Estimating the Hydrate Safety Margin in the Presence of Salt or

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Ind. Eng. Chem. Res. 2006, 45, 8207-8212

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Estimating the Hydrate Safety Margin in the Presence of Salt or Organic Inhibitor Using Refractive Index Data of Aqueous Solution Amir H. Mohammadi and Dominique Richon* Centre Energe´ tique et Proce´ de´ s, Ecole Nationale Supe´ rieure des Mines de Paris, CEP/TEP, 35 Rue Saint Honore´ , 77305 Fontainebleau, France

Gas hydrate inhibitors are currently injected at the upstream of pipelines based on the calculated/measured hydrate stability zone, worst case scenarios for pressure and temperature conditions, water cut, and the inhibitor loss to the nonaqueous phases. In general, no means of controlling and monitoring are available along the pipeline and/or downstream to assess the degree of hydrate inhibition. In many cases, high safety margins are used to account for the uncertainties in the above factors and minimize the gas hydrate formation risks. In this work, the possibility of predicting the hydrate safety margin from refractive index data of aqueous solutions is investigated using an artificial neural network method, which ensures high flexibility of the functional form for the regression. The developed method considers the changes in index of refraction with respect to refractive index of pure water for a given aqueous solution. Independent data are used to examine the reliability of this tool. The predictions of this method are in acceptable agreement with the independent experimental data, demonstrating the reliability of the artificial neural network method for estimating the hydrate safety margin in the presence of salt or organic inhibitor using refractive index data of aqueous solutions. 1. Introduction Gas hydrates are solid crystalline compounds stabilized by the inclusion of suitably sized gas molecules inside cavities, of different sizes, formed by water molecules through hydrogen bonding. They resemble ice in appearance, but unlike ice, they may form at temperatures well above the ice point. Gas hydrates have been reviewed in depth by Sloan.1 Gas hydrate formation can lead to serious problems in the petroleum industry. Oil and gas pipelines normally convey a cocktail of multiphase fluids including hydrocarbons and formation water with various concentrations of salts and organic inhibitors and may therefore be prone to hydrate formation, which potentially can block pipelines/transfer lines and lead to serious economic, operational, and safety problems. Therefore, the issue of hydrate phase boundary determination has received much attention over the years.1 Today, comprehensive thermodynamic models, mostly based on equations of state and statistical thermodynamics, are available for hydrate equilibrium predictions. Lately, a changing hydrate paradigm from apprehension to avoidance to risk management has been reported.2 Systematic ways of hydrate monitoring along the pipeline and/ or downstream to examine the degree of inhibition are very limited. Hydrate monitoring systems can be produced on the basis of properties of the aqueous phase. The aim of this work is to indicate the capability of artificial neural networks (ANN) for predicting hydrate inhibition effects of thermodynamic inhibitors from refractive index data of the aqueous phase. To our knowledge, this method has not been previously reported for predicting hydrate inhibition effects of thermodynamic inhibitors and can provide fast and accurate estimation of hydrate suppression temperature. Among various ANNs reported in the literature, the feed-forward (backpropagation) neural network (FNN) method with a modified Levenberg-Marquardt algorithm3,4 is used, which is known to be effective in representing the nonlinear relationships between * To whom correspondence should be addressed. Tel.: +(33) 1 64 69 49 65. Fax: +(33) 1 64 69 49 68. E-mail: [email protected].

variables in complex systems and can be regarded as a large regression method between input and output variables.5 The developed method is then used to predict independent data. It is shown that the results are in acceptable agreement demonstrating the ability and reliability of the ANN-based method for predicting hydrate inhibition effects of thermodynamic inhibitors from refractive index data of the aqueous phase. 2. Index of Refraction The refractive index (or index of refraction) of a material is the most important property of any optical system that uses refraction. Since refractive index is a fundamental physical property of a substance, it is often used to identify a particular substance, confirm its purity, or measure its concentration. Refractive index is used to measure solids, liquids, and gases. Most commonly it is used to measure the concentration of a solute in an aqueous solution. A refractometer is the instrument used to measure refractive index.6 A brief description of the principles of refractometers is given in the Appendix. The refractive index of a material is the factor by which the phase velocity, the rate at which the phase of the waveform is moving, of electromagnetic radiation is slowed in that material, relative to its velocity in a vacuum. It is usually given the symbol n and defined for a material by6

n ) xrµr

(1)

where r is the material’s relative permittivity and µr is its relative permeability. For a nonmagnetic material, µr is very close to 1; therefore,

n ≈ xr

(2)

