Measurements and Modeling of Phase Behavior, Density, and

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

pubs.acs.org/jced

Measurements and Modeling of Phase Behavior, Density, and Viscosity of Oil + Carbon Dioxide: Squalane + CO2 at Temperatures (313 to 363) K and Pressures up to 77 MPa Mohamed E. Kandil*

J. Chem. Eng. Data Downloaded from pubs.acs.org by COLUMBIA UNIV on 12/08/18. For personal use only.

Centre for Integrative Petroleum Research, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia ABSTRACT: New measurements of compressed liquid density, viscosity, and bubble pressures of mixtures of carbon dioxide and squalane are reported for CO2 mole fractions x = (0.199, 0.299, and 0.519) at temperatures (313, 338, and 363) K, and pressures from bubble points up to about 77 MPa. Density was measured using a “bare-bone” vibrating U-tube driven and scanned in the frequency domain with a lock-in amplifier where the resonance peak is acquired in complex form and density is determined with an expanded uncertainty of U(ρ) = 0.003ρ. Viscosity was measured with a custommade capillary viscometer made of a stainless steel 1/8 in. tube with a length of about 3 m and an internal diameter of about 0.4 mm, where the pressure drop is measured while the fluid mixture is swept through at a constant flow rate. Bubble pressures were determined from the discontinuity of p−V plots recorded during a series of isothermal constant composition expansion processes (CCE) in a variable volume pressure cell. The data reported in previous literature were modeled using Tait-like equations for each single composition, but in this work, equations of state and the Expanded Fluid Theory were used to model density and viscosity, respectively, over the whole surface of pTx reported in the literature. For density, Redlich−Kwong−Soave EOS gives best predictions with an average absolute deviation of 1.1%, where the deviations are high near the bubble points but also increase in a systematic manner with increasing CO2 mole fraction. Best predictions for bubble pressures were given by Peng−Robinson EOS. The excess molar volume is also calculated as a function of pressure and temperature. The Expanded Fluid viscosity theory reproduced all experimental measurements in this work and in the literature, with an average absolute deviation of 6.8%. Viscosity reduction effect of CO2 is also estimated and presented as a percentage of pure oil viscosity (η/ηw=0) as a function of CO2 mass fraction w.

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 CO2 in hydrocarbon rock formation for sequestration in geological storages. Injection of CO2 is also used for enhanced oil recovery (EOR) of residual heavy oils in mature oil fields1 which is a subset of unconventional hydrocarbons that comprise more than 50% of the estimated remaining world’s hydrocarbon reserves. Volumetric and viscosity properties play the fundamental role in determining the efficiency of EOR processes and measurements at high pressure help to accurately model and simulate how CO2 mixes with crude oil in hydrocarbon reservoirs. Experimental data at high pressure are becoming critical for such a multibillion dollar industry, especially for offshore oil and gas fields, where no enough data are available in the literature at elevated pressures. Recently, a major oil and gas company announced the Project2 20K to develop, by the end of 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 © XXXX American Chemical Society

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 considered one of the largest oil and gas fields in the world. Squalane (2,6,10,15,19,23-hexamethyltetracosane), with a molar mass of 422.8133 g/mol, is one of the “scarce” pure heavy alkanes that remains in liquid state not only at room temperature but also at a wide range of temperatures and pressures (mp = −38 °C, bp = 176 °C) due to the branched nature of its molecules. Viscosity of mixtures containing CO2 and squalane are also of interest to the refrigeration industry where mineral oils typically having paraffinic components are used as compressor lubricants in industrial refrigeration applications where CO2 is the working fluid, as reported by Marsh and Kandil3 (2002). Received: September 1, 2018 Accepted: November 22, 2018

A

DOI: 10.1021/acs.jced.8b00786 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Experimental Compressed Liquid Density and Viscosity Reported in the Literature at a Temperature Range T, and maximum pressure p, for xCO2 + (1-x)C30H62 First Author 11

Tomida

12

Ciotta Zambrano13 This work

T K

p MPa

x mole fraction

viscosity, density

293−353

20

viscosity, density density viscosity, density and bubble p

303−448 283−393 313−363

170 100 77

0.095, 0.201, 0.280, 0.362, 0.417 0.423, 0.604, 0.788 0.1001 and 0.2012 0.199, 0.299, and 0.519

Data

Density and viscosity data of pure squalane are reported in the literature (more than 26 publications) at different temperatures and pressures, with growing interest to use squalane as a calibrant fluid, first suggested by Sax and Stross4 in 1957, until recently, two sets of reference correlations are reported by Mylona et al.5 (2014) and Schmidt et al.6 (2015) covering a temperature range of T = (273 to 525) K and pressures up to about 200 MPa. The data of CO2 + squalane reported in the literature are scant. To the author’s knowledge, phase equilibria are reported by Liphard and Schneider7 (1975) and Brunner et al.8 (2009), and bubble pressure recently reported by Ferreira et al.9 (2017), while solubility is reported by Sovovfi and Khachaturyan10 (1997). Density and viscosity of compressed liquid phase are reported by Tomida et al.11 (2007) and Ciotta et al.,12 while Zambrano at al.13 (2016) reported density only. The range of measurements reported on density and viscosity by these three references are listed in Table 1. The data reported in this work fill some of the gaps in the literature reported on compressed liquid density and viscosity of this system {xCO2 + (1 − x)C30H60} as shown in Table 1. The method of viscosity measurements used in this work is different from those in the literature, where a capillary viscometer was used here, while Tomida et al.11 used a rolling ball viscometer, and Ciotta et al.12 used a vibrating wire viscometer. All experimental density data reported in this work and by Tomida et al.,11 Ciotta et al.,12 and Zambrano et al.13 are compared with predictions of advanced equations of state, commonly used in process simulators (RKS,14 PR76,15 and PR7816) EOS, calculated with volume translation correction of Peneloux et al.17 Simulated streams often deviate from those observed in actual operations; hence, selecting the right EOS for estimating stream properties is the most critical step toward reliable simulation and design. Excess molar volumes are also calculated for this system at pressures up to 70 MPa, using the same method reported by Zúñiga-Moreno et al.,18 Bessières et al.,19 and Jian et al.20 Viscosity data reported in previous literature were modeled using Tait-like equations for each single composition, but in this work, the Expanded Fluid Theory was used to model the experimental viscosity measurements over the whole surface of pTx reported in the literature.

