Ind. Eng. Chem. Process Des. Dev. 1980, 79, 709-711
700
The Prediction of COP Solubility and Swelling Factors for Enhanced Oil Recovery Charles A. Mulllken and Stanley I. Sandier' Department of Chemical Engineering, University of Delaware, Newark, Delaware 19711
The solubili of carbon dioxide in reservoir crudes and the swelling of the COTcrude mixture are important parameters for enhanced oil recovery. In this paper we show that both these parameters can be predicted with reasonable accuracy using the Peng-Robinson equation of state and a characterization of the crude which requires only the specific gravity and the mean average boiling point or Watson Kfactor.
Introduction As a result of the present shortage of crude oil, there is increased interest in the use of carbon dioxide as a tertiary oil recovery agent since: (a) at reservoir conditions it is highly soluble in the crude, (b) it promotes swelling (i-e., the volume of the COz-crude mixture is greater than that of the crude alone), (c) it greatly reduces the crude viscosity, (d) it can vaporize and extract portions of the crude, and (e) it can be transported chromatographicallythrough porous rock (Holm and Josendal, 1974; Simon, 1977). Holm (1976) compared the use of carbon dioxide as a miscible solvent for enhanced oil recovery to other solvents which included propime, light hydrocarbon enriched gases, and solvents which are mutually soluble in both crude oil and water. He concluded that the main advantages of COP are that it achieves miscible displacement at pressures of only 1000 to 3000 pnia, and that it is applicable to reservoirs that have been depleted of their gas and LPG components. Presently, there are few methods of predicting the carbon dioxide solubility and swelling factors of crudes. Simon and Graue (1.965) have correlated COz solubility, fluid swelling, and viscosity data for COP-oil mixtures obtained from several sources, including their own experimental data, for a temperature range of 110-250 OF and pressures to 23'76 psia for a variety of crude and refined oils covering the Watson (1935) K-factor range from 11.0 to 12.4. Unfclrtunately, their correlations are in graphical form, which are not convenient for computer calculations or reservoir simulation studies. Also, those correlations are not applicable for impure COz or mixed gases. Finally, since the Simon-Graue correlations are completely empirical, there is no theoretical basis for extrapolation outside their range or extension to other systems. Another approach.,used by Katz and Firoozabadi (1977), Firoozabadi et al. (3.978), and Baker and Luks (1978), is to use a simple equation of state to represent the oil-COz, treating the oil as a mixture of from 10 to 40 identifiable species of known properties and compositions. While this is a theoretically pleasing way to proceed and does provide a complete description of vapor-liquid equilibrium in C0,-oil systems, it does have a number of disadvantages. First, a detailed compositional analysis of an oil might not be available. Second, to use an equation of state for a multicomponent mixture requires the specification of an interaction parameter for each distinct binary pair (i.e., N ( N - 1)/2 interaction parameters are needed for an N-component mixture). Much experimental data or some form of generalized correlation would be needed to determine all these parameters. Finally, the prediction of
the properties of gas-oil systems is of primary importance for reservoir management simulators, which require enormous amounts of computer time. Since the time required for a thermodynamic calculation using an equation of state increases approximately linearly with the number of components, the use of a detailed multicomponent characterization of an oil in a simulation would be quite costly. The problem addressed in this communication is whether it is possible to develop an analytical, equationof-state based correlation for two important properties of COz-oil system, namely carbon dioxide solubility and fluid swelling, which involve only a simple characterization of the oil, but are of comparable accuracy to the graphical Simon and Graue correlations. There are two important results presented here. First, we show that it is possible to obtain such a correlation using the Peng-Robinson equation of state (1976) and treating the oil as a single pseudecomponent. Only the specific gravity and the mean average boiling point or Watson K factor (Watson et al., 1935) are needed to characterize the oil, and a COP-oil binary interaction parameter (which can be regressed from solubility or swelling data) is needed. Second, we develop a generalized correlation for the COz-oil interaction parameter, which can be used when no experimental data are available. The result of our work is a simple correlative/predictive method for COz solubility and swelling in oils which is rapidly executed on a digital computer, is easily extended to mixed gases, and requires only the specific gravity and mean average boiling point or Watson K factor to characterize the oil.
