- Email: [email protected]
Thermodynamic characterization of deepwater natural gas mixtures with heavy hydrocarbon content at high pressures
J. Chem. Thermodynamics 82 (2015) 134–142
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Thermodynamic characterization of deepwater natural gas mixtures with heavy hydrocarbon content at high pressures Mert Atilhan a,⇑, Santiago Aparicio b,⇑, Saquib Ejaz c, Jingjun Zhou c, Mohammed Al-Marri a,d, James J. Holste c, Kenneth R. Hall c,⇑ a
Department of Chemical Engineering, Qatar University, Doha, Qatar Department of Chemistry, University of Burgos, Burgos, Spain Chemical Engineering Department, Texas A&M University, College Stations, TX, USA d Gas Processing Center, Qatar University, Doha, Qatar b c
a r t i c l e
i n f o
Article history: Received 22 May 2014 Received in revised form 5 October 2014 Accepted 12 October 2014 Available online 31 October 2014 Keywords: Natural gas Density Phase envelope Phase equilibrium Equation of state
a b s t r a c t This paper includes high-accuracy density measurements and phase envelopes for deepwater natural gas mixtures. Mixtures primarily consist of (0.88 and 0.94) mole fraction methane and both mixtures includes heavy components (C6+) more than 0.002 mole fraction. Experimental density and phase envelope data for deep and ultra-deep reservoir mixtures are scarce in literature and high accuracy measurements for such parameters for such natural gas-like mixtures are essential to validate the benchmark equations for custody transfer such as AGA8-DC92 and GERG-2008 equation of states (EOS). Thus, in this paper we report density and phase envelope experimental data via compact single-sinker magnetic suspension densimeter and isochoric apparatuses. Such data help gas industry to avoid retrograde condensation in natural gas pipelines. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Natural gas is known as the most environmentally friendly fossil fuel found in abundant quantities [1]. Given increased activity in petroleum, cryogenic, liquefied natural gas (LNG) and natural gas businesses, accurate knowledge of the thermodynamic property estimates such as density, viscosity, heating value, compressibility factor, etc. . . Accurate measurements of such quantities are necessary to design engineering processes and determine operational performances [2]. Custody transfer of natural gas requires knowledge of the phase behavior of the fluid in the pipelines and a basic assumption in custody transfer of natural gas is that the gas remains in a single phase during the transportation and at measurement stages [3]. Hydrocarbon dew points for natural gas mixtures are important in contractual specifications throughout the supply chain. Avoiding the formation of liquid in natural gas is critically important. To avoid two-phase flow, it is essential to have reliable data or predictions of the cricondenbar (CB) and cricondentherm (CT). Phase boundaries of natural gas mixtures are sensitive to small fractions ⇑ Corresponding authors. E-mail addresses: [email protected] (S. Aparicio), [email protected] (K.R. Hall). http://dx.doi.org/10.1016/j.jct.2014.10.018 0021-9614/Ó 2014 Elsevier Ltd. All rights reserved.
(M.
Atilhan),
[email protected]
of heavier components, and prediction of the dew point curve with the current EOS appears unreliable [4]. Most common widely used equations that are used in predicting the density and phase behavior of multicomponent gas mixtures in oil and gas industry during custody transfer are simple cubic EOS such as Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Patel–Teja (PT), and Benedict–Webb–Rubin (BWR). However, such simple bi and tri parametric EOS mostly fails to predict the phase behavior for multi-component mixtures and gives large deviations especially at the retrograde condensation region [5,6]. Moreover Hall– Yarborough [7], and Dranchuk et al. [8] and Dranchuk [9] are other reputable and used EOS, but these EOS also lack the ability to predict phase boundaries as well. On the other hand cubic EOS as mentioned above have the usual problem for predicting properties at high densities for both liquids and supercritical fluids simply because of the reason lies in the nature of the intermolecular forces. As molecules touches to each other repulsive forces becomes dominant and increases exponentially with the distance of the molecules; which is another way of defining incompressible condition for liquid phase. On contrast, at distances greater than the usual separation distance between the molecules in a liquid state, the force is attractive. Molecules are deformed as they are pushed closer under pressure, thus their repulsive behavior rapidly increases. Such rapid increase in the
135
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
repulsive intermolecular force with distance requires a dependence on density function that is greater than the cubic relation. For industrial applications of natural gas such as pipeline distribution, choice of EOS plays an important role. Setting up the financial and legal aspects of the custody transfer is highly depended on the selection of EOS, which plays an important role on quantification at the measurement stations through the pipelines. Such requirement has led to parties to use ‘‘standard’’ equations or procedures with tailor made purposes, with a wider range of applicability and minimized prediction errors. Thus, it has been an ongoing interest of academia and industry to develop and fine-tune new EOS that would predict thermodynamic properties of multicomponent gas mixtures of interest for wide temperature and pressure ranges. Industry benchmark EOS that are used for this purpose are known as AGA8-DC92 EOS [10] and recently developed GERG-2008 EOS [11]. The AGA8-DC92 EOS was considered as a thermal equation of state explicit in compression factor, which allows the calculation of thermodynamic properties of multi-component gas mixtures (e.g. natural gases) consisting of up to 21 components. On the other hand, GERG2008 EOS is more advanced, complicated EOS and yet to be known as better EOS that can handle mixtures of 21 components with the addition of n-nonane, n-decane, and hydrogen sulfide to the preceding version GERG-2004 EOS. These standard EOS have progressively improved in physical accuracy over the range of pressures, temperatures, and compositions occurring in US and EU transmission pipelines and reservoirs. They have tended to be almost purely empirical. However, newly explored reservoirs with unprecedented compositions made researchers in both academia and industry to seek for the limits of these EOS. For this purpose, this work includes natural gas-like mixture that represents Gulf of Mexico reservoir fluids with heavy component composition more than 0.2% in mole. Collected experimental data were compared with AGA8-DC92 EOS and GERG-2008 EOS for density and most common cubic EOS for phase behavior. 2. Experimental This work uses a magnetic suspension densimeter (MSD) for accurate density measurements and an isochoric apparatus for phase envelope measurements. The sample mixtures have (0.88 and 0.94) mol fraction of methane with numerous other components as described below. Mixtures were named according to their methane mole fraction as M88C1 and M94C1. 2.1. Materials Accurate Gas Products prepared the synthetic mixture used in this work with the composition as presented in table 1. The gas mixture was prepared gravimetrically with traceability to the National Institute of Standards and Technology (NIST). The estimated uncertainty of the gas mixture is 0.12%, assuming that the uncertainty comes from the measuring balance and the impurities of the pure gases used in the preparation of the sample. 2.2. Apparatus The isochoric apparatus was designed and built to operate temperatures between (100 and 500) K with pressures up to 35 MPa. Apparatus uses an old but established technique for determining phase loops, which is based on the observation of the change on the slope of an isochore as it crosses the phase boundary. The change of slope does not occur at the cricondentherm (CT), which
TABLE 1 Mixtures composition in mole fraction, x. Component
Nitrogen Carbon dioxide Methane Ethane Propane 2-Methylpropane Butane 2-Methylbutane Pentane n-Hexanea 3-Methylpentane 2-Methylpentane n-Heptaneb n-Octane n-Nonane a b
x M88C1
M94C1
0.00262 0.00169 0.88023 0.05824 0.03292 0.00537 0.00936 0.00249 0.00236 0.00089 0.00045 0.00015 0.00189 0.00098 0.00036
0.00246 0.00143 0.94045 0.01867 0.01802 0.00356 0.00706 0.00201 0.00252 0.00199 0.00006 0.001 0.00052 0.00025
x(C6) = 0.00149 (M88C1) and 0.00205 (M94C1). x(C7+) = 0.00323 (M88C1) and 0.00177 (M94C1).