Correlations Grunberg− Nissan eq Tait-like eq Tait-like eq EF Theory, EOS

Measuring method rolling ball viscometer, glass piezometer vibrating wire, DMA HPM DMA HPM. capillary tube viscometer, U tube + lock-in amplifier and optical high-pressure cell

Table 2. Description of Chemical Samples Chemical Name carbon dioxide squalane

CAS

Source

124−38−9

Linde

111−01−3

S.

Puritya x> 0.9999 x > 0.99

Analysis Method

Additional Purification

GC

none

GC

degassed

Aldrich a

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

The experimental apparatus was described in previous papers,21,22 and only a description of the modification and the procedure is given here. The apparatus, as shown in Figure 1, consists of three variable-volume cells (cell-1, cell-2, cell-3) placed inside an air bath thermostat. The volume of cell-1 is changed with a piston driven mechanically using a servomotor (SM), while the volumes of cell-2 and cell-3 are changed hydraulically with pistons driven by a twin Quizix pump (QP). The bubble points were detected visually via a glass window fitted on the top of cell-1 during expansion and confirmed graphically from a p−V plot. A capillary tube viscometer (CV) and a “bare bone” Anton Paar vibrating U-tube (VTD) are connected in-line between cell-1 and cell-2. A pressure transducer (P2) is fitted at one end of the capillary tube to measure the pressure drop across when the fluid mixture is swept through at a constant flow rate supplied from cell-1 to cell-2 or vice versa. The vibrating U-tube (VTD) is forced to oscillate using a lock-in amplifier to measure resonance frequency with high precision. The procedure was quite simple, where a known mass of squalane was loaded in cell-1 and an initial volume Vi of CO2 was loaded in cell-3 at pressure p3. Valves v2 and v3 were kept open to fill the tubing at the same pressure in cell-3 up to the closed isolation valve v1. Then, by controlling v1, an amount of CO2 was injected into cell-1, while monitoring the pressure drop in cell-3. After closing v1, the pressure in cell-3 is increased again to p3, using the Quizix pump (QP), as prior to opening v1. The final volume Vf of cell-3 is recorded after equilibrium, and the amount of CO2 injected was calculated from the volume change (ΔV = Vi − Vf) at p3, using Span and Wagner23 CO2 EOS. For proper mixing, the fluid mixture was swept back and forth between cell-1 and cell-2, while maintained in the compressed liquid state. Mixing was also repeated after each measurement of pρTx. The standard uncertainty in the mixture composition is calculated as u(x) = 0.002, resulting mainly from a standard uncertainty in volume measurements of u(V) = 0.1 cm3. The thermostat is controllable within ±0.1 K, where the temperature was measured with a 4-wire platinum resistance thermometer, calibrated on ITS-90 to ±0.01 K, but because of a thermal gradient, measured as 0.2 K, inside the air bath, the expanded uncertainty in temperature measurements was

2. MATERIALS AND METHODS Ultra-high-purity carbon dioxide was supplied by LindeSIGAS, Specialty Gases Division (SGD), with a mole fraction purity xCO2 > 0.9999. Research grade squalane was supplied by Sigma-Aldrich, with a mole fraction purity xC30H62 > 0.99. No further purification was made but the sample was degassed at room temperature for 24 h under vacuum. Details are listed in Table 2. B



Article

Figure 1. Sketch of the experimental apparatus: C1, C2, C3 are high pressure variable volume cells placed inside an air bath thermostat; SM, servomotor; QP, twin Quizix pump; P1, P2, P3, pressure transducers; GW, glass window; CV, capillary tube viscometer; VTD, vibrating U-tube densimeter.

estimated as U(T) = 0.4 K, with a covering factor k = 2. The pressure was measured with three high precision Pain Electronics transducers (model 211-40-060-04) fitted on cell1 and cell-3, and at one end of the capillary viscometer calibrated with a Ruska dead weight piston gauge model 2485, traceable to NIST calibration report number 100525J501, and compensated on a temperature range from (297 to 450) K. The expanded uncertainty (k = 2) in pressure measurements was estimated as U(p) = 0.05 MPa, which covers all repeatability hysteresis, and temperature compensation. Density was measured using a “bare bone” vibrating U-tube fitted between cell-1 and cell-2, which is forced to oscillate using a lock-in amplifier, model Stanford Research SR830, to determine the complex resonance frequency. The shape of the resonance peak plotted as a function of frequency gives a clear indication about the fluid stability inside the vibrating U-tube. As indicated elsewhere,21,22 “Instability can arise from different effects such as strong electromagnetic field, mechanical vibration, etc., and amongst these is when the fluid inside the U-tube is not homogeneous (two co-existing 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.” The resonance frequency was measured using a similar method reported for driving a vibrating wire viscometer by Kandil et al.24,25 and Kurihara et al.26 where the signal was fit to Lorentzian function to accurately “pinpoint” the resonance frequency f 0. Density ρ was then calculated from the Chang and Moldover27 expression in eq 1: ρ=

k(p , T )τ 2 − 1 ν(p , T )

ature, pressure, and composition, at a confidence band better than 0.95. This value of the uncertainty in density is comparable to what was reported in similar high-pressure measurements in the Ken Marsh laboratories.28−30 As stated elsewhere,22 “The most important effect on the vibrating Utubes is their sensitivity to temperature and thermal hysteresis. Thermal hystereses don’t depend on the fluid inside the Utube, 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 doesn’t come back to its exact initial value as before. Another hysteresis effect also arises from the brazing filler metal that holds the U-tube to the manifold, which is made of an alloy different from the one that the U-tube is made of.” Fluid viscosity can also affect the vibration of the Utube where the peak signal becomes noticeably wider, and for viscous fluids of about 150 mPa·s, density measurements can increase by about δρ = 0.0005ρ as reported by Al Motari et al.30 Viscosity effect on density measurements, in this work, is considered negligible since the maximum viscosity was measured as 55 mPa·s. Further analysis on sensitivity of vibrating U-tubes is reported by Holcomb and Outcalt.31 Viscosity was measured with a custom-made high-pressure capillary viscometer made of 1/8 in. stainless steel tube with a length of about 3 m and an internal diameter of about 0.4 mm. The pressure drop was measured while the fluid is swept through at a constant flow rate. To provide a constant flow rate through the capillary viscometer, the servomotor SM was set to sweep the fluid from cell-1 to cell-2 at constant speed, while the Quizix pump was backing the piston of cell-2. Viscosity η of a Newtonian fluid flowing at a constant volumetric flow rate Q through a cylindrical tube with an internal radius R and a length L is determined from the Hagen−Poiseuille’s Law32,33 as a function of the pressure drop Δp shown in eq 2:

