Phase equilibrium calculations for unprocessed well streams containing hydrate inhibitors
Karen S. Pedersen a , * Michael L. Michelsen b Arne O. Fredheim c 9
a CALSEP A /S , Gl. Lundtoftevej 7, DK-2800 Lyngby, Denmark b Department of Chem. Eng., DTU, DK-2800 Lyngby, Denmark
c STATOIL Research & Development, Trondheim, Norway
Received 29 January 1996; accepted 31 May 1996
Abstract
It is shown that the phase distribution of methanol and water between a hydrocarbon gas phase, a hydrocarbon liquid phase and an aqueous phase can be represented using the Soave-Redlich-Kwong equation with a non-conventional mixing rule for the a-parameter suggested by Huron and Vidai. Model parameters are estimated from data for binaries of the type methanol-hydrocarbon and water-hydrocarbon. New experimental data are presented for two reservoir fluids and for one model system. The paper further presents a phase equilibrium algorithm for calculating the phase boundaries and the equilibrium compositions at the phase boundary for a system consisting of a gas, a liquid and a mixed aqueous phase.
Keywords: Model; Method of calculation; Equation of state; Data; Experimental method; Vapour-liquid equilibria
1. Introduction
Transport of unprocessed well streams in pipelines has become more frequent in recent years in the North Sea. This has to do with the fact that an increasing part of the North Sea oil and gas production comes from marginal fields. These are fields too small for a separate process plant to be economically attractive. Instead, the unprocessed well stream containing gas, oil and water is transported in a sub-sea pipeline to an existing process plant for separation into gas, oil and water. The lowest temperature achieved in a non-insulated pipeline will typically be about 4°C, which is approximately the sea water temperature in winter. The pipeline pressure will typically be of the order 50-100 bar.
14 K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28
When water and light gaseous compounds are in contact at these conditions, there is a potential risk of gas hydrate formation. Gas hydrates are crystalline compounds consisting of water and light gases. If gas hydrates form, the pipeline is likely to plug up and the flow will stop until the gas hydrates are dissociated again. This may take place by addition of a hydrate inhibitor and/or by de-pressurization of the pipeline. In either case the dissociation process is both time-consuming and costly. For this reason gas hydrate formation in pipelines is highly undesirable. The formation of gas hydrates may be prevented by addition of hydrate inhibitors. The most commonly used hydrate inhibitor is methanol. Calculation of the amount of methanol needed and the influence of this component on the phase behavior calls for a thermodynamic model and for phase equilibrium algorithms capable of handling mixtures of gas, oil, water and hydrate inhibitors.
Most phase equilibrium calculations on oil and gas mixtures are performed using a cubic equation of state as, for example, the Soave-Redlich-Kwong (SRK) (Soave, 1972) or the Peng-Robinson (Peng and Robinson, 1976) equations. Water is often handled by assuming binary interaction coefficients of the order of 0.5 for the hydrocarbon-water interactions. At usual pipeline conditions, this assumption will somewhat underestimate the solubility of water in hydrocarbon liquid phases and the solubility of hydrocarbons in any aqueous phase. With only hydrocarbons and water present, such approximate calculation results are nevertheless acceptable for many practical purposes including most pipeline flow simulations. If the pipeline fluid also contains methanol, this may have a significant impact on the phase behavior. The miscibility of methanol and especially light hydrocar- bons exceeds that of water, meaning that the assumption of almost no miscibility between the hydrocarbon liquid and water phases is no longer valid.
When evaluating potential thermodynamic models which can be used to represent the phase equilibria of hydrocarbon-methanol-water systems, it is essential to bear in mind that the quality of the calculation results at the limit of no methanol present should preferably be unaffected. A model reducing to a cubic equation of state with classical mixing rules when no methanol is present would be the most appropriate.
