Ind. Eng. Chem. Res. 1987, 26, 1168-1173
1168
An Analysis of Mass-Transfer Effects in Hydroformylation Reactions? Arijit Bhattacharya and Raghunath V. Chaudhari* Chemical Engineering Division, National Chemical Laboratory, Pune 411 008, India
T h e simultaneous absorption of two gases into a liquid, accompanied by a complex reaction with negative-order kinetics and typically observed in hydroformylation reactions, has been studied. An expression for enhancement factor has been derived which is applicable independent of the regime of absorption. Practical implications of this analysis have been illustrated with a hydroformylation reaction as an example, in which some unusual effects of parameters such as agitation speed on the rate of absorption have been observed. Under certain conditions, multiple solutions of enhancement factors can exist for the same set of parameter values. Several industrially important gas-liquid reactions, enhanced by homogeneous catalysis, involve simultaneous absorption of two or more gases followed by complex reaction kinetics. Some of the well-known examples (Falbe, 1980) are hydroformylation (oxo process) of ethylene, propylene, and higher linear olefins using soluble Co- or Rh-complex catalysts; carbonylation of ethylene using Ni-complex catalyst; homologation of alcohols by homogeneous Ru-complex catalysts; etc. For hydroformylation of propylene with the Co-complex catalyst, Natta et al. (1954) reported that the rate of reaction shows a negative-order dependence with respect to CO concentration and is first-order in H,concentration. They proposed the rate equation
Kinetic Model The kinetic model shown in eq 1 has a limitation that it would not be applicable at lower partial pressures of CO since it would predict the rate to be infinity in the limit. This is not true in practice. While the negative-order dependence prevails in a certain range of CO partial pressures, it has also been observed (Chaudhari and Deshpande, 1984) that the rate vs. CO partial pressure for hydroformylation of olefins passes through a maximum and even shows a positive slope at low enough CO partial pressure. Thus, the rate of hydroformylation for constant olefin concentration can be better represented by the following form of rate model (Chaudhari, 1984) rE =
where rE represents the rate of reaction of E (mol/(cm3 s)), Co the catalyst concentration (mol/cm3),and B, A, and E are the concentrations of olefin, hydrogen, and carbon monoxide, respectively (mol/ cm3). Further studies with RhLcomplex catalysts (Evans et al., 1968; Chaudhari and Deshpande, 1984) also reported a negative-order dependence of the rate with respect to CO partial pressure. The problem of simultaneous absorption of two gases in a reaction that follows simple kinetics has been extensively studied (Roper et al., 1962; Ramachandran and Sharma, 1971; Chaudhari and Doraiswamy, 1974; Juvekar, 1974; Hikita et al., 1977; Zarzycki et al., 1981). However, there has been no attempt so far to analyze a case of absorption accompanied by a reaction when the rate shows a negative-order dependence with respect to one of the gases. In particular, the consequences of the combined influence of mass-transfer limitation and negative-order kinetics on the overall rate of reaction have not been well-understood. The objective of this paper was to develop a generalized theoretical model to calculate the enhancement factor for the simultaneous absorption of two gases with a liquidphase reaction in which the rate is negative-order with respect to one of the gases and first-order with the other. This analysis should be applicable to hydroformylation and other reactions that follow similar rate model. Such an analysis is essential since hydroformylation reactions are known to be operating under conditions of significant mass-transfer limitation (Van Boven et al., 1975). Certain interesting practical implications of this analysis have been discussed with hydroformylation of 1-hexene as an illustrative example. NCL Communication 3881.
k3CoAE + KEE)"
(2)
(1
where KE and m are positive constants. For hydroformylation of olefins with H R ~ - C O S ( P P ~ ~ ) ~ catalyst, Evans et al. (1968) have proposed a mechanism, from which the following rate equation can be derived assuming hydrogenation of the species Rh.(CO)(PPh,),.(acyl) as a rate-determining step, rE =
k3CoAE 1 + KIE KzE2
+
(3)
It may be noted that eq 3 exhibits trends similar to eq 2 for m = 2 , and thus eq 2 provides a simplified but representative rate equation which is consistent with the mechanism of the reaction. Therefore, eq 2 will be used in the present analysis. For constant olefin and catalyst concentrations, it becomes kzAE rE = (4) (1 + KEE)' where kz = k3Co.
