性方法以理解多相系统中的水合物形成，开发了一种基于一维方法的零压波模型。这导致了建立从成核到动态生长的水合物演化机制的模型的基础。为了理解水合物在流动中的行为，数值方法的使用变得非常重要。除了在人工神经网络（ANN）、遗传算法（GA）等软计算方法上的主要发展外，大数据处理工具的应用改变了整个研究图景。为了弄清楚哪种技术能提供更详细的结果，已经检查了各种水合物形成温度（HFT）的估算方法[222]。

In the Engineering Equation Solver (EES) and Statistical Kit for Social Sciences (SPSS) software, a standard ANN model has been developed and compared with results obtained. With 30 percent of unseen data, the comparison of these results with the projected ANN model results indicates excellent performance by ANN. ANN was found to be more reliable than conventional approaches and to have even better results than the models suggested by EES & SPSS for HFT estimation correlations.
在工程方程求解器（EES）和社会科学统计包（SPSS）软件中，已开发了一个标准的人工神经网络（ANN）模型，并与获得的结果进行了比较。使用 30%的未见过数据，将这些结果与预测的 ANN 模型结果进行比较，表明 ANN 表现出色。研究发现 ANN 比传统方法更可靠，并且在 HFT 估计相关性的模型方面，其结果甚至优于 EES & SPSS 建议的模型。

A neural network model is developed for forecasting hydrate formation conditions for a wide range of pure gases, gas mixes, and inhibitors. The model was trained using 2387 input–output patterns gathered from several trustworthy sources. The predictions are compared to pre-existing correlations as well as to actual experimental results. The neural network model allows the user to properly forecast hydrate formation conditions for a particular gas combination without the need for expensive experimental tests. The relative importance of temperature and the various components in the mixture has also been studied. Finally, the novel model's use in an integrated control dosing system to prevent hydrate formation is explored [223].
开发了一种神经网络模型，用于预测多种纯气体、气体混合物和抑制剂中的水合物形成条件。该模型使用从多个可靠来源收集的 2387 个输入-输出模式进行训练。预测结果与现有的相关关系以及实际实验结果进行了比较。该神经网络模型允许用户在无需进行昂贵的实验测试的情况下，正确预测特定气体组合的水合物形成条件。此外，还研究了温度和混合物中各种成分的相对重要性。最后，探索了该新型模型在集成控制加注系统中防止水合物形成的应用 [223]。

The dangers of the development of gas hydrates have been greatly decreased with the use of thermodynamic additives, mainly methanol. Later, considering a thermodynamic strategy, the CPA (Cubic Plus Association) equation is used to test phase equilibria in multiphase transfer pipelines. The strong solution theory developed by Vander Waals and Platteeuw sculpts the determination of hydrate forming circumstances. In addition, the use of thermodynamic models developed with aqueous methanol solutions and H₂O was used to forecast the dissociation of hydrates of CH₄ and natural gases [224]. When the distinction between experimental data and data retrieved from existing ANN models is made, a substantial acceptance is found.
使用热力学添加剂（主要是甲醇）极大地降低了天然气水合物开发的危险性。后来，在考虑热力学策略的情况下，使用 CPA（立方加关联）方程来测试多相输送管道中的相平衡。范德华和普拉特尤开发的强溶液理论塑造了水合物形成条件的确定。此外，使用基于水溶液甲醇和 H₂O 开发的热力学模型来预测 CH₄和天然气的水合物解离[224]。当实验数据与从现有 ANN 模型检索的数据之间的差异被考虑时，发现具有显著的接受度。

In addition, with industrial cooperation, ANN models are built to satisfy novel requirements and prototypes are planned for the same function. Study on the application of ANN to maximize the rate of hydrate inhibition, in addition to the identification of hydrate safety margins, degree of hydrate inhibition and phase equilibrium [225]. In the industry, ANN models are commonly used for initial identification of pipeline blockage due to hydrate formation. For the identification of changes in the operating system due to the creation of hydrates, ANN models are useful and help to respond to blockage prevention [170]. Later, interest in hydrates began to grow into the possible use of hydrates as a potential source of fuel, gas transportation, gas separation and as a storage source for industries. The crucial application was found to have improved hydrate dissociation and gas extraction for the use of unconventional fuels.
此外，通过与工业合作，建立了 ANN 模型以满足新要求，并计划开发相同功能的原型。研究 ANN 在最大化抑制剂使用率方面的应用，以及识别水合物安全裕度、抑制剂程度和相平衡[225]。在工业中，ANN 模型通常用于初步识别由于水合物形成导致的管道堵塞。对于识别由于水合物形成导致的操作系统变化，ANN 模型很有用，有助于应对堵塞预防[170]。后来，对水合物的兴趣逐渐增长，开始考虑将其作为潜在的燃料来源、气体运输、气体分离以及工业储气源。关键应用被发现在提高水合物解离和气体提取方面，以用于非常规燃料。

