Test Gas Mixtures Research Articles

Preparation of low-concentration H2 test gas mixtures in ambient air for calibration of H2 sensors

Abstract. Using electrochemical gas sensors for quantitative measurements of trace gas components in ambient air introduces several challenges, of which interference, drift and aging of the sensor are the most significant. Frequent and precise calibration as well as thorough characterization of the sensor helps to achieve reliable and repeatable results. We therefore propose the use of a simple, lightweight and inexpensive setup to produce hydrogen calibration gases with precisely known concentrations in ambient air. The hydrogen is produced by electrolysis with electric current monitoring, and the output can be set to any value between ∼ 3 and ∼ 11 µgH2min-1. With a dilution flow of 500 mL min−1, for example, this results in a concentration range from ∼ 70 up to ∼ 240 ppm, but concentrations significantly below or above this range can also be covered with accordingly modified dilution flows. This setup can be used not only for calibration, but also for thorough and long-term characterization of electrochemical gas sensors to evaluate sensitivity, zero voltage and response time over extended periods of time.

ASSESSMENT OF METHODS FOR DETERMINING THE NATURAL GAS HEAT OF COMBUSTION

The shortage of fuel and energy resources, the increase in natural gas prices and the continuous increase in gas consumption indicate the relevance of the issues of measuring the natural gas amount and assessing its quality indicators. Ukraine is implementing the European methodology for calculating gas consumption based on its quality and efficiency. The problem of determining the gas quality in Ukraine requires a thorough assessment and research.
 The main physical and chemical indicator of the natural gas quality, which characterizes its energy value, is the specific volumetric gas heat of combustion. The value of this parameter differs for different gas fields. The gas heat of combustion determines the efficiency of its use both in everyday life and in industry.
 The aim of the work is to analyze the main methods for determining the calorific value of natural gas.
 The gas heat of combustion is determined by calorimetric, chromatographic and correlation methods.
 The calorimetric method is characterized by the complexity of the measurement process, complete combustion of the test gas, and long term process. This ensures the objectivity of the results, which is based on taking into account the moisture content of the gas and the presence of non-combustible components in it.
 The basis of the chromatographic method is the separation of the components of a gas sample in a chromatographic column. The result is a chromatogram that shows the percentage composition of hydrocarbons in the gas. The characteristic properties of the method are the identification of a wide range of components and the repeatability of the results.
 When using correlation methods for determining the heating value of natural gas, various physicochemical parameters of samples are measured (such as total hydrocarbon concentration, heat capacity, acoustic wave propagation velocity, carbon dioxide concentration, thermal conductivity, dielectric constant, dynamic viscosity, and others).
 Correlation dependence is based on the choice and association of such parameters. This dependence is studied on different test gas mixtures and allows us to determine the empirical dependence. The mixtures correspond to gases with different calorific values. The obtained empirical dependence is used to register the heat of combustion of real natural gas. The paper evaluates the features of these methods application and instruments based on them.

Effects of hydrogen addition on combustion and flame propagation characteristics of laser ignited methane/air mixtures

In this study, effects of hydrogen addition on combustion and flame propagation characteristics of methane/air mixtures were investigated in a constant volume combustion chamber. Tested gas mixtures are 100% CH4, 05% H2 – 95% CH4, 10% H2 – 90% CH4 and 15% H2 – 85% CH4, and such mixtures were ignited using a passively Q-switched Nd:YAG laser ignitor which has a pulse energy of 12.3 mJ, pulse duration of 2.4 ns and wave length of 1064 nm. A Schlieren setup coupled with a high-speed camera enabled evaluating flame propagation behavior, while pressure curve analysis provided necessary data for characterization of combustion properties. Additionally, lean flammability limits of gas mixtures were also determined at the test conditions. The unique properties of hydrogen (such as low density, high reactivity, high diffusivity etc) widened lean flammability limit. Rate of pressure rise and measured pressure values increased with hydrogen addition, regardless of the air-fuel equivalence ratio (λ). Lastly, hydrogen addition uniformly affected flame propagation characteristics and flame luminosity. Combustion process became more stable with hydrogen addition.

