Volumetric Properties of Propane, n-Octane, and Their Binary Mixtures

Article pubs.acs.org/IECR

Volumetric Properties of Propane, n‑Octane, and Their Binary Mixtures at High Pressures Juan M. Milanesio,† John. C. Hassler, and Erdogan Kiran* Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061, United States S Supporting Information *

ABSTRACT: Density, isothermal compressibility, isobaric expansivity, thermal pressure coefficient, and excess volumes for binary mixtures of propane + n-octane are reported over a wide range of temperatures (from 320 to 440 K), and pressures (up to 400 bar) for mixture compositions with 0, 20.4, 42.4, 58.9, 79.7, and 100 wt % propane. Densities were determined using a fully computerized variable-volume view-cell system. A motorized pressure generator is used to bring about changes in the position of a movable piston in the cell at controlled and adjustable rates thereby bringing about changes in the internal volume and thus pressure. A long stroke-length linear variable differential transformer is used to continually monitor the position of the piston and thus the cell volume in real-time. Knowing the initial loading of the cell and the cell volume at any moment as pressure is altered permits generation of continuous density profiles along pressure scans in increasing (compression) or decreasing (decompression) direction of pressure at a given temperature. The density isotherms are readily correlated with polynomial equations and are used to generate the derived thermodynamic quantities such as the isothermal compressibility, isobaric expansivity, pressure coefficient, and excess volume. The results are discussed in terms of the effect of temperature, pressure and fluid composition for which there is no prior information in the open literature. In going from n-octane to propane, the data shows that compressibilities and expansivities increase, but the pressure coefficients tend to decrease. As examples, at 200 bar and 400 K, in going from n-octane to propane, values of compressibilities increase from about 2.0 × 10−4 to 1.0 × 10−3 bar−1; isobaric expansivities increase from about 1.0 × 10−3 to 2.5 × 10−3 K−1, whereas thermal pressure coefficients decrease from about 4 to 3 bar/K. The excess volumes become more negative with increasing propane content, and the mixture with about 80 mol % (or 60 wt %) propane showing the largest negative excess volume of about −6.5 cm3/mol.

1. INTRODUCTION Volumetric properties of hydrocarbons and their mixtures at high pressures are of continuing interest because of their broad relevance to various industries ranging from fuels and petrochemicals to lubricants and oils but, in particular, for their potential utility in supercritical fluid science and technology and in processing of polymers. More specifically, knowledge of thermodynamic properties of mixtures that incorporate natural gas components are of importance for their storage, transportation, and processing.1,2 Volumetric properties of mixtures of light components with heavier hydrocarbons such as n-decane and oils are of significance and of recent interest in special lubrication applications pertaining to CO2refrigeration systems.3 A common practice in supercritical fluidbased processes is to modulate the solvent strength or the critical properties of the fluid by working with binary fluid mixtures in which one of the components has a relatively low critical temperature or pressure or significantly differs in its chemical nature and its ability to interact with the material being processed and thus differs in its solvent power. Often for such purposes mixtures of carbon dioxide are considered where CO2 (Tc = 304 K; Pc = 73.8 bar4) functions as either the nonsolvent or the low Tc component in the process fluid mixture. Propane is another fluid which is, like CO2, a gas at ambient conditions and has a comparatively low critical temperature and pressure (Tc = 370 K; Pc = 42.5 bar4) but is in general of greater solvating power for nonpolar substances such as oils, waxes, and polymers, in particular for polyolefins. © 2013 American Chemical Society

