Computations of the Formation

Chrmirul Enginrrring Sctence, Vol. 43, No. 10. pp. 2661 2612. 1988. cclc9 2509,RR S3.oOf0.00 Printed tn Great Britain. 8, 1988 Pergamon Press plc

COMPUTATIONS OF THE FORMATION OF GAS HYDRATES

JAN MUNCK’ and STEEN SKJOLDJ0RGENSEN CALSEP A/S, Lyngby, Denmark

and

PETER RASMUSSEN Instituttet for Kemiteknik, DTH, Bygning 229. 2800 Lyngby, Denmark

(First received 19 August 1987; accepted in rer;isrd,fiwm 28 Murch 1988)

Abstract-A simple method for predicting the formation of gas hydrates is described. The hydrate-forming compounds may be pure gases or constitute a mixture like a natural gas or an oil. The influence of inhibitors like alcohols, glycols or salts on the hydrate formation is accounted for by a very flexible and robust program based on the method. The calculated results are found to compare well with experimental results for a wide variety of pure compounds and mixtures, including two North Sea reservoir fluids.

I. INTRODUCTION

Gas hydrates are solid inclusion compounds which may be formed where light hydrocarbons and/or some other light gases and water are in contact at temperatures below approximately 310 K. As the hydrates may exist far above the freezing point of water they can cause plugging of pipes, nozzles and separation equip- ment which would not be foreseen by considering the possibility of ice formation alone.

The risk of hydrate formation may be reduced by reducing the water content of the hydrocarbon mixture. It is, however, necessary to reduce the water content significantly, so that the partial pressure of water in the mixture is below the very low equilibrium pressure above the gas hydrate. Another and much preferred alternative is therefore to lower the temperature at which hydrates may be formed by adding a so- called inhibitor. Inhibition is quite analogous to freezing-point depression and the compounds causing the largest freezing-point depressions for water are also the most powerful inhibitors. Alcohols, glycols and salts are examples of good inhibitors and methanol is the most commonly used.

The most important questions to be answered when checking for possible hydrate formation under given operating conditions are:

(1) (2)

(3)

Is there any risk of hydrate formation? What is the maximum permissible water content without hydrate formation? How are the hydrate formation conditions changed by the addition of inhibitors?

The model described in the following sections answers these questions for all natural gas/petroleum mixtures

‘To whom correspondence should be addressed.

using the most common alcohol, glycol and salt inhibitors.

Illustrations of the phase behavior of hydrates are shown in Figs 1 and 2.

Figure 1 illustrates the situation for a pure hydrate- forming gas. The solid curves are three-phase loci representing equilibria between hydrate (H), gas (G or L2) and water (1 or Ll). Points B and C are four-phase points.

The dot and dash line indicates the effect of adding an inhibitor. The three-phase curve is shifted towards lower temperatures at constant pressure. The slope of the CD section may be positive or negative since it depends on differences in (partial) molar volumes of the components in the different condensed states. These differences are very small and the CD section will therefore be almost vertical.

For a mixed gas the situation may become slightly more complex due to the possible interference with the phase envelope of the gas mixture. In Fig. 2 the lines AB, BC and DE represent three-phase loci while four phases coexist on line CD and at point B.

The procedure developed in this work for gas hydrate calculations does not include any real new theory. However, various previously published methods have been modified and combined in a consistent way resulting in a simple method with a very broad range of applicability.

2. A FEW FACTS ABOUT HYDRATES

Water can form two types of host lattices in addition to the well-known condensed states: liquid and ice. These lattices are not intrinsically stable, but may become sufficiently stabilized when a certain fraction of the lattice cavities are occupied by “guest” molecules. Some physical constants for the two lattice types are given in Table I.

Only gases of rather modest size and appropriate geometry can enter the cavities. Table 2 indicates the

266 1

2662 JAN MUNCK et al.

H + L2 ,

273.15

T(K)

Fig. 1. Coexistence curve for hydrate (H), gas (G), liquid hydrate-forming compound (L2). ice (I) and liquid aqueous solution (Ll) in the case of a pure hydrate-forming compound: (- . - . -) coexistence curve when hydrate formation is inhibited, e.g. by MEOH; (- - - - -) vapor pressure of the

pure hydrate-forming compound.