The speed of all electromagnetic radiation in a vacuum is the same, approximately 3 × 108 m/s, and is denoted by c. Therefore, if V′ is the velocity of radiation of a specific frequency in a specific material, the refractive index is given by6

10.1021/ie060773h CCC: $33.50 © 2006 American Chemical Society Published on Web 10/28/2006

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n)

c V′

(3)

This number is typically greater than one: the higher the index of the material, the more the light is slowed. However, at certain frequencies (e.g. near absorption resonances and for X-rays), n will actually be smaller than one. Many materials have a well-characterized refractive index, but these indices depend strongly upon the wavelength of light. Therefore, any numeric value for the index is meaningless unless the associated wavelength is specified. There are also weaker dependencies on temperature, pressure/stress, etc., as well as on precise material compositions (presence of dopants, etc.); for many materials and typical conditions, however, these variations are at the percent level or less. Thus, it is especially important to cite the source for an index measurement if precision is required.6 Refractive index data are normally reported at ambient temperature. There are empirical equations for calculating the influence of temperature on the index of refraction. In the present work, refractive index data at 293.15 K relative to air for sodium yellow light reported in CRC Handbook of Chemistry and Physics7 are used. To better represent the difference in refractive indexes of aqueous solutions, the indexes of refraction increments above the index of refraction of pure water (n0) at 293.15 K are employed. 3. Artificial Neural Network Artificial neural networks mimic the behavior of biological neurons and learn by trial and error.8 These methods have large numbers of computational units connected in a massively parallel structure9 and do not need an explicit formulation of the mathematical or physical relationships of the handled problem.3 The ANNs are first subjected to a set of training data consisting of input data together with corresponding outputs. After a sufficient number of training iterations, the neural network learns the patterns in the data fed to it and creates an internal model, which it uses to make predictions for new inputs.8 The accuracy of model representation depends directly on the topology of the neural network. The most commonly used ANNs are the feed-forward neural networks and the radial basis function (RBF) networks.10 Feedforward neural networks are the most frequently used and are designed with one input layer, one output layer, and hidden layers.9 The number of neurons in the input and output layers equals the number of inputs and outputs, respectively. The disadvantage of FNNs is the determination of the ideal number of neurons in the hidden layer(s); few neurons produce a network with low precision, and a higher number leads to overfitting and bad quality of interpolation and extrapolation. The use of techniques such as Bayesian regularization, together with a Levenberg-Marquardt algorithm, can help overcome this problem.9,10 The RBFs use a Bayesian decision strategy, and each input has normally its distance from the input vector calculated in the first layer. This process results in a vector whose elements indicate how close the input is in relation of the training input. The second layer produces a vector of probabilities that will be used in the determination of the input class.10 It is believed that the design of RBFs is faster than that of their feed-forward counterparts, and their generalization capabilities are good. However, the number of neurons for RBFs depends on the size of the input set, and the RBFs are therefore bigger than the FNNs.10

In this work, the FNN method with a single hidden layer9 is devoted to the computation of the hydrate suppression temperature (output neuron) as a function of the index of refraction increments above the index of refraction of pure water at 293.15 K and the molecular weight of the inhibitor (input neurons). In this method, each neuron of the hidden layer performs two tasks: a weighted summation of its input and the application of the transfer function to this summation.5 The neuron of the output layer simply performs a weighted summation of the outputs of the hidden neurons.5 Three types of transfer functions were tested: the exponential sigmoid, tangent sigmoid, and linear. The former transfer function yields better results. The bias is set to 1 in order to add a constant to the weighted sum for each neuron of the hidden layer.5 The mathematical form for the hydrate suppression temperature can be expressed by the following equation: m

∆T )

wif(Vi) ∑ i)1

(4)

1 1 + e-Vi

(5)

f(Vi) )

