research 1..28 - American Chemical Society

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A Review of Clathrate Hydrate Nucleation Maninder Khurana,† Zhenyuan Yin,†,‡ and Praveen Linga*,† †

Department of Chemical and Biomolecular Engineering, National University of Singapore, Engineering Drive 4, Singapore 117585 Lloyd’s Register Global Technology Centre Pte Ltd, Singapore 138522

‡

ABSTRACT: Clathrate hydrates are crucial from the point of view of flow assurance and future energy resources, as well as potential innovative and sustainable applications such as gas separation, CO2 sequestration, district and data center cooling, seawater desalination, and natural gas storage. Although proof of concept has been demonstrated, significant progress is necessary in order to achieve industrial-level validation and commercialization. Most of the applications possess a common requirement of enhanced kinetics in formation and dissociation. There is a need for a broader understanding of hydrate nucleation mechanisms, cause-effect relations, and investigation techniques. The stochastic nature of hydrate nucleation, confounding cause−effect relations, and spatial-temporal scales have made it even more challenging to study nucleation. The use of hydrate promoters, novel reactor configurations such as porous media in a packed bed, and nanoparticles and hydrogels necessitates us to obtain further insights about clathrate nucleation. This review provides an in depth analysis about the characteristics of clathrate hydrate nucleation and the techniques adopted for studying nucleation from an application-oriented perspective and enables further development of clathrate technology toward future applications. KEYWORDS: Gas hydrates, Nucleation, Clathrate hydrates, Stochastic nature, Molecular simulation, Porous media

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INTRODUCTION Clathrate hydrates are crystalline compounds of water molecules acting as host and guest molecules.1,2 Traditionally, natural gas hydrates have been a cause of major problems for the oil and gas industry in production lines, during drilling, and in workover operations.3,4 Hammerschmidt in 1934 first discovered that the natural gas pipelines were plugged due to hydrate formation rather than ice which was originally perceived.5 Hydrate formation can compromise the structural integrity of the pipelines/surface facilities and can cause disruptions in production.1 Hydrates have also been widely stated as a leading source of the deep-water flow assurance problem.6,7 Gas hydrate is a technology enabler for a number of applications in water, energy, and environment research domains. Notable applications with gas hydrate as an enabler are gas separation,8−15 energy storage,16−22 energy transport,23−27 cold energy storage,28,29 CO2 sequestration,30−32 and desalination applications.14,33−36 These applications of gas hydrates necessitated the systems to have higher throughput, lower energy consumption, and higher efficiency of separations. Hydrate formation including both nucleation and growth is an extremely crucial step of hydrate-based processes and thorough understanding of nucleation is necessary for the applications. Some applications such as desalination and gas separation requires continuous process operations and hence necessitates precise predictions and knowledge of each step. Clathrate hydrates require high pressure and low temperature for formation. The process of hydrate formation has many © 2017 American Chemical Society

similarities with that of crystallization; i.e., it can be divided into a nucleation phase and a growth phase. Three common clathrate structures exist (Table 1): structure I (sI, cubic), structure II (sII, cubic), and structure H (sH, hexagonal). The structure formed is found to depend upon the size of the guest molecule.37 The pentagonal dodecahedron (512 cage) is the basic building block in the two hydrate structures. The other two types of cages are 51262 and 51264. The other two types of cages observed are attributed to the inability of the dodecahedron to tessellate a 3D space. When two 512 cages are separated by bridging water molecules, they form 51262 cages as in sI. On the other hand, sII structure hydrates are formed when 512 cages share the faces and the resulted gaps are filled by creating 51264 cages. CH4, C2H6, and CO2 form sI hydrate, while propane and isobutane tend to form sII hydrate. Smaller molecules such as H2 or N2 also tend to form sII hydrate since they occupy smaller cages that are present in greater fraction in sII hydrates. The crystal structures of the sI hydrate and sII hydrate were first determined in the late 1940s and early 1950s by von Stackelberg and co-workers using X-ray diffraction.2 The third type of hydrate crystals (sH) are composed of three small 512 cages, two small 12-hedra 435663 cavities, and one large 18-hedra 51268 cage.38 Net equation of hydrate formation can be described as Received: September 13, 2017 Revised: October 29, 2017 Published: November 3, 2017 11176

DOI: 10.1021/acssuschemeng.7b03238 ACS Sustainable Chem. Eng. 2017, 5, 11176−11203

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ACS Sustainable Chemistry & Engineering Table 1. Structural Properties of Most Common Clathrate Hydrates Property

sI

sII

sH

Lattice type

Primitive cubic

Face centered cubic

Hexagonal

Unit cell parameters

a = 1.20

a = 1.70

a = 1.21, c = 1.01

12

2 (5 ) (S) 6 (51262) (L)

12

16 (5 ) (S) 8 (51262) (L)

3 (512) (S) 2 (435663) (S) 1 (51268) (L)

0.395 (S) 0.433 (L)

0.391 (S) 0.473 (L)

0.391 (S) 0.406 (S) 0.571 (L)

46

136

34

Unit Cell structure

Average cavity radius

Number of water molecules per unit cell

G + n w H 2O ⇌ G.n w H 2O

respect to nucleation. Ripmeester and Alavi41 in their recent review suggested that nucleation, decomposition, and the memory effect during reformation are among the most important outstanding issues to be understood regarding clathrate hydrate science. Understanding hydrate nucleation at a molecular level is challenging due to small time/length scales of nucleation and the stochastic nature of the process. Although there have been articles focused toward reviewing hydrate nucleation, the articles have been targeted toward particular aspects failing to draw a holistic understanding of clathrate nucleation necessary for application of hydrate in the fields of gas separation, energy storage, and transport. Hence, this work is an attempt to document the various works, techniques, and important results along with providing insights into the standing issues for clathrate nucleation. Next, we provide some basic background about nucleation and subsequently delve into various aspects pertinent to nucleation.

(1)

Figure 1 shows the schematic of a typical time evolution of gas consumption for hydrate formation in a semibatch reactor.

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Figure 1. Hydrate formation schematic represented by gas uptake in an experiment vs time showing three main phases in hydrate formation process: dissolution phase, supersaturated phase, and growth phase.

TYPES OF NUCLEATION AND CHARACTERISTICS There are two types of primary nucleation: homogeneous nucleation and heterogeneous nucleation. Homogeneous Nucleation. In homogeneous nucleation (HON), the nucleus of the hydrate phase emerges directly from the parent phase. Homogeneous nucleation is generally observed in systems without any impurities and considered to be stochastic in nature; i.e., the critical nucleus is formed because of a local thermodynamic fluctuation of the system.42 Before the critical radius is attained, the clusters of molecules formed may either grow or shrink as a result of thermodynamic fluctuation. At lower subcooling or driving force, near the equilibrium curve, homogeneous nucleation has low probability of occurrence since the critical radius can be substantially high.43 For instance, nucleation can take up to a thousand years in the case of hydrate formation from air inclusion in ice cores44. Knott et al.45 estimated the homogeneous nucleation rate under realistic conditions as 10−111 nuclei cm−3 s−1 by performing MD simulations of methane hydrates. In practical conditions, hydrate nucleation through homogeneous nucleation is very unlikely and proceeds through heterogeneous nucleation. Heterogeneous Nucleation. In the case of heterogeneous nucleation (HEN), the hydrate phase nucleates in contact with a third phase which can be either foreign particle or surface. When we consider the system free energy, it is more favorable to form hydrate on a two-dimensional surface than a three-

The different stages for the process of hydrate nucleation can be observed from the schematic. Since the guest species is present in the gas phase, the process starts with the increase in gas uptake due to dissolution into the liquid phase. After the dissolution phase, the super saturation phase begins when the pressure and temperature thermodynamically favor the formation of hydrates phase but still without the appearance of critical hydrate nuclei. A critical nucleus of a hydrate phase can be defined as the minimum amount of new phase that is capable of existing independently. The time interval between establishment of super saturation and the formation critical nuclei is called the induction time. Induction time has been confirmed experimentally in various literatures. It has been shown in independent studies that supersaturation does not always guarantee hydrate formation.39,40 This critical nucleus can then act as the center for further hydrate growth. The hydrate nucleation process is followed by the catastrophic growth process with rapid increase in the gas uptake. Finally, the gas uptake may end at different levels depending upon the mass transfer resistance and final hydrate formation as shown in Figure 1 by the dotted trajectories. While the thermodynamics of hydrate formation/dissociation is well established, there are lot of unanswered questions with 11177


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ACS Sustainable Chemistry & Engineering

They also calculated critical solubility of methane to be ∼1.7 molecules/nm3, beyond which metastable solution forms hydrate spontaneously and induction time is not observed. Similar enhanced nucleation has also been reported by Angeles and Firoozabadi62 near fluid−fluid spinodal decomposition. For a propane−water system, they demonstrated that propane density fluctuations near fluid−fluid spinodal decomposition produce enhanced nucleation rates and is more general than short-range attractive interactions.

dimensional nucleus in the bulk water phase. The presence of a third phase lowers the interfacial energy necessary to overcome in nucleation phenomenon. Hence, heterogeneous nucleation is more rapid than homogeneous nucleation, and the critical radius for nucleation is less than homogeneous.46,47 Similar effects have been reported for the case of ice nucleation as well.48,49 The contact angle between the hydrate and the preexisting surface controls the reduction in the specific superficial energy of the solution−hydrate interface, which, in turn, decreases the amount of work required for the formation of the new phase.50 The stabilization of hydrate nuclei in the presence of surfaces is discussed further in the section on Nucleation in the Presence of Porous Media. In the case of dispersed systems such as emulsions, water droplets behave as independent reactors, and the nucleation can be, to some extent, disjointed in each droplet.51−53 Droplet collision in shared systems or in concentrated emulsions may cause nucleation propagation between droplets and is called secondary nucleation.43 Site of Nucleation. To investigate the site for hydrate nucleation, Long and Sloan54 performed a series of experiments on nucleation of natural gas and carbon dioxide in a sapphire tube. They studied the effect of precipitated amorphous silica as the hydrate nucleating agent and sodium dodecyl sulfate (SDS) as a surface inhibitor. Carbon dioxide was chosen to establish the effect of higher guest solubility as compared to natural gas. While the induction times were found to be not predictable, hydrate nucleation was always initiated at an interface, at a vapor−water interface in most cases but along the sapphire tube or along the reactor walls in other cases. Higher solubility of carbon dioxide resulted in much faster hydrate growth in the solution. Various other studies in the literature have confirmed the nucleation site as the vapor−liquid interface for both methane and carbon dioxide hydrates.55 The preferential hydrate nucleation at the vapor−liquid interface has also been demonstrated by means of Molecular Dynamics (MD) simulations by Moon et al.56 Apart from the lowering of the Gibbs free energy at the interface as stated before, the interface has very high concentration of the host and guest molecules. The hydrate guest composition at the interface can be as high as 0.15 mole fraction compared to the maximum of 0.001 in the aqueous phase.2 The higher concentration that exists due to surface adsorption increases the probability of nucleation. Induction Time. Induction time is characterized by oversaturation and metastability of the solution. As stated previously, nucleation is a stochastic process. Various studies have shown that hydrate induction times have a significant scatter for experiments performed at constant temperatures.57−59 However, hydrate formation experiments at a constant cooling rate show significantly less scatter.2 Further, the degree of stochastic behavior is strongly affected by the magnitude of the driving force. Natarajan et al.60 showed that hydrate induction time is far more reproducible at higher pressures and subsequently formed empirical correlations for induction times as a function of supersaturation ratio. Guo and Rodger61 studied the prenucleation stage of methane hydrate formation using MD simulations. They studied methane solubility under metastable conditions and found that it can be increased by both reducing temperature and increasing pressure. But, lowering temperature was found more effective for promoting hydrate formation because increasing the pressure was found to reduce the number of water cages.