273.15

T(K)

Fig. 2. Coexistence curve for hydrate (H), gas (G), liquid hydrate-forming compounds (L2), ice (I) and liquid aqueous solution (Ll) in the case with a mixture of hydrate-forming compounds: (- - - -) phase envelope for the hydrate-forming

compounds, (0) critical point.

gases of interest to typical natural gas/petroleum

calculations and the cavities stabilized by each indi-

vidual gas.

3. THEORY

The calculations in this work are based on the following equilibrium criterion between water in the hydrate phase and water in a coexisting phase, Z:

pH=p= (1)

i.e. the chemical potential of water in the hydrate

Table 1. Some physical constants of the two possible water structures in hydrates

Property

Number of H,O molecules per unit cell

Number of small cavities per unit cell

Number of large cavities per unit cell

Cavity diameter (A) Small Large

Structure 1 Structure 2

46 136

2 16

6 8

7.95 7.82 8.60 9.46

phase, H, is equal to the chemical potential of water in phase c(, which can be ice (I), an aqueous solution (Ll) or gaseous water. A hydrate-forming substance or mixture in a gas (G) or liquid phase (L2) will also be present. The model used for the chemical potential qf water in the hydrate phase is the well-known van der Waals’ and Platteeuw (1959) adsorption model which has been used, e.g. by Parrish and Prausnitz (1972) and Erickson (1983):

$‘=#+RT~viln L

(1-p) (2)

i= 1, 2, . , NCAV

K=l, 2,. . . , NCOMP.

In this equation p refers to a hypothetical empty lattice state. vi is the number of cavities of type i. UKi denotes the probability of a cavity of type i being occupied by a hydrate-forming molecule of type K. According to the Langmuir adsorption theory this probability is calculated from

Y,,=cK&( 1 +Fc’ih)

j=l,2,...,NCOMP

(3)

wheref, is the fugacity of hydrate-forming component K and CKi is the adsorption constant at the temperature specified.

Many previous workers select a cell potential to calculate the CKis. However, this complex approach does not eliminate the necessity for adjustable parameters. In the present model the Langmuir constants are simply considered to be temperature-dependent according to

Cxi=(A,,IT) exp (B,ilT). (4)

This form may be derived from a square-well cell potential (Parrish and Prausnitz, I972), but it has been chosen here only because it offers a convenient two- parameter approach. The AKi and BKi parameters are found by a parameter estimation using a large number

Computations of the formation of gas hydrates 2663

Table 2. Gases of interest in natural gas hydrate formation and their occurrence in the different cavities of the water structure

Occupies cavities of type

Compound

Cl Methane c2 Ethane c3 Propane C4 Butane iC4 Isobutane

CO, Carbon dioxide

N, Nitrogen

H,S Hydrogen sulphide

Structure I Structure 2

Small Large Small Large cavity cavity cavity cavity

+ + + + _ + + _ - + _ + _ - + + + + + + + + + + + + +

Table 3. Physical constants used for the evaluation of eq. (7)+

Property Unit Structure 1 Structure 2

A&W AH,,(W AH,(ice) A V,,(liq) A V,,(ice)

AC,(liq)

J/mol 1264 883 J/mol -4858 -5201 J/mol 1151 808

cm’/mol 4.6 5.0 cm’jmol 3.0 3.4 Jjmol/k 39.16 39.16

‘A~~~,(liq) denotes the difference in the chemical potential of water in the empty hydrate lattice and in the liquid state at 273.15 K. AH,(liq) is the corresponding enthalpy difference. AH,(ice) denotes the difference in the molar enthalpy of water in the empty hydrate lattice and in the ice state at 273.15 K. AV,(liq) and AV,(ice) represent volume differences. AC,(liq) is the molar heat capacity ditkrence. Ajl,(ice) and AC,(ice) are set to zero.

ofexperimental data points as explained in the following section.

John et al. (1985) recently used a Kihara potential model for the derivation of the Langmuir constants.

The chrmicol pottwtiul ofwatrr in the r-phusr may in general be written as

,u~ = /F’ + R T In (f’“,/f”,,) (5)

where cc” is the chemical potential of pure water as ice or liquid water at temperature T and pressure P,,ft, is the fugacity of water in the r-phase and,f$ the fugacity of ice or liquid water.

