J. of Supercritical Fluids 61 (2012) 34–43
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Supercritical pressure–density–temperature measurements on CO2 –N2 , CO2 –O2 and CO2 –Ar binary mixtures Mario Mantovani a,b,∗ , Paolo Chiesa a , Gianluca Valenti a , Manuele Gatti a , Stefano Consonni a a b
Politecnico di Milano – Dipartimento di Energia – Via Lambruschini 4, 20156 Milano, Italy LEAP – Via Nino Bixio 27, 29100 Piacenza, Italy
a r t i c l e
i n f o
Article history: Received 24 May 2011 Received in revised form 31 August 2011 Accepted 1 September 2011 Keywords: Carbon dioxide Binary mixture Equation of state Binary interaction coefficients Volumetric measurements Vibrating tube densimeter
a b s t r a c t This paper presents new supercritical volumetric measurements on three binary mixtures mainly composed of carbon dioxide. The interest in the tested mixtures derives primarily from carbon capture and storage applications. In particular, CO2 -rich streams with low amounts of nitrogen, oxygen and argon are representative of the flows that are treated by the compression units and the purification units employed in the oxy-fuel fired power plants. These flows are then transported from power plants to storage sites in supercritical conditions. For each type of binary mixture, two different molar compositions are here considered. Isothermal pressure–density–temperature measurements are performed for all the mixtures in a temperature range from 303 K to 383 K and in a pressure range from 1 MPa to 20 MPa by way of a vibrating tube densimeter-based apparatus. The experimental data are used subsequently for the regression of new binary interaction coefficients for two types of cubic equations of state, the Peng–Robinson and the Redlich–Kwong–Soave–Peneloux, and a multi-parameter equation, the Benedict–Webb–Rubin–Starling. The absolute deviations with respect to experimental data are in the range 2.10–2.56%, 3.05–4.07% and 1.71–1.97% for the three equations respectively. The results confirm the superiority of the multi-parameter equation of state over the cubic models in the supercritical region. © 2011 Elsevier B.V. All rights reserved.
1. Introduction 1.1. Background and motivation One of the strategies recognized by the scientific community as an effective way to reduce the greenhouse gases emissions in the atmosphere in the mid term is Carbon Capture and Storage (CCS) [1]. This strategy is particularly appropriate for the combustion of coal, an energy source whose use will probably increase in the future, due to its lower cost (compared with natural gas and oil) and its more uniform distribution around the world [2]. The specific CO2 emission, expressed as kg of CO2 per electric MWh produced, of a coal-fired power station is more than twice that of a natural gas combined cycle due to the higher carbon content with respect to its heating value and the lower conversion efficiency of the Rankine cycle. Therefore, application of techniques aiming at reducing CO2 emissions into the atmosphere is an interesting option for the coal fired future power stations. Different approaches can be devised to remove CO2 that can be readily sequestered. The
∗ Corresponding author at: Politecnico di Milano – Dipartimento di Energia – Via Lambruschini 4, 20156 Milano, Italy. Tel.: +39 0523 35 6895; fax: +39 0523 62 3097. E-mail address:
[email protected] (M. Mantovani). 0896-8446/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2011.09.001
oxy-fuel approach, which entails burning hydrocarbons with pure oxygen so that combustion products are ideally composed only of CO2 and water (being the latter easily separated by condensation), seems the most viable for pulverized coal fired Rankine cycle power stations because of a better efficiency and a lower capital cost than those of plants with post-combustion CO2 capture by amines [3,4]. However, due to the fact that oxygen is generally supplied by an air separation unit at a 95% purity level, nitrogen and argon are present in the flue gases. Oxygen is also present because, on one side, an excess of oxidizer is required to avoid formation of carbon monoxide and unburned hydrocarbons during the combustion and, on the other, air leakage into the boiler may also happen, particularly in the case of retrofitted boilers. Pollutants entrained in the flue gas, as particulate matter, sulfur and nitrogen oxides are instead removed by those techniques adopted in the conventional plants, whereas water is separated by cooling/condensation and drying operations [3,4]. The concentration of nitrogen, oxygen and argon in the purified stream must not exceed a defined level depending on the final use of the captured CO2 -rich stream, as explained by de Visser et al. [5]. An additional purification process, based on cryogenic separation, can be optionally adopted to take the stream at conditions suitable for transport purposes [6]. In any case, a mixture composed mainly of CO2 with some N2 , O2 and Ar has to be compressed up to supercritical conditions [7,8]. In order to
M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