2. The Huron and Vidal model
Kristensen et al. (1993) have suggested modeling the phase behavior of mixtures of hydrocarbons, water and methanol using the SRK equation
RT a(T) P= V - b V(V+b) (1)
with the following a-parameter mixing rule as suggested by Huron and Vidal (1979) (H&V)
a = b i=~l - (2)
In these equations P is the pressure, R the gas constant, T the absolute temperature, V the molar volume, a and b equation of state parameters, z the mole fraction, i a component index, and G~ the
K.S. Pedersen et aL / Fluid Phase Equilibria 126 (1996) 13-28 15
excess Gibbs energy at infinite pressure. G E is found from a modified NRTL mixing rule (Huron and Vidal, 1979)
N
G E N E 7 . j i b j z j exp ( - - ° l j iT . j i )
_ _ : E Z i j = l N (3) RT i=1 y' bkZkeXp(_aki7.ki)
k = l
a 0 is a non-randomness parameter for taking into account that the mole fraction of molecules of type i around a molecule of type j may deviate from the overall mole fraction of molecules of type i in the mixture. When otij is zero the mixture is completely random. The parameter 7" is defined by the following expression
gji -- gii 7"ji = R T (4)
where gji is an energy parameter characteristic of the j - i interaction. The mixing rule of Eq. (3) is based on a modification of the NRTL-model (Renon and Prausnitz, 1968) and was shown by Huron and Vidal to have the interesting property that it reduces to the classical SRK mixing rule, if the parameters are selected to
Ogij = 0 (5 )
gii = ai ln2 (6) bi
yib gji= - 2 b i + b j ~ ( 1 - k i j ) (7)
where kij is the binary interaction parameter in the classical SRK mixing rule for the a-parameter. For binary pairs of components which are adequately described using the classical mixing rule, there is no need for estimating additional parameters. They may simply be found from Eqs. (5)-(7). This makes the Huron and Vidal model appropriate for describing mixtures of essentially hydrocarbons with some content of polar compounds, as for example water and methanol.
The a-parameter in Eq. (1) has the following temperature dependence
R2T~ a i = 0.42747 Pci [f(Tri)]2 (8)
f ( T r) is in the classical form found from the following expression
f(Tr) = 1 + Cl(1 - !/~,) (9)
where CI is a function of the acentric factor, w
C I = 0.48 + 1 .574w- 0.176w 2 (10)
This temperature dependence will in general give fairly accurate pure component vapor pressures for hydrocarbons. For polar compounds, as for example water or methanol, the calculated pure
component vapor pressures will be less accurate. For these compounds, a temperature dependence suggested by Mathias and Copeman (1983) may be more adequate
Kristensen et al. (1993) have estimated interaction parameters for the Huron and Vidal model for binary pairs consisting of methanol and one of the components H20, N2, CO 2, H2S, C 1, C2, C3, nC 4, iC 5, nC 5, C 6. When estimating these parameters they used the classical a-parameter tempera- ture dependence of Eq. (10) for all components.
3. Experimental data
Measurements of the phase distribution of methanol between a gas, an oil and an aqueous phase have been performed as part of an internal STATOIL project. Compositions for two different North Sea reservoir fluids are shown in Table 1. Additional measurements have been performed by Chen et al. (1988) for a 4-component model system consisting of water, methanol, C~ and n-C 7. The experiments were carried out by confining the mixtures in a windowed cell fabricated from stainless steel and tempered Pyrex glass that permitted through-observation of the contents. The cell had a total working volume of approximately 80 cm 3. The cell contents were confined over mercury which could be added or withdrawn using a high pressure pump to vary the volume and hence the pressure. The cell was mounted inside a temperature-controlled liquid bath. The cell could be rocked in order to mix the fluid, and thereby reducing the time for establishing the equilibrium. The pressure of the system
Table 1 Molar compositions (in mole%) of mixtures 1-4
Component Mixture 1 Mixture 2 Mixture 3 Mixture 4
N 2 0.15 0.64 0.64 0.24 CO 2 2.05 3.10 0.82 3.11 C I 25.52 72.74 71.47 74.56 C2 8.06 8.01 12.35 7.64 C 3 7.69 4.26 10.00 3.21 iC 4 1.78 0.73 1.08 0.63 F/C a 3.95 1.49 2.64 1.28 iC 5 1.82 0.53 0.38 0.54 nC 5 2.39 0.64 0.43 0.65 C 6 4.29 0.81 0.19 0.89 C 7 6.71 1.08 1.09 C 8 7.85 1.20 1.24 C 9 6.31 1.08 0.86 C Jo+ 3.38 3.70 4.06 C7+ MW (g mol- t) 158 169 187 C7+ density (g cm- 3) 0.83 0.82 0.82
K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28
Table 2 Phase compositions (mole%) for Mixture 1
17
Component Feed Hydrocarbon phase Aqueous phase
Exp. Calc. %Dev. Exp. Calc. %Dev.
