Isoplethic Equilibrium for the

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

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Experimental High-Pressure Isochoric/Isoplethic Equilibrium for the Systems Propane + n‑Pentane and Propane + Diethyl Ether Matías Menossi,† Pablo E. Hegel,‡ Juan M. Milanesio,† Severine Camy,§ and Marcelo S. Zabaloy*,‡

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†

Instituto de Investigación y Desarrollo en Ingeniería de Procesos y Química Aplicada (IPQA), Facultad de Ciencias Exactas Físicas y Naturales, Universidad Nacional de Córdoba, CONICET, Av. Vélez Sarsfield 1611, Ciudad Universitaria, X5016GCA Córdoba, Argentina ‡ Planta Piloto de Ingeniería Química (PLAPIQUI), Universidad Nacional del Sur (UNS), CONICET, Camino La Carrindanga Km 7 8000 Bahía Blanca, Argentina § INPT, UPS, Laboratoire de Génie Chimique, UMR CNRS 5503, Université de Toulouse, 4, Allée Emile Monso, F-31030 Toulouse, France S Supporting Information *

ABSTRACT: In this work, loci of isochoric (constant global density)− isoplethic (constant global composition) phase equilibria, generally made of heterogeneous and homogeneous segments, were experimentally studied for the binary systems propane (C3) + n-pentane and C3 + diethyl ether. The temperature and pressure ranges of the new binary experimental data are, roughly, from 320 to 470 K and from 1 to 25 MPa, respectively. The binary experiments were performed at varying overall density (ρ) and varying propane mole fraction (XC3). The obtained experimental loci made it possible to determine phase boundaries for the studied mixtures. Experimental results show that, at constant global composition, a decrease in the isochore global mass density implies both an increase in the isochore break-point temperature (bubble temperature) and a decrease in the isochoric pressure−temperature coefficient (slope) of the isochore homogeneous-liquid segment. Besides, at constant global mass density, the break-point temperature decreases with the increase in the light component global mole fraction. The experimental data obtained were correlated using the perturbed-chain statistical associating fluid theory equation of state. The model, at the set values for the model parameters, is capable of reproducing the single-phase pressure versus temperature behavior and the phase transitions. system. This fluid homogeneity should imply an increase in the reaction rate due to the absence of a fluid−fluid interphase and to the higher concentration achieved for one of the reactants (hydrogen) in the (only) fluid phase where the reaction takes place. Piqueras et al.1 showed that hydrogenation of sunflower oil, using platinum as the catalyst and supercritical propane (C3) as the solvent, can be up to 12 times faster than the conventional hydrogenation. The use of a solvent mixture containing a light component might speed up the hydrogenation reaction even in the presence of two fluid phases, due to an improvement in the values of the transport properties. The conventional hydrogenation of PB (presence of two fluid phases) can be accomplished using heterogeneous or homogeneous catalysts.2 When using heterogeneous catalysts, the PB hydrogenation process involves high conversions with minimum chain scission,2 but the process is relatively slow and it needs an

1. INTRODUCTION Linear low-density polyethylene (LLDPE) of polydispersity index close to unity can be obtained by hydrogenating polybutadienes (PBs) of narrow molecular weight distribution. Hydrogenation of unsaturated heavy polymers is conventionally carried out by dissolving the polymer in an organic solvent, such as toluene or cyclohexane, and injecting hydrogen (H2) into the reactor, which results in a reaction pressure significantly greater than the atmospheric pressure. During the reaction course, two fluid phases are present in the reactor because of the low solubility of H2 in the polymercontaining liquid phase. The addition of a second liquid solvent or a solvent mixture at relatively low pressures (up to 5 MPa) does not change the phase scenario, i.e., the unsaturated polymer remains dissolved in the liquid phase and the H2 remains concentrated in the other fluid phase. This implies a hydrogen mass transfer rate limitation due to the presence of the interphase between the liquid and vapor phases inside the reactor. Alternatively, the H2 and the heavy unsaturated compound can be made to coexist in a single homogeneous fluid phase if a supercritical solvent (or solvent mixture) is added to the © XXXX American Chemical Society

Received: March 20, 2019 Accepted: August 13, 2019

A

DOI: 10.1021/acs.jced.9b00249 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Properties of Pure Solvents21,a

elevated “catalyst/double bond” mole ratio, due to the “poisoning” of the catalyst caused by impurities present in the reaction media.2−7 The use of homogeneous catalysts for hydrogenating PB implies higher reaction times to achieve complete hydrogenation and also the need for higher temperatures and pressures, in comparison to the PB hydrogenation using heterogeneous catalysts. The high asymmetry of the reactive PB + H2 mixture, which is due to the large difference in the molecular size between the H2 and PB molecules, implies a high immiscibility level in the absence of the supercritical solvent or solvent mixture. Thus, to hydrogenate PB in a single fluid phase, the solvent (or solvent mixture) should be able to simultaneously dissolve PB and H2 at the initial stage of the reaction. Besides, the “solvent mixture” on one hand and the subsystem “PB + solvent mixture” on the other should be homogeneous under the conditions of temperature, pressure, and PB concentration at which hydrogenation is to be carried out. In this context, one of the main goals of the present work is to experimentally find conditions of homogeneity for the solvent mixtures propane (C3) + n-pentane (C5) and propane (C3) + diethyl ether (DEE). The chemicals C3, C5, DEE, and dimethyl ether (DME) have been previously identified as possible components of solvent mixtures for PB hydrogenation.2,8 Experimental data have also been obtained in this work for the pure compounds C3, DEE, C5, and DME. This work complements information available in previous works related to the search for convenient conditions to carry out hydrogenation of PB under fluid homogeneity conditions.2,8 To experimentally find, in this work, conditions of homogeneity for the solvent mixtures, the isochoric/isoplethic method was used. This method has been used by several authors to measure dew and bubble points and densities (PVT information) of fluids.9−13 With regard to modeling, the perturbed-chain statistical associating fluid theory (PC-SAFT)24 equation of state (EoS) was used in this work to describe the phase behavior of the studied solvent mixtures.

compound propane (C3) n-pentane (C5) diethyl ether (DEE) dimethyl ether (DME)

M (kg mol−1)

Tc (K)

pc (MPa)

ρc (kg m−3)

Tb (K)

0.0441 0.0722 0.0741

369.83 469.70 466.70

4.25 3.37 3.64

220 231 265

231.11 309.22 307.58

0.0461

400.10

5.37

271

248.31

M: molecular weight, Tc: critical temperature, pc: critical pressure, ρc: critical density, Tb: normal boiling point. a