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NUCLEATION PATHWAYS The hydrate nucleation mechanism has been a long-standing area of study, and opinions remain divided on the nucleation pathways. Both time-resolved experiments63−69 and simulations56,70−78 have been used in order to capture the pathway and obtain a deeper understanding of the nucleation process. However, due to the difficulty of obtaining direct evidence of nucleation, molecular simulations have been preferred over experiments to study nucleation pathways. Four major conceptual theories have been proposed for hydrate nucleation (Table 2). These are discussed in the subsequent section. Classical Nucleation Theory. Classical nucleation theory (CNT) has been well studied for the case of crystallization. CNT was originally derived for condensation of vapor into a liquid in the 1920s, and it has been later applied to crystallization of supersaturated solutions by analogy.79,80 CNT has been commonly used to predict the rate of nucleation and the height of the free energy barrier.79,81 CNT describes the activation barrier to nucleation as the sum of the increase in free energy due to creation of a new interface and the decrease in the energy from creating a more stable phase. Due to its analytical simplicity, it has been widely applied not just for crystallization but also clathrates. At the end of the 19th century, Gibbs developed a thermodynamic description of CNT by defining the free energy change required for cluster formation as the sum of free energy change for the phase transformation and the free energy change for the surface formation. ΔG = ΔG V + ΔGs

(2)

The phase transformation free energy change is negative and decreases the free energy of the system. However, the solid− liquid interface increases the free energy of the system, and the growth of the cluster depends upon the two conflicting terms. Figure 2 provides the free energy diagram for the nucleation process. The positive surface free energy term dominates at the critical radius rc beyond which the total free energy decreases continuously and the growth becomes energetically favorable. The free energy barrier corresponds to the increase in the free energy at the critical radius. The critical radius for hydrate is attained by means of random fluctuations, and subsequently, the hydrate growth is spontaneous. Various studies in the literature have adopted a unified approach for nucleation and growth by treating nucleation using classical theory and the modeling growth phase as a chemical reaction.3,82 The classical nucleation approach has two major shortcomings: (1) macroscopic treatment of the hydrate nucleus leading to substantial errors in excess free energy and critical radius estimations83 and (2) no insight into the nucleation pathways and the exact structure of hydrate structures. Labile Cluster Hypothesis (LCH). To obtain insights into the nucleation pathways, Sloan and Fleyfel first introduced 11178


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Heterogeneous Bai et al.271 Two-Step Formation Mechanism

Homogeneous Multipathway Nucleation

Jacobson et al.,95 Vatamanu et al.,76 Lauricella et al.,246 He et al.100 Bi et al.113 Blob Hypothesis: Two-Step Formation

Christiansen and Sloan Sloan and Fleyfel, Labile Cluster Hypothesis (LCH)

Homogeneous

Radhakrishnan and Trout71 Local Structuring Mechanism

Homogeneous

Long et al.,92 Kvamme et al.93 Nucleation at Interface Mechanism

Homogeneous

Homogeneous

Mostly adopted from other established domains such as crystallization and applied analogously to the case of hydrate formation. It has been shown in the literature that labile clusters are not thermodynamically favored, and the pathway is not correct for most cases of nucleation. Variation of LCH where labile clusters are formed at the interface and nucleation occurs at the interface prior to diffusing into bulk phase. Thermal fluctuations are the cause of the initial appearance of water cages and results in structuring of guest molecules. Concept differs from LCH by stating that guest structuring follows water structuring. First hypothesis to propose amorphous precursors to clathrate crystals in a two-step mechanism. A few other studies have supported the occurrence of amorphous precursors prior to amorphous−crystalline transition. Reports of direct crystalline cages like CNT along with two-step blob hypothesis suggesting these mechanisms might be occurring in parallel. Nucleation occurs along the three-phase line rather than vapor−liquid interface in a CO2/H2O/silica system. The silica surface acts as a stabilizer for CO2 amorphous crystals through hydrogen bonding and acts as nucleation sites. Englezos et al.

86 84

Sloan et al., Bishnoi et al., Classical Nucleation theory

Homogeneous

Nucleation type Comments

116 47 3

Studies supporting/adopting Pathway

Table 2. Compilation of Nucleation Pathways Reported in the Literature


Figure 2. Free energy change for hydrate nucleation process according to the classical nucleation theory.

labile cluster hypothesis (LCH) for hydrate nucleation from ice.84 Their work among others by Muller-Bongratz et al.85 and Christiansen and Sloan86 together form the foundation for LCH. According to LCH, labile ring nucleation structures exist in pure liquid water.84,87 Upon dissolution of the hydrate former gas, the critical nucleus is then formed by agglomeration of labile clusters around the guest molecules. Sloan and Fleyfel first analyzed two studies reported on reproduction of induction or hydrate metastability. The first study was by Barrer and Edge88 on the formation of hydrates of three inert gases, namely, argon, krypton, and xenon, from ice. It was reported that while argon and xenon formed hydrates immediately, krypton had an induction period of about 1 h. The induction phenomenon was reported to be similar to the metastability of the subcooled solutions in the absence of a seed crystal. The second study considered was of Falabella et al.89 based on determining the equilibrium and kinetic properties of hydrates of methane, ethane, ethylene, acetylene, carbon dioxide, and krypton at subatmospheric, constant pressures. Falabella et al.89 reported two distinct types of kinetic results: one with a clearly defined induction period for methane and krypton and second for all other gases without any induction period. The observed induction period for methane and krypton was related to hydrated metastability or primary nucleation. Sloan and Fleyfel84 proposed a new induction nucleation parameter, guest to cavity size ratio. They proposed a kinetic mechanism for hydrate formation with multiple intermediary steps and modeled the system as a set of chemical reactions as shown in Figure 3. The mechanism starts from the stable species initially as shown in Figure 3A and ends with the attainment of a critical hydrate radius and beginning of crystal monotonic growth species Figure 3D. Figure 3B shows a very rapid transition between different hydrate structures if they exist. Consequentially, two different paths for construction of sI and sII hydrates were proposed. The induction time observed in methane and krypton hydrate was explained on the basis of transition in the two paths proposed. They validated their model using the experimental results of Falabella et al.89 Skovberg et al.90 were the first study to challenge the LCH. They pointed out that the difference in driving force (ΔTsub) for the CH4 hydrate nucleation experiments was 19 K, whereas for C2H6 hydrate it was 49 K. Natarajan et al.91 showed a 11179


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Figure 3. Proposed kinetic mechanism for hydrate formation from ice by Sloan and Fleyfel.84

Figure 4. Schematic representing the local structuring mechanism.

where they get adsorbed on the aqueous surface. Subsequently, the molecules transport through surface diffusion to a suitable location where water molecules form first partial and then complete cages resulting in labile clusters. Kvamme et al.93 did not attempt to formulate a quantitative estimation of the rate of nucleation. Local Structuring Mechanism. Upon providing evidence against LCH, Radhakrishnan and Trout71 proposed a local structuring (Figure 4) mechanism for nucleation according to which thermal fluctuation causes the local ordering of CO2 molecules. The local ordering of the guest molecule induces ordering of the host molecules and finally leads to the formation of critical nucleus. Upon attaining the critical nucleus, the water molecules rearrange to form a proper hydrate framework, leading to hydrate crystallization. Their work was based on the following assumptions: (1) Free energy barrier to nucleation remains unaltered by the limited simulation size. (2) Nucleation is governed by equilibrium

similar driving force but with a driving force based on fugacity given below: Driving Force =

fg V feq

−1 (3) 71

Radhakrishnan and Trout showed, using the Landau free energy surface, that labile clusters proposed by Sloan and Fleyfal84 are easily formed by an activated process only for dilute solutions. For concentrations near the CO2−H2O interface, the free energy penalty of formation of labile clusters is large, and hence, nucleation cannot occur through labile cluster pathway. Nucleation at Interface Hypothesis. Long et al.92 and Kvamme et al.93 proposed a variation of the labile cluster hypothesis, where the assembly of the labile clusters takes place on the vapor side of the vapor−liquid interface. According to the hypothesis, gas molecules are transported to the interface 11180


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hydrophobic and hyrophillic guest molecules. They concluded that that formation of a blob of the hydrophobic (small) guest is a rare event and limits the rate of nucleation more compared to a more soluble guest. It was observed that blobs of hydrophobic guests are rarer and longer-lived than those for a hydrophilic guest. They established different blob pathways for nucleation of different guest molecules based on the guest size. In Figure 6,

thermodynamics. (3) A minimum free energy path lies within the chosen parameter space. A more fundamental difference between the local structuring mechanism and labile cluster hypothesis is whether water ordering is driven by a guest molecule or guest ordering is driven by a water molecule. Rodger and co-workers,73,56,94 Walsh et al.,75 and Guo et al.74 studied methane hydrate nucleation using MD simulations. The results were similar to those proposed by LCH; clusters of methane molecules were observed to be surrounded by water molecules. The difference, however, was that the structure was amorphous rather than crystalline as proposed by LCH. To explore this further, Jacobson et al.95 studied the amorphous precursors in the nucleation of clathrate hydrates and proposed a blob formation mechanism discussed next. Blob Formation Mechanism. Jacobson et al.95 proposed the nucleation pathway for hydrophobic guest molecules via blob formation. Jacobson et al.96 developed a coarse-grained model for molecular dynamics simulations and investigated the mechanisms of nucleation of clathrate hydrates. They introduced blob as a guest-rich amorphous precursor in the nucleation pathway of clathrates of hydrophobic guests. The blob comprises the same polyhedral cages as crystalline hydrates but lacks their long-range order. In the blob, the amorphous clathrate cage continuously forms and dissolves until a cluster of cages reaches a critical size. Figure 5 shows the

Figure 6. Effect of the size of a guest molecule on the reaction pathway for hydrate nucleation shown by Jacobson et al.96

three pathways for small (S), medium (M), and extra-large (XL) guest molecules can be observed. The S solute fills all the cages, M primarily fills the larger cages, and XL fills exclusively large cages. They observed that formation of empty 512 cages to be a parallel competing mechanism for nucleation. All the molecular simulations discussed until now were constant temperature simulations NPT or NVT. Ripmeester, Alavi, Englezos, and co-workers102−104 have shown by means of constant energy (NVE) simulations that the heat released due to hydrate significantly affects the mechanism and the rate of dissociation. Liang et al.105 performed NVE simulations of hydrate formation to understand a similar effect for hydrate nucleation. They observed a higher order of crystallinity for the case of NVE simulation, but the two-step mechanism of nucleation was confirmed in their simulation as well. Zhang et al.106 performed MD simulations to form hydrates with a methane non-bubble in liquid water at 250 K and 50 MPa to study the effect of different ensembles on nucleation kinetics of methane hydrates. They reported the sequence of nucleation rate in the ensembles as NPT > NVT > NVE. They reported that the order of crystallinity was reversed; i.e., the faster the hydrate forms the lower the crystallinity is. In terms of mimicking the real phenomenon in the early stage of nucleation, NVE is most suitable because the use of thermostat and/or a barostat in NPT and NVT ensembles is artificial since the exothermic heat of hydrate formation cannot be observed.105 NVE simulations however come at the cost significantly higher simulation time, ∼6.5 times slower than comparable NPT or NVT simulations.107 The formation of amorphous crystals in the simulation studies had one common thing though. The molecular simulations were performed at a high driving force by means of very high subcooling or pressurizing. Jacobson et al. in their subsequent work108 analyzed two major questions: How can crystalline hydrates arise from amorphous precursors? In

Figure 5. Schematic for blob formation mechanism as proposed by Jacobson et al.95

mechanism of hydrate nucleation via blob formation. The critical size was proposed to be a function of the temperature, and at 0.7 Tm subcooling, it is estimated at about five cages. After reaching the critical size, space-filling growth is achieved through face sharing between the cages. During its lifetime, a blob can produce many hydrate crystals until it finally dissolves into the solution. The blobs themselves are not stationary but diffuse in solution. In this perspective, blobs are large analogues of labile clusters. In the literature, similar mechanisms involving amorphous metastable states have been proposed for crystallization of proteins and colloids.97,98 This two-step nucleation mechanism of amorphous nuclei to crystalline clathrate has been observed in other studies by Vatamanu et al.,76 Liang et al.,78Sarupria et al.,99 and He et al.100 using different methodologies. These results contrast classical nucleation theory according to which nucleation of crystalline phase is taken through a buildup of monomer already arranged with the symmetry of the crystal phase. Experimentally, amorphous tetrahydrofuran (THF) hydrate solids have been synthesized under a high pressure of 1.3 GPa.101 In their later study, Jacobson et al.96 analyzed the effect of guest molecule solubility on the nucleation pathway. They studied the nucleation pathways for guest molecules varying over 2 orders of magnitude in solubility. They concluded that nucleation occurs through the blob formation pathway for both 11181


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Figure 7. Seven dominant cages in incipient clathrate hydrate formation as observed from MD simulations from the study of Walsh et al.112 The most common cages are shaded more prominently, and the number represents the number of water molecules in each cage. Gray dots (51261) represent cages with physical infeasibility.

