Ind. Eng. Chem. Fundam. 1983, 22, 361-364
361
Hydrate Decomposition Conditions in the System H,S-Met hane-Propane J. P. Schroeter and Rlki Kobayashi' Bpartment of Chemical Engineering, Rlce lJnlvers& Houston, Texas 7700 7
M. A. Hiidebrand Exxon Production Research Company, Houston, Texas 7700 1
We have experimentally investigated the hydrate decomposition conditions in three different H,Scontaining mixtures in the temperature reglon 0-30 OC. The three mixtures investigated were 4 % H2S, 7 % propane, 89% methane: 12% H2S, 7% propane, 81 % methane; and 32% H2S, 7 % propane, 61 % methane. Hydrate decomposition pressures and temperatures were obtained for each of these mixtures by observation of the pressure-temperature hysteresis curves associated with formation and decomposition of the hydrate crystals. A repeatable decomposition point was observed in every case,and this was identifled as the hydrate point. The results for the 4 % H2Smixture were used to adjust parameters in a computer model based on the Parrish and Prausnitz statistical thermodynamics method, coupled with the BWRS equation of state. After the parameter adjustment, the computer model correlated , and the 32% H2S mixtures within 2 O C . the behavior of the 12% HS
Introduction Though the existence of hydrates was demonstrated by Davy in the early part of the nineteenth century, current interest dates from 1934, when Hammerschmidt discovered that hydrates were responsible for plugging natural gas lines (Hammerschmidt, 1934). This discovery stimulated a number of studies to determine hydrate decomposition conditions. Van der Waals and Platteeuw (1959) derived equations for calculating the thermodynamic properties of gas hydrates based on a statistical thermodynamic model. This method was used by Parrish and Prausnitz (1972) for calculating hydrate-gas equilibria in multicomponent systems. A computer model has been developed which combines the approach of Parrish and Prausnitz with the BWRS equation of state phase behavior model (Lin and Hopke, 1974). The computer model was found to be very accurate for sweet systems, predicting hydrate decomposition conditions to within 2 "C for gas, liquid, and two-phase hydrocarbon systems. Data from the present study have been used to adjust model parameters in order to obtain comparable accuracy for sour systems. Hydrates crystallize into two kinds of lattice structures: structure I and structure 11. Each structure in turn has cavities of two sizes. Pure H2S, as well as gases composed of only methane, C 0 2 ,and H2S,form structure I hydrates. However, if a sufficient amount of propane or isobutane is present (1% or more), structure I1 hydrates will be formed. In the computer model the occupation of each type of hydrate cavity, by each hydrate forming gas, is given in terms of Langmuir constants. As in the work of Parrish and Prausnitz, the Langmuir constants are expressed in terms of the Kihara potential function, which represents the intermolecular forces between gas and water molecules. A t low temperatures the Langmuir constants are given by an empirical expression to save computation time. The calculations also require various cell parameters and thermodynamic constanb for each hydrate structure. Data on the system methane-hydrogen sulfide has been used to adjust Kihara potential parameters for H2S in hydrates of structure I. Additional data were required to 0196-4313/83/1022-0361$01.50/0
determine whether the Kihara parameters for H2S in structure I, when coupled with the cell parameters for structure 11, would be adequate for predicting hydrate decomposition conditions for systems containing significant amounts of H2S and forming structure I1 hydrates. The present study was conducted in order to elucidate the hydrate decomposition properties of the structure I1 forming systems containing H2S and both methane and propane. There are two popular experimental methods employed to determine the hydrate formation/decomposition point. At lower pressures, visual observation of the formation and decomposition of hydrate crystals in a windowed cell has been used successfully (Kobayashi and Katz, 1974). This method requires observation of the stability of hydrate crystals, at constant temperature, for periods of 6-8 h. It is therefore somewhat time consuming. Additionally, this method may only be used unambiguously at temperatures where there is no danger of confusion between hydrate crystals and ice crystals, i.e., above the freezing point of water (Verma, 1974). A less tedious, nonvisual technique which can be used at high as well as low pressures has been developed in our laboratory (Marshall et al., 1964; Schroeter and Kobayashi, 1979). This method employs the pressure change due to hydrate formation or decomposition in an isochoric (constant volume) cell. Since gas is evolved by decomposing hydrate crystals, a pressure increase accompanies hydrate decomposition. A similar drop in pressure signals the formation of the hydrates. This technique is more amenable to computer control than the visual method and offers the additional advantage of being applicable over the entire range of hydrate formation pressures and temperatures, except perhaps when nearly incompressible phases are involved. This technique was used in the present study.