has a collinear isochore [12,13]. Since the apparatus high pressure cell volume changes slightly at different pressure and temperature conditions, collected experimental data needs to be corrected by applying the cell distortion equation as shown below:
VðT; PÞ ¼ 1 þ cðP P 0 Þ þ bðT T 0 Þ; VðT 0 ; P0 Þ
ð1Þ
in which c is 2.53 105 MPa1 and b is 4.86 105 K1. A platinum resistance thermometer with calibration traceable to NIST measures temperature. The isochoric apparatus is designed to give maximum stability and uniformity of temperature within the cell as ±4 mK and to minimize the temperature gradients between the cell top and bottom as ±2 mK. A quartz pressure transducer from Paroscientific Inc. measures the pressure, and the manufacturer specifies the uncertainty for the transducer as ±0.01% of full scale. The transducer temperature is constant at 343.15 K during measurements, well above the mixture CT. Zhou et al. [14] performed measurements on pure carbon dioxide and propane to verify the capabilities of the isochoric apparatus. Eight vapor pressures of carbon dioxide measured between T = (230 and 290) K had a maximum relative deviation of ±0.055% compared to Span and Wagner [15] and ±0.04% when compared to the RefProp 8 as implemented by Lemmon et al. [16]. Seven vapor pressures of propane measured between T = (270 and 340) K had a maximum relative deviation of ±0.07% when compared to the same correlation. The estimated uncertainty for the temperature and pressure phase envelope data are 4.5 mK and 0.04%, respectively [17]. Details of isochoric apparatus were discussed in detail previously by Zhou et al., Acosta-Pérez et al., Atilhan et al. and Cristancho et al., more details regarding to apparatus drawings, operating principles and validation details can be found elsewhere [1,14,17,18]. Archimedes’ principle states ‘‘when a solid body is immersed in a fluid, it displaces a volume of fluid the weight of which is equal to the buoyancy force exerted by the fluid on the sinker’’. This relates the buoyancy force on the submerged object to fluid density. According to Archimedes’ principle, the density of the fluid is:
q¼
mv ma : V s ðT; PÞ
ð2Þ
In equation (2), mv is the ‘‘true’’ mass of the sinker in vacuum, ma is the ‘‘apparent’’ mass of the sinker in the fluid, and Vs is the calibrated volume of the sinker, which is a function of temperature
Isochore 1
Isochore 2
Isochore 3
136
TABLE 2 Experimental isochoric pressure, P, and temperature, T, data for M88C1. Isochore 4
Isochore 5
Isochore 6
Isochore 7
Isochore 8
Isochore 9
Isochore 10
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
302.05 287.65 280.65 274.65 270.65 255.50 250.65 248.65 247.65
18.184 17.099 15.741 14.381 13.292 11.459 10.680 10.309 10.189
311.15 303.15 293.15 283.15 275.15 261.70 255.65 252.65 251.65 250.65
18.184 17.099 15.741 14.381 13.292 11.459 10.680 10.309 10.189 10.068
320.15 308.35 302.15 293.15 283.15 273.00 264.65 262.65 260.65 259.65
16.918 15.601 14.907 13.898 12.773 11.627 10.737 10.528 10.325 10.221
328.95 320.15 308.15 302.65 293.15 284.40 273.15 271.15 270.15
15.639 14.832 13.729 13.220 12.338 11.523 10.521 10.348 10.261
338.95 328.95 320.15 308.15 300.15 293.6 285.15 281.15 279.15 278.15
14.404 13.654 12.992 12.085 11.475 10.975 10.352 10.062 9.917 9.845
326.15 322.15 318.15 314.15 310.15 305.40 296.15 291.15 288.15 285.15
10.226 10.024 9.830 9.620 9.418 9.169 8.715 8.467 8.318 8.168
335.15 332.15 328.15 324.15 320.15 308.80 303.05 300.15 296.15 292.15
9.317 9.193 9.027 8.860 8.693 8.216 7.978 7.859 7.693 7.528
335.15 332.15 328.15 324.15 320.15 310.70 303.15 300.15 297.15 293.15
8.106 8.004 7.866 7.729 7.591 7.265 7.004 6.901 6.797 6.660
342.45 329.15 325.15 321.15 316.15 313.00 310.15 306.15 301.65 297.15
5.855 5.565 5.478 5.391 5.282 5.214 5.150 5.063 4.964 4.864
332.15 329.15 325.15 321.15 317.15 310.15 305.00 306.15 301.65 297.15
1.787 1.770 1.747 1.713 1.700 1.660 1.630 1.636 1.610 1.583
Isochore 1
Isochore 2
Isochore 3
Isochore 4
Isochore 5
Isochore 6
Isochore 7
Isochore 8
Isochore 9
Isochore 10
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
301.15 286.45 277.95 266.95 261.95 242.55 235.99 232.15 231.35
19.288 17.114 15.847 14.212 13.468 10.599 9.625 9.145 9.045
301.15 287.75 279.95 267.95 261.95 247.42 242.55 238.55 237.45
17.044 15.377 14.403 12.903 12.158 10.339 9.791 9.332 9.204
313.35 306.35 301.35 289.45 277.95 258.88 252.85 251.85 247.85 246.85
16.338 15.616 15.099 13.866 12.663 10.657 10.083 9.986 9.595 9.496
333.35 323.35 313.35 303.35 290.45 284.45 277.15 274.15 270.15 267.15 263.15 260.15 257.15 254.46 253.45
16.031 15.186 14.337 13.484 12.378 11.861 11.231 10.974 10.632 10.379 10.047 9.554 9.473 9.331 9.250
335.45 325.35 315.35 305.35 292.95 289.50 286.95 281.95 277.05 271.95 266.95
12.370 11.785 11.203 10.617 9.889 9.680 9.537 9.247 8.964 8.670 8.382
335.45 327.05 320.15 313.15 305.15 294.94 292.95 287.95 281.95 277.05 271.95
10.820 10.417 10.082 9.743 9.353 8.855 8.757 8.508 8.226 7.990 7.743
335.45 327.15 320.15 313.15 305.15 298.64 292.95 287.95 281.95 277.05 271.95
9.514 9.178 8.894 8.608 8.281 8.013 7.782 7.579 7.334 7.135 6.927
335.45 327.15 320.15 313.15 305.15 303.71 295.95 292.95 287.95 281.95 277.05
7.348 7.108 6.905 6.702 6.469 6.426 6.200 6.113 5.966 5.791 5.648
335.45 327.15 320.15 313.15 305.15 304.52 295.95 292.95 287.95 281.95
3.542 3.442 3.358 3.274 3.177 3.169 3.065 3.028 2.967 2.893
335.45 327.15 320.15 313.15 305.15 294.03 287.95 281.95 277.05 271.95
1.493 1.454 1.422 1.389 1.352 1.299 1.270 1.242 1.218 1.194
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 3 Experimental isochoric pressure, P, and temperature, T, data for M94C1.
137
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
and pressure [19,20]. Rubotherm Präzisionsmesstechnik manufactured the singlesinker densimeter used in this work. Patil [21] described commissioning and operational details of the instrument. Wagner and Kleinrahm [22] and Kuramoto et al. [23] also provide discussions concerning the operation of these instruments. Measurements of the high purity pure fluids methane, [24] ethane, [25] nitrogen [26] and carbon dioxide [27] and reveal an uncertainty of less than 0.05% over the pressure range up to 200 MPa for density measurements in this apparatus. The force transmission error for the MSD is also studied, and details can be obtained in literature [28]. Similar works on the details of density measurements for multicomponent gas mixtures that are similar to this presented work were published previously elsewhere [29–31].
TABLE 4 Experimental phase envelope data. M94C1
M88C1
T/K
P/MPa
T/K
P/MPa
236.0 247.4 258.9 270.1 289.5 295.0 298.6 303.7 304.5 294.0
9.625 10.339 10.657 10.632 9.680 8.855 8.013 6.426 3.169 1.299
255.5 261.7 273.0 284.4 293.6 305.4 308.8 310.7 313.0 305.0
11.168 11.459 11.628 11.523 10.975 9.170 8.216 7.265 5.214 1.629
20
20
(a)
15
P / MPa
P / MPa
15
10
10
5
5
0
(b)
220
240
260
280 T /K
300
320
0
340
220
240
260
280 T /K
300
320
340
12
12
8
8
P / MPa
P / MPa
FIGURE 1. Isochoric apparatus data and experimental phase envelope for (a) M88C1 and (b) M94C1 mixtures. Symbols: (s) isochore 1, (h) isochore 2, (4) isochore 3, () isochore 4, (⁄) isochore 5, (+) isochore 6, (-) isochore 7, (–) isochore 8, (j) isochore 9, (N) isochore 10, and (d) experimental phase envelope.
4
0
0 240
260
280 T/K
300
320
220
240
260 280 T/K
300
320
220
240
260 280 T/K
300
320
220
240
260 280 T/K
300
320
12
8
P / MPa
P / MPa
12
4
8 4 0
0 240
260
12
280 T/K
300
320
12
8
P / MPa
P / MPa
4
4
8 4 0
0 240
260
280 T/K
300
320
FIGURE 2. Comparison of experimental phase envelopes and phase envelopes predicted with SRK, TRK, PR, TPR, PT, SW, MMM, GD, SAFT, PC-SAFT EOS for M88C1 and M94C1 samples; (d) experimental data.
138
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 5 Experimental cricondentherm and cricondenbar in comparison with EOS predictions. Deviations between experimental and EOS data are reported parenthesized for comparison purposes. Cricondentherm
Cricondenbar
T/K
P/MPa
T/K
Experimental SRK TRK PR TPR PT SW MMM GD SAFT PCSAFT
312.9 309.5 309.6 306.7 307.6 306.5 306.7 309.3 307.8 309.7 309.2
(3.4) (3.3) (6.2) (5.3) (6.4) (6.2) (3.6) (5.1) (3.2) (3.7)
M88C1 5.3 4.6 (0.7) 4.7 (0.6) 4.3 (1.0) 4.3 (1.0) 4.2 (1.1) 4.3 (1.0) 4.7 (0.6) 4.4 (0.9) 5.4 (0.1) 4.3 (1.0)
P/MPa
275.3 266.1 265.5 262.9 262.9 262.9 262.9 265.5 263.1 265.5 267.4
(9.2) (9.8) (12.4) (12.4) (12.4) (12.4) (9.8) (12.2) (9.8) (7.9)
11.6 11.4 11.7 11.0 11.3 11.0 11.0 11.7 11.5 11.7 10.2
(0.2) (0.1) (0.6) (0.3) (0.6) (0.6) (0.1) (0.1) (0.19 (1.4)
Experimental SRK TRK PR TPR PT SW MMM GD SAFT PC-SAFT
306.6 299.2 299.3 296.4 297.5 296.5 296.7 299.1 297.6 296.4 298.7
(7.4) (7.3) (10.2) (9.1) (10.1) (9.9) (7.5) (9.0) (10.2) (7.9)
M94C1 4.6 4.4 (0.2) 4.5 (0.1) 4.1 (0.5) 4.1 (0.5) 4.0 (0.6) 4.1 (0.5) 4.5 (0.1) 4.2 (0.4) 4.7 (0.1) 4.1 (0.5)
263.7 256.5 256.1 253.4 253.5 253.4 253.8 255.9 253.6 253.6 253.8
(7.2) (7.6) (10.3) (10.2) (10.3) (9.9) (7.8) (10.1) (10.1) (9.9)
10.7 11.2 11.5 10.8 11.0 10.6 10.8 11.5 11.2 11.2 10.2
(0.5) (0.8) (0.1) (0.3) (0.1) (0.1) (0.8) (0.5) (0.5) (0.5)
3. Results 3.1. Isochoric apparatus results This paper contains measurements for 10 isochores over a pressure range of (0 to 35) MPa and a temperature range of (220 to 300) K. The isochoric data for M88C1 are given in table 2 and M94C1 in table 3. Table 4 presents the phase boundary data determined for the measured mixtures. Figures 1a and b show the isochoric apparatus data, experimental phase envelope, and comparison with SRK and PR EOS are reported in figure 2 for both M88C1 and M94C1 mixtures. Experimental phase envelopes obtained from isochoric data shows that the large C6+ fractions in the studied heavy mixtures lead to two phase regions extending to high temperatures, i.e. the cricondentherms obtained from experimental data are 312.9 K/5.3 MPa and 306.6 K/4.6 MPa, for M88C1 and M94C1 samples respectively. M88C1 sample (with 0.00469 C6+ mole fraction) has a cricondentherm temperature 6.3 K larger than that for M94C1 (with 0.00382 C6+ mole fraction) sample, which shows the strong effect of small changes in the C6+ fraction in the cricondentherm region. Likewise, the cricondenbars obtained from experimental phase envelope data are 275.3 K/11.6 MPa and
263.7 K/10.7 MPa, for M88C1 and M94C1 samples, and thus, M88C1 sample has a cricondenbar pressure roughly 1 MPa larger than that for M94C1. These large cricondentherm temperatures and cricondenbar pressures should be considered for the custody transfer conditions of the studied mixtures. Phase envelopes of the studied gas mixtures were also calculated via most widely used EOS. Calculations performed using various EOS and they are presented in table 5 and figure 2. Various EOS were selected for this purpose; Soave–Redlich–Kwong (SRK) [32], Twu–Redlich–Kwong (TRK) [33], Peng–Robinson (PR) [34], and Twu–Peng–Robinson (TPR) [35], were selected as bi–parametric cubic EOS, Patel–Teja (PT) [36], Schmidt–Wenzel (SW) [37], Guo–Du (GD) [38], and Mohsen–Nia et al. (MMM) [39] were selected as tri-parametric cubic EOS. Moreover, molecular-based EOS using Wertheim perturbation theory [40] have gained acceptance in academia as statistical associating fluid theory (SAFT). Therefore, SAFT EOS [41] and PC-SAFT EOS [42] were selected as molecular based EOS to conduct a full comparison study on the complex fluids studied in the work. Bi-parametric cubic EOS was investigated in details as they are used by industry for predicting reservoir fluids for long time. The performance of SRK, TRK, PR and TPR EOS for the prediction of phase envelopes for the studied heavy mixtures showed remarkable deviations with experimental data both in the cricondentherm and cricondenbar regions. Cricondentherm temperature and cricondenbar pressure, which are key parameters for the characterization of phase behavior for natural gas transportation, obtained from PR and SRK EOS are reported in figure 3 in comparison with values obtained from experimental isochoric data reported in this work. Reported results show that SRK EOS predicts accurately the M94C1 cricondentherm region but fails for the M88C1, and it fails also in the prediction of the cricondenbar region of both regions. PR EOS leads to large deviations both in the cricondentherm and cricondenbar regions of both mixtures, with the only exception of M88C1 cricondenbar region. Therefore, SRK and PR EOS cannot be used for a reliable characterization of the studied mixtures, the use of these EOS for gas transportation purposes would require equipment overdesign to assure single phase flow, with the subsequent economical costs. On the other hand, both tri-parametric and molecular based EOS also showed similar behavior as bi-parametric cubic EOS. For both gas samples, none of the EOS were able to predict the cricondentherm accurately and they resulted with prediction deviations of almost up to 7 K. For bubble point section and in particular cricondentherm predictions for both mixtures with tri-parametric cubic EOS and molecular based EOS were better than cricondenbar predictions. It was observed that SAFT EOS performs superior than the PC-SAFT EOS for both mixtures in bubble point region. When all tri-parametric and molecular based EOS compared, MMM EOS performs the best amongst the others for the bubble point and dew point sections of the phase envelope.