By combination of eqs (I), (2) and (5) one gets

i (l-~Y~i>- (6)

It is seen that the left side of eq. (6) represents the difference between the chemical potentials of pure water as an empty lattice and as ice or liquid water at pressure P and temperature T. Based on classical thermodynamics and the assumptions given below one can write

#--PO APO s ‘r AH, + AC, (T- T,) dT

RT RT, ?‘, RTZ

J -- + -_ dP.

~0 R7- (7)

In this equation A,LL, denotes the difference in the chemical potential of water in the empty hydrate lattice and in ice or liquid water at T, = 273. IS K. AH, is the corresponding enthalpy difference, AC, the heat capacity difference and AV the volume difference. The pressure P, is the vapor pressure at To. Since P, is very small compared to P P, = 0 is used.

The temperature dependence of the PV term is averaged by using

;r;=(T+273.15)/2. (8)

Holder et al. (I 980) have used a modified form of eq. (7) which eliminated the need for calculating the average temperature from eq. (8).

AV and AH, are both considered to be pressure- independent because the pressure effects on condensed phases are small. AI/ is considered to be temperature- independent, while the temperature dependence of the enthalpy term is taken into account by means of a constant molar heat capacity difference AC,.

The constants shown in Table 3 are used for the evaluation of eq. (7). The constants are identical to the ones used by Erickson (1983) except for the molar heat capacity, which in the present approach is considered to be independent of temperature.

Combination of eqs (6) and (7) gives the final

2664 JAN MUNCK et ~1.

equation

A&

s

‘- AH,+AC,(T-T&T

RT” T, RT2

s ‘AV + -dP=ln

o RT (f”,/!X)-~vi In

I

(I -;yKi)- f9)

a-Phase: ice (I)

In this case Ap(,, differences between

AH,, AC, and AV represent the the empty lattice and ice. At the

same time the first term on the right side of eq. (9) will vanish.

x-Phase: liquid aqueous phase (Ll)

In this case Ap,. AH,, AC, and AV represent the difference between the empty lattice and liquid water. For substances like hydrocarbons, nitrogen and hydrogen sulphide the solubility in water is very low. This solubility is neglected. If no inhibitor has been added Ll is considered as pure liquid water. The first term on the right side of eq. (9) will therefore vanish. The solubility of carbon dioxide cannot be neglected. From Henry’s constants found in Wilhelm and Battino (1973) Wilhelm et al. (1977) and Weber (1984) it is possible to calculate the solubility of carbon dioxide (xcoJ at the given temperature and pressure. It is now assumed that Raoult’s law may be used for the aqueous phase and hence that f “,/f “, = x, = 1 - xCOlr where x, is the mole fraction of water in Ll. The Henry’s constant as a function of temperature is given by

In HCo2.r = HA, + HB,/T+ HC, . In T+ HD, . T.

(10)

For mixtures containing methanol as inhibitor the Henry’s constant is calculated as

In HCo2 = c XI In Hco~, I (11)

where the subscript I is used for water and methanol. The coefficients used for the evaluation of Henry’s constant in water and methanol are given in Table 4.

For mixtures with added inhibitors the first term on the right side of eq. (9) can be written as

In Z./X) = In (x,Y,) (12)

where y, is the activity coefficient of water. For non- electrolyte inhibitors the activity coefficients are calculated using the UNIQUAC equation (Abrams and Prausnitz, 1975) as proposed by Anderson and

Prausnitz (1986). For electrolyte inhibitors the activity coefficients are calculated from the extended UNIQUAC model dcvcloped by Sander ef al. (1986).

“Hydrocarbon phase” (G and L2)

For the hydrate-forming substances and the other components in the G or L2 phases the fugacities are calculated by means of the SoaveeRedlich-Kwong (SRK) equation of state (Soave, 1972). This equation was chosen partly because of its popularity in hydrocarbon phase equilibrium computations and partly because a very powerful characterization procedure is available for the application of the SRK equation to mixtures containing heavy hydrocarbons (Pedersen et

al., 1985). The G and L2 phases are in general considered to be

water-free which means that the fugacities needed for the calculation of Yki in eq. (3) can be directly calculated from known compositions of the G or L2 phases. Equation (9) may now be used to calculate corresponding values of pressure P and temperature T for equilibrium between phases H, I, G, or H, Ll, G, or H, Ll, L2. If a phase stability test (Michelsen, 1982) shows that two hydrocarbon phases exist the equilibrium will be between phases H, Ll, G and L2.

