Density, phase behavior keys to acid gas injection

An accurate fluid density is important for predicting injection pressures for acid gas disposal wells.

The design engineer should carefully consider the method for estimating fluid density and should be aware of the shortcomings of commercial simulator packages.

Each case needs to be considered individually for density, nonaqueous phase equilibrium, hydrate formation, and aqueous phase formation. The engineer should make his own approximate PVT diagram and phase envelope to ensure that the computer-generated results are not misleading.

As a rule of thumb, if the injection well pressures are greater than about 10 MPa (1,450 psia), then a second nonaqueous phase will generally not form. For pressures less than 10 MPa, the phase envelope should be checked to ensure that phase separation does not occur.

Excess methane can be the culprit when high injection pressures are encountered. Methane tends to reduce injection fluid density, which in turn increases the required injection pressure.

At higher flow rates to obtain accurate fluid temperature, the engineer must be certain that the following effects are indeed negligible:

• Pressure drop in the formation

• Pressure drop through the perforations

• Fluid friction in the tubing

• Heat transfer to the tubing at flowing conditions.

Pressure profiles

Injection compressor discharge pressure determines the compressor size needed. To obtain discharge pressure, one has to estimate the pressure at the wellhead (equation box).

If the fluid is an incompressible liquid (such as when the density is a constant and not a function of temperature and pressure), Equation 1 is easy to integrate to obtain the pressure profile. However, the fluids in acid gas injection are not incompressible. In fact, their densities are somewhat complicated functions of pressure and temperature.

First, the stream may be either gas or liquid depending upon temperature and pressure. Also, gases are highly compressible.

Second, near a critical point, which may occur, the density is very sensitive to changes in pressure and temperature.

Third, even in the liquid state, these streams are not completely incompressible, especially at pressures encountered in an injection scheme.

Thus, one must employ a method for integrating the equation that accounts for variable density.

In this article, the equation is integrated with a simple Euler method. This means that over a short distance (h), the density is assumed to be constant and equal to the temperature and pressure at the start of the interval (Equation 2).

Furthermore, lacking better information, it is assumed that there is a linear temperature profile from the surface to the formation. Thus, if one can calculate density as a function of temperature and pressure, one can obtain the pressure profile and, hence, the required injection pressure.

One important assumption in integrating this equation is that the fluid does not change phase over the length of the injection well. If there is a phase change, the fluid flow becomes more complicated and our simple analysis cannot be applied. For example, the well may start behaving as a very tall distillation column.

Phase change will be discussed later in this article.

Density calculations

It is clear, and not unexpected, that the injected fluid density is key for accurate injection pressure predictions.

The design engineer is well advised to understand the applicability range of the various methods that can calculate acid gas fluid density.

Tabulated data

When dealing with pure substances, the most accurate way to obtain density is from tabulated values. Tables are available for many substances, including methane, CO2, H2S, and water (commonly referred to as Steam Tables).^1-4

Unfortunately, these tables are significantly less useful for mixtures. Furthermore, few tables exist for mixtures.

Equations of state

Two common tools in process modeling are the Soave5 and Peng-Robinson6 equations of state. A well-known dichotomy is that, although these equations of state have the form as shown in Equation 3, they are not highly accurate for calculating densities, especially for liquids.

Other equations of state have been proposed that are better for liquid density calculations (such as the Patel-Teja and Trebble-Bishnoi), but these are not commonly available in commercial simulation programs.

The Benedict-Webb-Rubin equation is another more-accurate equation of state for density calculations. This is a multiconstant equation that is not cubic.

This equation and its modifications were once very popular but now are not commonly used. For example in Reference 7, the Benedict-Webb-Rubin equation rates very little coverage, except in relation to the Lee-Kesler correlation.

In a thorough review of cubic equations of state, Trebble and Bishnoi8 evaluated ten equations. They compiled a data base of 75 substances and calculated, among other things, saturated vapor and liquid densities.

