Journal of Natural Gas Science and Engineering 22 (2015) 377e394
Contents lists avai
Journal of Natural Gas Science and Engineering
journal homepage: www.elsevier .com/locate/ jngse
Investigation of volumetric fluid properties of (heptane þ hexadecane)at reservoir conditions
Reza Haghbakhsh, Ali Zolghadr, Sona Raeissi*, Shahab AyatollahiSchool of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Ave., Shiraz 71345, Iran
a r t i c l e i n f o
Article history:Received 27 October 2014Received in revised form2 December 2014Accepted 4 December 2014Available online
The paraffin group has a major role in the surface properties of hydrocarbon reservoirs. Because of itsimportance, this work reports new experimental density data for binary mixtures ofheptane þ hexadecane at temperatures and pressures ranging from 313.15 to 393.15 K, and 0.34 to44.47 MPa, respectively. Five compositions were investigated, consisting of pure heptane, pure hex-adecane, and their binary mixtures at heptane mole fractions of 0.4296, 0.6932, and 0.8748. An AntonPaar vibrating-tube densimeter was used to measure the densities. The resulting density data were fit toa Tait-type equation, showing deviations of less than 0.12% in AAD%. Excess volumes were calculatedfrom the experimental data and fit to the RedlicheKister equation. In addition, partial molar volumes ofthe components at infinite dilution and excess partial molar volumes of the components at infinitedilution were calculated. The isobaric expansion and the isothermal compressibility were also drivenfrom the Tait-type equation.
The demand for fossil energy is continuously increasing. Pe-troleum reservoirs are still the major source of energy in the world,however, the larger oil reserves are already depleted and the restare in the last decades of their production. Therefore, carefulplanning for maximum recovery from petroleum reservoirs, as wellas maximum efficiency in the refining of crude oils and naturalgases is vital (Canziani et al., 2009). Hydrocarbons form the basiccomponents of crude oil and natural gas. Their optimal recoveryfrom natural deposits depends also on the availability of extensiveand accurate knowledge of their thermodynamic properties and, inparticular, their phase behavior (Fenghour et al., 2001a). Theknowledge of thermophysical properties can assist in under-standing the nature, pattern, and extent of molecular interactions/aggregations in themixtures of concern (Dubey and Sharma, 2008).Such information can help in further developing the current ther-modynamic models, as it is impractical to measure the propertieswithin wide ranges of compositions and operating conditions(Amorim et al., 2007; Haghbakhsh et al., 2013). In addition, theknowledge of thermophysical properties of mixtures as a function
of composition, temperature and pressure is important for thedesign, operation, control, and optimization of industrial processes(Amorim et al., 2007; Pe�car and Dole�cek, 2003).
Normal hexadecane is one of the important compounds in thepetroleum industry, since it can be considered as a representativefor the moderately-heavy liquid hydrocarbons which must beprocessed and refined. Also, since hexadecane is a slightly largermolecule thanwhat is thought of as the average for petrodiesel, it isused as a surrogate to represent the heavier fractions for modelingdiesel fuel (Outcalt et al., 2010). Hence, the knowledge of hex-adecane phase behavior in relevant mixtures is important for suchindustrial applications.
Mixtures of hexadecane with alkanes are very common in hy-drocarbon processing (Outcalt et al., 2010; Matthews et al., 1987).Among the thermophysical properties of hexadecane þ alkanemixtures, the volumetric properties are particularly important dueto the relations that exist between volumetric properties and otherthermodynamic properties. An accurate model of density atdifferent conditions allows the derivation and calculation of otherthermodynamic properties, such as isobaric expansion andisothermal compressibility (Amorim et al., 2007).
The thermophysical properties of hexadecane þ alkane mix-tures at high pressures have been investigated in only a few studies(Fenghour et al., 2001a; Matthews et al., 1987; Banipal et al., 1991;Fenghour et al., 2001b). For example, Bolotnikov et al. measured the
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speed of sound and density for binary mixtures ofhexane þ hexadecane as a function of composition and tempera-ture along the saturation line between 293.15 and 373.15 K. Thedensity was measured by an OstwaldeSprengel-type pycnometer.The experimental results were then used to calculate deviations ofthe speed of sound, excess molar volume, and isentropiccompressibility (Bolotnikov et al., 2005). The objective of the pre-sent work is to provide new experimental data on the densities ofheptane þ hexadecane mixtures, and to estimate excess volumesand derived thermodynamic properties such as isothermal com-pressibilities and isobaric expansions using correlations and awell-known equation of state.
