Tauqir H. Syed, Thomas J. Hughes, Kenneth N. Marsh, and Eric F. May

Transcription

1 ISOBARIC HEAT CAPACITY MEASUREMENTS OF LIQUID METHANE, ETHANE, PROPANE AND BINARY MIXTURES BY DIFFERENTIAL SCANNING CALORIMETRY AT CRYOGENIC CONDITIONS Tauqir H. Syed, Thomas J. Hughes, Kenneth N. Marsh, and Eric F. May Centre for Energy, School of Mechanical and Chemical Engineering University of Western Australia 35 Stirling Highway, Crawley, WA 6009, Australia ABSTRACT The heat capacities of liquefied natural gas (LNG) fluids are important in the modelling and design of equipment for natural gas treatment and liquefaction plants. A commercial differential scanning calorimeter (DSC) has been modified to allow the measurement of isobaric heat capacities, c p, of cryogenic liquids at high pressures. Isobaric heat capacity measurements for liquid methane, ethane, and propane are presented at temperatures between ( and ) K and pressures between (1.1 and 6.35) MPa. The standard deviation of the measured c p from reference equation of state (EOS) calculated isobaric heat capacity, c p,ref, was c p for methane, 0.01 c p for ethane and c p for propane. Three key modifications allowed these measurements to be made accurately at high pressure cryogenic conditions; these were: (1) the development of methods to avoid removing the sample cell between experiments, (2) the installation of a ballast cylinder to buffer the pressure rise due to thermal expansion of the liquid and (3) the installation of heaters to the tubing leading from the calorimeters cells to prevent cold spots and fluid convection that adversely effected the DSC s heat flux stability. The DSC was also used to measure the c p of a heptane (1) + toluene (2) mixture with x 1 = 0.38 at atmospheric pressure and temperatures of (228.15, , and ) K. The measured values had deviations from those measured by adiabatic calorimetry of less than c p. In addition measurements of the c p of a methane (1) + propane (2) mixture with x 1 = (0.81 and 0.82) at pressure between (4.7 and 6.0) MPa were also completed. The standard deviation of the measured c p from the REFPROP 9.0 calculated c p using default pure fluid EOS and mixing rule and parameters was 0.01 c p. However, the deviations between the measured c p for this mixture and those predicted with the cubic Peng-Robinson EOS used most commonly in process simulators increased to more than 0.03 c p. EXPERIMENTAL Apparatus The specialized calorimeter was based on a Setaram BT2.15 Tian-Calvet heat flow DSC, which has an operational temperature range of (77 to 473) K. This base DSC was used previously to measure the heat capacity of ionic liquids by Hughes et al.(2011). The schematic of the modified calorimeter is shown in Fig 1. The stainless steel sample cells were provided by the manufacturer; they had a volume of about 8.5 ml, a pressure rating of 10 MPa and a connecting tube with an outside diameter (OD) of 4 mm and an inside diameter (ID) of 3 mm. This tube connected the sample cell with the high-pressure vapour ballast manifold. In addition, a stainless steel sample injection tube with OD of 1.59 mm (1/16 inch) 1