Maximum permissible water content without hydrate

formation

If a hydrocarbon mixture at a given pressure P and temperature Tcontains water, there may be the risk of hydrate formation. The maximum permissible content of water is found from eq. (9) in the following way. The fugacity f”, is calculated as

V”P f”,= P, exp ~

RT (13)

where P, is the vapor pressure of ice or liquid water and V0 is the corresponding molar volume ( V” for ice = 19.6 cm3/mol, V” for liquid water = 18.0 cm3/mol).

The vapor pressure P, is calculated as

In P,=a+h/T (14)

with values of a and h estimated from experimental vapor pressure data (Handbook of Chemistry and

Physics, 198 I-1982). For P, measured in atmospheres the values are for ice

a= 17.372, h= -6141 K

Table 4. Coefficients used for the evaluation of the Henry’s constant of

eq. (10)

HA HB Wm) (atm K)

HC (atm/ln K)

HD @tm/K)

Hz0 160.27 - 8764.5 -21.726 1.1055 x 10-A

MEOH 10.87 - 1783.5 0 0


The data base used for the parameter estimation is and for liquid water

a=14.484, b= -5351 K.

The values of the fugacities for the hydrate-forming substances and for water are calculated from the SRK equation of state. An iterative solution of eq. (9) will give the desired water content.

4. PARAMETER ESTIMATION

The parameters needed to calculate the Langmuir constants [eq. (4)7 were estimated by adjusting the A and B parameters to experimental data.

described in Table 5. In most cases parameters for a group of gases were estimated simultaneously. This in connection with the broad data base used ensures parameters of sufficient physical significance to pro- vide accurate predictions for mixtures not covered by the experimental data.

The parameters obtained appear in Table 6. The root mean squared temperature deviations for the 489 points in the data base is 0.66 K. Very few deviations exceed 2.0 K.

The pressure covered by the data base range be-

Table 5. Data used to establish parameters A and Bt

Data base

Parameters estimated Gas No. of Inhibitor

data points (methanol) Reference’

Structure 1 Cl: four parameters C2: two parameters N,: four ‘parameters

Structure 1 H,S: four parameters CO,: four parameters

Structure 2 C 1: four parameters C2: two parameters C3: two parameters

iC4: two parameters C4: two parameters

Structure 2 CO,: four parameters

N,: four parameters

Structure 2 H,S: four parameters

Cl 13 Cl 5 c2 25 c2 4 N, 28 CI fC2 21 ClfN, 39 C2+C3 7 Cl +C2+C3 4

H,S I4 H,S 5 Cl +H,S 10 CO, 23 Cl +co, 6 Cl fCO,+H*S 12

c3 ic4 Cl +c3 Cl +ic4 c1+c4 Cl +c3 C2tC3 Cl +C2+C3+

iC4+C4+C5

c3 + co, C3+N, Cl +C2+C3+ CO, + N,

Cl +C3+H,S 13 30

24 5

33 24 30

4 35

12

36 39

18

+

-

-

-

+ -

l-3 4 5-7 4 3, 8 9, 10

11 12 12

13 4

14 15, 16 17 18

19922 19, 23, 24 10, 25 10, 24, 26 10, 27 4

12

23

15 29

28

‘Four parameters are needed for compounds which can enter both small and large cavities. Only two parameters are needed for compounds which can enter only large cavities.