Overall, the Peng-Robinson equation had an absolute average error of 8.59% in predicting saturated liquid densities and 5.53% in the vapor densities. By comparison, the Soave equation had absolute average errors of 17.60% and 6.01% for the liquid and vapor densities respectively. Other cubic equations fared better, but, as mentioned earlier, these are not commonly used.

Although these numbers are averages, they are good estimates of the magnitude of the errors that should be expected for calculating densities. However, predictions with better and worse errors than this should be anticipated; often much better and often much worse.

The strength of the cubic equations of state lies in their utility for calculating vapor-liquid equilibrium. This is a topic that will be discussed later in this article.

The shortcomings of these equations seem to be accepted simply to obtain accurate phase equilibrium calculations.

Volume shifting

One popular method for correcting the density predicted by an equation of state is called volume shifting or volume translation. This method was originally proposed for the Soave equation, but works equally well for the Peng-Robinson equation.

In this method, the molar volume calculated using the cubic equation of state is corrected as Equation 4.

Usually the value of c is evaluated based on the molar volume of the substance at its normal boiling point, but can be evaluated at any point in the pressure-temperature plane.

Alternatively, it could be fit to density data over a range of temperatures and pressures. Thus, it can be optimized to the conditions examined by the user.

Table 1 [44685 bytes] lists volume corrections developed in this study and the information used to derive them. Note, the correction factor can be either positive, which means the equation of state predicts a density greater than the true value, or if negative, the density is less.

If c is a constant then this is a very simple correction. However, in reality, c is a function of temperature.9 For example, c changes rapidly near the critical point.

For a mixture, the correction is made using a mole fraction weighted average of the pure component volume corrections (Equation 5).

One advantage of this approach is that the fluid phase equilibrium calculations are unaffected by the volume shifting. Another advantage is that the densities calculated for light gases are unaffected by this correction. That is, c is small in comparison to the molar volume of a low-density gas.

As seen in Table 1, c is quite small, about the same order of magnitude as the molar volume of the liquid. On the other hand, the molar volumes of gases are large, often several orders of magnitude larger than those of the liquid.

Thus, for low-pressure gases, the volume correction should have little effect. However, as the gas density becomes more liquid-like, this contribution becomes significant.

Often the volume shifted densities for high-density gases are poorer than those from the original equation of state. This can be a significant disadvantage in acid gas injection schemes because the fluid is often a high-density gas.

When using commercial simulators, the engineer is often at the disadvantage of not knowing whether volume shifting is included in the calculation or not.

As an example, consider an H2S and CO2 mixture. Robinson, et al.,10 measured densities for two such mixtures at 71.1° C. (160° F.) for pressures up to about 10.5 MPa (1,500 psia).

When the original Peng-Robinson equation is used to calculate the densities, the average error is 3.3%. When the calculated Peng-Robinson volumes are corrected using the information in Table 1, the average error increases to 4.9%. This demonstrates that volume shifting can worsen gas-density predictions.

Lee-Kesler tables

The principle of corresponding states is a powerful tool of applied thermodynamics. Generalized charts and tables can quickly provide estimates of physical and thermodynamic properties. The most recommended are the tables of Lee and Kesler,11 which are reproduced in many books on thermodynamics, including Reference 7.

The Lee-Kesler tables are useful for rapid, accurate hand calculations, but less useful for calculations that must be repeated several times. In addition, the correlation can be difficult to apply to mixtures.

Reference 7 discuses the mixing rules for this correlation.

The Lee-Kesler correlation, or a modification of it, is included in many simulation programs. Usually the simulator has the original equations for deriving the tables and not the tables themselves.

Costald correlation

Among the many correlations for the density of saturated pure liquids, the Costald or HBT (for Hankinson-Brobst-Thomson) correlation is the most popular.7 For pure components, it is very accurate and it has been extended to mixtures as well.

The required parameters are listed for a wide range of substances. Reference 7 lists over 400 substances, and correlations are provided for materials not on the list.

