Determination of Gas Hydrate Safety Margin Using Specific Gravity

3852

Ind. Eng. Chem. Res. 2007, 46, 3852-3857

CORRELATIONS Determination of Gas Hydrate Safety Margin Using Specific Gravity Data of Salt or Organic Inhibitor 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, CNRS FRE 2861, 35 Rue Saint Honore´ , 77305 Fontainebleau, France

Injection of gas hydrate inhibitors at the upstream of oil/gas pipelines is normally 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 many cases, high safety margins are used to account for the uncertainties in the above factors and minimize the gas hydrate formation risks as no means of controlling and monitoring are generally available along the pipelines and/or downstream to assess the degree of hydrate inhibition. In this work, the possibility of predicting the hydrate safety margin from specific gravity data of aqueous solutions is investigated using a feed-forward artificial neural network method with a modified Levenberg-Marquardt algorithm. The method, which has been developed for various salts (NaCl, KCl, CaCl2, KBr, NaBr) and organic inhibitors (methanol, ethanol, ethylene glycol, glycerol) aqueous solutions, considers the changes in specific gravity of aqueous solution for estimating the hydrate stability zone. Independent data (not used in training and developing of the neural network) are used to examine the reliability of this tool. The predictions of this method are found to be in acceptable agreement with the independent experimental data, demonstrating the reliability of the artificial neural network method for estimating the hydrate safety margin using specific gravity data of salt or organic inhibitor aqueous solutions. 1. Introduction Gas hydrates are solid crystalline compounds formed from mixtures of water and guest molecules of suitable sizes. On the basis of hydrogen bonding, water molecules form unstable lattice structures with several interstitial cavities. The gas molecules can occupy the cavities and, when a minimum number of cavities are occupied, the crystalline structure becomes stable and solid gas hydrates are formed, even at temperatures well above the ice point.1,2 Formation of gas hydrates can lead to serious problems in the petroleum industry. Low temperatures combined with high fluid pressures can promote formation of gas hydrates in hydrocarbon-water fluid mixtures, which can block pipelines/ transfer lines and production/processing facilities.1,2 The conventional method to prevent or reduce gas hydrate formation risks is to use organic inhibitors, which shift the hydrate phase boundaries to high pressures/low temperatures. The common industry practice is to use methanol or ethylene glycol.1,2 Furthermore, for pipelines carrying a cocktail of multiphase fluids including hydrocarbons and formation water with different concentrations of salts, saline water may provide the required protection. Gas hydrate inhibitors are normally 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 organic inhibitor loss to the nonaqueous phases. In general, no means of controlling and monitoring are available along the pipeline and/or downstream * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +(33) 1 64 69 49 65. Fax: +(33) 1 64 69 49 68.

to assess the degree of gas 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.1-3 Downstream monitoring could significantly reduce the risks associated with gas hydrate formation. Systematic ways of hydrate phase equilibrium monitoring along the pipeline and/ or downstream to examine the degree of inhibition are very limited and can be produced on the basis of properties of the aqueous phase.3 The use of aqueous phase properties for determining hydrate inhibition effects of inhibitors can also be regarded as a useful remark to reduce experimental information required to evaluate the hydrate stability zone, as measuring these properties is normally easier than measuring the hydrate stability zone in the presence of inhibitor and can reduce the experimental costs.3 The aim of this work is to show the possibility of using the artificial neural network (ANN) method for estimating the hydrate stability zone from the specific gravity of aqueous phase. For this purpose, a brief review is first made on specific gravity definition and the measurement methods to provide a better understanding of specific gravity. Among various ANNs reported in the literature, the feed-forward (back-propagation) neural network (FNN) method with a modified LevenbergMarquardt algorithm4-7 is used, which is known to be effective to represent the nonlinear relationships between variables in complex systems and can be regarded as a large regression method between input and output variables.8 The developed method is then used as a predictive tool, and its reliability is checked against data not used in the neural network training step. As a result of this study, we show that the predicted results are in acceptable agreement with experimental data. The

10.1021/ie060908j CCC: $37.00 © 2007 American Chemical Society Published on Web 05/02/2007

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3853

developed ANN based method can be considered as a reliable tool for predicting hydrate inhibition effects of thermodynamic inhibitors from specific gravity data of aqueous phases. 2. Specific Gravity Specific gravity, sp.gr, is equal to the density of the material divided by some reference density (most often the density of water in well-defined conditions but sometimes the air when comparing to gases):9

sp.gr )