P - 120 bar and T ~ 6.5°C
Res. Fluid 60.48 99.815 99.731 - 0 . 1 - - -
M e t h a n o l 5.97 0.185 0.231 24.9 15.08 14.76 - 2.1 Water 33.55 - - - 84.92 84.89 0.0 P = 200 bar and T = 7.9°C
Res. Fluid 63.85 99.804 99.734 - 0 . 1 - - -
M e t h a n o l 5.46 0.196 0.228 16.3 15.08 14.71 - 2.5 Water 30.69 - - - 84.92 84.91 0.0
was m e a s u r e d wi th a c a l i b r a t e d 0 - 2 0 0 b a r H e i s e gauge . T h e p r e s s u r e was k n o w n wi th in ___ 20 kPa.
T e m p e r a t u r e s we re m e a s u r e d us ing a c a l i b r a t ed c o p p e r - c o n s t a n t a n t h e r m o c o u p l e wi th a d ig i t a l
r eadou t , so that the t e m p e r a t u r e s w e r e k n o w n to w i th in -I-0.1°C. T h e cel l was e v a c u a t e d b e f o r e
m e a s u r e m e n t s . The w a t e r and m e t h a n o l so lu t i on was p r e p a r e d by w e i g h i n g each o f the c o m p o n e n t s
into a mix tu re . T h e h y d r o c a r b o n mix tu r e w a s p r e p a r e d by r e c o m b i n i n g a s tock t ank oi l wi th l igh t gas
c o m p o n e n t s , in o r d e r to r e a c h a spec i f i ed to ta l c o m p o s i t i o n . A n accu ra t e ly m e a s u r e d a m o u n t o f the
m e t h a n o l - w a t e r so lu t i on was a d d e d to the ce l l , f o l l o w e d by an a c c u ra t e ly m e a s u r e d a m o u n t o f the
r e c o m b i n e d h y d r o c a r b o n mix tu re . A f t e r f i l l ing the cel l , the p r e s s u r e and t e m p e r a t u r e we re a d j u s t e d to
the d e s i r e d va lue . A r o c k i n g p e r i o d o f m i n i m u m 8 hours was u sed in o r d e r to c rea te e q u i l i b r i u m in the
cel l . A f t e r e q u i l i b r i u m w a s e s t ab l i shed , s a m p l e s w e r e t aken f r o m each p h a s e in o r d e r to a n a l y z e the
c o m p o s i t i o n . T h e r e are s o m e va r i a t ions b e t w e e n tes t p r o c e d u r e s used for the r e s e r v o i r f lu ids and the
m o d e l f lu ids . T h e s a m p l e f rom the gas p h a s e w a s w i t h d r a w n at cons t an t t e m p e r a t u r e and p r e s s u r e and
a n a l y z e d . T h e h y d r o c a r b o n l iqu id p h a s e was a n a l y z e d in two s teps . A po r t i on o f the h y d r o c a r b o n
l iqu id p h a s e was d i s p l a c e d into a c o n t a i n e r to w h i c h a k n o w n a m o u n t o f a so lven t w i th an in terna l
s t anda rd had p r e v i o u s l y been added , in o r d e r to ex t rac t the w a t e r and the m e t h a n o l f rom the l iqu id
h y d r o c a r b o n phase . T h e r e su l t ing s o l v e n t - w a t e r - m e t h a n o l so lu t ion w a s ana lyzed . A n o t h e r po r t i on o f
the h y d r o c a r b o n liquid was ana lyzed direct ly in order to establish the hyd roca rbon compos i t ion . A
sample o f the aqueous liquid phase was wi thdrawn at cons tant pressure and temperature . The sample was stabil ized and the gas phase and the liquid phase were analyzed. All o f the analyses were
pe r fo rmed us ing gas ch roma tog raphy . T he concent ra t ion o f water and methanol was detected us ing a
thermal conduc t iv i ty detector (TCD) , and the h y d r o c a r b o n concent ra t ion was detected us ing a f l ame ionizat ion de tec tor (FID). T he ma jo r c o m p o n e n t s were ana lyzed with an accu racy o f __+ 0.003 mole
fraction, and the mino r c o m p o n e n t s with an accu racy o f _ 10%. Methanol was ana lyzed with an
accuracy o f + 25 ppm. The phase equi l ibr ium data for the two reservoir f luids and the model sys tem
are shown in Tables 2 - 9 .
