Energy & Fuels 2005, 19, 1225-1229
1225
Experimental Determination of Solubility Parameters of Oils as a Function of Pressure† Sylvain Verdier, Diep Duong, and Simon I. Andersen* Engineering Research Centre IVC-SEP, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark Received July 19, 2004. Revised Manuscript Received April 15, 2005
In this work, the solubility parameter of dead and live crude oils was measured at 303.15 K and up to 300 bar, using the internal pressure approach. An indirect technique was chosen, using thermal expansivities (determined from microcalorimetric measurements) and isothermal compressibilities (calculated from density measurements). This method was tested on seven pure compounds, and the deviation with literature data is 99 >99.8 >99.8 >99.5 >99.9 (N45) >99.8 >99.9
proportional to thermal expansivity, according to eq 7:
δQ dP | ) - (RP - RV)VcellT dt T dt
(7)
where (δQ/dT)|T is the rate of heat measured by the microcalorimeter, RP the thermal expansivity of the fluid under investigation, RV the thermal expansivity of the stainless steel, Vcell the volume of the cell, T the temperature, and dP/dT the rate of increase in pressure. Several pure compounds were tested,6,11 and the uncertainty reaches, at most, a value of 2%. Isothermal compressibility (eq 8) was indirectly calculated using density measurements that were fitted to a modified Tait equation of state12 (eq 9):
κT ) F)
1 ∂V V ∂P
( )
) T
1 ∂F F ∂P
( )
T
F0(T) 1 - C(T) ln[(B(T) + P)/(B(T) + P0)]
(8)
(9)
where F0 is the density at P0 and B and C are constants that are fitted to the experimental data. The density was measured on an Anton Paar density measurement system for liquids and gases (Type DMA 512, for high pressures). The stainless-steel cylindrical sample tube, placed in a brass housing, is maintained at a constant temperature by a thermostat bath (Julabo F34 MD) (temperature stability: (0.01 K, display resolution of 0.1 K). The calibration through the entire pressure range is a key step, and the method that was developed by Lagourette et al.13 was used. The pressure was sustained and measured by means of a high-pressure syringe pump (ISCO pump 260 D). The uncertainty in the pressure range is guaranteed to be at least 0.5% of the full scale. The average deviation with literature data for several pure compounds was, at most, 0.11%.6 The deviation for compressibility of pure compounds was 2.7%, relative to direct compressibility measurements.6 This high deviation is due to the Tait equation itself, which is made to describe density measurements and is not for its derivatives. However, this method is widely used.14-16
Results The physical solubility parameter of five pure compounds was measured6 at 303.15 K and up to 300 bar. In this work, two new compounds have been investigated: n-pentane and toluene. The origin and the purity of the compounds are available in Table 1. All the compounds were used without any further purification. Figure 1 shows the physical solubility parameter for (12) Cibulka, I.; Zikova, M. J. Chem. Eng. Data 1994, 39, 876-886. (13) Lagourette, B.; Boned, C.; Saint-Guirons, H.; Xans, P.; Zhou, H. Meas. Sci. Technol. 1992, 3, 699-703. (14) Pecar, D.; Dolocek, V. Fluid Phase Equilib. 2003, 211, 109127. (15) Garcia Baonza, V.; Caceres Alonso, M.; Nunez Delgado, J. J. Chem. Soc., Faraday Trans. 1994, 90, 553-557. (16) Comunas, M. J. P.; Lopez, E. R.; Pires, P.; Garcia, J.; Fernandez, J. Int. J. Thermophys. 2000, 21, 831-851.
Solubility of Oils as a Function of Pressure
Energy & Fuels, Vol. 19, No. 4, 2005 1227
Figure 3. Thermal expansivity of oil 1 at 303.15 K: (s) live oil 1, fast decompression; (-2-) live oil 1, slow decompression; and (-9-) dead oil 1. Figure 1. Physical solubility parameter of pure compounds, as a function of pressure at 303.15 K: (s) n-hexane, (-0-) n-pentane, (-9-) n-heptane, (-×-) n-decane, (- - -) ethanol, (-2-) cyclohexane, and (-]-) toluene.
Figure 4. Solubility parameter of oil 1 at 303.15 K: (-4-) live oil 1, from internal pressure; (-2-) dead oil 1, from internal pressure; and (-9-) dead oil 1, from the refractive index. Figure 2. Physical solubility parameter crude oils at 303.15 K: (s) live oil 1, (-0-) dead oil 1, and (- - -) dead oil 2.
