METHOD PREDICTS HYDRATES FOP HIGH-PRESSURE GAS STREAMS

Mahmood Moshfeghian
Bushier University
Iran

R.N. Maddox
Consultant
Stillwater, Okla.

A new procedure extends the pressure range for estimating hydrate formation in high-pressure gas wells such as those now being developed in the North Sea.

The method applies for uninhibited as well as methanol and ethylene glycol inhibited hydrate-forming conditions of pure components and natural gas mixtures.

Accurate information concerning the conditions under which hydrates will form or exist in a natural gas stream are vital to the natural gas industry. As pressure-temperature conditions used for transporting natural gas become more severe, predicting hydrate forming conditions becomes increasingly difficult. Addition of a hydrate inhibitor, such as methanol or ethylene glycol, further complicates reliable prediction of hydrate-forming conditions.

HYDRATE FORMATION

The first generalized technique for predicting hydrate formation was presented in 1945.1 Vapor-solid equilibrium constants were used in a dew point-type calculation to estimate hydrate-forming conditions. An equation2 provided an estimation of the concentration of inhibitor required to prevent hydrate formation. This equation was similar to that for estimating the freezing point lowering of a component by addition of a second material.

Over the years, many different procedures have been presented for estimating hydrate-forming conditions with and without inhibitors. Also, much more has been learned about the nature and composition of hydrates.

One of the most recent techniques 3 for calculating hydrate-forming conditions used the basic approach of Reference 4, but obtained fugacities from Reference 5 (the Soave-Redlich-Kwong equation of state) and heats of formation for hydrates from Reference 6.

The suggested new method is an extension of the procedure from Reference 3 that includes the influence of pressure on the enthalpy change accompanying hydrate formation.

MODEL DEVELOPMENT

Hydrates are clathrates, a form of inclusion compound in which "guest" molecules fit into cavities in a crystalline lattice formed by the "host" molecules, but without chemical bonding. Hydrates may take on two different structural forms,7 each of which is composed of polyhedral cages and each of which has two different sized holes to accept guest molecules.

Fig. 1 shows the tetrakaidecahedron of Structure I and the hexakaidecahedron of Structure II hydrates. The open circles represent the oxygen atoms in the water molecules, and the solid lines represent the hydrogen bonds between them.

With those two different structures and with different sized and shaped guest molecules, there is also the possibility of a mixed hydrates In their body centered cubic cell, Structure I hydrates have 46 water molecules and six large (about 5.6 . mean diameter) and two small (about 5.1 . mean diameter) holes for accepting guest molecules.

Structure II hydrates have a diamond lattice composed of 136 water molecules. There are eight large cavities (about 6.7 . mean diameter) and 16 small cavities (about 5.0 . mean diameter).

The crystal structure of the gas hydrate will depend on the geometry of the guest gas molecule. Small gas molecules generally cause Structure I hydrates while large gas molecules generally cause Structure II hydrates.

Table 1 shows hydrate structures for most hydrate forming constituents of natural gas.7

The hydrate number is defined as the number of moles of water per mole of gas in the hydrate. The "ideal" or theoretical hydrate number is 5.75 (46/8 = 5.75) for Structure I and 5.67 for Structure II.

As shown in Fig. 2,8 9 these ratios are achieved only at very high pressure. At lower pressures, not all available holes are filled, and the hydrate number is larger than the ideal or theoretical value.

If the number of gas molecules in the hydrate varies with pressure, the enthalpy of formation for the hydrate should also change as pressure changes. The technique suggested by in Reference 6 for predicting hydrate formation in presence of an inhibitor can be modified as follows:

• Include a pressure dependency in the equation for the enthalpy of formation, Equation 1 (see equation and nomenclature box).

• The hydrate formation temperature is then calculated by Equation 2.

• As suggested in Reference 3, the activity coefficient can be obtained from the Margules equation (Equation 3).

The constants in the Margules equation are obtained from regression of the calculated activity coefficients for the individual inhibitors.

Fig. 3 shows the activity coefficient for water in methanol for concentrations to 90% by weight methanol and temperatures from - 100 to + 100 F. Fig. 4 shows the activity coefficient for water in ethylene glycol for various glycol concentrations to 65% by weight glycol and at temperatures from - 100 to + 100 F.

The water activity coefficient inhibitor concentration curves cover the full range of available experimental data for inhibited hydrate formation. Extrapolation beyond the plotted lines in Figs. 3 and 4 is not recommended.

PROOF

For the new model, the basic calculation uses enthalpies of formation and water activity coefficients correlated with the Margules equation.6 The calculations were established and proven in Reference 3.

When tested against the data available in Reference 3 and compared with available methods, the new method provides for significantly improved hydrate formation temperature predictions over a wide range of pure components, mixtures, temperatures, pressures, and inhibitor concentrations. Because of the extensive evaluation of the method in Reference 3, only a brief summary of the results of the most important of those voluminous calculations will be discussed.

Table 2 compares calculated hydrate temperatures from the new model with experimental measurements for ethane, propane, carbon dioxide, and hydrogen sulfide.10 For the most part, calculated and experimental measurements are in good agreement.