× 10−3 m. The cell has no sight glasses. The inner volume of the cell is 1.223 × 10−5 m3. The constant-volume cell is housed within an aluminum jacket (5) to assure temperature homogeneity at the outer surface of the stainless steel tube. A PID temperature controller (Novus N480D), connected to a thermocouple (9) and to a couple of heating resistances (3) (250 W each), is used to keep the cell temperature at the desired set value. The controller thermocouple (9) and the heating resistances (3) are located inside the aluminum shell (5). The “cell + shell + heating elements” system is placed within a chamber that has thermally insulated walls. The experimental setup does not include devices for stirring the fluid system inside the cell. The cell pressure is measured with a Bourdon-type manometer (1) (Winter PFP series, maximum pressure: 27.46, instrument uncertainty ±0.41 MPa). The temperature of the fluid system located inside the cell is measured with a Ktype thermocouple (4) independent of the temperature control system and indeed located inside the equilibrium cell too. The experimental temperatures reported in this work are those obtained using this K-type thermocouple (4). The atmospheric pressure is measured using a digital barometer (Paroscientific Inc., model 735). The readings of both pressure sensors are added to obtain the absolute pressure. Both thermocouples [cell (4) and controller (9)] were calibrated using an industrial temperature calibrator (Isotech, model: Fast-Cal ISO 9000, range: 303−623 K, accuracy: 0.3 K). The uncertainty in the recorded temperature values is estimated to be on the order of ±0.5 K. The manometer was calibrated against a hydraulic dead-weight tester (Fluke, model: P3124-3, accuracy 0.008%). To determine the amount of solvent loaded into the cell, a BP 410 Sartorius (0.41 ± 1 × 10−5 kg) electronic precision scale was used for both liquid and gaseous components (i.e., those compounds that are gaseous under ambient conditions). The masses of loaded chemicals obtained from the Sartorius scale were compared to those obtained from weighing the loaded equilibrium cell using a SEW-6000 Moretti (6 ± 1 × 10−4 kg) precision scale. The experimental window of conditions is determined by two physical limits, one is the degradation temperature of the poly(tetrafluoroethylene) tape (about 473 K) used to tighten the cell caps and the second is the bursting pressure of the cell, at which the cell rupture will occur (approximately 25 MPa). 2.3. Methodology. In a typical binary experiment, the constant-volume cell is loaded with a known amount of each compound of the binary mixture. Next, the temperature of the system is set, and after equilibrium is reached, the pressure is measured and recorded, together with the values of temperature, global density, and global composition. The equilibrium

2. EXPERIMENTAL SECTION 2.1. Materials. Transportadora de Gas del Sur (TGS, Bahia Blanca, Buenos Aires, Argentina) provided propane (C3) (7498-6 CAS number), 98% pure, according to gas chromatography (GC) analysis. Diethyl ether (DEE) (60-29-7 CAS number) with a purity level greater than 99% (GC) was provided by Dorwil S.A. (Martinez, Buenos Aires, Argentina), while dimethyl ether (DME) (115-10-6 CAS number), with a purity level greater than 99% (GC), was purchased from Sigma-Aldrich (Sheboygan, Wisconsin). Sintorgan (Villa Martelli, Buenos Aires, Argentina) provided n-pentane (C5) (109-66-0 CAS number, minimum purity 95 wt %, density at 20 °C = 0.627 ± 0.001 g mL−1, maximum water content = 0.01%, residue after evaporation = max 0.001%). Table 1 lists the values of some relevant physical properties for the chemicals used in our experiments. Table 2 summarizes the source and purity information of these chemicals. 2.2. Phase Equilibrium Apparatus. Figure 1 shows a schematic diagram of part of the experimental setup. The heart of the apparatus is an in-house constant-volume cell, which was built on the basis of equipment described in the literature.14 The cell (7) is a stainless steel tube (closed at both ends) with a nominal diameter of 1/2 in. and a wall thickness of 2.5 B



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Table 2. Description of Chemicals Used in This Work chemical name

CAS registry number

source

initial purity

purification method

propane (C3) n-pentane (C5) diethyl ether (DEE) dimethyl ether (DME)

74-98-6 109-66-0 60-29-7 115-10-6

TGS Sintorgan Dorwil S.A. Sigma-Aldrich

0.98a 95 wt %b >0.99a >0.99a

none none none none

final purity

analysis method GC GC GC GC

a

Mole fraction. bMinimum purity.

isochoric (constant overall density) phase equilibrium locus or trajectory. A discontinuous change in slope in this pressure versus temperature trajectory implies a phase transition, i.e., a change in the phase scenario inside the cell. For the sake of conciseness, we often refer to the mentioned trajectories simply as “isochores”. Pure compound isochores are obtained in the same way as binary isochores except that only a single component is loaded into the cell. For the binary mixtures, the total mass of chemicals, loaded into the cell, would be set so that the overall density value would correspond to a system having, at high enough temperature, a liquid nature or a liquid−liquid nature. In the case of the pure compounds, the overall density value always corresponded to a homogeneous liquid nature at high enough temperature. The uncertainties in the mixture composition were estimated through a very conservative propagation of error analysis,15 for all systems studied. According to Diamond,16 an isochore might have more than one two-phase/one-phase transition points, as shown in Figure 2, where, in all cases, the isochore has two of such transition points. These are characterized by both a discontinuity in the isochore slope and the intersection between the isochore and

Figure 1. Experimental setup: (1) manometer, (2) valve for loading/ discharging the cell, (3) heating resistances, (4) thermocouple, (5) aluminum shell, (6) charging line for gaseous solvents, (7) body of the constant-volume cell, (8) thermocouple fitting (removed to load liquid solvents), and (9) thermocouple of the temperature controller.

situation may correspond to an heterogeneous fluid system inside the cell or to a homogeneous fluid. Equilibrium is considered to be reached when the cell pressure remains constant for at least 30 min (indeed, the constancy of the cell temperature is also required). The measurement is repeated at other temperatures in the desired temperature range. The recorded pressure versus temperature experimental points constitute an isoplethic (constant overall composition) and

Figure 2. Schematic phase diagrams showing isochoric [pressure (P) vs temperature (T)] trajectories intersecting the same phase boundary twice, according to Diamond.16 C



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3. MODELING The phase behavior of the studied systems was modeled using the well-known perturbed-chain statistical associating fluid theory24 (PC-SAFT) equation of state (EoS). Commercial software Simulis Thermodynamics (PROSIM SA, Labege, France) was used for most computations involving the PCSAFT model. The PC-SAFT-EoS was used for computing phase envelopes, isolated dew and bubble pressures, isoplethic/ isochoric pressure vs temperature trajectories, and mixture critical points. The pure-compound parameters of the PCSAFT-EoS are the segment diameter σ, the number of segments m, and the dispersive energy ε/k (where k is the Boltzmann constant). For mixtures, the PC-SAFT-EoS provides an interaction parameter, kij, which appears in the combining rule that defines the crossed dispersive energy parameter εij. For computing, using the PC-SAFT-EoS, pure-compound isoplethic−isochoric pressure versus temperature trajectories, the selected task was the liquid−vapor flash computation at set temperature and set global molar volume. The output of this computation is the pressure of the system, the number of phases, and the relative amount of each phase at equilibrium, i.e., the vaporization ratio. The point of an isochore where the P versus T slope has a discontinuous change is, for the systems and conditions studied in this work, the bubble point of the mixture at the set isochore global composition and set global density (which equals the liquid phase density at the bubble point). A set of bubble points obtained from several isochores, all having the same global composition, describe part of an isoplethic phase boundary (phase envelope, see a number of figures later in this article). Bubble points estimated in this work from our experimental isochoric/isoplethic data (Tables 7 and 8) were used here to fit the kij parameter of the PC-SAFT-EoS. The optimization function to be minimized was defined as the sum of squared relative errors in the bubble pressure. The initial estimate was kij = 0 for both binary systems (C3 + C5 and C3 + DEE). Simulis Thermodynamics was used to compute the bubble points, at given temperature, liquid phase composition (i.e., global composition), and model parameter values. Once the optimum value of the binary interaction parameter kij was determined, a flash algorithm was used to compute complete binary isoplethic−isochoric pressure versus temperature trajectories, at constant overall composition and constant overall density. In this case, a flash algorithm at set temperature, pressure, and global composition was the chosen task. This task has the global density as one of its output variables. This flash calculation was an inner loop of a loop whose iteration variable was the pressure, which was changed until the computed overall density matched the experimental overall density.