4. Estimation of model parameters
To ensure reasonable p u r e - c o m p o n e n t vapor pressures, the Mathias and C o p e m a n tempera ture
dependence expressed in Eqs. (1 1) and (12) was used for water and methanol . The coeff ic ients C 1 - C 3
are g iven in Tab le 10. W h e n es t imat ing H & V interact ion parameters Kris tensen et al. (1993) did not
Table 10 Coefficients in Eq. (11) and Eq. (12) (Dahl and Michelsen, 1990)
Component C 1 C 2 C 3
Water 1.0873 - 0.6377 0.6345 Methanol 1.4450 - 0.8150 0.2486
20 K.S. Pedersen et a L / Fluid Phase Equilibria 126 (1996) 13-28
Table 11 Interaction energy parameters for binary mixtures of methanol and the indicated second component
2nd component ( g t2 - g 2 2 ) / R / K (g21 - g 1 1 ) / R / K ot 12 References
H20 288 276 1.20 1 N 2 357 1130 0.40 1-3 CO 2 247 2970 0.40 4,5 H2S 58 886 0.40 6 C l 77 2094 0.40 7 C 2 255 1610 0.40 8-10 C 3 465 1418 0.40 7,11 nC 4 516 1049 0.40 12 iC 5 675 1056 0.40 13 nC 5 774 1195 0.40 14 nC 6 829 1164 0.40 15,16 nC 7 5000 1561 0.48 17
References cited: 1. Griswold and Wong (1952), 2. Krichevskii and Lebedeva (1947), 3. Weber et al. (1984), 4. Ohagini and Katayama (1976), 5. Katayama et al. (1975), 6. Yorizane et al. (1969), 7. Schneider (1978), 8. Ma and Kohn (1964), 9. Ohagini et al. (1976), 10. Weber (1981), 11. Nagahama et al. (1981), 12. Churkin et al. (1978), 13. Ogorodnikov et ai. (1960), 14. Tenn and Missen (1963), 15. Ferguson (1932), 16. Wolff and Hoeppel (1968), 17. de Loos et al. (1988).
use the Mathias and Copeman temperature dependence but the classical one suggested by Soave. For this reason it was found necessary to refit Kristensen's H & V interaction parameters. The refitted parameters are shown in Table 11. H& V parameters for interactions with water were also estimated and are given in Table 12. H & V parameters for interaction between methanol and n C 7 and between water and nC 7 were determined from the data of Tables 4-9 . All parameters were estimated using an object function equal to the squared sum of the relative deviations between the measured and
Table 12 Interaction energy parameters for binary mixtures of water and the indicated second component
2nd component ( g 12 - g 2 2 ) / R / K ( g21 - g i l ) / R / K a t2 References
N 2 689 3921 0.15 1 CO 2 16 1652 0.15 2,3,4 H2S 118 1294 0.15 1 C l 410 2291 0.15 4,5 C 2 492 2281 0.15 3,6 C 3 847 2650 0.15 7 nC 4 793 2501 0.15 8 iC 5 1120 2900 0.15 9 nC 5 1109 2901 0.15 9 nC 6 1187 2878 0.15 9 nC 7 - 81 2741 0.15 Tables 2 -9
References cited: 1. International Critical Tables (1928), 2. Culberson and McKetta (1951), 3. Danneil et al. (1967), 4. Burd (1968), 5. Olds et al. (1942), 6. Reamer et al. (1943), 7. Kobayashi and Katz (1953), 8. Reamer et al. (1951), 9. Polak and Lu (1973).
calculated molar component concentrations in each phase. The calculation results obtained for the model system are given in Tables 4-9.
5. Test calculations
Phase equilibrium calculations were performed for the mixtures of Tables 2 and 3, i.e. for two reservoirs fluids mixed with methanol and water. This data material had not been used in the estimation of the model parameters and the test calculations therefore served to validate the model parameters for multicomponent mixtures. The two reservoir fluids were characterized using the procedure of Pedersen et al. (1989) with 12 pseudo-components. The H & V model and the parameters of Tables 11 and 12 were used for binaries including methanol and water. The H &V parameters estimated for n C 4 w e r e also used for iC 4 and the H&V parameters estimated for n C 7 w e r e used for all C7+-components. For all binaries not including water or methanol, the H & V parameters were determined from Eqs. (5)-(7). For all binaries not including N 2 and CO 2, k u = 0 was used. For binaries including N 2 and CO 2, the k U values recommended by Reid et al. (1977) were used. The results of the test calculations are shown in Tables 2 and 3.