Analysis and Correlation To describe the COz-crudeoil mixture we have used the equation of state of Peng and Robinson (1979) U p=--R T V - b V(V+ b) + b ( V - b) where, for mixtures
with
0196-4305/80/1119-0709$01.00/0@ 1980 American Chemical Society
710
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980 ~i
= 0.37464
+ 1.54226wi - 0.26992~~’
(7)
and bi
= O.O778ORT,/Pci
In P, = 8.3634 - 0.0566/SG - (0.24244 + 2.2898/SG + 0.11857/SG2) X lO-%”b + (1.4685 3.648/SG + 0.47227/SG2) X 10-7Tb2(0.42019 1.6977/SG2) X 10-’OTb3 (10)
+
+
+
+
0.1354K - 0.007465P 8.359(Tb/TC) (1.408 - 0.01063K)(Tc/Tb) for T b > 0.8Tc (11)
w = -7.904
or (Lee and Kesler, 1975) w = [In (14.7/PC)- 5.92714 + 6.O9648(Tb/Tc) + 1.28862 hl (Tb/T,) - o.169347(Tb/Tc)6]/[15,2518 15.6875(Tc/Tb) - 13.4721 In (Tb/T,) + 0.43577 (Tb/Tc)6] if T b < 0.8Tc (12)
In these equations Tb is the cubic average boiling point, S G is the specific gravity, P, is the critical pressure in psia, and w is the acentric factor. If T b has been measured, it can be used in the equations above. If, however, an oil is characterized by a Watson K factor, determined from viscosity for example, then T b can be found from Tb
= (KsSG)~
temp range,
(8)
In this work the crude was taken to be a single pseudocomponent. The problem that then arises is how to characterize the crude, that is, what values to assign for the critical properties and acentric factor of the crude oil pseudo-component. By correlating the enthalpy of petroleum fractions using corresponding states, Kesler and Lee (1976) have suggested the following relations T, = 341.7 + 811SG + (0.1174SG)Tb + (0.4669 -3.2623SG) X 105/Tb (9)
+
Table I. Binary Interaction Parameters for C0,-Identified Hydrocarbons Regressed from CO, Solubility Data
(13)
We have used these equations here. This leaves the binary interaction parameter 6, as the only unknown parameter. To determine this parameter, we modified a standard vapor-liquid equilibrium flash routine to use the Peng-Robinson equation of state and given the characteristics of the hydrocarbon (SG and K for the crude, T,, P,, and w for an identified hydrocarbon), the system temperature, pressure, and carbon dioxide mole fraction, to calculate the value of 6 needed to force the prediction of the COPsolubility to agree with experiment (the crudes and hydrocarbons do not vaporize appreciably at the conditions considered). This program was then used with the data for nine different oils of Simon and Graue (1965), as well as for COz solubility in n-butylbenzene and trans-decalin (Tiffin et al., 1978),n-eicosane (Huie, 1973), n-pentane (Besserer and Robinson, 1973), n-hexane and benzene (Ohgaki and Katayama, 1976), n-decane (Reamer and Sage, 1962), 2-methylnaphthalene (Kulkarni et al., 1974), and butane (Donnelly and Katz, 1954). The interaction parameters for the C02-identifiable hydrocarbon systems so obtained are presented in Table I, as these may be of interest to others. Next, we attempted to fit the 6’s determined in this way with a generalized correlation. Our first observation was that while the COz-oil interaction parameters were easily correlated, a single generalized correlation would not work for both the identifiable hydrocarbons and the pseudopure-component oils. This is not surprising, as (1)a generalized correlation cannot even be used to correlate the interaction parameters for both the aromatic hydrocarbons