the two-phase/one-phase boundary (this is the line that separates the gray region from the white region in Figure 2). 2.3.1. Cell Loading Procedure. 2.3.1.1. Loading of Pure Compounds (C3, C5, DME, and DEE). At laboratory ambient conditions (atmospheric pressure and approximately 298 K) C3 and DME are gases and C5 and DEE are liquids (see normal boiling point values in Table 1). 2.3.1.1.1. Loading of Pure Compounds That Are Gaseous at Ambient Conditions (C3 and DME). (a) The cell is first purged, without controlling the temperature, by making the gaseous pure compound (whose isochore is to be measured) flow through the cell. (b) An auxiliary cell (AC, which is equipped with a valve) is loaded, without temperature control, with the gaseous compound by connecting the AC to the gas reservoir (GR) where the compound is stored. (c) Next, the AC is disconnected from the GR, weighed in the Sartorius scale, and connected, at point (6) (Figure 1), to the main cell. (d) The AC is heated, and the AC valve and valve (2) shown in Figure 1 are opened to transfer part of the gaseous compound from the AC to the main cell. (e) When the main cell pressure becomes constant, both valves are closed and the AC is disconnected from the main cell and weighed again (Sartorius scale). (f) The amount of pure gaseous compound loaded is obtained from the weight loss of the auxiliary cell. This loss is compared to the weight increase of the main cell, which is quantified by the Moretti scale. 2.3.1.1.2. Loading of Pure Compounds That Are Liquid at Ambient Conditions (C5 and DEE). (g) For loading a liquid compound (DEE or C5), the thermocouple fitting (8) in Figure 1 is removed and the liquid is fed into the cell, at ambient temperature, using a regular syringe. (h) Next, fitting (8) is put back in its original place, and the cell is gently heated to make possible the vaporization of a very small fraction of the liquid, thus purging the cell. (i) The weight loss of the syringe, which practically equals the amount of liquid compound loaded into the cell, is measured using the Sartorius scale, and it is compared to the weight increase (Moretti scale) of the main cell. 2.3.1.2. Loading Procedure for Binary Systems (C3 + C5 or C3 + DEE). (a) The cell is first purged, without temperature control, with the gaseous compound (C3). (b) Then, a given amount of the liquid compound (DEE or C5) is loaded into the cell using a regular syringe (see item (g) in Section 2.3.1.1.2). (c) The gaseous compound is loaded into the cell without temperature control using the auxiliary cell, as described for the pure gaseous compounds in steps (b) (in Section 2.3.1.1.1) to (f) (in Section 2.3.1.1.1). (d) Again, the weight losses of the syringe and of the auxiliary cell are measured using the Sartorius scale. Such information is again compared to the weight increase (Moretti scale) of the main cell. Once the cell is loaded, the aluminum shell ((5) in Figure 1) is closed around it, and the system is placed within a chamber of thermally insulated walls.

4. RESULTS AND DISCUSSION 4.1. Pure Compounds. To validate the experimental technique, isochores were measured for the pure compounds C3, DEE, C5, and DME, at two-phase and single-phase conditions, and compared with data from the NIST Chemistry Webbook17 and from the literature.18−20 Some general information on isochoric loci for pure compounds is given in Appendix I included in the Supporting Information. D



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Table 3 presents the raw experimental isoplethic/isochoric pressure versus temperature data obtained in this work for the pure compounds C3, C5, DME, and DEE. Figure 3 shows the evolution of pressure as a function of temperature for pure C3 at a constant overall mass density. Table 3. Pressure as a Function of Temperature at Constant Overall Density for the Pure Compounds C3, C5, DME, and DEEa,b C3 ρ = 292 ± 11 kg m−3 T (K) 305.9 319.2 326.8 334.3 349.3 362.1 367.9 383.7 397.4 402.9 434.0

p (MPa)

phase conditionc

± ± ± ± ± ± ± ± ± ± ±

LV LV LV LV LV LV L SC SC SC SC

1.03 1.27 2.26 2.35 3.04 3.92 4.44 5.98 7.35 7.94 12.76

0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.48 0.51 0.67 C5

Figure 3. Pressure vs temperature at constant overall density (ρ) for pure C3. Experimental data: (pink open square) ρ = 292 kg m−3 (this work, Table 3); (black open triangle) ρ = 293.5 kg m−3 (ref 17); (green open triangle) ρ = 290.5 kg m−3 (ref 17); (red dashed line) calculated isochore at ρ = 292 kg m−3 (model: PC-SAFT); (blue line) pure-compound vapor−liquid equilibrium curve for C3.17

Our experimental data (Table 3) are shown by the square markers in Figure 3. They correspond to an overall density of 292 kg m−3. The pure C3 vapor−liquid equilibrium curve obtained from ref 17 is indicated in blue. Part of our data are biphasic (vapor−liquid, lower temperatures) and part are monophasic (liquid, higher temperatures). When going from lower to higher temperatures, the two-phase to one-phase transition would be indicated by a discontinuity in the isochore slope. Such discontinuity is not clearly noticed in Figure 3. This is because of the isochore global density value. In this case, as the experimental overall mass density (292 ± 11 kg m−3) is close, in relative terms, to the critical density of pure C3 (ρc,C3 = 220 kg m−3, Table 1), there is only a slight discontinuity in the slope when entering the liquid homogeneous region. The temperature at which the C3 saturated liquid density is 292 kg m−3 is approximately 367 K (ref 17), which is less than (but close to) the C3 critical temperature (369.83 K, Table 1). Hence, the transition from vapor−liquid heterogeneity to liquid homogeneity should happen at approximately 367 K in Figure 3. The green triangle markers in Figure 3 represent NIST17 data at a density 0.5% lower than ρ = 292 kg m−3, and the black triangles represent analogous data but at a density 0.5% higher than ρ = 292 kg m−3 (the uncertainty in NIST17 densities is 0.5%). The triangles in Figure 3 establish a pressure uncertainty band for the (not shown) NIST17 isochoric data at 292 kg m−3, which have an acceptable level of agreement with our (square markers) data, whose pressure uncertainty is reported in Table 3. The isochore computed using the PC-SAFT-EoS (red lines in Figure 3) also agrees with our data and the ref 17 data. The PC-SAFT parameter values used for the pure compounds are reported in Table 4. The square markers in Figure 4 represent our experimental data for the pure C5 isochore of global density 484 kg m−3.