Data for several natural gas mixtures were used in evaluating the new procedure for calculating hydrate-formation temperature. Table 3 lists the compositions of the different mixtures and the sources for the gas mixture data.

Because inhibited hydrate data are difficult to measure, a comparison of calculated hydrate-forming temperatures for gas mixtures with methanol present in varying concentrations showed that the overall average error of 2.8 F. for the 60 data points is within experimental error.

For Gas Mixture 5, all of the data were in excellent agreement whether uninhibited or inhibited by methanol or glycol. The overall error was 2.5 F.

Recently, Reference 11 presented very high-pressure hydrate formation temperature data for pure methane and also for a synthesized gas mixture. The reference graphically showed that the uninhibited methane hydrate formation temperature data were in excellent agreement with previously reported lower pressure results in References 8, 9, 12, and 13.

Fig. 5 and Table 4 show that calculated and experimental temperatures for uninhibited methane are in excellent agreement. The uninhibited hydrate formation data agree within an average overall error of 0.34 C.

The calculated methanol inhibited methane points are also in excellent agreement with experimental determinations. The methanol inhibited data agree within 1.19 C., including all points. For all but the lowest pressure point, the average temperature error for the methanol inhibited points is 0.44 C.

There appears to be a possible typographical error in the temperature reported for the lowest pressure point. If the minus was accidentally omitted and the correct temperature is - 4.7 C., that value is almost exactly equal to the calculated temperature.

Table 5 compares calculated and measured values for hydrate formation temperature of Gas Mixture 6 in the presence of water and with methanol inhibitor. It also shows calculated results for two other available computer programs for estimating hydrate-forming temperature.

One of the other programs fails above about 40 MPa (5,800 psi), and the second cannot be applied above about 60 MPa (8,700 psi). Even within their range of application, the superiorly, of the proposed calculation procedure is clearly evident from the data in Table 5.

REFERENCES

1. Katz, D.L., "Prediction of Conditions for Hydrate Formation in Natural Gases," Trans. AIME, Vol. 160, 1945, P. 140.

2. Hammerschmidt, E.G., "Formation of Gas Hydrates in Natural Gas Transmission Lines," Ind. & Eng. Chem., Vol. 26, 1934, P. 851

3. Maddox, R.N., Moshfeghian, M., Lopez, E., To, C.H., Shariat, A., and Flynn, A.J., "Predicting Hydrate Temperature at High Inhibitor Concentration," Lawrence Reid Gas Conditioning Conference, Norman, Okla., March 1991.

4. Parrish, W.R., and Prausnitz, J.M., "Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures," Ind. Eng. Chem. Proc. Des. Dev., Vol. 11, 1972, p. 26.

5. Soave, G., "Equilibrium Constants from a modified Redlich-Kwong equation of state," Chem. Engr. Sci., Vol. 27, 1972, p. 1197.

6. Pieroen, A.P., Recueil Trav. Chim, Vol. 74, 1955.

7. Kuustraa, V.A., and Hammershaimb, E.C., Handbook of Gas Hydrate Properties and Occurrence, National Technical Information Service, U.S. Department of Commerce, 1983

8. Marshall, D., Saito, R.S., and Kobayashi, R., "Hydrates at High Pressures, Part I,"AIChE Journal, Vol. 10, 1964, p. 734.

9. Marshall., D., Saito, R.S., and Kobayashi, R., "Hydrates at High Pressures, Part II,"AIChE Journal, Vol. 10, 1964, P. 734.

10. Ng, H.J., Chen, C.J., and Robinson, D.B., "The Effect of Ethylene Glycol or Methanol on Hydrate Formation in Systems Containing Ethane, Propane, Carbon Dioxide, Hydrogen Sulfide, or a Tv . pica] Gas Condensate," Research Report RR-92, Gas Processors Association, Tulsa, 1985.

11. Blanc, C., and Tournier-Lasserve, J., "Controlling Hydrates In High-Pressure Flowlines," World Oil, November 1990.

12. McLeod, H.O. Jr., and Campbell, J.M., "Natural Gas Hydrates at Pressures to 10,000 psia," JPT, Vol. 13, 1961, p. 390.

13. Holder, G.D., Corbin, G., and Papadopoulos, K.D., "Thermodynamic and Molecular Properties of Gas Hydrates from Mixtures Containing Methane, Argon and Krypton," Ind. Eng. Chem. Fund., Vol. 19, 1980, P. 282.

14. Ng, H.J., and Robinson, D.B., "Equilibrium Phase Composition and Hydrating Conditions in Systems Containing Methanol, Light Hydrocarbons, Carbon Dioxide, and Hydrogen Sulfide," Research Report RR-66, Gas Processors Association, Tulsa, 1983.

15. Ng, H.J., Chen, C.J., and Robinson, D.B., "The Influence of High Concentrations of Methanol on Hydrate Formation and the Distribution of Glycol in Liquid-Liquid Mixtures," Research Report RR-106, Gas Processors Association, Tulsa, 1987.

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