Design and optimisation of a multifunctional monolithic filter for fire escape masks

Commercial fire escape masks (FEMs) use packed bed filters to remove gaseous and vaporous toxic components in the event of building fires. Packed bed filters incur a high pressure drop and commercial masks have no method to remove environmental (fire) or process (reaction and adsorption) heats. Here we derive a computationally efficient numeric model based on a bi-linear driving force (LDF) model to investigate the purification of gas streams in a square channelled monolith filter containing an impregnated activated carbon (AC) section to adsorb and react toxic components, and a section consisting of shape stable phase change materials (SS-PCMs) to absorb heat. The modelled test gas mixture contained an adsorbing component, cyclohexane, and a reacting component, carbon monoxide, permitting the combined effects of heat generation, heat absorption, component reaction and component adsorption to be studied for a novel filter. The bi-LDF model was validated against a three-dimensional model and provided excellent accuracy at significantly reduced computational time ca. 99.7%. Additionally, the bi-LDF model was used to optimise the dimensions and configuration of the filter, specifically finding an optimal channel diameter, dch, to wall thickness, tw, aspect ratio of dch=1.3tw. The optimal configuration consisted of an initial 2.0 cm long impregnated AC section followed by a 2.5 cm SS-PCM section at the outlet, providing 18 min of thermal protection whilst preventing cyclohexane vapour breakthrough for 21 min. Pt/TiO2 was confirmed to be a viable CO oxidation catalyst with a minimum weight fraction within the impregnated monolith of 2.5 wt%. The success of this work represents a step change in FEM design and more widely in air purification devices where heat absorption is important.

Temperature-dependent absorption cross section measurements for propene, 1-butene, cis-/trans-2-butene, isobutene and 1,3-butadiene in the spectral region 8.4–11.7 µm

We present a comprehensive study on the temperature-dependent mid-infrared absorption spectra between 8.4 µm and 11.7 µm for a complete list of C3-C4 alkenes, namely propene, 1-butene, cis-/trans-2-butene and isobutene, as well as 1,3-butadiene, from room temperature to roughly 1000 K. The methodology deploys a rapid-tuning, broad-scan external-cavity quantum-cascade laser (EC-QCL) in a shock tube and can provide quantitative absorption information at a rate in excess of 30 cm−1/ms at spectral intervals between 0.35–0.6 cm−1. The experimental procedure was validated with room-temperature, nitrogen-diluted, static spectra measurements for propene, 1-butene, isobutene, and 1,3-butadiene, showing good agreement with existing spectroscopic databases. Spectral measurements were extended to higher temperatures with shock-heated test gas mixtures diluted by argon, at experimental conditions between 600–1000 K and 1.5–2.5 atm. The resulting spectra show strong temperature dependence and represent the first experimental collection of broadband high-temperature absorption spectra for these species. The measured high-temperature spectra are in reasonable agreement with predictions from fixed-wavelength absorption cross section correlations in the literature. The data presented are archived in the Stanford ShockGas-IR database and provide useful expansions of the existing knowledge on molecular absorption in the mid-infrared at elevated temperatures.

Comparison of Gas Sensing Properties of Reduced Graphene Oxide Obtained by Two Different Methods.

In this study, the sensitivity of reduced graphene oxide structures (rGO) to the action of selected gases (especially hydrogen, but also nitrogen dioxide and ammonia) was examined. Two sensing structures, based on rGO structures, obtained by different methods of oxidation (the modified Hummers, and the modified Tour’s method respectively), were investigated. We show here that the method used for the oxidation of rGO influences the sensitivity of the sensing structure during contact with various gaseous atmospheres. We performed our experiments in the atmosphere, containing hydrogen in a concentration range from 0 to 4% in nitrogen or synthetic air, both in dry and wet conditions. The temperature range was from 50 °C to 190 °C. Finally, we checked how the resistance of the samples changes when the other gases (NO2, NH3) appear in tested gas mixtures. The gas investigations were supplemented by the characterization of rGOs materials using scanning electron microscopy (SEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and N2 sorption method.

Two-temperature Collisional-radiative Modeling of Partially Ionized O2-Ar Mixtures over 8000-10,000 K Behind Reflected Shock Waves.