ρ = 484 ± 12 kg m−3 T (K) 406.9 417.1 428.0 436.6 446.3 453.2

p (MPa)

phase conditionc

± ± ± ± ± ±

LV L L L L L

1.30 3.06 6.07 8.34 10.73 12.73

0.41 0.42 0.41 0.41 0.58 0.57 DME

ρ = 451 ± 12 kg m−3 T (K) 382.8 402.8 411.6 419.5 425.4 429.8 432.6 437.2

p (MPa)

phase conditionc

± ± ± ± ± ± ± ±

L SC SC SC SC SC SC SC

4.58 8.58 10.36 12.15 13.67 14.60 15.21 16.20

0.41 0.44 0.58 0.74 0.85 1.02 1.03 1.04 DEE

ρ = 473 ± 12 kg m−3 T (K) 424.3 434.3 438.9 442.3 445.3 447.8 450.2 453.9 459.4

p (MPa)

phase conditionc

± ± ± ± ± ± ± ± ±

LV LV LV L L L L L L

1.79 2.15 2.39 3.25 3.75 4.20 4.75 5.68 6.89

0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41

Table 4. PC-SAFT Parameters for Pure Compoundsa m σ (Å) ε/κ (K)

a

Experimental data obtained in this work. T = absolute temperature; p = absolute pressure; ρ = overall density. bu(T) = ±0.5 K. u is the standard uncertainty in the measurement. cL = liquid. LV = liquid− vapor. SC = supercritical.

C3

C5

DME24

DEE

1.955 3.635 211.2

2.720 3.753 229.9

2.307 3.253 211.1

2.555 3.683 233.3

a

Parameter values for C3, C5, and DEE taken from the software database (Simulis Thermodynamics, 2015).

E



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Figure 4. Pressure vs temperature at constant overall density (ρ) for pure C5. Experimental data: (pink open square) ρ = 484 kg m−3 (this work, Table 3); (black open triangle) ρ = 486.4 kg m−3 (ref 17); (green open triangle) ρ = 481.6 kg m−3 (ref 17); (red dashed line) calculated isochore at ρ = 484 kg m−3 (model: PC-SAFT); (blue line) pure-compound vapor−liquid equilibrium curve for C5.17

Figure 5. Pressure vs temperature at set density (ρ) for pure DME. Experimental data: (pink open square) constant overall density: ρ = 451 kg m−3 (this work, Table 3); (black open triangle) data of density greater than ρ = 451 kg m−3 (ref 19, Table 11 in this article); (green open triangle) data of density less than ρ = 451 kg m−3 (ref 19, Table 11 in this article); (red dashed line) calculated isochore at ρ = 451 kg m−3 (model: PC-SAFT); (blue line) experimental pure-compound vapor−liquid equilibrium curve for DME.19

This density is significantly higher than the C5 critical density (231 kg m−3, Table 1). Hence, the transition to homogeneity (or break point) has to be a vapor−liquid to homogeneousliquid transition (bubble point). Consistently, our highertemperature data are clearly located in the liquid region (i.e., above the blue vapor−liquid curve). Besides, since 484 ≫ 231 kg m−3, the transition temperature should be significantly lower than the C5 critical temperature (469.70 K, Table 1). This is indeed verified by triangle markers in Figure 4, which correspond to ref 17: this reference states that the transition temperature is about 409.8 K (≪469.70 K) at an overall density of 484 kg m−3. The intersection point between the straight line described by the green triangles of higher temperature in Figure 4 and the curve described by the green triangles of lower temperature in Figure 4 has a temperature close to 409.8 K. The green triangles represent NIST17 data at a density 0.5% less than 484 kg m−3, while the black triangles are also NIST17 data but at a density 0.5% greater than 484 kg m−3. Our six experimental data for C5 (square markers), if considered in isolation, are not enough to identify the break point, due to the relatively large temperature difference between consecutive (squares) points. However, when combining our data with the C5 vapor−liquid equilibrium (blue) curve from ref 17, the break point is easily found by intersecting the line described by all our data lying above the blue curve with the blue curve. Again, the level of agreement between our data (see pressure uncertainty in Table 3), ref 17 data, and the PC-SAFT calculation results (red dashed line) is acceptable for pure C5 (Figure 4). The NIST17 data in Figure 4 show that the pressure of the homogeneous liquid is highly sensitive to small changes in density. This high sensitivity is related to the high density values of the isochores in Figure 4. The overall mass density was in all cases set at a value that implied (at high enough temperature) a liquid nature for the homogeneous isochore segment, as it is the case, e.g., in Figure 4. Figure 5 presents an isochore for DME at 451 kg m−3 global density (squares). The critical density of DME is 271 kg m−3 (Table 1, 271 ≪ 451 kg m−3). Hence, the homogeneous segment of the isochore must be of liquid type as verified from the location (above the experimental vapor−liquid equilibrium curve) of our experimental data (square markers) in Figure 5. Our data are consistent with the experimental data from ref 19

presented in both Figure 5 (triangles) and Table 11. Interpolated “data” from ref 19 are not shown in Figure 5 because of the significant difference in density for the pairs of data points to be used in the interpolation process, e.g., at 423.3 K, the data in ref 19 of density closest to 451 kg m−3 have densities of 402.16 and 470.72 kg m−3 (Table 11). Both values are too far from 451 kg m−3. Consistently, our data in Figure 5 (squares) have pressure values that fall in between the pressure values of the data from ref 19 (triangles). Our DME data (see pressure uncertainty in Table 3) are also quite consistent with the predicted PC-SAFT isochore (red dashed line in Figure 5). In ref 19, a variable-volume equilibrium cell was used. Figure 6 shows our isochoric data for pure DEE at global ρ = 473 kg m−3 (empty squares). It also shows literature data at the

Figure 6. Pressure vs temperature at constant overall density (ρ) for pure DEE. Experimental data: (pink open square) ρ = 473 kg m−3 (this work, Table 3); (black open triangle) ρ = 485.2 kg m−3 (ref 20); (green open triangle) ρ = 441.5 kg m−3 (ref 20); (red dashed line) calculated isochore at ρ = 473 kg m−3 (model: PC-SAFT); (blue line) pure-compound vapor−liquid equilibrium curve for DEE.18

global densities of 441.5 and 485 kg m−3 (ref 20), i.e., at the densities in ref 20 closest to 473 kg m−3. The information in Figure 6 and Table 3 indicates the consistency between our DEE data and those of ref 20. From our data in Figure 6, the DEE break-point temperature at global density ρ = 473 kg m−3 is about 438.9 K. This is similar to the temperature of 441 K, F



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Table 5. Experimental Equilibrium Pressure as a Function of Temperature at Constant Overall Composition (XC3) and Constant Overall Density (ρ) for the C3 + C5 Systema,b ρ = 567 ± 13 kg m−3

ρ = 507 ± 13 kg m−3

XC3 = 0.512 ± 0.0152 T (K) 320.4 326.1 332.0 337.7 341.2

p (MPa) 12.80 16.23 19.72 22.92 24.97

XC3 = 0.849 ± 0.012

phase conditionc

T (K)

L L L L L

319.6 324.9 328.6 331.8 336.2 340.8 345.3 349.2 353.6 357.2

±0.41 ± 0.41 ± 0.41 ± 0.41 ± 0.41

phase conditionc

± ± ± ± ± ± ± ± ± ±

L L L L L L L L L L

5.32 8.62 10.33 12.01 14.28 16.31 18.25 20.38 22.34 24.29

0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41

XC3 = 0.474 ± 0.022 401.6 409.3 419.2 428.9 439.5 449.2

phase conditionc

T (K)