Vi ) w1indiff + w2i ln(M) + w3i

(6)

ndiff ) [n - n0] × 104

(7)

where ∆T, w, f, V, ndiff, M, and m stand for hydrate suppression temperature in kelvin, weight, function, weighted sum of input to the hidden neuron i, the index of refraction increments above the index of refraction of pure water at 293.15 K × 104, the molecular weight of the inhibitor, and the number of neurons in the hidden layer, respectively. Subscript i represents the hidden layer. As can be seen, the inputs that represent the independent variables enter the neurons of the input layers, and then the transfer function f(Vi) converts the inputs to outputs in the neurons. The number of neurons in the hidden layer can be varied by searching for both the lowest value of the minimized objective function and generalizing the capability of the ANN method for various conditions. In fact by changing the number of neurons in the hidden layer, it is possible to change the mathematical form of the shape function aiming to a higher accuracy of the final model.9 Few hidden neurons hinder the learning process, and too many occasionally degrade the generalizing capability of the network.5 The parameters w1i, w2i, amd w3i in the summations, which are usually referred as the weights, are the fitting parameters of the ANN. These parameters can be found by applying a least-squares regression procedure to a given set of experimental data. The fitting procedure, which is normally referred as the learning of the ANN, is performed using a modified Levenberg-Marquardt algorithm.3,4,9 The objective function corresponding to the difference in hydrate suppression temperature is the sum of squares of relative deviations between the pseudo-experimental and calculated values. The above method is finally used to predict hydrate phase boundaries in the presence of salt or organic inhibitor using the following expression:

T ) T0 - ∆T

(8)

where T is the hydrate dissociation temperature of fluid (K) in the presence of aqueous solution containing salt or organic inhibitor and T0 represents the hydrate dissociation temperature of the same fluid system in the presence of distilled water (K),

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Figure 1. Hydrate suppression temperature as a function of the index of refraction increments above the index of refraction of pure water (i.e., (n - n0) × 104) at 293.15 K for various organic inhibitors and salts: 0, MeOH; [, EtOH; 2, EG; b. glycerol; O, NaCl; ], KCl; 4, CaCl2; ×, NaBr; +, KBr; 9, BaCl2; s, MgCl2; *, K2CO3; large open box, Na2SO4. Table 1. Maximum Weight Percent of Organic Inhibitor/Salt for Data of the Learning Sets on Hydrate Suppression Temperaturea and Refractive Index of Aqueous Solutionsb Used for Developing This Methodc organic inhibitor/salt MeOH EtOH EG glycerol NaCl KCl CaCl2 KBr NaBr BaCl2 MgCl2 K2CO3 Na2SO4

max wt %

no. of points

44 14 48 48 23 13 32 32 34 16 5 36 5

22 7 17 17 12 7 16 16 17 9 5 15 5

Figure 2. Topology of the neural network method used for predicting the hydrate suppression temperature as a function of the index of refraction increments above the index of refraction of pure water (i.e., (n - n0) × 104) at 293.15 K and molecular weight of inhibitor (1, bias; b, neuron; output neuron, hydrate suppression temperature; input neurons: (n - n0) × 104 at 293.15 K and the Neperian logarithm of inhibitor molecular weight. Table 2. Number of Neurons, Hidden Layers,a Parameters,b Data,c and Typed of Function Used in This Method layer

no. of neurons

1 2 3

2 7 1

a Number of hidden layers ) 1. b Number of parameters ) 29. c Number of data used for training ) 165. d Type of function: exponential sigmoid.

a Hydrate suppression temperatures for these systems were calculated from a previously reported predictive method.11 b Refractive index data reported in CRC Handbook of Chemistry and Physics7 were used. c All these aqueous systems were assumed to be in contact with methane.

which can be calculated using an appropriate predictive method such as the general correlation reported by Østerggard et al.12 4. Results and Discussions As shown in Figure 1 and Table 1, the hydrate suppression temperature and refractive index data for various aqueous solutions with wide ranges of salt or organic inhibitors were used in this study. All these aqueous systems were assumed to be in contact with methane, and the hydrate suppression temperatures for these systems were calculated at 20 MPa from a previously reported predictive method,11 and the effect of gas composition (and therefore hydrate structure) and the pressure of the system were ignored for engineering purposes.1 The ANN method shown in Figure 2 and detailed in Table 2 with one hidden layer is devoted to the computation of the hydrate suppression temperature in function of the index of refraction increments above the index of refraction of pure water at 293.15 K (i.e., (n - n0) × 104) and the Neperian logarithm of inhibitor molecular weight. The number of the hidden neurons was varied between 2 and 9, and the best value according to both the accuracy of the fit (minimum value of the objective function) and the predictive power of the neural network was found to be 7. Figure 3 compares the results of ANN with hydrate suppression temperatures used in developing this method. As can be seen, acceptable agreement was achieved.