Theory Consider a reaction of the type A(g)
+ vE(g) + B(1)
catalyst
product
(5)
which represents the hydroformylation (oxo) process. Since the concentration of the olefin, B, is usually in large excess compared to the dissolved concentrations of hydrogen, A, and carbon monoxide, E, and since the catalyst concentration remains constant, it can be assumed that there is negligible depletion of olefin and catalyst concentrations at any point in the liquid phase. The following assumptions were also made: (1) the film theory is applicable; ( 2 ) the gas-side mass-transfer resistance is neg-
0888-5885/87/2626-1168$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1169 ligible; (3) isothermal conditions prevail; (4) there is no net inflow or outflow of the liquid (i.e., semibatch mode of operation); and (5) the kinetics of the reaction are represented by eq 4. The problem of simultaneous absorption of A and E can be represented by the material balance equations d2a -_ de2
(1
(?Mae + kte)2
(6)
d2e -_
SMae (1 + k,e)2
(7)
de2
Once eo is known, the concentration profile e(t) can be evaluated by
The integrals in eq 16 and 17 can be evaluated by a numerical technique. Having found eo as above, the enhancement factor, I&, is given by
with the boundary conditions
@E
u=e=1
t = O
(8)
and e = l
e=e,
a=ao
The symbols are defined in the Nomenclature section. The boundary condition in eq 9 is written on the basis that for a steady-state semibatch reactor operation, the product of flux of species A at x = 6 (film-bulk boundary) and interfacial area a' would be equal to the rate of reaction in bulk liquid. A similar relationship would also hold for species E and hence fluxes of A and E at x = 6 (or t = 1) are related through solubility, diffusivity, and stoichiometric ratios. From eq 6 and 7, we have d2a
4
,=s[,]
d2e
RE = kLa'E*4E (19) Two comments regarding the above analysis are in order. Firstly, the determination of the enhancement factor, #E, as described above, is perfectly general in that one does not need to know a priori the regime of absorption. Secondly, no arbitrary values of the bulk concentrations of CO (E,) and Hz (A,) need to be assumed, as these are determined within the analysis as shown above. Once eo and $E are known, one can use eq 13 and 11to determine a, and $A in a routine manner. For a typically fast reaction regime (at large values of M'/2), -(de/dc),=l N 0
r
r
de
9
'
(18)
and the following asymptotic expression for @E can be derived
Integrating eq 10 once and using the boundary condition 9 leads to the following relationship between the fluxes of A and E a t any point within the film da
= PIc=O
Here PI,=^ can be evaluated by substituting e = 1in eq 15 and taking the absolute value of the square root. The rate of absorption of species E is defined as
T€=s[x] Integrating eq 11 and using the boundary condition 8, one gets the following relationship between the local concentrations of A and E a = (q/S)e
Also, we have at a0
t
+ 1- ( q / S )
(12)
= 1 (Le., in the bulk liquid) = (s/S)eo
+ 1- ( q / S )
(13)
Substituting the value of a from eq 12 in eq 7, we obtain SMe[(q/S)e + 1 - (S/S)l d2e _ de'
(1
+ k,e)2
(14)
Integrating eq 14 once and using the boundary condition 9, one gets
Results and Discussion Existence Criteria. Since in the above analysis the concentration derivative is evaluated by taking a square root, it is possible that for some values of the parameters the mathematical solution would lead to imaginary values of the derivative and hence the solution would not exist. The existence criterion for the general case, irrespective of the regime of absorption, is given by d e , - e) I(s/S)(l+ kt) - ktKe - eo) 2SM[ -k:(1 + kteo)(l + k,e) Sk,2
at all e (e, 5 e I 1). For the fast regime of absorption, the criterion simplifies as
where p , = -[de/de],. The bulk-liquid-phase concentration of CO, e,, can now be found from
1170 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
The physical significance of the criterion in eq 22 is easy to understand. For example, if q / S > 1,species A is the limiting reactant. Then for certain parameter combinations, a fast reaction regime with respect to species E will mean negative concentrations for species A, and hence a solution will not exist.
