Isobaric Heat Capacity Measurements of Supercritical R1234yf

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

pubs.acs.org/jced

Isobaric Heat Capacity Measurements of Supercritical R1234yf Maciej Z. Lukawski,† Mitchell P.E. Ishmael,‡ and Jefferson W. Tester*,§ †

Cornell Energy Institute and School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States Active Energy Systems, Inc., Fairview Technology Center, 11020 Solway School Rd, Suite 100, Knoxville, Tennessee 37931, United States § Cornell Energy Institute, School of Chemical and Biomolecular Engineering, and Atkinson Center for a Sustainable Future, Cornell University, Ithaca, New York 14853, United States ‡

S Supporting Information *

ABSTRACT: R1234yf (2,3,3,3-tetrafluoropropene) is a low global warming potential (GWP) replacement for R134a, a fluid commonly used as a refrigerant in domestic and automotive air conditioning systems and as a working fluid in organic Rankine cycles. The use of R1234yf in energy conversion cycles requires an accurate determination of its thermophysical properties, including the isobaric heat capacity (cP). Using a custom-made flow calorimeter, experimental cP measurements of supercritical R1234yf were made at temperatures T = 373.15 to 413.5 K and absolute pressures P = 3.5 to 10 MPa. The experimental apparatus was calibrated using R134a to increase the measurement accuracy. The heat capacity measurements of R1234yf were compared to available published experimental data and to values obtained from a multiparameter equation of state (EOS). The measured cP values agreed well with the EOS, providing an average absolute deviation (AAD) of 1.6%.

1. INTRODUCTION The hydrofluoroolefin R1234yf (2,3,3,3-tetrafluoropropene) was proposed as a drop-in replacement of R134a (1,1,1,2tetrafluoroethane), a working fluid commonly used in vaporcompression refrigeration, air-conditioning systems, and organic Rankine cycles.1,2 The structural formulas of both fluids are presented in Figure 1. While the R-134a does not contribute to

properties. The pressure−volume−temperature (P−V−T) properties of fluids are typically described by semiempirical equations of state (EOS) fitted to experimental measurement data. Therefore, the development of accurate EOS for R1234yf requires reliable property measurements performed over a wide range of temperatures, pressures, and densities. Many thermophysical properties of R1234yf, including its critical properties, vapor pressures, speed of sound, heat capacities, and densities, have already been experimentally measured and were summarized by Richter et al.6 and Liu et al.7 Among other thermodynamic properties, isobaric heat capacity (cP) is particularly important to engineering practice due to its relevance to many industrial processes. The uncertainty of cP evaluated by the current state-of-art EOS for R1234yf is estimated at 5%,6 which is substantially higher than 0.5 to 1% uncertainty provided by the EOS for R134a.8 More extensive experimental cP measurements of R1234yf would allow researchers to validate and potentially improve the accuracy of the EOS, especially at near-critical and supercritical conditions where little experimental data currently exists. 1.1. Previous cP Measurements of R1234yf. The existing experimental cP data ranges for R1234yf are presented in temperature−pressure (T−P) coordinates in Figure 2. Experimental heat capacity measurements made by Liu et al.,7 Gao et al.,9 and Tanaka et al.10 were primarily taken in the liquid

Figure 1. Structural formulas of R1234yf (2,3,3,3-tetrafluoropropene) and R134a (1,1,1,2-tetrafluoroethane).

depleting tropospheric ozone, it has a high 100-year global warming potential (GWP100) of 1430, as compared to GWP100 of 1 for CO2.3 To reduce its impact on the atmosphere, R134a will be successively replaced with other refrigerants with lower global warming potential, such as R1234yf with a GHP100 of 4.2 The use of R134a and other hydrofluorocarbons (HFCs) will likely be reduced by 80−85% by 2045 as a part of the Kigali Amendment to the Montreal Protocol.4 In addition, individual countries may impose stronger restrictions on the use of HFCs. For example, the European Union has banned the use R134a and other refrigerants with GWP100 above 150 in automotive air conditioning applications since 2017.5 The increased use of R1234yf in engineering applications requires an accurate determination of its thermophysical © XXXX American Chemical Society