FIGURE 3. Comparison of cricondentherm temperature (TCT) and cricondenbar pressure (PCB) obtained from experimental isochoric data reported in this work (subindex EXP) with values obtained from SRK and PR EOS (subindex EOS). Bar color code: (black bar) SRK, and (dashed bar) PR.
139
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142 TABLE 6 Experimental density results, q, and their deviations from AGA8-DC92 and GERG-2008 EOS for M94C1 (data for gas phase density). T/K
P/MPa
qexp kg m3
qAGA8 kg m3
qGERG08 kg m3
270.019 270.021 270.024 270.026 270.036 270.011 270.008 270.025 280.025 280.020 279.949 279.999 279.998 280.002 280.006 280.018 280.028 280.030 280.007 280.026 290.066 290.057 290.055 290.041 290.018 289.987 290.097 290.067 290.061 290.081 305.016 305.015 305.006 305.005 305.008 305.003 305.002 305.015 304.894 320.056 320.057 320.054 320.056 320.054 320.051 320.055 320.053 320.049 320.002 320.001 340.025 340.020 340.023 340.020 340.026 340.030 339.995 339.998 339.994 339.990 340.061
13.842 15.524 17.236 18.970 20.702 27.614 27.603 34.544 9.999 10.691 11.377 12.066 13.829 15.520 17.598 18.974 20.696 27.596 27.622 34.513 9.656 10.351 12.064 13.787 15.516 17.273 18.981 20.728 27.636 34.502 10.340 12.086 13.809 15.534 17.286 18.971 20.713 27.680 34.426 3.483 6.912 10.362 12.087 13.800 15.521 17.252 18.978 20.706 27.622 34.491 3.500 6.929 10.393 12.115 13.819 15.529 17.287 19.002 20.702 27.465 34.521
166.019 185.829 203.207 218.214 231.024 268.135 268.319 293.018 102.309 111.381 120.247 128.915 150.422 169.405 189.988 201.917 215.158 254.762 254.661 281.141 90.735 98.669 118.217 137.411 155.627 172.647 187.356 200.965 241.811 269.616 88.847 106.112 122.973 139.274 154.905 168.865 182.113 224.213 253.246 24.826 51.973 81.516 96.662 111.620 126.296 140.454 153.834 166.369 207.940 238.313 23.132 47.678 73.878 87.118 100.161 113.030 125.916 137.979 149.372 188.610 220.113
165.830 185.540 202.870 217.870 230.700 267.970 267.930 292.720 102.680 111.470 120.260 128.890 150.340 169.240 189.750 201.660 214.910 254.340 254.490 280.800 90.867 98.726 118.190 137.350 155.520 172.460 187.130 200.730 241.620 269.270 88.888 106.130 122.970 139.230 154.800 168.720 181.930 224.010 252.930 24.831 52.027 81.549 96.672 111.600 126.230 140.350 153.680 166.170 207.710 237.980 23.183 47.779 73.979 87.211 100.230 113.070 125.920 137.930 149.290 188.420 219.900
166.830 186.650 203.890 218.720 231.360 267.970 267.930 292.330 102.840 111.700 120.580 129.300 150.980 170.030 190.560 202.410 215.540 254.450 254.600 280.550 90.950 98.854 118.460 137.780 156.080 173.100 187.770 201.310 241.800 269.140 88.961 106.280 123.220 139.580 155.240 169.200 182.420 224.260 252.910 24.824 52.022 81.594 96.768 111.760 126.460 140.650 154.030 166.550 207.980 238.030 23.178 47.775 74.003 87.262 100.320 113.210 126.100 138.150 149.540 188.680 220.010
3.2. Densimeter results Experimental density results and their deviations from AGA8DC92 and GERG-2008 EOS are in given table 6 M94C1 for and table 7 for M88C1. For both EOS, density calculations were made by REFPROP 9.1 (NIST Reference Fluid Thermodynamic and Transport Properties Database) software available through NIST Thermophysical Properties Division [43]. Density experiments were conducted are along four different isotherms at T = (270, 290, 305,
Relative deviation% AGA8
GERG2008
0.114 0.156 0.166 0.158 0.140 0.062 0.145 0.102 0.361 0.080 0.011 0.019 0.054 0.098 0.126 0.127 0.115 0.166 0.067 0.121 0.145 0.057 0.023 0.044 0.069 0.109 0.121 0.117 0.079 0.128 0.046 0.017 0.002 0.032 0.068 0.086 0.101 0.090 0.125 0.018 0.104 0.041 0.011 0.018 0.052 0.074 0.100 0.119 0.111 0.140 0.220 0.212 0.136 0.107 0.069 0.036 0.003 0.035 0.055 0.101 0.097
0.486 0.440 0.335 0.231 0.145 0.062 0.145 0.235 0.516 0.286 0.276 0.298 -0.370 0.367 0.300 0.244 0.177 0.123 0.024 0.210 0.236 0.187 0.205 0.268 0.290 0.262 0.221 0.172 0.005 0.177 0.128 0.159 0.201 0.219 0.216 0.198 0.168 0.021 0.133 0.010 0.094 0.096 0.110 0.125 0.130 0.139 0.127 0.109 0.019 0.119 0.198 0.203 0.169 0.166 0.159 0.159 0.146 0.124 0.112 0.037 0.047
and 340) K for M88C1 and T = (270, 280, 290, 305, 320 and 340) K for M94C1 mixtures. For M88C1 temperature stability attained across the cell was ±4.2 mK at T = 270 K, ±5.9 mK at T = 290 K, and ±4.1 mK at T = 305 K and ±1.9 K at T = 340 K. Temperature stabilities were recorded as ±8.7 mK at T = 270 K, ±22 mK at T = 280 K, ±31 mK at T = 290 K, ±38 mK at T = 305 K, ±21 mK at T = 320 K and ±20 mK at T = 340 K. The experimental points on each isotherm range up to 35 MPa. Total number PqT points collected for M88C1 mixture is 32 and 56 for M94C1 with
140
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 7 Experimental density results and their deviations from AGA8-DC92 and GERG-2008 EOS for M88C1 (data for gas phase density). T/K
P/MPa
qexp kg m3
qAGA8 kg m3
qGERG08 kg m3
270.007 270.000 269.999 270.003 270.005 270.007 270.008 269.998 269.999 289.992 289.996 290.004 290.002 290.000 290.009 289.994 305.008 304.998 304.998 305.002 304.998 305.005 305.005 339.995 339.998 339.994 339.995 339.999 339.995 340.000 339.997 339.997
13.799 17.241 20.698 24.142 27.582 31.009 34.459 27.536 20.688 12.428 13.791 17.232 20.708 24.143 27.600 34.479 12.081 13.806 17.244 20.712 24.142 27.575 34.512 3.487 6.919 10.367 13.814 17.236 20.678 24.143 27.572 34.491
192.959 231.429 257.997 277.480 292.690 305.080 315.661 292.551 257.920 140.192 157.575 195.628 225.168 247.491 265.222 291.906 119.603 139.023 174.309 203.711 227.071 245.949 275.032 24.856 51.851 81.038 110.933 139.345 165.355 188.304 207.793 239.435
191.790 230.130 256.810 276.410 291.750 304.260 314.910 291.580 256.740 139.750 156.940 194.640 224.050 246.400 264.220 291.040 119.440 138.700 173.650 202.810 226.06 244.95 274.11 24.962 52.066 81.214 110.88 139.08 164.82 187.53 206.96 238.56
194.2 232.07 257.99 277 291.92 304.14 314.6 291.75 257.93 140.63 158.08 196.04 225.22 247.22 264.72 291.08 119.92 139.4 174.67 203.84 226.9 245.55 274.32 24.962 52.09 81.332 111.17 139.56 165.45 188.2 207.57 238.95
1.0
1.0
(a)
0.5
0.5
0.0
0.0
-0.5
-0.5
Relative deviation% AGA8
GERG2008
0.610 0.564 0.462 0.387 0.322 0.270 0.239 0.333 0.460 0.317 0.405 0.508 0.499 0.443 0.379 0.297 0.136 0.233 0.380 0.444 0.447 0.408 0.336 0.424 0.412 0.217 0.047 0.191 0.325 0.413 0.403 0.367
0.639 0.276 0.003 0.173 0.264 0.309 0.337 0.274 0.004 0.311 0.319 0.210 0.023 0.110 0.190 0.284 0.264 0.270 0.206 0.063 0.075 0.163 0.260 0.424 0.458 0.361 0.214 0.154 0.057 0.055 0.107 0.203
(b)
-1.0
-1.0 0
10
20 P / MPa
30
40
0
10
20 P / MPa
30
40
FIGURE 4. Density deviations compared to predictions from (a) AGA8-DC92 and (b) GERG2008 EOS, for M88C1 mixture. Symbols: (}) T = 270 K, (4) T = 290 K, (h) T = 305 K, and (s) T = 340 K.