Uniqueness of Steady State A discussion of the uniqueness of steady-state solutions of eq 6 9 is pertinent to the practical usage of the solutions. The type of the rate model considered in this work is very similar to the Langmuir-Hinshelwood expression for a bimolecular surface reaction based on dual-site adsorption mechanism of gas-solid catalytic reactions. For such a rate model, the presence of isothermal multiplicity is wellknown (Robertsand Satterfield, 1966). Thus, it is expected that, for the distributed parameter model under consideration in this paper, isothermal multiplicity of steadystate concentration profiles and enhancement factors will be observable under some conditions while in other situations the solutions will be unique. In what follows, we first discuss the exact uniqueness criteria applicable to our rate model, following Luss and Amundson (1967) and Luss (1968). By use of eq 14, a rather conservative criterion for uniqueness is obtained by ensuring monotonicity of the rate function, i.e., min 1aeao de d[
SMe{(q/S)e + 1 - (q/S)l [l + k,eI2
which reduces to the criterion k, S [l + 2/(S/q - l ) ]
for
1
>0
(23)
(q/S) S 1 (24)
{[(S/q) - 11 + 2e - [(S/q) - llk,eJ 3 0 for (q/S)
> 1 (25)
provided (1 + k,e) # 0. From the above criteria, we can conclude that for q / S = 1, the system will admit only unique solutions for all values of i k f / 2or k,. The same conclusion also holds true for q/S > 1 as can be derived from eq 25. Under the latter condition, the following criterion should hold true in order that the rate function remains always nonnegative e 3 W / q ) - 11 (26) Hence, the inequality in eq 25 will be always satisfied. Thus, steady-state multiplicity for our rate model is possible only for q / S < 1 for which criterion 24 holds. As pointed out by Luss (1968), a stronger uniqueness criterion than given by eq 24 can be derived based on topological arguments. For our rate model, this is given by 1> sup
OGeG1
(e - 1)[S/q - 1 + 2e - (S/q - l)k,e] e(1 + k,e)(e
+ S/q
- 1)
The values of e (emax)for which the right-hand side of inequality 27 assumes the largest value are given by emax= [ l - 2k,(S/q - 1) + [(l - 2k,(S/q - 1)i2+ 3k,2(S/q - 1) -'6kJ'J2]/3kt (28) for k,(S/q - 1)> 'I2.By a trial and error procedure using eq 27 and 28, one can calculate the maximum value of k,, for a prescribed value of q/S, for which criterion 27 is satisfied and unique solutions for all values of M1j2are ensured. This criterion turns out to be k , 13 for the present case.
-
di/kt
a
lo2
Figure 1. Plot of & vs. W / * / kshowing , multiplicity.
Having established the conditions where unique solutions will exist, we now present some results where multiple solutions do occur (Figure 1). In this region, onset of multiplicity is expected to depend on values of &PI2, q/S, k,, and @. There is no simple analytical method for a precise prediction of bounds on these parameters within which multiple steady-state solutions would exist, and this has also been pointed out by Luss (1971). However, our detailed calculations show that for a given q/S and @, the appearance and disappearance of multiplicity depends on the values of M1J2and k,. From Figure 1 it is seen that for any given W J there 2 is a certain range of M1J2/k, over which multiple steady states occur. The parameter (M1/2/k,) represents an effective MIJzvalue in the sense of conventional gas absorption with reaction following power-law kinetics. Isothermal multiplicity in the present context is a result of interaction between diffusion to and complex reaction in the bulk liquid phase. Thus, by varying ikfJ2/kt,one moves from the diffusional subregime of the slow reaction regime to the kinetic regime, and multiple steady states would first appear and then disappear as shown in the Figure 1. It appears from these calculations that the onset of multiplicity takes place approximately a t a value of M1/2/k, = 0.02. Finally, it is likely that all of the multiple solutions evaluated may not be stable, and this aspect will have to be established later by a dynamic analysis of the system.
Enhancement Factor In order to show the parametric sensitivity of the enhancement factor, +E, for this case, effect of the parameter, h,, on +E was evaluated. The results are presented in Figure 2. These results were calculated under conditions of a unique steady state, and this generalized chart represents all the regimes of absorption. In the fast reaction regime, an increase in k, decreased the enhancement factor, +E. This is quite expected as, for the kinetics considered here (eq 4), an increase in k, will decrease the rate of chemical reaction in relation to the diffusion rate, which would lead to lower +E values. The trend of +E vs. M1/* in the slow reaction regime ($E 1) was found to be most interesting. In this region, dE is less influenced by a change in MI2at lower k , values than at higher h, values. At lower
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1171 IO0
Tomporaturr = 40.C
S
1
1.3
0
12.0
4.0
a .so
A
12.0
4.0
3.30
0
60.0
2.0
0.24
6 a
=
n\
0.1
c
-
\
5
0
0.01
1~
0.01
E e0.1
10
I
100
o a
4
Y
fi
K
Figure 2. Effect of kt on plot of enhancement factor vs. M112 for S = 1, q = 1, and j3 = 1 X
I
P c
n
/
3
K
IO0
0 v)
m 4
2
(L
0 10
W
4 K
a’ 0 L
0
0
.