Received: October 31, 2017 Accepted: January 9, 2018

A

DOI: 10.1021/acs.jced.7b00946 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

calorimeter developed in our research group. The design of the apparatus and its operating principles are described in detail in our earlier publication12 and are only briefly summarized here. The accuracy of the calorimeter has been validated using carbon dioxide, methanol, and CO2−methanol mixtures at temperatures up to 423 K and pressures up to 30 MPa.12,13 The flow calorimeter approximates the definition of the isobaric heat capacity of a pure fluid by performing a cP measurement over a small but measurable temperature difference: c P(T , P) =

region, below the critical temperature of 368 K for R1234yf.11 In addition Liu et al. measured cP of supercritical R1234yf along the 373 K isotherm. All three existing sets of cP measurements7,9,10 show good agreement with the EOS by Richter et al.6 in the subcooled liquid region, with typical discrepancies of less than 2% at pressures under 5 MPa and less than 4% at 5 to 12 MPa. In particular, the measurements by Gao et al. provide a very good agreement with the EOS as determined by the average absolute deviation (AAD) of just 0.3%.9 However, the existing cP measurements of R1234yf at supercritical conditions show a higher AAD of 3.2%, indicating a much larger divergence from the EOS.7 This study adds to the previous work by providing cP measurements of R1234yf in the supercritical region at T = 373.15 to 413.15 K and P = 3.5 to 10 MPa. These include measurements in a close proximity to critical point located at T = 367.85 K and P = 3.382 MPa. The heat capacity measurements from this study at 373.15 K provide a closer match to the EOS predictions6 than data from Liu et al.7 In addition, the cP measurements along the 393.15 and 413.15 K isotherms constitute the first experimental heat capacity data for R1234yf at such high temperatures. The following sections discuss the design of experimental method and apparatus, the physical calibration of the calorimeter performed with R134a, and a comparison between the measured cP values and the existing experimental data and EOS.

2. EXPERIMENTAL MEASUREMENT 2.1. Chemicals. The identifying information, source, and purity of the fluids used in the measurements are included in Table 1. Table 1. Fluid Samples Used in the Analysis R1234yf

R134a

IUPAC name CAS number sample source mass-fraction purity method of purification

2,3,3,3-tetrafluoropropene 754-12-1 Honeywell International Inc. 99.99% none

1,1,1,2-tetrafluoroethane 811-97-2 Airgas Inc. 99.96% none

ΔP → 0

(1)

During steady-state operation of calorimeter, thermal energy Q̇ (0.65 to 1.8 W) is delivered to the fluid passing through a U-tube at a constant mass flow rate ṁ (∼0.22 g·s−1). The induced temperature difference ΔT (1.4 to 2.4 K) is recorded by the thermocouples located upstream and downstream of the heating element. Figure 3 provides a simplified process flow diagram of the measurement apparatus (A) and a more detailed schematic of the calorimeter cell, in which the cP measurement is taken (B). The calorimeter cell (B) consists of a small-diameter U-tube placed in a vacuum chamber, which is submerged in a temperature-controlled sand bath to reduce the heat loss from the calorimeter. A detailed description of the apparatus including specifications of individual subcomponents and design solutions used to improve measurement accuracy is provided in our earlier publication.12 2.3. Experimental Method. During the experiment, the fluid was pumped at a constant mass flow rate ṁ , which was measured using a Coriolis mass flow meter. Initially, steady-state operation was established without addition of any heat to the measured fluid (Q̇ = 0). The temperature differential between two thermocouples was recoded and denoted as ΔTb,1. This temperature difference typically had a nonzero value as a result of the offset of the two thermocouples, small temperature variations within the sand bath, Joule−Thompson effect, and other nonidealities. The measurement of ΔTb,1 is a well-established procedure in flow calorimetry and is typically referred to as a blank experiment.14,15 As a next step, the resistive heater was switched on to deliver a constant heat flow Q̇ to the measured fluid. After reaching a new steady state, the resulting temperature differential ΔTh was recorded. The quantity ΔT used in eq 1 was then calculated as a difference of ΔTh and ΔTb,1, which eliminated the effects of the Joule−Thompson effect and the offset of the thermocouples. As a last step, the resistive heater was switched off again (Q̇ = 0 W) and after re-establishing a steady state, temperature differential ΔTb,2 was recorded. ΔTb,2 was compared to ΔTb,1 and consistently found within 0.006 K from one another, most likely as a result of small temperature fluctuations in the sand bath. Both the careful design of the calorimeter and performing blank experiments reduced the experimental heat capacity error. To account for the remaining sources of systematic error, such as the heat loss, calorimeters measuring absolute cP typically require calibration.12,16−18 In this work, physical calibration using R134a was performed prior to making cP measurements of R1234yf. R134a was chosen as a reference fluid because it has similar thermodynamic properties to R1234yf and its heat capacity has been accurately measured14,19,20 and quantified using highly accurate, multiparameter EOS.8 To calibrate the calorimeter, cP measurements of R134a were performed at the same pressure and temperature conditions as for R1234yf.

