Measurements and Modeling of Volumetric and Phase Behavior of

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Measurements and Modeling of Volumetric and Phase Behavior of Carbon Dioxide + Higher Alkanes: CO2 + n‑Pentadecane at Temperatures 313 to 410 K and Pressures up to 77 MPa Mohamed E. Kandil* Centre for Integrative Petroleum Research, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia ABSTRACT: Experimental compressed liquid density and bubble pressure of {xCO2 + (1 − x)C15H32} are reported for x = 0.376, 0.562, and 0.757 at temperatures from 313, 363, and 410 K and pressures from bubble points up to about 77 MPa. Density was measured using a vibrating Utube driven and scanned in frequency domain by a lock-in amplifier to accurately measure the resonance peak in complex form where density is determined with an expanded uncertainty of U(ρ) = 0.003ρ. The experimental measurements are compared with cubic equations of state of Redlich−Kwong−Soave (RKS), Peng−Robinson 1976 (PR76), and the improved version Peng− Robinson 1978 (PR78) with and without volume translation correction. PR78 EOS gives best predictions with an average deviation of 1.2%. The deviations are maximum near the bubble points and increase in a systematic manner with increasing CO2 mole fraction x. Bubble pressures were determined from the discontinuity of p−V plots completed during a series of isothermal constant composition expansion processes. Bubble pressures are limited to 353 K in literature but extended in this work to 412 K. No previous data on compressed liquid density of this system available in literature at high pressure. pentadecane, reported by Tanaka et al.3 at pressures only from 1.7 to 6.4 MPa at a single isotherm of T = 313 K, and five data point reported by Kodama et al.4 at same temperature of 313 K and a similar pressure range from 2.9 to 6.8 MPa. In this work, experimental measurements of compressed liquid density and bubble pressures of {xCO2 + (1 − x)C15H32} are reported at temperatures from 313 to 410 K and at pressures near bubble points up to about 77 MPa. The experimental measurements are compared with predictions of three equations of state, commonly used in process simulators (RKS,5 PR76,6 and PR787) EOS, calculated with and without Peneloux et al.8 volume translation correction. Simulated streams often deviate from those observed in actual operations so selecting the right EOS for estimating stream properties is the most critical step toward reliable simulation and design. Although only three compositions are reported in this work, however, the experimental measurements were made to the maximum limit of the vibrating U-tube (410 K and 77 MPa). The advantage of using a lock-in amplifier in this work is that the old frequency counter DMA 60 that comes with the DMA 512 vibrating tube is difficult to interface with computers and does not give details on stability condition. The lock-in amplifier is used to scan, both, the in-phase and quadrature voltages to determine the complex resonance frequency, and the shape of the resonance peak plotted as a function of frequency can give a clear indication about the fluid stability inside the vibrating U-tube. Instability arises from different

1. INTRODUCTION Climate change is a real risk and to reduce carbon emissions modern technologies are rapidly evolving for effective capture and confinement of CO2. One of the proven technologies is the injection of CO 2 in hydrocarbon rock formation for sequestration in geological storages and also for enhanced recovery of residual heavy oils in mature oil fields.1 Accurate knowledge of thermodynamic properties of CO2 and heavy hydrocarbons are required for successful design and operation of CO2 injection facility. Thermodynamic properties of hydrocarbons + CO2 at high pressure are also important for offshore oil and gas industry where no enough data is available in literature at elevated pressures. Experimental data at high pressure is becoming critical for such a multibillion dollar industry. Recently, a major oil and gas company announced Project2 20K to develop, by the end of the year 2020, the technologies necessary for production from deepwater reservoirs at pressures up to 140 MPa (20,000 psi) at the mudline and at temperatures up to 450 K. These technologies will help to unlock the world’s most challenging deepwater basins in the Gulf of Mexico’s ultradeepwater Paleogene, Egypt’s West Nile Delta, and offshore Azerbaijan including the giant Shah Deniz field in the Caspian Sea which represents the largest gas discovery in BP’s 100 year history and remains one of the largest oil and gas fields in the world. Pentadecane is one of the highest liquid alkanes at room temperature (mp = 283.1 K). To the author’s knowledge, no literature data reported previously on compressed liquid density of CO2 + n-pentadecane, except eight data points on the saturation line for calculating solubility of CO2 in n© XXXX American Chemical Society