2. Experimental
An Anton Paar DMA HPM vibrating-tube densitometer was usedto measure densities at different pressures and temperatures. Thisdevice is schematically shown in Fig. 1. Density measurement inthis equipment, is based on the period of oscillation of a vibratingU-shaped tube which is filled with a sample. The U-tube is locatedinside the DMA HPM. The U-tube period of oscillation and
temperature is measured by an interface module. The data need tobe transferred to an mPDS 2000 V3, which calculates the density ateach single temperature and pressure. The density is determinedusing Equation (1), in which r is the density of the sample fluid, t isthe period of oscillation of the sample fluid, and A and B areapparatus constants that are determined by using standard cali-bration materials, 1 and 2, with known densities at selected pres-sures and temperatures.
r ¼ At2 � B (1)
Table 2Experimental densities, r, for (x heptane þ (1 � x) hexadecane) at various compo-sitions, temperatures and pressures.a
a Standard uncertainty in T is ±0.05 K and in p is ±0.05 MPa. The combinedexpanded uncertainty in r is ±2 � 10�5 g cm�3 (level of confidence ¼ 0.95).
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A ¼ r1 � r2
t21 � t22
(2)
B ¼ t22r1 � t21r2
t21 � t22
(3)
In Equations (2) and (3), r1, r2 and t 1, t 2 represent the densitiesof standards 1 and 2, and the periods of oscillation of standards 1and 2, respectively. Prior to the measurements, calibration wasdone, at first, using low-density material (in this case, nitrogen)within all temperatures (standard 1 (National Institute of Standardsand Technology)). Also, two high-density materials, in this case
Fig. 2. Experimental density measurements (points) and optimized correlations base
water at temperatures lower than 353.15 K (standard 2) anddodecane at temperatures higher than 353.15 K (standard 2) wereused (Wagner and Pruß, 2002). The necessary water density wasobtained from the equation of state (EoS) reported by Wagner andPruß (2002). The uncertainties in density of this EoS are 0.0001% ata pressure of 0.1 MPa, 0.001% at pressures between 0.1 and 10 MPa,and 0.003% within the pressure range of 10e100 MPa (up to amaximum temperature of 423 K) (Comu~nas et al., 2008). The dataof dodecane and nitrogen for calibration within the indicatedtemperature and pressure ranges were taken from the NationalInstitute of Standards and Technology (NIST) Database (NationalInstitute of STA). The program automatically calculates the A andB constants. In this way, themPDS 2000 V3 calculates the density ofunknown fluids while the fluids are entering at calibrated tem-peratures and pressures. The detailed description of the calibrationprocedure can be found in previous publications (Comu~nas et al.,2008; Zolghadr et al., 2013).
To measure the density, the first step is to connect the vacuumpump to V2, evacuating the circuit between V1 and V2 (including thevibration tube). The measurement circuit is then filled with thesample, while the vacuum pump, connected to V2, is still running.Then, the pressure system (pump and transfer vessel) is connectedto V2 and the sample is introduced to the measurement circuit toreach the suitable pressure. The capacity between the V1 and V2valves is 12.0 cm3, and the transfer vessel volume is 30 cm3.
A thermal bath (Peter Huber K€alte Maschinenbau GmbH, Ger-many) is used to control the U-tube temperature by circulatingliquid around it. The DMA HPM is covered by thermal insulation tokeep the temperature constant. The temperature is measured in-side the cell block using an AOIP 5207 thermometer which wascalibrated to within 0.05 K. The pressure is measured with a Hot-tinger Baldwin Messtechnik (HBM) manometer with an uncer-tainty of 0.05 MPa. When the period of oscillation becomesabsolutely stable (up to two digits after the decimal), the equilib-rium density is recorded. The experimental uncertainty for densityis approximately ±2� 10�5 g cm�3. The method of measurement ofuncertainty is described in reference (Qiu et al., 2013).
Thematerials used, their suppliers and their purities are listed inTable 1. The binary mixtures, composed of hexadecane þ heptane,were prepared immediately before use at atmospheric pressureand ambient temperature by weighing using a Sartorius balance
d on Equation (4) (curves) for (x heptane þ (1 � x) hexadecane) at T ¼ 313.15 K.
Fig. 3. Experimental density measurements (points) and optimized correlations based on Equation (4) (curves) for (x heptane þ (1 � x) hexadecane) at T ¼ 393.15 K.