Experimental Section We chose to employ the pressure change associated with hydrate formation and decomposition in a constant volume cell as an indicator of the hydrate point. A limitation of 0 1983 American Chemical Society
362 Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 Table I. Hydrate Decomposition Conditions compn,a % N T
E
1
TEMPERATURE SENSOR
t
R F
n C
LJ f
E
-1
n PRINTER
HEATER i
R E FA IGERATION
Figure 1. Block diagram of the hydrate formation equipment.
this technique is the rate at which pressure data can be collected. In a practical experiment, the observer collects data at a variety of different equilibrium temperatures. Since hydrates are slow to form near their decomposition point, relatively long periods of time are required for the pressure to come to equilibrium after a temperature change (Marshall et al., 1964). Generally, the cell is allowed to heat (or cool) a t a rate which is much slower than the inverse pressure equilibration time. Typically, this rate of change of temperature must be restricted to less than 0.3 OC/h. It has frequently been demonstrated that hydrate-forming compounds can exist in metastable states at temperatures substantially below the formation temperature. Often, systems may exhibit as much as 10 "C supercooling. Thus,a precise determination of the hydrate formation/decomposition temperature requires an experiment spanning at least 10 "C. If the initial guess of the location of the hydrate point is not correct, an experiment can easily require 50 h for even one pass through the hydrate formation/decomposition point. Usually at least three passes are necessary to accurately locate the hydrate point. Such a long experiment, requiring that a data point be collected at approximately 0.5-h intervals for 50 h, cannot be conducted by a single experimenter. Using a Commodore PET microcomputer, we have constructed a device which automatically controls the temperature, reads the pressure at specified intervals, and stores the data for later read-out. This frees the experimenter from the more tedious parts of the experiment and permits around-the-clock data acquisition. Figure 1is a block diagram of the system. The cell is placed inside the temperature controlled bath. To ensure equilibrium of the phases present in the cell, the cell was rocked about its horizontal position using a gear motor and cam. Two 3/4-in.stainless steel ball bearings were placed inside the cell. Thus, the rocking cell acted as a ball mill in order to expose and convert liquid water which could be trapped between the gas-hydrate interface and the cell wall. The agitation caused by the motion of the balls was observed to shorten the pressure equilibration time substantially. Temperature control was provided by a refrigeration unit coupled with the computer-controlled heater. The computer controls the duty cycle of the heater in order to maintain the bath temperature a t the value specified by the experimenter. This temperature set point can change with time to provide the slow heating or cooling necessary in a hydrate formation experiment. In addition to its function as a temperature controller, the computer also reads bath temperature and pressure inside the cell at specified temperature intervals. These data are stored in memory as well as output to the printer. The temperature sensor was a Platinum Resistance Thermometer (Rosemount Engineering Model 118BN)calibrated against another PRT (Leeds and Northrup Model 8167-25) which
a
H,S
methane
propane
temp, "C
press., psia
4.174 4.174 4.174 4.174 4.174 11.975 11.975 11.975 31.710 31.710 31.710 31.710 31.710
7.172 7.172 7.172 7.172 7.172 7.016 7.016 7.016 7.402 7.402 7.402 7.402 7.402
88.654 88.654 88.654 88.654 88.654 81.009 81.009 81.009 60.888 60.888 60.888 60.888 60.888
2.8 4.6 11.0 14.2 18.0 2.7 10.4 19.5 7.2 13.1 19.1 24.3 27.8
81.4 102.4 205.8 293.5 488.3 49.2 118.5 408.0 53.4 99.5 209.5 370.5 620.0
Stated by Matheson.
had recently been recalibrated to an accuracy stated as 0.002 OC. We estimate an accuracy for this thermometer of at least 0.01 "C. The pressure sensors were Setra Systems Model 204, with a stated accuracy of 0.1%. All software for the system was written in BASIC, as this language is resident in the PET computer. Since speed was not essential in this application, BASIC was sufficiently fast to perform both the data collection and temperature control functions. I t required experimentation to establish the optimum temperature control routine. The most successful functional form was a modified linear function of the temperature displacement, A T , below the set point At = C1 A T + C 2 (if -0.01 IA T 50.05) F,(T) (1) = 0.09C1 + C2 (if A T =0
(if A T
> 0.05)
< -0.01)
For our system optimal values of C1 and C2 were found to be 500 s/"C and 5 s, respectively. At is the time the heater is on, in seconds. The heater was off for 10 s of each cycle, while data collection functions were performed. Many highly successful analogue temperature controllers employ proportional-integral-derivative (PID) algorithms for temperature control. This corresponds to the addition of two terms to our expression for At
where t denotes time. In our system the degree of control was quite insensitive to C3 or C4. Optimal control occured in the range where C3 N C4 0. Thus, for our system, nothing seemed to be gained with the commonly used PID algorithmn. Before each run was started, the cell was removed from the bath and cleaned thoroughly with water, acetone, and ethanol. After cleaning, the cell was rinsed for approximately 0.5 h with triply distilled water in order to remove any possible contamination from the cleaning agents. After it was replaced in the bath, the cell (volume = 135 cm3) was evacuated and then filled with 25 cm3 of deionized water. Calculations revealed that the differential solubility of H2S in water-as compared to that of methane and propane-should change the H2Sconcentration in the gas phase by no more than approximately 0.2%. Later experimental determination of the H2S gas phase concentration was consistent with this calculation. After the cell was filled with water, gas was introduced directly from the cylinder until the pressure had reached that value chosen for the experiment. The gas samples were obtained from
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 363 102 I
lo.m
I
100 ..