..
-
1
1
I
8
12
I
I
16 -.,BY
AGITATION SPEED, N
,r pa
Figure 4. Effect of agitation speed on the rate of absorption.
c 0
w
I
4
01
6
5’1.3, N = l O r p s , P n p : 6 0 a t m
0 01
01
I
10
100
fi Figure 3. Effect of parameter @ on plot of +E vs. IW’’ for S = 1, q = 1.5, and k, = 5.
k,, chemical reaction rate would be higher according to eq 4 and, hence, the contribution of mass transfer would
dominate, leading to a mild variation of & with W f 2over a certain range. At higher k, values and with a decrease in MI2,the chemical reaction rate would decrease in comparison to the mass-transfer rate, leading to chemical-reaction control. This explains the observed sharp decrease of C#IE a t higher k, values. Effect of parameter /3 on C#IE vs. MI2plot is shown in Figure 3. In the fast reaction regime, C#IEis not dependent on /3, but in the lower range of MI2 (the slow reaction regime), /3 is an important parameter. An increase in /3 a t constant iW2implies an increase in the interfacial area, a’, which should increase the mass-transfer rate in comparison to the chemical reaction rate, thus shifting the regime to chemical-reaction control. Therefore, the observation of a decrease in I#IE with an increase in P is mainly due to the increased contribution of reaction-kinetic parameters. In a similar manner, I#IE can be evaluated for any given set of parameters.
Illustrative Example: Practical Implications in Hydroformylation of 1-Hexene Some implications of the present theoretical analysis have been illustrated by considering hydroformylation of 1-hexene as an example. Consider the following reaction
Y
K
H tK 0 Ba k
w
c a
3
2 -
1 -
K
2
4
6
8
10
P A R T I A L P R E S S U R E OF CO, a t m
Figure 5. Effect of partial pressure of CO on the rate of absorption.
in the presence of the homogeneous catalyst, HRhCO(PPhJP, H2+ CO + 1-hexene products The parameters chosen for this illustration are presented in Table I. By use of these data, the enhancement factor, C#IE, was calculated from eq 15-18 and then the rate of absorption of E was found by eq 19. The effects of agitation speed and partial pressure of CO on the rate were evaluated, and the results are shown in Figures 4 and 5. Figure 4 shows the effect of agitation speed on the rate of hydroformylation for P H =~ 60 atm, PCO= 2 atm (Le.,
-
1172 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table I. Parameters Used for Illustrative Example parameter value k?
KE DA DE
source
2.43 X 10" ( ~ m ~ / m o l ) ~ / s 8.67 X los cm3/mol 5.26 X cm2/s 4.04 X cm2/s calculated from the following correlations
Deshpande, 1986 Wilke-Chang eq (1955)
Calderbank and Moo-Young, 1961 kL
H A
HE T
2.0 x 10 iiiol/(cm3 atm) mol/(cm3 atm) 5.9 x 313 K
q = O . l ) , and PHp = 12 atm and Pco = 4 atm (Le., q = 1). For q = 0.1, reactant E is limiting and A would be in excess. The results in Figure 4 for this case show that, at lower agitation speed, the rate increases with an increase in agitation; it then passes through a maximum at higher agitation speed, and eventually it becomes independent of agitation. At lower agitation speed, Eo tends to be zero, indicating diffusion control and hence an increase in rate with an increase in agitation speed is observed. Eo becomes significant, with a further increase in agitation, leading to a decreased rate of absorption according to the kinetics in eq 4. In this case, reactant A being in excess, A, A* and hence only E, is influenced with a change in agitation. With a further increase in agitation, Eo E*, thus approaching the kinetic regime, and the rate tends to be independent of agitation. For q = 1,two cases are shown in Figure 4 at different catalyst concentrations. At a higher catalyst concentration, such as Co = 8.52 X mol/cm3, the plot of rate vs. agitation speed passes through a maximum and shows a trend similar to that for q = 0.1. This is a result of a transition in the regimes of absorption from diffusion to kinetic control with increases in agitation speed. For C, = 3.33 X lo4 mol/cm3 (A@', = 0.5),the reaction in the bulk liquid phase was found to be significant. Here, the rate was found to be almost independent of agitation speed over a certain range, though the mass-transfer resistance was significant as evidenced by the magnitude of 4Ewhich was in the range 0.25-0.98. This unusual observation is the result of the combined effect of a negative order with CO, first order with H,, and the presence of significant masstransfer resistance. With an increase in agitation speed, both A. and Eo would increase and, according to the kinetics in eq 4, an increase in A , will increase the rate while an increase in Eo will decrease the rate, leading to a negligible change in the rate of absorption. These observations imply that the effect of mass transfer on the hydroformylation rate is unusual due to the complex negativeorder dependence of the reaction rate on CO. The effect of partial pressure of CO on the rate of absorption is shown in Figure 5 for the parameters given in Table I and for two catalyst concentrations. In both cases the rate was found first to increase and then to decrease with an increase in partial pressure of CO. At lower Pco, the rate of chemical reaction according to eq 4 is higher in comparison to the mass-transfer rate, thus leading to a diffusion-controlled regime. Hence, an increase in the rate occurs when Pco increases. As Pro is further increased, the intrinsic chemical reaction rate should decrease, while the mass-transfer rate should increase, leading to a shift from diffusion to a kinetically controlled regime.
