Jingfa Li1, Yue Su2, Bo Yu1, Peng Wang1, Dongliang Sun1. 1. School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil and Gas Development, Beijing Institute of Petrochemical Technology, Beijing 102617, China. 2. Beijing Key Laboratory of Process Fluid Filtration and Separation, College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China.
Abstract
Blending hydrogen into the natural gas pipeline is considered as a feasible way for large-scale and long-distance delivery of hydrogen. However, the blended hydrogen can exert major impacts on the Joule-Thomson (J-T) coefficient of natural gas, which is a significant parameter for liquefaction of natural gas and formation of natural gas hydrate in engineering. In this study, the J-T coefficient of natural gas at different hydrogen blending ratios is numerically investigated. First, the theoretical formulas for calculating the J-T coefficient of the natural gas-hydrogen mixture using the Soave-Redlich-Kwong (SRK) equation of state (EOS), Peng-Robinson EOS (PR-EOS), and Benedict-Webb-Rubin-Starling EOS (BWRS-EOS) are, respectively, derived, and the calculation accuracy is verified by experimental data. Then, the J-T coefficients of natural gas at six different hydrogen blending ratios and thermodynamic conditions are calculated and analyzed using the derived theoretical formulas and a widely used empirical formula. Results indicate that the J-T coefficient of the natural gas-hydrogen mixture decreases approximately linearly with the increase of the hydrogen blending ratio. When the hydrogen blending ratio reaches 30% (mole fraction), the J-T coefficient of the natural gas-hydrogen mixture decreases by 40-50% compared with that of natural gas. This work also provides a J-T coefficient database of a methane-hydrogen mixture with a hydrogen blending ratio of 5-30% at a pressure of 0.5-20 MPa and temperatures of 275, 300, and 350 K as a reference and a benchmark for interested readers.
Blending hydrogen into the natural gas pipeline is considered as a feasible way for large-scale and long-distance delivery of hydrogen. However, the blended hydrogen can exert major impacts on the Joule-Thomson (J-T) coefficient of natural gas, which is a significant parameter for liquefaction of natural gas and formation of natural gas hydrate in engineering. In this study, the J-T coefficient of natural gas at different hydrogen blending ratios is numerically investigated. First, the theoretical formulas for calculating the J-T coefficient of the natural gas-hydrogen mixture using the Soave-Redlich-Kwong (SRK) equation of state (EOS), Peng-Robinson EOS (PR-EOS), and Benedict-Webb-Rubin-Starling EOS (BWRS-EOS) are, respectively, derived, and the calculation accuracy is verified by experimental data. Then, the J-T coefficients of natural gas at six different hydrogen blending ratios and thermodynamic conditions are calculated and analyzed using the derived theoretical formulas and a widely used empirical formula. Results indicate that the J-T coefficient of the natural gas-hydrogen mixture decreases approximately linearly with the increase of the hydrogen blending ratio. When the hydrogen blending ratio reaches 30% (mole fraction), the J-T coefficient of the natural gas-hydrogen mixture decreases by 40-50% compared with that of natural gas. This work also provides a J-T coefficient database of a methane-hydrogen mixture with a hydrogen blending ratio of 5-30% at a pressure of 0.5-20 MPa and temperatures of 275, 300, and 350 K as a reference and a benchmark for interested readers.