pathways for hydrate nucleation.107,113 An extremely interesting observation made by Bi et al.113 in their recent work shows that although theories vastly different than CNT have been proposed for nucleation the free energy curves for the nucleation in their study is very close to that predicted by CNT. On the basis of multiple nonclassical pathways and yet CNT-like energy curves, Bi et al.113 concluded that hydrate nucleation occurs through energetically similar yet different pathways. Moreover, it was conjectured that hydrate nucleation is an entropically driven kinetic process. Future work needs to be undertaken to corroborate these conjectures, but the evidence thus far lays the foundation for coming endeavors.

addition, are the amorphous precursors stable even at a lower driving force for temperatures closer to equilibrium? They showed in their study that at a high driving force, the amorphous nuclei are kinetically favorable over crystalline nuclei because of lower barriers of formation. They also reported that both amorphous and crystalline nuclei lead to the formation of crystalline clathrates. An implication of this finding is that macroscopic evidence for crystalline clathrates cannot be used to rule out amorphous precursors. Similar results have been reported in parallel studies.74 Interestingly, they also showed that cross nucleation of sII clathrates from sI nuclei is also possible in cases where both sI and sII structures are more stable than liquid water. They were not able to completely answer the question about the stability of amorphous crystals at a lower driving force. Nucleation studies based on diffraction and spectroscopic experiments have reported formation of a mixture of different crystal structures.68,109−111 Even though the presence of amorphous structures observed might be subject to time scales and the driving force, Walsh et al.112 suggested that both experiments and simulations suggest a post-nucleation solidsolid rearrangement. Walsh et al. suggested that even though the presence of amorphous structures observed might be subject to time scales and the driving force both experiments and simulations suggest a postnucleation solid−solid rearrangement. To study the transformation from amorphous crystals to hydrate crystals by means of solid−solid rearrangement, Walsh et al.112 performed 20 MD simulations of methane clathrate. Walsh et al.112 reported the seven types of cages (Figure 7) observed in all nucleation. They identified two types of cage− cage transformations: (a) insertion type and (b) rotation type. They concluded that templates for exclusive growth of the thermodynamically favorable crystalline phase could form almost immediately upon nucleation, different than the amorphous crystals intermediates. Multipathway Nucleation. It is evident from the discussion that there is enough evidence to support for the intermediate amorphous precursors. The stability of amorphous nuclei as compared to crystalline nuclei and the interconversion between them are a few things that could still require more proof to be conclusively established. More recently, studies have shown evidence of the two-step hydrate nucleation and direct crystalline nuclei occurring in parallel as competing

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NUCLEATION RATE, CRITICAL RADIUS, AND WORK OF FORMATION Vysniauskas and Bishnoi et al.82,114 in their seminal work reviewed the kinetics of hydrate formation and developed a semiempirical model to correlate experimental data on methane and ethane hydrate formation. In their work, the hydrate formation modeling did not include the hydrate nucleation. The driving force for the hydrate formation was considered to be the degree of supercooling that is the difference between the equilibrium temperature and the experimental temperature. Their study was the first attempt to describe quantitatively and model the formation kinetics of gas hydrates. A similar driving force had been adopted in various other studies as well before.115 Englezos et al.116 subsequently modified the experimental procedure of Vysnauskas and Bishnoi to achieve homogeneous hydrate nucleation conditions. With the new obtained experimental results, Englezos et al.116 then proposed a mechanistic model (Englezos−Bishnoi model) for hydrate growth including nucleation with only one tunable parameter, r, that represents the rate of reaction. The overall driving force for the process was proposed as the fugacity difference between the equilibrium and the experimental conditions. Δf = f − feq

(4)

Englezos et al.116 also estimated the critical radius by starting from the Gibbs free energy change in formation of a new phase ΔG = ΔGs + ΔGv = A pσ + Δg v Vp 11182

(5)


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ACS Sustainable Chemistry & Engineering where σ is the surface free energy, and Δgv is the difference in phase free energies. Assuming a spherical nucleus, at critical radius d ΔG/dr = 0, we obtain critical radius as following: rc =

−2σ Δg v

hydrate nucleus and the work of nucleus formation as a function of supersaturation in their subsequent work.118 Based on classical theory of nucleation, work, W, (J) to form a hydrate cluster for three-dimensional nucleation of one component of the condensed phase to hydrate nucleation at a given supersaturation Δμ (J) is given by42

(6)

⎤ ⎡ 2 ⎛f ⎞ n w vw(P − P∞) ⎥ RT ⎢ b, j ⎟ ⎜ ( −Δg v ) = ∑ θj ln⎜ ⎟ + ⎥ v h ⎢⎣ 1 RT ⎝ f∞ , j ⎠ ⎦

W (n) = −nΔμ + cνh2/3σef n2/3

In the formula, Δμ is a known function of the pressure, P, or the temperature, T, taken from their previous study.118 The number of building units, n*, constituting the hydrate nucleus and nucleation work (the value of W at n = n*) can be estimated from the above equation. At n = n*, dW/dn = 0 and results in the following general formula for critical size and the work done

(7)

where vh and vw are the molar volumes of hydrate and water, respectively; f b,j and f∞,j are the bulk phase and equilibrium fugacities, and nw is the number of water molecules per gas molecule. Using the above expression, Englezos et al.116 calculated the critical radius of methane to be 30−170 Å. Skovberg et al.90 expressed the driving force for nucleation as the difference in the chemical potential of water in the hydrate phase and water in the water phase. They showed that induction times for methane, ethane, and mixed methane− ethane hydrate formation varies exponentially with the driving force. (8)

47

116

⎞−m ⎛fV g ⎜ =K − 1⎟ ⎟ ⎜f ⎠ ⎝ eq

(14)

2

(15)

where c is the shape factor, and σef is the effective superficial energy for the hydrate−solution interface. The kinetic factor, A (m−3 s−1) accounts for the attachment mechanism to hydrate building units. The kinetic factor (A) contains the information about the kind of nucleation and the mechanism through which the hydrate building blocks attach to the hydrate nucleus. Typically, A is orders of magnitude lower for HEN than HON. With the appropriate value of the driving force Δμ calculated from their previous study,117 the above equation provides the nucleation rate for different cases. Kashchiev and Firoozabadi117 performed an analysis on the effect of pressure and temperature on the nucleation rate of the methane hydrate under isothermal (273.2 K) and isobaric (19.4 MPa) supersaturation, respectively. A rapid increase in the nucleation rate with an increase in the supersaturation was reported. They also reported that for smaller values of supersaturation homogeneous nucleation was an order of magnitude smaller than heterogeneous nucleation. While at higher supersaturation, homogeneous nucleation becomes dominant. Due to the rapid reduction of the nucleation rate with reducing supersaturation, a minimum supersaturation was identified below in which the nucleation is virtually arrested. Multicomponent Nucleation: Anklam and Firoozabadi Model for Mixture Predictions. The model is based on the difference in chemical potentials as the driving force. As in their previous study,117 hydrate formation was considered as an aqueous phase reaction for a multicomponent system:

(9)

(10)

They obtained a general expression for the driving force as

∑ niGi + n w H2O ⇌ n1G1n2G2...nngGng.n w H2O

Δμ = kT ln[γ(P , T , C)υ W C ] + μgs*(P , T ) + n W (P , T )μ W ( P , T ) − μ h ( P , T )

W * = 4c 3v h2σef3 /27Δμ2

Jnuc = AeΔg / kT e−4c vHσef /27kT(Δg )

where K is a constant, m is the index, and both are species dependent. The work of Natarajan et al.91 was limited to modeling pure component nucleation. This was in light of the experimental observation from Flabella et al. that methane−ethane mixtures do not show induction time, whereas pure methane hydrates have a nonzero induction time. Kaschiev et al.117 considered the crystallization of hydrates analogous to precipitation of salts. The driving force for the formation of a new phase was considered the difference in chemical potential between the existing phase and the new phase.42 Δμ = μgs + n w μw − μ h

(13)

Based on the estimations of work done, Kashchiev and Firoozabadi then established a general expression for the nucleation rate of a one-component gas hydrate as

Bishnoi et al. followed up the study of Englezos et al. and provided a unified description of the kinetics of hydrate nucleation, growth, and decomposition. They modeled the induction time for methane, ethane, and carbon dioxide as a function of driving force expressed as the fugacity difference between experimental conditions and equilibrium. Natarajan et al.91 adopted a similar approach in modeling the induction times. t ind

n* = 8c 3v h2σef3 /27Δμ3

3 2 3

Δμwater = μwater liq − μwater hyd

(12)

i

(16)

The driving force per unit cell is given by

(11)

Δμ =

Further expressions were derived for the cases when the solution is in chemical equilibrium with the gas phase and depending on the isothermal or isobaric regime of supersaturation in the solution. Upon establishing the driving force based on chemical potential, Kashchiev and Firoozabadi estimated the size of the

∑ ni(P , T , x)μgi (P , T ) + n w (P , T )μsw (P , T , x) i

− μ H (P , T , z )

(17)

In the equation, μgi is the chemical potential of gas species i in the solution, μsw is the chemical potential of water in the 11183


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ACS Sustainable Chemistry & Engineering solution, and μH is the chemical potential of hydrate. The composition and the type of hydrate was shown as a function of n z where zi = ∑ in .

model by Chen and Guo121 to calculate the chemical potentialbased driving force for a mixture. The first step is the formation of a basic hydrate cage in which the basic cavity (larger cavity) is filled. The second step comprises adsorption of the gas molecules into smaller empty cages. Based on this model, they proposed the driving force as

j j

They first derived the expression for the driving force for the isothermal operation, with the assumptions of the gas-saturated liquid, negligible compressibility of the coefficient for liquid and hydrate phases, and most importantly, composition of the hydrate phase fixed as the equilibrium composition. The expression was effectively the same expression as given by Christiansen and Sloan:87 ⎡ f G (T , P , y ) ⎤ op ⎥ Δg = ∑ ni(T , Peq , y)kT ln⎢ iG ⎢ f ( T , P ⎣ i ⎦ eq , y) ⎥ i=1

Δμ = λ1 ln(1 − RT xi* =

NG

(18)

(19)

The final expression for an isothermal supersaturation process is ⎫ ⎧ ⎡ 1 − ∑ θ (T , P , y) ⎤⎪ ⎪ op k jk ⎥⎬ Δg = n w ⎨(Pop − Peq)(vw − vHw) − kT ∑ vj ln⎢ ⎪ ⎪ ⎢⎣ 1 − ∑k θjk(T , Peq , y) ⎥⎦⎭ ⎩ j

(20)

where θjk is the fraction of species j in cavity k and is given by Langmuir adsorption theory as θjk =

Cjkfgj 1 + ∑j Cjkfgj

(21)

The expression derived for the critical radius in the study is

rc =

2σn w vHw Δg

j

i

f i0 fi

(23)

fi λ1/ λ 2 f i0 ⎡⎣1 − ∑j θj ⎤⎦

(24)

It is evident from eq 23 that filling of small cavities by small guest molecules can increase the driving force. In THF + CH4 or THF + H2 clathrates, THF fills the basic or the larger cavity first, and subsequently, the smaller molecule, either H2 or CH4, occupies the smaller cages. This is highly relevant for the application of storage and transport of CH4 as solidified natural gas (SNG) and hydrogen. In these applications, THF acts as a promoter and results in formation of binary clathrates with THF occupying the larger cages. Ma et al.120 also evaluated the difference between fixed vs variable fractional filling of the cavity. Their results corroborated those previously by Anklam and Firoozabadi. Lee et al.22 studied the formation of H2−THF binary hydrates and reported that they exhibit a “tuning-effect” and the wt % of H2 can be controlled. Lee et al.22 observed a maximum storage capacity of 4.0 wt % for 0.15 mol % of THF concentration. This has a very strong implication for H2 storage application as the capacity and composition of H2 can be controlled as shown by Lee et al.22 This control was proposed due to partial occupancy of large cages by THF and hence increasing the sites available for H2 storage which can occupy the large cages quadruply or the smaller cages doubly. Strobel et al.122 showed that the amount of H2 stored exhibits Langmuir behavior and saturates asymptotically to 1 wt % H2 with increase in pressure. Here, 1 wt % H2 corresponds to one H2 molecule each occupying the smaller cages (512) and one THF molecule occupying the large cage (51264). The results of Strobel et al. contradicted the study of Lee et al., who were able to attain as high as 4 wt % H2 loading. Several other studies also have failed to attain the 4 wt % loading and have observed a maximum of 1 wt %.123−125 Song et al.126 studied the growth of binary clathrates using molecular simulations. Their results showed that the stabilization energy of binary clathrate with larger cages occupied by XL molecules and smaller cages by SS molecules were larger than the sum of the stabilization energies of a clathrate with only a larger cage occupied by XL molecules and a smaller cage occupied by SS molecules. This is somewhat different than the pure-component nucleation mechanism of Jacobson et al.96 as discussed in a previous section. The additional stability was attributed to a decrease in low-frequency modes of a water network when all cages are occupied as stated by Rodger et al.127 In their study, an XL molecule was similar to the size of THF, while an SS molecule corresponded to H2. Another major finding from their result was that the composition of clathrates at a higher driving force is not necessarily the same as of the most stable phase. This should be kept in consideration while estimating the fractional cage occupancy. Their result showed that THF can act as both a thermodynamic and kinetic