an uncertainty in pressure of 0.01%. These density measurements are corrected for the force transmission error caused by the magnetic suspension coupling as described by Cristancho et al. [28] Density deviations compared to predictions from AGA8-DC92 EOS appear in figure 4a for M88C1 and figure 5a for M94C1 and deviations compared to predictions from GERG-2008 EOS appear in figure 4b for M88C1 and figure 5b for M94C1. At low temperature and at low pressure the deviations from AGA8-DC92 EOS are more than expected according to the deviation regions as explained in the original AGA report. It is clear from these results that AGA8-DC92 has issues in predicting density at low pressures for the T = (270, 305, and 340) K isotherms. A closer inspection of data used for AGA8-DC92 EOS development shows that, except for one mixture, the mole fraction of C6 + components does not
exceed 0.12%, [44] and data sets comes from gas mixtures consisting of mostly binary or ternary combinations of methane, ethane, propane, butane, nitrogen, and carbon dioxide are used during the development and validation of AGA8-DC92. Thus, for any natural gas samples or mixtures with C6+ higher than the normal or expanded range, the application of AGA8-DC92 is an extrapolation, and the accuracy compared to the normal range mentioned in the original AGA report is questionable. Results obtained from GERG2008 EOS reported in figures 4b and 5b show also remarkable deviations with experimental data, the average absolute percentage errors for M88C1 mixture are 0.37% and 0.22%, using AGA8DC92 and GERG2008, respectively, whereas for M94C1 are 0.09% and 0.19%, using AGA8-DC92 and GERG2008, respectively. Therefore, although GERG2008 predictions are slightly better than those
141
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
1.0
1.0
(a)
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
(b)
-1.0 0
10
20 P / MPa
30
40
0
10
20 P / MPa
30
40
FIGURE 5. Density deviations compared to predictions from (a) AGA8-DC92 and (b) GERG2008 EOS, for M94C1 mixture. Symbols: (}) T = 270 K, (h) 280 K, (4) 290 K, () 305 K, (⁄) 320 K, and (s) 340 K.
from AGA8-DC92 for M88C1 sample, it also showed some prediction issues in the low-pressure region as AGA8-DC92. Likewise, GERG2008 predictions are worse than those from AGA8-DC92 for M94C1 sample. Therefore, both AGA8-DC92 and GERG2008 EOS have density predicting issues (density deviations are larger than the 0.1%) especially for pressures lower than 10 MPa for the studied mixtures that contains heavy samples. Total error and uncertainty analysis were conducted by taking random and systematic errors into consideration. Random errors that were considered include the uncertainty in pressure and temperature measurement, molar compositional analysis, and measurement of the sinker mass under vacuum and at. On the other hand, uncertainty in sinker volume, which includes uncertainty in sinker volume determination at a reference temperature and pressure, as well as uncertainty in the functional dependence of sinker volume on temperature and pressure, was considered as systematic error. Yet, the force transmission error also contributes to systematic error as well. The error in density caused by pressure, temperature, and composition is:
Dq ¼
8" < @ q :
@P
#2
DP T;x
" #2 " #2 91=2 = @q @q þ DT þ Dxi : ; @T P;x @xi P;T;xi–j ð3Þ
We did an uncertainty analysis for a natural gas mixture sample that was previously studied by Patil [21]. Moreover fluid specific force transmission related and balance calibration related uncertainties were previously studied by Cristancho [28] as (36 and 5) ppm respectively. These values contributed total uncertainty caused by the densimeter data as 0.001%. Uncertainty from temperature measurements is estimated as 0.005%. Estimated total uncertainty in pressure transducer calibration caused by the deadweight gauge and differential pressure indicator 0.005%, and the total uncertainty of the pressure transducer is 0.02%. Majority of the overall uncertainty comes from the mixture preparation and quality. The estimated uncertainty of the gas mixture is 0.12%. As sum, overall total estimated uncertainty of the density measurements were was calculated as 0.13%. 4. Conclusions New, accurate experimental data are collected for the phase envelopes and densities of a multicomponent natural gas-like mixture. Phase envelope measurements do not agree with most widely used EOS predictions. Density measurements agree with GERG-2008 EOS more than AGA8-DC92 EOS especially at higher pressures that are close to custody transfer conditions. At low
pressures neither AGA8-DC92 EOS nor GERG2008 EOS predictions showed deviations lower than 0.1% in density. More measurements on multicomponent mixtures containing heavy components and comparisons with EOS predictions appear necessary at low pressures. It seems new GERG-2008 EOS development process with the inclusion of more multi-component data sets and the use of accurate EOS in the form of fundamental equations for each mixture component along with several functions developed for the binary mixtures of the components to take into account the residual mixture behavior, helped to achieve more accurate property predictions especially for multi-component mixtures over a wide range of compositions including heavy component mixtures when compared with predecessor version.
Acknowledgments This work was made possible by NPRP Grants # 30-6-7-1 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. The authors express their gratitude to Mardi Gras Transportation Systems, LLC for the funding provided. The authors also appreciate support from Premier Measurement Services and Savant Measurement Corporation. Financial support also came from the Texas Engineering Experiment Station and the Jack E. & Francis Brown Chair funds.
References [1] M. Atilhan, S. Ejaz, J. Zhou, D. Cristancho, I. Mantilla, J. Holste, K.R. Hall, J. Chem. Eng. Data 55 (11) (2010) 4907–4911. [2] P. Patil, S. Ejaz, M. Atilhan, D. Cristancho, J.C. Holste, K.R. Hall, J. Chem. Thermodyn. 39 (8) (2007) 1157–1163. [3] K.R. Hall, J.C. Holste, Flow Meas. Instrum. 1 (1990) 127–132. [4] E.F. May, T.J. Edwards, A.G. Mann, C. Edwards, R.C. Miller, Fluid Phase Equilib. 185 (1–2) (2001) 339–347. [5] K.K. Botros, Chem. Eng. Commun. 189 (2) (2002) 151–172. [6] R. Gharbi, A.M. Elsharkawy, Pet. Sci. Technol. 21 (1–2) (2003) 53–79. [7] K.R. Hall, L. Yarborough, Oil Gas J. 71 (25) (1973) 82. [8] P.M. Dranchuk, R.A. Purvis, D.B. Robinson, Computer calculations of natural gas compressibility factors using the standing and Karz correlation, Institute of Petroleum Technical Series No. IP 74-008, 1974. [9] P.M. Dranchuk, J.H. Abou-Kassem, J. Can. Pet. Technol. 14 (3) (1975) 34. [10] K.E. Starling, J.L. Savidge, Compressibility factors of natural gas and other related hydrocarbon gases, American Gas Association, Arlington, VA, 1992. [11] O. Kunz, W. Wagner, J. Chem. Eng. Data 57 (11) (2012) 3032–3091. [12] P.T. Eubank, M.A. Barrufet, AIChE J. 33 (1987) 1882–1887. [13] P.T. Eubank, L.L. Joffrion, M.R. Patel, W. Warowny, J. Chem. Thermodyn. 20 (1988) 1009–1034. [14] J. Zhou, P. Patil, S. Ejaz, M. Atilhan, J.C. Holste, K.R. Hall, J. Chem. Thermodyn. 38 (11) (2006) 1489–1494. [15] R. Span, W. Wagner, J. Phys. Chem. Ref. Data 25 (1996) 1509–1596. [16] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST reference fluid thermodynamic and transport properties REFPROP, Version 8.0; National
142
[17] [18] [19] [20] [21]
[22] [23] [24] [25] [26] [27] [28] [29] [30]
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142 Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, MD, 2007. P.L. Acosta-Perez, D.E. Cristancho, I.D. Mantilla, K.R. Hall, G.A. Iglesias-Silva, Fluid Phase Equilib. 283 (1–2) (2009) 17–21. D.E. Cristancho, I.D. Mantilla, L.A. Coy, A. Tibaduiza, D.O. Ortiz-Vega, K.R. Hall, G.A. Iglesias-Silva, J. Chem. Eng. Data 56 (4) (2011) 826–832. R. Kleinrahm, W. Wagner, Prog. Rep. VDI J. 3 (92) (1984) 2. H.W. Losch, VDI Verlag, Dusseldolf, 1987. P.V. Patil, Commissioning of a magnetic suspension densitometer for highaccuracy density measurements of natural gas mixtures (Dissertation), Texas A&M University, College Station, TX, 2005. W. Wagner, R. Kleinrahm, Metrologia 41 (2) (2004) S24. N. Kuramoto, K. Fujii, A. Waseda, Metrologia 41 (2) (2004) S84. D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesia-Silva, J. Chem. Eng. Data 55 (2) (2010) 826–829. D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (8) (2010) 2746–2749. I.D. Mantilla, D.E. Cristancho, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (10) (2010) 4227–4230. I.D. Mantilla, D.E. Cristancho, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (11) (2010) 4611–4613. D.E. Cristancho, D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, G.A. IglesiasSilva, M. Atilhan, Int. J. Thermophys. 31 (4–5) (2010) 698–709. M. Atilhan, S. Aparicio, S. Ejaz, D. Cristancho, K.R. Hall, J. Chem. Eng. Data 56 (2) (2011) 212–221. M. Atilhan, S. Aparicio, S. Ejaz, D. Cristancho, I. Mantilla, K.R. Hall, J. Chem. Eng. Data 56 (10) (2011) 3766–3774.
[31] M. Atilhan, S. Aparicio, F. Karadas, K.R. Hall, R. Alcalde, J. Chem. Thermodyn. 53 (2012) 1–8. [32] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203. [33] C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilib. 105 (1995) 61–69. [34] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [35] C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilib. 105 (1995) 61–69. [36] N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37 (1982) 463–473. [37] G. Schmidt, H.A. Wenzel, Chem. Eng. Sci. 35 (1980) 1503–1512. [38] T.M. Guo, L. Du, Fluid Phase Equilib. 52 (1989) 47–57. [39] M. Mohsen-Nia, H. Modarress, G.A. Mansoori, Fluid Phase Equilib. 206 (2003) 27–39. [40] M.S. Wertheim, J. Stat. Phys. 35 (1984) 19–34. [41] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709–1721. [42] F. Tumakaka, J. Gross, G. Sadowski, Fluid Phase Equilib. 228 (2005) 89–98. [43] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2013. [44] J.L. Savidge, S.W. Beyerlein, E.W. Lemmon, Technical Reference Document for the 2nd Edition of AGA Report No. 8, Gas Research Institute: Des Plaines, IL, Topical Report No. GRI-93/0181, 1995.