With
the increasingly serious global warming and the depletion
of traditional fossil fuels, clean renewable energy has attracted
considerable attention in recent years.[1] However, due to the uneven distribution of renewable resources,
system-wide oversupply, and other reasons, renewable energy has not
been fully utilized and consumed. The waste of surplus renewable energy
generation is commonly seen in many countries. As a kind of clean
energy carrier, hydrogen has the advantages of wide sources and zero-carbon
emission. It can be produced from renewable energies such as wind
energy, nuclear energy, electric energy, etc. Through the power-to-gas
(P2G) technology, surplus renewable energy generation can be converted
to gaseous hydrogen; thus, it is viewed as an effective way to solve
the wastage of renewable energy generation.[2−5] The research of P2G technology
can date back to earlier years in countries such as Germany and the
United States. For example, in Europe alone there are more than 45
P2G projects in operation and under construction. Between hydrogen
generation by P2G projects and hydrogen consumption by users, hydrogen
delivery is a key link. For larger economic benefits and shorter transportation
periods, blending hydrogen into natural gas is considered as one of
the best feasible ways to achieve large-scale, long-distance transport
of hydrogen using existing natural gas pipelines or pipe networks.[6]For gas transportation, consideration must
be given to the Joule–Thomson
(J–T) effect (also known as the throttling effect). The J–T
effect was first observed in an experiment conducted by James Prescott
Joule and William Thomson in 1852 and is a thermodynamic process that
occurs when a fluid expands from high pressure to low pressure at
constant enthalpy.[7] If the J–T coefficient
is positive, then the fluid cools upon expansion, and if it is negative,
the fluid warms upon expansion. The cooling produced in J–T
expansion has been a double-edged sword in natural gas engineering.
For example, the temperature drop caused by the J–T effect
during natural gas transportation can cause gas hydrate blockage at
the pipeline valves;[8,9] in the production of natural gas
hydrate, the temperature change induced by the J–T effect has
significant impacts on the production efficiency;[10] in natural gas liquefaction, the cooling produced in the
J–T expansion can be used to liquefy natural gas,[11] etc. Therefore, it is of great engineering significance
to study the J–T effect of natural gas. Compared with traditional
natural gas without hydrogen, the composition and relative content
of natural gas are changed upon hydrogen blending, resulting in variations
in its physical and thermodynamic properties. Thus, for the natural
gas–hydrogen mixture, hydrogen blending can exert great influences
on the J–T effect. Accurately calculating the J–T coefficient
of the natural gas–hydrogen mixture and revealing the influences
of hydrogen blending on the J–T effect are of great importance.
At present, the widely used methods for predicting the J–T
coefficient include experimental measurement,[12−16] pressure–enthalpy chart,[7] empirical formula,[7] molecular
simulation,[17−19] theoretical calculation using equation of state (EOS),[20−24] etc.In the aspect of experimental measurements, many scholars
measured
the J–T coefficient of different gases via experiments. The
basic experimental principle of J–T expansion can be summarized
as follows: a gas with volume V1, pressure p1, and temperature T1 flows through a porous membrane, pushed by a piston at pressure p1; the gas expands against a piston at a lower
pressure p2 until all of the gas has been
transferred to the other side of the membrane with a final volume V2 and temperature T2, and then the J–T coefficient can be calculated by the pressure
and temperature changes before and after expansion. From the 1970s
to the 1990s, Francis et al.[12−14] designed flow calorimeters to
measure the specific heat capacity and the J–T coefficient.
The J–T coefficients of ethanol, benzene, and cyclohexane vapors
at different temperatures and pressures were measured in their study.
Cuscó et al.[15] applied an improved
flow calorimeter to measure the J–T coefficients of N2 and CO2 at high temperature and high pressure. Ernst
et al.[16] measured the J–T coefficients
of CH4, CH4–C2H6 mixture, and natural gas at different conditions, and the experimental
results provide an important reference and contribute to the experimental
basis for the formulation of an EOS.In terms of numerical calculation,
current calculation methods
for the J–T coefficient mainly include the pressure–enthalpy
chart,[7] empirical formula,[7] molecular simulation,[17−19] and theoretical calculation
using EOS.[20−24] When the temperature and pressure before expansion and the pressure
after expansion are known, the temperature after expansion can be
obtained by reading the pressure–enthalpy chart, and the J–T
coefficient can be calculated.[7] This pressure–enthalpy
chart is simple to read and is commonly used in engineering practice.