Figure 2. Temperature T and pressure P range of the isobaric heat capacity cP measurements of R1234yf reported in this work (×); Liu et al.7 (□); Gao et al.9 (○); and Tanaka et al.10 (Δ). Colors of the markers indicate the difference in cP compared to the EOS:6 green (4%). The vapor− liquid saturation line is terminated by the critical point located at T = 367.85 K and P = 3.382 MPa.

chemical name

⎛ ∂H ⎞ Q̇ ⎜ ⎟ ≈ ⎝ ∂T ⎠ P ṁ ·ΔT

2.2. Experimental Apparatus. The isobaric heat capacity of R1234yf was measured using a custom-made flow B



Article

Figure 3. (A) A simplified schematic of the experimental apparatus. The flow path of the measured fluid is marked in blue. (B) A detailed schematic of the calorimeter cell. The vacuum chamber (1) contains a thin-walled, 1/4″ (6.35 mm) U-tube (2) through which the measured fluid is pumped at a constant mass flow rate ṁ . Thermocouples (3 and 4) are used to measure the induced temperature change ΔT between locations downstream and upstream of the electric resistance heater (5), through which heat rate Q̇ is delivered to the measured fluid. Pressure is measured both upstream and downstream of the heater using pressure transducers (6 and 7). The vacuum chamber (1) is placed inside a temperature-controlled sand bath shown in (A).

cP values to specific temperatures and pressures: u(T) and u(P); and (3) uncertainties resulting from the calibration of calorimeter using R134a: u(EOS) and u(c). The values of the first two groups of uncertainties are listed in Table 2 and were estimated based on equipment specifications and repeated property measurements. Thermocouples were calibrated using a platinum resistance thermometer (PRT) at the measurement temperatures. No additional calibration of pressure transducers was made and the uncertainty u(P) reflects the manufacturer specifications. The value of u(EOS) represents the accuracy of EOS for R134a, which was used for calibration of the calorimeter. Based on the comparison of the cP values evaluated using the EOS by Tillner-Roth et al.8 and the experimental data from Ernst et al.,14 u(EOS) was set to 0.7% of the measured cP value. The u(c), calculated as 2.2% of the measured cP, denotes the standard deviation of the differences between the measured cP of R134a and the cP predicted using EOS, that are not accounted for by the calibration function. The calibration function is described in detail in the next section and in the Supporting Information. The expanded uncertainty U(cP) of a cP measurement is calculated as

A correction function was developed by comparing the measured cP values of R134a with the values from the EOS.8 The correction function was then applied to the measurements for R1234yf. The experiments were performed for one isotherm at a time by taking a series of measurements at increasing pressures. After completing the series, the measurements for the same isotherm were typically repeated by going from the highest pressure to the lowest. The experimentally determined cP values were assigned to temperature and pressure conditions corresponding to the average of values measured upstream and downstream of the resistive heater, as shown in Figure 3B. These temperature values were then rounded up to decimal values using partial derivatives

∂c P ∂T P

( )

obtained from the EOS.6 The temperature correc-

tions were small and, on average, equal to about 0.15 ± 0.1 K. The resulting cP corrections were typically less than 0.2%, but could reach 3% near the critical point. 2.4. Uncertainty Assessment. The sources of uncertainty in experimental cP values include: (1) uncertainties in the measured values of constitutive properties: u(Q̇ ), u(ṁ ), and u(ΔT); (2) uncertainties resulting from assigning the calculated