(1)

where τ is period of oscillation (τ = 1/f 0), and v(p,T) and k(p,T) are volume and stiffness functions (in pressure and temperature) determined from calibration as reported elsewhere.21 The expanded uncertainty in the measurements of period of oscillation is U(τ) = 0.1 μs with a covering factor k = 2, that resulted in an expanded uncertainty of density as U(ρ) = 0.003ρ, covering all uncertainties propagated from temper-

η=

πR4Δp mρ Q − 8LQ 8πL

(2)

where m is Hagenbach kinetic energy correction, and ρ is density. The Hagen−Poiseuille equation is based on the C



Article

assumptions that the flow is laminar, incompressible, and L ≫ R. The influence of the variations in kinetic energy and end effect are assumed negligible by maintaining a laminar flow regime with a Reynolds number Re < 100, while the ratio of length of the tube to its radius is sufficiently high (L/R ≈ 7500). More details on the capillary viscometers corrections can be found elsewhere.34−36 Gravity and flow hysteresis effects were eliminated by averaging pressure drop measured after sweeping the fluid in both directions: upward from cell-1 to cell-2, then downward from cell-2 to cell-1. Measurements were made at different volume flow rates to ensure no dependency on the flow speed, where viscosity measurements remained constant, as shown in Figure 2, at different flow rates Q = (1, 2, 3, and 4) mL/min.

expanded uncertainty of viscosity measurements, including those propagated from T, p, x, was estimated as U(η) = 0.02η, with a covering factor k = 2. The main source of this uncertainty is resulting from the uncertainty of the experimental measurements of the differential pressure Δp. The bubble points were visually detected through the glass window located at the top of cell-1, during constant composition isothermal expansion processes, and confirmed by the intersection of the two lines fitted to the data points at both sides of the discontinuity of the p − V plot recorded during the expansion process as shown in Figure 3.

3. RESULTS AND DISCUSSION 3.1. Density and Viscosity of Pure Squalane. The experimental densities ρ and viscosities η of pure squalane are listed in Table 3, that were compared alongside the experimental data reported by Tomida et al.,11 Ciotta et al.,12 and Schmidt et al.6 with the reference equations reported by Mylona et al.5 for density in Figure 4, viscosity in Figure 5, and by Schmidt et al.6 for viscosity in Figure 6. The formulations of these reference equations for pure squalane are based on the Tait-like expressions for density in eq 3, and viscosity in eq 6: É−1 ÅÄÅ i p + B yzÑÑÑÑ Å zzÑÑ ρ = ρ0 ÅÅÅ1 − C log10jjj ÅÅÇ k 0.1 + B {ÑÑÖ

Figure 2. Consistent viscosity η measurements of pure squalane at different flow rates Q, at different conditions: □, (313 K, 68 MPa); ○, (313 K, 45 MPa); △, (313 K, 23 MPa); ◇, (313 K, 5 MPa); ×, (338 K, 11 MPa); and +, (363 K, 10 MPa).

(3)

2

ρ0 =

∑ ai(T /K)i

(4)

i=0

Since viscosity depends on the fourth power of the internal radius of the tube, as shown in eq 2, it is very important to determine the radius with maximum accuracy, which is not simple. The internal radius R was determined using a “calibration” method, similar to the one reported by Kandil et al.37 for determining the radius of the vibrating wire viscometers. The calibrant fluid used, in this case to adjust R, is n-decane, and the reference viscosity values were obtained from Refprop38 based on the equation of Huber et al.39 The

2

B=

∑ bi(T /K)i i=0

Ä ÉD ij Bη yzÅÅÅÅ p + Eη ÑÑÑÑ η zzÅÅ ÑÑ η = A η expjjjj z j T + Cη zzÅÅÅÅ p + Eη ÑÑÑÑ k {Ç 0 Ö

(5)

(6)

Figure 3. p − V plot measured during isothermal expansion of cell-1, where bubble pressure is located at the intersection of the two lines fitted to the data points at both sides of the discontinuity. D



Article

Table 3. Experimentala Density ρ and Viscosity η of Squalane Measured at Temperatures T and Pressures p p MPa

ρ kg/m 3

η mPa·s

p MPa

ρ kg/m 3

η mP ·a

p MPa

ρ kg/m 3

η mPa·s

5.7 13.5 23.5 45.7 68.0

T = 313.15 K 798.1 804.3 811.4 822.6 832.5

16.52 19.37 23.38 35.26 52.85

7.9 11.0 22.5 45.6 60.5 76.3

T = 338.15 K 783.2 785.2 793.3 807.5 814.6 820.5

7.82 8.05 10.19 14.40 18.07 22.98

10.6 21.5 42.5 63.7

T = 363.15 K 769.9 777.9 791.1 802.4

4.50 5.38 7.21 9.47

a

Expanded uncertainties of measurements (k = 2) are U(T) = 0.4 K, U(p) = 0.05 MPa, U(ρ) = 0.003ρ, U(η) = 0.02η.

Figure 4. Relative deviations of the experimental density of pure squalane ρexptl from the reference equation ρref reported by Mylona et al.5 as a function of full range of (a) temperature T, (b) pressure p, reported by △, this work; ◇, Ciotta et al.;12 ○, Tomida et al.;11 □, Schmidt et al.6

Figure 5. Relative deviations of the experimental viscosity of pure squalane ηexptl from the reference equation ηref reported by Mylona et al.5 as a function of (a) temperature T, (b) pressure p, reported by △, this work; ◇, Ciotta et al.;12 ○, Tomida et al.;11 □, Schmidt et al.6

2

Dη =

∑ di(K/T )i i=0

Schmidt at al.6 were not used in the fit, because it was published after the release of the Mylona et al.5 equations. The deviations in viscosity from the Mylona et al.5 equation are maximum at high temperature, as shown in Figure 5, while all experimental data agree within an average absolute deviation of about 3%. The viscosity deviations from the Schmidt et al.6 equation are less than those from the Mylona et al.5 equation, as shown in Figure 6, where all experimental data agree with an average absolute deviation of only 2%. The Schmidt et al.6 equation is more accurate because their recent experimental data were used in the regression of their reference equation. 3.2. Density and Viscosity of CO2 + Squalane. Compressed liquid densities and viscosity of {xCO2 + (1 − x)C30H62} are listed in Table 4, at T = (313, 338 and 363) K, starting from pressures very close to bubble points up to about 75 MPa. The data listed in Table 4 are correlated using the Tait density eq 3 and the modified Tait-like viscosity eq 6, as suggested by Comuñas et al.42 and Pensado et al.43 and employed previously5,6,12,13 for this system. The coefficients of eq 3 to 8, obtained by regression of the data listed in Table 4,

(7)