Its mixtures with higher alkanes or other hydrocarbons do not change the nonpolar chemical nature of the mixture and as such have been of value in applications that involve polymer formation and modifications in dense fluids at high pressures. In this context, propane has been explored for solubilization and fractionation of polyethylene5−7 or long chain hydrocarbons such as waxes up to 102 C-atoms8,9 and polystyrene,10,11 for solubilizing polyisoprene and ethylene-propylene copolymers,12 for miscibility and processing of polypropylene13−15 and copolymers of ethylene with octene-1,16 for separation of polymer blends such as polyethylene and polystyrene into their components,17 for miscibility of poly(dodecyl methacrylate)18 or polybutadiene,19 for polymerization and foaming of poly(methyl methacrylate-co- ethylene glycol-dimethacrylate),20 for impregnation of modified polyethylene,21 for micellization of block copolymers of styrene with isoprene or butadiene,22−24 or for polymerization of ethylene.25 Unlike propane, literature on the use of n-octane for miscibility and processing of polymers at high pressures is extremely limited. Nonetheless, miscibility of polyolefins in nalkanes is well-known to increase in going from propane to higher alkanes such as butane, pentane, hexane, heptane, or octane.26−30 Received: Revised: Accepted: Published: 6592

March 4, 2013 April 11, 2013 April 19, 2013 April 19, 2013 dx.doi.org/10.1021/ie4007084 | Ind. Eng. Chem. Res. 2013, 52, 6592−6609

Industrial & Engineering Chemistry Research

Article

Figure 1. (a) Schematic diagram of the experimental system. VC = view cell, MPG = motorized pressure generator; LVDT/PPS = linear variable differential transformer/piston position sensor; VVP = variable-volume part of the view cell; MP = movable piston; LS = light source; PS = Photosensor; Itr = Transmitted light intensity; TV = transfer vessel. (b) Photographs of the view cell which can be tilted horizontally for full view of the cell interior across the sapphire windows.

In a recent study, we explored for the first time the miscibility of ethylene−propylene diene monomer (EPDM) elastomers in mixtures of propane and n-octane.31 These solutions display lower critical solution temperature (LCST), and the phase boundary is shifted to lower temperatures in the presence of the light hydrocarbon propane which has significant industrial consequences in terms opening alternative pathways for energy efficient separation processes. During the course of that investigation on the solubility of EPDM, a literature search led to the conclusion that the volumetric properties were lacking even for the mixtures of propane and n-octane, in the absence of polymer. The only prior work on propane + noctane fluid mixtures that could be identified is limited in its scope and reports only on the saturation temperatures and pressures of isopletic mixtures and the critical loci for the binary.32 In the present paper, we now report comprehensive volumetric (density) data for pure propane and n-octane and their binary mixtures with 20.4, 42.4, 58.9, and 79.7 wt % propane over a wide range of temperatures and pressures up to 440 K and 390 bar. The measurements have been conducted using a high-pressure variable-volume view-cell that permits continuous real-time recording of the position of a movable piston using a dedicated and fully computerized long strokelength LVDT (linear variable differential transformer). The piston position is altered with the aid of a pressure generator that has been fully motorized and permits conducting pressure

scans in either the increasing or the decreasing directions of pressure at desired rates. Since the position can be converted to volume and the initial mass loading in the cell is known, the technique permits continues evaluation of the density of the mixtures. Depending upon the rate of pressure change and the data sampling rate employed, thousand of density values are generated which result in essentially continuous density vs pressure plots which are readily correlated with smooth polynomial functions. These ρ(P) functions are then manipulated to obtain other thermodynamic properties such as the isothermal compressibility, isobaric expansivity, thermal pressure coefficient, and excess volumes. The basic methodology has been previously used in determining the volumetric properties of CO2,33 pentane,33 and mixtures of CO2 with ethyl acetate34 and more recently for evaluations of solutions of poly(lactide-co-glycolide) in acetone + CO2 mixtures.35 In addition to providing volumetric data, the technique permits also the precise assessment of the conditions when liquid− vapor regions are entered upon which densities change without a change in pressure with further increase in the internal volume of the cell. Also, as has been demonstrated recently, generation of continuous density and compressibility data provides insights into the consequences of special interactions of components of a fluid mixture with polymers that affect the packing density and free volume in the mixture.35 6593

dx.doi.org/10.1021/ie4007084 | Ind. Eng. Chem. Res. 2013, 52, 6592−6609


Article

Figure 2. Real time recording of experimental data during up-and-down pressure scans for propane at 380 K showing (a) pressure vs time, (b) piston position vs time, and (c) cell volume vs time.