simulate all the sub-processes that compose the overall purification and transport system, an accurate estimate of the thermodynamic properties of the treated fluids is required. Thermodynamic properties are not given in general as a set of experimental points mainly because the high number of different compositions and thermodynamic conditions require a time consuming and cost effective experimental activity. Equations of state models are instead used, but they still need to be calibrated on a limited amount of experimental data. Accurate predictions of the phase change properties require a calibration against vapor–liquid equilibria data rather than volumetric data [9,10]. In contrast, the calibration against volumetric experimental data can improve reliability of the equations of state in high pressure, single phase and supercritical regions. A recent detailed review on the availability of experimental data of CO2 -based mixtures relevant for CCS applications, carried out by Li et al. [11], identifies some knowledge gaps on volumetric measurements. In particular, Li et al. show that some bibliographic references are available for binary mixtures relevant for oxy-fuel CCS, mainly for the CO2 –N2 binary pair. However, most of these data, related to CO2 –N2 mixtures [12–15] and CO2 –O2 mixtures [16], are from the sixties and the seventies. In addition, all of them are Vapor–Liquid Equilibria data (VLE), exception made for one [15]. Two papers published in 1989 [17,18], report volumetric data for CO2 –N2 mixtures, but only for high N2 concentration (among the mixtures therein investigated, the one richest in CO2 has almost 50% of nitrogen molar content). For CO2 –Ar mixtures, a more recent publication is available but only on VLE measurements [19]. Therefore, even regarding those papers focused on volumetric measurements of binary pairs [15,17,18], the bibliographic analysis shows that the investigated mixtures are not so specifically representative of oxy-combustion applications. VLE data for CO2 –N2 –O2 ternary mixtures are available in one investigation [20]. No experimental data about quaternary CO2 –Ar–N2 –O2 mixtures needed for the model calibration, detailed by the authors in [21], seem to be available in literature. This lack of data spurred the authors to set up an experimental apparatus to retrieve such information. The first results of this activity regarding two components CO2 based mixtures are presented in the present paper.
1.2. Equations of state models The choice of the Equations Of State (EOS) is carried out by considering two main factors. The first one is how much a model is suitable for the description of supercritical fluids. The second one is the availability of the models in commercial codes for the simulation of complex power stations or chemical plants. In Mantovani’s dissertation [9], an extensive evaluation of the capability of several cubic models to predict the volumetric behavior of pure carbon dioxide is performed. Results show that Peng–Robinson (PR) model [22] yields the lowest average absolute deviation with respect to the values predicted by the Span and Wagner method [23], achieving an accuracy better than 0.05%. Furthermore, the same calculations are performed for the two binary mixtures containing CO2 and N2 considered by Duarte Garza et al. [15]. Also in this case the Peng–Robinson equation of state achieves the lowest average absolute deviation. In the present investigation, the Redlich–Kwong equation [24] with the improvements introduced by Soave [25] and the volume translation introduced by Peneloux [26] (the equation is thus indicated by the acronym RKSP) is also considered because, despite not as accurate as Peng–Robinson model for the supercritical conditions, it provides reliable predictions for the vapor–liquid equilibria calculations [27].
35
Relation (1) reports the mathematical expression of the RKSP model: p=
RT a˛(TR , ω) − (v + c) − b (v + c)(v + c + b)
(1)
while relation (2) reports that of the PR model: p=
RT
v−b
−
a˛(TR , ω)
(2)
v2 + 2bv − b2
where p is the pressure, T the temperature, v the specific volume, R the gas constant, a the energy parameter, b the covolume, c the volume translation parameter, ˛ a dimensionless function, ω the acentric factor and the subscript R indicates reduced properties. The energy parameter and the covolume of each pure component are calculated according to the formulations proposed by Soave [25] for RKSP and by Li and Yan [27] for PR. These parameters depend on the pure component properties: the critical temperature, the critical pressure and the acentric factor. The translation parameter c used in RKSP is calculated according to Peneloux et al. [26] with the additional pure species parameter, called Rackett compressibility factor, as defined by Spencer and Danner [28]. The formulation of the alpha function employed in both cubic models is the one by Soave, adopting again the coefficients proposed by Soave himself [25] for the RKSP and those by Li and Yan [27] for the PR. The pure component properties are retrieved from the default database of Aspen Properties [29], namely Pure 20, and included in Table 1. Mixture parameters are obtained from pure component parameters and molar compositions by means of mixing rules. As suggested by Reid et al. [10] as well as by Sengers et al. [30], linear mixing rules are used to calculate the covolume and translation parameters of the mixture. The calculation of the energy parameter is instead more complex and requires binary interaction parameters kij that are defined depending on the possible pairs of species present in the mixture [10,30]: a=