system
6
C0,-n-butane C0,-n-pentane C0,-n-hexane C0,-n-decane C0,-n-eicosane C0,-benzene C0,-n-butylbenzene C02-2-methylnaphthalene C0,-trans-decalin
0.099 0.115 0.105 0.100 0.093 0.076 0.116 0.142 0.169
O F
90-93 40-100 77-105 40-400 98-212 77-105 32-68 94-212 32-236
data points 2 5 5 11 32 4 14 24 41
(benzene, n-butylbenzene, 2-methylnaphthalene and trans-decalin) and the paraffic hydrocarbons (butane, pentane, hexane, decane and eicosane) as seen from Table I, and (2) the values of the C02-0ilinteraction parameters would be systematically affected by any uncertainty in the correlations for the oil critical properties. Since our interest is in COz solubility in crude oil, the following correlation was developed for the C02-0il mixtures of Simon and Graue 6 = 0.5010 - 0.3576 ( T / T , ) - 0.18285SG - 0.0961~(14) The empirical correlation of eq 14, which exhibits the moderate temperature dependence characteristic of equation of state interaction parameters for hydrocarbon-nonhydrocarbon systems (Peng and Robinson, 1979; Kabadi and Danner, 1979), produces an average error on only 1.9% in the predicted C02mole fraction in the oil; this is to be compared with an average error of 2.3% with the Simon-Graue correlation. The maximum error was 8.8% (see Table 11). As an independent test of the correlation we computed the swelling factor, which is defined as the ratio of the volume of the oil-COz mixture at saturation pressure and temperature to the oil volume at the saturation temperature and atmospheric pressure. The swelling factor is an important parameter in tertiary oil recovery since it provides information on the extent to which crude is pushed out of pores by expansion. Its prediction here was accomplished by applying the Peng-Robinson equation twice: once to the COz-saturated crude at saturation conditions and then again to the crude at 1 atm and the same temperature. In this calculation the predicted rather than experimental COz solubility was used. The results, shown in Table I, have an average error of 1.4% and a maximum error of 6.7%. When comparing this with the average error of 0.5% reported by Simon and Graue, one should remember that the swelling factor predictions reported here (a) used the predicted COz solubility, and (b) has no adjustable parameters; the single unknown binary interaction parameter has been obtained from the generalized correlation for the solubility data.
Conclusions The work here establishes that a relatively simple equation of state and a rudimentary characterization of a crude oil, using only the specific gravity and Watson K factor, can be used to make reasonably accurate predictions of C02solubility and swelling factors needed for enhanced oil recovery. Further, since the correlation has a theoretical basis, its extension to mixed gases or impure C02 is easily accomplished, and its extrapolation should presumably be less risky than with empirical correlations. We conclude with a cautionary note. The nine oils considered by Simon and Graue all had vapor pressures
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980 711
Table 11. Comparison of Experimental Data of Simon and Graue artd Predicted Values for CO, Solubility and Swelling Factor
tion A
OF”
110
200
B
160
c
120
D
120
E
250 120
F
120
G
130
H
130
I
145 200
psia
exptl
pred.
exptl
pred.