2 and ID of 1.08 mm ( in) was inserted into the connecting tube and sealed using Swagelok fittings so that (liquid) samples could be delivered and displaced from the cell without removing it from the calorimeter block. A high-pressure liquid chromatography (HPLC) pump was used to deliver liquid phase samples to the bottom of the DSC sample cell. For pure fluids that are gases at room temperature, filling was achieved by setting the calorimeter block to a sufficiently low temperature (such that freezing did not occur) and rapidly pressurizing the evacuated sample cell so that the fluid quickly condensed. For mixtures that are gases at room temperature, filling was achieved by passing volumes of the gas from a bottle containing a gravimetrically prepared mixture placed in the ballast cylinder bath (refer to Fig 1) into the evacuated lines bound by valves 1M, 2M, 3M, 7M and 8M (a volume of about 17 ml). The bottle valve was then closed and valve 2M to the evacuated sample cell at low temperature was then opened. The temperature of the sample cell was set low enough to condense liquid at atmospheric pressure but not to freeze out components. The pressure in the lines was observed to drop to atmospheric pressure or below and then valve 2M was closed and more sample was charged into the lines from the bottle and the process was repeated. In total 5 to 6 charges were required. By this method it was possible to condense a liquid in the calorimeter with the same composition as the gas mixture. To remove samples from the cells, a working vacuum was applied to the manifold and then dry nitrogen was delivered through the sample injection tube to displace the sample and/or flush out the sample cell. 10 Burst Disk HPLC Pump 11 Sample Injection Tubing Connecting Tubing 12 Vent 1R Reference Regulator P 2R 3R 5R 6R 7R 9 2M 3M 7M P 6M 1M Measurement Regulator 5M Vent 4R Reference Gas Cylinder 8R T 8M Measurement Gas Cylinder 4M Measurement DSC cell Reference DSC cell Ballast Cylinder Bath Calorimetric Housing Vacuum Pump Measurement Cell Detail Fig. 1: Modified Setaram BT2.15 DSC for high pressure measurements of the heat capacities of volatile liquids at low temperature. The left hand side shows an enlarged view of the measurement cell that contains the sample fluid. Three heaters (H1, H2 and H3) were mounted on the tubing supplying the fluid to the measurement cell with six platinum resistance thermometers (PRTs) to monitor the temperature profile along the tube. The reference cell side (not shown) was identically fitted with heaters and PRTs. The right hand side shows the gas supply and ballast manifold. Gas was supplied to each cell and ballast cylinder individually via a regulator. Ballast cylinders (one each for the measurement cell and reference cell) were temperature controlled in a glycol + water bath at (306 ± 1) K. 2

3 The location of the liquid-vapour interface within the apparatus is crucial. If the liquid s enthalpy of vaporization is significant then the interface cannot be within the calorimetric block during a temperature scan without affecting the measured value of c p. In addition the position of the interface will change during a temperature scan as the liquid expands, and to prevent significant changes in pressure, it is necessary to allow for this expansion. Schrödle et al. (2008) described modifications to the Setaram C80 DSC which enabled high-pressure c p measurements of aqueous solutions at high temperatures (323 K to 573 K). A ballast vessel containing N 2 connected to the DSC sample cell allowed the system pressure to remain nearly constant as the aqueous solution expanded. The level of the liquid-n 2 interface was kept at a sufficient height in the connecting tube so that any vaporization effects would have minimal effect on the calorimetric signal. Thus, the method of Schrödle et al. (2008) leads to measurements of the liquid s volumetric heat capacity at constant pressure and conversion of these data to specific isobaric heat capacities requires knowledge of the fluid s density at the measured temperature and pressure. The first attempt to make measurements with the Setaram BT 2.15 calorimeter on propane using the technique described by Schrödle et al. (2008) led to an unstable calorimetric signal, most-likely caused by convection with in the connecting tube. Schrödle et al. (2008) used a preheater to prevent convection from occurring in their connecting tube; however the design and low operational temperature range of the BT 2.15 calorimeter makes the problem much more severe than for the Setaram C80 DSC which can only operate at temperatures above ambient whereas the BT 2.15 uses liquid nitrogen and its boil-off vapour as a coolant. To demonstrate convective effects, six platinum resistance thermometers were mounted on the outside of the connecting tube so that its temperature profile could be monitored when the cell was located in the calorimetric block. When the connecting tube was filled with liquid, as it must be for high-pressure liquid c p measurements, temperature inversions were observed which gave rise to convective heat flow, resulting in an unstable calorimetric signal. This problem was overcome by the addition of three heaters spaced along the connecting tube as shown in Fig. 1; similar heaters were also added to the connecting tube for the reference cell. These heaters were controlled using a PID algorithm to prevent temperature inversions and to maintain a smoothly increasing temperature profile from the cell to auxiliary furnace [refer to Fig 1, the auxiliary furnace was maintained at either ( or ) K]. Method and materials The suppliers and purities of the gases and liquids used in this work are listed in Table 1. A mixture of heptane (1) + toluene (2) was gravimetrically prepared with x 1 = (0.38 ± 0.02). The mixture was prepared at this composition because it is near to the maximum excess heat capacity for the binary system at the temperatures studied, and it facilitated comparison with the adiabatic calorimetry results of Holzhauer & Ziegler (1975). In addition, two gas mixtures of methane (1) + propane (2) were gravimetrically prepared with x 1 = (0.81 and 0.82). Tab. 1: Chemical suppliers and purities of the gases and liquids Chemical Name Supplier Supplier Mole Fraction Purity Methane Air Liquide Ethane Coregas pty Ltd Propane Air Liquide Heptane RCI Lab Scan Limited 0.95 Toluene Sigma Aldrich