6. Phase envelope calculation
Phase envelope calculations are frequently used to give an overview of the phase behavior of hydrocarbon reservoir fluids at various conditions. With water and hydrate inhibitors present, three phases have to be considered. Michelsen (1981) has presented a phase envelope algorithm for calculation of hydrocarbon phase boundaries in the presence of a pure water phase. It gives the corresponding temperature (T) and pressure (P) values for which the vapor phase equals a specified mole fraction of the total hydrocarbon phases. The algorithm takes into account the solubility of water in the hydrocarbon phases, but neglects the solubility of foreign components in the water phase. With methanol present, the approach of Michelsen is not readily applicable. The water phase also contains methanol and it is no longer obvious that the solubility of hydrocarbons in the water + methanol phase can be neglected. There is the need for an extension of the former algorithm which can take into consideration that the aqueous phase is a mixed phase in which hydrate inhibitors as well as hydrocarbons may be present.
An N-component mixture with overall molar composition z is considered. Mole fractions in the hydrocarbon liquid phase, the vapor phase and the aqueous phase are denoted x, y and w, respectively. The phase fraction of the aqueous phase is /3 w, and the vapor fraction /3 is defined as the ratio of the molar vapor amount to the molar amount of vapor plus hydrocarbon liquid. In all calculations /3 is kept fixed, usually at 1 or 0.
At equilibrium, the following 3N + 2 equations must be satisfied
lny i + l n q ~ - lnx i - lnq~ = 0 i = 1,2 . . . . , N (13)
l n w i + l n q ~ ? - l n x i - l n q ~ ] = O i = 1,2 . . . . . N (14)
/ 3 w w i + ( 1 - / 3 w ) ( / 3 y i + ( 1 - / 3 ) x i ) - z i = O i = 1,2 . . . . . N (15)
22 K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28
N
Y ' ~ ( Y i - X i ) = O i= l
N
E w i - - l = O i=1
The set of equations is reduced by introducing equilibrium factors
wi . Ki = __Yi Ki w = - - t = 1,2 . . . . . N
X i X i
and substitution of these expressions into the material balance, Eq. (15), yields
x i
Yi
Zi
/3wK~w + (1 - /3w)( /3Ki + 1 - - /3)
Ki Z~
/3wKiw + (1 - / 3w) ( /3Ui - J¢ - 1 - / 3 )
K w i z i
wi= /3wKiw + (1 - / 3 w ) ( / 3 K i + 1 - / 3 )
and the equilibrium equations become
InK i + l n C v - l n ~ ] = 0 i = 1 , 2 . . . . . N
l n K i w + l n ~ p W - l n ¢ ] = 0 i = l , 2 , . . . , N
s ( K i - 1)Zi
Y'. /3wK,w+(1 _ /3w) ( /3Ki+ 1 _ /3 ) = 0 i= l
N K i w Zi
Y'. /3wK,w + ( l _ / 3 w ) ( / 3 K , + l _ / 3 ) i=1
(16)
(17)
(18)
(19)
(20)
(21)
(22)
- 1 = 0 ( 2 3 )
These 2N + 2 equations relate the 2N + 3 variables (K, K w, T, P and /3w), and the family of solutions defines the phase envelope for the given value of /3. K and K w are vectors of K-factors.
The calculations are initiated by specifying a low value for the pressure on the dew-point side, e.g. P = 1 bar. At low pressures the vapor phase is nearly ideal, and the same is usually the case for the hydrocarbon liquid. Initial estimates are created by means of the Wilson K-factor approximation, and we take
where Tel, Pci and o) i are the critical temperature, the critical pressure and the acentric factor for component i.
For the liquid phases we use the Wilson expression for the fugacity coefficients of the hydrocarbon components in the hydrocarbon phase and the aqueous components (water and methanol) in the
K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28 2 3
aqueous phase. For the aqueous components in the hydrocarbon phase and the hydrocarbon compo- nents in the water phase, we set
In ~i = In ~0~'Wil'°" + 10 (25)
The use of these initial approximations reduces the equation set to 2, Eq. (22) and Eq. (23), and for specified P these can be solved for T and /3 w. Next, mole fractions x, y and w are calculated. Finally the full set of equations is solved at the specified pressure by a partial Newton's method where the composition derivatives of the Jacobian are neglected in the calculation of the Jacobian matrix.