N N
xi xj
ai aj (1 − kij )
(3)
i=1 j=1
where the subscripts i and j refer to the pure component properties and xi the i-th component molar fraction. In particular, it holds true that kij equals kji . No binary interaction parameters are considered for the covolume calculation. In addition to the mentioned cubic equations of state, a so-called multi-parameter EOS is here considered because it is expected to achieve a better accuracy. Benedict along with Webb and Rubin [31] proposed a multi-parameter model that later Starling [32] modified yielding an eleven parameters equation (indicated by BWRS):
p = RT + B0 RT − A0 −
+˛ a +
d T
6 +
C0 D0 E0 + 3 − 4 T2 T T
2 + bRT − a −
c3 (1 + 2 ) · exp(−2 ) T2
d T
3 (4)
The eleven composition-dependent parameters (A0 , B0 , C0 , D0 , E0 , a, b, c, d, ˛, ) are calculated according to the mixing rules reported by Starling himself [32]. The pure component constants appearing in the definition of such parameters are calculated by the Aspen Physical Property System with the generalized correlations given by Han and Starling in [33] and using the critical temperatures, the critical volumes and the acentric factors reported in Table 1. It is worth noting that only the mixing rules defining A0 , C0 , D0 and E0 are influenced by the value of the binary interaction parameter kij . For the assigned EOS, the capability to properly describe the behavior of a mixture depends on the possibility to calibrate the
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Table 1 Equation of state parameters. Pure substance parameter
Mw [kg/kmol] Tc [◦ C] pc [MPa] Vc [m3 /kmol] ω ZRA
Substance
Equation of state
CO2
N2
O2
Ar
44.0098 31.06 31.00 7.383 7.376 0.094 0.223621 0.231 0.27256
28.01348 −146.95 −147.00 3.400 3.394 0.08921 0.0377215 0.045 0.28997
31.9988 −118.57 −118.38 5.043 5.080 0.0734 0.0221798 0.019 0.28924
39.948 −122.29 −122.44 4.898 4.864 0.07459 0 0 0.2931
binary interaction parameters kij on a reliable set of experimental data. In the next section the experimental activities and theoretical procedure adopted for kij calibration are described.
Table 2 Mixture molar composition.
CO2 N2 O2 Ar
2. Experimental method 2.1. Mixture preparation The mixture preparation requires the successive introduction in a tank of the pure species that compose the mixture [34]. Since the molecular weight of the single chemical specie is known, from the measurement of the weight of the tank, the molar composition of the mixture can be calculated. First, the tank is connected to the supply line and a vacuum pump. Vacuum conditions are created inside the filling circuit and the tank. A pressure lower than 10 Pa is reached. The own weight of the tank is then measured by means of a balance manufactured by Orma (model bc) with an uncertainty on mass measurement equal to ±10−3 g. The less volatile fluid (in this case CO2 ) is then introduced because it is supplied at lower pressure respect to the other substances. The liquid phase must be introduced into the tank in order to maximize the mass supplied. To introduce liquid CO2 inside the empty tank a cooling circuit is used in the manner shown in Fig. 1. This operation is possible because pure carbon dioxide critical temperature is sufficiently high. The amount of carbon dioxide introduced is calculated as a difference of the actual weight and the one measured at the former step. The introduction of further chemical species is performed in the same way already described for the introduction of carbon dioxide. The only difference is that in this case no cooling circuit is needed
RKSP, PR, BWRS RKSP, BWRS PR RKSP PR BWRS RKSP, BWRS PR RKSP
N1
N2
O1
O2
A1
A2
0.9585 0.0415 – –
0.9021 0.0979 – –
0.9393 – 0.0607 –
0.8709 – 0.1291 –
0.9692 – – 0.0308
0.8306 – – 0.1694
because these species (N2 , O2 or Ar) are introduced in gaseous phase. On one hand this procedure allows to precisely know the final composition of the mixture prepared in the tank, however on the other it does not permit an easy control of the single added species, so that several filling attempts are needed to get a mixture whose composition results to be close enough to the desired one. For each couple of pure species, two different mixtures are investigated by changing the molar fraction of the non-condensable species. To easily refer to the different mixture samples some acronyms are used. All the acronyms and their corresponding molar compositions are resumed in Table 2. Carbon dioxide is supplied by Rivoira S.p.A. at a purity level higher than 99.998%. Nitrogen, oxygen and argon too are furnished by the same supplier at a slightly higher purity level higher than 99.999%. The average uncertainty on the calculated molar fraction is ±2 × 10−4 . 2.2. Experimental apparatus The scheme of the experimental apparatus is shown in Fig. 2, while the labels used to indicate the different components are defined in Table 3. The apparatus allows to perform simultaneous
Fig. 1. Tank loading circuit.