JCT 14-291
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Thermodynamic characterization of deepwater natural gas mixtures with heavy hydrocarbon content at high pressures Mert Atilhan a,⇑, Santiago Aparicio b,⇑, Saquib Ejaz c, Jingjun Zhou c, Mohammed Al-Marri a,d, James J. Holste c, Kenneth R. Hall c,⇑ a
Department of Chemical Engineering, Qatar University, Doha, Qatar Department of Chemistry, University of Burgos, Burgos, Spain Chemical Engineering Department, Texas A&M University, College Stations, TX, USA d Gas Processing Center, Qatar University, Doha, Qatar b c
a r t i c l e
i n f o
Article history: Received 22 May 2014 Received in revised form 5 October 2014 Accepted 12 October 2014 Available online 31 October 2014 Keywords: Natural gas Density Phase envelope Phase equilibrium Equation of state
a b s t r a c t This paper includes high-accuracy density measurements and phase envelopes for deepwater natural gas mixtures. Mixtures primarily consist of (0.88 and 0.94) mole fraction methane and both mixtures includes heavy components (C6+) more than 0.002 mole fraction. Experimental density and phase envelope data for deep and ultra-deep reservoir mixtures are scarce in literature and high accuracy measurements for such parameters for such natural gas-like mixtures are essential to validate the benchmark equations for custody transfer such as AGA8-DC92 and GERG-2008 equation of states (EOS). Thus, in this paper we report density and phase envelope experimental data via compact single-sinker magnetic suspension densimeter and isochoric apparatuses. Such data help gas industry to avoid retrograde condensation in natural gas pipelines. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Natural gas is known as the most environmentally friendly fossil fuel found in abundant quantities [1]. Given increased activity in petroleum, cryogenic, liquefied natural gas (LNG) and natural gas businesses, accurate knowledge of the thermodynamic property estimates such as density, viscosity, heating value, compressibility factor, etc. . . Accurate measurements of such quantities are necessary to design engineering processes and determine operational performances [2]. Custody transfer of natural gas requires knowledge of the phase behavior of the fluid in the pipelines and a basic assumption in custody transfer of natural gas is that the gas remains in a single phase during the transportation and at measurement stages [3]. Hydrocarbon dew points for natural gas mixtures are important in contractual specifications throughout the supply chain. Avoiding the formation of liquid in natural gas is critically important. To avoid two-phase flow, it is essential to have reliable data or predictions of the cricondenbar (CB) and cricondentherm (CT). Phase boundaries of natural gas mixtures are sensitive to small fractions ⇑ Corresponding authors. E-mail addresses: [email protected] (S. Aparicio), [email protected] (K.R. Hall). http://dx.doi.org/10.1016/j.jct.2014.10.018 0021-9614/Ó 2014 Elsevier Ltd. All rights reserved.
(M.
Atilhan),
[email protected]
of heavier components, and prediction of the dew point curve with the current EOS appears unreliable [4]. Most common widely used equations that are used in predicting the density and phase behavior of multicomponent gas mixtures in oil and gas industry during custody transfer are simple cubic EOS such as Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Patel–Teja (PT), and Benedict–Webb–Rubin (BWR). However, such simple bi and tri parametric EOS mostly fails to predict the phase behavior for multi-component mixtures and gives large deviations especially at the retrograde condensation region [5,6]. Moreover Hall– Yarborough [7], and Dranchuk et al. [8] and Dranchuk [9] are other reputable and used EOS, but these EOS also lack the ability to predict phase boundaries as well. On the other hand cubic EOS as mentioned above have the usual problem for predicting properties at high densities for both liquids and supercritical fluids simply because of the reason lies in the nature of the intermolecular forces. As molecules touches to each other repulsive forces becomes dominant and increases exponentially with the distance of the molecules; which is another way of defining incompressible condition for liquid phase. On contrast, at distances greater than the usual separation distance between the molecules in a liquid state, the force is attractive. Molecules are deformed as they are pushed closer under pressure, thus their repulsive behavior rapidly increases. Such rapid increase in the
135
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
repulsive intermolecular force with distance requires a dependence on density function that is greater than the cubic relation. For industrial applications of natural gas such as pipeline distribution, choice of EOS plays an important role. Setting up the financial and legal aspects of the custody transfer is highly depended on the selection of EOS, which plays an important role on quantification at the measurement stations through the pipelines. Such requirement has led to parties to use ‘‘standard’’ equations or procedures with tailor made purposes, with a wider range of applicability and minimized prediction errors. Thus, it has been an ongoing interest of academia and industry to develop and fine-tune new EOS that would predict thermodynamic properties of multicomponent gas mixtures of interest for wide temperature and pressure ranges. Industry benchmark EOS that are used for this purpose are known as AGA8-DC92 EOS [10] and recently developed GERG-2008 EOS [11]. The AGA8-DC92 EOS was considered as a thermal equation of state explicit in compression factor, which allows the calculation of thermodynamic properties of multi-component gas mixtures (e.g. natural gases) consisting of up to 21 components. On the other hand, GERG2008 EOS is more advanced, complicated EOS and yet to be known as better EOS that can handle mixtures of 21 components with the addition of n-nonane, n-decane, and hydrogen sulfide to the preceding version GERG-2004 EOS. These standard EOS have progressively improved in physical accuracy over the range of pressures, temperatures, and compositions occurring in US and EU transmission pipelines and reservoirs. They have tended to be almost purely empirical. However, newly explored reservoirs with unprecedented compositions made researchers in both academia and industry to seek for the limits of these EOS. For this purpose, this work includes natural gas-like mixture that represents Gulf of Mexico reservoir fluids with heavy component composition more than 0.2% in mole. Collected experimental data were compared with AGA8-DC92 EOS and GERG-2008 EOS for density and most common cubic EOS for phase behavior. 2. Experimental This work uses a magnetic suspension densimeter (MSD) for accurate density measurements and an isochoric apparatus for phase envelope measurements. The sample mixtures have (0.88 and 0.94) mol fraction of methane with numerous other components as described below. Mixtures were named according to their methane mole fraction as M88C1 and M94C1. 2.1. Materials Accurate Gas Products prepared the synthetic mixture used in this work with the composition as presented in table 1. The gas mixture was prepared gravimetrically with traceability to the National Institute of Standards and Technology (NIST). The estimated uncertainty of the gas mixture is 0.12%, assuming that the uncertainty comes from the measuring balance and the impurities of the pure gases used in the preparation of the sample. 2.2. Apparatus The isochoric apparatus was designed and built to operate temperatures between (100 and 500) K with pressures up to 35 MPa. Apparatus uses an old but established technique for determining phase loops, which is based on the observation of the change on the slope of an isochore as it crosses the phase boundary. The change of slope does not occur at the cricondentherm (CT), which
TABLE 1 Mixtures composition in mole fraction, x. Component
Nitrogen Carbon dioxide Methane Ethane Propane 2-Methylpropane Butane 2-Methylbutane Pentane n-Hexanea 3-Methylpentane 2-Methylpentane n-Heptaneb n-Octane n-Nonane a b
x M88C1
M94C1
0.00262 0.00169 0.88023 0.05824 0.03292 0.00537 0.00936 0.00249 0.00236 0.00089 0.00045 0.00015 0.00189 0.00098 0.00036
0.00246 0.00143 0.94045 0.01867 0.01802 0.00356 0.00706 0.00201 0.00252 0.00199 0.00006 0.001 0.00052 0.00025
x(C6) = 0.00149 (M88C1) and 0.00205 (M94C1). x(C7+) = 0.00323 (M88C1) and 0.00177 (M94C1).
has a collinear isochore [12,13]. Since the apparatus high pressure cell volume changes slightly at different pressure and temperature conditions, collected experimental data needs to be corrected by applying the cell distortion equation as shown below:
VðT; PÞ ¼ 1 þ cðP P 0 Þ þ bðT T 0 Þ; VðT 0 ; P0 Þ
ð1Þ
in which c is 2.53 105 MPa1 and b is 4.86 105 K1. A platinum resistance thermometer with calibration traceable to NIST measures temperature. The isochoric apparatus is designed to give maximum stability and uniformity of temperature within the cell as ±4 mK and to minimize the temperature gradients between the cell top and bottom as ±2 mK. A quartz pressure transducer from Paroscientific Inc. measures the pressure, and the manufacturer specifies the uncertainty for the transducer as ±0.01% of full scale. The transducer temperature is constant at 343.15 K during measurements, well above the mixture CT. Zhou et al. [14] performed measurements on pure carbon dioxide and propane to verify the capabilities of the isochoric apparatus. Eight vapor pressures of carbon dioxide measured between T = (230 and 290) K had a maximum relative deviation of ±0.055% compared to Span and Wagner [15] and ±0.04% when compared to the RefProp 8 as implemented by Lemmon et al. [16]. Seven vapor pressures of propane measured between T = (270 and 340) K had a maximum relative deviation of ±0.07% when compared to the same correlation. The estimated uncertainty for the temperature and pressure phase envelope data are 4.5 mK and 0.04%, respectively [17]. Details of isochoric apparatus were discussed in detail previously by Zhou et al., Acosta-Pérez et al., Atilhan et al. and Cristancho et al., more details regarding to apparatus drawings, operating principles and validation details can be found elsewhere [1,14,17,18]. Archimedes’ principle states ‘‘when a solid body is immersed in a fluid, it displaces a volume of fluid the weight of which is equal to the buoyancy force exerted by the fluid on the sinker’’. This relates the buoyancy force on the submerged object to fluid density. According to Archimedes’ principle, the density of the fluid is:
q¼
mv ma : V s ðT; PÞ
ð2Þ
In equation (2), mv is the ‘‘true’’ mass of the sinker in vacuum, ma is the ‘‘apparent’’ mass of the sinker in the fluid, and Vs is the calibrated volume of the sinker, which is a function of temperature
Isochore 1
Isochore 2
Isochore 3
136