‘I, Roberts et al. (1940); 2, Frost and Deaton (1946a); 3, Marshall et al. (1964); 4, Ng and Robinson (1983); 5, Deaton and Frost (1937); 6, Deaton and Frost (1938); 7, Deaton and Frost (1940a); 8, van Cleef and Diepen (1960); 9, Holder (1976); 10, Campbell and McLeod (1961); 11, Jhaveri and Robinson (1965); 12, Holder and Hand (1982); 13, Selleck et al. (1952); 14, Noaker and Katz(l954); 15, Robinson and Metha (1971); 16, Berecz and Balla-Achs (1983); 17, Unruh and Katz (1949); 18, Robinson and Hutton (1967); 19, Holderand Godbole(l982);20, Deaton and Frost (1940b); 21, Frost and Deaton (1946b); 22, Wilcox et al. (1941); 23, Roudher and Barduhn (1969); 24, Wu et al. (1976); 25, Deaton and Frost (1946); 26, Ng and Robinson (1976a); 27, Ng and Robinson (1976b): 28, Wilcox er al. (1939); 29, Ng er al. (1977-1978); 30, Schroeter et al. (1983).

2666 JAN MUNCK et al.

Table 6. Parameters A and B for the calculation of Langmuir constants [eq. (4)]

Gas Structure

Small cavity ..____

A x lo3 Watm)

Large cavity

Ax IO3

Watm)

Cl

c2

c3 ic4 c4 N,

CO,

H,S

1 0.7228 3187 23.35 2653 2 0.2207 3453 100.0 1916 1 0.0 0.0 3.039 3861 2 0.0 0.0 240.0 2967 2 0.0 0.0 5.455 4638 2 0.0 0.0 189.3 3800 2 0.0 0.0 30.51 3699 1 1.617 2905 6.078 243 1 2 0.1742 3082 18.00 1728 I 0.2474 3410 42.44 2813 2 0.0845 361.5 851.0 2025 1 0.0250 4568 16.34 3737 2 0.0298 4878 87.2 2633

Table 7. kij values to be used in the SRK equation for interactions between H,O and

other components

Component kij

N2 0.08 co* 0.25 H,S 0.03 Cl 0.55 c2 0.51 c3 0.50 ic4 0.53 c4 0.53 C5f 0.50

tween 0 and 500 atm (even higher for NJ and the temperature vary between 250 and 305 K.

Some of the binary interaction parameters, k,, in the SRK equation were estimated based on experimental vapor phase water contents for the relevant hydrates. Only interactions between water and hydrocarbon gases and carbon dioxide were estimated. All other kij values were adopted from Reid et al. (1977). The estimated parameters appear in Table 7.

The UNIQUAC interaction parameters used for the prediction of inhibitor effects are based on freezing point depression data. The parameters are shown in Table 8.

T IK)

Fig. 3. Calculated coexistence curves for methane, hydrate and aqueous solutions of MEOH. Experimental data points: Roberts et al. (1940), Frost and Deaton (1946a), Ng and Robinson (1983), Holder (1976),

Campbell and McLeod (1961), Ng and Robinson (1984a).


Table 8. UNIQUAC parameters (aij) for interactions between water and inhibitors to be used in the model of Sander et al. (1986)’

Inhibitor*

MEOH ETOH EG PG DEG TEG Na+ Ca2 + Cl-

a12 431.0 196.5 - 129.7 439.9 41.46 258.4 - 1411.3 -2912.6 -461.0 %I -313.02 -252.1 -- 124.3 - 186.7 - 195.3 - 273.5 8 I 58.5 -461.8 -437.5

-.

‘For the interaction parameter (hi, ,) between the salt ions in aqueous solution the following values are used: NaCl= -407.7, CaCI, = -480.8.

*For abbreviations see text.

10 0 wt % EC

266 270 274 278

T (K) Fig. 4. Calculated coexistence curves for propane, hydrate and aqueous solutions of EG. Experimental data points: Ng

et al. (1982), Verma (1974), Wilcox et al. (1939).

5. IMPLEMENTATION OF THE MODEL

A computer program based on the model has been developed for the calculation of diagrams of the type shown in Figs 1 and 2. For gas mixtures the algorithms developed by Michelsen (1982) are used to check for stability of the mixture under consideration; this ensures correct prediction of the number of phases present.

Furthermore, for situations corresponding to Fig. 2 the phase envelope is calculated according to Michelsen’s ( 1980) procedure.

For mixtures containing heavy hydrocarbons (C7+) the method has been interfaced with the characterization procedure developed by Pedersen rt al. (1985).

The program provides a simple but very useful and robust method for checking complex flow sheets for

the risk of hydrate formation. At any new set of

conditions the method can answer important questions like the ones indicated in Section I.