290 460 790 1900 1139 2361 467 861 1291 2039 461 892 1535 2376 471 996 1496 549 403 759 1553 1782 518 1115 1093 1540 2321 401 1335 1856 820 1472 2200 720 1681
0.196 0.294 0.455 0.667 0.423 0.625 0.235 0.380 0.531 0.675 0.313 0.495 0.667 0.717 0.299 0.508 0.632 0.215 0.251 0.457 0.669 0.677 0.283 0.498 0.555 0.658 0.708 0.251 0.584 0.650 0.418 0.598 0.681 0.328 0.553
0.196 0.292 0.446 0.638 0.423 0.643 0.239 0.395 0.524 0.662 0.303 0.503 0.662 0.708 0.289 0.506 0.616 0.211 0.273 0.450 0.657 0.676 0.291 0.507 0.562 0.662 0.721 0.249 0.589 0.658 0.415 0.596 0.683 0.313 0.565
1.025 1.039 1.092 1.245 1.070 1.196 1.048 1.104 1.193 1.370 1.053 1.112 1.220 1.303 1.040 1.116 1.202 1.031 1.024 1.051 1.148 1.163 1.049 1.129 1.128 1.205 1.252 1.013 1.117 1.159 1.068 1.152 1.232 1.049 1.133
1.025 1.043 1.083 1.178 1.083 1.201 1.045 1.094 1.158 1.279 1.045 1.104 1.199 1.237 1.041 1.104 1.162 1.031 1.030 1.065 1.152 1.164 1.046 1.116 1.114 1.173 1.221 1.029 1.124 1.164 1.068 1.141 1.202 1.046 1.131
of less than 1 atm a t the temperatures of their studies (110-200 OF). This indicates that their oils were depleted of the light hydrocarbon components (C, to C3). Thus while the procedure considered here, that of treating an oil as a single pseudlo-component, should have general
applicability, we do not know whether the specific correlation for the CO,-oil binary interaction parameter (eq 14) will be useful for reservoir fluids containing light components. Nomenclature a , b = constants in the Peng-Robinson equation K = Watson or UOP characterization factor P = pressure R = gas constant S G = specific gravity T = temperature V = volume x = mole fraction a = term in Peng-Robinson equation 6 = binary interaction parameter K = constant in Peng-Robinson equation w = acentric factor Subscripts b = boiling point value c = critical point value i, j = components i, j Literature Cited Baker, L. E., Luks, K. D., paper SPE 7478,presented at the 53rd Annual Fall Technical Conference of the Society of Petroleum Engineers, Houston, Oct
1-3,1978. Besserer, G. J., Robinson, D. B., J. Chem. Eng. Data, 18, 416 (1973). Donnelly, H. G.,Katz, D. L., Ind. Eng. Chem., 48,51 1 (1954). Firoozabadi, A., Heklm, Y., Katz, D. L., Can. J. Chem. Eng., 58,610 (1978). Hule, N. C., Luks, K. D., Kohn, J. P., J. Chem. Eng. Data, 18, 311 (1973). Holm, L. W., Josendal, A., J. Pet. Techno/., 28, 76 (1976). Holm, L. W., J. Pet. Technol., 28, 76 (1976). Kabadi, V., Danner, R. P., ACS Symp. Ser., to be published, 1979. Katz, D. L., Firoozabadi, A., SOC.Pet. Eng. Fall Meeting (Paper SPE 6721).
1977. Kesler, M. G., Lee, B. I., Hydrocarbon Process., 153 (Mar 1976). Kulkarni, A. A., Luks, D. D., Kohn, J. P., J. Chem. Eng. Data, 19, 349 (1974). Ohgakl, K., Katayama, T., J. Chem. Eng. Data, 21, l(1976). Peng, D., Robinson, D. B.,ACS Symp. Ser., to be published, 1979. Reamer, H. H., Sage, 6. H., J. Chem. Eng. Data, 9, 508 (1963). Simon, R., Graue, D. J., J. Pet. Technol., 13, 102 (1965). Simon, R., in “Phase Equllibrla and Fluid Propertles In the Chemical Industry”, p 241,T. S. Stwvick and S. I. Sandier, Ed., American Chemical Soc., p 241 Washington, D.C., 1977. Tiffin, D. L., Devera, A. L., Luks, K. D., Kohn, J. P., J. Chem. Eng. Data, 23,
45 (1978). Watson, K. M., Nelson, E. F., Murphy, G. B., Id.Eng. Chem., 27, 1460 (1935).
Received for review June 15,1979 Accepted January 14,1980
This research was supported in part by the National Science Foundation under Grant ENG 76-82102 to the University of Delaware.