Methods for incorporating the effect of pressure have also been suggested. The correlation was designed for saturated liquids and thus, its range is limited to reduced temperatures of 0.95.

Many process simulators offer the user a split method for calculating fluid phase densities. Recognizing that cubic equations of state are not highly accurate for liquid densities, the user can choose a different approach for the liquid densities, and often this is the Costald correlation.

The simulator switches back to the equation of state once the conditions are outside the range of the liquid density correlation. One problem with this approach is that it generates a discontinuity in fluid density as the conditions change from a point where the fluid is clearly a liquid to one where the fluid is supercritical.

In this supercritical state, the fluid is often liquid-like, such as having a relatively high density. This is particularly true for acid gas injection schemes, where at the bottom hole conditions the fluid is supercritical with liquid-like densities.

Commercial simulators

Commercial simulation programs often do not indicate whether the equation of state uses volume shifting, a split equation, or how the program determines if it is in liquid or gas phase near the critical point.

For example, Fig. 1 [37598 bytes] is a density calculation printout from Hysim (Hyprotech Ltd.), using the Hyprotech enhanced Peng-Robinson for pure CO2. Here it can be seen that although the pressures are well above the critical pressure for CO2 of 1,070 psia (7.376 MPa), the program is automatically changing density correlations at the critical temperature 87.8° F. (31.0° C. or 304.2° K.).

Without a printout of Fig. 1, it would be hard to see that the calculations were in error. Also, another popular simulation package, Prosim (Bryan Research & Engineering) can give equally misleading results.

Usually the problem does not lie in the simulation package itself, but rather the default liquid density correlations that the user has control over.

The program defaults at run-time to the industry favorite correlation, which unfortunately may be a poor choice for acid gas.

Process simulation packages are sophisticated, and a lot of development has gone into them. There are good reasons why certain choices have been made by the developers. But it is ultimately up to the engineer to be satisfied that the models used in the simulation are appropriate for their application.

Phase equilibrium

The pure components involved in acid gas injection schemes, H2S, CO2, and methane, have been studied thoroughly, and their properties, including the vapor-liquid equilibrium, such as vapor pressure, are well understood.

Multicomponent mixtures have also been studied. Table 2 [101050 bytes] summarizes the experimental investigations into systems containing H2S, CO2, and methane. It is not an exhaustive list, but it is sufficient for our purposes. Note that many of the references include phases that are unlikely to occur in acid gas injection schemes, notably solid CO2.

Other investigations are at temperatures and pressures outside the range of interest in acid gas injection. These are included because a good correlation should be able to calculate equilibrium over a wide range of conditions.

Calculating phase equilibrium

The Peng-Robinson equation of state has a proven track record for accurate prediction of the phase equilibrium in petroleum systems. One advantage of performing phase equilibrium calculations with an equation of state is that it is theoretically possible to calculate the equilibrium right up to the critical point, although numerical stability often makes such calculations difficult.

In fact, equations of state can even be used to calculate the critical point. The reason is that the same model is used for both vapor and liquid.

Methods in which the vapor and the liquid have separate models are known to be very inaccurate at high pressures. These methods cannot be used to estimate critical points. One such example is the Chao-Seader correlation.

One trick for getting an equation of state to accurately calculate phase equilibrium is to include a binary interaction parameter. This parameter usually comes from experimental data, but some correlations also exist.

The importance of these parameters should not be underestimated. Occasionally, excluding them may predict the formation of "false" phases, (phases that do not exist in reality) or predicting an azeotrope that does not exist or not predicting one that does.

Carroll and Mather12 found that for mixtures of methane and H2S, the average error in the predicted bubble point pressures using the Peng-Robinson equation was 16.66% when an interaction parameter of zero was used. The error was reduced to 3.55%, a factor of more than four, when the optimal value was used.

This is a very significant improvement, but unfortunately, the user of commercial simulation packages is often unaware whether or not these parameters have been included. Or if they have not been included, they may not be able to add them.