However, it is worth noting that this method is not a general approach
because the pressure–enthalpy chart is usually plotted for
a specific natural gas mixture. Compared with the pressure–enthalpy
chart, the empirical formula for calculating the J–T coefficient
of natural gas is a general method with wide application scopes.[7] When the specific heat capacity, the reduced
temperature and pressure, and the critical temperature and pressure
of natural gas are known, the J–T coefficient can be calculated
using the empirical formula. However, the calculation accuracy of
the empirical formula is relatively low. For the mechanism study,
molecular simulation is a valuable tool for investigating the J–T
effect from a microscopic point of view. For example, Vrabec et al.[17] applied molecular simulation and four equations
of state to calculate the J–T coefficients of six different
natural gas mixtures. It was found that the molecular simulation is
competitive with state-of-the-art EOS in predicting J–T inversion
curves. Figueroa-Gerstenmaier et al.[18] carried
out molecular simulations on the J–T coefficient of various
refrigerants over a wide range of thermodynamic conditions, and the
simulation results were compared with pseudo-experimental-results
obtained from the REFPROP software package. Zhang et al.[19] analyzed the throttling mechanism of CO2 at different states from a molecular perspective, and a method
for predicting the J–T coefficient of pipeline CO2 was put forward using the multivariate nonlinear regression method.
It is worth pointing out that although molecular simulation can reveal
the mechanism of the J–T effect and calculate the J–T
coefficient from a microcosmic perspective, the application of this
method is always limited by the high computational costs. In addition,
the molecular simulation system is usually simplified and it cannot
fully reproduce the real physical system of natural gas.For
theoretical calculation of the J–T coefficient using
the EOS, the accuracy depends on the selected EOS, and there have
been extensive related studies. Tay et al.[20] applied the population balance model to simulate the condensation
process of nonequilibrium water, and the influence of the J–T
effect on the dehydration process of natural gas was analyzed using
SRK-EOS. Haghighi et al.[21] compared the
performance of five EOSs to predict the J–T inversion curve.
Results illustrated that the selected EOSs can well predict the low-temperature
branch of the J–T inversion curve, except for the Mohsennia–Modarres–Mansoori
EOS. In addition, the high-temperature branch and peak value of the
inversion curve turned out to be sensitive to the adopted EOS. Abbas
et al.[22] calculated the J–T coefficients
of CO2, Ar, CO2–Ar mixture, and CH4–C2H6 mixture by the group contribution
equation of state VTPR, and the computed J–T coefficients were
in good agreement with the experimental data. Ghanbari and Check[23] applied the J–T inversion curve data
of CH4 and CO2 to adjust the supercritical cohesion
parameters for SRK-EOS. The modified SRK-EOS was verified to present
good predictions of J–T inversion curve data. Regueira et al.[24] compared the performance of SRK, PR, perturbed
chain statistical associating fluid theory (PC-SAFT), and Soave–Benedict–Webb–Rubin
(SBWR) EOSs in modeling the specific heat capacity and the J–T
coefficient. Results demonstrated that the PC-SAFT-EOS is most accurate
in predicting the specific heat capacity, and the SBWR-EOS has the
best performance in calculating the J–T coefficient. Generally
speaking, the theoretical calculation of the J–T coefficient
using the EOS can be well applied to practical engineering as it is
based on a real gas model, and the calculated J–T coefficient
is more accurate than that obtained from pressure–enthalpy
chart, empirical formula, or the molecular simulation method.For hydrogen transportation using existing natural gas pipelines,
blending hydrogen into natural gas may produce different J–T
effects, which unfortunately has rarely been reported. As the physical
and thermodynamic properties of hydrogen and natural gas are quite
different, the influence of hydrogen blending on the J–T coefficient
of the natural gas–hydrogen mixture is still unclear. In this
research, the effect of hydrogen blending on the J–T coefficient
of natural gas is numerically investigated, and the mechanism of J–T
coefficient variation with the hydrogen blending ratio is revealed.