these seven compounds. The physical solubility parameters increase slightly with pressure, up to 0.8 MPa1/2 for cyclohexane. The presence of hydrogen bonding is visible with the parameter δliterature - π1/2: this difference is 9 MPa1/2). Because this is an indirect measurement, uncertainties add up and it can induce a strange shape (for instance, the n-pentane curve, which is slightly decreasing at the end). The fitting procedure of the modified equation is quite crucial as well.17 Two dead oils and one live oil were also investigated. Their physical solubility parameters are shown in Figure 2. Live oil 1 was recombined from the dead oil and methane (2.5 wt %). The addition of methane decreases the solubility parameter, compared to its dead oil values, as expected. Furthermore, the bubble point of the live oil could be detected with the microcalorimeter. Indeed, a fast decompression is inducing a change in the signal, as shown in Figure 3 for live oil 1. This was confirmed by the P-V curve. Discussion To verify the consistency of our results, a method based on the refractive index data was used at a pressure of 1 bar and extrapolated to higher pressures. According to Wang,18 the relationship between the (17) Duong, D. Determination of Solubility Parameters for Crude Oils, Master’s Thesis, Technical University of Denmark, 2004.
solubility parameter and the refractive index n is
(
δ ) 53.827
)
n2 - 1 + 2.418 n2 + 2
(10)
This correlation was made with paraffinic and aromatic hydrocarbons under ambient conditions. The refractive index was measured at 303.15 K and 1 bar with an Abbemat digital automatic refractometer. The calibration was run with distilled water and toluene, and the deviation was below or within the experimental uncertainty of the apparatus. The Lorentz-Lorenz equation then was used:
(
)
R n2 - 1 ) F(T,P) MW n2 + 2
(11)
where R is the molar refraction, Mw the molecular weight, n the refractive index, and F the density. Both R and Mw are assumed to be independent of temperature and pressure.18 Every crude oil was then considered as a pseudo-component, and the ratio R/Mw was calculated and assumed to be constant. In this case, the solubility parameter can be written as follows:
R δ(T,P) ) 53.827 F(T,P) + 2.418 Mw
(12)
As seen in Figure 4, this method gives a relatively constant deviation with internal pressure measure(18) Wang, J. Predicting asphaltene flocculation in crude oils, Ph.D. Thesis, New Mexico Institute of Mining and Technology, Socorro, New Mexico, 2000.
1228
Energy & Fuels, Vol. 19, No. 4, 2005
Verdier et al.
ments for dead oil 1 in the range of 0.6-0.8 MPa1/2. This is not such a big difference, considering the combined uncertainties inherent to the internal pressure determination. Besides, it is interesting to note that, in eq 12, the solubility parameter is a linear function of density, whereas it is not in the original definition (eq 1). Indeed, one can write eq 1 as follows:
δ(T,P) )
x
- E(T) F(T,P)1/2 Mw
(13)
This difference is due to eq 10, which was correlated under ambient conditions and theoretically justified, using the van der Waals equation of state,19 which cannot be applied to complex systems. However, another definition of cohesion energy, such as -E ) Uvap(T,P ) 0) - Uliq(T,P), which is sometimes present in the literature,6 would lead to a different dependence of δ with density. The other goal of this work was to study the ability of cubic equations of state (EOSs) to describe the solubility parameter. In this work, two EOSs will be investigated for dead oil 1: the Peng-Robinson (PR) EOS (eq 14) and the Soave-Redlich-Kwong (SRK) EOS (eq 15).20
P)
a(T) RT V - b V(V + b) + b(V - b)
(14)
a(T) RT V - b V(V + b)
(15)
P)
The descriptions of a and b can be found in the work by Smith et al.20 According to eqs 1 and 2, the solubility parameter δ is given as
δ)
(
)
Uvap(T,P ) 0) - Uliq(T,Psat(T)) V(T,P)
1/2
(16)
If eqs 14 and 15 are applied to eq 16, combined with eq 3, one can write
δPR )
{
[(
Vsat + b(x2 + 1) x2 da a-T ln 4b dT Vsat - b(x2 - 1)
(
δSRK )
)
[(
) (
)]( )}
)( )]
da b 1 1 a-T ln 1 + b dT Vsat V
1 V
1/2
(17)
Table 2. Composition and Physical Properties of Live Oil 1 component
composition (mol %)
molecular weight, Mw (g/mol)
densitya (kg/m3)
nitrogen carbon dioxide methane ethane propane i-butane n-butane i-pentane n-pentane C6 C7 C8 C9 C10+
0.45 0.02 30.02 4.08 4.85 1.99 4.08 2.45 2.98 4.32 6.38 4.32 6.38 5.78
84.6 92.9 107.3 120.6 279.0
668.1 727.7 744.4 764.1 884.9
a
Measured at 1 bar and 298.15 K.