2

Eη =

∑ ei(T /K)i i=0

(8)

Density is only compared with the Mylona et al.5 equation, as shown in Figure 4, because the value of the coefficient C reported by Schmidt et al.6 (9.305 × 10−4 in their papersee Table 8, page 145) is probably wrong, where it should be commonly taken as 0.20 for alkanes, as recommended by Dymond and Malhotra,40 Assael et al.,41 and Mylona et al.5 It seems the coefficients bi and C reported by Schmidt et al.6 may be typed in the wrong order. The deviations in density from the equation of Mylona et al.5 are maximum at lower pressures, as shown in Figure 4, where all experimental data, including this work, agree within an average absolute deviation of 0.16%. Some of the data reported by Tomida et al.11 and Ciotta et al.12 were used in the optimization of this reference equation, but the data of E



Article

Figure 7. Relative deviations of the (a) experimental density ρexptl from the calculated density ρcalc with eq 3; (b) experimental viscosity ηexptl from the calculated viscosity ηcalc with eq 6, using the coefficients listed in Table 5 for △, x = 0.199; □, x = 0.299; ◇, x = 0.519.

Figure 6. Relative deviations of the experimental viscosity of pure squalane ηexptl from the reference equation ηref reported by Schmidt et al.6 as a function of (a) temperature T, (b) pressure p, reported by △, this work; ◇, Ciotta et al.;12 ○, Tomida et al.;11 □, Schmidt et al.6

The relative deviations of the experimental density from PR78-EOS and RKS-EOS, calculated with Multiflash44 at the same p, T, x listed in Table 4, are shown in Figure 8 and Figure

for density (a0, a1, a2, b0, b1, b2, C), and for viscosity (Aη, Bη, Cη, d0, d1, d2, e0, e1, e2) are listed in Table 5.

Table 4. Experimentala Densities ρ, Excess Molar Volume VmE, and Viscosity η of Mixtures of {xCO2 + (1 − x)C30H62} Measured at Temperatures T and Pressures p Vm E cm 3/mol

p MPa

ρ kg/m 3

2.79 12.56 23.44 45.24 60.14 74.43

T/K = 313.15 796.7 11.40 804.5 13.39 812.5 16.14 826.3 22.88 834.5 28.70 841.6 35.87

−150.65 −1.68 −0.95 −1.39 −1.73 −1.99

3.10 11.69 21.99 42.87 57.57 69.97

3.90 12.32 23.10 44.51 58.57 73.41

T/K = 313.15 799.1 9.20 805.8 10.50 813.6 12.46 828.1 17.08 836.5 21.56 844.9 26.51

−146.44 −2.98 −1.05 −1.19 −1.56 −2.09

3.32 11.18 21.99 42.69 57.33 71.03

5.30 11.29 21.91 42.90 57.15 71.14

T/K = 313.15 804.5 5.10 810.3 5.59 819.7 6.47 836.1 8.58 846.0 10.52 854.8 12.50

−158.95 −7.11 −2.24 −1.31 −1.47 −1.69

6.44 10.86 21.26 42.14 56.66 70.40

η mPa·s

p MPa

ρ kg/m 3

η mPa·s

x = 0.199 T/K = 338.15 780.2 5.61 787.3 6.41 795.1 7.61 808.7 10.48 817.1 12.79 823.5 15.43 x = 0.299 T/K = 338.15 782.1 4.69 788.3 5.36 796.2 6.16 810.4 8.30 819.2 10.09 826.9 12.17 x = 0.519 T/K = 338.15 787.1 2.96 791.5 3.18 801.0 3.58 817.7 4.78 827.7 5.67 836.4 6.59

Vm E cm 3/mol

p MPa

ρ kg/m 3

−148.80 −12.84 −1.68 −0.70 −0.67 −0.72

2.67 11.09 21.42 42.49 56.73 70.78

T/K = 363.15 763.2 3.20 770.2 3.71 778.2 4.33 792.2 5.75 800.5 6.83 807.9 8.08

−196.21 −24.71 −3.60 0.13 0.56 0.82

−206.92 −23.59 −2.89 −0.83 −0.69 −0.82

3.82 10.84 21.18 42.25 56.39 70.32

T/K = 363.15 766.2 2.86 771.7 3.14 779.2 3.59 793.2 4.80 801.8 5.69 809.6 6.81

−194.68 −40.57 −6.59 −0.40 0.34 0.64

−144.22 −45.77 −5.93 −1.77 −1.23 −1.09

7.28 10.74 21.34 42.18 56.17 70.12

T/K = 363.15 769.5 1.93 772.7 2.06 782.5 2.31 799.3 3.00 809.2 3.43 818.0 4.08

−142.57 −72.38 −12.31 −2.23 −0.92 −0.30

η mPa·s

Vm E cm 3/mol

a

Expanded uncertainties (k = 2) 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, and U(η) = 0.02η. F



Article

Table 5. Coefficients of Density and Viscosity eqs 3 to 8 and Statistical Parameters density coefficients of eqs 3 to 5 coefficients a0/kg·m−3 a1/kg·m−3·K−1 a2/kg·m−3·K−2 b0/MPa b1/MPa·K−1 b2/MPa·K−2 C 102 AAD 102 max dev. 102 std dev.

x = 0.199 990.300 −0.584598 −0.000132 140.7356 −0.285381 0.000213 0.183 0.01 0.02 0.01 viscosity coefficients

coefficients ln(Aη) Bη/K Cη/K d0 d1/K−1 d2/K−2 e0/MPa e1/MPa·K−1 e2/MPa·K−2 102 AAD 102 MAD 102 std dev.

x = 0.199 −3.435177 1074.433 −128.3496 −0.159113 1233.53 279445.02 470.3277 −0.2954861 −0.0000308 0.77 1.66 0.58

x = 0.299 987.599 −0.573954 −0.000123 142.7123 −0.215095 0.000228 0.239 0.01 0.01 0.01 of eq 6 to 8

x = 0.299 −4.095925 1369.494 −93.8731 −0.042690 567.0111 454781.82 552.6402 −0.4060473 −0.0004405 0.79 1.6 0.57

x = 0.519 1016.489 −0.651697 −0.000137 131.9556 −0.262682 0.000217 0.217 0.01 0.02 0.01 x = 0.519 −3.364756 988.628 −112.2804 27.463774 −19395.51 4731259.34 3770.7295 −14.0252294 0.0161123 0.85 2.38 0.74