98
3
..
O=COMPOSITION B 0.81009 c, 0.07016 C, 0.11975 H,S
96-
n=COMPOSITION
P
C
0.60888 C? 0.07402 Cr
0
94
..
92 ..
90
10
-6
0
5
10 15 20 TEMPERATURE, O C
25
30
Figure 4. Hydrate point pressure w.temperature data and hydrate program predictions for the three sour gas compositions. The solid line is the computer model prediction. Table 11. Parameters for Calculating Langmuir Constants of H,S and C,H, in Structure I1 Hydrates P
C3H8a
H2S 4
1
T
1.684 X
lo-,
3.6035 X 103
1.2277 X 10-2 2.5931 X
4.412 X 103 7.7589 X
lo2
Figure 3. The idealized pressure-temperature behavior near the hydrate point. Note that the amount of supercooling on each of the cooling curves Sl,S2, and S3 is related to the starting temperatures Sl, S2, and S3 of each curve.
These coefficients are only used for structure I1 hydrates of propane in mixtures at temperatures below 60 O F . There are no coefficients for propane in the small cavities, because it can only fit in the larger cavities.
Matheson Gas Co. and were certified by them to have the compositions reported in Table I. After the highest pressure experimental run for each concentration, a gas sample was drawn from the cell and analyzed for H2S concentration by both gravimetric and titrimetric means. There was no detectable variation from the compositions given by Matheson. Results Figure 2 shows the results obtained from a typical experimental run of the system H2S-methane-propane. As expected, the region near the hydrate formation point shows a hysteresis curve in pressure vs. temperature space. The hysteresis is a result of the metastability of hydrate forming compounds on the cooling (downward) portion of the curve. In this case, supercooling of as much as 5 “C was observed on the initial downward pass. Due to the hysteresis, the location of the “point” of hydrate formation was found to be very much a function of its history. The decomposition conditions were much less ambigous, but the crystals exhibited some resistance to total decomposition. The upper point of divergence of the heating and cooling curves was observed to be repeatable over the complete range of temperature drift rates and starting temperatures. Additionally, this is the expected point of complete hydrate decomposition in an equilibrated system. We therefore take it as the hydrate point. The location of this point can be determined in our experiment with an accuracy of 0.1 OC in temperature and 0.1 psia in pressure. In the example of Figure 2, the hydrate point is determined to be T = 13.1 OC and P = 99.5 psia.
Note that the amount of supercooling varies from pass to pass in Figure 2. For example, the initial downward pass shown in that figure exhibits more supercooling than does the second pass. We have observed this phenomenon to depend upon the starting temperature, as shown ideally in Figure 3. In that figure, the three different cooling curvw, SI,S2,and S3,correspond to three different starting temperatures. In general, we have observed that the amount of supercooling increases as the starting temperature increases. We speculate that this phenomenon is due to the persistence of micro-crystals of hydrate above the decomposition point. These micro-crystals would act as nucleation sites for hydrate formation on the cooling cycle of the curve. As the system is cycled to higher and higher starting temperatures, it is expected that fewer of the crystals survive. We suspect that systems containing a smaller number/size of nucleating micro-crystals would exhibit a greater amount of supercooling, thus accounting for the starting temperature dependence of the supercooling effects. Table I gives the results for the hydrate decomposition points for the three different gas concentrations. The data are also plotted in Figure 4. The experimental data could not be adequately represented with structure I1 cell parameters and the Kihara parameters for H2S, which were determined from pure H2S structure I hydrate data. A good fit of the data was obtained when Langmuir constants for H2S in hydrate structure I1 were expressed by the following equation C J T ) = (A,i/T) exp(B,i/T) (3)
Ind. Eng. Chem. Fundam. 1983, 22, 364-366
364
Table 111. Kihara Parameters for Hydrate-Gas Interactions
.. methane propane (I
K
.. 3.2363 3.3049
0.30017 0.67964
153.22 200.92
= Boltzmann constant.
t 5
c'H'
?Q 20
30 40 50 MI 70 80 MOLE%INGASPHASE
90
'"
Figure 5. Hydrate point conditions for propane-hydrogen sulfide mixtures at -3 O C . The solid points are the data of Plateeuw and Van der Waals. The line corresponds to the calculations of the computer model.