Figure 3. Calculated hydrate suppression temperature (HST) from the ANN method versus data of the learning sets reported in Table 1: 0, MeOH; [, EtOH; 2, EG; b, glycerol; O, NaCl; ], KCl; 4, CaCl2; ×, NaBr; +, KBr; 9, BaCl2; s, MgCl2; *, K2CO3; 0, Na2SO4.

Figure 4 shows a comparison between the predictions of this method, the HWHYD thermodynamic model11 and experimental data for hydrate dissociation conditions of carbon dioxide in the presence of various concentrations of methanol. Figures 5-7 compare predictions of this method and the HWHYD model11 for the hydrate phase boundary of methane in the presence of various concentrations of NaCl, methanol, and ethylene glycol aqueous solutions, respectively. As can be observed, the agreement between the predictions of the ANN method and the HWHYD model11 is generally acceptable. However, there are some deviations between the results of these predictive methods and experimental data. These deviations can be attributed to uncertainty at some experimental points. Limited information

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Figure 4. Hydrate phase boundary of carbon dioxide (liquid water-vaporhydrate equilibrium) in the presence of methanol. Experimental data: O, 10 wt % methanol;13 0, 20.02 wt % methanol;13 4, 35 wt % methanol;14 ], 50 wt % methanol;14 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.11

Figure 5. Hydrate phase boundary of methane in the presence of aqueous solutions composed of NaCl. Experimental data: ], 3 wt % NaCl;15 4, 10 wt % NaCl;16 O, 20 wt % NaCl;16 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.11

Figure 6. Hydrate phase boundary of methane in the presence of aqueous solutions composed of methanol. Experimental data: ], 10 wt % methanol;13 4, 20 wt % methanol;13 0, 35 wt % methanol;14 O, 50 wt % methanol;14 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.11

is available on hydrate dissociation conditions of fluids in the presence of calcium chloride and potassium chloride aqueous solutions. Figures 8 and 9 compare the predictions of the method developed in this work and the HWHYD thermodynamic

Figure 7. Hydrate phase boundary of methane in the presence of aqueous solutions composed of ethylene glycol. Experimental data: 0, 10 wt % ethylene glycol;17 4, 30 wt % ethylene glycol;17 ×, 50 wt % ethylene glycol;17 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.11

Figure 8. Hydrate phase boundary of a synthetic gas mixture containing 97.25% methane + 1.42% ethane + 1.08% propane + 0.25% 2-methylpropane in the presence of aqueous solution composed of 10 wt % KCl. Experimental data: O, 10 wt % KCl;18 bold solid curve, predictions of this predictive method; solid curve, predictions of the HWHYD model.11

Figure 9. Hydrate phase boundary of a synthetic gas mixture containing 97.25% methane + 1.42% ethane + 1.08% propane + 0.25% 2-methylpropane in the presence of aqueous solution composed of 10 wt % CaCl2. Experimental data: 4, 10 wt % CaCl2;18 bold solid curve, predictions of this predictive method; solid curve, predictions of the HWHYD model.11

model11 with experimental data for hydrate dissociation conditions of a synthetic gas mixture containing 97.25% methane + 1.42% ethane + 1.08% propane + 0.25% 2-methylpropane in