-
-+
Seidell, 1940 Dake and Chaudhari, 1985
This explains the observed decrease in the rate at higher
pco.
The present analysis can be useful in optimizing the process conditions and in experimental identification of the regime of control for a given set of conditions from the observed magnitude of the calculated enhancement factor. Conclusion The problem of simultaneous absorption of two gases accompanied by a complex reaction with negative-order kinetics, typically observed in hydroformylation reactions, has been analyzed. An expression for enhancement factor, has been derived which is applicable irrespective of the regime of absorption. The effects of different parameters on have been discussed. Practical implications of this analysis have been illustrated with an example of the hydroformylation reaction. I t was found that under certain conditions, the dependence of the rate of absorption on parameters such as agitation speed was rather unusual. This phenomenon has been explained as a combined effect of complex negative-order kinetics and mass transfer. It has also been shown that, under certain conditions, multiple concentration profiles and enhancement factors can exist for the same set of parameter values.
Nomenclature a = dimensionless concentration of species A, A / A * a' = gas-liquid interfacial area per unit volume of liquid A = species A, hydrogen A = concentration of A in liquid B = species B, olefin B = concentration of B in liquid Co = concentration of catalyst dI = impeller diameter D = diffusion coefficient, subscript indicating the species e = dimensionless concentration of species E, E/E* E = species E, carbon monoxide E = concentration of E in liquid g = acceleration due to gravity h i = reaction rate constant in eq 2 and 3 h L = liquid-phase mass-transfer coefficient h2 = second-order reaction rate constant h, = dimensionless constant, defined as KEE* K,, K,, KE = constants in eq 2-4 m = constant in eq 2 M = parameter defined as D A k z A * / k L 2 N = agitation speed y = parameter defined as E*/uA* rE = rate of reaction of species E RE = rate of absorption of species E S = parameter defined as D A / D E S , = surface tension of liquid u g = linear gas velocity x = distance from the gas-liquid interface
Znd. Eng. Chem. Res. 1987,26, 1173-1179 Greek Symbols
p = parameter defined as a’6 6 = liquid film thickness 6 = dimensionless distance from gas-liquid interface, defined
as x / 6 q = liquid holdup = stoichiometric coefficient 4~ = enhancement factor for species E, defined as -(de/dt),,,, or RE/(kLa‘E*) pG = gas density pL = liquid density kL = viscosity of liquid Y
Superscript * = gas-liquid interface Subscripts
0 = liquid bulk
A = species A E = species E
Literature Cited Calderbank, P. H.; Moo-Young, M. B. Chem. Eng. Sci. 1961,16,39. Chaudhari, R. V. In Frontiers in Chemical EngineeripgProceedings of the International Chemical Reaction Engineering Conference held in Poona; Doraiswamy, L. K., Mashelkar, R. A. Eds.; Wiley: Eastern, New Delhi, 1984;p 291. Chaudhari, R. V.; Deshpande, R. M. Progress in Catalysis and Chemical Engineering Proceedings of the 1st Indo-Soviet Con-
1173