M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
37
Fig. 2. Experimental apparatus.
measurements of density, pressure and temperature and reconstructing the volumetric behavior of a single phase fluid substance. Temperature measurements are provided by two Pt100 probes (PP1 and PP2). Probes and the related measurement chain are calibrated by the Politecnico di Milano calibration center. The uncertainty on temperature measurements is lower than ±0.05 K. Pressure measurements are provided by two sensors (VPT) with upper pressure limits equal to 6 MPa and 25 MPa. Both of them are supplied by GE Druck and are part of the PTX611 series. They
Table 3 Acronyms of the apparatus components. Label
Component
DA DL1 DL2 DL3 EH1 EH2 HE HP LC MA MT PC PG1 PG2 PP1 PP2 PT RD TB TC1 TC2 TV V VTD VP
Personal computer for data acquisition Data logger for temperature probes and pressure transmitters Data logger for the vibrating tube densimeter Data logger for the vacuum sensors Electric heating resistance of VPT block Electric heating resistance of tube heater block Heat exchanger Hand pump Loading cell Manometer Main thermoregulated bath Pressurizing cell Pirani gauge 1 for vacuum measurements Pirani gauge 2 for vacuum measurements Platinum probe 1 Platinum probe 2 Pressure transmitters Rupture disk Thermoregulated bath Thermocouple 1 Thermocouple 2 Thermoregulated bath for vibrating tube densimeter Valves Vibrating tube densimeter Vacuum pump
are calibrated against a dead weight pressure balance (supplied by Scandura), which in its turn is calibrated by the Scandura calibration center in the pressure ranges 1–6 MPa and 6–20 MPa. Corrections for local temperature, sensor position and local gravity are applied. The resulting uncertainty on pressure measurements is ±0.03% of the read value in all the pressure range. Both temperature probes and pressure sensors are connected to an Agilent data logger model 34970A (DL1). The vibrating tube densimeter (VTD) is the model DMA 512 – HPM manufactured by Anton Paar. The vibrating periods are measured by an Anton Paar device mPDS 2000 V3 (DL2). The uncertainty on vibrating period data is ±10−8 s. Vibrating periods are then converted into density values by means of the forced path mechanical calibration model proposed by Richon and Bouchot [35] and described also by Romani et al. [36]. The model formulations in the two papers are slightly diverse. The difference is due to the fact that in [35] the effect of the external pressure on the tube is considered negligible, while in [36] it is taken into account. In this paper the formulation proposed by Richon and Bouchot [35] is used because calculations show that such effect is negligible in the considered pressure range and it is not possible to measure accurately enough the pressure of the thermoregulating fluid inside the vibrating tube densimeter. The model parameters are derived from a study by Sanmamed et al. [36]. Due to the low effect of the isothermal linear expansion coefficient [9], this parameter is kept constant. Calibrations are carried out using pure carbon dioxide as reference fluid whose density values are calculated using the Span and Wagner model. The global uncertainty on density measurements resulting from the conversion of the vibrating period in density values, is ±0.2 kg/m3 , over the whole range of measurements [9,35]. The temperature is maintained at the desired value inside the vibrating tube densimeter and inside the measurement circuit by two thermoregulated baths. Bath T1 is produced by Huber, model CC3-K12 with a temperature range from −20 ◦ C to 200 ◦ C. Bath TB
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M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
Fig. 3. Experimental and calculated (by means of the BWRS model) p––T data. In the left column from the top to the bottom N2. O2 and A2 mixture measurements are plotted. In the right column from the top to the bottom N1. O1 and A1 mixture measurements are plotted. experimental 303.22 K, experimental 323.18 K, experimental 343.15 K, *experimental 363.15 K, 䊉 experimental 383.14 K; - BWRS.
is by Huber, model CC1-Variostat with a temperature range from −20 ◦ C to 150 ◦ C. All the regulated baths have a stability of ±0.02 K. Vacuum inside the measurement circuit is achieved with a vacuum pump (VP, Wigam, model RS 9D). When the vacuum pump works for several hours before a test, a pressure level lower than 200 Pa is obtained in the most remote point from the suction end. 2.3. Experimental procedure The mixture sample is pressurized up to approximately 20 MPa by means of a nitrogen circuit, whose pressure level can be controlled by means of the hand pump HP. This pressure level guarantees that only a single phase fluid exists inside the loading cell and, hence, the fluid entering the measurement circuit remains at the same initial composition. For supercritical measurements, TB and T1 baths are set at the temperature value of the desired isothermal line. In contrast to investigations similar to the present [37–41], no temperature differences are here required because no
phase change occurs during the experiments. The measurement circuit is evacuated employing the vacuum pump VP keeping the valves V5, V6 and V9 open. The pump works for several hours until low enough pressures are reached inside the measurement circuit and, then, all the valves are closed. The filling procedure starts when V4 is completely opened and V6/V6R are slightly opened in order to set the pressurization speed at values lower than 0.005 MPa/s, as suggested in other works [37–41]. Low pressurizing speed is required to approximate successive equilibrium conditions. Pressure, temperature and density are measured every second. In this way the number of experimental data for each isothermal line is equal to several thousands. During the transient process, when the pressure approaches 6 MPa, valve V12 is closed to preserve the integrity of the low pressure transmitter. When the pressure reaches the 20 MPa value, valve V4 is closed and the test ends. The measurement circuit is then evacuated by opening valves V9 and V10B. V12 must be opened to release the fluid retained in that branch of the circuit. Pressure and density sampled during depressurization match well the data collected along the pressurizing
M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
39
Fig. 4. Density relative percentage deviations plotted against pressure at 303.22 K (upper plot), 343.15 K (central plot) and 383.14 K (lower plot) for mixture N2 and for the three equation of state models. BWRS is indicated by the continuous line. PR dashed line and RKSP dot and dashed line.