Anklam and Firoozabadi119 challenged the assumption of the constant hydrate phase composition especially for conditions where they are far away from the gas−liquid−hydrate equilibrium. In their subsequent work, Anklam and Firoozabadi incorporated varying fractional cage occupancy to account for hydrate phase composition different than at equilibrium. They derived expressions for the critical nucleus size and the composition by taking the partial derivatives of the work of formation with respect to the number of molecules of individual components in the new phase. The generic expression derived for estimating the work done and the critical radius was: 2σVβ̅ j − Δμj = 0 R*

∑ θj) + λ 2 ∑ xi* ln

(22) 119

Anklam and Firoozabadi analyzed the difference in driving force estimation by the two approaches:fixed hydrate phase composition vs varying hydrate phase composition. The difference was found to be negligible for the case of pure methane gas and at lower pressure for the case of a 75% methane and 25% ethane mixture (sI hydrate). The difference at higher pressure was found to be even larger for the case of a 75% methane, 20% ethane, 5% propane mixture (sII hydrate). A larger driving force in the case of mixtures leads to faster nucleation rates, lower work required for hydrate phase formation, smaller critical radius, and reduced induction times. However, the results were not confirmed by experiments and required further inspection. In another study, Ma et al.120 studied hydrate formation kinetics of methane + ethylene + THF + H2O by experiments and modeling. They adopted the two-step hydrate formation 11184


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ACS Sustainable Chemistry & Engineering promoter for H2−THF clathrates. However, there lies a tradeoff between the promoting effect of THF and the storage capacity. For the application of H2 storage, the storage capacity is crucial. While THF facilitates formation of hydrates at milder conditions and increases the rate of formation, it reduces the H2 uptake capacity by occupying the larger cages. Song et al.126 showed that the fractional occupancy can be tuned by varying the growth temperature. Veluswamy et al.128 in their in depth review of H2 storage in clathrate hydrates suggested that the combined use of NMR and Raman spectroscopy simultaneously to analyze H2 inside the hydrate phase might help resolve the ambiguity of the “tuning-effect” further. Presence of binary components or a higher number of hydrate formers can not only affect the cage occupancy but also can affect the structure of the hydrate formed. For example, the addition of 1 mol % propane to methane can change from type I to type II hydrates.129 Since natural gas at pipeline conditions mostly has small amounts of propane, hydrate plugs in pipelines usually have sII structures.130 Abay and Svartaas131 studied multicomponent gas hydrate nucleation for the effect of cooling rate and gas composition. They used two synthetic natural gas mixtures for studying the secondary nucleation rate at equilibrium (secondary nucleation) and the stochasticity of nucleation. They showed that that systems with different gas compositions respond differently to changes in cooling rates. The implications of the results involve the uncertainty in systems employing varying amounts of additives in the form of KHIs (discussed in the next section) in the system. The studies discussed above treat the interface boundary as distinct, whereas the actual interface for the hydrate nuclei constitutes a diffuse region. The sharp interface assumed by the CNT-based studies is valid for the case where the interface is significantly smaller than the critical radius of the nuclei. Within the diffuse interface region, the properties vary continuously between the values of the individual phases. There have been many studies reporting the diffuse nature of the nuclei.132−135 The diffuse nature of the interface can be incorporated within the modeling studies by means of phase field theories as shown by Kvamme et al.,136,137 Granasy et al.,138 and Svandal et al.139 Next, we briefly discuss the phase field theory applied by Kvamme et al.136 Phase Field Theory-Based Model: Kvamme Model. Kvamme et al.136 developed a generic hydrate nucleation model based on phase field theory for describing the nucleation of CO2 hydrate in aqueous solutions. The phase field theory developed in the study was shown to be considerably more accurate than the sharp-interface droplet model of the classical nucleation theory. Based on the thermodynamic and interfacial properties, it was shown that the size of the critical fluctuations (nuclei) is comparable to the interface thickness, implying that the droplet model should be rather inaccurate. They proposed the local state of matter to be characterized by two fields: (i) A structural order parameter, m, called the phase field. This field describes the transition between the disordered liquid and ordered crystalline structures. (ii) A conserved field, χ, which maybe the coarse-grained density, ρ, or the solute concentration, c. Subsequently, they formulated Helmholtz free energy as a function of these fields. The resultant formula upon analysis was observed to have two minima, and the critical fluctuation (hydrate nucleus) being found at the extreme of the free energy function. The final expression for steady state provided by their model was

JSS = J0 e−W * /kT

(25)

There are two key parameters necessary for accurate prediction of the nucleation rate: superficial energy and thickness of the interfacial region. It was proposed that the two can be obtained using molecular simulations for a given system. Critical Radius Estimation Using Molecular Simulations. Radhakrishnan and Trout71 in their study of CO2 hydrate nucleation using Monte Carlo (MC) simulations and non-Boltzmann sampling proposed an alternative approach for the estimation of critical radius. They implanted nuclei of two sizes, 9.6 and 19.3 Å, and analyzed the trajectory of the two implants. Out of the two, the smaller crystal dissolved with time, whereas the larger crystal grew, and the entire system was observed to be converted to hydrates. Hence, it was concluded that the critical radius lies between the two values. They further calculated a Landau−free energy hypersurface as a function of a set of order parameters and plotted the first-order distribution functions for implants of sizes of 9.6, 14.5, and 19.3 Å. Upon observing the first-order distribution, it was observed that the minima in the free energy shifts toward values of the clathrate phase, as the system appears more clathrate like. It was concluded that the critical radius should lie between 9.6 and 14.5 Å. This was significantly smaller than ∼32 Å predicted using CNT in an independent study by Larson and Garside.140 The Gibbs−Thomsom equation for spherical particles is108 Tm(R ) = Tmbulk −

R*(T ) =

2K GT T bulkγν , where K GT = m R ΔHm

2γ −2γ ≈ Δμ(T )ρl (ρΔSm(Tmbulk − T ))

(26)

(27)

where γ is the liquid−solid surface tension, ΔH is the bulk enthalpy of melting, and v is the molar volume. The expression correlates melting temperature and the radius of the solid phase. At critical radius, the value of Tm equates with the bulk temperature T. Using the above approach, Jacobson et al.108 calculated the critical radii for both amorphous and crystalline nuclei in their study as discussed previously in the nucleation pathway section. Barnes et al.141 used the order parameter (OP) MCG-1 for estimating the critical nucleus size and nucleation rates. They estimated the critical nucleus size in terms of the OP MCG-1 by following the trajectory of each nucleus. Upon the observation, they proposed a MCG-1 value of 16 as the critical nuclei. They evaluated the quality of the proposed MCG value by performing a pB histogram test and showed that it has binomially shaped peaking near 0.5. This concludes that the proposed value is a good estimate. Yuhara et al.142 analyzed the results of Barnes et al.141 and calculated the nucleation rates and critical nucleus size of methane hydrates by implementing the work originally applied to the domain of vapor−liquid nucleation.143 In an attempt to reduce the computational load of direct numerical simulations performed by Barnes et al.,141 Yuhara et al.142 used mean firstpassage time (MFPT)144 and survival probability (SP)145 methods for estimating the nucleation rates and the critical nucleus size of methane hydrates. They obtained similar nucleation rates but a higher critical nucleus; however, since MFPT and SP only require the simulation trajectories, they are computationally less intensive. 11185


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ACS Sustainable Chemistry & Engineering Effect of Hydrate Inhibitors. The discussion on inhibitors, its mechanism, and properties discussed in the current work are restricted to the transport of the hydrocarbons in the oil and gas industry. Various methods have been adopted to curb the formation of hydrates such as raising the temperature/heating, lowering the pressure, and removal of water. However, these options are not cost-effective, and the quest for lowering the cost has driven research toward new techniques. To prevent the formation of hydrates in pipelines, thermodynamic hydrate inhibitors (THI) such as methanol, glycols, etc. have been used traditionally. This type of inhibitor acts by shifting the hydrate formation phase boundary away from the operating conditions of the process in question. However, the use of THI was not feasible due to economic and environmental reasons. As per the current trends in the oil and gas production industry, concentrations as high as 60 vol % methanol could be required for effective hydrate control. Koh146 in her review on natural gas hydrates estimated that for a small two-well satellite field producing 5.66 × 106 m3 gas per day at 379 K and 33 MPa the amount of methanol required would be 20 tonnes per day ($5 million per year). This clearly demonstrates the economic infeasibility of using THIs. As an alternative to high volume and subsequently high cost THIs, low dosage hydrate inhibitors (LDHIs) have been developed to reduce hydrate formation. These include two types: kinetic hydrate inhibitors (KHIs) and antiagglomerates (AAs). Both classes of additives are added at low concentrations, typically around 0.1−1 wt %. LDHIs do not lower the three-phase equilibrium but rather kinetically inhibit the formation of hydrates and crystal growth so that hydrate formation does not occur in the transport and operations.146,147 It has been suggested that LDHIs act by adsorbing onto the hydrate surface and hinder hydrate growth.148−150 The efficiency of LDHIs, subsequently, depends upon the adsorption affinity. Anderson et al.149 identified the two molecular characteristics that lead to strongly binding inhibitors as charge distribution on the edge of the inhibitor and congruence of the size of the inhibitor with respect to the available space at the hydrate-surface binding site. KHIs are water-soluble polymers or copolymers such as PVP, poly(N-vinylpyrrolidonem), N-vinylcaprolactam, dimethylaminoethyl acrylate, etc. Efficient KHIs are commonly reported to have both amide groups and hydrophobic parts. Kelland et al.59 in their study reported that the major issues with application of KHIs are performance, overall cost, environmental impact, and compatibility. Conventionally, it has been proposed that the adsorption of KHIs is mainly due to the hydrogen bonds between the amide groups and water molecules on the hydrate surface.151,147 Carver et al.152 demonstrated the adsorption caused as a result of hydrogen bonding in the hydrate−gas interface by means of Monte Carlo simulations. Yagasaki et al.153 subsequently suggested that this adsorption effect would be affected for the case of a hydrate−water interface since KHIs are water-soluble polymers. To further understand the adsorption of KHIs on the hydrate cages, Yagasaki et al.153 studied the role of hydrogen bonding and the effect of a hydrate−water interface by means of MD simulations. They concluded that contrary to prior suppositions hydrogen bonding does not affect the affinity of KHIs adsorption on hydrate cages. It was reported that the adsorption affinities of KHIs is a result of entropic stabilization arising from the presence of cavities at the surface of the hydrates. Amide groups