The initial composition estimates generated by means of the Wilson K-factors are not very accurate for the hydrocarbon components in the aqueous phase and for the aqueous components in the hydrocarbon liquid. The estimates, however, have the property that they generate a hydrocarbon liquid where water and methanol are virtually absent, and similarly the hydrocarbon content in the aqueous phase is low and the quality of the estimates is adequate for the subsequent convergence of the full set.
Subsequent points on the phase envelope are calculated by solving the set of Eqs. (20)-(23) using a full Newton's method where all derivatives are accounted for in the Jacobian matrix. Sensitivities with respect to the specification variables are used in a similar manner as in the two-phase phase envelope procedure of Michelsen (1980). These sensitivities enable us to interpolate between calculated points, locate critical points and extrema on the phase boundary accurately and to extrapolate to provide good initial estimates for subsequent points by means of third-order polynomi- als.
When the mixture contains only lighter hydrocarbons (up to C 7) and the amounts of aqueous components are not very small, the liquid aqueous phase is present along the entire phase envelope. An example of this behavior is seen in Fig. 1 which presents the phase envelope of Mixture 3 in Table 1 to which 0.1 mole of water has been added per mole hydrocarbon. If heavier hydrocarbons are present or if the amount of water and methanol is very small, it is possible to enter a temperature
Temperature (C) Fig. 1. Mixture 3 with water present along the whole phase boundary.
24 K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28
range where the aqueous components are completely dissolved in the hydrocarbon phases ( flw = 0). If the two-phase boundary is followed through the temperature maximum and back again to lower temperatures, the solubility of the aqueous components decreases and the water phase reappears. An example of this behavior is seen in Fig. 2 which shows the phase envelope of Mixture 3 with 0.0075 mole of water added per mole hydrocarbon. In principle, one could check for the reappearance of the aqueous phase by means of stability analysis but an alternative approach was chosen.
We replace Eq. (21) by
In Kiw + In ~pw _ In q~] + 0 = 0 (26)
When flw > 0, O is set to zero and the usual equilibrium equations are recovered. When a region where the aqueous phase is absent is encountered, we set flw = 0 and replace /3 w by 0 as the new independent variable. A phase composition w satisfying Eq. (26) corresponds to a stationary point of the tangent place distance for any of the hydrocarbon phases (Michelsen, 1982), a negative value of 0 indicating stability of the hydrocarbon phases and a positive value instability. At the point of incipient formation of the aqueous phase, 0 equals zero.
A typical calculation proceeds as follows: At the initial low pressure point, an aqueous phase is present (flw > 0) and 0 is therefore fixed at zero. As we follow the dew line towards higher temperatures and pressures, we arrive at a point (T, P) where /3 w is exactly zero. We now keep the value of flw fixed at zero and solve the set of equations with the K-factors, T, P and 0 as the independent variables. Along this branch where we have two-phase equilibrium, 0 is negative, goes through a minimum and again increases at lower temperatures. The point where 0 again becomes zero marks the reappearance of the aqueous phase and we can return to the original set of variables.
The main advantage of this procedure is that it enables us to "keep track" of the composition of the aqueous phase even when this phase is not present at equilibrium. In addition, the points of disappearance and reappearance for the aqueous phase can be precisely located.
120
0 80 CO
f f l
m 4o I1)
cl
Hydrocc~'bon Ph se Boundary _ _ Water Dew L ne /
f
/ /
/x /
CP I
J \ f
/ S
- 1 0 0 ' ' ' ' ' ' ' 1 _ . 5 0 , , i , I i i 0 i I , , i t i 1 5 0
Temperature (C) Fig. 2. Mixture 3 with water phase disappearing and reappearing.
K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28 25
The calculation of the entire phase envelope in this manner can be performed when the temperature along the equilibrium line is well below the critical temperature of water. When very heavy hydrocarbons are present, however, the temperature along the dewpoint branch may easily exceed 600 K. In this case, an aqueous liquid composition satisfying Eq. (26) cannot be determined and it becomes necessary to initiate the calculations in a different manner.