9 as a function of (a) pressure p, (b) temperature T, and (c) CO2 mole fraction x. For accurate liquid volume prediction, both PR78-EOS and RKS-EOS were calculated with volume translation correction of Peneloux et al.17 To evaluate the performance of these EOS, all experimental density was reported in the literature: Tomida et al.11 and Ciotta et al.12 and recently by Zambrano et al.13 (2016) are included in the comparison. The reported data for pure squalane (x = 0) are also included in the calculations. The average of the absolute deviations (AAD) from PR78-EOS, as shown in Figure 8 is calculated as 1.5%, while from RKS-EOS, shown in Figure 9, is calculated as 1.1%. The deviations of density systematically increase with increasing pressure as can be seen in Figure 8a, and are also high at pressures approaching bubble points, plausibly because of the high uncertainty associated with density determination on liquid saturation line. Also, as shown in Figure 8a, the experimental data of Zambrano et al.13 reported at x = 0.1001 agree well with the other data, but their data at x = 0.2012 do not agree. A clear biased deviation with temperature, of about +1%, in PR78-EOS, as shown in Figure 8b, which is significantly less in RKS-EOS, as shown in Figure 9b, providing that Zambrano et al.13 data at x = 0.2012 are excluded. Another systematic error with increasing CO2 mole fraction is seen clearly in Figure 8c and slightly in Figure 9c. The average of the absolute deviations from RKS-EOS calculated as AAD = 1.1%, can be considered “acceptable” considering the known deficiency in cubic equations of state in predicting liquid density, and also the largely asymmetric fluids this system is made of. Both PR78-EOS and RKS-EOS are widely used in industry and the advantage of these equations is that they take less computing time and only require the critical properties and the acentric factors. To improve the predictions of these EOS, the

Figure 8. Relative deviations of experimental density ρexptl from predictions of PR78-EOS ρPR78 as a function of full range of (a) pressure p; (b) temperature T; and (c) CO2 mole fraction x, including x = 0 for pure squalane, reported by △, this work; ○, Tomida et al.;11 ◇, Ciotta et al.;12 + , Zambrano et al.13 (at x = 0.1001); × , Zambrano et al.13 (at x = 02012).

Peneloux et al.17 volume translation correction has been employed in the calculations of density, as mentioned earlier. The formulations of PR78-EOS are the same as for classical PR76-EOS15 shown in eqs 9 and 10, except the parameter mi(ωi) is calculated with two different treatments, as in eq 11, based on the acentric factors whether ωi ≤ 0.491 or ωi > 0.49. This model removes a defect in the original equation where heavy components with higher acentric factors become more volatile than components with lower acentric factors. p=

a(T ) RT − v−b v(v − b) + b(v − b)

ÄÅ ij R2Tc2, i ÅÅÅÅ ÅÅ1 + mijjj1 − ai = 0.45724 jj pc , i ÅÅÅÅ k Ç RTc , i bi = 0.07780 pc , i G

T Tc , i

É2 yzÑÑÑÑ zzÑÑ zzÑÑ zÑÑ {ÑÖ

(9)

(10)



Article N

a=

N

N

∑ ∑ xixj

aiaj (1 − kij)

i=1 j=1

b=

∑ xibi i=1

(15)

where p is the pressure, T the temperature, R the ideal gas constant, v the molar volume, Tc the critical temperature, pc the critical pressure, ω the acentric factor, xi the mole fraction of component i, and kij the binary interaction parameter between molecules i and j. The volume translation correction proposed by Peneloux et al.17 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 16 N

vL = v −

∑ cixi i=1

(16)

where the volume shift c is calculated from pure components as linear function of T as in eq 17 ci = ci0 + ci1T

the values of ci for pure components CO2 and C30H62 are listed in Table 6, along with the binary interaction parameter and the critical parameters used as the default values in Multiflash.44 These coefficients are chosen in Multiflash44 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 source of Tc and pc of squalane, listed in Table 6, is the DIPPR database, based on the correlations of Ambrose45,46 (1978, 1979); however, various values are reported in the literature, as listed Table 7, which indicate large discrepancies in these fundamental parameters. More details on the critical properties of squalane can be found in the study of Nikitin and Popov.47 3.3. Excess Molar Volume. The excess molar volumes VmE for the mixture {xCO2 + (1 − x)C30H62} were calculated at each mixture density ρ listed in Table 4 using the relations in eqs 18 and 19:

Figure 9. Relative deviations of experimental density ρexptl from predictions of RKS-EOS ρRKS as a function of full range of (a) pressure p; (b) temperature T; and (c) CO2 mole fraction x, including x = 0 for pure squalane, reported by △, this work; ○, Tomida et al.;11 ◇, Ciotta et al.;12 + , Zambrano et al.13 (at x = 0.1001); × , Zambrano et al.13 (at x = 0.2012).

VmE = Vm − [xV1 + (1 − x)V2]

(18)

xM1 + (1 − x)M 2 ρ

(19)

if ωi ≤ 0.49 → mi = 0.37464 + 1.54226ωi − 0.26992ωi2

Vm =

if ωi > 0.49 → mi = 0.379642 + 1.48503ωi − 0.164423ωi2 + 0.016666ωi3

where Vm is the mixture molar volume, V1 and V2 are the pure component molar volumes calculated at the same T and p of the mixture, and M1 and M2 are the molecular mass of CO2 and squalane, respectively. The molar volumes of CO2 were determined from Span and Wagner23 EOS, and for squalane, determined from the Mylona et al.5 reference equation. The range of molar volumes measured for this system is Vm = (265 to 548) cm3.mol−1 with an expanded uncertainty calculated as U(Vm) = 0.003V cm3.mol−1, and for the excess molar volume is calculated as U(VmE) = 0.003VmE with a covering factor k = 2. The VmE data listed in Table 4 have been interpolated and plotted in Figure 10, at smoothed pressures from (10 to 70) MPa, as a function of CO2 mole fraction, at x = (0.199, 0.299, 0.519) measured in this work, and also at x = 0.788 taken from ref 12. The excess molar volume becomes less negative with increasing pressure as shown in Figure 10a,b,c, respectively. An inflection region, where VE moves toward the positive region with increasing p > 20 MPa, is also clearly shown at the three isotherms (313, 338, 363) K, shown in Figure 11a−e at p =

(11)

while the formulations of the RKS-EOS are as follows p=

a(T ) RT + v−b v(v + b)

ÄÅ ij R2Tc2, i ÅÅÅÅ ÅÅ1 + mijjj1 − ai = 0.42748 jj pc , i ÅÅÅÅ k Ç RTc , i bi = 0.08664 pc , i mi = 0.48 + 1.574ωi − 0.176ωi2

T Tc , i

É2 yzÑÑÑÑ zzÑÑ zzÑÑ zÑÑ {ÑÖ

(17)

(12)

(13) (14)

The values of a and b are calculated for N components, using the standard (van der Waals 1-fluid) mixing rule in eq 15 for both PR78-EOS and RKS-EOS. H


9.41185 × 10 0.00164 0.223 1.02875 7.377 0.868 304.13 863 CO2 squalane

Article

Table 7. Variation in Squalane Critical Temperature Tc and Critical Pressure pc in the Literature

a 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 17 c0 and c1 used to calculate PR78-EOS and RKS-EOS shown in Figure 8 and Figure 9, respectively.