Received: November 14, 2017 Accepted: March 19, 2018

A

DOI: 10.1021/acs.jced.7b00995 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Description of Chemical Samples

a

chemical name

CAS

source

puritya

analysis method

additional purification

carbon dioxide pentadecane

124-38-9 629-62-9

Linde S. Aldrich

x > 0.9999 x > 0.99

GC GC

none degassed

Purity as stated by the supplier, x is mole fraction.

effects such as strong electromagnetic field, mechanical vibration, and so forth and among these is when the fluid inside the U-tube is not homogeneous (two coexisting phases for example). A clean and repeatable resonance peak can only be observed when the vibrating U-tube becomes completely stable, which will never happen if the fluid exists in more than one phase, and that has been confirmed and clearly demonstrated in this work. The effect of viscosity of pentadecane (η < 4 mPa·s) on the vibration of the U-tube is considered negligible. For viscous fluids (close to 150 mPa·s) the peak signal becomes noticeably wider and the effect on density measurements can increase by about δρ = 0.0005ρ as reported by Al Motari et al.9 The most important effect on the vibrating U-tubes is their sensitivity to temperature and thermal hysteresis. Thermal hystereses do not depend on the fluid inside the U-tube, whether pure or mixture, but after exposing the metal of the U-tube to few thermal cycles, especially at its maximum temperature rating, the spring constant of oscillation is changed and does not come back to its exact initial value as before. Another hysteresis effect can also arise from the brazing filler metal that holds the U-tube to the manifold, which is made of an alloy different from the one of which the U-tube is made. Excess molar volumes are also reported for this system at pressures up to 76 MPa, using the same method of ZuınigaMoreno et al.,10 Bessières et al.,11 and Jian et al.12 reported at pressures 0.9999. Analytical grade n-pentadecane was supplied by Sigma-Aldrich with a mole fraction purity xC15H32 > 0.99. The sample was degassed at room temperature for 24 h under vacuum prior to use with no further purification performed. More details are listed in Table 1. The experimental apparatus was described in detail in a previous paper13 and only a brief description of the procedure is given here. The apparatus, shown in Figure 1, consists of three variable-volume cells where a known mass of C15H32 was loaded in cell 1 and an initial volume Vi of CO2 was loaded in cell 3, while valves v3 and v2 remained open to keep the tubing, up to the isolation valve v1, filled at same pressure p3 in cell 3. An amount of CO2 was then injected in cell 1, by controlling v1, while monitoring the pressure drop in cell 3. After closing v1, the pressure in cell 3 is increased to p3 again (as prior to opening v1) using the Quizix pump (QP). After complete equilibrium in cell 3 the final volume Vf of cell 3 is recorded and the amount of CO2 injected was calculated from the volume drop (Vi − Vf) at p3, using Span and Wagner14 CO2 EOS. The fluid mixture was then mixed, after closing v2, by moving it forth and backward between cell 1 and cell 2, while maintained in compressed liquid phase. The mixture was also mixed after each measurement of pTx and density measurement was also repeated. The piston of cell 1 is driven mechanically by a servomotor (SM) while the pistons of cell 2 is driven B



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Figure 2. Illustration for the lock-in amplifier in-phase output voltage when (a) “clean” resonance peak at stable homogeneous conditions (b) unstable distorted peak when the fluid is not homogeneous or exists in two phases (p < pb).

and Kurihara et al.17 for driving a vibrating wire viscometer. The frequency generated by the synthesizer of the lock-in amplifier was stepped over the resonance frequency of the Utube while the in-phase and quadrature voltages were recorded and fit to Lorentzian function to accurately “pinpoint” the resonance frequency f 0. Density ρ was then determined from period of oscillation τ = 1/f 0 using the Chang and Moldover18 expression in eq 1:

Figure 3. p−V plot measured during an isothermal constant composition expansion (CCE) in cell 1. Bubble pressure is located at the intersection of the two lines fitted to the data points at both sides of the discontinuity of the p−V plot.