Only the data for the mixture containing 4% H2S were used to determine Amiand Bmi. The same empirical expression is used to represent the Langmuir constant of propane a t temperatures below 60 O F . The values of the constants Amiand Bmiare given in Table I1 for each size cavity of structure I1 hydrates. The Langmuir constants for methane at all temperatures and for propane above 60 O F were evaluated using the Kihara potential function r I 2ai U(r)= m;
V(r)= 4ei
[(- ( ui
r - 2ai
)12-
ui
r - 2ai
)"I
;
r
> 2ai (4)
The Kihara potential parameters (ai, ui, and ci) for methane and propane are given in Table 111. Predictions using the computer model are shown in Figure 4, along with the data. The predictions are good for all three gas compositions, with a maximum temperature deviation from the data of approximately 2 "C.
There is one data set available in the oDen literature for structure I1 hydrates containing H2S (PGtteeuw and Van der Waals, 1959). These data are displayed in Figure 5. In that figure, the hydrate formation pressure is plotted vs. the C3H8-H2Sgas-phase composition in mole percent. The data are shown as points, and the model predictions as a solid line. Again, agreement between the predictions and data is good. Consequently, predictions of hydrate formation conditions in sour systems using the computer model appear to be accurate within 2 "C, just as in sweet systems. Conclusion Using a computerized data collection device, we have examined the hydrate formation/ decomposition behavior in the system H2S-methane-propane by the pressure change technique. The experiment revealed the expected hysteresis behavior in pressure vs. temperature space near the hydrate point. We observe a repeatable hydrate decomposition point, which can be located with an accuracy of better than 0.1 "C and 0.1 psia. The data on the H2Smethane-propane system were used to adjust parameters in a computer model so as to fit the behavior of sour gas systems which form structure I1 hydrates. As seen in Figure 4, the model agrees quite well with the data. Registry No. H2S, 7783-06-4; CHI, 74-82-8; C3Hs, 74-98-6.
Literature Cited Hammerschmidt, E. G. Ind. Eng. Chem. 1934, 26, 851. Kobayashi, R.; Katz. D. L. Trans. AIME 1949, 126, 66. Lin, C. J.; Hopke, S. W. AIChE Symp. Ser. No. 140, 1974, 70, 37. Marshall, D. R.; Saito, S.; Kobayashi, R. AIChEJ. 1964, 10(2),202. Parrish, W. R.; Prausnitz, J. M. Ind. Eng. Chem. Process D e s . Dev. 1972, 1 1 , 26. Piatteeuw, J. C.; Van der Waals, J. H. Recl. Trav. Chem. 1959, 78, 126. Schroeter, J. P.; Kobayashi, R. "ComputerizedControl, Data Acquisition, and Storage in the Determination of Hydrate Formation Conditions",Presented at 72nd AIChE Meeting, San Francisco, Nov 1979. Van der Waals, J. H.; Platteeuw, J. C. A&. Chem. fhys. 1959, 2 , 1. Verma, V. W.D. Thesis, University of Michigan, Ann Arbor, MI, 1974.
Received for reuiew March 1, 1982 Revised manuscript received May 12, 1983 Accepted July 20, 1983 The authors acknowledge the support of the Exxon Production Research Company over the duration of these studies.
Equation Suitable for Estimation of Ternary Liquid-Liquid Equilibria with Binary Wilson Parameters MRsuyasu Hlranuma Tomakomai Technical College, 443, Nishikloka, Tomakomai, Mkkaido, 059- 12, Japan
A four-parameter equation is proposed for systems having unusual behavior or for partially miscible systems. An extension of the equation appks to mutkomponent solutions. I f one binary pair of compounds in a ternary mixture is completely miscible, Wilson's parameters already collected from binary data may be used for the ternary system. The proposed method yields almost the Same size of immiscibility regions as those observed for the ternary liquid mixtures tested.
Introduction The original third Wilson parameter, c , is the same for all constituent binaries, but it must be changed for each multicomponent system. In a previous paper (Hiranuma,
19811, c was set as an adjustable parameter for component
i to remove the disadvantage. However, to correlate the VLE or the LLE data more precisely, it is convenient to
use binary parameters because they can be selected in-
0196-4313/83/1022-0364$01.50/00 1983 American Chemical Society