TABLE 2 Experimental isochoric pressure, P, and temperature, T, data for M88C1. Isochore 4
Isochore 5
Isochore 6
Isochore 7
Isochore 8
Isochore 9
Isochore 10
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
302.05 287.65 280.65 274.65 270.65 255.50 250.65 248.65 247.65
18.184 17.099 15.741 14.381 13.292 11.459 10.680 10.309 10.189
311.15 303.15 293.15 283.15 275.15 261.70 255.65 252.65 251.65 250.65
18.184 17.099 15.741 14.381 13.292 11.459 10.680 10.309 10.189 10.068
320.15 308.35 302.15 293.15 283.15 273.00 264.65 262.65 260.65 259.65
16.918 15.601 14.907 13.898 12.773 11.627 10.737 10.528 10.325 10.221
328.95 320.15 308.15 302.65 293.15 284.40 273.15 271.15 270.15
15.639 14.832 13.729 13.220 12.338 11.523 10.521 10.348 10.261
338.95 328.95 320.15 308.15 300.15 293.6 285.15 281.15 279.15 278.15
14.404 13.654 12.992 12.085 11.475 10.975 10.352 10.062 9.917 9.845
326.15 322.15 318.15 314.15 310.15 305.40 296.15 291.15 288.15 285.15
10.226 10.024 9.830 9.620 9.418 9.169 8.715 8.467 8.318 8.168
335.15 332.15 328.15 324.15 320.15 308.80 303.05 300.15 296.15 292.15
9.317 9.193 9.027 8.860 8.693 8.216 7.978 7.859 7.693 7.528
335.15 332.15 328.15 324.15 320.15 310.70 303.15 300.15 297.15 293.15
8.106 8.004 7.866 7.729 7.591 7.265 7.004 6.901 6.797 6.660
342.45 329.15 325.15 321.15 316.15 313.00 310.15 306.15 301.65 297.15
5.855 5.565 5.478 5.391 5.282 5.214 5.150 5.063 4.964 4.864
332.15 329.15 325.15 321.15 317.15 310.15 305.00 306.15 301.65 297.15
1.787 1.770 1.747 1.713 1.700 1.660 1.630 1.636 1.610 1.583
Isochore 1
Isochore 2
Isochore 3
Isochore 4
Isochore 5
Isochore 6
Isochore 7
Isochore 8
Isochore 9
Isochore 10
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
T/K
P/MPa
301.15 286.45 277.95 266.95 261.95 242.55 235.99 232.15 231.35
19.288 17.114 15.847 14.212 13.468 10.599 9.625 9.145 9.045
301.15 287.75 279.95 267.95 261.95 247.42 242.55 238.55 237.45
17.044 15.377 14.403 12.903 12.158 10.339 9.791 9.332 9.204
313.35 306.35 301.35 289.45 277.95 258.88 252.85 251.85 247.85 246.85
16.338 15.616 15.099 13.866 12.663 10.657 10.083 9.986 9.595 9.496
333.35 323.35 313.35 303.35 290.45 284.45 277.15 274.15 270.15 267.15 263.15 260.15 257.15 254.46 253.45
16.031 15.186 14.337 13.484 12.378 11.861 11.231 10.974 10.632 10.379 10.047 9.554 9.473 9.331 9.250
335.45 325.35 315.35 305.35 292.95 289.50 286.95 281.95 277.05 271.95 266.95
12.370 11.785 11.203 10.617 9.889 9.680 9.537 9.247 8.964 8.670 8.382
335.45 327.05 320.15 313.15 305.15 294.94 292.95 287.95 281.95 277.05 271.95
10.820 10.417 10.082 9.743 9.353 8.855 8.757 8.508 8.226 7.990 7.743
335.45 327.15 320.15 313.15 305.15 298.64 292.95 287.95 281.95 277.05 271.95
9.514 9.178 8.894 8.608 8.281 8.013 7.782 7.579 7.334 7.135 6.927
335.45 327.15 320.15 313.15 305.15 303.71 295.95 292.95 287.95 281.95 277.05
7.348 7.108 6.905 6.702 6.469 6.426 6.200 6.113 5.966 5.791 5.648
335.45 327.15 320.15 313.15 305.15 304.52 295.95 292.95 287.95 281.95
3.542 3.442 3.358 3.274 3.177 3.169 3.065 3.028 2.967 2.893
335.45 327.15 320.15 313.15 305.15 294.03 287.95 281.95 277.05 271.95
1.493 1.454 1.422 1.389 1.352 1.299 1.270 1.242 1.218 1.194
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 3 Experimental isochoric pressure, P, and temperature, T, data for M94C1.
137
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
and pressure [19,20]. Rubotherm Präzisionsmesstechnik manufactured the singlesinker densimeter used in this work. Patil [21] described commissioning and operational details of the instrument. Wagner and Kleinrahm [22] and Kuramoto et al. [23] also provide discussions concerning the operation of these instruments. Measurements of the high purity pure fluids methane, [24] ethane, [25] nitrogen [26] and carbon dioxide [27] and reveal an uncertainty of less than 0.05% over the pressure range up to 200 MPa for density measurements in this apparatus. The force transmission error for the MSD is also studied, and details can be obtained in literature [28]. Similar works on the details of density measurements for multicomponent gas mixtures that are similar to this presented work were published previously elsewhere [29–31].
TABLE 4 Experimental phase envelope data. M94C1
M88C1
T/K
P/MPa
T/K
P/MPa
236.0 247.4 258.9 270.1 289.5 295.0 298.6 303.7 304.5 294.0
9.625 10.339 10.657 10.632 9.680 8.855 8.013 6.426 3.169 1.299
255.5 261.7 273.0 284.4 293.6 305.4 308.8 310.7 313.0 305.0
11.168 11.459 11.628 11.523 10.975 9.170 8.216 7.265 5.214 1.629
20
20
(a)
15
P / MPa
P / MPa
15
10
10
5
5
0
(b)
220
240
260
280 T /K
300
320
0
340
220
240
260
280 T /K
300
320
340
12
12
8
8
P / MPa
P / MPa
FIGURE 1. Isochoric apparatus data and experimental phase envelope for (a) M88C1 and (b) M94C1 mixtures. Symbols: (s) isochore 1, (h) isochore 2, (4) isochore 3, () isochore 4, (⁄) isochore 5, (+) isochore 6, (-) isochore 7, (–) isochore 8, (j) isochore 9, (N) isochore 10, and (d) experimental phase envelope.
4
0
0 240
260
280 T/K
300
320
220
240
260 280 T/K
300
320
220
240
260 280 T/K
300
320
220
240
260 280 T/K
300
320
12
8
P / MPa
P / MPa
12
4
8 4 0
0 240
260
12
280 T/K
300
320
12
8
P / MPa
P / MPa
4
4
8 4 0
0 240
260
280 T/K
300
320
FIGURE 2. Comparison of experimental phase envelopes and phase envelopes predicted with SRK, TRK, PR, TPR, PT, SW, MMM, GD, SAFT, PC-SAFT EOS for M88C1 and M94C1 samples; (d) experimental data.
138
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 5 Experimental cricondentherm and cricondenbar in comparison with EOS predictions. Deviations between experimental and EOS data are reported parenthesized for comparison purposes. Cricondentherm
Cricondenbar
T/K
P/MPa
T/K
Experimental SRK TRK PR TPR PT SW MMM GD SAFT PCSAFT
312.9 309.5 309.6 306.7 307.6 306.5 306.7 309.3 307.8 309.7 309.2
(3.4) (3.3) (6.2) (5.3) (6.4) (6.2) (3.6) (5.1) (3.2) (3.7)
M88C1 5.3 4.6 (0.7) 4.7 (0.6) 4.3 (1.0) 4.3 (1.0) 4.2 (1.1) 4.3 (1.0) 4.7 (0.6) 4.4 (0.9) 5.4 (0.1) 4.3 (1.0)
P/MPa
275.3 266.1 265.5 262.9 262.9 262.9 262.9 265.5 263.1 265.5 267.4
(9.2) (9.8) (12.4) (12.4) (12.4) (12.4) (9.8) (12.2) (9.8) (7.9)
11.6 11.4 11.7 11.0 11.3 11.0 11.0 11.7 11.5 11.7 10.2
(0.2) (0.1) (0.6) (0.3) (0.6) (0.6) (0.1) (0.1) (0.19 (1.4)
Experimental SRK TRK PR TPR PT SW MMM GD SAFT PC-SAFT
306.6 299.2 299.3 296.4 297.5 296.5 296.7 299.1 297.6 296.4 298.7
(7.4) (7.3) (10.2) (9.1) (10.1) (9.9) (7.5) (9.0) (10.2) (7.9)
M94C1 4.6 4.4 (0.2) 4.5 (0.1) 4.1 (0.5) 4.1 (0.5) 4.0 (0.6) 4.1 (0.5) 4.5 (0.1) 4.2 (0.4) 4.7 (0.1) 4.1 (0.5)
263.7 256.5 256.1 253.4 253.5 253.4 253.8 255.9 253.6 253.6 253.8
(7.2) (7.6) (10.3) (10.2) (10.3) (9.9) (7.8) (10.1) (10.1) (9.9)
10.7 11.2 11.5 10.8 11.0 10.6 10.8 11.5 11.2 11.2 10.2
(0.5) (0.8) (0.1) (0.3) (0.1) (0.1) (0.8) (0.5) (0.5) (0.5)
3. Results 3.1. Isochoric apparatus results This paper contains measurements for 10 isochores over a pressure range of (0 to 35) MPa and a temperature range of (220 to 300) K. The isochoric data for M88C1 are given in table 2 and M94C1 in table 3. Table 4 presents the phase boundary data determined for the measured mixtures. Figures 1a and b show the isochoric apparatus data, experimental phase envelope, and comparison with SRK and PR EOS are reported in figure 2 for both M88C1 and M94C1 mixtures. Experimental phase envelopes obtained from isochoric data shows that the large C6+ fractions in the studied heavy mixtures lead to two phase regions extending to high temperatures, i.e. the cricondentherms obtained from experimental data are 312.9 K/5.3 MPa and 306.6 K/4.6 MPa, for M88C1 and M94C1 samples respectively. M88C1 sample (with 0.00469 C6+ mole fraction) has a cricondentherm temperature 6.3 K larger than that for M94C1 (with 0.00382 C6+ mole fraction) sample, which shows the strong effect of small changes in the C6+ fraction in the cricondentherm region. Likewise, the cricondenbars obtained from experimental phase envelope data are 275.3 K/11.6 MPa and
263.7 K/10.7 MPa, for M88C1 and M94C1 samples, and thus, M88C1 sample has a cricondenbar pressure roughly 1 MPa larger than that for M94C1. These large cricondentherm temperatures and cricondenbar pressures should be considered for the custody transfer conditions of the studied mixtures. Phase envelopes of the studied gas mixtures were also calculated via most widely used EOS. Calculations performed using various EOS and they are presented in table 5 and figure 2. Various EOS were selected for this purpose; Soave–Redlich–Kwong (SRK) [32], Twu–Redlich–Kwong (TRK) [33], Peng–Robinson (PR) [34], and Twu–Peng–Robinson (TPR) [35], were selected as bi–parametric cubic EOS, Patel–Teja (PT) [36], Schmidt–Wenzel (SW) [37], Guo–Du (GD) [38], and Mohsen–Nia et al. (MMM) [39] were selected as tri-parametric cubic EOS. Moreover, molecular-based EOS using Wertheim perturbation theory [40] have gained acceptance in academia as statistical associating fluid theory (SAFT). Therefore, SAFT EOS [41] and PC-SAFT EOS [42] were selected as molecular based EOS to conduct a full comparison study on the complex fluids studied in the work. Bi-parametric cubic EOS was investigated in details as they are used by industry for predicting reservoir fluids for long time. The performance of SRK, TRK, PR and TPR EOS for the prediction of phase envelopes for the studied heavy mixtures showed remarkable deviations with experimental data both in the cricondentherm and cricondenbar regions. Cricondentherm temperature and cricondenbar pressure, which are key parameters for the characterization of phase behavior for natural gas transportation, obtained from PR and SRK EOS are reported in figure 3 in comparison with values obtained from experimental isochoric data reported in this work. Reported results show that SRK EOS predicts accurately the M94C1 cricondentherm region but fails for the M88C1, and it fails also in the prediction of the cricondenbar region of both regions. PR EOS leads to large deviations both in the cricondentherm and cricondenbar regions of both mixtures, with the only exception of M88C1 cricondenbar region. Therefore, SRK and PR EOS cannot be used for a reliable characterization of the studied mixtures, the use of these EOS for gas transportation purposes would require equipment overdesign to assure single phase flow, with the subsequent economical costs. On the other hand, both tri-parametric and molecular based EOS also showed similar behavior as bi-parametric cubic EOS. For both gas samples, none of the EOS were able to predict the cricondentherm accurately and they resulted with prediction deviations of almost up to 7 K. For bubble point section and in particular cricondentherm predictions for both mixtures with tri-parametric cubic EOS and molecular based EOS were better than cricondenbar predictions. It was observed that SAFT EOS performs superior than the PC-SAFT EOS for both mixtures in bubble point region. When all tri-parametric and molecular based EOS compared, MMM EOS performs the best amongst the others for the bubble point and dew point sections of the phase envelope.