Table 2. Experimentala Densities ρ of Pure n-Pentadecane Measured at T = 313.15 K

2

ρ=

k(T , p)τ − 1 v (T , p)

(1)

where k(T,p) and v(T,p) are stiffness and volume functions (in temperature and pressure), determined from calibration with two reference fluids, N2 and H2O, at the same range of temperature at pressures from vacuum up to 77 MPa. The calibration procedure and verification are reported in detail elsewhere.13 The expanded uncertainty (k = 2) of the measurements of period of oscillation is U(τ) = 0.1 μs, combined with uncertainties propagated from temperature, pressure, and composition resulted in expanded uncertainty of density, at a confidence band better than 0.95, as U(ρ) = 0.003ρ. Same value was typically obtained in the Ken Marsh laboratories9,19,20 for similar models where the main source of uncertainty was usually raised from the thermal hysteresis. A complete evaluation and analysis on sensitivity of vibrating Utubes to temperature, pressure, and the calibrant fluids and their reference equations is reported by Holcomb and Outcalt.21 Bubble points were detected visually through the glass window GW located at the top of cell 1 during an isothermal constant composition expansion (CCE) process. The bubble pressure was determined at the intersection of the two lines fitted to the data points at both sides of the discontinuity of the pV data plotted during the CCE process as shown in Figure 3.

p/MPa

ρ/kg·m−3

0.10 6.91 20.79 34.67 55.49 76.93

752.2 757.8 766.9 776.1 787.5 797.3

a Expanded uncertainties: U(ρ) = 0.003ρ, and U(p) = 0.05 MPa with a coverage factor k = 2.

Figure 4. Relative deviations of experimental density ρ of pure npentadecane from predictions ρRefprop of Refprop22 based on Lemmon23 EOS as a function of pressure p at T = 313.15 K, ▲, this work using a vibrating U-tube; △, Daridon et al.;25 ○, Dovnar et al.;24 ◊, Cutler et al.;26 −·−·−, PR76 EOS; − − − , PR76 EOS (VT) corrected with Peneloux volume translation.

3. RESULTS AND DISCUSSION 3.1. Density of Pure n-Pentadecane. Densities of pure npentadecane, measured at pressures up to 77 MPa at T = 313.15 K, are listed in Table 2. As shown in Figure 4, the relative deviations from the predictions of Refprop22 based on Lemmon23 reference equation, along with literature data reported by Dovnar et al.24 and Daridon et al.25 (from speed of sound) are all within 0.1%. The deviations of the data reported by Cutler et al.26 (from volume measurements using a flexible bellows) are shown less by about 2%, which was previously described as “probably erroneous” by Cibulka and Hnedkovsky27 in their evaluation of experimental measurements of density of different higher alkanes. The deviations of

the predictions of PR76 EOS from Refprop are at least −14% but significantly reduce to 0.6% when Peneloux volume translation correction is included in the calculations, as also shown in Figure 4. 3.2. Density of CO2 + n-Pentadecane. Compressed liquid densities and excess molar volumes of {xCO2 + (1 − x)C15H32} are listed in Table 3 at T = 313, 363, and 410 K, starting from pressures very close to bubble points up to a pressure of about 77 MPa. The relative deviations of RKS, PR76, and PR78 EOS calculated with Multiflash28 at the same temperatures and pressures listed in Table 3 from the experimental data are shown in Figure 5. The deviations of C



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Table 3. Experimentala Densities ρ and Excess Molar Volumesb VE of Mixtures of {xCO2 + (1 − x)C15H32} Measured at Temperatures T and Pressures p p/MPa

ρ/kg·m−3

VE/cm3·mol−1

p/MPa

T/K = 313.15 6.91 20.79 34.67 55.49 76.31

6.36 20.79 34.67 55.49 76.31

8.80 11.29 13.85 20.79 34.67 55.49 76.31

770.0 784.0 795.8 809.0 825.4 T/K = 313.15 779.4 796.8 808.8 829.0 841.5 T/K = 313.15 798.3 804.2 810.2 828.1 843.2 867.8 885.9

ρ/kg·m−3

VE/cm3·mol−1

p/MPa

T/K = 363.15 −66.75 −1.92 −1.16 −0.60 −1.46

6.94 20.82 34.70 55.52 76.34

−121.49 −2.52 −0.77 −0.73 −0.26

10.73 20.82 34.70 55.52 76.34

−39.11 −10.06 −6.56 −3.97 −1.48 −0.80 −0.43

17.13 20.82 34.70 55.52 76.34

ρ/kg·m−3

VE/cm3·mol−1

T/K = 410.15

x = 0.376 725.3 744.5 754.3 775.6 787.0 T/K = 363.15

−109.70 −9.66 −2.07 −1.37 −0.17

x = 0.562 730.3 745.5 768.8 784.7 800.8 T/K = 363.15 x = 0.757 738.8 749.2 780.0 812.3 831.7