phase. To measure another isothermal line, the procedure must be repeated from the beginning.
3. Results and discussion 3.1. Experimental results and equations of state calibration The new experimental measurements are shown in Fig. 3 as a plot of pressure against density at five different temperatures: 303.22 K, 323.18 K, 343.15 K, 363.15 K, 383.14 K. Dots represent part of the experimental data given at a pressure step of about 1 MPa. Continuous lines represent the density values predicted by the BWRS model, which is chosen because its higher accuracy as
indicated below. For ease of use, the experimental data are also reported in Tables 4–9. Subsequently, the data are utilized for the calibration of the binary interaction parameters employing Peng–Robinson, Redlich–Kwong–Soave–Peneloux and Benedict–Webb–Rubin–Starling equations of state. The maximum likelihood algorithm is used to calculate the optimal value of kij for each mixture and equation of state with the help of the commercial code Aspen Properties [29]. It consists in the minimization of the following function: 1 ˚= N N
i=1
calc − exp
2 (5)
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M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
Table 4 Mixture N1 experimental data. T = 303.22 K
T = 323.18 K
T = 343.15 K
T = 363.15 K
T = 383.14 K
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
1.001 2.000 3.001 4.001 5.001 6.000 7.001 8.001 9.001 10.002 11.001 12.001 13.001 14.002 15.004 16.001 17.003 18.001 19.005 20.001
17.91 37.75 60.12 85.65 116.38 155.97 213.29 330.92 544.54 634.72 683.11 715.67 740.35 759.32 774.69 788.63 801.56 813.51 824.42 833.58
1.001 2.004 3.000 4.001 5.003 6.001 7.001 8.001 9.001 10.001 11.002 12.001 13.001 14.001 15.002 16.001 17.001 18.003 19.002 20.001
16.79 34.95 54.72 76.45 100.80 128.50 160.99 200.41 249.73 312.81 389.63 467.33 532.26 582.79 619.85 649.44 673.37 693.69 711.83 728.16
1.003 2.001 3.001 4.002 5.003 6.002 7.000 8.001 9.000 10.001 11.002 12.000 13.000 14.000 15.001 16.001 17.003 18.001 19.002 20.004
15.20 32.23 50.12 68.52 89.33 111.99 136.56 163.71 193.75 227.23 264.48 305.25 348.75 393.00 435.95 475.71 510.93 541.92 569.42 593.72
1.002 2.002 3.000 4.002 5.001 6.001 7.002 8.005 9.003 10.001 11.002 12.002 13.001 14.000 15.001 16.002 17.001 18.001 19.001 20.002
14.03 30.39 46.57 63.73 81.83 101.20 121.60 143.48 166.64 191.38 217.83 245.86 275.07 305.51 336.55 367.63 397.82 426.94 454.58 480.85
1.002 2.001 3.000 4.003 5.003 6.000 7.003 8.001 9.002 10.001 11.002 12.002 13.002 14.002 15.002 16.001 17.001 – – –
13.08 27.55 42.75 58.60 74.95 92.10 109.94 128.59 148.16 168.52 189.95 212.12 234.83 258.37 282.34 306.66 331.02 – – –
Table 5 Mixture N2 experimental data. T = 303.22 K
T = 323.18 K
T = 343.15 K
T = 363.15 K
T = 383.14 K
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
1.000 2.000 3.001 4.001 5.000 6.002 7.000 8.001 9.000 10.003 11.002 12.003 13.000 14.002 15.002 16.001 17.005 18.001 19.003 20.001
17.42 36.62 58.04 82.12 110.12 144.00 187.15 248.76 341.94 453.92 541.32 599.42 640.25 671.43 695.05 715.04 731.98 747.85 761.75 773.45
1.002 2.000 3.003 4.001 5.001 6.000 7.002 8.001 9.000 10.001 11.002 12.001 13.000 14.002 15.001 16.000 17.001 18.000 19.001 20.001
16.15 33.57 52.68 73.32 95.85 121.04 149.69 182.41 220.69 265.42 316.33 371.76 426.12 475.97 519.15 554.51 584.29 610.03 632.79 652.97
1.001 2.003 3.001 4.001 5.003 6.003 7.003 8.001 9.002 10.000 11.001 12.002 13.001 14.001 15.001 16.000 17.002 18.002 19.001 20.002