± ± ± ± ± ±

LV LV L L L SC

361.8 368.8 377.4 385.9 392.2 394.8 404.7 410.5 418.3

0.50 0.55 0.60 0.65 0.70 0.75

T (K)

p (MPa)

phase conditionc

370.5 2.90 ± 0.41 380.9 3.40 ± 0.41 388.2 3.81 ± 0.43 397.7 4.52 ± 0.49 406.5 5.64 ± 0.53 416.5 6.76 ± 0.58 428.6 8.28 ± 0.65 437.3 9.61 ± 0.69 447.3 10.72 ± 0.74 456.4 12.26 ± 0.79 ρ = 401 ± 16 kg m−3

LV LV LV LV L SC SC SC SC SC

XC3 = 0.551 ± 0.021

p (MPa) 3.10 3.61 4.73 6.56 8.28 10.01

XC3 = 0.780 ± 0.021

p (MPa)

ρ = 384 ± 12 kg m−3 T (K)

ρ = 311 ± 11 kg m−3

p (MPa)

phase conditionc

± ± ± ± ± ± ± ± ±

LV LV LV LV LV LV L L L

1.88 2.18 2.49 2.79 3.10 3.25 4.01 4.62 5.64

0.41 0.41 0.41 0.42 0.46 0.47 0.52 0.55 0.59

Experimental data obtained in this work. T = absolute temperature; p = absolute pressure; XC3 = overall C3 mole fraction. bu(T) = ± 0.5 K. u is the standard uncertainty in the measurement. cEstimated phase condition. L = liquid. LV = liquid−vapor. SC = supercritical. a

which is obtained from ref 21 by looking for the temperature at which the DEE saturated liquid density equals 473 kg m−3. The homogeneous segment of the ρ = 473 kg m−3 isochore in Figure 6 is of liquid type, as expected from the fact that the global isochore density (ρ = 473 kg m−3) is greater than the DEE critical density (265 kg m−3, Table 1). The PC-SAFTEoS (red lines) slightly overpredicts the vapor−liquid equilibrium temperature (i.e., break-point temperature) at 473 kg m−3 saturated liquid density and gives an isochore pressure versus temperature slope, for the homogeneous-liquid segment, similar in value to the one given by our experimental data. 4.2. Binary Systems. Isochoric/isoplethic pressure versus temperature trajectories were measured at varying overall densities and varying overall compositions for the binary systems C3 + C5 and C3 + DEE. The experimental results are reported in Tables 5 and 6. Again, sudden (discontinuous) changes in the slope of the isochore correspond to phase transitions, which are here regarded as bubble points. At a bubble point, the transition is from a liquid−vapor system to a homogeneous liquid system (indeed, as temperature increases, at constant overall density and constant overall composition). 4.2.1. System C3 + C5. Figures 7 and 8 show, for the binary system C3 + C5, our experimental isoplethic/isochoric pressure vs temperature trajectories for five different combinations of global density and global composition. The corresponding experimental data for the system C3 + C5 are reported in Table 5. In Figure 7, for each of the three experimental isochores, there are two distinguishable segments: a biphasic low-

temperature segment, where the isochore follows a slightly curved trajectory, and a high-temperature quasi-linear segment, where there is a single phase, i.e., a liquid phase, inside the cell. For a given isochore, the point at which the P versus T slope changes suddenly is a bubble point at the given global composition for the corresponding binary system. The isochore global density is also the saturated liquid density at such a bubble point. The bubble points estimated from Figure 7 for the C3 + C5 binary system are reported in Table 7. Such bubble points were used to estimate the PC-SAFT-EoS interaction parameter kC3,C5 as previously explained, being the resulting optimum value kC3,C5 = 0. Figure 7 also shows the phase envelopes (thin solid lines), of the same global composition as the experimental data, calculated with the PC-SAFT-EoS. Their cricondentherms (temperature of the phase envelope point of maximum temperature) increase with the decrease in the light component (C3) global concentration, as expected. The computed isoplethic/isochoric homogeneous-liquid-mixture segments (dashed lines) agree well with the experimental data except for the [ρ = 401 kg m−3, XC3 = 0.551] case at higher pressure (black dashed line and black circle markers), where we see that PC-SAFT overpredicts the isochoric pressure−temperature coefficient (or isochore slope). Notice that in Figure 7 the pure-compound vapor−liquid equilibrium curves are also shown. We computed, using the algorithms of ref 22 for kC3,C5 = 0, the C3 + C5 mixture critical pressure, critical temperature, and critical mass density, in particular, at the compositions in Figure 7. The results are shown in Table 9. G



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Table 6. Experimental Equilibrium Pressure as a Function of Temperature at Constant Overall Composition (XC3) and Constant Overall Density (ρ) for the C3 + DEE Systema,b

T (K) 341.7 355.4 362.8 370.3 379.4 387.9 397.1 407.7 419.2

T (K) 337.2 346.1 351.8 359.2 369.5 379.4 391.1 401.1 411.4

XC3 = 0.651 ± 0.016

XC3 = 0.655 ± 0.019

XC3 = 0.651 ± 0.024

ρ = 474 ± 12 kg m−3

ρ = 401 ± 12 kg m−3

ρ = 311 ± 11 kg m−3

p (MPa)

phase conditionc

T (K)

± ± ± ± ± ± ± ± ±

LV LV LV L L L L L L

367.3 379.7 386.4 394.9 401.9 405.6 412.0 422.6 429.6 437.5 447.6 455.0

p (MPa)

phase conditionc

XC3 = 0.748 ± 0.014

2.49 ± 0.41 3.10 ± 0.41 3.51 ± 0.43 4.01 ± 0.47 5.03 ± 0.51 5.64 ± 0.53 6.76 ± 0.56 8.79 ± 0.62 10.21 ± 0.65 11.74 ± 0.69 13.67 ± 0.75 15.20 ± 0.78 XC3 = 0.743 ± 0.017

ρ = 474 ± 12 kg m−3

ρ = 401 ± 12 kg m−3

1.17 1.57 2.08 3.91 6.66 9.30 12.25 15.71 19.36

0.41 0.41 0.41 0.41 0.41 0.43 0.48 0.54 0.60

p (MPa)

phase conditionc

T (K)

± ± ± ± ± ± ± ± ±

LV LV LV L L L L L SC

346.6 359.2 372.0 382.7 390.1 401.1 410.7 419.7 430.4 437.5 452.4

1.47 1.78 2.08 4.11 7.47 10.83 14.59 17.84 21.60

0.41 0.41 0.41 0.41 0.41 0.41 0.45 0.50 0.56

LV LV LV LV L L L SC SC SC SC SC

T (K) 392.6 400.1 409.2 418.5 429.1 438.5 449.0 458.5 467.4 470.0

± ± ± ± ± ± ± ± ± ±

LV LV LV L SC SC SC SC SC SC

3.71 4.11 4.62 5.13 6.25 7.27 8.39 9.50 10.62 10.93

0.46 0.50 0.55 0.59 0.65 0.70 0.75 0.80 0.85 0.86

XC3 = 0.742 ± 0.024

phase conditionc

T (K)