2 2 2 2 2 ⎛ ⎛ ⎛ ⎛ ⎛ ∂c P ⎞ ∂c P ⎞ ∂c P ⎞ ∂c P ⎞ ∂c P ⎞ 2 2 ̇ ⎟ + ⎜u(P) ⎟ + ⎜u(Q ) ⎟ + ⎜u(ΔT ) U (c P) = k ⎜u(T ) ⎟ + ⎜u(ṁ ) ⎟ + u (EOS) + u (c) ̇ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ∂P ∂Q ⎠ ∂ṁ ∂(ΔT ) ⎠ ∂T ⎝ ⎝

where k is the coverage factor equal to 2 for the expanded uncertainty U(cP) used in this work or to 1 for the combined standard uncertainty uc(cP). The expanded uncertainty corresponds to 95% confidence intervals. The first two partial derivatives in eq 2 are evaluated using the EOS and the remaining three are calculated using eq 1.

(2)

R134a. As a part of the calibration process, cP of R134a was measured at the same temperatures and pressures as for R1234yf. The measured cP values of R134a were compared to the values from the EOS8 to provide a calibration function. The calibration function was then applied to the R1234yf measurements. The accuracy of the EOS for R134a8 was validated using prior experimental cP measurements presented in Figure 4. The measured cP values of R134a were typically within 1% from the EOS.14,19,20 In particular, Ernst and co-workers14 measured cP of R134a in the supercritical region, at temperatures and pressures explored in this work. At these conditions, the

3. RESULTS AND DISCUSSION 3.1. Calibration of the Calorimeter with R134a. The physical calibration of the calorimeter was performed using C



Article

Table 2. Estimated Standard Uncertainties u of Parameters Used in Determining the Measured Isobaric Heat Capacity cP Values standard uncertainty

measured property

u(T) u(P) u(Q̇ ) u(ṁ ) u(ΔT)

temperature pressure heat flow mass flow rate differential temperature

range

magnitude of uncertainty

sources of uncertainty

373.15 to 413.15 K 3.5 to 10 MPa 0.6 to 1.8 W 0.19 to 0.22 g·s−1 1.4 to 2.4 K

0.1 K 0.02 MPa 0.02 W 1.67 × 10−3 g·s−1 0.006 K

PRT standard (0.05 K) and thermocouple accuracy (0.05 K) accuracy of pressure transducer accuracy and stability of resistive heater Coriolis mass flow meter accuracy (8.3 × 10−4 g·s−1) and signal drift (8.3 × 10−4 g·s−1) inconsistency of temperature difference before and after experiment (ΔTb,1 − ΔTb,2)

The measured heat capacities and their respective uncertainties are presented in Table 4 and Figure 5. Both Table 4 and Figure 5 provide cP values for a calibrated calorimeter, and the raw data is included in the Supporting Information. The repeated measurements at the same pressures and temperature conditions yielded similar cP values, on average within 0.6% from each other, unless the measurement was taken very close to the critical point (i.e., at T = 373 K and P = 3.5 to 4.5 MPa) in which case repeatability was lower. The measured cP values had an average absolute deviation (AAD) from the EOS predications of 1.6%. The AAD was higher (2.4%) for the measurements at 373.15 K, due to the sensitivity of heat capacity to changes in temperature and pressure near the critical point at T = 367.85 K and P = 3.382 MPa. The AAD of the measurements at T = 393.15 and 413.15 K was lower at 1.1%. For the purpose of this work, the EOS results for the 413.15 K isotherm were extrapolated using REFPROP software22 2 K beyond the range of applicability of this EOS. Despite that, the EOS provided an accurate representation of the measured heat capacity values. The differences between the measured cP values and the predictions of the EOS are illustrated in Figure 6. Both the relative differences in cP and the experimental uncertainty increase near the critical point located at 367.85 K and 3.382 MPa. The error bars in Figures 5 and 6 correspond to expanded uncertainty (i.e., k = 2 in eq 2). Near the critical point (at T = 373.15 K and P = 3.5 to 4.2 MPa), the main contribution to the expended uncertainty is the pressure measurement error. Away from the critical point, the expanded uncertainty is largely controlled by the uncertainty of the calibration function, which increases the 95% confidence intervals for measured cP from approximately 2 to 5%. Figures 2 and 5 indicate that cP values reported by Liu et al.7 were measured at similar temperatures and pressures as those presented in this work, namely, 373.15 K and 4.5, 5, 6, and 8 MPa. At these conditions, our measured cP values provided a closer match to the equation of state (EOS) predications (AAD of 1.2%) than the measurements of Liu et al. (AAD of 3.6%). This is likely due to lower ΔT values used in this work and the calorimeter design measures aimed to reduce heat losses at high temperatures. Even though the expanded uncertainties reported for the data by Liu et al.7 were lower than in this work and equaled approximately 0.7% of the measured cP values, we did not include their results in Figure 6 because they did not account for the uncertainty of the calibration function and therefore cannot be directly compared to the expanded uncertainty calculated in this work. Richter et al. estimated the uncertainty of their EOS in evaluating cP at 5%.6 The experimental cP measurements suggest that this estimate is conservative at most temperature and pressure conditions. The cP measurements of Gao et al. for liquid R1234yf up to 5 MPa are within 1% from the EOS predications and provide AAD of 0.3%. For liquid R1234yf above 5 MPa, the measurements of Liu et al. are within 4.2% from the EOS