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the presence of aqueous solution composed of 10 wt % KCl and CaCl2, respectively. As shown in the figures, the predictions of the methods are generally in acceptable agreement with the independent data. However, the results of these predictive methods show some deviations. These deviations can be attributed to unreliability of experimental data. Clearly, this method cannot provide reliable results for thermodynamic inhibitors that take part in hydrate formation (e.g., 2-propanol). 5. Conclusions The possibility of estimating the hydrate safety margin in the presence of salt or organic inhibitor using refractive index data of aqueous solutions was investigated in this work by developing an artificial neural network method. The method achieved acceptable accuracy when compared with independent experimental data. 6. Appendix There are four main types of fluid refractometers: traditional handheld refractometers, digital handheld refractometers, Abbe refractometers, and inline process refractometers.6 A traditional handheld refractometer is a handheld analogue instrument for measuring refractive index that works on the critical angle principal. It utilizes lenses and prisms to project a shadow line onto a small glass reticle inside the instrument, which is then viewed by the user through a magnifying eyepiece. In use, a sample is sandwiched between a measuring prism and a small cover plate. Light traveling through the sample is either passed through to the reticle or totally internally reflected. The net effect is that a shadow line is formed between the illuminated area and the dark area. It is at the point that this shadow line crosses the scale that a reading is taken. Because refractive index is temperature-dependent, it is important to use a refractometer with automatic temperature compensation. Compensation is accomplished through the use of a small bimetal strip that moves a lens or prism in response to temperature changes.6 A digital handheld refractometer operates on the same general critical angle principle as a traditional handheld refractometer. The difference is that light from an LED (light-emitting diode) light source is focused on the underside or a prism element. When a liquid sample is applied to the measuring surface of the prism, some of the light is transmitted through the solution and lost, while the remaining light is reflected onto a linear array of photodiodes creating a shadow line. The refractive index is directly related to the position of the shadow line on the photodiodes. The more elements there are in the photodiode array, the more precise the readings will be, and the easier it will be to obtain readings for emulsions and other difficult-toread fluids that form fuzzy shadow lines. Once the position of the shadow line has been automatically determined by the instrument, the internal software will correlate the position to refractive index, or to another unit of measure related to refractive index, and display a digital readout on an LCD (liquid crystal display) or LED scale. Digital handheld refractometers are generally more precise than traditional handheld refractometers. Users should look for instruments with a digital display that is capable of displaying not just a reading but also the unit of measure of the substance (Brix, freezing point, boiling point, and concentration, etc.). A stainless steel sample holder makes it easier to clean, and an opaque cover over the sample area can prevent sample evaporation or ambient light from interfering with readings. Some instruments are available with multiple scales. It is important to select an instrument that can be set to

distilled water and can also accept traceable calibrations at an upper span point.6 An Abbe or laboratory refractometer is a benchtop refractometer that offers the highest precision of the different types of refractometers. Nearly a century and a half after their introduction, refractometers have come a long way in terms of usefulness, though their principle of operation has changed very little. These first instruments had built-in thermometers and required circulating water to control instrument and fluid temperatures. They also had adjustments for eliminating the effects of dispersion. These first instruments had analogue scales from which the readings were taken and still required the use of circulating water baths to control instrument and fluid temperature. They did, however, have the ability to electronically compensate for the temperature differences of certain fluids. The most advanced instruments of today use solid-state Peltier effect devices to heat and cool the instrument and the sample, eliminating the dependence on an external water bath. The software on most of the current instruments is now very advanced. One manufacturer utilizes Microsoft Windows as the operating system, providing familiar controls for the user, which translates into ease of use.6 An inline process refractometer is designed for the continuous measurement of a fluid flowing through a pipe or inside a tank. These refractometers typically consist of a sensor, placed inline with the fluid flow, coupled to a control box. The control box usually provides a digital readout as well as 4-20 mA analogue outputs and relays outputs for controlling pumps and valves.6 Nomenclature ANN ) artificial neural networks FNN ) feed-forward (back-propagation) neural network HST ) hydrate suppression temperature LCD ) liquid crystal display LED ) light-emitting diode M ) molecular weight of inhibitor RBF ) radial basis function network T ) hydrate dissociation temperature of fluid in the presence of aqueous solution containing salt or organic inhibitor T0 ) hydrate dissociation temperature of fluid in the presence of distilled water f ) function m ) number of neurons in the hidden layer n ) refractive index n0 ) index of refraction of pure water ndiff ) index of refraction increments above the index of refraction of pure water at 293.15 K × 104 V ) weighted sum of input to the hidden neuron i V′ ) phase velocity of radiation of a specific frequency in a specific material w ) weight Greek Letters ∆T ) hydrate suppression temperature r ) relative permittivity µr ) relative permeability Subscript i ) hidden layer Literature Cited (1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker Inc.: New York, 1998.