4 For samples that are liquids at room temperature the measurement cell was filled using the HPLC pump connected to the narrow bore injection tube leading to the bottom of the cell. The line to the vapor ballast manifold was broken after valve 2M in Fig. 1 and a tube was connected in its place to a graduated beaker. This ensured that once the injected liquid appeared in the beaker, the entire volume of tubing inside the calorimetric housing was filled with liquid at atmospheric pressure. Heat capacities were measured using the step method;(schrödle et al., 2008) for the measurements of toluene, heptane and their mixture the heating rate was 0.03 K min -1 and the calorimeter was held at constant temperature for 5.5 hours before and after each step (i.e. eleven hours at the temperature between two temperature ramps). Two 10 K steps were measured over the range ( to ) K and another two 10 K steps were measured from ( to ) K. To remove the sample from the measurement cell the calorimeter was heated to the normal boiling point temperature of the liquid and dry nitrogen was flushed through the cell. The liquid that was displaced out the cell was collected in graduated beaker. This flushing was continued for period of at least twelve hours to ensure that all the liquid had been displaced or evaporated. For methane, propane and ethane, steps of 10 K were also used but the heating rate was increased to 0.15 K min -1 and the calorimeter was held at constant temperature before and after each scan for four hours and six hours, respectively (ten hours total between scans). These hold times were found to be necessary to allow the net heat flow signal to return to a stable baseline. To remove the sample, the system was depressurized by venting and the calorimeter was heated, if necessary, to above the fluid s normal boiling point temperature. Propane has a saturation pressure of less than 1 MPa at 300 K which was close to the maximum temperature at which the vapor ballast temperature could be set. Thus to make propane measurements at pressures greater than 1 MPa, it was not possible to use pure propane vapor in the ballast. To achieve higher pressures, compressed nitrogen was added into the ballast vessel. Any mass transfer of nitrogen into the liquid propane contained within the calorimetric measurement cell would be greatly limited by the small surface area of the vapor-liquid interface and long length of tubing between the interface and the calorimetric block. There was no evidence of any effect of dissolved N 2 on the measured propane heat capacities. Isobaric heat capacities were calculated by the two-step method. This method requires knowledge of the density of the liquid in the sample cell as a function of temperature and pressure. The isobaric massic heat capacities were calculated from: sd bd ρ cell step (1) cp = Φ t Φ t V T where Φ dt s is the integrated heat flow difference between the measurement cell filled with sample and the reference cell containing dry N 2 over the temperature step (scan), Φ dt b is the integrated heat flow difference for the calibration scans where both the measurement and reference cells were filled with dry N 2, ρ is the fluid density found at the mean temperature of the step, V cell is the volume of the cell (a volume which equates to the volume of fluid for which the thermopile is measuring a heat flux signal) and T step is the temperature step. Liquid densities were calculated using the (default) reference EOS implemented in the software REFPROP 9.0 (Lemmon et al., 2010), which were Setzmann & Wagner (1991) for methane, Bucker & Wagner (2006) for ethane, Lemmon et al. (2009) for propane, Span & Wagner (2003) for heptane, and Lemmon & Span (2006) for toluene. 4