2. EXPERIMENTAL SECTION 2.1. Materials. Propane was obtained from Scott Specialty Gases. It was instrument grade with 99.5 wt % purity, and the tank was supplied with an educator tube. The higher alkane, noctane, was obtained from Sigma Aldrich. It had a purity of 98 wt %. They were used as received. 2.2. Experimental System Description and Operational Procedures. Figure 1 is a schematic diagram of the view-cell and the other components of the experimental system. The high-pressure variable-volume view-cell (VC) incorporates a long stroke-length LVDT for continuous sensing of the position of the movable piston (MP) inside the variable-volume part (VVP) of the cell. A motorized pressure generator (MPG) is used to change the pressure on the back side of the movable piston using ethanol as the pressurizing fluid. Pressure and temperature in the cell are monitored with a Dynisco diaphragm pressure transducer which also incorporates a Jtype thermocouple. Pressure and temperature are measured with an accuracy of 0.6 bar and ±0.5 °C. The maximum internal volume of the cell (when the movable piston is in upper most position) is 23.0 cm3. Two sapphire windows permit visual observations as well as the option to record changes in the transmitted light intensities (Itr) during a given experiment to assess the phase state or demixing conditions. Four cartridge heaters imbedded in the cell body (not shown in the figure) are used to heat the cell. Pressure, temperature, piston position, and transmitted light intensities are recorded in

real-time with a dedicated computer using a data acquisition board (National Instruments) and a customized software that allows recording of the data at any sampling rate desired depending upon the rate of pressure change employed. In a typical experiment n-octane is charged first to the cell. This is followed by charging propane from a preloaded transfer vessel using an HPLC-type liquid pump. The exact amount of propane charged is determined from mass loss of the transfer vessel using a high capacity (6100 g) balance with 0.01 g accuracy (Mettler PM 6100). Total charge was typically about 10 g. After charging the system, the cell is heated to the temperature while mixing the content with a magnetic stirring bar. Once the thermal and mechanical equilibrium are achieved, pressure scans are carried with the aid of the motorized pressure generator. Pressure is changed continuously up to the desired high pressure and then lowered back. The lowest pressures that can be reached are limited by the initial loading of the cell and when the piston reaches its all-the-way out, topmost position. Under a continuous and slow pressure change, the fluid experiences a smooth expansion or compression. The pressure changes being brought about very slowly, the temperature control unit of the system compensates for any thermal changes associated with expansion or compression of the fluid. The experiments are thus conducted under quasi equilibrium state conditions. Figure 2 shows the real-time recording of (a) pressure, (b) piston position, and (c) the internal volume as a function of 6594



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Figure 3. Pressure vs piston position and pressure vs density for propane at 380 K along the compression and decompression paths shown in Figure 2.

Figure 4. Real time recording of experimental data during up-and-down pressure scans for n-octane at 420 K showing (a) pressure vs time, (b) piston position vs time, and (c) cell volume vs time.

time during a pressure increase (compression) and pressure reduction (decompression) cycle for pure propane at 380 K. The internal volume was changed from 22.5 to 18 cm3 over a 1650 s (27.5 min) time-interval by increasing the pressure from 90 to 390 bar and then reducing it back by manipulation of the motorized pressure generator. This particular data set corresponds to about 3300 data points with data being recorded every 0.5 s during the scans. The resulting pressure vs piston position and pressure vs density curves from this experiment are shown in Figure 3. As shown in these figures,

there is a very high degree of reproducibility of the piston position and density along the up and down direction of the pressure scans at the rate of pressure change (0.67 bar/s) that has been employed. The differences in the piston position or density readings in the up and down pressure scans can be rendered even smaller by further reducing the rate of pressure increase or decrease. It should also be noted that, alternatively, one can change the pressure to a new value, hold it there for a while to ensure full equilibration, and then move to a new equilibrium state and 6595



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Figure 5. Pressure vs piston position and pressure vs density for n-octane at 420 K along the compression and decompression paths shown in Figure 4.