± ± ± ± ± ± ± ± ± ± ±

LV LV LV L L L SC SC SC SC SC

372.4 377.7 393.2 399.9 407.5 417.7 429.1 437.8 447.3 459.0 466.1

0.41 0.41 0.41 0.41 0.45 0.50 0.55 0.60 0.66 0.69 0.77

phase conditionc

ρ = 311 ± 11 kg m−3

p (MPa) 1.78 2.49 3.10 4.11 5.34 7.67 9.71 11.64 13.77 15.30 18.65

p (MPa)

p (MPa)

phase conditionc

± ± ± ± ± ± ± ± ± ± ±

LV LV LV LV L SC SC SC SC SC SC

2.79 3.10 4.01 4.42 5.13 6.25 7.57 8.59 9.71 11.22 12.15

0.41 0.41 0.46 0.50 0.54 0.59 0.65 0.69 0.74 0.80 0.84

Experimental data obtained in this work. T = absolute temperature; p = absolute pressure; XC3 = overall C3 mole fraction. bu(T) = ± 0.5 K. u is the standard uncertainty in the measurement. cEstimated phase condition. L = liquid. LV = liquid−vapor. SC = supercritical. a

Figure 8. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + C5. Experimental data (this work, Table 5): (gray open circle) ρ = 567 kg m−3, XC3 = 0.512; (purple open triangle) ρ = 507 kg m−3, XC3 = 0.849. Computed isochoric/isoplethic loci (model: PC-SAFT, kC3,C5 = 0): (gray dashed line) ρ = 567 kg m−3, XC3 = 0.512; (purple dashed line) ρ = 507 kg m−3, XC3 = 0.849. Computed phase envelopes (model: PC-SAFT, kC3,C5 = 0): (gray line) XC3 = 0.512 (only bubble points are shown in this case); (purple line) XC3 = 0.849. Pure compound vapor−liquid equilibrium curves: (red dot-dashed line) C3;17 (blue dot-dashed line) C5.17 XC3: C3 mole fraction.

Figure 7. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + C5. Experimental data (this work, Table 5): (pink open square) ρ = 311 kg m−3, XC3 = 0.780; (black open circle) ρ = 401 kg m−3, XC3 = 0.551; (green open triangle) ρ = 384 kg m−3, XC3 = 0.474. Computed isochoric/isoplethic loci (model: PC-SAFT, kC3,C5 = 0): (pink dashed line) ρ = 311 kg m−3, XC3 = 0.780; (black dashed line) ρ = 401 kg m−3, XC3 = 0.551; (green dashed line) ρ = 384 kg m−3, XC3 = 0.474. Computed phase envelopes (model: PC-SAFT, kC3,C5 = 0): (pink line) XC3 = 0.780; (black line) XC3 = 0.551; (green line) XC3 = 0.474. Pure compound vapor−liquid equilibrium curves: (red dot-dashed line) C3;17 (blue dot-dashed line) C5;17 XC3: C3 mole fraction.

As it can be seen, the isochore overall mass density in Figures 7 and 8 is, in all cases, higher than the corresponding H



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Table 7. Bubble Pointsa for the C3 + C5 Binary Mixtureb,c XC3 = 0.780 ± 0.021

XC3 = 0.474 ± 0.022

XC3 = 0.551 ± 0.021

ρ = 311 ± 11 kg m−3

ρ = 384 ± 12 kg m−3

ρ = 401 ± 16 kg m−3

T (K)

p (MPa)

T (K)

p (MPa)

T (K)

p (MPa)

397.7

4.52 ± 0.49

409.3

3.61 ± 0.55

394.8

3.25 ± 0.47

Figure 9 presents a test of the experimental setup for binary systems. It shows three isochoric/isoplethic loci for the C3 +

a

Estimated from the isoplethic/isochoric experimental data of Table 5 plotted in Figure 7. bT = absolute temperature; p = absolute pressure; XC3 = overall C3 mole fraction; ρ = overall density (i.e., saturated liquid density). cu(T) = ±0.5 K. u is the standard uncertainty in the measurement.

Table 8. Bubble Pointsa for the C3 + DEE Binary Mixtureb,c XC3 = 0.651 ± 0.016

XC3 = 0.655 ± 0.019

XC3 = 0.651 ± 0.024

ρ = 474 ± 12 kg m−3

ρ = 401 ± 12 kg m−3

ρ = 311 ± 11 kg m−3

T (K)

T (K)

T (K)

p (MPa)

p (MPa)

p (MPa)

362.8 2.08 ± 0.41 XC3 = 0.748 ± 0.014

394.9 4.01 ± 0.47 XC3 = 0.743 ± 0.017

409.2 4.62 ± 0.55 XC3 = 0.742 ± 0.024

ρ = 474 ± 12 kg m−3

ρ = 401 ± 12 kg m−3

ρ = 311 ± 11 kg m−3

T (K)

p (MPa)

T (K)

p (MPa)

T (K)

p (MPa)

351.8

2.08 ± 0.41

372.0

3.10 ± 0.41

399.9

4.42 ± 0.50

Figure 9. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + C5. Experimental data: (purple open square) ρ = 401 kg m−3, XC3 = 0.551 (this work, Table 5); (pink open circle) ρ = 400 kg m−3, XC3 = 0.55 (Table 10, interpolated data from ref 23); (green open triangle) ρ = 385 kg m−3, XC3 = 0.55 (Table 10, interpolated data from ref 23). Pure compound vapor−liquid equilibrium curves: (red dot-dashed line) C3;17 (blue dot-dashed line) C5.17 XC3: C3 mole fraction.

a

Estimated from the isoplethic/isochoric experimental data of Table 6 plotted in Figures 10−12. bT = absolute temperature; p = absolute pressure; XC3 = overall C3 mole fraction; ρ = overall density (i.e., saturated liquid density). cu(T) = ±0.5 K. u is the standard uncertainty in the measurement.

C5 system at XC3 = 0.55 global composition. Figure 9 also presents the pure C3 and pure C5 vapor−liquid equilibrium curves. The circles (ρ = 400 kg m−3) and the triangles (ρ = 385 kg m−3) represent the data presented in Table 10, which were Table 10. Isochoric/Isoplethic Data for the C3 + C5 System Obtained by Interpolating Raw Experimental Data from Ref 23: Equilibrium Pressure as a Function of Temperature at Constant Overall C3 Mole Fraction (XC3) and Constant Overall Density (ρ)a

computed C3 + C5 mixture critical mass density (Table 9). This implies a liquid nature for the isochore homogeneous segment and in principle a P vs. T slope of the homogeneous segment greater than the slope of the isochore vapor−liquid segment. These implications are verified in Figure 7. Figure 8 shows two experimental data series at global densities higher than those in Figure 7. The phase condition of the experimental data in Figure 8 is “homogeneous liquid”. Within the temperature range of Figure 8, the two calculated phase envelopes (thin solid lines) are located in the relatively low-pressure range. The computed critical temperatures at XC3 = 0.512 and XC3 = 0.849 (Table 9) are greater than the maximum temperature in Figure 8. Clearly, the isochore global densities in Figure 8 are sufficiently high to imply a transition to the homogeneous liquid at temperatures much lower that the transition temperatures in Figure 7. In Figure 8, the PCSAFT EoS properly captures the trends for the pressure of the homogeneous binary liquid as a function of temperature, density, and composition.

ρ = 400 kg m−3

ρ = 385 kg m−3

XC3 = 0.55

XC3 = 0.55

T (K)

p (MPa)

T (K)

p (MPa)

327.4 344.1 360.7 377.4 394.1 410.8

1.03 1.45 1.97 2.55 3.24 5.62

327.4 344.1 360.7 377.4 394.1 408.2 416.5

1.03 1.45 1.93 2.45 3.13 4.44 5.45

a T = absolute temperature; p = absolute pressure; XC3 = overall C3 mole fraction.