5 RESULTS AND DISCUSSION To test the modifications that were made to the DSC, measurements of the heat capacity of heptane (1), toluene (2) and the mixture of toluene and heptane were completed at atmospheric pressure. Isobaric heat capacities, c p, for heptane, and toluene were measured at T = (228.15, , and ) K. Holzhauer and Ziegler (1975) measured these fluids and their mixtures with an adiabatic calorimeter over the temperature range of (180 to 320) K with a stated accuracy of c p and an estimated standard uncertainty of about c p. They presented their c p results as a smoothed correlation of temperature and composition. Fig 2. shows a comparison of the c p values measured in this work for the pure liquids and their mixture with calculated c p values, c p,calc, from the Holzhauer & Ziegler (1975) correlation. The maximum deviation of our data from the correlation is c p. Fig. 2 also shows a comparison of c p values for toluene, heptane and the mixture studied in this work calculated using the corresponding recommended EOS implemented in the software REFPROP 9.0 (Lemmon et al., 2010). For the pure fluids, the deviations of the EOS predictions from high accuracy literature heat capacity data is stated to be less than 0.01 c p for heptane (saturated heat capacity data at temperatures greater than 200 K) (Span & Wagner, 2003) and c p for toluene (at temperatures less than 560 K) (Lemmon & Span, 2006). The comparisons for the pure fluids shown in Fig. 2 are consistent with these bounds. However, the model used in REFPROP to estimate the mixture s heat capacity deviates from c p,calc by c p at K. The developers of REFPROP have indicated that only room temperature data were used for this mixture s model development because the number of data available were very limited, and more mixture data are needed to remedy the situation (Lemmon, 2012). (c p -c p,calc )/c p,calc T/K Fig. 2: Relative deviations of toluene, heptane and heptane (1) + toluene (2) with x 1 = 0.38 heat capacities, c p, from c p,calc, calculated from the correlation of Holzhauer and Ziegler (1975) This work:, toluene;, heptane;, heptane (1) + toluene (2) with x 1 = 0.38;, Fortier and Benson (1976) (calculated from difference in excess heat capacities using Fortier and Benson s polynomial fit to their experimental results and Holzhauer and Ziegler s correlation);, Grolier and Faradjzadeh (1979) with x 1 = Calculated: ---, toluene using EOS of Lemmon and Span (2006);, heptane using EOS of Setzmann and Wagner (1991);, heptane (1) + toluene (2) with x 1 = 0.38 calculated using default pure fluid EOS and mixing rule and parameters of REFPROP 9.0. (Reference EOS calculations were implemented in REFPROP 9.0). Methane isobaric heat capacities were measured between ( and ) K at two pressures of about (4.3 and 6.4) MPa. Fig. 3 shows a relative deviation plot of methane 5

6 isobaric heat capacity measurements from the reference EOS calculated values. The reference EOS of Setzmann & Wagner (1991) for methane is estimated to predict c p with an uncertainty of 0.01 c p. The mean and maximum deviations of our data are (0.002 and 0.005) c p respectively from this reference EOS. (c p -c p,ref )/c p,ref T/K Fig. 3: Relative deviations of the isobaric heat capacity of methane, c p, from the reference EOS (Setzmann & Wagner, 1991) heat capacity, c p,ref., this work at 6.34 MPa;, this work at 4.3 MPa;,Wiebe & Brevoot (1930);, Hestermans & White (1961);, Jones et al. (1963) at 4.3 MPa; +, Jones et al. (1963) at 5.5 MPa;, van Kasteren & Zeldenrust (1979) (c p -c p,ref )/c p,ref T/K Fig. 4: Relative Deviations of the isobaric heat capacity of ethane, c p, from the reference EOS (Bucker & Wagner, 2006) heat capacity, c p,ref., this work at 4.2 MPa;, this work at 2.0 MPa;, this work at 1.2 MPa;, Wiebe et al. (1930);, Witt & Kemp (1937);, Roder et al. (1976); +, Grini et al.(1996) Ethane heat capacities were measured between ( and ) K at pressures of (1.2, 2.0, and 4.2) MPa. Fig. shows a relative deviation plot of ethane isobaric heat capacity measurements from the reference EOS calculated values. The reference EOS of Bucker & Wagner (2006) for ethane is estimated to calculate c p with an uncertainty of 0.02 c p for most of the range of our measurements, increasing to 0.03 c p for temperatures below 130 K. The mean and maximum deviations of our data are (0.005 and 0.01) c p respectively from this reference EOS. Propane heat capacities were measured between ( and ) K at pressures of (1.1, 5.2 and 5.3) MPa. Fig. 5 shows a relative deviation plot of propane isobaric heat capacity measurements from the reference EOS calculated values. Lemmon et al. 6