Figure 6. Real time recording of experimental data during up-and-down pressure scans for propane−n-octane mixture with 42.4 wt % propane at 400 K showing (a) pressure vs time, (b) piston position vs time, and (c) cell volume vs time.

employing slow pressure changes over long times. Motorization brings convenience to the experiments. Figure 4 shows the real-time recording of pressure, piston position, and cell volume as a function of time during compression and decompression cycles for pure n-octane at 420 K. The internal volume was changed from 15.9 to 17.6 cm3 over a 1945 s (32 min) time-interval by increasing the pressure from 0.4 to 375 bar and then reducing it back. This particular data set corresponds to about 3900 data points with readings

generate the pressure-position and thus pressure−density curves. However, the slow and motorized scanning procedure that is employed traverses quasi equilibrium states leading to a high degree of flexibility in the efficiency of generating data without loss of reliability. It should be further noted that, for these measurements, motorization of the pressure generator is not an absolute requirement, and equally reproducible results can be obtained by manipulating the pressure generator by hand.34 However, operation by hand becomes demanding when 6596



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Figure 7. Pressure vs piston position and pressure vs density for propane−n-octane mixture with 42.4 wt % propane at 400 K along the compression and decompression paths shown in Figure 6.

3. RESULTS AND DISCUSSION 3.1. Propane. 3.1.1. Density. Even though density of propane is documented in the literature and there are extensive

having again been taken every about 0.5 s during the experiment. Here the rate of pressure change was 0.45 bar/s. As shown in Figure 5, there is again remarkable reproducibility in the piston position and density along the up and down directions of the pressure scans. Figure 6 shows the real-time recording of pressure, piston position, and the cell volume as a function of time during the compression and decompression cycles for a binary mixture containing 42.4 wt % propane at 400 K. The internal volume was changed from 22.6 to 17 cm3 over a 2125 s (35 min) timeinterval by increasing the pressure from 25 to 385 bar and then reducing it back at a rate of 0.58 bar/s. This particular data set corresponds to about 4250 data points with readings having again been taken every about 0.5 s during the experiment. Figure 7 shows the pressure vs piston position and density along the compression and decompression paths. Figure 7 highlights a special feature and a unique value of continuous density recordings. It pertains to the assessment of the pressure conditions, at the prevailing temperature, where transition from a homogeneous liquid phase to a two-phase liquid−vapor domain occurs. As pressure is lowered, upon formation of the vapor phase, a marked change in density occurs. With a further increase in the cell volume, density continues to decrease but without a change in pressure. Along the pressure reduction direction, this demarcation pressure corresponds to the bubble point pressure and can be readily identified. From single-point density determinations, precise determination of this pressure would not be easy and it would require extrapolations. In the increasing pressure direction this pressure is not as sharp but occurs basically at the pressure indicated along the pressure decrease directions. Continuous pressure scans does allow assessment of the appearance of the vapor phase even when visual observation may be obscured to assess the formation of vapor. The primary sources of error in the determination of density are linked to the uncertainties on the exact amount of the fluid charged to the cell, and the errors associated with the LVDT reading and its relation to the position of the piston. The balance was accurate to 0.01 g. The nonlinearity of the LVDT sensor was ±0.30%. Based on calibration experiments conducted with CO2 and comparisons with NIST database, as well as comparisons of density data for pure propane and for pure n-octane with the NIST database which will be presented in the following sections, the average error in density determinations is less than 1%.

Figure 8. Variation of density with pressure for propane at different temperatures. Comparisons with the density values from the NIST database3 (shown as dashed curves) at the respective temperatures.

databases such as those available through NIST,36,37 for internal consistency and for further use in the comparisons with mixtures with n-octane explored in the present study, we measured the density of propane at 320, 340, 360, 380, 400, 420, and 440 K over a pressure range from 30 to 390 bar. The results are shown in Figure 8. Also included in the figure are the values from the NIST database (shown as dashed curves). As can be observed, the present density data are in good agreement with the values from the NIST database with the average error increasing slightly with temperature while remaining less than 1%. The increased error at the higher temperatures appears to stem from the effect of temperature on the LVDT sensor, which leads to slightly higher values of the piston position reading (which in turn leads to slightly smaller volumes and higher densities). In these density determinations, the rates of pressure increase and decrease were between 0.192 and 0.645 bar/s. The average piston velocities during pressure increase and decrease stages were between 0.017 and 0.025 mm/s. Densities cover a range from about 0.386 to 0.521 g/cm3. From 320 to 360 K, propane 6597