present on the KHIs do not enhance the adsorption affinity but enhance the solubility of the KHIs and hence are essential. Although certain KHIs have been shown to act through a surface adsorption mechanism,154 there have been studies that show the mechanism might be molecule dependent rather than general.72 While molecules like PVCap19149 and PDMAEMA155 have been shown to adsorb on the hydrate surface, Moon et al.72 showed that this is not the case for the PVP molecule in their study based on MD simulation of methane hydrate. It was observed that the PVP molecule remained at least 5−10 Å away from the surface of the hydrate crystal. However, Moon et al.72 explained the results in terms of increased interfacial energy due to PVP. An increase in the hydrate−liquid interfacial energy results in an increase in critical radius and a decrease in the stability of the particles below critical radius, thereby increasing the induction time of the system and delaying the nucleation. It was argued that the hydrate−water interface has been observed to be diffuse at a molecular level with the structure of water changing to a distance of 10−15 Å.55 Hence, this would place the PVP molecule in the middle of the hydrate−water interface and hence increasing the interfacial surface energy. Authors suggested that this alternate pathway of PVP inhibition might also be responsible for synergistic effects upon combination of PVP and other KHIs such as PVPCap.156 The results corroborated those by Anderson et al.149 which showed an absence of a free energy driving force (ΔGads = 0.4 ± 3.9 kcal/ mol) for the case of PVP, as the authors quoted. However, it can be clearly seen that the result cited from the work of Anderson et al.149 was of a poly(ethylene oxide) (PEO) molecule mistook for a PVP molecule. In the study, PVP was shown to have a binding energy of −20.6 kcal/mol which should be considered as physisorption. Even though not corroborated by the results of Anderson et al.149 as claimed in their work, results of Moon et al.72 and the proposed hypothesis should be investigated further for veracity. Certain organisms that can survive at low temperatures do so by means of producing antifreeze proteins (AFP) which adsorb to microscopic ice crystals and prevent their further growth. These AFPs have also been used as KHIs for hydrate formation and are called “green inhibitors”.157 AFPs are generally produced by purifying from the organism that produces it such as bacteria, yeast, algae, etc. While AFPs have been found as effective as other commercial KHIs such as PVP,157−164 large-scale production and nonreproducible performance remain some of the major issues toward their implementation. Walker et al.165 provided an insightful review on the application of AFPs as gas hydrate inhibitors. For the purpose of evaluating KHIs and obtaining an understanding of synthesizing better KHIs, various experimental and simulation techniques have been employed in the literature. The most common of them are rocking cell150 and high-pressure cell or autoclaves166,167 or both in combination being used.168,169 Techniques such as nuclear magnetic resonance (NMR) microscopy160 and NMR combined techniques such as in situ powder X-ray diffraction,170 highperformance differential scanning calorimetry53 (HP-DSC), and ultrasonic testing techniques171 have all been used to study the impact of KHIs on the hydrate nucleation and growth kinetics. KHIs have also been evaluated on a larger setup by means of high-pressure flow loops by Talaghat et al.172 High pressure automated lag time apparatus (HP-ALTA) is another technique that has been recently adopted for the purpose of 11186


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limit for the AAs to be effective is approximately 50%; otherwise, the slurry becomes too viscous for transporting.147 While KHIs are effective in delaying hydrate formation, a major downside of KHIs is the possibility of significantly enhancing hydrate growth (catastrophic growth) after hydrates nucleate.183,184 Recently, Sharifi and Englezos185 introduced the hydrate catastrophic index (HCI) to quantify the onset of the enhanced hydrate growth phenomenon based on laboratory data and the type of experimental conducted. Ohno et al.186 in their study of AFPs with hydrocarbon hydrates also showed nucleation and growth inhibition to be independent processes. In principal, materials for controlling hydrate plugging may operate either by inhibiting nucleation or growth or both. The difference in the two modes is suggestive toward two separate adsorption characteristics of KHIs: (1) adsorption with prenucleation clusters and foreign particles to “poison” the nucleation sites in case of heterogeneous nucleation and (2) adsorption on hydrate crystal surfaces. Hence, caution should be taken with the application of KHIs to limit pipeline plugging. A multiscale approach is necessary for a complete evaluation of KHIs. Walker et al.165 outlined such a methodology involving the use of apparatuses ranging from XRD, Raman, and NMR to stirred autoclaves. Apart from THIs and KHIs, applying localized high temperature,2,130 external electric and electro-magnetic fields have also been tried to disrupt the already-formed hydrates. Makogon130 reported that electric field intensity of 107 V/m would have to be employed to have any significant effect on equilibrium. English and MacElroy187 performed nonequilibrium MD simulation to evaluate how an external electromagnetic field disrupts the formation of methane hydrate nanocrystals They concluded that shifting dipolar alignment inside the crystals weakens the structure. The effect is intensity and frequency dependent and required at least 0.01−0.05 V/Å for tangible results. Effect of Hydrate Promoters. Surfactants are one class of molecules that have been used in the literature as hydrate promoters because of their diverse agglomeration characteristics. Surfactants are organic compounds that lower the interfacial tension in a liquid−gas system by adsorbing at the interface. They are amphiphilic molecules, i.e., have both hydrophobic (nonpolar tail) and hydrophilic (polar head) groups. Three major types of surfactants are anionic, cationic, and nonionic surfactants and are classified based on the charge that the hydrophilic head possesses, negative, positive, and neutral, respectively. The presence of dual centers in surfactants results in diverse surface impacts in gas−liquid, solid−liquid, and hydrate−liquid interfaces. Recently, Kumar et al.188 published a review on the role of surfactants in promoting gas hydrate formation. In their work, Kumar et al.188 compiled a list of various molecules that have been used as surfactants for promoting gas hydrates. The focus of the current work has been restricted on the phenomenon of the promoter mechanism and its effects pertaining to nucleation. We recommend other works for a further elaborate account on surfactants. Kalogerakis et al.189 experimentally investigated the effect of four surfactants on the kinetics of methane hydrates. In their study, they included anionic and nonionic surfactants. The liquid side mass transfer coefficient was found to reduce for both cases and more so for the anionic surfactant. Anionic surfactants enhanced the rate of hydrate formation more as compared to nonionic surfactants. Karaaslan et al.190 also

studying hydrate formation. The main advantage of HP-ALTA is the ability to perform a large number of experiments in a relatively short time as compared to the conventional techniques such as rocking cell or autoclaves. HP-ALTA provides a setup for measuring sufficient data in the hydrate formation system and allows representation in terms of probability distribution function173 and hence reduces the effects of intrinsic stochasticity of the process. Maeda et al.174,175 adopted the original version of HP-ALTA from the work of Heneghan, Heymat, and Wilson.176−178 HP-ALTA allows a large number (>100) of nucleation and growth events to be recorded for a given sample under controlled pressure− temperature conditions. HP-ALTA cools a given sample at a specified rate until it detects formation of hydrates from a sudden reduction in the transmitted light through the sample. The formation temperature, Tf is recorded, and then the sample is heated to 10−15 K above equilibrium dissociation temperature and maintained for some time. After this, the sample cooling is started again, and the system is repeated. Here, Tf is recorded for each run and can be used for further analysis and representation by using a probability density function. The traditional HP-ALTA was modified for studying hydrate formation in which the gas−liquid phase is separate and there is either a requirement for enhancing the mass transfer by mixing or focus the detection system at the gas−water interface. They modified the HP-ALTA to be able to operate in two configurations: bulk-transmittance configuration that detects hydrate formation in bulk in conjunction with stirring and interfacial-transmittance configuration that detects the gas− hydrate surface. There are two major shortcomings in HP-ALTA: relative smaller size and quiescent setup. The size of HP-ALTA is smaller than other conventional techniques such as autoclave or a flow loop. As the sample size increases, the probability of nucleation occurring also increases. This could result in having a wider variation in onset of nucleation. Hence, HP-ALTA might lead to overestimation of the stochasticity. This is paradoxical since the intention of using HP-ALTA is to predict the stochasticity in the beginning. The use of a linear cooling ramp causes the solution to be undersaturated, and since the system is quiescent, the mass transfer to from the gas phase represents a resistance.179 We also need to keep in consideration that these setups might still be orders of magnitude smaller than the industrial or actual implementation. It is peremptory to understand the effect of scale up on stochasticity. Antiagglomerants (AAs), on the other hand, allow hydrates to form but prevent them from agglomerating and accumulating into large masses. Some of the best performing AAs operate at higher subcooling than KHIs. There are two mechanisms by which AA operates depending on their physical structure. Quaternary AAs180,181 are designed with hydrophilic headgroups and hydrophobic tail groups. The hydrophilic group at the quaternary center binds to the hydrate particles, whereas the long hydrophobic tail prevents the hydrate from continuing to grow on the surface. The hydrophobic tail also makes the surface more attractive to the hydrocarbon phase and hence easily disperses the particles in the hydrocarbon phase. The second class of AAs form a special water-in-oil emulsion.182 Hydrate formation is subsequently restricted to within the water phase, and the end product is a slurry of oil with a dispersed water−hydrate phase. In general, the upper water 11187


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studies later.194,195,197 Watanabe et al.195 studied the effect of SDS on hydrate formation in a quiescent system using HFC-32. Apart from other reasons in an argument to the micelle hypothesis proposed by Zhong and Rogers, the main argument provided was that the Kraft point of SDS was significantly higher than the hydrate-forming conditions adopted in their work (∼279 K). Hence, micelle formation was not possible, and subsequently, the results should be considered cautiously. Di Profio et al.194 later corroborated the absence of micelle formation in the hydrate-forming conditions when using SDS and sodium oleate (SO), among other anionic surfactants. Watanabe et al.195 also challenged the CMC calculated in the study of Zhong and Rogers and Sun et al.198 since it was an order of magnitude lower than reported at atmospheric conditions in the absence of methane or ethane. An important consideration generally forgotten is the impact that surfactants can have on the foam formation during hydrate dissociation. Higher concentrations of surfactants would expectedly increase the formation of foam during dissociation and hinder the process performance. Hence, it is important that the surfactant has the desired effect on hydrate formation with lower concentration. Effect of Promoters on Surface Tension. The hydrate formation for immiscible liquids is found to be highly dependent on the surface properties of the phase boundary. Surfactants reduce the interfacial surface tension of the gas− liquid systems and increase the interfacial area of the system.199−201 Surfactants have also been found to reduce the liquid side mass transfer coefficients in those studies. There is a divided opinion on cause of this reduction. Some studies report that surfactants induce a local modification in slip velocity at the interface which is responsible for reduced mass transfer.202,203 Some studies have reported that surfactants create a hydrodynamic change at the interface and an addition of a new resistance at the boundary layer film due to reduced local diffusion.200,204 The third reasoning proposed is that by reducing the surface tension at the interface promoters reduce the interfacial renewal rate and hence have a lower mass transfer rate.205 The structure of the surfactant has been found to play a key role in its effect on surface tension. Surfactants with large hydrophobic and hydrophilic heads show lower interfacial tension than similar surfactants with smaller heads.206,207 Contrasting Effects of SDS. Across the various studies reported, sodium dodecyl sulfate (SDS) has been shown to perform better than other anionic surfactants in terms of both rate of hydrate formation and the total hydrate formation in quiescent systems.208−210,191,211,212 It was claimed by Zhang et al.94 that the effect of SDS is restricted to light hydrocarbons. For CO2 hydrate, SDS was found to have had no promoting effect.94 To understand the absence of promoting effect of SDS, Zhang et al.213 later studied the competitive adsorption between SDS and carbonate on THF hydrates. The reasoning provided was that the mechanism of SDS promotion is through surface adsorption of DS− on the hydrate crystals. Since at higher concentration of CO2 the carbonate ions are sufficient to provide the adsorption promoted hydrate formation, the promotion effect of SDS is not observed for CO2 hydrates. SDS was also reported to have no promoting effect for methane−propane clathrates on the bubble surface.214 Contrary to the above studies, there also have been various studies across the literature in which the effect of SDS has been clearly observed even for CO2 hydrates.215−217 Hence, the

studied the performance of cationic, anionic, and nonionic surfactants in varying concentrations for natural gas hydrate formation. It was reported that the hydrate kinetics was enhanced with anionic surfactants under all concentrations. However, for cationic surfactants, enhanced kinetics was observed at lower concentrations and a contrasting effect (hydrate inhibition) at higher concentrations. Nonionic surfactants had the least affect out of them all. Kumar et al.191 studied the effect of three different porous media and the effect of nonionic surfactant Tween-80 (T-80), cationic dodecyltrimethylammonium chloride (DTACl), and anionic sodium dodecyl sulfate (SDS) on CO2 hydrates at constant pressure (3.55 MPa) and temperature (274 K). SDS was found to be most effective in reducing the induction time and enhancing the rate of hydrate formation. Before we discuss further the mechanism of action for surfactants, let us review the solubility and micelles formation in surfactants. Krafft Point and Critical Micelle Concentration. Zhong and Rogers192 studied the effect of sodium dodecyl sulfate (SDS) as a surfactant in methane−water and natural gas−water systems. It was reported that SDS can increase the hydrate formation rates up to 700 times in quiescent systems. Zhong and Rogers calculated the critical micellar concentration (CMC) of the SDS molecule to be 242 ppm at hydrate forming conditions. Critical micelle concentration is defined as the minimum concentration that is required at a given temperature to form micelle. They reported that above CMC, the hydrate initiated in the subsurface around the micellesolubilized hydrocarbon gas. The significantly enhanced hydrate growth was attributed to the micelle solution with the micelles providing more nucleation sites apart from the interfacial region which was observed as the initiation for hydrate growth quiescent systems. These developing hydrate particles migrated subsequently due to buoyancy to the water− gas interface and water−wet cell walls. Ramaswamy et al.193 in their study also concluded that SDS significantly reduces the induction time above CMC. Ganji et al.18 reported that for cationic and nonionic surfactants, values much higher than 1000 ppm are required to have the desired promotor effect. However, the solubility of many surfactants can be significantly lower than it, and hence, the desired effect is not attainable.194 To have a better understanding of the surfactant system, let us look at the different phases present for a surfactant−water system (Figure 8). Here, TK as shown in the figure is the Krafft point of a given ionic surfactant below which the solute does not form micelle but rather precipitates as a hydrated solid.196 The hypothesis of Zhong and Rogers was challenged by various