14.29 30.68 47.56 66.13 85.97 107.13 129.96 154.43 181.20 210.13 241.54 275.24 310.56 346.77 382.74 417.63 450.07 480.07 507.72 532.73
1.001 2.001 3.000 4.003 5.003 6.001 7.001 8.004 9.002 10.001 11.001 12.000 13.002 14.000 15.001 16.001 17.003 18.000 19.001 20.001
13.43 28.57 44.28 61.87 79.14 97.56 116.91 137.17 158.53 181.15 204.87 229.68 255.53 282.04 309.00 336.03 362.76 388.68 413.59 438.02
1.000 2.003 3.001 4.001 5.002 6.001 7.000 8.003 9.001 10.000 11.001 12.002 13.000 14.002 15.001 16.001 17.001 18.001 19.002 20.002
12.48 26.68 41.50 56.89 72.61 88.97 106.00 123.69 142.03 161.18 180.90 201.21 222.01 243.35 264.96 286.73 308.77 330.77 352.16 373.05
Table 6 Mixture O1 experimental data. T = 303.22 K
T = 323.18 K 3
T = 343.15 K 3
T = 363.15 K 3
T = 383.14 K 3
p [MPa]
[kg/m ]
p [MPa]
[kg/m ]
p [MPa]
[kg/m ]
p [MPa]
[kg/m ]
p [MPa]
[kg/m3 ]
1.003 2.004 3.000 4.000 5.002 6.003 7.000 8.001 9.002 10.001 11.002 12.004 13.000 14.000 15.002 16.001 17.001 18.001 19.006 20.003
17.93 37.39 59.69 84.80 114.54 152.04 203.61 289.70 461.14 588.57 651.97 691.78 721.43 743.52 761.68 777.53 791.43 804.78 816.57 826.46
1.000 2.003 3.003 4.002 5.001 6.001 7.003 8.001 9.001 10.001 11.000 12.001 13.000 14.000 15.001 16.001 17.001 18.000 19.001 20.003
16.79 34.81 54.28 75.65 99.33 126.15 156.99 193.32 237.43 291.61 356.07 426.04 491.28 543.71 586.85 620.78 648.03 671.45 691.46 709.44
1.020 2.006 3.001 4.010 5.002 6.001 7.001 8.003 9.001 10.003 11.000 12.001 13.001 14.002 15.003 16.001 17.001 18.002 19.002 20.002
15.27 31.71 48.82 67.22 88.50 110.67 134.86 161.06 189.88 222.01 257.28 295.23 335.99 377.88 418.59 457.59 493.83 525.51 553.76 579.12
1.004 2.010 3.011 4.006 5.000 6.000 7.003 8.002 9.004 10.002 11.001 12.000 13.001 14.000 15.003 16.001 17.001 18.001 19.001 20.003
13.75 29.69 45.05 62.67 81.48 100.75 120.60 142.17 164.80 188.99 214.48 241.38 269.73 299.13 329.23 359.23 388.81 417.42 444.67 471.17
1.009 2.002 3.001 4.001 5.002 6.001 7.000 8.001 9.000 10.000 11.000 12.002 13.002 14.002 15.001 16.000 – – – –
12.82 27.15 42.34 58.12 74.46 91.55 109.21 127.60 146.88 167.03 187.90 209.57 231.83 254.66 278.16 301.72 – – – –
M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
41
Table 7 Mixture O2 experimental data. T = 303.22 K
T = 323.18 K
T = 343.15 K
T = 363.15 K
T = 383.14 K
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
1.001 2.001 3.000 4.001 5.002 6.001 7.001 8.002 9.003 10.000 11.003 12.003 13.002 14.004 15.001 16.003 17.003 18.005 19.001 20.001
16.96 35.97 56.91 80.03 106.48 137.25 175.07 222.69 286.10 369.36 453.81 524.28 577.68 618.47 651.77 678.16 700.31 719.80 737.04 751.82
1.004 2.002 3.004 4.006 5.001 6.001 7.002 8.002 9.002 10.001 11.000 12.001 13.000 14.001 15.001 16.002 17.001 18.001 19.003 20.001
15.67 33.23 51.85 71.91 93.51 117.62 144.29 174.22 208.25 246.73 289.90 336.79 385.09 432.34 475.61 514.04 547.48 577.29 602.71 625.50
1.000 2.003 3.001 4.001 5.001 6.006 7.003 8.005 9.000 10.001 11.001 12.002 13.002 14.003 15.001 16.003 17.001 18.001 19.001 20.001
14.27 30.63 47.70 64.98 84.15 104.83 126.59 149.97 174.89 201.76 230.56 261.07 293.20 326.31 359.74 392.71 424.32 453.96 481.53 507.09
1.000 2.002 3.002 4.000 5.002 6.003 7.002 8.003 9.000 10.003 11.000 12.000 13.000 14.000 15.002 16.001 17.001 18.000 19.001 20.003
13.33 28.81 44.41 60.55 77.51 95.46 114.20 133.65 154.09 175.66 197.98 221.25 245.22 270.00 295.20 320.51 345.47 369.97 394.15 417.75
1.002 2.003 3.003 4.004 5.005 6.001 7.003 8.003 9.000 10.002 11.000 12.001 13.000 14.003 15.001 16.002 17.001 18.000 19.001 20.001