The collisional excitation kinetics of atomic oxygen was studied behind reflected shock waves using tunable diode laser absorption spectroscopy. A test gas mixture of 1% O2/Ar was shock-heated to temperatures between 8000 and 10,000 K and pressures between 0.15 and 1 atm. The time evolution of the atomic oxygen population in the 3 s 5S0 state was monitored by laser absorption at 777.2 nm. The measured O(3 s 5S0) population revealed multistage behavior that was not observed in previous measurements over a temperature range of 5300-7200 K. To interpret the multistage behavior, a three-level collisional-radiative model for atomic oxygen excitation kinetics was developed. The model utilized two independent temperatures, that is, heavy particle translational temperature Ttr and electron translational temperature Te, to describe the fundamental rate constants of atomic oxygen excitation because of collisions with heavy particles and electrons, respectively. The heavy particle excitation rate was inferred from the early stage of the measurement to be k(3P →5S0) = 3.4 × 10-27 (T/K)0.5(1.061 × 105 + 2 (T/K)) exp(-1.061 × 105 K/T) ± 50% m3 s-1. The electron impact excitation rate constant of oxygen, electron impact, and heavy particle impact ionization rate constants of Argon were modified in the model to match the experimental population time histories. The modified rate parameters are also reported for the temperature range explored in the current study.

Determination of the JP10 + OH → Product Reaction Rate with Measured Fuel Concentrations in Shock Tube Experiments.

The overall reaction rate for JP10 + OH → products was measured directly via laser absorption of OH in shock tube experiments from 931 to 1308 K and 0.94 to 1.44 atm. The JP10 concentration of test gas mixtures was measured in the shock tube for several experiments using a 3.39 μm laser fuel diagnostic. The measured JP10 concentrations indicated fuel losses due to adsorption of 11-31% compared to values calculated manometrically from mixture preparation. OH was generated via rapid thermal decomposition of tert-butyl hydroperoxide behind reflected shock waves, and post-shock OH profiles were measured via laser absorption at 308.6 nm. The measured OH profiles were fit with a chemical kinetic model for JP10 chemistry to determine the overall JP10 + OH reaction rate. A recommendation is made for the JP10 + OH overall reaction rate over the temperature range explored in this study as k1 (931-1308 K) = 1.622 × 1014 exp(-1826/T [K]) ± 12%. To the authors' knowledge, these data are the first direct measurements of the overall reaction rate for JP10 + OH.

Experimental Investigation of Flame Characteristics of H2/CO/CH4/CO2 Synthetic Gas Mixtures

ABSTRACT Chemical composition of synthetic gas and concentration of its components depend on gasification process and feedstock. Synthetic gas mainly consists of hydrogen (H2) and carbon monoxide (CO), and may contain trace amounts of carbon dioxide (CO2) and methane (CH4). In this study, combustion and emission characteristics of H2/CO/CH4/CO2 blending syngas mixtures with high H2/CO ratio were experimentally investigated in a swirl-stabilized premixed combustor. Furthermore, stable operating ranges (flashback and blowout equivalence ratios) of such mixtures and flame response of 67.5%H2-22.5%CO-5%CO2-5%CH4 mixture to acoustic forcing were also detected. During the experiments, CH4 amount in tested gas mixtures varied between 5% and 20% by volume (at intervals of 5%), and H2/CO ratio and CO2 concentration were kept constant at the values of 3 and 5%, respectively. As a consequence, mixtures of 67.5%H2-22.5%CO-5%CO2-5%CH4, 63.75%H2-21.25%CO-5%CO2-10%CH4, 60%H2-20%CO-5%CO2-15%CH4 and 56.25%H2-18.75%CO-05%CO2-20%CH4 were derived and tested under the same boundary and physical conditions. All experiments were conducted at 0.4 equivalence ratio (Φ) and 0.2 geometric swirl number (SN). Preliminarily, stable operating ranges of respective gas mixtures were determined to find an equivalence ratio at which all gas mixtures could be tested without causing any flame instability and then, CH4 addition effects on combustion and emission characteristics of such mixtures were evaluated via utilizing axial and radial temperature, CO and O2 profiles. Lastly, flame behavior of 67.5%H2-22.5%CO-5%CO2-5%CH4 mixture was evaluated under externally modified acoustic conditions. Acoustic field in the combustor was mechanically altered by using side-mounted loudspeakers in the frequency range of 30–200 Hz. To identify flame instabilities and to evaluate the degree of coupling between heat release and pressure oscillations, pressure sensors and photodiodes installed on combustion chamber and burner were utilized. Results of this study showed that CH4 addition to synthetic gas mixtures improves rich flammability limits, and increases flame temperature, flame height and emissions. Under externally modified acoustic conditions, flame behavior slightly alters (flashback and blowout does not occur). Additionally, pollutant emissions improve in an environment-friendly manner under such conditions.

