Article pubs.acs.org/JPCC
Ice Particle Size and Temperature Dependence of the Kinetics of Propane Clathrate Hydrate Formation Joel J. Rivera and Kenneth C. Janda* Chemistry Department, The University of California, Irvine, 317C Rowland Hall, Irvine, California 92607, United States ABSTRACT: The effects of ice particle size and temperature on the conversion rate of ice to propane clathrate hydrate are presented in this work. Results from this study are interpreted in terms of the three-stage shrinking core model: stage I, initiation of the water and propane enclathration reaction at the surface of the ice particles; stage II, mass transfer through pores on the outer clathrate hydrate shell; and stage III, diffusion of propane molecules through the hydrate layer surrounding the inner core of ice. For the smaller ice particles studied, the initial growth rate and total percent conversion are both higher than for larger particles due to a higher surface to volume ratio. Surprisingly, the peak conversion rate of propane clathrate hydrate increases with decreasing temperatures over the temperature range studied in this work, while the total percent conversion increases for higher temperatures, most likely due to improved mass transfer and diffusion in the later stages of the reaction. For the smallest particles studied, an activation energy of −5.5 ± 0.1 kJ/mol (H2O) is measured for up to 20% conversion. This is the first reported value for the activation energy of propane hydrate formation from ice.
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INTRODUCTION Gas clathrate hydrates were first discovered in 1810 by Sir Humphry Davey who found that mixtures of chlorine and water solidified well above the melting point of ice to form what is now known as chlorine clathrate hydrate.1 Since Davey’s discovery, a variety of gas clathrate hydrates have been studied, and it is now well-known that these compounds exist in a variety of structures, the most common being structure I, structure II, and structure H. Structure-I clathrate hydrates consist of unit cells containing two dodecahedral (512) cages and six tetrakaidecahedral (51262) cages, while the unit cell of a structure-II clathrate hydrate contains 16 dodecahedrons and eight hexakaidecahedrons (51264).2 Many naturally occurring gas clathrate hydrate deposits have been discovered beneath the ocean sediment and in the permafrost regions.3 Methane clathrate hydrate deposits are especially important because they provide a promising solution to meet future needs for energy. It is estimated that 3 × 1013 m3 of recoverable gas clathrate hydrate deposits exists worldwide.4 With the ability to harvest, store, and transport methane efficiently, methane clathrate hydrate deposits could provide a viable, long-term energy source. Many advances have been made in the development of an energy infrastructure powered by methane clathrate hydrate deposits. Harvesting methods have been developed at several test sites,3 and clathrate hydrates have shown promise as a storage/transportation medium for methane and other natural gases: the equivalent of 150 m3 of methane gas at STP can be stored in 1 m3 of methane clathrate hydrate.5 Considerable research has been dedicated to realizing the commercial storage and transportation of combustible gases in clathrate hydrates; however, this process has been hindered by several issues including slow production methods.6 Several kinetic models have been developed to understand the © 2012 American Chemical Society
conversion of ice to gas hydrate that occurs when ice particles are exposed to gaseous guest molecules at an appropriate temperature and pressure.7,8 The conversion of an ice particle to gas hydrate was described in terms of a “shrinking core” by Jander in 1927.9 In this version of the shrinking core model, conversion to gas hydrate begins with the formation of a gas hydrate shell around the surface of the ice particle. Further conversion is achieved by diffusion of gaseous molecules through the outer gas hydrate shell. This model was expanded by Fujii et al.10 and successfully used to model data for the formation of CO2 and CH4 hydrate by Henning et al. and Wang et al.10,12 Staykova et al. further extended the model by adding a third stage to account for the existence of pores on the gas hydrate shell.13 The three stages are (1) formation of a gas hydrate shell around the surface of the ice particle, (2) transfer of ice and/or gas through pores on the gas hydrate shell, and (3) diffusion of gas molecules through the gas hydrate layer.13 The conversion rate of ice to gas hydrate during each respective stage is limited by (1) the rate of the gas−water enclathration reaction, (2) the rate of mass transfer through pores on the gas hydrate shell, and (3) the diffusion rate of the guest molecules through the gas hydrate layer.13 The three-stage model by Staykova et al.13 has been successful in modeling the conversion of ice particles to CO2 and CH4 hydrate but was later revised to a two-stage model as described by Kuhs et al.14 due to low hydrate conversion rates, which made it difficult to distinguish between the second and third stages. The shrinking core model suggests that to achieve a commercially viable hydrate formation process, the ice particle Received: April 12, 2012 Revised: August 6, 2012 Published: August 14, 2012 19062
dx.doi.org/10.1021/jp3035049 | J. Phys. Chem. C 2012, 116, 19062−19072
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Figure 1. Two nearly identical apparatuses were used in this study. The main components of each apparatus are shown in the diagram. Specific differences are discussed in the Experimental Section.