Figure 8. Effect of temperature on surfactant concentration demonstrating the critical micelle concentration.195 11188


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ACS Sustainable Chemistry & Engineering attribution of the absence of the SDS promotion effect to CO2 seems very likely to be incorrect. Ho et al.218 in their study on CO2 hydrates in an unstirred reactor showed that SDS in the presence of cyclopentane (CP) has no promotor effect in their system. Since CP has a density of ∼750 kg/m3, it forms a layer above water in a quiescent system. The layer of CP above water inhibits the effect of SDS as a promoter and hence indirectly indicates the importance of the effect of surfactant on lowering the surface tension. It was also shown by Zhang et al.219 in their study that SDS does not act as a promoter in the case of heterogeneous nucleation for the CH4 + THF system. It was further conjectured that the enhancement effect of SDS might be eclipsed due to the higher nucleation rates present in heterogeneous systems. It may be argued that this acts as proof that promoters function by adsorption on the surface of hydrate crystals. Lo et al.220 qualitatively investigated the adsorption of DS− on cyclopentane (CP) hydrates and proposed that the orientation of DS− on CP hydrates changes from “lie-down” to “stand-up” mode as the concentration of SDS increases. In the “stand-up” configuration, the head groups attach themselves to the hydrate surface, while the tail orients toward the liquid phase forming hydrophobic microdomains on the hydrate surface.219,220 Hydrate formers such as methane can then solubilize in the hydrophobic microdomains, increasing their concentration at the interface and hence enhance the growth rate. To quantify the adsorption effects of surfactants, Lo et al.221 studied the adsorption of SDS and dodecyl-trimethylammonium bromide (DTAB), a cationic surfactant on CP hydrates. CP hydrates were chosen because of their stability under ambient pressure at less than 280 K suitable for the analytical techniques adopted. Based on the abundant literature, it can be clearly seen that SDS has been proposed to be the best available promoter in certain cases, while it has been found to have no impact in some. The effect of SDS, apart from its concentration, can be seen to depend on the guest molecule (and hence hydrate structure) and reactor configuration as well. Dependence of the reactor configuration and guest molecule clearly indicates competing effects of the surfactant on hydrate nucleation and growth. Surfactants act as promotors of hydrate nucleation and growth by reducing the surface tension, increase the solubility of the guest molecule, and adsorption on hydrate cages. They acts as inhibitors forming a layer at the gas−liquid interface and increase the mass transfer resistance. The pathway mechanism for surfactants can be seen as a result of the competing effects and hence is system dependent. Figure 9 shows the various impacts of surfactants and the system configuration impacting the overall effect of the surfactant. Apart from the nucleation rates and the effects discussed above, surfactants have also been observed to affect the morphology of the gas hydrates formed.195,189,222−225 In the current work, we have not covered the morphology aspects of hydrate growth, and readers are requested to refer to the cited articles for further readings.

Figure 9. Various parameters to be considered while understanding the effect of surfactants on hydrate nucleation and growth.

empirically observed in systems with prior ice melt apart from hydrate -melt.227,228 Sefidroodi et al.229 examined the hydrate of cyclopentane from dissociated water and showed that a small amount of dissociated water was enough to induce the memory effect comparable to 100% dissociated water. The general consensus among researchers in the field is that if the system is heated to sufficiently high temperatures or long enough the memory effect will be destroyed. A further complicating attribute of nucleation observed is the intrinsic stochasticity.227,145 The stochasticity nature of the memory effect reported from empirical studies implies that two systems can have different memory effects even while having the same thermal history. These attributes have made memory effect a mysterious phenomenon, but in the pursuit of explaining it, two major hypotheses have been put forward and tested. These are the residual cage structure hypothesis and higher local concentration in the solution. There have three primary methods to capture the nature of memory effect in the literature: (i) measuring physical properties to detect the residual cage structures existing in the system, (ii) spectroscopic methods for direct microscopic measurement of the nature of the system, and (iii) use of molecular simulation studies to obtain pathway insights. These are discussed with the supporting theories in the next section. Residual Hydrate Cage Structures. Upon these empirical observations, it was hypothesized that memory effect originates from residual clusters of water molecules after hydrate/ice dissociation. Surviving residual hydrate-like structures provide the precursor crystals for hydrates for nucleation once its thermodynamically favorable to form hydrates again. Makogon et al.130 in their work provided data in support of this concept showing that hydrates do not completely decompose on dissociation but leave a partial structure that enables hydrate formation in the subsequent cycles. There have been various experimental techniques that have been adopted to capture the change in the liquid water after hydrate formation that would corroborate the residual cage hypothesis. Sloan et al.230 estimated effective kinematic viscosity of the liquid water phase by measuring the time taken by a stainless steel ball to travel one inch in the liquid. They reported an increase in the kinematic viscosity of the liquid water phase after hydrate formation. Kato et al.231 performed simultaneous surface tension and kinematic viscosity measurements using a surface light scattering method. It was observed that the two properties

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MEMORY EFFECT AND HYPOTHESIS Memory effect is termed as the phenomenon in which hydrate nucleation is faster in hydrate-melt or ice-melt systems than from fresh water systems. This concept originated from empirical observations such as that of Bishnoi and coworkers226,82 and Takeya et al.227 in which the induction times for methane hydrates was found to drastically reduce in the system with prior hydrate formation. This effect was also 11189


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in water before the hydrate formation and after hydrate dissociation, and there is some dissolved residual gas after melting. Overall, the evidence supporting the hypothesis remains thin and circumstantial and hence should be considered cautiously. Surface Imprint Hypothesis. Zeng et al.157,239 studied the effect of antifreeze proteins on the nucleation, growth, and the memory effect of THF hydrates. They reported that AFPs were able to eliminate the memory effect. They first estimated the homogeneous nucleation temperature of THF hydrate to be 237 K using DSC. Since the temperatures considered in the study were far above 237 K, the authors concluded that they are operating in the regime of heterogeneous nucleation. They did not observe any memory effect for homogeneous nucleation in the THF system. They argued against a residual structure hypothesis since that should be an intrinsic property and should have been observed in their system. They provided an alternative hypothesis for the memory effect in the form of surface imprint hypothesis. The hypothesis states that growth of hydrate might alter the surface properties of the impurity. In heterogeneous nucleation, these altered sites promote further nucleation resulting in the memory effect. Contact with the aqueous solution will allow the surface to return to its original state and limits the memory effect to a certain temperature and time scale. An important point to note is that their study on the effect of AFPs cannot distinguish whether they are hindering nucleation or growth. Effect of AFPs might be restricted to growth and might be mistaken for nucleation. Factors Affecting Memory Effect. As discussed before, memory effect has been found to be mostly restricted to conditions close to the equilibrium curve, and increasing the system temperature for a longer duration has been observed to remove the memory of the system.240 Takeya et al.227 reported that nucleation rate was an order of magnitude of higher for CO2 hydrates at 1.9 K of superheating than at a higher temperature. The memory effect was completely lost at 298 K (25 K superheating). Ohmura et al. measured the induction time distributions of HCFC-141b hydrate from dissociated water at different superheatings (0.5, 1, 1.5 K).145 They reported that the memory effect had started to wane at 1.5 K superheating. They also reported that there remains a degree of stochasticity to the memory effect as different samples with same thermal history behave differently. Sefidroodi et al.229 investigated the strength and source of the memory effect for cyclopentane hydrates. They studied the effect of melting temperatures and melting duration on the onset temperature of hydrate reformation. The effect of the memory effect is not limited to increasing the onset temperature of hydrate reformation but also reduces the stochasticity of hydrate nucleation. The spread of the onset temperature reduces as the melting temperature increases. Their results showed that the memory effect reduces with increasing melting temperature and duration. Sefidroodi et al.229 also showed that memory effect is transferable between solutions by showing its presence when they spiked a fresh solution with only 3 and 1 mL of hydrate-melted water. They showed that the average onset temperature of the solutions was identical for the spiked systems and a completely hydratemelted solution. This provides an extremely strong evidence for residual cage hypothesis. Memory effect has been found to be affected by various additives as well. THF has been found to not affect the memory effect, whereas antifreeze proteins have been found to remove

increase just after the hydrate dissociation. In contrast to the above stated supporting studies, Bylov and Rasmussen232 reported no detectable difference in the refractive index of the liquid water before hydrate formation and just after dissociation at a water surface in contact with methane or natural gas. Following these studies, Ohmura et al.233 measured the interfacial tension at the surface a sessile drop of a dense hydrate-forming liquid immersed in a liquid water pool. The memory effect was experimentally validated in their system without any change in the interfacial tension. Hence, it was concluded that the memory effect did not arise from the molecular structuring in the liquid exerting a considerable effect on the surface tension. Apart from measuring physical properties, molecular simulations are the second means that have been used for studying the memory effect. In one such study, Baez et al.70 used MD simulations to study crystal growth and dissolution of natural gas hydrates. They concluded the persistence of a dodecahedron cage (512 cage) preferentially over other cages as the reason for the memory effect. Subsequently, Yasuoka et al.234 showed that all dissociation is agnostic to the cage structure by means of MD simulations of methane hydrate. However, it was conjectured in the study that the memory effect is due to the residual structures of hydrate cages. The third means of understanding the memory effect has been spectroscopic techniques in an attempt for direct microscopic measurement. In one such study, Gao et al.235 used NMR to monitor the hydrate formation and decomposition in THFheavy water mixtures. They studied the spin−lattice relaxation time, T1 to monitor the dynamics of THF during formation and decomposition. A marked increased in T1 was shown to be evidence for the residual structures in the solution. Higher Local Concentration of Guest Molecules. An opposing hypothesis to the residual hydrate cage structure that has been proposed states that memory effect is due to the presence of a higher concentration of guest molecules and retards diffusion upon melting. Although less in number as compared to the studies supporting residual cage hypothesis, there are various studies which support this hypothesis. It has been admitted that the higher local concentration of guest molecules would not explain the presence of memory effect in ice-melt systems. Rodger et al.236 studied the memory effect phenomenon in methane hydrates by using long time scale MD simulations of a methane hydrate−methane gas interface. The thermodynamic conditions (15−20 °C above the equilibrium temperature) were chosen to ensure gentle melting of the hydrates and enable the capture of the memory effect, if any. They observed a significant increase in crystal structures in the melt, both hydrate like and ice like. The structures were predominantly ice like. However, it was reported that there is no evidence of structured water molecules clusters, and hence, the authors concluded that memory effect is not related to long-lived metastable hydrate precursors. As a corollary, the authors concluded that memory effect is attributed to higher methane concentration and retarded diffusion which they observed in their studies. Chapman et al.237 in their unpublished study based on NMR spectroscopy on tetrahydrofuran also concluded that the higher concentration and retarded diffusion is more related to the memory effect than the structural residuals. Buchanan et al.238 used neutron diffraction with H/D isotopes in combination with gas consumption measurements. They concluded that there is no significant structural difference 11190


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Table 3. Compilation of Order Parameters Used in Molecular Simulation Studies for Establishing Nucleation Pathways OP F3i, F4φi, F4ti

Study Rodger et al.,236 Moon,56 Hawtin et al.69

Scale

Comment

Based on host ordering Global Ordering

Guo et al.73

Global Ordering

Matsumo et al.,207 Jacobson et al.216

Local Ordering

Vertex OP based on cage identification

Jacobson et al.253

Local/Global Ordering

Local methane density

Vatmanu et al.72

Face-saturated incomplete cage analysis (FSICA) Cage identification algorithm based on ring perception