13.91 20.85 34.73 55.55 76.37

−76.67 −13.07 −4.52 −0.85 0.08

13.90 20.85 34.73 55.55 76.37

−29.90 −16.92 −4.76 −1.65 −0.18

21.95 27.79 34.73 55.55 76.37

−46.49 −19.64 −6.16 −1.51 0.02

693.8 702.6 723.3 742.3 757.3 T/K = 410.15

−69.30 −30.23 −8.82 −2.35 −0.63

686.5 701.8 724.9 749.5 769.3 T/K = 410.15

−33.14 −18.46 −10.91 −3.33 −1.81

682.7 702.0 723.5 763.8 796.1

a

Expanded uncertainties are U(T) = 0.4 K, U(p) = 0.05 MPa, U(x) = 0.004, U(ρ) = 0.003ρ, U(VE) = U(Vm) = 0.003Vm with a coverage factor k = 2. Expanded uncertainty in the mixture molar volume Vm is calculated as U(Vm) = 0.3−0.60 cm3·mol−1 for the range of molar volumes of this mixture Vm = 96 to 215 cm3·mol−1. b

volume translation correction (VT) was included in the EOS as shown in Figure 5b. The deviations from PR78 EOS remained, almost unchanged, within ±2.5% after including the volume translation. It is not surprising that PR78 EOS gives improved predictions of liquid density of this system without the need for a volume shift, as it was originally developed to yield accurate vapor pressure of heavy hydrocarbons. The formulations of PR78 EOS are shown in eq 2 to 5, same for PR76 EOS, except the parameter mi(ωi) is calculated in eq 4 with two different treatments for acentric factors ωi ≤ 0.49 and ωi > 0.49. p=

a(T ) RT − v−b v(v − b) + b(v − b)

⎛ R2Tc2, i ⎡ ⎢1 + m ⎜1 − ai = 0.457235529 i⎜ pc , i ⎢⎣ ⎝ bi = 0.0777960739 Figure 5. Relative deviations of the experimental density ρ from the predictions of EOS ρEOS calculated in (a) without volume translation using yellow open square, RKS; green open diamond, PR76; purple triangle, PR78; and in (b) with volume translation (VT) using yellow closed square, RKS (VT); green closed diamond, PR76 (VT); purple closed triangle, PR78 (VT). All EOS were calculated at same pTx listed in Table 3. exptl

(2)

T Tc , i

⎞⎤ ⎟⎥ ⎟⎥ ⎠⎦

2

RTc , i pc , i

(3)

if ωi ≤ 0.49 → mi = 0.37464 + 1.54226ωi − 0.26992ωi2 if ωi > 0.49 → mi = 0.379642 + 1.48503ωi − 0.164423ωi2 + 0.016666ωi3

(4)

the values of a and b are calculated for a mixture of N components, using the classical mixing rules in eq 5 N

a=

RKS and PR76 EOS are significantly reduced from −20% and −10% as shown in Figure 5a to within about ±4% when the

N

∑ ∑ xixj i=1 j=1

D

N

aiaj (1 − kij),

b=

∑ xibi i=1

(5)



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Table 4. Critical Parameters and Volume Translation Used in the Calculations of EOSa RKS EOS (VT)

PR76 EOS (VT)

i

Tc/ K

pc/MPa

ω

vc cm3·mol−1

kij

c0/m3·mol−1

c1/m3·mol−1·K−1

c0/m3·mol−1

c1/m3·mol−1·K−1

CO2 C15H32

304.13 707.71

7.377 1.52

0.223 0.706

9.41185e-05 0.00088

0.09544519

3.63125328e-6 8.56338107e-5

0 −8.687601e-11

−1.03345291e-6 5.56131842e-5

0 −3.1011196e-11

Critical temperature Tc, critical pressure, pc, acentric factor ω, critical molar volume vc, the binary interaction parameter kij, and the volume translation coefficients of eq 7 c0 and c1 used to calculate RKS (VT) and PR76 (VT) shown in Figure 5b. a

where p is the pressure, T is the temperature, R is the ideal gas constant, vc is the critical molar volume, Tc is the critical temperature, pc is the critical pressure, ω is the acentric factor, xi is the mole fraction of component i, and kij is the binary interaction parameter representing molecular interactions between molecules i and j. The volume translation correction proposed by Peneloux et al.8 is used to shift the volume v calculated from the equation of state by a quantity c to match that for liquid volume vL as eq 6 N

vL = v −

∑ cixi i=1

(6)

where the volume shift c is calculated from pure components as linear function of temperature as in eq 7 ci = ci0 + ci1T