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with an uncertainty of ±0.001 g. Three different binary mixtureswith mass percent values of 25.000, 50.000, and 75.000% of hep-tane, were prepared with a total mass of 50.000 g. On molar basis,these samples are equivalent to heptane molar compositions of0.4296, 0.6932, and 0.8748, respectively. The experimental uncer-tainty in the reported mole fraction is less than ±5 � 10�5. TheDensity data were measured at the temperatures of 313.15, 333.15,353.15, 373.15, and 393.15 K over a range of pressures from 0.34 to44.47 MPa.
Fig. 4. Comparison between heptane density in this work in the form of the Tait-like equaSchilling et al., 2008).
3. Methodology
3.1. Density correlation with a Tait-type equation
In order to correlate densities within a wide range of pressuresand temperatures, and also to calculate various derivative proper-ties from densities, it is necessary to have a mathematical equationfor density as a function of temperature and pressure. The followingTait-like equation is used (Alaoui et al., 2011a; Boned et al., 2008;Mikkelsen and Andersen, 2005; Milhet et al., 2005; Miyake et al.,2007, 2008; Comu~nas et al., 2000; Comu~nas et al., 2001; Alaouiet al., 2011b).
tion (Eq. (4)) and experimental literature data (Alaoui et al., 2013; Toscani et al., 1989;
Fig. 5. Comparison between hexadecane density in this work in the form of the Tiat-like equation (Eq. (4)) and experimental literature data (Outcalt et al., 2010; Dymond et al.,1979; Banipal et al., 1991).
Table 3Optimized coefficients of the Tait-like equation for the whole temperature and pressure range of the experimental density data of this study at each composition (xheptane þ (1 � x) hexadecane), and standard deviations, s, and absolute average deviation percent, AAD %.
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r
0BB@T; p
1CCA ¼ r0ðTÞ
1� C ln�
BðTÞþpBðTÞþ0:1Þ
� (4)
Where
r0
�T�¼ A0 þ A1T þ A2T
2 þ A3T3 (5)
B�T�¼ B0 þ B1T þ B2T
2 (6)
Where T and p are in Kelvin andMPa, respectively. Coefficients Ai, Biand C can be determined by simultaneously fitting density valuesover various pressures and temperatures for each composition, forexample based on the least squared error method. The accuracy ofthe resulting equation was investigated using absolute averagedeviation percent (AAD %) and standard deviation (s).
where N is the number of data, rexp:i and rcalc:i are the experimentaland correlated densities, respectively, and m is the number ofadjustable parameters (which is equal to eight here).
3.2. Excess molar volumes
The excess molar volumes of the mixtures were calculated usingEquation (9) (Abdulagatov et al., 2008).
VEm
�p; T ; x
�¼ Vm
�p; T ; x
�� xVm
�p; T ;1
���1� x
�Vm
�p; T ;0
�(9)
Table 4Comparison of the Tait-like correlation in this study with literature density data.
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where x is the mole fraction of heptane, Vm (p, T, x) is the experi-mentally measured molar volume of a mixture of composition x attemperature T and pressure p, and V1¼ Vm (p, T, 1) and V2¼ Vm (p, T,0) are the molar volumes of the pure components (heptane andhexadecane, respectively) at the same pressure and temperature(Abdulagatov et al., 2008).
For deriving the partial molar volumes of the components in themixture, a relation of excess molar volume as a function ofcomposition is required. The excess molar volume of the mixturecan be correlated to a RedlicheKister polynomial of the type(Redlich and Kister, 1948):
VEm ¼ x
1� x
!Xni ¼ 0
Dið2x� 1Þi (10)
Where Di is an adjustable coefficient, which can be calculated byfitting to the experimental data with the least squared errormethod.
a Uncertainty in excess molar volume ¼ ±10�4 cm3 mol�1.
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V�2 ¼ VE
m þ V*2 � x1
vVE
mvx1
!T;p
(12)
Where V1* and V2
* are the pure molar volumes of heptane andhexadecane, respectively. Vm
E is the mixture molar volume, and
Fig. 6. Variations of excess molar volume, VE, vs. mole fraction for (x heptane þ (1 �
vVE
mvx1
!T ;p
and
vVE
mvx1
!T ;p
are calculated from the differentiation of
Equation (10). The excess partial molar volumes, V�E
1 and V�E
2 of eachcomponent of the mixture were calculated using Equations (13)and (14).