0 −2.4635705 × 10−7 −1.0334529 × 10 2.256347 × 10−4 0 −2.08603 × 10−7 0.0768296

3.6312532 × 10 2.951131 × 10−4

−6

c0/ m ·mol kij vc/m .mol

ω Tc/K i

pc/MPa

−5

−1 3

−1 3

Table 6. Critical Parameters and Volume Translation Coefficients Used in the Calculations of EOSa

RKS EOS

3

−1

c1/ m ·mol ·K

−1

3

c0/ m ·mol

−1

−6

PR78 EOS

c1/ m3·mol−1·K−1


source

year

Tc/K

pc/MPa

method

8

2009 2005 2000 1978 1987

822.89 822 795.9 863 851

1.13 0.70 0.59 0.868 0.61

correlation experimental experimental correlation predictive

Bruner et al. Nikitin and Popov47 VonNiederhausern et al.48 Ambrose45,46 Joback and Reid49

Figure 10. Experimental excess molar volumes VmE as function of CO2 mole fraction x, at three isotherms: (a) 313 K, (b) 338 K, (c) 363 K; at pressures: − − , 10 MPa; +, 15 MPa; ×, 20 MPa; ∗, 30 MPa; −◇−, 40 MPa; −□−, 50 MPa; −○−, 60 MPa; −△−, 70 MPa. The data at x = 0.788 were taken from ref 12.

(30, 40, 50, 60, 70) MPa, respectively. These inflection regions indicate the change in the mixture density due to the dramatic increase of CO2 density at high pressures, especially at lower temperatures. However, 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 VmE do not strictly meet the condition of an excess property from a thermodynamic point of view, as indicated by Bessières et al.19 3.4. Viscosity Correlation. The recently developed compositional viscosity model based on the Expanded Fluid Theory (EF) was selected to model this system, while suitable to model asymmetric fluid mixtures containing a dissolved gas such as this system of CO2 + squalane. This correlation relates I



Article

β=

ρs* =

the viscosity of the fluid to its density over a range of p and T and the dilute gas viscosity as a third input. According to the concept of Hildebrand,50 when fluid expands, its fluidity increases due to the greater distance between the molecules, and when the fluid is compressed, fluidity decreases as the molecules become too close together to move in viscous flow. The viscosity η of the fluid (inverse of fluidity) is expressed in the equations as a departure function from the dilute gas viscosity η0 according the relations reported by Motahhari et al.51 in eqs 20 to 23 (20)

η0 = A + BT + CT 2

(21)

1 n ρs*

( ) ρ

| o − 1} o−1 ~

(22)

ρs0 exp( −c3p)

(23)

where c1, c2, c3 are fitting parameters, and A, B, C are the dilute gas viscosity parameters taken from Yaws52 handbook (listed in Table 8), and β is a correlating parameter between viscosity and fluid expansion, ρ is fluid density, ρs* is fluid density in the compressed state, ρs0 is fluid density in the compressed state under vacuum, n is an empirical exponent to improve the predictions near the critical region and is taken as (n = 0.4872), and p is pressure. The mixing rule used is based on mass fraction, as suggested by Motahhari et al.,51 while the mixing rule of dilute gas viscosity is calculated using the Wilke53 method. The experimental viscosity reported for CO2 + squalane, listed in Table 4, and those reported by Tomida et al.11 and Ciotta et al.12 have been regressed to the EF correlation, where new parameters c1, c2, ρs0 were obtained. These new parameters, listed in Table 8, significantly improved the accuracy of the model for this system. The relative deviations of the experimental data from the EF correlation using the parameters listed in Table 8 are shown in Figure 12, with an average absolute deviation of AAD = 6.8% over reported range of p,T,x in the literature, as shown in Figure 12a,b,c, respectively. 3.5. Viscosity Reduction of Heavy Oil. This section demonstrates how CO2 is efficient, as a viscosity reduction agent, in applications related to enhanced oil recovery. Viscosity reduction is more effective at lower temperatures, due to the increased solubility of CO2. Viscosity is plotted on three isotherms (303, 313, and 338) K, as a function of CO2 mole fraction x, at two arbitrary pressures covering the pore pressure in deep and moderate oil reservoirs, as shown in Figure 13(a) at 70 MPa, and (b) at 35 MPa. The normalized viscosities (relative to pure squalane at same corresponding temperatures) calculated as η/η(x=0) were found similar at both pressures of 70 and 35 MPa. The normalized viscosity, shown in Figures 13(c), clearly demonstrates that CO2 becomes more efficient in viscosity reduction in mature oil fields at temperatures up to 338 K (65 °C = 149 °F) where oil viscosity can be reduced to 25% using CO2 mass fraction of w = 0.1 (equivalent to x = 0.519). 3.6. Bubble Pressure Measurements. The experimental measurements of bubble pressures are listed in Table 9, and shown on Figure 14, with most recent literature data reported by Ferreira et al.9 (2017) at two isotherms (313.15 and 363.15) K. PR78-EOS give better predictions for bubble pressures; however, RKS-EOS gave more accurate compressed liquid densities. The predictions of PR78-EOS, calculated at same T, x listed in Table 9, are shown alongside the experimental data, and all are clearly in good agreement as shown in Figure 14. The deviations of all experimental bubble

Figure 11. Change in excess molar volume VmE calculated in this work as a function of CO2 mole fraction x, at temperatures: blue line, 313 K; orange line, 338 K; red line, 363 K; and pressures (a) 20 MPa, (b) 30 MPa, (c) 40 MPa, (d) 50 MPa, and (e) 70 MPa. Data at x = 0.788 were taken from ref 12.