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(2) Sloan, E. D. A changing hydrate paradigmsFrom apprehension to avoidance to risk management. Fluid Phase Equilib. 2005, 228-229, 6774. (3) Rivollet, F. Etude des proprie´te´s volume´triques (PVT) d′hydrocarbures le´gers (C1-C4), du dioxyde de carbone et de l′hydroge`ne sulfure´: Mesures par densime´trie a` tube vibrant et mode´lisation. Ph.D. Thesis, Paris School of Mines, France, December 2005 (in French). (4) Wilamowski, B.; Iplikci, S.; Kayank, O.; Efe, M. O. International Joint Conference on Neural Networks, Proceedings (IJCNN’01) Washington, DC, July 15-19, 2001; Institute of Electrical and Electronics Engineers: Piscataway, NJ, 2001; pp 1778-1782. [Also: Marquardt, D. An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 1963, 11, 431-441. Levenberg, K. A method for the solution of certain problems in least squares. Q. Appl. Math. 1944, 2, 164168]. (5) Normandin, A.; Grandjean, B. P. A.; Thibault, J. PVT data analysis using neural network models. Ind. Eng. Chem. Res. 1993, 32, 970-975. (6) Wikipedia Encyclopedia, http://en.wikipedia.org/wiki/Refractive_index (7) Weast, R. C.; Astle, M. J.; Beyer, W. H. CRC Handbook of Chemistry and Physics, 65th ed.; CRC Press Inc.: Boca Raton, FL, 1984-1985. (8) Elgibaly, A. A.; Elkamel, A. M. A new correlation for predicting hydrate formation conditions for various gas mixtures and inhibitors. Fluid Phase Equilib. 1998, 152, 23-42. (9) Chouai, A.; Laugier, S.; Richon, D. Modeling of thermodynamic properties using neural networks: Application to refrigerants. Fluid Phase Equilib. 2002, 199, 53-62 (Also: Piazza, L.; Scalabrin, G.; Marchi, P.; Richon, D. Enhancement of the extended corresponding states techniques for thermodynamic modelling. I. Pure fluids. Int. J. Refrig. 2006, 29 (7), 1182-1194. Scalabrin, G.; Marchi, P.; Bettio, L.; Richon, D. Enhancement of the extended corresponding states techniques for thermodynamic modelling. II. Mixtures. Int. J. Refrig. 2006, 29 (7), 1195-1207.

(10) Schmitz, J. E.; Zemp, R. J.; Mendes, M. J. Artificial neural networks for the solution of the phase stability problem. Fluid Phase Equilib. 2006, 245, 83-87. (11) Heriot-Watt UniVersity Hydrate Model, http://www.pet.hw.ac.uk/ research/hydrate/ (Also: Østergaard, K. K.; Masoudi, R.; Tohidi, B.; Danesh, A.; Todd, A. C. A general correlation for predicting the suppression of hydrate dissociation temperature in the presence of thermodynamic inhibitors. J. Pet. Sci. Eng. 2005, 48 (1-2), 70-80). (12) Østergaard, K. K.; Tohidi, B.; Danesh, A.; Todd, A. C.; Burgass, R. W. A general correlation for predicting the hydrate-free zone of reservoir fluids. SPE Prod. Facil. 2000, 15 (4), 228-233. (13) Ng, H.-J.; Robinson, D. B. Hydrate formation in systems containing methane, ethane, propane, carbon dioxide or hydrogen sulfide in the presence of methanol. Fluid Phase Equilib. 1985, 21, 145-155. (14) Robinson, D. B.; Ng, H.-J. Hydrate formation and inhibition in gas or gas condensate streams. J. Can. Pet. Technol. 1986 (Jul-Aug), 2630. (15) Dholabhai, P. D.; Englezos, P.; Kalogerakis, N.; Bishnoi, P. R. Equilibrium conditions for methane hydrate formation in aqueous mixed electrolyte solutions. Can. J. Chem. Eng. 1991, 69, 800-805. (16) Kobayashi, R.; Withrow, H. J.; Williams, G. B.; Katz, D. L. Gas hydrate formation with brine and ethanol solutions. Proc. Annu. ConV. Nat. Gasoline Assoc. Am., Tech. Pap. 1951, 30, 27-31. (17) Robinson, D. B.; Ng, H. J. J. Can. Petrol. Technol. 1986 (JulAug), 26. (18) Mei, D. H.; Liao, J.; Yang, J. T.; Guo, T. M. Hydrate formation of a synthetic natural gas mixture in aqueous solutions containing electrolyte, methanol, and (electrolyte + methanol). J. Chem. Eng. Data 1998, 43, 178182.

ReceiVed for reView June 16, 2006 ReVised manuscript receiVed August 30, 2006 Accepted September 19, 2006 IE060773H