Many process simulators and phase equilibrium packages allow the user to predict a wide range of phase equilibrium including phase envelopes. These are highly useful tools for understanding the system under consideration.

Water

Acid gases leave the amine plant saturated with water. The presence of water in the acid gas stream creates the possibility of forming condensed phases such as a hydrate and an aqueous liquid.

Hydrates

Generally, there are two forms of hydrates: Type I and Type II. Small molecule gases such as methane, CO2, and H2S form Type I hydrates whereas larger molecules such as propane form Type II.

Another interesting feature of gas hydrates is that they are nonstoichiometric. That is, a stable hydrate forms without all of the cages being filled with a guest molecule. Thus, the hydrate composition is a function of pressure and temperature.

Some misconceptions exist about when hydrates will form. The necessary conditions for hydrate formation are as follows:

• Low temperature

• Sufficiently high pressure

• Enough water to form a hydrate (not necessarily enough to form an aqueous liquid phase)

• A hydrate former such as methane, H2S, and CO2.

• In acid gas injection systems, hydrates can persist at seemingly high temperatures. For example, H2S hydrate can form at temperatures greater than 30° C. (85° F.).

The methane hydrate can persist to very high temperatures as well, but only under extreme pressures. For example, the methane hydrate can form at 37.1° C. (98.8° F.) but only under a pressure of 152.7 MPa (22,000 psia), well above the range of interest in acid gas injection.

The CO2 hydrate can form at temperatures to about 10° C. (50° F.).

Hydrate formation is also sensitive to pressure. If the pressure is not sufficiently high, then the hydrate will not form. This was shown before for the methane hydrate. For the H2S hydrate to form at 30° C., a pressure of 2.25 MPa (325 psia) is required. At pressures less than this, no hydrate will form.

Note that it is unnecessary to have a water phase to form hydrates. Hydrates can form with only a vapor present.

The water must be of sufficient amount to form hydrates. This is significantly less than required to form an aqueous liquid phase. Thus, the hydrate could exist in equilibrium with a vapor.

Another popular misconception is that hydrates will not form in the presence of liquid hydrocarbons. Once again, this is not true. Provided the four criteria outlined about are met, hydrates can form.

The presence of liquid hydrocarbons increases the pressure required, the second criteria, and thus reduces the likelihood of hydrate formation; but they do not eliminate the possibility of hydrates forming.

Hydrates have been studied quite thoroughly. Some recent reviews are by Sloan,13 Englezos,14 and Holder, et al.15 These reviews discuss hydrate formation for pure H2S, CO2, and methane, as well as hydrate formation in mixtures. Methods for predicting hydrate formation are also included.

Hydrate formation is predicted by most commercial software packages. However, the engineer is advised to check these calculations against the methods presented in the GPSA Engineering Data Book,16 notably the correlation of Baille and Wichert.

Aqueous phase

Another significant problem is the formation of an aqueous liquid phase. The acid gas leaving the amine plant is saturated with water. As the acid gas is compressed for injection, some water is knocked out, but a small amount of water remains in the gas.

The aqueous phase contains some dissolved acid gases and is highly corrosive. The coolest point is where the aqueous phase will most likely be present.

Thus, the aqueous phase is most likely to form in an injection well and become apparent as tubing corrosion at 300-400 m below the surface. This assumes a 40° C. plus injection temperature.

In addition, the formation of this phase will affect injection hydraulics. A liquid aqueous phase would rain through the less dense nonaqueous phases. Thus, it is important to accurately predict the aqueous phase dew points in these mixtures.

Phase equilibrium in the binary systems of H2S-water and CO2-water have been studied thoroughly. Corroll13 reviewed the equilibria in the H2S-water system. Recent reviews of CO2-water include those by Carroll, et al.,18 and by Crovetto.19

The definitive studies of the methane-water system, at the conditions of interest to reservoir engineering, are those by Olds, et al.,20 who measured the vapor compositions, and Culberson and McKetta,21 who measured the solubilities.