7 (2009) estimate that their EOS calculates c p to an uncertainty of c p. However, this seems optimistic given the offset of the EOS from the adiabatic calorimetry data of Perkins et al. (2009) as well as the distribution of deviations for that data set. The mean and maximum deviations of the c p derived from Perkins et al. (2009) from the EOS of Lemmon et al. (2009) are (0.08 and 0.016) c p in the temperature range of (80 to 280) K. This is consistent with the mean and maximum deviations of our data from this EOS which are (0.009 and 0.017) c p, respectively. (c p -c p,ref )/c p,ref T/K Fig. 5: Relative deviations of the isobaric heat capacity of propane, c p, from the reference EOS (Lemmon et al., 2009) heat capacity, c p,ref., this work at 5.3 MPa;, this work at 5.2 MPa;, this work at 3.7 MPa;, this work at 1.1 MPa;,Kemp & Egan (1938); +, Perkins et al. (2009) (note the data of Perkins et al. was converted from c v using densities, coefficients of thermal expansion, and isothermal compressibilities calculated using the Lemmon et al. (2009) EOS in REFPROP 9.0) (c p -c p,ref )/c p,ref T/K Fig. 6: Relative deviations of the isobaric heat capacity of methane(1) + propane (2) mixtures, c p, from the REFPROP 9.0 calculated isobaric heat capacity using default pure fluid EOS and mixing rule and parameters, c p,ref., this work with x 1 = 0.81 at 6.0 MPa;, this work with x 1 = 0.82 at 5.2 MPa;, this work with x 1 = 0.81 at 4.7 MPa;, Yesavage (1970) with x 1 = 0.49 at 6.9 MPa. Calculated: ---, Peng Robinson EOS with x 1 = 0.81 at 6.0 MPa (calculated in Refprop 9.0); Peng Robinson EOS with x 1 = 0.82 at 5.2 MPa (calculated in Refprop 9.0);, GERG EOS with x 1 = 0.81 at 6.0 MPa; GERG EOS with x 1 = 0.82 at 5.2 MPa. Methane (1) + Propane (2) mixture heat capacities with x 1 = (0.81 and 0.82) were measured between ( and ) K at pressures of (4.7, 5.2 and/or 6.0) MPa. Fig. 6 shows a relative deviation plot of the measured isobaric heat capacities from the 7

8 REFPROP 9.0 calculated isobaric heat capacity using default pure fluid EOS and mixing rule and parameters. The mean and maximum deviations of our data from this EOS were ( and 0.018) c p, respectively. Also shown in Fig 6 are lines calculated at our experimental conditions using the Peng Robinson EOS. This EOS deviates by about 0.03 c p at 160 K but less than c p at 160 K. From our previous work (Hughes et al., 2011) and results of heat capacity measurements of toluene and heptane we estimate our combined uncertainty at the 95 % confidence limit (k 2) in the heat capacity to be about 0.02 c p. The reduction in the uncertainty of the heat capacity from our previous work from (0.03 to 0.02) c p is attributed to the effect of not having to remove the sample cells and the resulting improvement in the baseline scan repeatability. REFERENCES BUCKER, D. & WAGNER, W A Reference Equation of State for the Thermodynamic Properties of Ethane for Temperatures from the Melting Line to 675 K and Pressures up to 900 MPa. Journal of Physical and Chemical Reference Data, 35, FORTIER, J.-L. & BENSON, G. C Excess Heat Capacities of Binary Liquid Mixtures Determined with a Picker Flow Calorimeter. Journal of Chemical Thermodynamics, 8, GRINI, P. G., MAEHLUM, H. S., BRENDENG, D. & OWREN, G. A Enthalpy Increment Measurements on Liquid Ethane Between the Temperatures K and K, at Pressures ( 1.6, 3.20, and 5.07) MPa. Journal of Chemical Thermodynamics, 28, GROLIER, J. P. E. & FARADJZADEH, A Excess Heat Capacity. Toluene- Heptane System. International DATA Series, Selected Data on Mixtures, Series A: Thermodynamic Properties of Non-Reacting Binary Systems of Organic Substances, 132. HESTERMANS, P. & WHITE, D The Vapor Pressure, Heat of Vaporization and Heat Capacity of Methane from the Boiling Point to the Critical Temperature. Journal of Physical Chemistry, 65, HOLZHAUER, J. K. & ZIEGLER, W. T Temperature Dependence of Excess Thermodynamic Properties of n-heptane-toluene, Methylcyclohexane- Toluene, and n-heptane-methylcyclohexane Systems. Journal of Physical Chemistry, 79, HUGHES, T. J., SYED, T., GRAHAM, B. F., MARSH, K. N. & MAY, E. F Heat Capacities and Low Temperature Thermal Transitions of 1-Hexyl and 1- Octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide. Journal of Chemical and Engineering Data, 56, JONES, M. L., JR., MAGE, D. T., FAULKNER, R. C., JR. & KATZ, D. L Measurement of the Thermodynamic Properties of Gases at Low Temperature 8

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