Research on the effect of heat transfer and mass transfer on the decomposition of CH₄ Hydrate is performed and it is summarized those constant molecular dynamics of energy are used for simulations. It is observed that the decomposition of CH₄ hydrate is influenced by the rate of heat and mass transfer due to the release of methane gas into the liquid phase due to the dissociation of methane hydrates. As the dissociation of gas hydrates is an endothermic reaction, as the pattern of dissociation of CH₄ hydrate is observed, temperature gradients are formed between the remaining solid hydrate and the solution phases, the release of a tonne of CH₄ near the Solid–Liquid interface, which can frame bubbles that affect the rate of mass exchange between the phases. Creation of ANN models is used to solve energy equations.
研究了传热和传质对 CH₄水合物分解的影响，并总结指出在模拟中使用了恒定分子动力学能量方法。观察到 CH₄水合物的分解受传热和传质速率的影响，这是由于甲烷水合物分解时释放甲烷气体进入液相。由于甲烷水合物的分解是吸热反应，在观察到 CH₄水合物分解模式时，剩余固体水合物与溶液相之间形成温度梯度，甲烷在固液界面附近释放，形成气泡，影响相间物质交换速率。创建人工神经网络模型用于求解能量方程。

In general, artificial neural network (ANN) connections are used to associate parameters, and it is noteworthy that ANN is a realistic technique for linking a small number of test data with the variables needed in certain specific cases. It is also stated that for multi-parameter associations, ANN is more potent. The concentrations of thermodynamic inhibitors/KHI/AA and salts can be calculated at the same time by means of ANN correlations using measured electrical conductivity, acoustic velocity and temperature [226]. An Artificial Neural Network (ANN) is trial-and-error-trained and does not require an empirical formula or knowledge of the physical relationships behind it. This is done to accomplish a novel technique for LDHIs [227]. An argument has been made that ANN is mainly used for particular applications where interaction involves multi-parameter connections, and the relationships between the intentional parameters are not observable. A large ANN model is proposed for anticipating conditions of hydrate formation for unadulterated gases and gas mixtures. The ANN model helps the customer to reliably predict the requirements for hydrate arrangement for a specified gas mixture, reducing the expense of experimental assessment. In advancing inhibitor infusion speeds, reducing the impact on the planet and operating expenses, the latest Artificial Neural Network (ANN) has been created [228]. In cases of malfunction such as pumping faults and adjustments in operating parameters such as water cutting, the models are helpful in enhancing the stability of operations and output as they aid in observing the protection margin and hence help in preserving or protecting the machine. These findings helped to infer that ANN models for the determination of different inhibitor structures such as methanol (CH₃OH), mono ethylene glycol (C₂H₄O) and kinetic inhibitor salts are known to be feasible with high accuracy [229].
通常情况下，人工神经网络（ANN）连接用于关联参数，值得注意的是，ANN 是一种将少量测试数据与特定情况下所需变量相连接的实用技术。同时也有指出，对于多参数关联，ANN 更具效力。通过使用 ANN 关联，可以根据测量的电导率、声速和温度同时计算热力学抑制剂/KHI/AA 和盐的浓度[226]。人工神经网络（ANN）通过试错法进行训练，无需经验公式或了解其背后的物理关系。这是为了实现一种针对 LDHIs 的新技术[227]。有观点认为，ANN 主要用于特定应用，其中交互涉及多参数连接，而有意参数之间的关系不可观测。提出了一种大型 ANN 模型，用于预测纯净气体和气体混合物中水合物的形成条件。 ANN 模型帮助客户可靠地预测特定气体混合物中水合物形成的条件，从而减少实验评估的费用。在提高抑制剂注入速度、减少对环境的影响和运营成本方面，最新的人工神经网络（ANN）已被开发出来[228]。在出现故障（如泵送故障）或操作参数调整（如含水率变化）等情况下，这些模型有助于提高操作稳定性和输出，因为它们有助于监测保护裕度，从而有助于保护或维护设备。这些发现表明，用于确定不同抑制剂结构（如甲醇（CH3OH）、单乙二醇（C2H6O）和动力学抑制剂盐）的 ANN 模型是可行的，并且具有很高的准确性[229]。