An obvious alternative would be to start the calculations from the bubble point side. The low-pressure (1-5 bar) bubble point for methane-containing mixtures is usually in the range 140-170 K but in this temperature range gas condensates in particular tend to exhibit liquid-liquid immiscibil- ity. Since the calculation procedure does not account for immiscible hydrocarbon liquids, a false (i.e. unstable) bubble point curve would result, leading to subsequent breakdown.
The region of particular practical interest is the coexistence curve in the temperature range 250-450 K. Immiscible liquid hydrocarbon phases are usually not encountered above 200 K, and it is therefore attractive to initiate calculations at or around a temperature of 200 K. At this temperature, however, the saturation pressure is substantial and can easily exceed 100 bar, and the Wilson approximation is inadequate for initiating the calculation. On the other hand, at 200 K water and methanol have a very low solubility in the hydrocarbon phases and the hydrocarbons are similarly virtually insoluble in the aqueous phase. We have therefore chosen to determine the initial point by means of a preliminary calculation of the phase envelope using a composition corresponding to only the hydrocarbon part of the mixture in question. Starting this two-phase calculation from the dewpoint, the problem with immiscible liquid phases at low temperatures is avoided. The calculation provides us with the saturation pressure and the corresponding composition of the equilibrium phases at 200 K. Next, the aqueous components are added and a separate calculation of the coexistence curve in the temperature range 200-500 K is unproblematic.
Fig. 3 shows the hydrocarbon phase boundary of Mixture 4 in Table 1. Also shown is the hydrocarbon phase boundary when 0.03 moles of water and 0.05 moles of methanol have been added to this mixture. At temperatures below approximately - 50°C the two phase boundaries are practically
q" (3 £13
E
co u3
Cu
500,
4OO
300
200
/ -\
\
Io Water md M e t h o l o l later and ~ethano l ~resent
. . . . , i , i i
o ~oo 2oo ~oo 4oo Temperature (C)
tO0
- ] 0 0
Fig. 3. The effect of methanol/water on the hydrocarbon phase boundary of mixture 3.
26 K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28
identical, while at temperatures above 0°C the presence of methanol and water influences the location of the phase boundary significantly.
7. Discussion of the results
The measured phase equilibrium data in Tables 2-9 show that the miscibility between aqueous and hydrocarbon liquid phases is fairly limited at the conditions of the experiments. The water and methanol mole fractions in the hydrocarbon liquid phases are generally small and the same is the case for the hydrocarbon mole fractions in the aqueous phase. The deviations between the measured and the calculated phase compositions may appear quite high in some cases but it is essential to keep in mind that the mole fractions to be compared are in most cases fairly small.
8. Conclusion
The experimental data and the calculation results presented indicate that the Huron and Vidal model can correlate reasonably well the phase distributions of methanol and water between an aqueous phase and two hydrocarbon phases as well as the solubility of methane and n-heptane in an aqueous phase. Moreover, as the mixing rule has the interesting property that it reduces to the classical SRK mixing rule in the limit with no polar compounds present, it seems well suited for mixtures of essentially non-polar compounds which also contain a few polar compounds. Hydrocar- bon phase boundaries for systems which may also contain a separate aqueous phase may be tracked using a new phase envelope algorithm presented in this paper. This algorithm is capable of handling phase boundaries where the water phase disappears at high pressures on the dewpoint line and reappears again at lower pressures.
9. List of symbols
a
b C l - C 3
CP
f G g K K MW N P R T
equation of state parameter equation of state parameter constants defined in Eq. (9), Eq. (11) and Eq. (12) critical point function defined in Eq. (9), Eq. (11) and Eq. (12) Gibbs free energy energy interaction parameter equilibrium factor vector equilibrium factor molecular weight number of components pressure gas constant temperature
K.S. Pedersen et a l . / Fluid Phase Equilibria 126 (1996) 13-28 27
letters non-randomness parameter ratio of molar amount of vapor to the molar amount of vapor plus hydrocarbon liquid fugacity coefficient parameter defined in Eq. (4) acentric factor parameter defined in Eq. (26)
Sub and super indices
C
E i
J k 1 r
v
w (3t3
critical property excess property component index component index component index liquid reduced property (property at actual conditions divided by property at critical point) vapor aqueous phase infinite pressure
R e f e r e n c e s
S.D. Burd, Jr., Phase Equilibria of Partially Miscible Mixtures of Hydrocarbon and Water, Ph .D. Dissertation, The Pennsylvania State University, 1968.