FIGURE 3. Comparison of cricondentherm temperature (TCT) and cricondenbar pressure (PCB) obtained from experimental isochoric data reported in this work (subindex EXP) with values obtained from SRK and PR EOS (subindex EOS). Bar color code: (black bar) SRK, and (dashed bar) PR.
139
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142 TABLE 6 Experimental density results, q, and their deviations from AGA8-DC92 and GERG-2008 EOS for M94C1 (data for gas phase density). T/K
P/MPa
qexp kg m3
qAGA8 kg m3
qGERG08 kg m3
270.019 270.021 270.024 270.026 270.036 270.011 270.008 270.025 280.025 280.020 279.949 279.999 279.998 280.002 280.006 280.018 280.028 280.030 280.007 280.026 290.066 290.057 290.055 290.041 290.018 289.987 290.097 290.067 290.061 290.081 305.016 305.015 305.006 305.005 305.008 305.003 305.002 305.015 304.894 320.056 320.057 320.054 320.056 320.054 320.051 320.055 320.053 320.049 320.002 320.001 340.025 340.020 340.023 340.020 340.026 340.030 339.995 339.998 339.994 339.990 340.061
13.842 15.524 17.236 18.970 20.702 27.614 27.603 34.544 9.999 10.691 11.377 12.066 13.829 15.520 17.598 18.974 20.696 27.596 27.622 34.513 9.656 10.351 12.064 13.787 15.516 17.273 18.981 20.728 27.636 34.502 10.340 12.086 13.809 15.534 17.286 18.971 20.713 27.680 34.426 3.483 6.912 10.362 12.087 13.800 15.521 17.252 18.978 20.706 27.622 34.491 3.500 6.929 10.393 12.115 13.819 15.529 17.287 19.002 20.702 27.465 34.521
166.019 185.829 203.207 218.214 231.024 268.135 268.319 293.018 102.309 111.381 120.247 128.915 150.422 169.405 189.988 201.917 215.158 254.762 254.661 281.141 90.735 98.669 118.217 137.411 155.627 172.647 187.356 200.965 241.811 269.616 88.847 106.112 122.973 139.274 154.905 168.865 182.113 224.213 253.246 24.826 51.973 81.516 96.662 111.620 126.296 140.454 153.834 166.369 207.940 238.313 23.132 47.678 73.878 87.118 100.161 113.030 125.916 137.979 149.372 188.610 220.113
165.830 185.540 202.870 217.870 230.700 267.970 267.930 292.720 102.680 111.470 120.260 128.890 150.340 169.240 189.750 201.660 214.910 254.340 254.490 280.800 90.867 98.726 118.190 137.350 155.520 172.460 187.130 200.730 241.620 269.270 88.888 106.130 122.970 139.230 154.800 168.720 181.930 224.010 252.930 24.831 52.027 81.549 96.672 111.600 126.230 140.350 153.680 166.170 207.710 237.980 23.183 47.779 73.979 87.211 100.230 113.070 125.920 137.930 149.290 188.420 219.900
166.830 186.650 203.890 218.720 231.360 267.970 267.930 292.330 102.840 111.700 120.580 129.300 150.980 170.030 190.560 202.410 215.540 254.450 254.600 280.550 90.950 98.854 118.460 137.780 156.080 173.100 187.770 201.310 241.800 269.140 88.961 106.280 123.220 139.580 155.240 169.200 182.420 224.260 252.910 24.824 52.022 81.594 96.768 111.760 126.460 140.650 154.030 166.550 207.980 238.030 23.178 47.775 74.003 87.262 100.320 113.210 126.100 138.150 149.540 188.680 220.010
3.2. Densimeter results Experimental density results and their deviations from AGA8DC92 and GERG-2008 EOS are in given table 6 M94C1 for and table 7 for M88C1. For both EOS, density calculations were made by REFPROP 9.1 (NIST Reference Fluid Thermodynamic and Transport Properties Database) software available through NIST Thermophysical Properties Division [43]. Density experiments were conducted are along four different isotherms at T = (270, 290, 305,
Relative deviation% AGA8
GERG2008
0.114 0.156 0.166 0.158 0.140 0.062 0.145 0.102 0.361 0.080 0.011 0.019 0.054 0.098 0.126 0.127 0.115 0.166 0.067 0.121 0.145 0.057 0.023 0.044 0.069 0.109 0.121 0.117 0.079 0.128 0.046 0.017 0.002 0.032 0.068 0.086 0.101 0.090 0.125 0.018 0.104 0.041 0.011 0.018 0.052 0.074 0.100 0.119 0.111 0.140 0.220 0.212 0.136 0.107 0.069 0.036 0.003 0.035 0.055 0.101 0.097
0.486 0.440 0.335 0.231 0.145 0.062 0.145 0.235 0.516 0.286 0.276 0.298 -0.370 0.367 0.300 0.244 0.177 0.123 0.024 0.210 0.236 0.187 0.205 0.268 0.290 0.262 0.221 0.172 0.005 0.177 0.128 0.159 0.201 0.219 0.216 0.198 0.168 0.021 0.133 0.010 0.094 0.096 0.110 0.125 0.130 0.139 0.127 0.109 0.019 0.119 0.198 0.203 0.169 0.166 0.159 0.159 0.146 0.124 0.112 0.037 0.047
and 340) K for M88C1 and T = (270, 280, 290, 305, 320 and 340) K for M94C1 mixtures. For M88C1 temperature stability attained across the cell was ±4.2 mK at T = 270 K, ±5.9 mK at T = 290 K, and ±4.1 mK at T = 305 K and ±1.9 K at T = 340 K. Temperature stabilities were recorded as ±8.7 mK at T = 270 K, ±22 mK at T = 280 K, ±31 mK at T = 290 K, ±38 mK at T = 305 K, ±21 mK at T = 320 K and ±20 mK at T = 340 K. The experimental points on each isotherm range up to 35 MPa. Total number PqT points collected for M88C1 mixture is 32 and 56 for M94C1 with
140
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
TABLE 7 Experimental density results and their deviations from AGA8-DC92 and GERG-2008 EOS for M88C1 (data for gas phase density). T/K
P/MPa
qexp kg m3
qAGA8 kg m3
qGERG08 kg m3
270.007 270.000 269.999 270.003 270.005 270.007 270.008 269.998 269.999 289.992 289.996 290.004 290.002 290.000 290.009 289.994 305.008 304.998 304.998 305.002 304.998 305.005 305.005 339.995 339.998 339.994 339.995 339.999 339.995 340.000 339.997 339.997
13.799 17.241 20.698 24.142 27.582 31.009 34.459 27.536 20.688 12.428 13.791 17.232 20.708 24.143 27.600 34.479 12.081 13.806 17.244 20.712 24.142 27.575 34.512 3.487 6.919 10.367 13.814 17.236 20.678 24.143 27.572 34.491
192.959 231.429 257.997 277.480 292.690 305.080 315.661 292.551 257.920 140.192 157.575 195.628 225.168 247.491 265.222 291.906 119.603 139.023 174.309 203.711 227.071 245.949 275.032 24.856 51.851 81.038 110.933 139.345 165.355 188.304 207.793 239.435
191.790 230.130 256.810 276.410 291.750 304.260 314.910 291.580 256.740 139.750 156.940 194.640 224.050 246.400 264.220 291.040 119.440 138.700 173.650 202.810 226.06 244.95 274.11 24.962 52.066 81.214 110.88 139.08 164.82 187.53 206.96 238.56
194.2 232.07 257.99 277 291.92 304.14 314.6 291.75 257.93 140.63 158.08 196.04 225.22 247.22 264.72 291.08 119.92 139.4 174.67 203.84 226.9 245.55 274.32 24.962 52.09 81.332 111.17 139.56 165.45 188.2 207.57 238.95
1.0
1.0
(a)
0.5
0.5
0.0
0.0
-0.5
-0.5
Relative deviation% AGA8
GERG2008
0.610 0.564 0.462 0.387 0.322 0.270 0.239 0.333 0.460 0.317 0.405 0.508 0.499 0.443 0.379 0.297 0.136 0.233 0.380 0.444 0.447 0.408 0.336 0.424 0.412 0.217 0.047 0.191 0.325 0.413 0.403 0.367
0.639 0.276 0.003 0.173 0.264 0.309 0.337 0.274 0.004 0.311 0.319 0.210 0.023 0.110 0.190 0.284 0.264 0.270 0.206 0.063 0.075 0.163 0.260 0.424 0.458 0.361 0.214 0.154 0.057 0.055 0.107 0.203
(b)
-1.0
-1.0 0
10
20 P / MPa
30
40
0
10
20 P / MPa
30
40
FIGURE 4. Density deviations compared to predictions from (a) AGA8-DC92 and (b) GERG2008 EOS, for M88C1 mixture. Symbols: (}) T = 270 K, (4) T = 290 K, (h) T = 305 K, and (s) T = 340 K.