Fobject Freference

(1)

where F denotes density. Because water’s density is 1.0 × 103 kg/m3 in SI units at standard conditions, the specific gravity of a material is approximately the density of the material measured in kg/m3 divided by 1000 (the density of water). Specific gravity is stated for a certain temperature normally at 293.15 K.9 There are empirical equations for calculating the influence of temperature on density. A common device for measuring fluid density (and therefore specific gravity) is a pycnometer, which is also known as a specific gravity bottle.9 A pycnometer is a flask with a closefitting ground glass stopper with a fine hole through it, so a given volume can be accurately obtained.9 If the flask is weighed empty, full of water, and full of a liquid whose specific gravity is desired, the specific gravity of the liquid can easily be calculated.9 The pycnometer may not be an easy method to use in the purpose of monitoring, as batch analyses should be done after taking samples. The Vibrating tube densimeter can be preferred.10 The principle of a vibrating tube densimeter is the phenomenon in which the vibration period of the U-shaped tube changes with the densities of the sample fluid enclosed in the tube. The vibrating tube densimeter is the equipment that measures directly the vibration period of the U-shaped tube completely filled with the sample fluid, and then it relatively computes the densities of the sample fluid by applying a principle of a fixed relation between vibration period and density. It allows real time measurement by using a parallel circulation tubing and quasi-continuous specific gravity calculation to feed the computer fitted with an ANN method.10 In the present work, specific gravity data of various aqueous solutions containing salt or organic inhibitor at 293.15 K reported in the CRC Handbook of Chemistry and Physics11 were used. To better represent the specific gravity data of aqueous solutions, they were multiplied by 1000. 3. Artificial Neural Network Neural networks have many computational units connected in a massively parallel structure, learn by trial and error, and do not need an explicit formulation of the mathematical or physical relationships of the handled problem.12-15 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.12 The accuracy of model representation depends directly on the topology of the neural network. The most commonly used ANNs are the FNNs, which are designed with one input layer, one output layer, and hidden layers.13-16 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 such as Bayesian regularization, together with a Levenberg-Marquardt algorithm, can help overcome this problem.13-16 In the present work, the FNN method with a single hidden layer13-15 was devoted to the computation of the hydrate suppression temperature (or suppression of hydrate dissociation temperature (output neuron) which is defined as the difference between hydrate dissociation temperature in the presence of salt aqueous solution and hydrate dissociation temperature in the presence of distilled water at a given pressure) as a function of the specific gravity of aqueous solution at 293.15 K and molecular weight of inhibitor (input neurons, which represents the type of inhibitor). 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.8 The neuron of the output layer simply performs a weighted summation of the outputs of the hidden neurons.8 Three types of transfer functions were tested: the tangent sigmoid, exponential sigmoid, and linear. The former transfer function yields better results. The bias is set to 1 to add a constant to the weighted sum for each neuron of the hidden layer.8 The mathematical form for the hydrate suppression temperature can be expressed by the following equation: m

∆T )

wif(Vi) ∑ i)1

(2)

1 - e-Vi 1 + e-Vi

(3)

f(Vi) )

Vi ) w1i × sp.gr + w2i × M + w3i

(4)

where ∆T, w, f, V, sp.gr, M, and m stand for hydrate suppression temperature in K, weight, function, weighted sum of input to the hidden neuron i, specific gravity of the aqueous solution at 293.15 K, molecular weight of inhibitor, and number of neurons in the hidden layer, respectively. Subscript i represents the hidden layer. In the above equations, 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 searching for both the lowest value of the minimized objective function and generalizing 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.13-15 The parameters w1i, w2i, and w3i in the summations, which are usually referred to as the weights, are the fitting parameters of the ANN (these parameters are available on request). 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 to as the learning of the ANN, is performed using a modified Levenberg-Marquardt algorithm.4-7 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 can provide predictions of hydrate phase boundaries in the presence of salt or organic inhibitor using the following equation:

3854

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007

T ) T0 - ∆T

(5)

where T represents hydrate dissociation temperature of fluid (K) in the presence of aqueous solution containing salt or organic inhibitor and T0 stands for hydrate dissociation temperature of the same fluid system in the presence of distilled water (K), which can be calculated using an appropriate predictive method such as the general correlation reported by Østerggard et al.18 4. Results and Discussions The hydrate suppression temperature and specific gravity data for various aqueous solutions with wide ranges of salt or organic inhibitors were used in this study as shown in Figure 1. As can be seen, hydrate suppression temperature versus specific gravity for aqueous solutions containing salt or organic inhibitor show a complex behavior, and therefore ANNs can be used to correlate these data. Table 1 indicates concentration ranges and the number of data used in this work. As can be seen, the data for more frequently used organic inhibitors and salts were employed for developing the neural network. The results coming from a general predictive method17 for hydrate suppression temperature due to the presence of salt or organic inhibitor in aqueous solution were used as pseudo-experimental hydrate suppression temperature. It should be mentioned that the hydrate suppression temperature is generally a function of various factors such as pressure and fluid composition.17 These factors can be ignored for engineering purposes in calculating hydrate suppression temperatures due to the presence of salt or organic inhibitor aqueous solutions. However, they become important in systems containing mixed salt and organic inhibitor, especially at high concentrations. In this study, the effect of gas composition (and therefore hydrate structure) and the pressure of the system on hydrate suppression temperature were ignored for engineering purposes. All the aqueous systems were then assumed to be in contact with methane, and the hydrate suppression temperatures for these systems were calculated at 20 MPa from the predictive method.17 The reasons for using the computed data for hydrate suppression temperatures rather than real experimental data are as follows: 1. The amount of experimental hydrate suppression temperature data is limited. 2. Because of the limited experimental data, any error could easily result in unreliable correlation. 3. Experimental data can be used for validation of correlation. The ANN method shown in Figure 2 and detailed in Table 2 with one hidden layer was devoted to the computation of the hydrate suppression temperature as a function of the specific gravity of the aqueous solution and molecular weight of the inhibitor (salt or organic inhibitor). 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 8. Figure 3a compares the calculated hydrate suppression temperature from the ANN with hydrate suppression temperatures used in developing (training) this method. The differences between pseudo-experimental hydrate suppression temperatures (∆Texp) employed for training and calculated hydrate suppression temperatures (∆Tcal) from the ANN in function of the pseudo-experimental hydrate suppression temperatures are also shown in Figure 3b for various salt and organic inhibitor aqueous solutions. As can be seen, acceptable agreement was achieved (maximum difference equals 1 K).

Figure 1. Hydrate suppression temperature (∆T, K) as a function of the specific gravity (sp.gr) of aqueous solution at 293.15 K for various salts and organic inhibitors: b, glycerol; 4, CaCl2; ×, NaBr; +, KBr; O, NaCl; 2, EG; ], KCl; [, EtOH; and 0, MeOH. The results coming from a general predictive method17 for hydrate suppression temperature due to the presence of salt or organic inhibitor in aqueous solution were employed as the pseudoexperimental hydrate suppression temperature. Specific gravity data of aqueous solutions at 293.15 K were taken from ref 13. All the aqueous systems were assumed to be in contact with methane, and the hydrate suppression temperatures for these systems were calculated at 20 MPa from the predictive method.17 Table 1. Maximum Weight Percents and Number of Experimental Points for the Data of the Learning Sets on Hydrate Suppression Temperature and Specific Gravity (at 293.15 K) of Aqueous Solution Used for Developing this Method salt or organic inhibitor

maximum wt %

no. of points

NaCl KCl CaCl2 KBr NaBr MeOH EtOH EG glycerol

23 13 32 32 34 44 14 48 48

12 7 16 16 17 22 7 17 17

Figure 2. Topology of the neural network method used for predicting the hydrate suppression temperature as a function of the specific gravity of the aqueous solution at 293.15 K and molecular weight of inhibitor for salts and organic inhibitors shown in Table 1 (1, bias; b, neuron; output neuron, hydrate suppression temperature; input neurons, specific gravity of aqueous solution at 293.15 K and molecular weight of inhibitor).

It is of interest to compare predictions of the method developed in this work with some selected experimental data from the literature. Figure 4 shows a comparison between the predictions of this method, the HWHYD thermodynamic

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3855 Table 2. Number of Neurons, Hidden Layers, Parameters, Data, and Types of Function Used in This Methoda layer

number of neurons

1 2 3

2 8 1

a Number of hidden layers ) 1. Number of parameters ) 33. Number of data used for training and testing ) 131. Type of function: tangent sigmoid.