Figure 4. Temperature T and pressure P range of the isobaric heat capacity cP measurements of R134a reported in this work (×); Ernst et al.14 (□); Nakagawa et al.19 (Δ); Saitoh et al.20 (○). The measurements described in this work were used only for physical calibration of the calorimeter. For the prior studies, colors of markers indicate the difference in cP compared to EOS predictions:8 green (4%). The vapor−liquid saturation line is terminated by the critical point located at T = 374.25 K and P = 4.059 MPa.

average difference between their measurements and the EOS predictions was 0.7%, which validated the accuracy of using EOS predicted values of cP in this application. The measured cP values of R134a are listed in Table 3. The measurements of R134a presented in this work were performed solely for the purpose of calibrating our equipment and are somewhat less accurate than available literature data.14 The average absolute deviation (AAD) between the cP values measured in this work and the EOS predictions was 3.3%. The measured cP values were typically underestimated and the error increased with ΔT. A linear correlation between ΔT and the measurement error provided a high coefficient of determination (R2) of 0.65 indicating that the error is strongly correlated with the imposed ΔT. This linear correlation was used for the physical calibration of the calorimeter and applied to the cP measurements of R1234yf. Both the calibration function and the correction factors applied to the R1234yf measurements are presented in the Supporting Information. Using an empirical correlation for calibration of calorimeter was deemed more appropriate than assigning specific correction values to individual temperature and pressure conditions. R134a and R1234yf have different critical temperatures and pressures and, as a result, their relative heat capacities vary significantly in the nearcritical region. The applied correction factors ranged from 0.3 to 6.8% with an average value of 3.6%, which is relatively low compared to corrections of 2 to 15% used by other researchers in calibrating their calorimeters.16−18,21 3.2. Results for R1234yf. Following the calibration with R134a, the flow calorimeter was used to measure cP of R1234yf. The measurements were performed along the 373.15, 393.15, and 413.15 K isotherms and at pressures ranging from 3.5 to 10 MPa. D



Article

Table 3. Isobaric Heat Capacity cP Measurements of R134a Used To Calibrate the Experimental Apparatusab T/K

P/MPa

ΔT/K

cP,Exp/J·g−1·K−1

cP,EOS/J·g−1·K−1

(cP,Exp−cP,EOS)/cP,EOS

373.05 372.85 372.85 372.95 373.15 373.15 373.15 373.35 373.25 373.15 373.15 373.05 373.35 393.15 393.05 393.25 393.35 393.15 393.15 393.25 393.05 393.15 393.15 393.35 393.55 393.55 413.25 413.25 413.35 413.25 413.05 412.95 413.15 413.15 413.05 413.15 413.05 413.05 413.05

3.37 3.37 3.37 4.05 4.44 4.55 4.90 5.05 6.06 6.06 7.94 7.94 8.08 3.90 4.08 4.95 4.95 5.55 5.55 5.55 5.89 6.12 7.92 7.93 9.89 9.89 3.97 3.97 4.10 5.07 5.08 5.96 6.08 7.02 7.03 7.97 7.98 9.86 9.86