an uncertainty in pressure of 0.01%. These density measurements are corrected for the force transmission error caused by the magnetic suspension coupling as described by Cristancho et al. [28] Density deviations compared to predictions from AGA8-DC92 EOS appear in figure 4a for M88C1 and figure 5a for M94C1 and deviations compared to predictions from GERG-2008 EOS appear in figure 4b for M88C1 and figure 5b for M94C1. At low temperature and at low pressure the deviations from AGA8-DC92 EOS are more than expected according to the deviation regions as explained in the original AGA report. It is clear from these results that AGA8-DC92 has issues in predicting density at low pressures for the T = (270, 305, and 340) K isotherms. A closer inspection of data used for AGA8-DC92 EOS development shows that, except for one mixture, the mole fraction of C6 + components does not
exceed 0.12%, [44] and data sets comes from gas mixtures consisting of mostly binary or ternary combinations of methane, ethane, propane, butane, nitrogen, and carbon dioxide are used during the development and validation of AGA8-DC92. Thus, for any natural gas samples or mixtures with C6+ higher than the normal or expanded range, the application of AGA8-DC92 is an extrapolation, and the accuracy compared to the normal range mentioned in the original AGA report is questionable. Results obtained from GERG2008 EOS reported in figures 4b and 5b show also remarkable deviations with experimental data, the average absolute percentage errors for M88C1 mixture are 0.37% and 0.22%, using AGA8DC92 and GERG2008, respectively, whereas for M94C1 are 0.09% and 0.19%, using AGA8-DC92 and GERG2008, respectively. Therefore, although GERG2008 predictions are slightly better than those
141
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142
1.0
1.0
(a)
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
(b)
-1.0 0
10
20 P / MPa
30
40
0
10
20 P / MPa
30
40
FIGURE 5. Density deviations compared to predictions from (a) AGA8-DC92 and (b) GERG2008 EOS, for M94C1 mixture. Symbols: (}) T = 270 K, (h) 280 K, (4) 290 K, () 305 K, (⁄) 320 K, and (s) 340 K.
from AGA8-DC92 for M88C1 sample, it also showed some prediction issues in the low-pressure region as AGA8-DC92. Likewise, GERG2008 predictions are worse than those from AGA8-DC92 for M94C1 sample. Therefore, both AGA8-DC92 and GERG2008 EOS have density predicting issues (density deviations are larger than the 0.1%) especially for pressures lower than 10 MPa for the studied mixtures that contains heavy samples. Total error and uncertainty analysis were conducted by taking random and systematic errors into consideration. Random errors that were considered include the uncertainty in pressure and temperature measurement, molar compositional analysis, and measurement of the sinker mass under vacuum and at. On the other hand, uncertainty in sinker volume, which includes uncertainty in sinker volume determination at a reference temperature and pressure, as well as uncertainty in the functional dependence of sinker volume on temperature and pressure, was considered as systematic error. Yet, the force transmission error also contributes to systematic error as well. The error in density caused by pressure, temperature, and composition is:
Dq ¼
8" < @ q :
@P
#2
DP T;x
" #2 " #2 91=2 = @q @q þ DT þ Dxi : ; @T P;x @xi P;T;xi–j ð3Þ
We did an uncertainty analysis for a natural gas mixture sample that was previously studied by Patil [21]. Moreover fluid specific force transmission related and balance calibration related uncertainties were previously studied by Cristancho [28] as (36 and 5) ppm respectively. These values contributed total uncertainty caused by the densimeter data as 0.001%. Uncertainty from temperature measurements is estimated as 0.005%. Estimated total uncertainty in pressure transducer calibration caused by the deadweight gauge and differential pressure indicator 0.005%, and the total uncertainty of the pressure transducer is 0.02%. Majority of the overall uncertainty comes from the mixture preparation and quality. The estimated uncertainty of the gas mixture is 0.12%. As sum, overall total estimated uncertainty of the density measurements were was calculated as 0.13%. 4. Conclusions New, accurate experimental data are collected for the phase envelopes and densities of a multicomponent natural gas-like mixture. Phase envelope measurements do not agree with most widely used EOS predictions. Density measurements agree with GERG-2008 EOS more than AGA8-DC92 EOS especially at higher pressures that are close to custody transfer conditions. At low
pressures neither AGA8-DC92 EOS nor GERG2008 EOS predictions showed deviations lower than 0.1% in density. More measurements on multicomponent mixtures containing heavy components and comparisons with EOS predictions appear necessary at low pressures. It seems new GERG-2008 EOS development process with the inclusion of more multi-component data sets and the use of accurate EOS in the form of fundamental equations for each mixture component along with several functions developed for the binary mixtures of the components to take into account the residual mixture behavior, helped to achieve more accurate property predictions especially for multi-component mixtures over a wide range of compositions including heavy component mixtures when compared with predecessor version.
Acknowledgments This work was made possible by NPRP Grants # 30-6-7-1 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. The authors express their gratitude to Mardi Gras Transportation Systems, LLC for the funding provided. The authors also appreciate support from Premier Measurement Services and Savant Measurement Corporation. Financial support also came from the Texas Engineering Experiment Station and the Jack E. & Francis Brown Chair funds.
References [1] M. Atilhan, S. Ejaz, J. Zhou, D. Cristancho, I. Mantilla, J. Holste, K.R. Hall, J. Chem. Eng. Data 55 (11) (2010) 4907–4911. [2] P. Patil, S. Ejaz, M. Atilhan, D. Cristancho, J.C. Holste, K.R. Hall, J. Chem. Thermodyn. 39 (8) (2007) 1157–1163. [3] K.R. Hall, J.C. Holste, Flow Meas. Instrum. 1 (1990) 127–132. [4] E.F. May, T.J. Edwards, A.G. Mann, C. Edwards, R.C. Miller, Fluid Phase Equilib. 185 (1–2) (2001) 339–347. [5] K.K. Botros, Chem. Eng. Commun. 189 (2) (2002) 151–172. [6] R. Gharbi, A.M. Elsharkawy, Pet. Sci. Technol. 21 (1–2) (2003) 53–79. [7] K.R. Hall, L. Yarborough, Oil Gas J. 71 (25) (1973) 82. [8] P.M. Dranchuk, R.A. Purvis, D.B. Robinson, Computer calculations of natural gas compressibility factors using the standing and Karz correlation, Institute of Petroleum Technical Series No. IP 74-008, 1974. [9] P.M. Dranchuk, J.H. Abou-Kassem, J. Can. Pet. Technol. 14 (3) (1975) 34. [10] K.E. Starling, J.L. Savidge, Compressibility factors of natural gas and other related hydrocarbon gases, American Gas Association, Arlington, VA, 1992. [11] O. Kunz, W. Wagner, J. Chem. Eng. Data 57 (11) (2012) 3032–3091. [12] P.T. Eubank, M.A. Barrufet, AIChE J. 33 (1987) 1882–1887. [13] P.T. Eubank, L.L. Joffrion, M.R. Patel, W. Warowny, J. Chem. Thermodyn. 20 (1988) 1009–1034. [14] J. Zhou, P. Patil, S. Ejaz, M. Atilhan, J.C. Holste, K.R. Hall, J. Chem. Thermodyn. 38 (11) (2006) 1489–1494. [15] R. Span, W. Wagner, J. Phys. Chem. Ref. Data 25 (1996) 1509–1596. [16] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST reference fluid thermodynamic and transport properties REFPROP, Version 8.0; National
142
[17] [18] [19] [20] [21]
[22] [23] [24] [25] [26] [27] [28] [29] [30]
M. Atilhan et al. / J. Chem. Thermodynamics 82 (2015) 134–142 Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, MD, 2007. P.L. Acosta-Perez, D.E. Cristancho, I.D. Mantilla, K.R. Hall, G.A. Iglesias-Silva, Fluid Phase Equilib. 283 (1–2) (2009) 17–21. D.E. Cristancho, I.D. Mantilla, L.A. Coy, A. Tibaduiza, D.O. Ortiz-Vega, K.R. Hall, G.A. Iglesias-Silva, J. Chem. Eng. Data 56 (4) (2011) 826–832. R. Kleinrahm, W. Wagner, Prog. Rep. VDI J. 3 (92) (1984) 2. H.W. Losch, VDI Verlag, Dusseldolf, 1987. P.V. Patil, Commissioning of a magnetic suspension densitometer for highaccuracy density measurements of natural gas mixtures (Dissertation), Texas A&M University, College Station, TX, 2005. W. Wagner, R. Kleinrahm, Metrologia 41 (2) (2004) S24. N. Kuramoto, K. Fujii, A. Waseda, Metrologia 41 (2) (2004) S84. D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesia-Silva, J. Chem. Eng. Data 55 (2) (2010) 826–829. D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (8) (2010) 2746–2749. I.D. Mantilla, D.E. Cristancho, S. Ejaz, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (10) (2010) 4227–4230. I.D. Mantilla, D.E. Cristancho, K.R. Hall, M. Atilhan, G.A. Iglesias-Silva, J. Chem. Eng. Data 55 (11) (2010) 4611–4613. D.E. Cristancho, D.E. Cristancho, I.D. Mantilla, S. Ejaz, K.R. Hall, G.A. IglesiasSilva, M. Atilhan, Int. J. Thermophys. 31 (4–5) (2010) 698–709. M. Atilhan, S. Aparicio, S. Ejaz, D. Cristancho, K.R. Hall, J. Chem. Eng. Data 56 (2) (2011) 212–221. M. Atilhan, S. Aparicio, S. Ejaz, D. Cristancho, I. Mantilla, K.R. Hall, J. Chem. Eng. Data 56 (10) (2011) 3766–3774.
[31] M. Atilhan, S. Aparicio, F. Karadas, K.R. Hall, R. Alcalde, J. Chem. Thermodyn. 53 (2012) 1–8. [32] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203. [33] C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilib. 105 (1995) 61–69. [34] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [35] C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilib. 105 (1995) 61–69. [36] N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37 (1982) 463–473. [37] G. Schmidt, H.A. Wenzel, Chem. Eng. Sci. 35 (1980) 1503–1512. [38] T.M. Guo, L. Du, Fluid Phase Equilib. 52 (1989) 47–57. [39] M. Mohsen-Nia, H. Modarress, G.A. Mansoori, Fluid Phase Equilib. 206 (2003) 27–39. [40] M.S. Wertheim, J. Stat. Phys. 35 (1984) 19–34. [41] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709–1721. [42] F. Tumakaka, J. Gross, G. Sadowski, Fluid Phase Equilib. 228 (2005) 89–98. [43] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2013. [44] J.L. Savidge, S.W. Beyerlein, E.W. Lemmon, Technical Reference Document for the 2nd Edition of AGA Report No. 8, Gas Research Institute: Des Plaines, IL, Topical Report No. GRI-93/0181, 1995.
JCT 14-291