Figure 4. Hydrate dissociation conditions of methane in the presence of aqueous solutions composed of NaCl. Experimental data: ], 3 wt % NaCl;19 4, 10 wt % NaCl;19 O, 20 wt % NaCl;20 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.17

Figure 3. a: Calculated hydrate suppression temperature (∆T, K) from the ANN method versus data of the learning sets mentioned in Table 1. b: Difference between pseudo-experimental hydrate suppression temperature (coming from a general predictive method;17 ∆Texp, K) and calculated hydrate suppression temperature (from the ANN method; ∆Tcal, K) as a function of the pseudo-experimental hydrate suppression temperature for various salt and organic inhibitor aqueous solutions (maximum difference equals 1 K): b, glycerol; 4, CaCl2; ×, NaBr; +, KBr; O, NaCl; 2, EG; ], KCl; [, EtOH; and 0, MeOH.

model,17 and experimental data19,20 for hydrate dissociation conditions of methane in the presence of aqueous solutions containing different concentrations of NaCl. Figures 5 and 6 compare the predictions of this method, the HWHYD thermodynamic model,17 and experimental data21,22 for the hydrate phase boundary of methane in the presence of aqueous solutions containing different concentrations of methanol and ethylene glycol, respectively. As shown in the figures, the predictions of the methods are generally in acceptable agreement with the experimental data. However, the results of these predictive methods show some deviations at some points. These deviations can be attributed to unreliability of some experimental data, as the logarithm of the hydrate dissociation pressure (P) versus temperature of the system is approximately linear and, therefore, any deviation of experimental data from the linear behavior indicates unreliability of the data.

Figure 5. Hydrate dissociation conditions of methane in the presence of aqueous solutions composed of methanol. Experimental data: ], 10 wt % methanol;21 4, 20 wt % methanol;21 0, 35 wt % methanol;22 O, 50 wt % methanol;22 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.17

Figures 7 and 8 compare the predictions of the method developed in this work and the HWHYD thermodynamic model17 with experimental data23 for hydrate dissociation conditions of a synthetic gas mixture containing 97.25 mol % methane + 1.42 mol % ethane + 1.08 mol % propane + 0.25 mol % 2-methylpropane in the presence of 10 wt % KCl and 10 wt % CaCl2 aqueous solutions, respectively. As shown in the figures, the predictions of the methods are generally in acceptable agreement with each other. However, the results of these predictive methods show some deviations from experimental data. These deviations may be attributed to unreliability of experimental data. The use of this predictive method is not recommended at very high concentrations of salts, as the data up to intermediate concentrations of salts (Table 1) have been used for developing this method and high concentrations may lead to salt precipitation, which may affect calculations of the hydrate phase boundary. This method cannot clearly provide reliable results for organic inhibitors that take part in hydrate formation.24 5. Conclusions A feed-forward ANN method was developed for estimating hydrate suppression temperature from specific gravity data of

3856

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007

Figure 6. Hydrate phase boundary of methane in the presence of aqueous solutions composed of ethylene glycol. Experimental data: 0, 10 wt % ethylene glycol;22 4, 30 wt % ethylene glycol;22 ×, 50 wt % ethylene glycol;22 bold solid curves, predictions of this predictive method; solid curves, predictions of the HWHYD model.17

Figure 8. Hydrate phase boundary of a synthetic gas mixture containing 97.25 mol % methane + 1.42 mol % ethane + 1.08 mol % propane + 0.25 mol % 2-methylpropane in the presence of aqueous solution composed of 10 wt % CaCl2. Experimental data: O, 10 wt % CaCl2;23 bold solid curve, predictions of this predictive method; solid curve, predictions of the HWHYD model.17

sp.gr ) specific gravity V ) weighted sum of input to the hidden neuron i w ) weight Greek Symbols ∆T ) hydrate suppression temperature (or suppression of hydrate dissociation temperature), K, which is defined as the difference between hydrate dissociation temperature in the presence of salt aqueous solution and hydrate dissociation temperature in the presence of distilled water at a given pressure F ) density Subscripts Figure 7. Hydrate phase boundary of a synthetic gas mixture containing 97.25 mol % methane + 1.42 mol % ethane + 1.08 mol % propane + 0.25 mol % 2-methylpropane in the presence of aqueous solution composed of 10 wt % KCl. Experimental data: 0, 10 wt % KCl;23 bold solid curve, predictions of this predictive method; solid curve, predictions of the HWHYD model.17

cal ) calculated property exp ) (pseudo)experimental property i ) hidden layer 0 ) index for hydrate dissociation temperature of the fluid system in the presence of distilled water

aqueous solutions containing salt or organic inhibitor. The developed neural network was combined with a previously reported general correlation, which is capable of predicting hydrate phase boundaries of petroleum fluids in the presence of distilled water, to estimate the hydrate stability zone using specific gravity data of salt or organic inhibitor aqueous solution. The method achieved acceptable accuracy when its predictions were compared with independent experimental data. The developed method can be regarded as a practical tool for estimating hydrate safety margin in oil and gas production, transportation and processing facilities.