melting of the surface ice layer to expedite the exothermic enclathration reaction.7,8,11,24 However, it is interesting to note that Chen et al. observed faster formation rates for methane hydrate if their procedure was initiated at a lower temperature.23 To further investigate the effects of ice particle size and initial temperature, we report experiments to study propane hydrate formation using ice particles in a 106−425 μm range. As expected from the “shrinking core” model, the reaction rate varies strongly with time and the percent uptake of propane. In particular, a fast initial uptake is observed for each particle size when the propane pressure reaches a threshold. Reaction initiation is followed by slower long-time reactions. Interestingly, for the smallest particle size, a clearly discernible intermediate stage was observed between these two limits. Under our conditions, the fast initiation reaction lowers the system pressure so that it approaches the equilibrium vapor pressure during stage II; this is especially dramatic at lower temperatures. The experiments in this study were conducted using irregular ice particles produced by a coffee grinder. Although irregular ice particles are less than ideal for mathematical modeling, the particles used in this study yield fast formation kinetics that may be useful for practical applications, and the results of similar runs are surprisingly reproducible. The effect of initial temperature for the smallest particles was investigated over a temperature range of 251−263 K and revealed a strong inverse temperature dependence for the early portion of clathrate growth. Activation energy values are extracted for two kinetic regions of ice conversion to hydrate.
size should be as small as possible so that stage III of the reaction does not slow the complete conversion of ice particles to hydrate as shown in a number of previous studies by Stern et al.7,8,15 Stern et al. have also developed a “seeding” method to convert granulated ice to methane clathrate hydrate at high yields and demonstrated the superheating of ice during the enclathration reaction.7,8,15 Stern8 and Rawn16 et al. have succeeded in full conversion of ice particles to propane hydrate using high pressures of liquid propane and heating above the ice melting point. However, complete conversion of ice to clathrate can still be quite slow. Prado et al. also used a seeding method to demonstrate how methane gas can be stored efficiently at near ambient conditions by occupying the 512 cages of a structure-II propane clathrate hydrate, and Abbondondola et al. accelerated the formation rate of propane clathrate hydrate by employing xenon as a promoter molecule.17,18 Gulluru et al. have also demonstrated rapid formation rates of several ether clathrate hydrates at low temperatures using nanocrystals; a combination of ethers and small promoter molecules, such as CO2 and N2, also expedited formation of these clathrate hydrates at low temperatures.19 Abay et al. have also shown that methanol, a widely used gas clathrate hydrate growth inhibitor, promotes formation rates when used in ultralow concentrations.20 Despite much progress, the fundamental kinetics of gas clathrate hydrate formation have yet to be fully characterized.21 Smaller ice particles provide higher surface area to volume ratios, which are expected to result in higher formation rates, but the opposite trend can also be observed under certain conditions. For instance, the conversion of micrometer-sized ice particles does not follow the mechanism described by the shrinking core model.22 Studies by Falenty et al. have shown that the formation of a hydrate shell does not occur for ice particles smaller than 20 μm; total hydrate conversion was also much lower for these particles.22 Chen et al. have also reported lower conversion rates for particles smaller than 180 μm and have attributed this observation to ice particle packing effects.23 Although enclathration is inherently exothermic, one expects the activation energy to be positive for rearrangement of the water lattice. Higher temperatures, for instance, might promote
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EXPERIMENTAL SECTION Because propane clathrate hydrate forms at temperatures and pressures near ambient conditions, relatively simple experimental methods could be employed in this study. First, ice particles were prepared with a coffee grinder and size-sorted using liquid nitrogen cooled sieves. Next, the ice particles were exposed to propane gas that flowed through a fixed aperture created by a needle valve. Comparing the pressure rise with and 19063