(7)

the values of ci for pure components CO2 and C15H32 are listed in Table 4 with other critical parameters obtained from the default values in Multiflash.28 These coefficients are chosen in Multiflash28 to match density at 290.7 and 315.7 K and to reproduce the density and thermal expansivity of liquids over a range of temperatures “centered” on ambient conditions. The relative deviations of the experimental data, listed in Table 3, from PR78 EOS calculated at same pTx are shown in Figure 6a as a function of pressure p and in Figure 6b as a function of mole fraction x. The deviations systematically increase when pressure decreases, approaching bubble points, as shown in Figure 6a, plausibly because of the high uncertainty associated with density determination at liquid saturation line. The color code in Figure 6a is shown in different shades to identify the different CO2 concentration on each isotherm. For example, magenta color is used for T = 410 K with lightest shade for x = 0.376 and darkest shade for x = 0.757. Thus, a systematic error that increase with increasing CO2 concentration can be clearly seen in Figure 6a with noticeable dependency on temperature. This is confirmed in Figure 6b, where the deviations for x = 0, calculated with Refprop at 313 and 410 K from 0.1 to 77 MPa, and those reported by Tanaka et al.3 and Kodama et al.4 at 313 K from 1.7 to 6.4 MPa, are also increasing in the same trend with increasing x with a clear dependency on temperature as well. This temperature dependency is not surprising because the volume shift is calculated as a linear function of temperature centered on ambient, where density is matched at 290 and 315 K as mentioned earlier. The average deviation of the experimental measurements from PR78 EOS calculated as ±1.2% is considered “perhaps” reasonable, considering the known deficiency in cubic equations of state in predicting liquid density and also the largely asymmetric fluids of which this system is made. 3.3. Excess Molar Volumes. The excess molar volumes VE for the mixture {xCO2 + (1-x)C15H32} were calculated at each mixture density ρ listed in Table 3 using the relations:

Figure 6. Relative deviations of experimental density ρexptl from predictions of PR78 EOS ρPR78 represented in (a) as a function of pressure p and (b) as a function of CO2 mole fraction x for blue closed triangle, this work (313 K); green closed circle, this work (363 K); purple closed diamond, this work (410 K); blue + sign, Tanaka et al.3 (313 K); blue × sign, Kodama et al.4 (313 K); blue open triangle, Refprop (313 K), green open circle, Refprop (363 K); purple open diamond, Refprop (410 K).

V E = Vm − [xV1 + (1 − x)V2]

(8)

xM1 + (1 − x)M 2 ρ

(9)

Vm =

where Vm is the mixture molar volume, V1 and V2 are the pure component molar volumes calculated at the same temperature and pressure of the mixture, M1 and M2 are the molecular mass of CO2 and pentadecane, respectively, and x is the mole fraction of CO2. The molar volumes of CO2 and n-pentadecane were determined from Span and Wagner14 EOS and Lemmon23 EOS respectively. The expanded uncertainty in the excess molar volume of the mixture is calculated as U(VE) = 0.003Vm cm3.mol−1. The range of molar volumes measured for this system is Vm = 96−215 cm3·mol−1 and the expanded uncertainty in excess molar volumes is calculated as U(VE) = 0.3−0.60 cm3·mol−1. To demonstrate the behavior of the excess molar volume for this mixture, the data have been interpolated and plotted at smoothed pressures of 15, 20, 40, 50, 60, and 70 MPa as a function of CO2 mole fraction x, shown in Figure 7. The excess molar volume becomes less negative with increasing pressure at the three isotherms 313, 363, 410 K shown in Figure 7a−c, respectively, except an inflection region, shown in Figure 7a at x < 0.5, where VE becomes more negative with E



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Table 5. Experimentala Bubble Pressure pb for {xCO2 + (1 − x)C15H32} Measured at Temperature T pb/MPa T/K

x = 0.376

x = 0.562

x = 0.757

313.15 363.15 412.15

4.59 6.68 8.59

6.18 10.66 13.78

8.80 17.01 21.73

a

Expanded uncertainties are U(T) = 0.4 K, U(p) = 0.05 MPa, U(x) = 0.004 with a coverage factor k = 2.