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Table 1. Density (g/cm3)−Pressure (bar) Correlations for Pure Propane propane

ρ ρ ρ ρ ρ ρ ρ

= = = = = = =

−3.1534 −4.2347 −5.4755 −5.8767 −7.7715 −5.8652 −4.3671

× × × × × × ×

10‑7 10‑7 10‑7 10‑7 10‑7 10‑7 10‑7

P2 P2 P2 P2 P2 P2 P2

+ + + + + + +

3.3047 4.1375 5.1201 5.7228 7.1462 6.5246 5.7592

× × × × × × ×

10‑4 10‑4 10‑4 10‑4 10‑4 10‑4 10‑4

P P P P P P P

+ + + + + + +

4.4093 4.0594 3.6823 3.3443 2.8959 2.7170 2.6244

10‑1 10‑1 10‑1 10‑1 10‑1 10‑1 10‑1

for for for for for for for

320 340 360 380 400 420 440

K K K K K K K

30 bar < P < 372 bar 50 bar < P < 370 bar 85 bar < P < 375 bar 125 bar < P < 390 bar 150 bar < P < 365 bar 195 bar < P < 375 bar 245 bar < P < 370 bar

Figure 10. Variation of isothermal compressibility of propane with pressure at different temperatures.

Figure 9. Variation of density with temperature for propane at different pressures.

is subcritical (Tc = 370 K; Pc = 42.5 bar4) and there is a phase transition from one to two-phases at lower pressures as displayed by the sharp demarcations in the density. At temperatures above Tc, the variation of density with pressure is smooth and there is no phase transition. The density− pressure isotherms in the homogeneous domains were fitted to polynomic equations of the form ρ = a + bP + cP2. These equations are given in Table 1. Figure 9 shows the variation of density with temperature at selected pressures from 100 to 350 bar. At these pressures in the temperature interval evaluated, densities basically decrease linearly with temperature. Density−temperature correlations that were generated from Figure 6 are given in Table 2. 3.1.2. Derived Thermodynamic Properties: Isothermal Compressibility, Isobaric Expansivity, and Isochoric Pressure Coefficients. Using the equations describing the variation of density with pressure and temperature given in Tables 1 and 2, isothermal compressibility kT, isobaric expansivity αP, and isochoric thermal pressure coefficient γρ, for propane have been evaluated using the thermodynamic relationships: kT = −

× × × × × × ×

Figure 11. Variation of isobaric expansivity of propane with temperature at different pressures.

αP =

1 ⎛ ∂Vm ⎞ 1 ⎛ ∂ρ ⎞ ⎜ ⎟ = ⎜ ⎟ Vm ⎝ ∂P ⎠T ρ ⎝ ∂P ⎠T

γρ =

1 ⎛ ∂Vm ⎞ 1 ⎛ ∂ρ ⎞ ⎜ ⎟ =− ⎜ ⎟ ρ ⎝ ∂T ⎠P Vm ⎝ ∂T ⎠P

⎛ ∂P ⎞ αP ⎜ ⎟ = ⎝ ∂T ⎠ ρ kT

Table 2. Density (g/cm3)−Temperature (K) Correlations for Pure Propane propane

ρ ρ ρ ρ ρ ρ

= = = = = =

−1.4649 −1.2810 −1.1551 −9.7852 −9.6455 −8.9412

× × × × × ×

10‑3 10‑3 10‑3 10‑4 10‑4 10‑4

T T T T T T

+ + + + + +

9.4176 8.9485 8.6439 8.1498 8.2026 8.0381

× × × × × ×

10‑1 10‑1 10‑1 10‑1 10‑1 10‑1

for for for for for for 6598

100 150 200 250 300 350

bar bar bar bar bar bar

320 320 320 320 320 320

K K K K K K

< < < < <

Volumetric Properties of Propane, n-Octane, and Their Binary Mixtures

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