In addition, CSMHyk is used for the development of hydrate formation prediction models in the prevalent structures of water, oil and gas [230]. This model helps to forecast the creation of transient and spatial hydrates and the relation of flow lines of systems dominated by gas, oil and also water, which are commonly used and are of high value in flow assurance.
此外，CSMHyk 被用于开发水、油和气常见结构中的水合物形成预测模型[230]。该模型有助于预测瞬态和空间水合物的形成，以及主要由气、油和水主导的系统中流动线的关联，这些方法通常被使用，并在流动保证方面具有很高的价值。

Gas hydrates have been experimentally analysed and then soft computational models such as GA, ANN, PSA (Particle Swarm Algorithm) and ICA (Imperialist Competitive Algorithm) are used to refine the data produced experimentally, and curve fitting is applied to improve the precision of the correlations observed [231]. The findings of this novel correlation were contrasted with those of previous works and found that the proposed novel correlation had better precision and minimal error. A comparative study has been carried out on the results of accuracy in predicting hydrate formation pressure in binary mixtures. This distinction was made between the CSMHYK and ANN models developed [232]. This result was very impressive because, relative to the CSMHYK model, the ANN model demonstrated greater precision.
天然气水合物已通过实验分析，然后使用 GA、ANN、PSA（粒子群算法）和 ICA（帝国竞争算法）等软计算模型来优化实验产生的数据，并应用曲线拟合来提高观测相关性的精度[231]。这项新相关性的研究结果与先前工作的结果进行了对比，发现所提出的新相关性具有更高的精度和更小的误差。对预测二元混合物水合物生成压力的准确性进行了比较研究。在 CSMHYK 和 ANN 模型之间进行了这种区分[232]。这个结果非常令人印象深刻，因为相对于 CSMHYK 模型，ANN 模型表现出更高的精度。

An experimental study of the formation of gas-hydrate and particle transportability was carried out using a high-pressure flow loop in distributed multiphase-flow systems, and an ANN prediction model was developed. Later, with many current field data, this model was checked and found that the model acts as an effective model of prediction [233].
使用高压流动回路在分布多相流系统中进行了一项关于天然气水合物形成和颗粒输运性的实验研究，并开发了一个人工神经网络预测模型。后来，利用许多当前现场数据对该模型进行了验证，发现该模型是一个有效的预测模型[233]。

As CO₂ hydrates are a crucial threat to flow assurance relative to CH₄ hydrates, interest in carbon dioxide hydrates is of high value. Preliminary assessment has been carried out and a thermodynamic model has been built alongside the Artificial Neural Network (ANN) model to estimate the solubility of CO₂ in L-phenylalanine aqueous sodium salt. This was done to improve technologies for the inhibition process [234]. In addition, a novel Artificial Neural Network (ANN) model for aqueous Tetra Butyl Ammonium Hydroxide and Piperazine efficiency estimation along with their carbon dioxide (CO₂) capture blends. This work aims to enhance the mechanism of carbon dioxide capture and hydrate inhibition to achieve improved flow assurance [235].
由于 CO ₂ 水合物相对于 CH ₄ 水合物对流动安全构成关键威胁，因此对二氧化碳水合物的兴趣具有重要价值。已进行初步评估，并建立了热力学模型和人工神经网络（ANN）模型，以估算 CO ₂ 在 L-苯丙氨酸水钠盐中的溶解度。此举旨在改进抑制过程技术[ 234]。此外，还开发了一种新型人工神经网络（ANN）模型，用于估算水合四丁基氢氧化铵和吡唑啉的效率及其二氧化碳（CO ₂ ）捕集混合物。这项工作旨在增强二氧化碳捕集和水合物抑制的机理，以实现更优的流动安全[ 235]。

Several models of the Artificial Neural Network (ANN) have been developed to test hydrate kinetics and to approximate inhibition rates for the prevention of hydrate formation in flow lines [236].
已开发出几种人工神经网络（ANN）模型，用于测试水合物动力学，并近似估算用于防止管路中水合物形成的抑制率[236]。

The details of the various prominent AI models applied over the years for various conditions are tabulated below in Table 6 for a clear understanding.
多年来应用于各种条件下的各种突出 AI 模型的详细信息已列于表 6 中，以便清晰理解。

Table 6 Synopsis of Various AI models applied on gas hydrates study
表 6 应用于天然气水合物研究的各种 AI 模型概览