There is significantly less information regarding the equilibrium in multicomponent aqueous mixtures. However, Huang, et al., did an important investigation.22 They measured two and three-phase equilibria in two mixtures of methane, CO2, H2S, and water. These data are useful for evaluating equilibrium models for these systems.

Examples

Three examples, a simple injection scheme, a shallow injection well, and a Canrock injection well, show how the calculations are applied.

Simple injection scheme

Consider an injection well with a depth of 2,500 m (8,202 ft) and a bottom hole pressure of 30 MPa (4,350 psia). The injection fluid is assumed to enter the well at a temperature of 5° C. (41° F.), and the bottom hole temperature is 80° C. (176° F.). The temperature profile is linear from top to bottom.

To integrate the hydrostatic equation, the well was segmented into ten sections, such that Dh = 250 m.

The integration starts at the bottom of the well, where the pressure is known, and proceeds to the top. The pressure at the top is the injection pressure.

The first integrations were performed assuming the injection of pure H2S gas. The first run used NBS Table 3 [47413 bytes] to provide a base line for the additional calculations. Several subsequent calculations were performed using:

• Peng-Robinson equation of state

• Volume shifted Peng-Robinson equation

• Lee-Kesler

• Prosim Version 96.0 with the Peng-Robinson and Costald options

• Hysim Version C2.50 with the Hyprotech enhanced Peng-Robinson option.

• The Peng-Robinson equation of state predicts an injection pressure that is 12.0% less than the NBS Tables.

The volume shifted Peng-Robinson predicts an injection pressure 5.6% larger than the NBS Tables. This is not completely unexpected because over the entire range of pressure and temperature of the simulation the H2S is a "true" liquid. That is, the temperature of the simulation is always less than the critical temperature, and the pressure is always greater than the vapor pressure.

As discussed previously, volume shifting should improve the density prediction of a true liquid. The Lee-Kesler correlation compares very well with the value obtained using the NBS Tables. This further demonstrates that the Lee-Kesler is accurate for hand calculations.

Finally, both commercial simulators are an excellent match with the NBS Table method.

The second set of calculations is similar to the first except this time the injection fluid is pure CO2. A base line injection pressure was set by performing the simulation using the Iupac tables.2 As with H2S, three additional simulations were performed using:

• Peng-Robinson equation of state

• Volume shifted Peng-Robinson equation

• Lee-Kesler

• Prosim

• Hysim.

Unlike H2S, for CO2 the original Peng-Robinson equation is more accurate than the volume-shifted version. The original Peng-Robinson equation predicted an injection pressure 1.3% greater than the Iupac tables, whereas the volume shifted equation is 6.7% greater.

The reason is that CO2 is not a true liquid over the pressure and temperature range of the simulation. For most of the range it is a supercritical fluid.

This raises a question as to which method, the original Peng-Robinson or volume shifted, should be used for mixtures of CO2 and H2S. There are justifications for using either method.

Again, the Lee-Kesler result is very similar to that obtained from the Iupac tables. Hysim is also in excellent agreement with the Iupac tables. Considering the calculations presented previously (Fig. 1), this is somewhat surprising.

The explanation is that the integration step was sufficiently large as to step over the discontinuity in the density calculation. Thus, the region where the density prediction is the worst is missed by the integration.

On the other hand, Prosim was not accurate in this case. The injection pressure based on densities from Prosim is 56% too great. Prosim predicts good densities when the CO2 is a true liquid, but is very poor for the supercritical liquid.

In fact, Prosim densities are ap[ bytes]proximately a constant volume of 447 kg/cu m, regardless of temperature and pressure. This indicates that the program used something other than the Peng-Robinson liquid density.

A set of integrations was then performed on a mixture of CO2 and H2S. First the simulation used the original Peng-Robinson equation and then volume shifting. The two methods were within 1 MPa (145 psi), which is a reasonably good agreement.