The inhibitors which are included in the program

are methanol (MEOH), ethanol (ETOH), ethylene glycol (EG), propylene glycol (PC), di- and tri-

200 0 -

,500 -

0

-E

5 100.0 -

a

/ l

50.0 -

0.0 I I I I I I 270.0 275.0 280.0 285 0 290 0 295.0 300.0

T(K)

Fig. 5. Calculated coexistence curve for a seven-component mixture. ( l ) Experimental data points: Ng and Robinson (1984~). Mixture composition (mole %): N,=5.96, CO,= 14.18, Cl =71.61. C2=4.73. C3= 1.94,

nC4 = 0.79. nC5 = 0.79.

2668 JAN MUI

ethylene glycol (DEG and TEG), and sodium and calcium chlorides (NaCl and CaCl,).

6. RESULTS AND DISCUSSION

The calculated coexistence curves for hydrates of pure methane and pure propane are shown in Figs 3 and 4 which also show the influence of the addition of methanol or ethylene glycol as the inhibitor.

The agreement between the experimental and calcu-

VCK et al.

lated values is good even up to high concentrations of inhibitor in the aqueous phase. Point B-in Fig. 3 is a four-phase point with an equilibrium between ice (I), water (Ll), hydrate (H) and methane (G).

Figures 5 and 6 represent multicomponent mixtures. In Fig. 6 the phase envelope is also given. This means that the experimental points in Fig. 6 corre- spond to the equilibrium between hydrate (H), aqueous solution (Ll) and liquid “gas” mixture (L2).

150.0

1200

90.0

-z

z a

60.0

T(K)

Fig. 6. Calculated coexistence curve for a four-component mixture. (a) Experimental data points: Ng and Robinson (1976a). (- -) Calculated phase envelope. Mixture composition (mole O/O): CO, = 25.5, C2= 17.0,

C3 = 38.6, iC4 = 18.9.

200.0

150.0

E

4 e 100.0

50 0

0.c 2:

I-

,-

30 c

50

I

l

t

35 Owt%MEOH

I 3 240 0 250 0 260 0 270.0 280.0 290 0 300 0

T(K)

Fig. 7. Calculated coexistence curves for a seven-component mixture and aqueous solutions of MEOH. (0) Experimental data points: Ng and Robinson (1984b). (. - -) Phase envelope. Mixture composition

(mole %): N,=5.26, CO,=13.37, Cl =73.90, C2=3.85, C3=2.02, &4=0.X0, &5=0.X0.


Figure 7 shows the results for a seven-component results for the conditions where hydrates are formed mixture. The addition of methanol is seen to lower the from two North Sea reservoir fluids. The molar com- decomposition temperatures in a given pressure range position of the two mixtures are given in Table 9. AIso so much that one enters into the phase envelope and shown in Fig. 9 are results where the hydrate forma- thereby a four-phase region (H, G, Ll and L2). The tion has been inhibited by addition of EG. In Fig. 10 agreement between the calculated and experimental are shown similar results where MEOH is used as values is good even at a very high methanol concentra- inhibitor. It is seen that the experimental and the tion. calculated results agree very well.

Figure 8 shows the effect of using CaCl, as inhibitor for the formation of hydrate from a natural gas mixture. No experimental data could be found for comparisons.

Figures 9 and 10 show experimental and calculated

Table 10 and Figs 11 and 12 show experimental and calculated vaiues of the water content in hydrocarbons which are in equilibrium with hydrate. This

water content represents the maximum content which

can be accepted in a hydrocarbon or hydrocarbon

700.0 -

600.0 -

20 10 5 0wt%CaC12

500.0 -

F 5 400.0 -

a

300.0 -

200.0 -

100.0 -

0.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0

T(K)

Fig. 8. Calculated coexistence curves for natural gas, hydrate and aqueous solutions of CaCI,. (0) Experimental data points: Campbell and McLeod (1961). Mixture composition (mole %): Cl =90.6,

C2=6.6, C3=1.8, ic4=0.5, nC4=0.5.