Combustion and emission characteristics of premixed CNG/H2/CO/CO2 blending synthetic gas flames in a combustor with variable geometric swirl number

This paper presents the results of experimental studies conducted on premixed CNG/H2/CO/CO2 blending synthetic gas flames in a laboratory scale combustor, with particular emphasis on effects of swirl number (from 0.2 to 1.6, at intervals of 0.2) and equivalence ratio (0.6, 0.8 and 1.0) on combustion and emission characteristics of such mixtures. Furthermore, effects of swirl number on lean blowout and flashback limits of studied mixtures were also investigated. Irrespective of the swirl number and equivalence ratio, H2/CO ratios of tested gas mixtures were kept constant (1.0), and mixtures of H2/CO/CNG/CO2 which were diluted with different amount of CO2 (0–20%, at intervals of 5%) were derived. Considering broadest operating range, mixture of 20%CNG/30%H2/30%CO/20%CO2 was determined as base fuel to be tested. Combustion and emission behavior of tested gas mixtures were assessed by examining axial and radial temperature, NOx, CO and CO2 distributions. Besides, swirl number and equivalence ratio effects on flame structure were evaluated by investigating instantaneous flame images (with the same focal length and exposure time). Results of this study showed that effects of swirl number on flame characteristics (temperature and pollutant emission distributions) is not monotonous, and equivalence ratio dependent flame behavior alters differently at different swirl numbers.

SHOCK-TUBE EXPERIMENTAL STUDY AND KINETIC MODELING OF JP-10 PYROLYSIS

Pyrolysis of JP-10 hydrocarbon fuel was studied in a single-pulse shock tube over temperature range from 1150 K to 1300 K. The main decomposition products were identified by gas chromatography as ethylene, acetylene, propylene, $n$-butene, 1,3-butadiene, cyclopentadiene, cyclopentene, benzene, toluene, and a small amount of methane, ethane, xylene and 1-methylcyclopentene. By summation of all product concentrations in each run, the rate coefficient of JP-10 pyrolysis was experimentally determined. Comparative rate measurements were used to eliminate the effects of shock's non-ideality and boundary layer. A small amount of the internal standard compound, whose rate expression for decomposition is well established, was added in the test gas mixtures, and the reaction temperatures were determined according to the decomposition extents of the internal standard compound under the same experimental conditions in a shock tube. The reaction temperatures determined from the decomposition extents of the internal standard compound are usually less than those at the region 5 behind reflected shock calculated by shock velocity measurements. The temperatures determined by two methods are consistent between 1150 K and 1300 K, the difference is within 20 K, and the difference increases with the temperature increase. Based on the experimental study, kinetic modeling of JP-10 pyrolysis was carried out according to San Diego Mechanism. The yields of three main products, ethylene, acetylene and 1,3-butadiene, have a good agreement between the experimental and the simulation results,while the experimental results of cyclopentene yield are much higher than simulation,indicating that both fully and partially ring-opening reactions in JP-10 pyrolysis are important decomposition reaction pathways.

Effects of synthetic gas constituents on combustion and emission behavior of premixed H2/CO/CO2/CNG mixture flames

In this study, effects of synthetic gas constituents on combustion and emission behavior of premixed H2/CO/CO2/CNG blending synthetic gas flames were experimentally investigated in a swirl stabilized laboratory scale combustor. Effects of these constituents on flashback and blowout equivalence ratios of respective mixtures were also determined. Firstly, mixtures of CNG/H2/CO with varying H2/CO ratios were tested and then each mixture was diluted with the same amount of CO2 (20% by volume) to better represent synthetic gas. H2/CO ratios of tested gas mixtures were so adjusted that heating value of each gas mixture was low, moderate or high. Combustion behavior of such mixtures was evaluated with respect to measured axial and radial temperature values. Moreover, emission behavior was analyzed by means of emitted CO, CO2 and NOx levels. Flame temperature measurements were conducted with B and K type thermocouples. Emission measurements were performed with a flue gas analyzer, which was equipped with a ceramic coated probe, as well. Results of this study revealed the great impact of gas composition on combustion and emission behavior of studied flames. Two main findings are: H2/CO ratio slightly alters temperature distribution throughout combustor, while hydrogen reaction kinetics play the most significant role in synthetic gas combustion (1), CO2 addition tremendously increases emissions of CO (2).