V�E
1 ¼ V�1 � V*
1 (13)
V�E
2 ¼ V�2 � V*
2 (14)
Equations (11)e(14) can also be used for the calculation of thelimiting partial molar volumes and limiting excess partial molarvolumes of the components at infinite dilution when x1 or x2 go to
zero (V�∞
1 , V�E;∞
1 , V�∞
2 , V�E;∞
2 ) (Redlich and Kister, 1948).
3.4. Isothermal compressibility and isobaric expansion
Isothermal compressibility, k, and isobaric expansion, a, for themixture can be calculated from Equations (15) and (16), respec-tively (Zhou et al., 2010).
k ¼ �1V
�vVvp
�T ;x
¼�vln r
vp
�T;x
(15)
a ¼ 1V
�vVvT
�p;x
¼ ��vln r
vT
�p;x
(16)
The density derivative of Equation (4) was used for theisothermal compressibility (Equation (15)). However, for theisobaric expansion, it is recommended to use isobaric densities toderive the differential in Equation (16), because the estimatedisobaric expansion depends on the form of the functions B(T) andr0(T) in Equations (5) and (6) (Alaoui et al., 2011b; Cerdeiri~na et al.,2001; Troncoso et al., 2003). Therefore, an isobaric density corre-lation, as given by Equation (17), is fit to the experimental densitydata at each pressure.
x) hexadecane) at different temperatures and a constant pressure of 0.34 MPa.
Fig. 7. Variations of excess molar volume, VE, vs. mole fraction for (x heptane þ (1 � x) hexadecane) at different temperatures and a constant pressure of 44.47 MPa.
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rp
�T�¼ a0 þ a1T þ a2T
2 þ a3T3 (17)
4. Results and discussion
Experimental measurements were carried out for both of thepure components and their mixtures. The experimental results arepresented in Table 2. Some selected results, for both pure compo-nents and mixtures, are shown in Figs. 2 and 3 at 313.15 and393.15 K, respectively. It is seen that as the composition of heptaneincreases in the mixture, a slight curvature is observed. Thisbehavior is visible in Fig. 3 at heptane compositions of 0.8748 and1.0.
There were no density data available in literature on this binarymixture at the exact temperatures and pressures of our data, in
Fig. 8. Variations of excess molar volume, VE, vs. mole fraction for (x heptane þ (1 �
order to estimate deviations. However, to validate the trends of ourmeasured data, the experimental results of pure heptane andhexadecane are compared to the literature values by Alaoui et al.(2013), Toscani et al. (1989) and Schilling et al. (2008) for hep-tane, and Outcalt et al. (2011), Dymond et al. (1979), and Banipalet al. (1991) for hexadecane in Figs. 4 and 5, respectively. Asshown in Figs. 4 and 5, our data closely follow the trends of theliterature isotherms. However, although Fig. 4 provides a ratheraccurate comparison since both sets of data are at the same tem-peratures (although not at the same pressures), this does not holdfor Fig. 5. In the case of Fig. 5, neither the temperatures nor thepressures from literature are exactly the same as those measured inthis study.
The values of the coefficients of Equation (1) for each compo-sition, and the corresponding statistical parameters, are presentedin Table 3. The curves on Figs. 2 and 3 represent the Tait-like cor-relation, which show good agreement with the experimental data.
x) hexadecane) at different pressures and a constant temperature of 313.15 K.
Fig. 9. Variations of excess molar volume, VE, vs. mole fraction for (x heptane þ (1 � x) hexadecane) at different pressures and a constant temperature of 393.15 K.
Table 6Coefficients Di of the RedlicheKister equation and standard deviations s for (xheptane þ (1 � x) hexadecane) at various temperatures and pressures.
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In addition, the deviations between densities correlated by the Tait-like equation in this study and the literature density data for pureheptane and pure hexadecane are presented in Table 4. In Figs. 4and 5, the Tait-like equation was also interpolated at isothermsfor which literature data were available, but were temperatureswhich were notmeasured in this study. These results also fit well tothe experimental literature data. Table 4 actually quantifies theerrors of Figs. 4 and 5. This table also confirms that the Tait-likeequation, representative of our experimental data, has goodagreement with literature density data, even at interpolated tem-peratures and pressures.
The calculated values of excess molar volumes of the mixture atdifferent compositions, pressures and temperatures are presentedin Table 5.
The behavior of the excess molar volume at the lowest andhighest pressures are shown on Figs. 6 and 7, respectively, wherethe isobaric behavior of excess molar volume of the mixtures at0.34 and 44.47 MPa are depicted at different temperatures withrespect to heptane molar composition. The excess molar volume ofthe mixtures at the lowest and highest isotherms (313.15 and393.15 K) are presented on Figs. 8 and 9, respectively, with respectto heptane molar composition at different pressures.