3000 r 20 0 wt % EG

Fig. 9. Calculated coexistence curves for a North Sea oil in the (a) experimental hydrate point, (0) experimental bubble point,

presence of aqueous solutions of EG: ( -) calculated hydrate curve, (- . -)

calculated bubble point curve. Experimental data points: Ng et al. (1987).

CES 43:10-H

2670 JAN MUNCK er al.

300.0 - 29 16 Owt%MEOH

250.0 -

200.0 -

I 260 0 270 0 280 0 290 0 300 0

T(K)

Fig. 10. Calculated coexistence curves for a North Sea gas condensate in the presence of aqueous solutions of MEOH: (0) experimental data point, ( -) calculated hydrate curves. Experimental data points: Ng

e’t ul. (I 987).

0.0 1 I I I 240 0 250.0 260 0 270 0 290.0

T(K)

Fig. 11. Water content [x,,. (mole fraction)] in liquid propane in equilibrium with hydrate at 7.62 atm: (0) experimental data from Sloan er ul. (1986). (- -) predicted water content.

Table 9. Compositions of the North Sea reservoir fluids for which hydrate results are shown in Figs 9

and 10 [Ng et ul. (1987)]

Component Mixture A Mixture B

N, 0.16 0.64 CO, 2.10 3.11 Cl 26.19 73.03 c2 8.27 8.04 c3 7.50 4.28 ic4 1.83 0.73 nC4 4.05 1.50 iC.5 1.85 0.54 PIGS 2.45 0.60 C6+ 45.60 7.53

Molecular weight 90.2 32.4

mixture without a possible hydrate formation. It is seen that there is a good agreement between the calculated and the experimentak results. It should be noticed that for these two-phase calculations both pressure and temperature have to be specified, while only pressure or temperature can be specified for the calculation of the three-phase coexistence curves in Figs l-10.

7. CONCLUSlON

A method for predicting the formation of gas hydrates has been developed. The calculations compare well with experimental data where comparisons are possible since the parameters have been estimated

Computations of the formation of gas hydrates 267 1

Table 10. Water content of liquid hydrocarbon in equilibrium with hydrate at 34.05 atm

Water concentration Hydrocarbon (mole %) composition Temperature

(mole %) (K) Experimental’ Predicted

Ethane 10.2 247.75 0.0095 0.0084 Propane 89.8 273.45 0.0137 0.0127

Ethane 64.6 263.45 0.0064 0.0054 Propane 35.4 276.15 0.0161 0.0140

Ethane 91.5 263.95 0.0057 0.0053 Propane 8.5 274.95 0.0 134 0.0121

Methane 10.1 264.05 0.0056 0.0054 Ethane 4.4 270.65 0.0 124 0.0090 Propane 26.1 Pentane 59.4

‘Sloan et al. (1986).

450.0

c

l

400.0

350.0

300.0

P = 34.01 atm

T(K)

Fig. 12. Water content [x, (mole fraction)] in a gaseous mixture of methane (mole fraction 0.0531) and propane (mole fraction 0.9469) in equilibrium with hydrate at various pressures (P) and temperatures (T):

(e, A, tl, 0) experimental data from Song and Kobayashi (1982), (- -) predicted water content.

from a very large data base. The method combines existing models for gas hydrates with well-known liquid models like UNIQUAC and the SRK equation of state. The procedure is robust and the checks for phase stability are based on the algorithms developed by Michelsen (1982). This means that no a priori information about the actual phases has to be pro- vided.

Acknowledgements-The authors are pleased to thank K. S. Pedersen and F. Fogh for fruitful discussions and for help in the computations. The support of Teknologiradet, Denmark, is gratefully acknowledged.

A B

a, b

C

NOTATION

Langmuir parameters constants in vapor pressure expression

[es. (L4)1 Langmuir adsorption constant

AC, .r AH NCAV NCOMP V

AV

X

Y

Y p V

Subscripts

i

K

0

W

heat capacity difference fugacity enthalpy difference number of cavities number of components molar volume of water (ice or liquid) volume difference mole fraction in aqueous phase probability of a filled cavity activity coefficient chemical potential number of cavities

type of cavity component at reference temperature 273.15 K water

2672 JAN MVNCK et al.

Superscripts H hydrate

0 ice or liquid water

c( non-hydrate phase

P empty Iattice

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Computations of the Formation

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