11.84 25.91 40.57 55.67 71.22 87.23 103.83 120.96 138.66 157.10 176.05 195.51 215.35 235.59 256.19 276.93 297.68 318.73 339.37 359.41
Table 8 Mixture A1 experimental data. T = 303.22 K
T = 323.18 K
T = 343.15 K
T = 363.15 K
T = 383.14 K
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
p [MPa]
[kg/m3 ]
p [MPa]
[kg/m3 ]
p [MPa]
1.003 2.001 3.001 4.000 5.001 6.002 7.000 8.001 9.002 10.005 11.001 12.002 13.001 14.001 15.003 16.001 17.001 18.004 19.006 20.007
18.14 38.32 61.25 87.64 119.81 161.73 228.26 455.32 643.49 699.66 738.09 763.71 783.20 799.34 813.25 825.60 837.22 847.99 858.59 866.61
1.001 2.002 3.003 4.001 5.000 6.000 7.000 8.001 9.000 10.000 11.000 12.002 13.003 14.002 15.003 16.003 17.002 18.003 19.003 20.002
16.99 35.39 55.47 77.71 102.51 131.35 165.37 207.32 260.66 332.11 417.56 502.33 567.42 616.14 651.85 679.86 702.82 722.64 739.79 755.35
1.001 2.003 3.000 4.001 5.003 6.000 7.004 8.002 9.000 10.001 11.001 12.001 13.003 14.006 15.003 16.004 17.001 18.001 19.001 20.003
15.84 32.95 50.83 69.03 90.50 113.83 139.40 167.77 199.54 235.38 275.77 320.76 368.58 416.20 462.14 504.43 541.21 573.06 600.37 624.25
1.005 2.005 3.002 4.002 5.003 6.002 7.001 8.003 9.001 10.003 11.003 12.001 13.002 14.002 15.003 16.001 17.002 18.001 19.001 20.004
14.76 30.57 47.08 64.57 83.15 103.02 124.09 146.77 170.92 196.85 224.69 254.32 285.79 318.50 351.99 384.62 417.31 448.33 477.32 505.01
1.010 2.001 3.003 4.001 5.003 6.001 7.003 8.003 9.000 10.003 11.001 12.000 13.001 14.000 15.001 16.000 17.001 18.002 19.001 20.003
14.31 28.84 44.32 60.28 76.90 94.35 112.51 131.60 151.50 172.55 194.39 217.23 240.85 265.19 290.23 315.41 340.76 366.36 391.23 415.12
Table 9 Mixture A2 experimental data. T = 303.22 K
T = 323.18 K 3
T = 343.15 K 3
p [MPa]
[kg/m ]
p [MPa]
[kg/m ]
1.002 2.003 3.000 4.003 5.002 6.002 7.002 8.003 9.001 10.000 11.000 12.002 13.002 14.001 15.003 16.001 17.001 18.000 19.001 20.004
17.70 37.39 58.81 82.66 109.64 141.43 179.99 229.06 294.03 377.70 465.25 538.57 594.05 635.79 668.49 695.11 717.84 737.35 755.04 769.49
1.036 2.003 3.005 4.002 5.001 6.007 7.000 8.001 9.000 10.001 11.001 12.002 13.002 14.000 15.005 16.001 17.003 18.002 19.007 20.005
16.39 34.27 53.07 73.42 95.22 119.39 145.74 175.11 208.10 244.80 285.24 328.93 373.81 418.72 461.68 500.31 535.06 565.87 593.01 617.44
p [MPa] 1.019 2.000 3.001 4.000 5.001 6.001 7.003 8.005 9.004 10.001 11.001 12.004 13.002 14.004 15.003 16.003 17.003 18.001 19.006 –
T = 363.15 K p [MPa] 15.29 31.41 47.86 66.41 85.94 106.64 128.43 151.85 176.67 203.17 231.27 261.01 291.94 323.97 356.44 388.27 419.02 448.22 476.05 –
3
[kg/m ] 1.004 2.001 3.001 4.001 5.002 6.001 7.000 8.001 9.000 10.003 11.001 12.001 13.001 14.002 15.001 – – – – –
T = 383.14 K p [MPa] 13.84 29.57 45.56 62.17 79.51 97.51 116.44 136.15 156.77 178.32 200.65 223.90 247.96 272.48 297.60 – – – – –
[kg/m3 ]
p [MPa]
1.004 2.000 3.001 4.001 5.001 6.000 7.001 8.001 9.003 10.000 11.000 12.001 13.000 14.002 15.001 16.002 17.003 18.001 19.004 20.003
12.62 26.98 41.97 57.44 73.27 89.50 106.40 123.74 141.71 160.36 179.40 199.01 218.97 239.30 259.93 280.74 301.71 322.56 343.41 363.60
42
M. Mantovani et al. / J. of Supercritical Fluids 61 (2012) 34–43
Table 10 Binary interaction parameters regressed against the new experimental data in the supercritical region and percentage average absolute deviations (defined as absolute value and indicated by AAD%) between the calculated values and the experimental samples. EOS
CO2 –N2 kij