Figure 7. Experimental excess molar volumes of the xCO2 + (1 − x)C15H32 at (a) T = 313.15 K; (b) T = 363.15 K; (c) T = 410 K; at pressures − −, 15 MPa; ---, 20 MPa; −◊−, 40 MPa; −□−, 50 MPa; −○−, 60 MPa; −△−, 70 MPa.

increasing pressure for p ≥ 40 MPa. To confirm this behavior, another set of experiments is recommended to be made for x < 0.5 at low temperatures and elevated pressures ≥40; however, the values of VE in this range are all within the expanded uncertainty of U(VE) = 0.3 cm3·mol−1. No other inflection observed for T = 363 and 410 K, as clearly shown in Figure 7b,c, respectively, where all excess molar volumes become less negative with increasing pressure for all pressure range. It should be noted that while CO2 and the mixture are not in the same state (CO2 is supercritical and the mixture is liquid), the values of VE obtained from eqs 8 and 9 do not strictly meet the condition of an excess property from a thermodynamic point of view, as indicated by Bessières et al.11 3.4. Bubble Pressure Measurements. The experimental measurements of bubble pressures are listed in Table 5. These experimental data are in good agreement with the predictions of PR78 EOS, calculated at the same T,x listed in Table 5, as shown in Figure 8a. A comparison with literature data, reported by Tanaka et al.3 (1993), Secuianu et al.29,30 (2007 and 2010), and very recently, Gui et al.31 (2017), is shown in Figure 8a−c. At 313 K, a good agreement with the predictions of PR78 EOS is shown in Figure 8a and also with the experimental data of Tanaka et al.3 and Secuianu et al.30 However, starting from x ≈ 0.77, the predictions of PR78 EOS sharply increase and similarly, the data of Secuianu et al.30 but at a slower rate

Figure 8. Experimental bubble pressures pb as a function of CO2 mole fraction x are represented in (a) at T = 313, 363, and 412 K, (b) at T = 353 K, and (c) as deviations from PR78 EOS for ■, this work (412 K); ▲, this work (363 K); ⧫, this work (313 K); gray diamond, Secuianu et al.30 (313 K); ●, Tanaka et al.3 (313 K); gray square, Secuianu et al.30 (353 K); gray triangle, Secuianu et al.29 (316 K); gray circle, Secuianu et al.30 (333 K); □, Gui et al.31 (353 K); △, Gui et al.31 (363 K); , PR78 EOS (313 K); −.−, PR78 EOS (363 K); − − , PR78 EOS (412 K); ····, PR78 EOS (353 K).

plausibly due to the onset of a second liquid phase in that region. At 363 K, also in Figure 8a, the bubble pressures measured in this work are also in good agreement with the predictions of PR78 EOS, but those reported by Gui et al.31 (2017) systematically deviate with increasing x to about Δp ≈ 4 MPa. The reason for this disagreement is not clear. At 353 K, a similar disagreement is also shown, as in Figure 8b, where the data reported by Gui et al.31 are consistently less than those reported by Secuianu et al.30 up to about Δp ≈ 3 MPa, although Gui et al.31 reported in their paper (Figure 4) that F