Guest coordination (GC) OP

Bond orientational OP, Q6 Largest cluster of solventseparated guests (LCSSG) Mutually coordinated guest (MCG) Voronoi tessellation

F3i (three-body parameter) is used to identify water molecules in a perfect tetrahedral network, while F4φi, F4ti (four-body parameters) is used to distinguish between ice and hydrate crystals. Identifies all possible face-saturated complete and incomplete cages Identifies five-member and six-member rings first and then dodecahedron cages (512 cages) and tetrahedron cages (51262 cages) referred as cups. Identification of sI, sII, and amorphous types lattice upon identification of cage

Based on guest ordering Local Ordering

Vatamanu et al.76 proposed this as a critical OP in early stages of methane nucleation and explanation for the presence of memory effects. Local Ordering Calculates the coordination number of guest molecules upon Jacobson et al.253 identifiction of LCSSG Based on both guest and host ordering Local/Global Ordering Sensitive to the degree of global orientational order in the system Steinhardt et al.,254 Wolde et al.282 Local Ordering First identify solvent-separated guests (SSG), and then use a clustering Jacobson et al.253 algorithm for connecting adjacent SSG and finding the largest cluster. Local Ordering Compatible with defective cages; combines the use of both guest and Barnes et al.141 host molecules Local Ordering Sensitive to both perfect crystals and amorphous crystals; Chakraborty et al.209 computationally less intensive since uses only guest coordinates

the memory effect.157 May et al.241 in their study quantitatively compared the effect of various KHIs and memory effect using HP-ALTA. Performance of six structurally different KHIs was evaluated along with the memory effect in the systems. Interestingly, it was empirically shown that the memory effect is found to vary with the structure of KHIs given the same thermal history. Hence, it was conjectured that the result corroborates the residual structure hypothesis which would imply that residual structures interact differently with KHIs depending upon the structure of the KHI. While there have been significant studies demonstrating the presence of the memory effect, there are also studies which have shown no memory effect at all.232,242−244 These studies either involved a superheating temperature significantly higher243 or involved guest molecules such as THF with high solubility so that supersaturation hypothesis cannot be refuted.242 Recently, Sowa and Maeda studied the memory effect in model natural gas hydrate systems179 using HP-ALTA. They used four identical boat-shaped custom-made glass sample cells (“boats”). Their results varied across each boat. They argued that the walls of the glass sample have an effect on the memory effect. They also critically analyzed the three hypothesis proposed for the memory effect. They were not able to conclusively prove any of the hypotheses. In the future, maybe a combination of hypothesis can be proposed to explain the elusive memory effect completely.

equilibrium path sampling,141 and generalized replica exchange method.247 English et al.248 in their review provided an insightful summary on the various molecular simulation techniques employed for hydrates. In our current work, we have not covered such details considering the broad scope of the study, and the readers are recommended to find the molecular simulations in the in depth work by English et al.248 among other works. Next, we discuss the order parameters which form a key component of the molecular simulation studies but one that has been generally overlooked by literature review studies. Order parameters (OPs) are guidance parameters used in molecular simulation studies for estimating the progress of hydrate formation and other key properties. In general, order parameters are a quantitative measure of the degree of order in the system. The order parameters are system dependent and are usually determined based on the symmetry of the ordered phase and how it differs from the disordered phase. Hydrate nucleation and growth is more complex and may involve multiple intermediary species. A broad spectrum of order parameters have been used in the study of gas hydrates such as detecting the solvent structure of water to classify as being ice, liquid, or hydrate phase73,249 or to classify hydrate cages,250 etc. OPs for hydrate nucleation have been based on guest species,251−253 host molecules (water),245,252 or both141 (Table 3). Another classification of OPs is whether it considers a system structure metric or global metric250 or a local cluster structuring metric. First, we discuss the three OPs based on water structuring: F3, F4φ, F4t. These OPs were specifically designed to distinguish between different types of water structuring. They are derived from a two-level description of water molecule, and a central molecule at location A is used to identify set of water molecules (Bi) in its solvation shell. F3 is a three-body OP designed for probing angle deviation from those of a tetrahedral hydrogen bonding network. The value of F3 is zero for tetrahedral structures and larger than zero otherwise. F4φ and F4t were originally designed as a test for a clathrate-like structure by

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MOLECULAR SIMULATION TECHNIQUES AND ORDER PARAMETERS Due to the complex nature of hydrate nucleation, different molecular simulation techniques have been developed to obtain qualitative and quantitative insights into the process. The molecular simulation domain has evolved rapidly from gaining insights on trajectories through direct numerical simulation under a high driving force to obtaining statistical insights under more realistic conditions. These improvements have been achieved by means of advanced sampling methods such as forward flux sampling,245 well-tempered metadynamics,246 11191


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than the cage count code) in detecting an ordered environment. However, VP lacks in differentiating between cage structures or detecting empty or doubly occupied cages. Ideally, VP could be combined with cage differentiating OPs such as vertex OP developed by Jacobson et al.253 to provide an optimum combination of computational speed and desired cage detection. All the OPs discussed above have been single component OPs that are based on either guest or host structuring. Motivated from the work of Walsh et al.75 showing adsorbed guest molecules on the water cages, Barnes et al.141 were the first to propose a two-component OP and quantified nucleation and growth. Barnes et al.141 proposed an order parameter combining the use of both guest and solvent ordering, mutually coordinated guest (MCG). MCG quantifies the appearance and connectivity of molecular clusters composed of guests separated by water clusters. Based on the set parameters, the unit MCG monomers are identified, and the monomers adjacent to other monomers are classified as a cluster. The guests must be within distance Rgcut of each other, and the water molecules must be within distance Rwcut of each guest. A given minimum number of water molecules, Nw, must be within a specified angle φ of the guest−guest vector as shown in Figure 10. Barnes et al.141

probing into torsional angles within a hydrogen bonding network and maybe defined in terms of a quartet of oxygen atoms. An analogous parameter can be defined in terms of dimers of water molecules rather than through all water tetramers by assuming that those O−H bonds are not involved in the dimer and are computationally advantageous. F4φ is 0.7 for a clathrate-like structure, 0.3 for ice, and close to 0 for liquid water.55 Moon et al.72 adopted the three OPs for evaluating the effect of additives on nucleation and growth by means of direct simulations. They used instantaneous values of OPs to assign the water molecules to local phase and determine the extent of hydrate formation. They showed that the method is 95% accurate in estimating the phase of a molecule for those within the stable hydrate and ice phases. Radhakrishnan and Trout71 in their study showed that the Steinhardt bond-orientational OP254 was rendered useless for the case of crystalline clathrate and aqueous CO2 solution. They used tetrahedral OP as the leading OP for their analysis. As shown by Radhakrishnan and Trout, the combined use of the above OPs allows for the identification of regions of solid clathrates. However, these OPs cannot distinguish between amorphous and crystalline or different crystalline clathrate regions. For the purpose of comprehensive pursuit of hydrate nucleation, Jacobson et at.253 used a portfolio of OPs. As a first step, they employed the largest cluster of solvent-separated guests (LCSSG) OP for tracking and identifying the densification of guest molecules. LCSSG tracks the formation of blob in the system but is insensitive toward the ordering of SSG and cannot distinguish between blob, amorphous crystals, or crystalline clathrates. A cage OP was subsequently used to identify 5126n polyhedral water cages. The cage OP, however, does not distinguish between crystalline and amorphous nuclei.255 Finally, for distinguishing between amorphous and crystalline phases and between different crystalline phases, they used a vertex order parameter. In clathrate crystals, each water molecule is hydrogen bonded to four other water molecules and constitutes the vertex shared by four polyhedral cages. The vertex order parameter differentiates between the different clathrate structures on the basis of types of cages in the vertices. The vertex OP developed in their study was based solely on water structuring. They provided an argument against guestbased OP that although not any more difficult to implement it is not advisible due to two reasons. First, the dual cages formed by the guest molecule is inherently larger than the water cages, and it is not suitable for identifying small or nascent crystallites. Second, not all cages in clathrates are necessarily filled with guests and hence reduces the symmetry of the guest ordering. Moreover, since it requires solely guest coordinates, it is computationally inexpensive to implement. Chakraborty et al.252 also utilized the computational advantage only solely for guest coordinates in their work based on application of Voronoi tessellation analysis of clathrate hydrates.252 Voronoi tessellation has been applied to other domains of research such as Leonard-Jones solids,256 glass-forming liquids,257 phospholipid membranes,258 and more to study local structuring but is new for hydrate MD simulation studies. The simulation space is first tessellated (divided) based on guest molecule positions and results in Voronoi polyhedra (VP). The topological and metric properties of VP are further used to provide local ordering analysis and is used as OPs. Chakrobarty et al.252 showed that the real advantage of using VP lies in computation speed (2 orders of magnitude faster

Figure 10. Mutually coordinated guest order parameter along with the tunable model parameters.253

compared the performance of MCG with other order parameters such as F4⊖ global metric, 512 water cage count,250,259,112 potential energy trace, and the LCSSG OP proposed by Jacobson et al.253 It was shown that MCG and the global metric have higher resolution as compared to cage count to detect events such as nucleation and critical nucleus size. MCG OP is structure neutral and detects blobs and crystalline nuclei. Apart from their work on development of OPs for clathrate nucleation, Barnes et al.260 also conducted a review for the advances in molecular simulation advancement. They identified key advanced sampling methods, developing optimal OPs, and a better understanding of the gas−water interface as some of the major issues that remain to be tackled in the coming times. MD simulations of clathrate hydrates nucleation to date have been mostly limited to conditions not identical with real experimental conditions in terms of driving force, time scales, and homogeneous nucleation. The use of advanced sampling methods along with a suitable order parameter and computations involving free energy landscape formulation and subsequent analysis form the barebones of the MD simulation studies. To move toward more realistic simulations, it requires an understanding and improvements on each component apart from the above listed shortcomings. As stated previously, under realistic conditions, the homogeneous nucleation is rate is extremely low, and nucleation is almost certainly to proceed through heterogeneous nucleation. Hence, the future efforts should be focused toward the understanding of heterogeneous nucleation, the effect of various surfaces on 11192


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Figure 11. Gas uptake measurement curve along with thermocouple data provided by Linga et al.264

nucleation does not occur simultaneously in different locations. Linga et al.264 monitored the temperature inside a packed bed by means of multiple thermocouples. Figure 11 shows the gas uptake measurement curves along with six thermocouple data for the hydrate formation. Hydrate nucleation and catastrophic growth process was detected by the heat released due to the process shown by the peaks in the recorded temperature in Figure 11A. The peak in the temperature was asynchronous for the thermocouples demonstrating the spatial heterogeneity in hydrate nucleation, and nucleation in one part of the bed does not ensure or spread into other regions. Similar results have been shown in other studies as well. Linga et al.264 attributed higher overall hydrate formation in the experiment and hence higher throughput as the advantage of multiple nucleation. Linga and Clarke267 also reported that the new porous media materials employed need to be tested within the scope of industrial application. Scaling up and further testing is fundamental toward the development of industrially viable hydrate based processes. Experimental research on hydrate formation in porous media encounters difficulty because of temporal and spatial limitations of monitoring techniques268 to provide detailed nucleation mechanism and a molecular level understanding. To obtain molecular level insights to hydrate formation in porous media, there have been various MD simulation studies to understand hydrate nucleation and growth on solid surfaces.269,270 Bai et al.269,271 performed MD simulations of CO2 hydrate formation from hydroxylated silica surfaces toward the application of CO2 sequestration. They reported that nucleation tends to occur on the silica layer due to the stabilization effect of the silica layer. They concluded that solid surfaces with different hydrophilic characters will affect the nucleation pathways in different ways, and hence, further studies need to be conducted. They proposed a three-step nucleation mechanism for hydrate growth in the presence of solid surfaces.269 First, on a

hydrate nucleation, and the mechanism of stabilization of hydrate nuclei in the presence of surfaces. Some part of this is discussed in the next section on Nucleation in the Presence of Porous Media.