A final set of calculations used this injection well to estimate the effect of methane on the injection pressure. Three additional mixtures were studied. All were 50-50 in CO2 and H2S on a methane-free basis and all simulations used the original Peng-Robinson equation.

Not unexpectedly, as methane in the gas increases, so does the injection pressure. Methane is lighter than CO2 and H2S and it reduces the injection fluid density. In our experience, a high methane content of the acid gas is often responsible for injection pressure being much greater than predicted.

Table 3 [47413 bytes] summarizes the complete set of integrations for this well.

Shallow injection well

In the previous well, the pressure and temperature were such that the injection fluid was always a single phase. But consider a shallower well, depth 1,605 m (5,266 ft) with a bottom hole temperature of 65° C. and pressure of 14.03 MPa.

For the injection fluid, a typical acid gas mixture of 32% H2S, 64% CO2, and 4% methane was selected.

As with the previous example, to obtain the injection pressure we begin at the bottom of the well and integrate to the top. The results of this integration are tabulated in Table 4 [13971 bytes]. Clearly, there is a problem with this simulation. How can the pressure near the top of the well be negative? The explanation is simple. The reason is that the density prediction is calculating near-liquid densities and the height of this "liquid" column and its resultant hydrostatic head result in a low wellhead pressure.

However, a look at the phase envelope shows that once the conditions reach a certain point, the liquid starts to vaporize, which is the bubble point. The density of the two-phase fluid is significantly less than the density of the liquid, so in reality the wellhead pressure will be much higher than the integration indicates.

Furthermore, the presence of two phases complicates the fluid mechanics of the injection, and the simple analysis presented here simply does not apply.

This simulation demonstrates the need for accurate prediction of the phase equilibrium in these systems.

Canrock injection well

Canrock Pipeline Co. Ltd. has an acid gas disposal well as part of its Fourth Creek gas plant. The target formation for acid gas disposal is the Belloy sandstone, which is a noncommericial, thick (over 30 m) aquifer near the disposal well.

A static gradient was obtained on the initial well completion to establish the base line well bore pressure and temperature profile. A three-point step rate injectivity test was conducted with produced water to determine in situ formation permeability thickness (kh).

The kh is a key factor in calculating sandface injection pressure using the Darcy radial flow equation.

Acid gas injection into the Canrock ^15-11 well commenced in July 1996 at 3,000 cu m/day at a wellhead pressure just under 9,000 kPa (1,300 psi). This was about 2,500 kPa (360 psi) greater than anticipated.

After a review, it was concluded that the higher-than-anticipated injection pressure was likely caused by lower-than-expected fluid density from the higher-than-foreseen hydrocarbon content, and/or formation damage (skin) of completion fluids (KCl water).

It was decided that an injection gradient be taken to determine the dynamic (injection) well bore pressure and temperature profile. This gradient allowed us to compare the theoretical and real wellhead pressure and sandface pressure drop. It was further assumed that pressure drop due to friction was negligible because of the relatively low injection rate.

Table 5 [37035 bytes] summarizes the initial static and injection gradients. For the injection gradient, the density was estimated using the hydrostatic head equation. That is, the density was approximated by dividing the pressure gradient by the acceleration due to gravity.

An injection fluid sample was obtained 1 day after measuring the injection gradient. This confirmed the suspicion of an abnormally high methane content (greater than 28%). This high methane content resulted in a significantly lower density than expected and thus a considerably greater injection pressure.

The source of the methane was found to be the amine flash tank. The fluid to be disposed of was made up of the vapor stream from the flash and the gas from the regenerator reflux accumulator.

Therefore, instead of disposing of the vapor from the amine flash, it should be returned to the process for further treatment because of its significant methane content. Furthermore, foaming in the amine contactor can worsen the problem. Methane becomes entrained in the foam and is released in the flash tank.

At the Canrock plant, methane in the fluid has been reduced and the current injection wellhead pressure is about 5,000 kPa (725 psi).