2.24 2.22 2.22 1.43 2.14 2.24 2.20 2.25 2.29 2.29 2.24 2.24 2.30 2.30 2.22 2.37 2.19 1.98 1.99 1.99 2.01 2.13 2.24 2.25 2.26 2.26 2.20 2.16 2.22 2.22 2.18 2.26 2.22 2.30 2.29 2.27 2.26 2.24 2.24

1.93 1.94 1.94 6.42 3.11 2.81 2.38 2.33 1.93 1.92 1.70 1.70 1.69 1.58 1.66 2.72 2.69 4.13 4.12 4.11 3.96 3.46 2.02 2.02 1.73 1.73 1.41 1.40 1.42 1.66 1.69 2.06 2.09 2.40 2.41 2.32 2.33 1.95 1.94

1.93 1.95 1.95 5.55 3.02 2.84 2.45 2.37 2.00 2.00 1.76 1.76 1.76 1.63 1.74 2.83 2.82 4.25 4.25 4.23 3.84 3.43 2.12 2.12 1.82 1.82 1.40 1.40 1.42 1.70 1.70 2.11 2.17 2.55 2.55 2.44 2.44 2.02 2.02

−0.4% −0.4% −0.1% 15.8% 3.0% −0.8% −2.8% −1.8% −3.7% −3.9% −3.4% −3.5% −3.7% −3.2% −4.1% −3.9% −4.4% −2.8% −3.0% −2.8% 2.9% 1.0% −4.6% −4.9% −5.3% −5.3% 0.6% 0.3% −0.2% −2.3% −0.9% −2.6% −3.8% −5.8% −5.7% −5.1% −4.6% −3.6% −3.8%

a

The experimentally determined heat capacity values (cP,Exp) at temperatures T and pressures P are compared to the values obtained from the EOS8 for R134a (cP,EOS). ΔT is the temperature difference induced in the calorimeter to measure cP,Exp. bStandard uncertainties of T, P, and ΔT are u(T) = 0.1 K, u(P) = 0.02 MPa, and u(ΔT) = 0.006 K, as listed in Table 2.

Table 4. Isobaric Heat Capacity Values of R1234yf (cP,Exp) Measured at Temperatures T and Pressures P Are Compared To the Isobaric Heat Capacity Values Predicted by the EOS (cP,EOS)6ab P/MPa



102Ur(cP)

(cP,Exp−cP,EOS)/cP,EOS (%)

T = 373.15 K 3.498 4.114 4.160 4.441 4.642 4.921 5.047 5.955 6.023 8.021 8.024 8.020

3.60 3.46 3.40 2.53 2.40 2.15 2.09 1.85 1.85 1.65 1.65 1.64

12.8 7.3 6.2 5.3 5.2 5.0 4.9 4.9 4.9 4.8 4.8 4.9

4.039 4.040

1.92 1.91

5.2 5.3

3.51 3.28 3.11 2.53 2.32 2.14 2.08 1.83 1.82 1.62 1.62 1.62

2.6 5.6 9.4 0.1 3.2 0.5 0.5 1.0 1.8 1.4 1.5 1.2

1.95 1.95

−1.4 −1.9

T = 393.15 K

E



Article

Table 4. continued P/MPa


102Ur(cP)


(cP,Exp−cP,EOS)/cP,EOS (%)

4.943 4.944 5.417 5.417 5.958 6.022 7.949 8.043 10.032 10.032

3.03 2.98 2.83 2.83 2.44 2.42 1.80 1.80 1.65 1.65

4.9 5.0 5.0 5.0 4.9 4.9 4.8 4.8 4.8 4.8

3.04 3.04 2.88 2.88 2.44 2.40 1.81 1.80 1.63 1.63

−0.5 −1.9 −1.9 −1.8 0.3 0.9 −0.6 0.0 1.2 1.3

4.015 4.989 5.045 6.037 6.963 6.965 8.042 8.043 10.030

1.52 1.82 1.83 2.14 2.15 2.12 2.00 2.00 1.77

4.9 4.9 4.9 4.8 4.8 4.8 4.8 4.8 4.8

1.50 1.81 1.84 2.16 2.14 2.14 1.97 1.97 1.74

1.4 0.5 −0.4 −1.0 0.4 −1.3 1.4 1.6 2.0

T = 413.15 K

a The relative expanded uncertainty (k = 2) of the measured cP values is listed as Ur(cP). bStandard uncertainties of P and T are u(P) = 0.02 MPa and u(T) = 0.1 K, respectively.