oil, a modified solubility parameter was used and defined as follows:6
δ)
(
)
Uvap(T,P ) 0) - Uliq(T,P) Vliq(T,P)
1/2
(19)
This definition removes the equilibrium facet of δ, but the difference between eqs 16 and 19 is small (up to 0.2 MPa1/2 at 300 bar and 303.15 K for n-heptane6). This deviation is not much and usually is within the experimental uncertainties (for instance, in Barton,5 at 298.15 K, the solubility parameter of n-hexane is 14.9 MPa1/2 (page 11), 14.8 MPa1/2 (page 48), and 15 MPa1/2 (page 53), depending on the method used to estimate it). Thus, this approach was chosen. Furthermore, Maloney and Prausnitz21 and Allada22 also used this modified version to treat polyethylene and supercritical fluids, respectively. Therefore, the modified solubility parameters are similar to those described by eqs 17 and 18, except that Vsat is now V(T,P). Live oil 1 was divided into 14 components and pseudocomponents, as seen in Table 2. The oil was then flashed at 1 bar and 298.15 K by means of the in-house PVT software SPECS, using both the SRK EOS and the PR EOS to calculate the composition of the dead oil (presented in Table 3). The difference induced by the two equations is relatively small. Using the Pedersen procedure,23 the critical constants and the acentric factors then were determined. The following mixing rules were applied: Nc N c
1/2
(18)
where Vsat represents the saturated molar volume (Vsat ) V(T,Psat)). If the volume is given as an input, the PR EOS can describe the solubility parameter of n-heptane quite accurately6 (with an average absolute deviation with the physical solubility parameter of 0.16 MPa1/2). However, because the saturated pressure is not known for a crude (19) Buckley, J. S.; Hirasaki, G. J.; Liu, Y.; Von Drasek, S.; Wang, J.-X.; Gill, B. S. Pet. Sci. Technol. 1998, 16, 251-285. (20) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics, 5th Edition; McGraw-Hill: New York, 1996.
a)
xixj(aiaj)1/2 ∑ ∑ i)1 j)1
(20)
Nc
b)
xi b i ∑ i)1
(21)
where xi (or xj) is the molar fraction of the compound i (or j) and Nc is the number of compounds (the interactions coefficients are not included, because there is no (21) Maloney, D. P.; Prausnitz, J. M. J. Polym. Sci. 1974, 18, 27032710. (22) Allada, S. R. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 344348. (23) Pedersen, K. S.; Fredenslund, A.; Thomassen, P. Properties of Oils and Natural Gases; Gulf Publishing Company: Houston, TX, 1989.
Solubility of Oils as a Function of Pressure
Energy & Fuels, Vol. 19, No. 4, 2005 1229
Table 3. Composition and Physical Properties of Dead Oil 1 composition (mol %) component
live oil
dead oil (PR)
dead oil (SRK)
nitrogen carbon dioxide methane ethane propane i-butane n-butane i-pentane n-pentane C6 C7 C8 C9 C10+
0.45 0.02 30.02 4.08 4.85 1.99 4.08 2.45 2.98 4.32 6.38 4.32 6.38 5.78
0.00 0.00 0.25 0.22 0.92 0.78 2.21 2.32 3.26 6.61 11.37 10.63 6.90 54.54
0.00 0.00 0.26 0.23 0.94 0.81 2.28 2.39 3.33 6.69 11.53 10.60 6.85 54.10
CO2 and N2). The interactions coefficients kij factors are assumed to be equal to zero. The measured densities were used to give the molar volumes as an input. The average molecular weight was Nc calculated (Mw ) ∑i)1 xiMw,i) and was determined to be equal to 194.4 g/mol. As shown in Figure 5, the solubility parameters deduced from the EOSs are quite far from the experimental results (the average deviation with the PR EOS is 4.9 MPa1/2, and that for the SRK EOS is 6.5 MPa1/2). This might be due to the characterization procedure, because the EOSs are able to describe δ for pure compounds.6,17 A more appropriate characterization method should be used instead.24 It could not be applied in this work, because the bubble point pressure and the density at this point are required. In addition, it can be noted that more than 50% of dead oil 1 belongs to the C10+ fraction. This fraction mainly contributes to the solubility parameter. The available characterization is likely not to be sufficient to give accurate results with (24) Quin˜ones-Cisneros, S.; Zeberg-Mikkelsen, C. K.; Stenby, E. H. Fluid Phase Equilib. 2003, 212, 233-243.
Figure 5. Solubility parameter of the dead oil 1 at 303.15 K: (-4-) using the SRK EOS, (-9-) using the PR EOS, (-2-) from RI measurement, and (s) this work.
the EOS. This could explain why the computed values of solubility parameters are at the highest end of the data that have been reported in the literature. Conclusion Solubility parameters of one recombined live oil and two dead oils were successfully measured at a temperature of 303.15 K and pressures up to 300 bar. The deviation with the refractive index method is within 1 MPa1/2; however, this measurement was performed only at 1 bar. A comparison was made to higher pressures; however, because the correlation using refractive index data was made under ambient conditions, it might not be valid. Two cubic equations of state (EOSs) were tested with a dead oil, to describe the solubility parameter as a function of pressure. Densities were measured and a characterization of the oil was performed. However, the average deviation was larger than 6.5 MPa1/2 with the Soave-Redlich-Kwong (SRK) EOS and 4.9 MPa1/2 with the Peng-Robinson (PR) EOS. Hence, better results should be obtained with a more-realistic characterization of the oil. EF049827V