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without ice particles in the cell provides the uptake rate of gas into hydrate as a function of time and temperature. Figure 1 shows a schematic diagram of the apparatus. A 310 mL detachable sample cell was partially filled with ice particles and attached to a 90 mL stainless steel gas manifold to be exposed to propane. The temperature of the cell was controlled using an ethylene glycol bath cooled by a Thermo Neslab RTE 7 programmable refrigeration unit. A regulated, constant propane pressure was applied behind a needle valve so that the flow rate could be determined by the pressure drop across the valve. The manifold pressure was measured using an Omega model number PX302-200GV transducer, and the temperature inside the cell was measured using three Type-T thermocouples, Omega model number TJC36-CPSS-040U-12SMP-M. The stated accuracy was ±0.25% for the pressure transducer and ±0.1 °C for the temperature probes. Temperature and pressure readings were recorded at 100 s intervals under computer control using an Omega model number OMB DAQ 56 data acquisition module. Sample temperatures were controlled via a thermo Neslab RTE 7 programmable refrigeration unit. The apparatus for the temperature dependence studies was very similar to that described above except for a smaller 35 mL stainless steel gas manifold and an Omega model PX303-1KG5 V transducer. A. Ice Particle Preparation. Approximately 3 mm ice pellets were prepared by dripping nanopure water through a buret and into a Dewar of liquid nitrogen. The ice pellets were then ground into fine powder using a coffee grinder operated in a laboratory freezer set to 253 K. The ice particles were sizeselected using sieves with pore diameters of 425, 250, 180, and 106 μm. In each case, the ice particle size was limited by the larger and smaller sieve pore size used in the sorting process. The largest particles used in this study were passed through the 425 μm mesh, but not the 250 μm mesh, and will subsequently be referred to as large particles. The two other particle sizes were between 180 and 106 μm, referred to as medium particles, and >106 μm, referred to as small particles. To avoid subsequent changes in particle size, the sorting process was carried out at liquid nitrogen temperature; only one size was prepared for any given run and was studied as quickly as possible after preparation. The characterization of the particles will be discussed in the results section. B. Procedure To Study Propane Uptake as a Function of Particle Size. Figure 2 shows a vapor pressure versus
temperature curve for propane hydrate using data from Yasuda et al.25 At temperatures below the freezing point of water, a propane-rich vapor phase is in equilibrium with ice and the hydrate. Above the freezing point, the propane-rich vapor phase is in equilibrium with a water-rich liquid phase and the hydrate. All four phases exist in equilibrium at the quadruple point of the phase diagram. For this system, the quadruple point occurs at a temperature of 273.2 K and 0.170 MPa.25 For the experiments described in detail below, we leak propane gas into a cell containing ice particles and measure the effect of hydrate formation on the propane pressure in the cell. In general, hydrate formation starts well after the hydrate vapor pressure is exceeded, and our leak rate is high enough that after this point the cell pressure remains above the hydrate vapor pressure. Because the leak rate can be determined, the hydrate formation rate can be inferred from the pressure versus time curve of the formation runs. Our data analysis depends on the assumption that the propane is either in the hydrate phase or in the vapor phase. So, we were careful to always keep the propane pressure below the vapor pressure of liquid propane. Approximately 31 g of prepared ice particles was placed in the sample cell precooled with liquid nitrogen. The cell was connected to the gas manifold, and the temperature was allowed to equilibrate in the 270 K temperature bath for 2 h. The cell was then evacuated to 0.13 kPa and quickly refilled with research grade propane to 76 kPa, below the pressure required to initiate hydrate formation. The reason for this step was to minimize the time delay and particle sintering between particle preparation and initiation of hydrate formation. Additional propane was then added via the needle valve with the regulator set to 0.39 MPa. Propane flow was maintained until the pressure of the cell reached that of the pressure regulator. After each experimental run, the product was decomposed and the mass of the liquid water was measured and used in subsequent data analysis. C. Procedure To Study Propane Uptake as a Function of Temperature. Studying the formation of propane hydrate at temperatures below 270 K required a slight modification of the above procedure to avoid liquid propane formation in the sample cell and to accommodate for initiation of hydrate formation at lower pressures for lower temperatures. The initial pressure of propane was reduced to 34 kPa, and the pressure behind the needle valve was reduced to 0.14 MPa; only the smallest particles were used for this study. Although the temperature bath maintained a constant temperature during the course of the reaction, heat transfer was too slow to maintain a constant ice temperature. The degree of temperature variation due to reaction exothermicity will be discussed below.