Application of fuzzy logic to determine the odour intensity of model gas mixtures using electronic nose

The paper presents the possibility of application of fuzzy logic to determine the odour intensity of model, ternary gas mixtures (α-pinene, toluene and triethylamine) using electronic nose prototype. The results obtained using fuzzy logic algorithms were compared with the values obtained using multiple linear regression (MLR) model and sensory analysis. As the results of the studies, it was found the electronic nose prototype along with the fuzzy logic pattern recognition system can be successfully used to estimate the odour intensity of tested gas mixtures. The correctness of the results obtained using fuzzy logic was equal to 68%.

Quantitative decoding of the response a ceramic mixed potential sensor array for engine emissions control and diagnostics

The development of on-board sensors for emissions monitoring is necessary for continuous monitoring of the performance of catalytic systems in automobiles. We have fabricated mixed potential electrochemical gas sensing devices with Pt, La0.8Sr0.2CrO3 (LSCO), and Au/Pd alloy electrodes and a porous yttria-stabilized zirconia electrolyte. The three-electrode design takes advantage of the preferential selectivity of the Pt+Au/Pd and Pt+LSCO pairs towards different species of gases and has additional tunable selectivity achieved by applying a current bias to the latter pair. Voltages were recorded in single, binary, and ternary gas streams of NO, NO2, C3H8, and CO. We have trained artificial neural networks to examine the voltage output from sensors in biased and unbiased modes to both identify which single test gas or binary mixture of two test gases is present in a gas stream as well as extract concentration values. We are able to identify single and binary mixtures of these gases with accuracy of at least 98%. For determining concentration, the peak in the error distribution for binary mixtures was 5% and 80% of test data fell under <12% error. The sensor stability was also evaluated over the course of over 100days and the ability to retrain ANNs with a small dataset was demonstrated.

Computational Design of Metal–Organic Framework Arrays for Gas Sensing: Influence of Array Size and Composition on Sensor Performance

Gas sensors are used widely in applications ranging from food quality assessment to environmental monitoring. When put in arrays, they are called “electronic noses” and have improved capability in distinguishing varied gas mixtures. Metal–organic frameworks (MOFs) are promising materials for use in electronic noses due to their high surface areas, reproducibility, and tunability. However, due to the number of MOFs to choose from and the even larger number of ways they can be combined in arrays, it is a challenge to select the right combination of materials for any given sensing application. In this work, we show how well a wide range of CO2, N2, C2H6, and CH4 gas mixtures can be distinguished by combining sensing input from arrays of different types of MOFs. We simulated adsorption of 78 gas mixtures in five MOFs (IRMOF-1, HKUST-1, NU-125, UiO-66, and ZIF-8) at 1 and 10 bar via classical grand canonical Monte Carlo (GCMC) methods. We then defined a scoring metric, the sensor array gas space (SAGS) score, which quantifies the potential of various MOF sensor arrays for distinguishing among the tested gas mixtures assuming only the total mass of the adsorbed mixture could be measured. We found that combining sensing input from multiple types of MOFs can significantly increase the SAGS score, well beyond what could be achieved with only an individual MOF sensor. We also compare different MOF combinations to determine the optimal array at different pressures and find that there is little correlation between the best arrays at 1 bar versus 10 bar.

Measurement of CO2 concentration at high-temperature based on tunable diode laser absorption spectroscopy

A diode laser sensor based on absorption spectroscopy has been developed for sensitive measurement of CO2 concentration at high-temperature. Measurement of CO2 can provide information about the extent of combustion and mix in a combustor that may be used to improve fuel efficiency. Most methods of in-situ combustion measurement of CO2 use the spectroscopic parameters taken from database like HITEMP which is mainly derived from the theoretical calculation and remains a high degree of uncertainty in the spectroscopic parameters. A fiber-coupled diode laser system for measurement of CO2 in combustion environment by use of the high-temperature spectroscopic parameters which are obtained by experiment was proposed. Survey spectra of the R(50) line of CO2 at 5007.787cm−1 were recorded at high-temperature and various pressures to determine line intensities. The line intensities form the theoretical foundation for future applications of this diode laser sensor system. Survey spectra of four test gas mixtures containing 5.01%CO2, 10.01%CO2, 20.08%CO2, and 49.82%CO2 were measured to verify the accuracy of the diode laser sensor system. The measured results indicate that this sensor can measure CO2 concentration with 2% uncertainty in high temperatures.