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(4) Kodama, D.; Kanakubo, M.; Kokubo, M.; Hashimoto, S.; Nanjo, H.; Kato, M. Density, viscosity, and solubility of carbon dioxide in glymes. Fluid Phase Equilib. 2011, 302, 103−108. (5) Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27, 1197. (6) Peng, D. Y.; Robinson, D. B. A new two constants equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (7) Peng, D. Y., Robinson, D. B. The characterization of the heptanes and heavier fractions for the GPA; Research Report RR-28; Gas Processors Association: Tulsa, OK, 1978. (8) Péneloux, A.; Rauzy, E.; Fréze, R. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilib. 1982, 8, 7−23. (9) Al Motari, M. M.; Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Density and viscosity of diisodecyl phthalate C6H4(COOC10H21)2, with nominal viscosity at T = 298 K, and p = 0.1 MPa of 87 mPa.s, at temperatures from (298.15 to 423.15) K and pressures up to 70 MPa. J. Chem. Eng. Data 2007, 52, 1233−1239. (10) Zuıniga-Moreno, A.; Galicia-Luna, L. A.; Camacho-Camacho, L. E. Compressed liquid densities and excess volumes of CO2 + decane mixtures from (313 to 363) K and pressures up to 25 MPa. J. Chem. Eng. Data 2005, 50, 1030−1037. (11) Bessieres, D.; Saint-Guirons, H.; Daridon, J.-L. Volumetric behavior of decane + carbon dioxide at high pressures. Measurements and calculation. J. Chem. Eng. Data 2001, 46, 1136−1139. (12) Jian, W.; Song, Y.; Zhang, Y.; Nishio, M.; Zhan, Y.; Xing, W.; Shen, Y. Densities and excess volumes of CO2 + decane solution from 12 to 18 MPa and 313.15 to 343.15 K. Energy Procedia 2013, 37, 6831−6838. (13) Kandil, M. E.; Al-Saifi, N. M.; Sultan, A. S. Simulation and measurements of volumetric and phase behavior of carbon dioxide + higher alkanes at high pressure: CO2 + n-decane at temperatures (313−410) K and pressures up to 76 MPa. Int. J. Greenhouse Gas Control 2016, 53, 198−206. (14) Span, R.; Wagner, W. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509− 1596. (15) Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Vibrating wire viscometer with wire diameters of (0.05 and 0.15) mm: results for methylbenzene and two fluids with nominal viscosities at T = 298 K and p = 0.01 MPa of (14 and 232) mPa·s at temperatures between (298 and 373) K and pressures below 40 MPa. J. Chem. Eng. Data 2005, 50, 647−655. (16) Kandil, M. E.; Harris, K. R.; Goodwin, A. R. H.; Hsu, K.; Marsh, K. N. Measurements of the viscosity and density of a reference fluid with nominal viscosity at T = 298 K and p = 0.1 MPa of 29 mPa·s, at temperatures between (273 and 423) K and pressures below 275 MPa. J. Chem. Eng. Data 2006, 51, 2185−2196. (17) Kurihara, K.; Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Measurements of the viscosity of liquid cyclopentane obtained with a vibrating wire viscometer at temperatures between (273 and 353) K and pressures below 45 MPa. J. Chem. Eng. Data 2007, 52, 803−807. (18) Chang, R. F.; Moldover, M. R. High-temperature high-pressure oscillating tube densimeter. Rev. Sci. Instrum. 1996, 67, 251−256. (19) Kandil, M. E.; Harris, K. R.; Goodwin, A. R. H.; Hsu, K.; Marsh, K. N. Measurement of the viscosity and density of a reference fluid, with nominal viscosity at T = 298 K and p = 0.1 MPa of 29 mPa·s at temperatures between (273 and 423) K and pressures below 275 MPa. J. Chem. Eng. Data 2006, 51, 2185−2196. (20) Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Measurement of the viscosity, density, and electrical conductivity of 1-Hexyl-3methylimidazolium Bis(trifluorosulfonyl)imide at temperatures between (288 and 433) K and pressures below 50 MPa. J. Chem. Eng. Data 2007, 52, 2382−2387. (21) Holcomb, C. D.; Outcalt, S. L. A theoretically-based calibration and evaluation procedure for vibrating-tube densimeters. Fluid Phase Equilib. 1998, 150−151, 815−827.

their measured pressures are higher than those of Secuianu et al.30 Even though, these “particular” data measured by Secuianu et al.30 at 353 K, experience the largest deviations from PR78 EOS as clearly shown in Figure 8c. Figure 8c shows the deviations of all experimental pb measured on six different isotherms at 313, 316, 333, 353, 363, and 412 K from the predictions of PR78 EOS, pPR78 (represented by the zero line). The data of Gui et al.31 (2017) are not included in Figure 8c. The experimental data agree with those calculated with PR78 EOS within an average of ±0.5 MPa for x < 0.5, and then increase to about ±0.7 MPa at x ≈ 0.75, then sharply increase to about −5% at x ≈ 0.9. These relatively high deviations, especially at 353 K, shown in Figure 8c, suggest the need for further accurate data of phase equilibria for this system and also for improving the EOS predictions at x > 0.75, perhaps by using a different mixing rule.