Table 9. Computeda Critical Pressures (pc), Critical Temperatures (Tc), and Critical Densities (ρc) at Set Composition (XC3) for the Binary Systems C3 + C5 (kC3,C5 = 0) and C3 + DEE (kC3,DEE = 0)b C3 + C5

C3 + DEE

XC3

Tc (K)

pc (MPa)

ρc (kg m−3)

XC3

Tc (K)

pc (MPa)

ρc (kg m−3)

0.512 0.849 0.780 0.474 0.551

439.5 400.3 409.8 443.3 436.0

4.85 5.00 5.04 4.78 4.90

228.0 222.7 202.8 263.6 221.0

0.65 0.75

419.7 408.8

5.08 5.06

242.4 236.4

a

Model: PC-SAFT-EoS. Pure compound parameters in Table 4. bXC3 = overall C3 mole fraction. I



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Figure 10 shows three isochores for the system C3 + DEE of practically equal global composition (XC3 ≅ 0.65; this unique

obtained by interpolating experimental data from Sage and Lacey.23 The squares represent our experimental data at ρ = 401 kg m−3. In general, the pressure values of circles and triangles do not differ much, i.e., at a given temperature, the pressure at ρ = 400 kg m−3 (circles) is close to the pressure at ρ = 385 kg m−3 (triangles) for the data of Table 10 (see Figure 9). Besides, as it can be observed in Figure 9, our data (squares, uncertainty in Table 5) are in good agreement with the data for ρ = 400 kg m−3 of Table 10. Uncertainties Table 11. Density as a Function of Temperature and Pressure for Pure DMEa T (K)

p (MPa)

ρ (kg m−3)

403.3 403.3 413.3 413.3 418.3 418.3 423.3 423.3 428.3 428.3 433.3 433.3 438.3 438.3

5.02 10.00 9.99 15.01 10.00 14.99 9.99 15.00 9.99 15.01 14.99 20.00 14.98 19.99

137.43 476.07 442.27 493.84 423.38 482.36 402.16 470.72 379.30 458.33 445.7 486.18 432.73 476.53

a

Figure 10. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + DEE. Experimental data (this work, Table 6): (purple open square) ρ = 474 kg m−3, XC3 = 0.651; (purple open triangle) ρ = 401 kg m−3, XC3 = 0.655; (purple open circle) ρ = 311 kg m−3, XC3 = 0.651. Computed isochoric/isoplethic loci (model: PC-SAFT, kC3,DEE = 0): (purple dashed line) ρ = 474 kg m−3, XC3 = 0.651; (purple dot-dashed line) ρ = 401 kg m−3, XC3 = 0.655; (purple dotted line) ρ = 311 kg m−3, XC3 = 0.651. Computed phase envelope (model: PC-SAFT, kC3,DEE = 0): (purple line) XC3 = 0.65. Pure compound vapor−liquid equilibrium curves: (red dot-dashed line) C3;17 (blue dot-dashed line) DEE.18 XC3: C3 mole fraction.

reported for the overall density of our experimental data were estimated through a conservative propagation of error analysis, i.e., for the squares in Figure 9, ρ = 401 ± 16 kg m−3 (Table 5). The pressure range for the experimental data of Sage and Lacey23 for the C3 + C5 system is up to about 5 MPa, while the maximum pressure for our data (Table 5) is very close to 25 MPa. The equilibrium cell of Sage and Lacey23 consisted of a Pyrex glass tube filled with mercury up to the desired level, to have control on the total volume available to the fluid sample, i.e., their cell was a variable-volume equilibrium cell. In contrast, our cell has a constant volume. As for the case of ref 23, the binary C3 + C5 experimental data reported by Kay25 and by Vejrosta and Wichterle26 have pressure values less than 5 MPa. 4.2.2. System C3 + DEE. The second binary system studied in this work is C3 + DEE. C3 and DEE differ in polarity. This feature makes the C3 + DEE solvent mixture an interesting medium for the supercritical hydrogenation of PB, as discussed in ref 8, since it would make it possible to dissolve both the reactant (PB) and the product polymer (hydrogenated PB or LLDPE), at less harsh conditions of pressure and temperature. The isochoric/isoplethic experimental information obtained in this work for the system C3 + DEE is presented in Table 6. From the information in Table 6, a number of bubble points were estimated and reported in Table 8. We stress that the isochore global density value associated with a given bubble point in Table 8 is also the saturated liquid density for such a bubble point. From the bubble points in Table 8, the kC3,DEE (PC-SAFT interaction parameter) was obtained, being the found optimum value (also) kC3,DEE = 0.

composition implies a unique calculated phase envelope). It is seen that, at constant global composition, [a] the isochore break-point temperature (bubble temperature) increases with the decrease in the global isochore mass density (Table 8) and [b] the isochoric pressure−temperature coefficient (slope) of the homogeneous-liquid segment decreases with the decrease in the global isochore mass density (Figure 10). Behaviors [a] and [b] coincide with the known behavior of pure compounds at densities greater than the pure-compound critical density. The C3 + DEE critical density predicted by the PC-SAFTEoS at XC3 = 0.65 is ρc = 242.4 kg m−3 (Table 9), which is significantly less than the overall densities in Figure 10. This figure shows a good level of agreement between the model and the experimental data (pressure uncertainty in Table 6). Figures 10 (XC3 ≅ 0.65) and 11 (XC3 ≅ 0.75) differ from each other in the propane content of the mixture, even though they show the pressure versus temperature trajectories at the same mass densities. The behavior in Figure 11 is analogous to the one in Figure 10. Thus, the conclusions reached from Figure 10 are also valid for Figure 11. We emphasize that in the case “C3 + DEE”, two different phase envelopes were calculated, one at XC3 = 0.65 (Figure 10) and the other at XC3 = 0.75 (Figure 11). These global compositions are not exactly the same as the experimental ones but are close enough to them to represent quite well the behavior of the binary mixture in the biphasic region (the bubble pressure break point). The acceptable reproduction by the PC-SAFT model, of the homogeneous-liquid isochore segments, seen in Figures 10 and 11, means that the model reproduces well the volumetric behavior of the mixture within the experimental window of conditions studied in this work, for the C3 + DEE system. Figure 12 shows, at a given global mass density, the effect of changing the propane global mole fraction. Two experimental

Experimental data at supercritical temperatures from ref 19. These data are plotted in Figure 5 (triangle markers). T = absolute temperature; p = absolute pressure; ρ = density.