Figure 5. Isobaric heat capacity cP measurements of R1234yf are presented as a function of pressure P for three temperatures: 373.15 K (black), 393.15 K (red), and 413.15 K (green). The cP measurements reported in this work (×) are compared to the measurements by Liu et al.7 (□) and the predictions of EOS by Richter et al.6 (solid line for 373.15 K, dashed line for 393.15 K, and dotted line for 413.15 K). Error bars indicate expanded uncertainty U(cP) corresponding to a level of confidence of 95%.

Figure 6. Relative difference (cP,Exp − cP,EOS)/cP,EOS in the isobaric heat capacity of R1234yf obtained from experimental measurements cP,Exp and estimated using an equation of state cP,EOS.6 Results reported in this work for temperatures of 373.15 K (×, black), 393.15 K (□, red), and 413.15 K (○, green) are presented as a function of pressure P. Error bars indicate expanded uncertainty U(cP) corresponding to a level of confidence of 95%. Dashed horizontal lines denote the estimated 5% uncertainty of EOS in predicting cP.6

and provide AAD of 2.2%. At supercritical conditions away from the critical point (at temperatures above 373.15 K or pressures above 4.7 MPa), our results are within 2% of the EOS predictions and provide AAD of 1.1%. Only in a close vicinity of the critical point (T = 373.15 K and P = 3.5 to 4.7 MPa) the maximum measured cP deviation from EOS was 9.4% with an AAD of 4.2%.

quantified by the average absolute deviation (AAD) of 1.6%. The agreement was even better for the measurements further away from the critical isotherm as quantified by AAD of 1.1 for the heat capacities measured at T = 393.15 and 413.15 K. To achieve high measurement accuracy, our flow calorimeter was calibrated using R134a. The collected cP data can be used to validate and improve the accuracy of EOSs, primarily at near-critical and supercritical conditions, where experimental data are scarce.

4. CONCLUSIONS Experimental isobaric heat capacity (cP) measurements of supercritical R1234yf were made at temperatures T = 373.15 to 413.15 K and pressures P = 3.5 to 10 MPa using a flow calorimeter. These measurements provided new cP data in the previously unexplored domain above 373 K and in the close vicinity of the critical point (367.85 K and 3.382 MPa). The measured cP values agreed well with the EOS predications,6 as

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00946. A spreadsheet containing measured cP values of R1234yf before and after applying the correction function and F



■

Article

Carbon Dioxide, Methanol, and Carbon Dioxide-Methanol Mixtures. J. Supercrit. Fluids 2016, 117, 72−79. (13) Ishmael, M. P.; Stutzman, L. B.; Lukawski, M. Z.; Escobedo, F. A.; Tester, J. W. Heat Capacities of Supercritical Fluid Mixtures: Comparing Experimental Measurements with Monte Carlo Molecular Simulations for Carbon Dioxide-Methanol Mixtures. J. Supercrit. Fluids 2017, 123, 40−49. (14) Ernst, G.; Gurtner, J.; Wirbser, H. Massic Heat Capacities and Joule−Thomson Coefficients of CH2FCF3 (R134a) at Pressures up to 30 MPa and Temperatures between about 253 and 523 K. J. Chem. Thermodyn. 1997, 29, 1113−1124. (15) Ernst, G.; Hochberg, U. E. Flow-Calorimetric Results for the Specific Heat Capacity Cp of CO2, of C2H6, and of (0.5CO2 + 0.5C2H6) at High Pressures. J. Chem. Thermodyn. 1989, 21, 407−414. (16) Smith-Magowan, D.; Wood, R. H. Heat Capacity of Aqueous Sodium Chloride from 320 to 600 K Measured with a New Flow Calorimeter. J. Chem. Thermodyn. 1981, 13, 1047−1073. (17) Rogers, P. S. Z.; Pitzer, K. S. High-Temperature Thermodynamic Properties of Aqueous Sodium Sulfate Solutions. J. Phys. Chem. 1981, 85, 2886−2895. (18) Fortier, J. L.; Benson, G. C.; Picker, P. Heat Capacities of Some Organic Liquids Determined with the Picker Flow Calorimeter. J. Chem. Thermodyn. 1976, 8, 289−299. (19) Nakagawa, S.; Sato, H.; Watanabe, K. Specific Heat at Constant Pressurefor Liquid New Refrigerants. Proceedings, Natl. Heat Transfer Symp. Japan 1990, 421−423. (20) Saitoh, A.; Nakagawa, S.; Sato, H.; Watanabe, K. Isobaric Heat Capacity Data for Liquid HFC-134a. J. Chem. Eng. Data 1990, 35, 107−110. (21) White, D. R.; Downes, C. J. Heat Loss Corrections for Heat Capacity Flow Calorimeters. J. Solution Chem. 1988, 17, 733−750. (22) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1; 2013.