η − η0 = c1(exp(c 2β) − 1)

l o expm o n

Table 8. Parameters of the Diluted Gas Viscosity and the EF eqs 20 to 23 i CO2 squalane

c1 /mPa·s 0.179839

c2 0.201774 0.251716

c3 /kPa−1

ρs0 /kg·m−3

A

B

C

1479.68 889.22

11.811 1.72 × 10−7

0.49838 8.17 × 10−9

−1.09 × 10−4 1.47 × 10−12

−07

1.87 × 10 3.77 × 10−07 J



Article

Figure 12. Relative deviations of the experimental viscosity ηexptl from the EF correlation ηEF using the parameters listed in Table 8, as a function of a full range of (a) temperature T, (b) pressure p, and (c) CO2 mole fraction x, reported by △, this work; ◇, Ciotta et al.;12 ○, Tomida et al.11

Figure 13. (a) Viscosity η at 70 MPa; (b) viscosity η at 35 MPa; smoothed data reported by ◆, Ciotta et al.12 at 303 K; gray ◆ Ciotta et al.12 at 313 K; gray ▲, this work at 313 K; ◇, Ciotta et al.12 at 338 K, △, this work at 338 K. (c) viscosity reduction (η /ηsqualane) as a function of CO2 mass fraction w at: □, 338 K; ■, 313 K; gray ■, 303 K.

pressures pb measured in this work, and those reported by Ferreira et al.9 for a range of CO2 mole fraction x = (0.4738 to 0.8002) at temperatures T = (303.40 to 393.67) K, from the predictions of PR78 EOS (represented by the zero line) are shown in Figure 15. The absolute average of these deviations is 0.2 MPa, over the whole range of CO2 mole fractions x ≈ 0.8. The predictions of bubble pressure using RKS EOS are also shown in Figure 15, and agree well with experimental data in the range x < 0.6, but then sharply deviate to less than −2 MPa at x > 0.7. Same behavior was observed in previous studies21,22 on CO2 + higher alkanes, plausibly due to the onset of a second CO2 liquid phase in the region x > 0.8 at high pressures.

Table 9. Experimentala Bubble Pressure pb for {xCO2 + (1 − x)C30H62} Measured at Temperature T pb/MPa T/K

x = 0.119

x = 0.299

x = 0.519

313.15 338.15 363.15

1.32 1.65 1.92

2.10 2.65 3.14

4.29 5.56 6.78

a

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

Expanded Fluid viscosity theory were used to model density and viscosity on the whole reported surface of pTx. The Redlich−Kwong−Soave equation gives best predictions for density with an average deviation of ±1.1%. The deviations in density are maximum near bubble pressure and increase in a systematic manner with increasing CO2 mole fraction x. The excess molar volume is generally negative but starts to become positive at pressures >30 MPa, due to the dramatic increase of CO2 density. The Peng and Robinson (1978) equation gives better predictions for bubble pressures and agree with

4. CONCLUSIONS New experimental measurements are reported for liquid density, excess molar volume, and viscosity of mixtures of CO2 and squalane, which is used as a viscous model oil and a reference calibrant fluid. The experimental data reported in this work include measurements at low pressures very close to the liquid saturation line. The data in previous literature were modeled with the Tait-like equations for each single composition, but in this work, equations of state and the K



■

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) https://www.bp.com/en_az/caspian/technology-1/technology/ project-20K.html (available online as of September 2018). (3) Marsh, K. N.; Kandil, M. E. Review of thermodynamic properties of refrigerants plus lubricant oils. Fluid Phase Equilib. 2002, 199, 319− 334. (4) Sax, K. J.; Stross, F. H. Squalane: A standard. Anal. Chem. 1957, 29, 1700−1702. (5) Mylona, S. K.; Assael, M. J.; Comuñas, M. J. P.; Paredes, X.; Gaciño, F. M.; Fernández, J.; Bazile, J. P.; Boned, C.; Daridon, J. L.; Galliero, G.; Pauly, J.; Harris, K. R. Reference correlations for the density and viscosity of squalane from 273 to 473 K at pressures to 200 MPa. J. Phys. Chem. Ref. Data 2014, 43, No. 013104, 1−11. . (6) Schmidt, K. A. G.; Pagnutti, D.; Curran, M. D.; Singh, A.; Trusler, J. P. M; Maitland, G. C.; McBride-Wright, M. New experimental data and reference models for the viscosity and density of squalane. J. Chem. Eng. Data 2015, 60, 137−150. (7) Liphard, K. G.; Schneider, G. M. Phase equilibria and critical phenomena in fluid mixtures of carbon dioxide + 2,6,10,15,19,23hexamethyltetracosane up to 423 K and 100 MPa. J. Chem. Thermodyn. 1975, 7, 805−814. (8) Brunner, G.; Saure, C.; Buss, D. Phase Equilibrium of Hydrogen, Carbon Dioxide, Squalene, and Squalane. J. Chem. Eng. Data 2009, 54, 1598−1609. (9) Ferreira, F. A. V.; Barbalho, T. C. S.; Oliveira, H. N. M.; Chiavone-Filho, O. Vapor-liquid equilibrium measurements for carbon dioxide + cyclohexene + squalane at high pressures using a synthetic method. J. Chem. Eng. Data 2017, 62, 1456−1463. (10) Sovovfi, H.; Khachaturyan, J. J. M. Solubility of squalane, dinonyl phthalate and glycerol in supercritical CO2. Fluid Phase Equilib. 1997, 137, 185−191. (11) Tomida, D.; Kumagai, A.; Yokoyama, C. Viscosity measurements and correlation of the squalane + CO2 mixture. Int. J. Thermophys. 2007, 28, 133−145. (12) Ciotta, F.; Maitland, G.; Smietana, M.; Trusler, J. P. M.; Vesovic, V. Viscosity and density of carbon dioxide + 2,6,10,15,19,23hexamethyltetracosane (squalane). J. Chem. Eng. Data 2009, 54, 2436−2443. (13) Zambrano, J.; Gómez-Soto, F. V.; Lozano-Martín, D.; Martín, M. C.; Segovia, J. J. Volumetric behaviour of (carbon dioxide + hydrocarbon) mixtures at high pressures. J. Supercrit. Fluids 2016, 110, 103−109. (14) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27, 1197. (15) Peng, D. Y.; Robinson, D. B. A new two constants equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (16) 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, Okla, 1978. (17) Péneloux, A.; Rauzy, E.; Fréze, R. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilib. 1982, 8, 7−23. (18) Zúñiga-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. (19) Bessières, 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. (20) 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. (21) Kandil, M. E.; Al-Saifi, N. M.; Sultan, A. S. Simulation and measurements of volumetric and phase behavior of carbon dioxide +

Figure 14. Experimental bubble pressures pb as a function of CO2 mole fractions x; ▲, this work at 313 K.15; △, this work at 363.15 K; ◆, Ferreira et al.9 at 313.22 K; ◇, Ferreira et al. at 363.15 K; −−, predictions of PR78-EOS at 313.15 K; − − , prediction of PR78-EOS at 363.15 K.