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NUCLEATION IN THE PRESENCE OF POROUS MEDIA As clathrate technology has moved toward the potential applications of gas separation and energy storage and transport, there is a pressing need for improving the mass transfer kinetics and heat transfer properties of the reactor configuration. Traditional stirred tank reactors face the problems of agglomeration of hydrate crystals at the surface and reduction of the mass transfer coefficients.19 Hydrate promoters are one of the agents that have been employed to improve the hydrate formation rate and increase process throughput. Along with promoters, various novel reactor configurations have been tried that might enable a higher surface area for hydrate nucleation, better mass transfer properties, and higher hydrate conversions. As a result, water saturated porous media such as in packed beds has gained preference over other reactor configurations.261−264 Further, applications such as CO2 sequestration involve replacing CH4 with CO2 in the reservoirs to necessitate a better understanding of hydrate formation in porous media. Hydrate formation in the presence of solid surfaces or porous media has been reported to be much faster than bulk solution because they provide nucleation sites for hydrate formation.265 An interesting phenomenon observed for the case of hydrate formation in porous media is the presence of multiple nucleation sites that have been experimentally observed. Apart from nucleation being heterogeneous, spatial heterogeneity has been observed in hydrate nucleation in the case of porous media.264,266 This is somewhat in line with nucleation in dispersed systems where each droplet can act as an independent reactor, and due to the stochasticity of nucleation, 11193


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quantifying temporal stochasticity desirable for industrial applications. It is very important to quantify the effect of scale-up on the stochasticity. In porous media, the spatial heterogeneity adds to the complexity further. Efforts need to be undertaken to understand the phenomenon of the spatial and temporal stochastic nature of hydrate nucleation in porous media in order to develop hydrate-based processes toward industrial applications. Molecular Simulation Improvement for Simulating Closer to Experimental Conditions. As discussed in the review, most of the molecular simulations due to computational limitations simulate systems with artificially high driving forces or lacking potential models. The nucleation pathways and results obtained are reliant on the conditions and can lead to artificial pathways nonexistent in the real world. Hence, the results should be considered carefully along with an effort to bring the MD simulations closer to the real conditions. More emphasis should be placed on the study of heterogeneous nucleation since under realistic conditions nucleation is most likely to occur through this pathway. As stated by English et al.,248 the massively parallel implementation of MD simulations on supercomputers and the increasing use of GPU278 for parallel implementation of MD are techniques that will play important roles. Establishing Effects of Hydrate Promoters and Porous Media on the Process. The effect of hydrate promoters is clearly multidimensional, and the overall effect varies with the setups. The porous media also plays a key role in the hydratebased process and requires to be optimized for the application. In order to develop hydrate-based technology, a better understanding of these variables not simply in isolation but confounding effects needs to be clearly established. Multiscale Simulation Approach to Hydrate-Based Processes. There have been molecular simulation studies focused at obtaining molecular level understanding, experimental studies in search of validation at lab-scale setups and process or macro-level simulation studies to provide process performance indicators. Developing hydrate-based technologies toward industrial applications is truly a multidisciplinary effort and requires a common thread to bind the different domains of studies. There is a need for integration of molecular simulation studies of realistic hydrate processes to design experimental setups and seek validation. Taking on Challenges toward Industrial Implementation. Hydrate processes are extremely complex due to all the reasons listed in the current review and more. Apart from technical challenges such as optimizing the conditions, materials, and additives, there is a requirement for overcoming the stochastic nature of the process by means of either statistical modeling or reducing it within bounds that do not alter the process performance significantly. Applications such as gas separation or desalination or energy storage and transport require a semibatch or continuous process with precise control over the process and little scope for stochasticity. Scaling up is a significant part of the challenge toward industrial implementation of any technology, and generally, a reduction in performance is observed upon scaling up. Veluswamy et al.279 provided a multiscale experimental validation of rapid methane hydrate formation for developing a cost-effective large-scale energy storage system. They studied methane uptake in the presence of a THF−water system at three scales: small scale (2 mL), medium scale (53 mL), and large scale (220 mL). Their results showed a reduction in induction time with increasing

nanosecond time scale, an ice-like layer is formed closest to the substrate. On the microsecond scale, a CO2 hydrate motif layer is observed that acts as nucleation seeds, while the intermediate step is formed by an intermediate structure that transforms the ice-like layer and the final motif. Cygan et al.272 investigated the behavior of CH4 hydrate in a clay interlayer. They reported that the CH4 hydrate structure in clays was different than in aqueous solution and bulk CH4 hydrate. Following their work, Yan et al.270 performed MD simulations of the CH4 hydrate nucleation and growth process in a system containing a bulk solution layer and a clay layer. As per the study, CH4 diffuses first from the bulk to the clay surface that promotes the formation of semicages, and subsequently, hydrate grows along with a stacking fault in the bulk solution region. CH4 molecules diffuse into the clay nanopore to form the “interlayer” hydrate. The molecular diffusion of CH4 molecule into the nanopore is slow due to steric hindrance provided by hydrate crystals blocking the entrance of the pore. He et al.273 studied the effect of substrates on CH4 hydrate formation in microsecond MD simulations. They investigated CH4 hydrate formation from a gas−water two-phase system between a hydrophilic silica surface and a hydrophobic graphite surface. CH4 is preferentially adsorbed to the graphite surface, while water bonds with silanol groups in silica. A cylindrical nanobubble is formed that leads to higher aqueous CH4 concentration and hydrate formation. The studies clearly have demonstrated that hydrate nucleation and growth are more complex in porous media and a require deeper understanding of the phenomenon. There also have been efforts to perform macroscopic numerical simulations consisting of multiphase flows in porous media and modeling of hydrate formation.274−277 These works either use equilibrium reaction models or kinetic models based on intrinsic rate kinetics such as by Kim and Bishnoi.47 These works focus on the macro-level parameters and can provide useful tools for evaluating the process level performance. However, they do use empirical parameters for the simulations based on the physical setup such as characteristics of porous media or hydrate formation rates among others and require prior knowledge of the systems.

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FUTURE PERSPECTIVES Further Development of Experimental Techniques. There have been various spectroscopic studies adopted for studying the hydrate nucleation process and obtaining direct evidence in support of theories or exploratory studies. However, as the application of hydrates have expanded toward the use of porous media and other reactor configurations, experimental techniques need to be adapted toward these applications. As discussed for the case of studying KHIs and in multicomponent nucleation for studying the “tuning-effect”, a multiscale approach needs to be adopted ranging from XRD to NMR to Raman spectroscopy to stirred autoclaves. Further, in situ experimental techniques for detection and study in porous media needs to be further developed. Understanding the Spatial−Temporal Stochastic Nature of Hydrate Nucleation in Porous Media. The stochastic nature of hydrate nucleation, induction time, and memory effect makes it challenging to design a process application such as gas separation and desalination that requires a continuous process for hydrate applications. Experimental setups such as HP-ALTA have been adopted to statistically represent induction time in bulk solutions. The limitation of HP-ALTA to small size makes it challenging to use for 11194


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questioned. So apart from scaling up, the environmental aspects of the system need to be evaluated. Along with the use of a novel reactor configuration and hydrate promoter, novel techniques such as electronucleation have also been proposed recently.280,281 Carpenter and Bahadur showed that pure THF hydrates can be reduced to an order of a few minutes by applying 100 V for a few minutes prenucleation. They performed experiments at −5 °C and in a 5 mL system. In a follow up study, Shahriari281 et al. showed that using Al foam as the anode reduced the induction time further to only tens of seconds. They proposed that the effect is due to two mechanisms, bubble formation and metal compound formation at the anodes, both of which promote hydrate formation. Interestingly, the effect of increasing voltage on the induction time is observed to have a similar effect of increasing the reactor size shown by Veluswamy et al.279 The induction times reduce and also the stochasticity. There is a need for developing such novel techniques and demonstrate the effect of scale-up aspects. Figure 13 shows the schematic representing the facets of hydrate nucleation discussed in the current review and clathrate process-level performance parameters. The translation is not simple, but effective implementation can only be brought about by keeping the broader picture in perspective.

reactor volume. Also, they showed that the error bars spread for the induction time reduced, which means that the stochasticity of induction time reduced with increasing scales. They were able to attain this scale up without significant loss in methane uptake. Figure 12 shows the results taken from their study.

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CONCLUSIONS From being traditionally considered a source of trouble in flow assurance and pipelines, clathrates are now seen as a potential for various applications such as gas separation, energy storage and transport, desalination, and CO2 sequestration. Hydrate nucleation is a key step in the process and hence requires detailed understanding. While much efforts have been undertaken toward nucleation, pathways still remain up for debate, and it seems likely that nucleation occurs through multiple competing pathways with varying degrees, each depending upon the studies. Molecular simulation studies have provided significant insights to the nucleation pathways, nucleation rates, and related effects and will continue to do so. While the effect of hydrate inhibitors on nucleation is more aligned, the effect of hydrate promoters is observed to vary significantly. Hydrate promoters are found to have promoting effects on hydrate nucleation in the form of reducing the surface tension, increasing the solubility of the guest molecule,

Figure 12. Positive effect of process scale up on nucleation time (or induction time) in a methane storage system experimentally validated by Veluswamy et al.279

Their study shows that scaling up in certain cases might turn out to be in favor of a hydrate-based technology which might be counterintuitive at first. The use of THF, however, has strong impacts on the environment and hence has been

Figure 13. Schematic representing facets of nucleation and its translation into overall clathrate process performance. 11195


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ACS Sustainable Chemistry & Engineering and adsorption on hydrate cages. They also act as inhibitors forming a layer at the gas−liquid interface and increasing the mass transfer resistance. The overall effect is an outcome of the two contrasting effects. The memory effect has been experimentally validated, but the presence of additives and the reactor media alters the memory effect. These effects have been studied in isolation but clearly cannot be reliable when other parameters change as well. The outlook for clathrate has shifted focus toward new applications, and experimental proof of concepts have been conducted. Newer reactor configurations have been adopted toward better mass/heat transfer properties and faster kinetics. Significant progress is still required in terms of our understanding of clathrate processes, scaling up of processes, and process development for these applications.

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Zhenyuan Yin: Mr. Zhenyuan Yin is currently a Ph.D candidate in the Department of Chemical and Biomolecular Engineering at the National University of Singapore (NUS), Singapore. He is a recipient of the Industrial Postgraduate Program scholarship from Economic Development Board of Singapore and Lloyd’s Register Global Technology Centre. He holds a 1st Class honors degree in Chemical and Biomolecular Engineering from NUS. The primary focus of his research is numerical modelling and reservoir modelling of the kinetic behaviour of methane hydrate formation and dissocaition in porous medium. He is the finalist for the 2017 IChemE Singapore Young Industrialist Award.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (P. Linga). ORCID

Praveen Linga: 0000-0002-1466-038X Notes

The authors declare no competing financial interest. Biographies

Praveen Linga: Professor Praveen Linga is an associate professor in the Department of Chemical and Biomolecular Engineering at the National University of Singapore (NUS). He is also the colead for natural gas research in the centre for energy research & technology (CERT) at the Faculty of Engineering, NUS. His research interests are in the areas of clathrate (gas) hydrates, storage and transport of fuels, carbon dioxide capture, storage & utilization (CCS & U), seawater desalination and recovery of energy. His research group at NUS particularly focuses on enhancing the kinetics of hydrate formation for several applications of interest by developing novel reactor designs, experimental methods and techniques. Up to date, he has published more than 75 research articles and delivered about 50 keynote/invited talks and seminars. He has won numerous local and international awards including the 2017 NUS Young Researcher Award, 2017 NUS Engineering Young Researcher Award, 2017 Energies Young Investigator Award and the 2017 Donald W. Davidson Award for outstanding contributions to gas hydrate research.

Maninder Khurana Dr. Maninder Khurana received his Ph.D. in Chemical Engineering from the National University of Singapore in 2016 under the supervision of Professor Farooq Shamsuzzaman on the topic of integrated optimization of vacuum swing adsorption for postcombustion carbon capture. His Ph.D. research involved adsorbent evalution, first-principles modelling, developing in-house process simulation tools and economic analysis of CO2 capture. He is currently working as a Postdoctoral Research Fellow with Professor Praveen Linga and works on gas hydrate kinetic modelling,

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thermodynamic analysis and numerical simulations for hydrate processes. His current research interests are process systems

ACKNOWLEDGMENTS The work was funded in part under the Energy Innovation Research Programme (EIRP, Award No. NRF2015EWTEIRP002-002), administrated by the Energy Market Authority

engineering, developing simulation platforms for novel technologies with application towards CO2 capture, energy storage and clean energy. 11196


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(EMA), Singapore. We also acknowledge Lloyd’s Register Global Technology Center Singapore for funding support.

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