J



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Table 8). Figure 12 also shows a pure propane isochore (red17) of the same global mass density as the one of the C3 + DEE data (ρ = 401 kg m−3) and a pure DEE isochore (blue20) of global mass density (ρ = 394.8 kg m−3) close to that of the C3 + DEE data (ρ = 401 kg m−3). The break-point temperature for pure propane (red) is about 343 K, and the one for pure DEE (blue) is about 460 K. Just from looking at the behavior of the pure compounds, we would anticipate, for the binary system C3 + DEE, at constant global mass density, the reduction of the break-point temperature with the increase in C3 concentration, which is confirmed by the two C3 + DEE isochores in Figure 12 (reduction from 394.9 to 372.0 K). The homogeneous-liquid isochoric pressure−temperature coefficient (slope) does not have a noticeable change when going from XC3 = 0.655 to 0.743 (Figure 12). Notice in Figure 12 that, at a given temperature, the pressure of the isochoric/isoplethic locus decreases with the decrease in propane concentration. Phase envelopes and isochores computed using the PC-SAFT-EoS are shown together with the experimental data in Figure 12. The level of agreement between the model and the experimental data is acceptable (see pressure uncertainty of the experimental data in Table 6). Figure 13 was made in part from the information in Table 8. It shows, at a given global mass density, the break-point

Figure 11. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + DEE. Experimental data (this work, Table 6): (green open square) ρ = 474 kg m−3, XC3 = 0.748; (green open triangle) ρ = 401 kg m−3, XC3 = 0.743; (green open circle) ρ = 311 kg m−3, XC3 = 0.742. Computed isochoric/isoplethic loci (model: PC-SAFT, kC3,DEE = 0): (green dashed line) ρ = 474 kg m−3, XC3 = 0.748; (green dot-dashed line) ρ = 401 kg m−3, XC3 = 0.743; (green dotted line) ρ = 311 kg m−3, XC3 = 0.742. Computed phase envelope (model: PC-SAFT, kC3,DEE = 0): (green line) XC3 = 0.75. Pure compound vapor−liquid equilibrium curves: (red dot-dashed line) C3;17 (blue dot-dashed line) DEE.18 XC3: C3 mole fraction.

Figure 13. Break-point temperature as a function of isochore global density at varying C3 content for system C3 + DEE: (blue line) pure DEE,1 XC3 = 0.0; (pink open triangle) C3 + DEE, average XC3 = 0.652 (Table 8); (green open square) C3 + DEE, average XC3 = 0.744 (Table 8); (red line) pure C3;17 XC3 = 1.0. The dotted lines were added to facilitate visualization. XC3: C3 mole fraction.

Figure 12. Pressure vs temperature at constant overall composition (XC3) and constant overall density (ρ) for the system C3 + DEE. Experimental data (this work, Table 6): (green open triangle) ρ = 401 kg m−3, XC3 = 0.743; (purple open triangle) ρ = 401 kg m−3, XC3 = 0.655. Computed isochoric/isoplethic loci (model: PC-SAFT, kC3,DEE = 0): (green dot-dashed line) ρ = 401 kg m−3, XC3 = 0.743; (purple dot-dashed line) ρ = 401 kg m−3, XC3 = 0.655. Computed phase envelopes (model: PC-SAFT, kC3,DEE = 0): (green line) XC3 = 0.75; (purple line) XC3 = 0.65. Pure compound vapor−liquid saturation curves: (red dot-dashed line) C3;17 (blue dot-dashed line) DEE;18 (red open triangle) pure C3 isochore17 at ρ = 401 kg m−3; (blue open triangle) pure DEE isochore20 at ρ = 394.8 kg m−3. XC3: C3 mole fraction.

temperature (i.e., bubble temperature) for the system C3 + DEE at global C3 mole fraction values XC3 = 0.0, 0.652, 0.744, and 1.0. Figure 13 also confirms that at a constant global mass density the break-point temperature decreases with the increase in the global C3 mole fraction. Notice that the red curve is the temperature versus saturated liquid density relationship for pure C3. The blue curve is the analogous relationship, but for pure DEE. The green squares provide, at XC3 = 0.744, the mixture saturated liquid density as a function of temperature. The pink triangles do the same, but at XC3 = 0.652. Finally, Figure 13 shows that, at set XC3, the break-point temperature decreases with the increase in the global mass density (Table 8). 4.2.3. System C3 + C5: Comparison with Literature Data. Figure 14 presents a comparison among bubble pressures estimated from our isochoric/isoplethic data and bubble pressures obtained from information available in the literature for the system C3 + C5. The agreement is good.

isochoric/isoplethic data series at a constant global mass density of 401 kg m−3 are displayed. They have different overall compositions of the mixture, i.e., XC3 = 0.655 (violet) and 0.743 (green). As it can be seen, the increase in propane overall concentration at constant mass density shifts the passage to liquid homogeneity toward lower temperatures. More specifically, at 401 kg m−3 and at XC3 = 0.743, the estimated break-point temperature is 372.0 K (green data in Figure 12, Table 8), while at the same global mass density and at XC3 = 0.655, such value is 394.9 K (violet data in Figure 12, K



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Behavior of pure-compound fluid isochoric loci (Appendix I) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Marcelo S. Zabaloy: 0000-0002-8183-9523 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by grants from Consejo Nacional de ́ Investigaciones Cientificas y Técnicas de la República Argentina (CONICET, PIP 11220150100918), Agencia ́ Nacional de Promoción Cientifica y Tecnológica (ANPCyT, PICT-2017-1235), Universidad Nacional del Sur (UNS, PGI 24/M148), and Universidad Nacional de Córdoba (UNC, SECyTUNC: 30720130101115CB). We also wish to thank Guillermo D.B. Mabe (PLAPIQUI/CONICET) and Cristian M. Piqueras (PLAPIQUI/UNS/CONICET) for their valuable input.

Figure 14. Bubble pressure vs liquid phase propane mole fraction (XC3) for the system C3 + C5. Bubble pressures estimated from experimental data of this work (Table 7): (pink solid square) T = 397.7 K; (black solid circle) T = 394.8 K; (green solid triangle) T = 409.3 K. Bubble pressures obtained through interpolation/extrapolation of experimental data from ref 25: (pink open diamond) T = 397.7 K; (black open diamond) T = 394.8 K; (green open diamond) T = 409.3 K.

5. CONCLUSIONS Using a constant-volume equilibrium cell, isochoric/isoplethic pressure versus temperature trajectories were experimentally studied for the binary systems “C3 + C5” and “C3 + DEE”. This experimental information will be important in the frame of the potential hydrogenation of PB under fluid homogeneity conditions. The experimental results will guide the selection of a convenient solvent mixture and convenient temperature and global density conditions to carry out PB hydrogenation in batch mode. The same isochoric/isoplethic method will be used in future works for the determination of homogeneity conditions in ternary and quaternary mixtures obtained by adding the reactant polymer and H2. The experimental results show that the homogeneous-liquid isochoric pressure−temperature coefficient (P vs T slope) decreases with the decrease in the global density at constant overall composition (e.g., Figure 10) and that at constant global mass density the temperature at which the isochore enters into the homogeneous liquid region increases with the decrease in the concentration of the light component (e.g., Figures 12 and 13, where the light component is C3 and the heavy component is DEE). This qualitative behavior can be anticipated from looking at the break-point temperatures of the pure compounds at the set global mass density value (Figures 12 and 13). Besides, for the homogeneous liquid, at a given temperature and global composition, a higher global mass density implies a higher pressure (e.g., Figure 10). Also, at given temperature and given global mass density, under liquidstate conditions, the pressure increases with the increase in the concentration of the light component (e.g., at 430 K in Figure 12, where C3 is the light component). The PC-SAFT EoS with zero interaction parameters was used to compute isoplethic/isochoric loci and also phase envelopes, achieving, in general terms, an acceptable level of agreement with the experimental data.

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REFERENCES

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00249. L



Article

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