After obtaining the gas sample, it was speculated that perhaps the high injection pressure may have been due to liquefied acid gas vaporization in the tubing. The phase envelope was generated for this mixture using Prosim (Fig. 2 [23653 bytes]).

From Fig. 2, it appears that the fluid at the top of the well is at its bubble point. There may be a small gas cap at the top of the well. However, as it travels down the well, the profile moves away from the phase envelope and thus vaporization is not a problem in this case.

References

1. Canjar, L.N., and Manning, F.S., Thermodynamic Properties and Reduced Correlations for Gases, Gulf Publishing, Houston, 1967.

2. Angus, S., Armstrong B., and de Reuck K.M., CO2 International Thermodynamic Tables of the Fluid State-3, Pergamon Press, Oxford, 1976.

3. Goodwin, R.D., "H2S Provisional Thermophysical Properties from 188 to 700 K at Pressure to 75 MPa," NBS Report No. NBSIR 83-1694, U.S. Dept. Commerce, Washington, 1983.

4. Haar, L., Gallagher, J.S., and Kell, G.S. NBS/NRC Steam Tables, Hemisphere, Washington, 1984.

5. Soave, G., Chem. Eng. Sci., Vol. 21, 1972, pp. 1197-203.

6. Peng, D.Y., and Robinson, D.B., Ind. Eng. Chem. Fundam., Vol. 15, 1976, pp. 59-64.

7. Reid, R.C., Prausnitz, J.M., and Poling, B.E., The Properties of Gases & Liquids, 4th Edition, McGraw-Hill, New York, 1987.

8. Trebble, M.A., and Bishnoi, P.R., Fluid Phase Equil., Vol. 29, 1986, pp. 465-74.

9. Mathias, P.M., Naheiri, T., and Oh, E.M., Fluid Phase Equil., Vol. 47, 1989, pp. 77-87.

10. Robinson, D.B., Macrygeorgos, C.A., and Govier, G.W., Petro. Trans. AIME, Vol. 219, 1960, pp. 54-60.

11. Lee, B.I., and Kesler, M.G., AIChE J., Vol. 21, 1975, pp. 510-27.

12. Carroll, J.J., and Mather, A.E., "Fluid Phase Equil.," Can. J. Chem. Eng., Vol. 105, 1995, pp. 221-28.

13. Sloan, E.D., Clathrate Hydrates of Natural Gas, Marcel Dekker, New York, 1990.

14. Englezos, P., Ind. Eng. Chem. Res., Vol. 32, 1993, pp. 1251-74.

15. Holder, G.D., Zetts, S.P., and Pradhan, N., Reviews Chem. Eng., Vol. 5, 1988, pp. 1-70.

16. GPSA Engineering Data Book, 10th Edition, Gas Processor Suppliers Association, Tulsa, 1994.

17. Carroll, J.J., PhD Thesis, Department of Chemical Engineering, University of Alberta, Edmonton, 1990.

18. Carroll, J.J., and Mather, A.E., Can. J. Chem. Eng., Vol. 69, 1991, pp. 1206-12.

19. Crovetto, R., J. Phys. Chem. Ref. Data, Vol. 20, 1991, pp. 575-89.

20. Olds, R.H., Sage, B.H., and Lacey, W.N., Ind. Eng. Chem., Vol. 34, 1944, pp. 1223-27.

21. Culberson, O.L., and McKetta, J.J., Petrol. Trans. AIME, Vol. 192, 1951, pp. 223-26.

22. Huang, S.S.S., Leu, A.D. Ng, H.J., and Robinson, D.B., Fluid Phase Equil., Vol. 19, 1985, pp. 21-32.

Bibliography

1. Carroll, J.J., Chem. Eng., Vol. 101, 1994, p. 143.

2. Carroll, J.J., Slupsky, J.D., and Mather, A.E., J. Phys. Chem. Ref. Data, Vol. 20, 1991, pp. 1201-09.