gress on Catalysis, Novosibirsk, USSR, 1984,p 63. Chaudhari, R. V.; Doraiswamy, L. K. Chem. Eng. Sci. 1974,29,675. Dake, S. B.; Chaudhari, R. V. J. Chem. Eng. Data 1985,30, 400. Deshpande, R.M.Ph.D. Thesis, University of Poona, India, 1986. Evans, D.; Osborn, J. A.; Wilkinson, G. J.Chem. SOC. A . 1968,3133. Falbe, J. Synthesis with Carbon Monoxide; Springer-Verlag: Berlin, 1980. Hikita, H.; Asai, S.; Ishikawa, H. Ind. Eng. Chem. Fundam. 1977,16, 215. Juvekar, V. A. Chem. Eng. Sci. 1974,29,1842. Luss, D.Chem. Eng. Sci. 1968,23,1249. Luss, D. Chem. Eng. Sci. 1971,26,1713. Luss, D.; Amundson, N. R. Ind. Eng. Chem. Fundam. 1967,6,457. Natta, G.; Ercoli, R.; Castellano, S.; Berbieri, F. H. J . Am. Chem. SOC.1954,76,4049. Ramachandran, P. A.; Sharma, M. M. Trans. Inst. Chem. Eng. 1971, 49, 253. Roberts, G.W.; Satterfield, C. N. Ind. Eng. Chem. Fundam. 1966, 5,317. Roper, G.H.;Hatch, T. F.; Pigford, R. L. Ind. Eng. Chem. Fundam. 1962,1 , 144. Seidell, A. Solubilities of Inorganic and Metal Organic Compounds; D. Van Nostrand: New York, 1940;Vol. 1. Van Boven, M.; Alemdarogly, N. H.; Penninger, J. M. L. Ind. Eng. Chem. Prod. Res. Deu. 1975,14,259. Wilke, C. R.; Chang, P. AIChE J . 1955,1, 264. Yagi, H.; Yoshida, P. Ind. Eng. Chem. Process Des. Deu. 1975,14, 488. Zarzycki, R.; Ledakowicz, S.; Starzale, M. Chem. Eng. Sci. 1981,36, 105.
Received for review August 12, 1985 Accepted February 2, 1987
Two-Phase Liquid Hydrocarbon-Hydrate Equilibrium for Ethane and Propane E. Dendy Sloan,* Kevin A. Sparks, and Jeffrey J. Johnson Chemical Engineering and Petroleum Refining Department, Colorado School of Mines, Golden. Colorado 80401
An experimental method was generated and proven for the measurement of the water content of a liquid hydrocarbon which is in equilibrium only with hydrates. The method was used to determine the water content of both liquid propane and liquid ethane when hydrates were present, without the presence of a free water phase. The dielectric constant apparatus enabled the water concentration measurement of the hydrocarbon liquid without sample withdrawal. T h e temperature range was 246-276 K with pressures of 0.77 MPa (propane) and 3.5 MPa (ethane), and the water concentrations in the hydrocarbon were from 16 t o 176 ppm (mol). An a priori predictive method, based on parameters determined from three-phase equilibria, was determined to be accurate, with mean absolute errors of 2.5% and 5.8% for ethane and propane, respectively. Natural gas hydrates are solid enclosure compounds which form when water encages a hydrocarbon, such as methane, ethane, or propane. Hydrates, which are extensively reviewed by Davidson (1973) and Makogon (1981), are important industrially because they can plug transmission lines, foul heat exchangers, and erode expanders. The primary objective of this work was to measure the amount of water in a predominately hydrocarbon liquid phase in the region where hydrates exist. The two hydrocarbons studied were ethane and propane, as a function of temperature and pressure. Such measurements give the natural gas liquids processor an indication of how dry the liquid hydrocarbon must be in order to prevent hydrate formation. The work may best be understood by considering the qualitative isobaric propanewater phase diagram of Figure
1, taken from Kobayashi (1951); the lines of the diagram are not to scale. This diagram has four single-phase regions: a vapor area marked “A”, a liquid water area marked “B”, a liquid propane area marked “C”, and a hydrate line marked “H”. In our experiments, two-phase equilibrium existed between lines H and L1. We measured the water concentration along line L1, as a function of temperature and pressure for both propane and ethane. In order to achieve this objective, we had to generate and verify an experimental method to measure low water concentrations in a hydrocarbon in equilibrium with.hydrates. The method was constructed to include the advantages of in situ measurement so that many of the problems accompanying the measurement of small water contents (typically less than 0.001 mol fraction) are not encountered. No other experimental data exist, which were
0888-5885/87/2626-1173$01.50/0 0 1987 American Chemical Society