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RESULTS AND DATA ANALYSIS The results of this study will be discussed in the context of the shrinking core model to describe the growth kinetics of propane hydrate. Although the nonuniform ice particles prevent the use of a rigorous quantitative model, useful insights can still be derived from these experiments. Distinct kinetic domains are clearly observed for the smallest particle sizes, but the precise transition point from stage I to stage II is difficult to identify. For the smallest particles, the transition to stage III is distinguished by substantially slower kinetics and a change in sign of the activation energy. A. Characterization of Ice Particles. We first describe the nature of the ice particles before and after propane uptake. Figure 3 shows several typical particles that passed through the
Figure 2. Pressure−temperature equilibria for the C3H8 (g) + hydrate + H2O (s) and C3H8 (g) + hydrate + H2O (1) systems. The quadruple point for all four phases is reported as 273.2 K and 0.170 MPa. Values were obtained from Yasuda et al.25 19064
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upon scraping of the hydrate solid. This indicates that for the smallest particles a greater percent of the overall reaction occurred at the interfaces between particles. Given that the ice surface is rapidly roughened upon reaction initiation, it may be that using purely spherical particles would not change the observed results to an appreciable extent except for very short reaction times. From the photographs of the particles before and after enclathration, we conclude that even though the surface area of the particles is greater than it would be for perfect ice spheres, the essence of the shrinking core model still applies; that is, there are clearly distinguished regions of each particle that can be characterized as either near the surface or in the bulk. B. Propane Uptake Rate as a Function of Ice Particle Size. Figure 4a shows pressure versus time curves for three
Figure 3. (a) Photograph of four particles from the large ice particle sample prior to enclathration. The 250 μm metal wire to the right of the ice particle serves as a size reference. (b) A photograph of two particles from the large ice particle sample taken after the enclathration process. The particle on the left appears to be a single ice particle, whereas the particle on the right appears to be a combination of two individual ice particles.
425 μm sieve, but not the 250 μm sieve. The photographs were taken of sample particles spread over a microscope slide cooled by dry ice. A 250 μm diameter wire was included in the photograph for reference. Figure 3a shows four of the ice particles before propane uptake. Their shape is quite irregular; the surfaces are not smooth, but neither are they extremely rough on the 50 μm scale. Although small cracks and crevices will not be visible in the photographs, it is safe to say that most of the ice is in the bulk and not on a surface. However, as time passed, new ice from the atmosphere was deposited on the surface of the particles, and the surface features assumed a more dendritic quality. We believe that in the sample runs described below, the ice surfaces remained quite smooth because the particles were minimally exposed to ambient air. Photographs of the other particle sizes yielded similar pictures, except that for the smaller particles, observed at higher magnification, the dendritic growth of new ice on the surface was more prominent. In each case, the sieving procedure was quite effective at determining the range of particle sizes. Figure 3b shows two particles after propane uptake. The propane was added to the cell using the procedure described above for the kinetics runs. At the end of a run, the hydrate is a single solid mass, indicating that hydrate growth served to fuse all of the particles together. However, upon scraping the surface of the solid with a spatula, the solid flaked into particles whose sizes were similar to those of the starting material. Figure 3b shows one example of an individual particle and one example where two particles appear to have remained fused upon scraping. It was more typical for several particles to remain fused than for an individual particle to result. For the smallest size,