C.J. Chen, H.-J. Ng and D.B. Robinson, GPA Research Report RR-117, 1988. V.N. Churkin, V.A. Gorshkov, S.Yu. Pavlov, E.N. Levicheva and L.L. Karpacheva, Zh. Fiz. Khim., 52 (1978) 488. O.L. Culberson and J.J. McKetta, Trans. AIME, 192 (1951) 223. S. Dahl and M.L. Michelsen, AIChE J., 36 (1990) 1829-1836. A. Danneil, K. Todheide and E.U. Franck, Chem. Ing.-Tech., 13 (1967) 816-821. J.B. Ferguson, Phys. Chem., 36 (1932) 1123. J. Griswold and S.Y. Wong, Chem. Eng. Prog. Symp. Ser., 48 (1952) 18. M.J. Huron and J. Vidal, Fluid Phase Equilibria, 3 (1979) 255-271. International Critical Tables, McGraw-Hill, 1928. T. Katayama, K. Ohgahi, G. Mackawa, M. Goto and T. Nagano, J. Chem. Eng. Jpn., 8 (1975) 89. R. Kobayashi and D.L. Katz, Ind. Eng. Chem., 45 (1953) 440-446. I.R. Krichevskii and E.S. Lebedeva, Zh. Fiz. Khim., 21 (1947) 715.
J.N. Kristensen, P.L. Christensen, K.S. Pedersen and P. Skovborg, Fluid Phase Equilibria, 82 (1993) 199-206. T.W. de Loos, W. Poot and L. de Swan Arons, Fluid Phase Equilibria, 42 (1988) 209. Y.H. Ma and J.P. Kohn, J. Chem. Eng. Data, 9 (1964) 3. P.M. Mathias and T.W. Copeman, Fluid Phase Equilibria, 13 (1983) 91-108. M.L. Michelsen, Fluid Phase Equilibria, 4 (1980) l - l 0. M.L. Michelsen, Three-Phase Phase Envelope and Three-Phase Flash Algorithms with a Liquid Water Phase, SEP Report
8123, Institut for Kemiteknik, The Technical University of Denmark, 1981. M.L. Michelsen, Fluid Phase Equilibria, 9 (1982) 1-40. K. Nagahama, S. Suda, T. Hakura and M. Hirata, Sekiyu Gakkai Shi, 14 (1981) 252. S.K. Ogorodnikov, U.B. Kogan and M.S. Nemtsov, Zh. Prikl. Khim., 33 (1960), 2685. K. Ohagini and T. Katayama, J. Chem. Eng. Data, 21 (1976), 53. K. Ohagini, F. Sano and T. Katayama, J. Chem. Eng. Data, 21 (1976) 55. R.H. Olds, B.H. Sage and W.N. Lacey, Ind. Eng. Chem., 34 (1942) 1223. K.S. Pedersen, P. Thomassen and Aa. Fredenslund, Adv. Thermodyn., 1 (1989) 137-152. D.-Y. Peng and D.B. Robinson, Ind. Eng. Chem. Fundam., 15 (1976) 59-64. J. Polak and B.C.-Y. Lu, Can. J. Chem., 51 (1973) 4018-4023. H.H. Reamer, R.H. Olds, B.H. Sage and W.N. Lacey, Ind. Eng. Chem., 35 (1943) 790-793. H.H. Reamer, B.H. Sage and W.N. Lacey, Ind. Eng. Chem., 43 (1951) 2515. R.C. Reid, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids, 3rd edn., McGraw Hill, New York,
1977. H. Renon and J.M. Prausnitz, AIChE J., 14 (1968) 135-144. Schneider, Doktor-Ingenieur Dissertation, TUB, Berlin, 1978. G. Soave, Chem. Eng. Sci., 27 (1972) 1197-1203. F.G. Tenn and T.W. Missen, Can. J. Chem., 41 (1963), 12. W. Weber, S. Zeck and H. Knapp, Fluid Phase Equilibria, 18 (1984) 253. W. Weber, Experimentelle Bestimmung und Korrelation der Loslichkeit von Gasen in Alkoholen, Doktor-Ingenieur
Dissertation, TUB, Berlin, 1981. H. Wolff and H.E. Hoeppel, Ber. Bunsenges. Phys. Chem., 72 (1968) 710. M. Yorizane, S. Adadmoto, H. Masuoka and Y. Eto, Kog. Kag. Zashio, 72 (1969) 2174.