As can be seen from Figs. 6e9 and Table 5, the values of excessmolar volume calculated from the experimental density data ofheptane þ hexadecane mixtures (the dots in Figs. 6e9) are positive(up to 6.5 cm3 mol�1) for all of the measured temperatures andpressures over the entire composition range. However, based onthe RedlicheKister polynomial (Eq. (10)), some values of the excessmolar volume are negative between heptanemolar compositions of0.0e0.1 at the temperature of 313.15 K. The curves of VE
m vs. x arealmost symmetrical, with the maximum ranging between 0.5 and0.6 heptanemole fraction. The large values of VE
m is the result of thenon-ideal nature of the heptane þ hexadecane mixture, as heptaneand hexadecane are two unlike molecules. Hexadecane has a longchain which has more than twice the length of the heptane chain.Figs. 6 and 7 show that at constant pressure, as the temperatureincreases, the mixture acts more non-ideal and the values of theexcess molar volumes increase, while in Figs. 8 and 9, as thepressure increases at constant temperature, the value of the excess
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molar volumes decreases and the mixture deviates less from ide-ality. Therefore, increasing temperature at constant pressure anddecreasing pressure at constant temperature contribute toincreasing non-ideality of the system.
Table 6 presents the values of the coefficients optimized tothe excess molar volumes over the entire composition range(therefore, they are composition-independent coefficients) fordifferent temperatures and pressures. The values of the stan-dard deviations are also reported in this table. The excessmolar volumes, correlated with the RedlicheKister polynomial,are indicated as the continuous curves on Figs. 6e9. It isobserved that they have good agreement with the experi-mental data.
Table 7 presents the values of partial molar volumes at infinitedilution, as well as excess partial molar volumes at infinite dilutionfor the mixtures of different composition at various temperaturesand pressures.
Tables 8 and 9 present the values of isothermal compressibilitiesand isobaric expansions, respectively, for the mixtures at differenttemperatures, pressures and compositions. For the calculation ofisobaric expansion, Equation (17) was used as the density functionin Equation (16). The coefficients of Equation (17), ai, are reported inthe Supplementary Data Section.
The behavior of the isothermal compressibility and isobaricexpansion with respect to pressure at constant temperature isshown in Figs. 10 and 11, respectively.
As Tables 8 and 9, as well as Figs. 10 and 11, indicate, theisothermal compressibility and isobaric expansion decrease aspressure increases, and increase as temperature increases at con-stant composition.
5. Conclusions
In this study, the densities of mixtures of heptane and hex-adecane have been measured experimentally. Mixture densitieswere measured for the pure components and three differentbinary mixtures with heptane mass percentages of 25%, 50% and75%, which are equivalent to molar compositions of 0.4296,0.6932 and 0.8748, respectively. Experiments on the pure com-ponents and mixtures were carried out at temperatures of 313.15,353.15, 373.15, and 393.15 K over a pressure range of0.34e44.47 MPa. The density data were correlated with a Tait-like equation, as well as a polynomial equation, in order toderive isothermal compressibility and isothermal expansion re-lations, respectively. Isothermal compressibilities and isobaricexpansions of the mixture were shown to decrease as the pres-sure increased at constant temperature. In fact, a convergingtrend was indicated for the different compositions as the pres-sure increased. Excess molar volumes of the mixture were alsocalculated and the values were correlated with the Red-licheKister polynomial to derive the partial molar volumes of thesystem. It is observed that at low pressures for certain temper-atures, negative values of excess molar volumes are obtained.
In addition, partial molar volumes and excess partial molarvolumes at infinite dilution were calculated.Heptane þ hexadecane mixtures are non-ideal as indicated by thelarge values of excess molar volumes. This non-ideality effect in-creases as the temperature increases and the pressure decreases.The maximum non-ideality of the system is observed at almostequimolar compositions of the components in the mixture, asindicated by the largest values of excess volumes occurring atthese compositions.
Fig. 10. Variation of isothermal compressibility, k, vs. pressure for the (x heptane þ (1 � x) hexadecane) system at different compositions and a constant temperature of 393.15 K.
Fig. 11. Variations of isobaric expansion, a, vs. pressure for the (x heptane þ (1 � x) hexadecane) system at different compositions and a constant temperature of 373.15 K.
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Acknowledgment
The authors are grateful to Shiraz University for supporting thisresearch.
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.jngse.2014.12.005.
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