Literature Cited

Nomenclature ANN ) artificial neural network FNN ) feed-forward (back-propagation) neural network M ) molecular weight of inhibitor (which represents the type of inhibitor) P ) hydrate dissociation pressure, MPa T ) hydrate dissociation temperature, K f ) function m ) number of neurons in the hidden layer

(1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker, Inc.: New York, 1998. (2) Sloan, E. D. A changing hydrate paradigmsfrom apprehension to avoidance to risk management. Fluid Phase Equilib. 2005, 228-229, 6774. (3) Najibi, H.; Mohammadi, A. H.; Tohidi, B. Estimating the Hydrate Safety Margin in the Presence of Salt and/or Organic Inhibitor Using Freezing Point Depression Data of Aqueous Solutions. Ind. Eng. Chem. Res. 2006, 45, 4441-4446. (4) 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). (5) Wilamowski, B.; Iplikci, S.; Kayank, O.; Efe, M. O. International Joint Conference on Neural Networks (IJCNN′01), Washington, DC, July 15-19, 2001; pp 1778-1782. (6) Marquardt, D. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. SIAM J. Appl. Math. 1963, 11, 431-441. (7) Levenberg, K. A Method for the Solution of Certain Problems in Least Squares. Q. Appl. Math. 1944, 2, 164-168. (8) Normandin, A.; Grandjean, B. P. A.; Thibault, J. PVT Data Analysis Using Neural Network Models. Ind. Eng. Chem. Res. 1993, 32, 970975. (9) Wikipedia encyclopedia. http://en.wikipedia.org/wiki/density (accessed July 2006).

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3857 (10) Bouchot, C.; Richon, D. Direct Pressure-Volume-Temperature and Vapor-Liquid Equilibrium Measurements with a Single Equipment Using a Vibrating Tube Densimeter up to 393 K and 40 MPa: Description of the Original Apparatus and New Data. Ind. Eng. Chem. Res. 1998, 37, 32953304. (11) Weast, R. C.; Astle, M. J.; Beyer, W. H. CRC Handbook of Chemistry and Physics, 65th ed.; CRC Press, Inc.,: Boca Raton, FL, 19841985. (12) 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. (13) Chouai, A.; Laugier, S.; Richon, D. Modeling of thermodynamic properties using neural networks: Application to refrigerants. Fluid Phase Equilib. 2002, 199, 53-62. (14) 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, 1182-1194. (15) Scalabrin, G.; Marchi, P.; Bettio, L. and Richon, D. Enhancement of the extended corresponding states techniques for thermodynamic modelling. II. Mixtures. Int. J. Refrig. 2006, 29, 1195-1207. (16) 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. (17) Heriot-Watt University Hydrate model. http://www.pet.hw.ac.uk/ research/hydrate/ (accessed July 2006) (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, 70-80). (18) 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, 228-233.

(19) 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. (20) Kobayashi, R.; Withrow, H. J.; Williams, G. B.; Katz, D. L. Gas Hydrate Formation with Brine and Ethanol Solutions. Proceedings of 30thAnnual ConVention Natural Gasoline Association of America; 1951; pp 27-31. (21) 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. (22) Robinson, D. B.; Ng, H.-J. Hydrate formation and inhibition in gas or gas condensate streams. J. Can. Pet. Technol. 1986 (July-August), 26-30. (23) 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, 178-182. (24) Østergaard, K. K.; Tohidi, B.; Anderson, R.; Todd, A. C.; Danesh, A. Can 2-Propanol Form Clathrate Hydrates? Ind. Eng. Chem. Res. 2002, 41, 2064-2068.

ReceiVed for reView July 13, 2006 ReVised manuscript receiVed March 19, 2007 Accepted April 2, 2007 IE060908J