correction function based on the cP measurements of R134a used for calibration of the calorimeter (XLSX)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Maciej Z. Lukawski: 0000-0002-0534-0317 Funding

The authors thank the Cornell Energy Institute, the EarthEnergy Systems NSF IGERT program at Cornell University, and the Atkinson Center for a Sustainable Future for partial financial support of this research. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to thank Honeywell Performance Materials & Technologies for the donation of R1234yf used in the measurements. They would also like to express their gratitude to Mr. Glenn Swan for manufacturing components of the flow calorimeter and Dr. Adam Carr for his contributions to the early work on this project.

■

REFERENCES

(1) Navarro-Esbrí, J.; Mendoza-Miranda, J. M.; Mota-Babiloni, A.; Barragán-Cervera, A.; Belman-Flores, J. M. Experimental Analysis of R1234yf as a Drop-in Replacement for R134a in a Vapor Compression System. Int. J. Refrig. 2013, 36, 870−880. (2) Lee, Y.; Jung, D. A Brief Performance Comparison of R1234yf and R134a in a Bench Tester for Automobile Applications. Appl. Therm. Eng. 2012, 35, 240−242. (3) IPCC. Changes in Atmospheric Constituents and in Radiative Forcing. In Climate Change 2007: The Physical Science Basis; Cambridge University Press: Cambridge, UK, 2007; pp 129−234. (4) Shah, N.; Khanna, N.; Karali, N.; Park, W.; Qu, Y.; Zhou, N. Opportunities for Simultaneous Efficiency Improvement and Refrigerant Transition in Air Conditioning; 2017. (5) EU. Directive 2006/40/EC of the European Parliment and of the Council Relating to Emissions from Air-Conditioning Systems in Motor Vehicles and Amending Council Directive 70/156/EEC; 2006. (6) Richter, M.; McLinden, M. O.; Lemmon, E. W. Thermodynamic Properties of 2,3,3,3-Tetrafluoroprop-1-Ene (R1234yf): Vapor Pressure and p−ρ−T Measurements and an Equation of State. J. Chem. Eng. Data 2011, 56, 3254−3264. (7) Liu, Y.; Zhao, X.; Lv, S.; He, H. Isobaric Heat Capacity Measurements for R1234yf from 303 to 373 K and Pressures up to 12 MPa. J. Chem. Eng. Data 2017, 62, 1119−1124. (8) Tillner-Roth, R.; Baehr, H. D. An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 to 455 K at Pressures up to 70 MPa. J. Phys. Chem. Ref. Data 1994, 23, 657−729. (9) Gao, N.; Jiang, Y.; Wu, J.; He, Y.; Chen, G. Measurements of the Isobaric Heat Capacity of R1234yf in Liquid Phase at Temperatures from 305K to 355K and Pressures up to 5 MPa. Fluid Phase Equilib. 2014, 376, 64−68. (10) Tanaka, K.; Higashi, Y.; Akasaka, R. Measurements of the Isobaric Specific Heat Capacity and Density for HFO-1234yf in the Liquid State. J. Chem. Eng. Data 2010, 55, 901−903. (11) Tanaka, K.; Higashi, Y. Thermodynamic Properties of HFO1234yf (2,3,3,3-Tetrafluoropropene). Int. J. Refrig. 2010, 33, 474−479. (12) Ishmael, M. P.; Lukawski, M. Z.; Tester, J. W. Isobaric Heat Capacity (Cp) Measurements of Supercritical Fluids Using Flow Calorimetry: Equipment Design and Experimental Validation with G


Isobaric Heat Capacity Measurements of Supercritical R1234yf

Recommend Documents