2.8.1 Way Forward
2.8.1 发展方向

It can be observed from the table that most AI modelling techniques were ANN models and are applied on kinetics and performance studies. The application of ANN models to thermodynamic study is limited. Also, the prediction model development for various promoters and inhibitors is still unclear. Also, there is no clear modelling applied for the promoters and inhibitors on various gas mixtures at high pressures. The models can be applied to various chemicals applied on hydrate research. The models can be applied on desalination using hydrates, carbon separation, carbon storage. The AI research can be further extended by applying other modelling techniques like GA, PSA, ICA.
从表格中可以看出，大多数 AI 建模技术是人工神经网络模型，主要应用于动力学和性能研究。人工神经网络模型在热力学研究中的应用有限。此外，针对不同促进剂和抑制剂的预测模型开发仍不明确。此外，在高压下针对不同气体混合物的促进剂和抑制剂的建模应用尚无明确方案。这些模型可以应用于 hydrate 研究中的各种化学品。这些模型可以应用于利用 hydrate 进行海水淡化、碳分离、碳储存。通过应用遗传算法、粒子群优化、独立成分分析等其他建模技术，AI 研究可以进一步拓展。

3 Summary
3 总结

Research on gas hydrates has made considerable advances in experimental analysis over the last 3 decades, contributing to the creation of several models for testing and forecasting the behavior of gas hydrates under different conditions. This paper provides a detailed evaluation of several gas hydrate modelling techniques. The main features of the thermodynamic models, Kinetic models, Statistical Models, Models developed using Computational Fluid Dynamics (CFD) and AI techniques are highlighted. A clear discussion on the features of the thermodynamic models and kinetic models and their application is made. Also, the advancements in statistical modelling techniques for the prediction of gas hydrate conditions was discussed. The latest sophisticated modelling techniques like CFD and ANN are also clearly discussed to understand the applicable advancements on gas hydrates. Finally, the limitations and future perspectives are also discussed. There is no unified model, irrespective of the suggestion of different models, representing all the observations claimed or studied. There is a distinctly noted lack of relation between physical actions and chemical existence. A multi-scale physics that groups everything is important for the creation of such a unified model. A novel model for estimating the rate of hydrate formation in three-phase gas, the oil–water method, is also still to be proposed. An exact model that covers semi-empirical parameters is needed for functional industrial applications. This helps to treat gas hydrates in the construction of concrete reactors. However, during the introduction of these Semi-Empirical parameters to the apparatus, the scaling of these Semi-Empirical parameters is very important. Numerical modelling, especially for porous media and transmission pipelines, may be influential in the formulation of gas hydrates. But for effective prediction and validation, it needs real time data (either field or experimental). We agree as true that, along with the experimental study, the extension of the research on the development and growth of gas hydrates can intensify far by developing or constructing successful prediction models. This would continue to greatly boost flow assurance in the oil and gas sector.
过去三十年来，天然气水合物研究在实验分析方面取得了显著进展，促成了多个模型的建立，用于测试和预测天然气水合物在不同条件下的行为。本文对几种天然气水合物建模技术进行了详细评估。重点介绍了热力学模型、动力学模型、统计模型、计算流体动力学（CFD）和人工智能技术开发的模型的主要特征。对热力学模型和动力学模型的特点及其应用进行了清晰讨论。此外，还讨论了统计建模技术在预测天然气水合物条件方面的进展。最新复杂的建模技术，如 CFD 和人工神经网络（ANN），也得到了清晰讨论，以了解其在天然气水合物方面的适用性进展。最后，还讨论了局限性和未来展望。无论提出多少种模型，都不存在一个统一的模型能够代表所有声称或研究过的观测结果。物理作用与化学存在之间明显缺乏关联。 一个将所有尺度物理现象综合起来的多尺度物理模型对于构建这种统一模型至关重要。一种用于估算三相气体中水合物形成速率的新型模型——油水法——也尚未被提出。需要一种包含半经验参数的精确模型，以实现工业应用。这有助于在混凝土反应堆的建设中处理水合物。然而，在将这些半经验参数引入设备时，这些半经验参数的尺度化非常重要。数值模拟，特别是针对多孔介质和输运管道，可能对水合物的形成有重要影响。但对于有效的预测和验证，需要实时数据（无论是现场数据还是实验数据）。我们坚信，随着实验研究的深入，对水合物发展和生长的研究扩展可以通过开发或构建成功的预测模型来显著加强。这将持续极大地推动油气行业的流态保障。