4. CONCLUSIONS New experimental liquid density of CO2 and a heavy hydrocarbon (n-pentadecane) is reported at a wide range of pTx. A vibrating U-tube was scanned by a lock-in amplifier to accurately measure the resonance peak in complex form where density was determined with an expanded uncertainty of U(ρ) = 0.003ρ. The Peng and Robinson 1978 EOS gave best predictions with an average deviation of ±1.2% from the experimental data with noticeable improvement from volume translation. The deviations are maximum near bubble pressure and increase in a systematic manner with increasing CO2 mole fraction x. Bubble pressures were found in good agreement with PR78 EOS which agree with literature data only at x < 0.75; then, the predictions of EOS become unreliable at x > 0.75. The bubble pressures reported in this work significantly extend the range of phase equilibria data for this system to 412.15 K, higher than currently available by about 60 K.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mohamed E. Kandil: 0000-0001-8545-5909 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges the partial funding from Research Institute, and the support of Dr. Abdullah Sultan of King Fahd University. The author thanks Dr. Eric Lemmon of National Institute of Standards and Technology for assistance with Refprop and the n-pentadecane reference equation and Dr. Alessandro Speranza of KBC for assistance with Multiflash.

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REFERENCES

(1) Adebayo, A. R.; Kandil, M. E.; Okasha, T. M.; Sanni, M. L. Measurements of electrical resistivity, NMR pore size and distribution, and x-ray CT-scan for performance evaluation of CO2 injection in carbonate rocks: A pilot study. Int. J. Greenhouse Gas Control 2017, 63, 1−11. (2) Project 20K. https://www.bp.com/en_az/caspian/technology-1/ technology/project-20K.html (accessed March 2018). (3) Tanaka, H.; Yamaki, Y.; Kato, M. Solubility of carbon dioxide in pentadecane, hexadecane, and pentadecane + hexadecane. J. Chem. Eng. Data 1993, 38, 386−388. G



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(22) NIST Reference Fluid Thermodynamic and Transport Properties Database, version 9.4; Applied Chemicals and Materials Division, National Institute of Standards and Technology: Boulder, CO, 2017. (23) Lemmon, E. W. Private communication. NIST, Boulder, CO 2017. (24) Dovnar, D. V.; Lebedinskii, Y. A.; Khasanshin, T. S.; Shchemelev, A. B. The thermodynamic properties of n-pentadecane in the liquid state, determined by the results of measurements of sound velocity. High Temp. 2001, 39, 835−839 (Translated from Teplofizika Vysokikh Temperature, 39, 899−903). (25) Daridon, J. L.; Carrier, H.; Lagourette, B. Pressure dependence of the thermophysical properties of n-pentadecane and n-heptadecane. Int. J. Thermophys. 2002, 23, 697−708. (26) Cutler, W. G.; McMickle, R. H.; Webb, W.; Schiessler, R. W. Study of the compressions of several high molecular weight hydrocarbons. J. Chem. Phys. 1958, 29, 727−740. (27) Cibulka, I.; Hnedkovsky. Liquid densities at elevated pressures of n-alkanes from C5 to C16: A critical evaluation of experimental data. J. Chem. Eng. Data 1996, 41, 657−668. (28) Infochem Multiflash, version 6; Infochem KBC Advanced Technologies plc: London, U.K., 2014. (29) Secuianu, C.; Feroiu, V.; Geana, D. Investigation of phase equilibria in the ternary system carbon dioxide + 1-heptanol + npentadecane. Fluid Phase Equilib. 2007, 261, 337−342. (30) Secuianu, C.; Feroiu, V.; Geana, D. Phase behavior for the carbon dioxide + n-pentadecane binary system. J. Chem. Eng. Data 2010, 55, 4255−4259. (31) Gui, X.; Wang, W.; Gao, Q.; Yun, Z.; Fan, M.; Chen, Z. Measurement and correlation of high pressure phase equilibria for CO2 + alkanes and CO2 + crude oil systems. J. Chem. Eng. Data 2017, 62, 3807−3822.

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Measurements and Modeling of Volumetric and Phase Behavior of

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