Figure 15. Deviations of experimental bubble pressures pb from the predictions of PR78-EOS pEOS (represented by the zero line) as a function of CO2 mole fraction x; △, all points measured in this work at x = (313.15, 338.15, 363.15 K); ◇, all points reported by Ferreira et al.9 at x = (303.4 to 393.67) K; −−, predictions of RKS-EOS at 313.15 K; − − , predictions of RKS-EOS at 363.15 K.

experimental data within an average of 0.2 MPa, while the predictions of the Redlich−Kwong−Soave equation sharply deviate to more than −2 MPa at x > 0.7. The Expanded Fluid viscosity theory can reproduce all experimental viscosity measured in this work and the literature within an average absolute deviation of 6.8% over the full pTx range reported. The new methods presented for density measurements using a lock-in amplifier, and to determine the internal radius of capillary viscometers, are accurate and simple to implement.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

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

The author declares no competing financial interest.

■

ACKNOWLEDGMENTS The author wishes to thank Dr Abdullah Sultan of the Department of Petroleum Engineering for the advice on EOR, Professor Luis Galicia-Luna, of Instituto Politecnico Nacional, for kind advice on the design of capillary viscometers, Dr. Alessandro Speranza and Dr. Nuno Pedrosa of KBC for kind support and advice on the advanced versions of EOS. L



Article

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. (22) Kandil, M. E. Measurements and modeling of volumetric and phase behavior of carbon dioxide + higher alkanes: CO2 + npentadecane at temperatures 313 to 410 K and pressures up to 77 MPa. J. Chem. Eng. Data 2018, 63, 1389−1396. (23) 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. (24) 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. (25) 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 (273and 423) K and pressures below 275 MPa. J. Chem. Eng. Data 2006, 51, 2185−2196. (26) 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. (27) Chang, R. F.; Moldover, M. R. High-temperature high-pressure oscillating tube densimeter. Rev. Sci. Instrum. 1996, 67, 251−256. (28) 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. (29) 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. (30) 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. (31) 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. (32) Poiseuille, J. L. M. Recherches Expérimentales Sur Le Mouvement Des Liquides Dans Les Tubes De Très Petits Diamètres; II. Influence De La Longueur Sur La Quantité De Liquide Qui Traverse Les Tubes De Très Petits Diamètres; III. Influence Du Diamètre Sur La Quantité De Liquide Qui Traverse Les Tubes De Très Petits Diamètres. C. R. Acad. Sci. 1840, 11, 1041−1048. (33) Hagenbach, E. Uber die Bestimmung der Zähigkeit einer Flüssigkeit durch den Ausfluss aus Röhren. Ann. Phys. 1860, 185, 385−426. (34) Kao, J. T. F.; Ruska, W.; Kobayashi, R. Theory and Design of an Absolute Viscometer for Low Temperature-High Pressure Applications. Rev. Sci. Instrum. 1968, 39, 824−834. (35) Kestin, J.; Sokolov, M.; Wakeham, W. A. Theory of Capillary Viscometers. Appl. Sci. Res. 1973, 27, 241−264. (36) Pimentel-Rodas, A.; Galicia-Luna, L. A.; Castro-Arellano, J. J. Capillary Viscometer and Vibrating Tube Densimeter for Simultaneous Measurements up to 70 MPa and 423 K. J. Chem. Eng. Data 2016, 61, 45−55. (37) 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 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.

(38) 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. (39) Huber, M. L.; Laesecke, A.; Xiang, H. W. Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and ndecane. Fluid Phase Equilib. 2004, 224, 263−270. (40) Dymond, J. H.; Malhotra, R. Densities of n-alkanes and their mixtures at elevated pressures. Int. J. Thermophys. 1987, 8, 541−555. (41) Assael, M. J.; Dymond, J. H.; Exadaktilou, D. An improved representation for n-alkane liquid densities. Int. J. Thermophys. 1994, 15, 155−164. (42) Comuñas, M. J. P.; Baylaucq, A.; Boned, C.; Fernández, J. High pressure measurement of the viscosity and density of two polyethers and two dialkyl carbonates. Int. J. Thermophys. 2001, 22, 749−768. (43) Pensado, A. S.; Comuñas, M. J. P.; Lugo, L.; Fernández, J. High-Pressure Characterization of Dynamic Viscosity and Derived Properties for Squalane and Two Pentaerythritol Ester Lubricants: Pentaerythritol Tetra-2-ethylhexanoate and Pentaerythritol Tetranonanoate. Ind. Eng. Chem. Res. 2006, 45, 2394−2404. (44) Infochem Multiflash version 6; Infochem KBC Advanced Technologies plc, London, UK, 2014. (45) Ambrose, D. Correlation and Estimation of Vapour-Liquid Critical Properties: I. Critical Temperatures of Organic Compounds; Natl. Phys. Lab. Report Chem. 92; Middlesex, United Kingdom, 1978. (46) Ambrose, D. Correlation and Estimation of Vapour-Liquid Critical Properties. II. Critical Pressures and Critical Volumes of Organic Compounds; Natl. Phys. Lab. Report Chem. 98; Middlesex, United Kingdom, 1979. (47) Nikitin, E. D.; Popov, A. P. Vapor−liquid critical properties of squalane measured by the pulse-heating technique. Fluid Phase Equilib. 2005, 237, 16−20. (48) VonNiederhausern, D. M.; Wilson, G. M.; Giles, N. F. Critical point and vapor pressure measurements at high temperatures by means of a new apparatus with ultralow residence times. J. Chem. Eng. Data 2000, 45, 157−160. (49) Joback, K. G.; Reid, R. C. Estimation of pure component properties from group contributions. Chem. Eng. Commun. 1987, 57, 233−243. (50) Hildebrand, J. H. Viscosity and Diffusivity, A Predictive Treatment; John Wiley and Sons: New York, 1977. (51) Motahhari, H.; Satyro, M. A.; Yarranton, H. W. Predicting the viscosity of asymmetric hydrocarbon mixtures with the expanded fluid viscosity correlation. Ind. Eng. Chem. Res. 2011, 50, 12831−12843. (52) Yaws, C. L. Chemical Properties Handbook: Physical, Thermodynamic, Environmental, Transport, Safety, and Health Related Properties for Organic and Inorganic Chemicals; McGraw-Hill: New York, 1999. (53) Wilke, C. R. A. Viscosity equation for gas mixtures. J. Chem. Phys. 1950, 18, 517−519.

M


Measurements and Modeling of Phase Behavior, Density, and

Recommend Documents