Monte Carlo Simulations of Proficiency Testing for Geometric Distributed Test Results

The scope of the paper is the investigation of the effect of probability value variations on the dispersion of extreme values of geometric random process results. The practical background of the investigation is the study of values obtained in the process of low currents testing in explosive gas mixtures. In the first part of the paper, the process of testing by using spark test apparatus and explosive test gas mixtures was briefly shown. In the second part of the paper, the geometric type of distribution process associated to tests results was emphasized. In the third part, the simulation method used together with Monte Carlo simulation process were introduced. The simulation results and discussions were presented in the last part.

A novel diagnostic principle for alveolar6capillary membrane permeability disorders

The aim of this study was to estimate the diffusing capacity of the alveolar"capillary membrane (Dm) and the alveolar volume of the lungs (Va) based on measured CO concentration and basic spirometric parameters.Methods. Previously, we calculated CO concentration in the exhaled air during tidal and forced breathing. Experimental data of a healthy volunteer were analyzed with presumable predicted values of Dm = 60 and Va = 7.0. Then, the real Dm and Va were estimated.Results. We determined an equation for the present case (male; 176 cm of height; 50 years of age). This equation was too intricate for the routine use, so we developed an online calculator to estimate values in the real"time regimen on the basis of DELPHI platform.Conclusion. Our findings could make reasonability for further investigation to develop a new method for Dm and Va estimation that could be more feasible because it do not need test gas mixtures.

Measurements of Oxygen Dissociation Using Laser Absorption

The dissociation rate coefficient for oxygen in argon, , was measured using laser absorption near 216 nm in the Schumann–Runge system in a shock tube. A mixture of 2% oxygen in argon was studied behind reflected shocks at initial equilibrium temperatures from 4400 to 7900 K and pressures from 0.2 to 1 atm. The dissociation was modeled decoupled from vibrational relaxation because dissociation was evident only after the test gas mixture was near vibrational equilibrium. The dissociation rate coefficient was determined by fitting the measured oxygen absorbance time history for each experiment using temperatures based on the incident shock speed and the shock relations and adjusting the A-factor of the dissociation rate coefficient. Good agreement was found with the prior experimental work and model of Camac and Vaughan. Consistent results were also obtained for measurements with constant pressure as well as increasing pressure, validating our method to account for pressure changes by including the pressure profile in the dissociation model.

Study of the Effect of the Degree of Overcooling During the Formation of Hydrates of a Methane-Propane Gas Mixture on the Equilibrium Conditions of Their Decomposition

A study is made of the effect of the initial degree of supercooling on the equilibrium conditions of decomposition of hydrates of a model gas mixture comprised of 95.66 mol % CH4 + 4.34 mol. % C3H8. To ensure a high degree of conversion of water to hydrate, 0.1 wt. % sodium dodecyl sulfate (SDS) solution was used as the liquid phase in experiments performed in an RCS6 Sapphire Rocking Cell instrument. The hydrates were produced by cooling under isochoric conditions in a GHA350 gas hydrate autoclave and under isochoric-isothermic conditions on the RCS6 instrument. The hydrated samples that were obtained were decomposed by heating under isochoric conditions at the rate of 0.2 K/h. Analysis of the decomposition curves indicates that, depending upon the initial conditions, both mixed methane-propane hydrates of various compositions and methane hydrate are formed when the test gas mixture is hydrated. It is demonstrated that the proportion of the CH4 hydrate which is formed increases with an increase in the initial degree of overcooling during hydrate formation. The curve depicting the equilibrium hydrate decomposition conditions for the gas mixture has a more complex configuration than the simple exponential curve proposed earlier. The data that is obtained points to the existence of a multiplicity of equilibrium conditions for the hydrate decomposition of gas mixtures, with the exact conditions in a specific case depending on the degree of overcooling of the system during hydrate formation.