AAD%calc−exp
kij
AAD%calc−exp
kij
AAD%calc−exp
also for carbon dioxide based binary mixtures. Between the cubic models, Peng–Robinson is the most accurate. Further developments in this activity will be the extension of the measurements to the subcritical region for mixtures of similar composition. The availability of new data at a lower temperature is extremely important to study long range transportation of the carbon dioxide rich streams to the sequestration sites.
PR RKSP BWRS
−0.097 −0.512 −0.037
2.10 3.05 1.71
0.151 0.169 0.057
2.37 3.92 1.97
−0.031 0.408 −0.041
2.56 4.07 1.75
Acknowledgements
CO2 –O2
CO2 –Ar
where N is the number of experimental data, calc is the density value predicted by the model, exp is the measured density and is the uncertainty on density measurements, described in Section 2.2. Table 10 reports the new binary interaction parameters and the percentage average absolute deviation (AAD%calc−exp ) between the densities calculated by means of the calibrated models and the experimental ones. The percentage average absolute deviations are as follows:
calc − exp 1 100 N exp N
AAD%calc−exp =
(6)
i=1
It can be seen that the BWRS model performs better than the cubic models for each case. Between the cubic models evaluated, Peng–Robinson approximates the experimental data better than the RKSP. The results obtained are in good agreement with the analysis carried out in Mantovani’s dissertation [9] for both pure carbon dioxide and binary mixtures (for mixtures binary interaction coefficients were regressed on VLE data). In further agreement with the dissertation [9], all the models seem to work better for CO2 –N2 mixtures rather than for the other binary mixtures. Fig. 4 focuses on part of the results resumed in Table 10 in terms of relative density percentage deviation for mixture N2 against pressure at fixed temperatures (303.22 K, 343.15 K and 383.14 K) for the three considered equation of state models. Mixture N2 is chosen for the figure because with this mixture models achieve their highest accuracy. The temperatures are chosen in order to cover the whole temperature range. At 303.22 K all the models yield higher errors in the surroundings of the critical point, RKSP being the worst one. BWRS model is better in the single phase regions far from the critical point. At 343.15 K and at 383.14 K the percentage error tends to increase at the lower pressures because density deviation maintain the same order of magnitude in the whole pressure field, while density changes one order of magnitude. At pressures lower than 11 MPa RKSP is more accurate than BWRS, while at pressures higher than 17 MPa PR is more accurate than BWRS. In average BWRS is a better compromise over the whole pressure field. 4. Conclusions New p––T experimental data are presented for six carbon dioxide-based mixtures in the supercritical region at five different temperature levels. Two mixtures contain nitrogen, two oxygen and two argon, which are the main contaminants in the flue gases produced by oxy-fuel combustion processes. Starting from the experimental data, new binary interaction coefficients are regressed for the Peng–Robinson, Redlich–Kwong– Soave–Peneloux and Benedict–Webb–Rubin–Starling equations of state. In agreement with other investigation, this work confirms that the BWRS model allows a more accurate prediction of the volumetric behavior in the supercritical field respect to the cubic models
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