This work is expected to provide a beneficial reference for natural
gas engineering, such as for prevention and control of gas hydrate
in pipeline transport of the natural gas–hydrogen mixture,
liquefaction of hydrogen-enriched natural gas, etc.The remainder
of this paper is organized as follows: in Section , the theoretical
formulas for calculating the J–T coefficient of natural gas
using SRK-EOS, PR-EOS, and BWRS-EOS are mathematically derived; in Section , the predicted
J–T coefficients by EOSs and empirical formula are validated
by experimentally measured J–T coefficients of pure methane,
methane–ethane mixture, and natural gas at different pressures
and temperatures; in Section , the J–T coefficient of natural gas at six different
hydrogen blending ratios and thermodynamic conditions is calculated,
and the effect of hydrogen blending on the J–T coefficient
is analyzed in detail. To provide a valuable reference and a benchmark
for future research on the natural gas–hydrogen mixture, the
J–T coefficient database of the methane–hydrogen mixture
at different hydrogen blending ratios, pressures, and temperatures
is presented; and in Section , concluding remarks of this study are summarized and the
future study is discussed.
Joule–Thomson Coefficient
of the Natural
Gas Mixture
Derivation of the Joule–Thomson Coefficient
The J–T effect can be described by means of the J–T
coefficient, which is the partial derivative of temperature with respect
to pressure at constant enthalpy. For a pure component i, the isenthalpic J–T coefficient can be expressed as followswhere μ is the J–T coefficient of pure component i; T is the temperature; p is the
pressure; and the subscript H denotes an isenthalpic
process. The thermodynamic parameters use SI units unless otherwise
specified.Based on the relation of thermodynamic parameters, eq can be reformulated aswhere c is the molar specific heat capacity of component i at constant pressure.Equation can be
further rearranged as[7] follows (see the Supporting Information)where υ is the molar volume. The term in eq can be written asSubstituting eq and
the relation between molar volume and molar density υ = 1/ρ
into eq , the following
J–T coefficient of component i can be obtainedIt should be noted
that eq represents
the J–T coefficient of the natural gas
mixture provided that the parameters ρ and c in eq adopt the values of the natural gas mixture. For calculation
convenience, accuracy, and efficiency in engineering practice, the
J–T coefficient can also be predicted by the pressure–enthalpy
chart, empirical formulas, and molecular simulation. To comprehensively
explore the influences of hydrogen blending on the J–T coefficient
of the natural gas–hydrogen mixture, in this study, one widely
used empirical formula and three commonly used EOSs in engineering
practice, i.e., SRK-EOS, PR-EOS, and BWRS-EOS, are chosen as representatives
to calculate the J–T coefficient of the natural gas–hydrogen
mixture.
Joule–Thomson Coefficient by the Empirical
Formula
In an empirical formula, the J–T coefficient
of the natural gas–hydrogen mixture is closely related to critical
parameters, reduced parameters, and the molar specific heat capacity
at constant pressure. The following presents a widely used empirical
formula for calculating the J–T coefficient[7]where f(p,T) = 2.343T–2.04 – 0.071p + 0.0568; T and p are the reduced temperature
and pressure, respectively; T and p denote
the critical temperature and pressure,
respectively; and c is
the molar specific heat capacity of a gas at constant pressure. For
the mixture of natural gas and hydrogen, the parameters in eq are those of the natural
gas–hydrogen mixture.
Joule–Thomson Coefficient
by SRK-EOS
SRK-EOS[25] is a cubic-type
equation of
state that has been widely used in natural gas engineering in the
past. It is a modification of RK-EOS[26] by
correcting the a/√T term
of RK-EOS using a function α involving the temperature and the
acentric factorwhere p is the system pressure,
kPa; T is the system temperature, K; υ is the
molar volume, m3/kmol; R is the universal
gas constant, R = 8.3145 kJ/(kmol·K); the attraction
parameter a = a(T)α, where and ; ; T and p are the
critical temperature and critical pressure, respectively; T is the reduced temperature, ; and κ = 0.48508 + 0.55171ω
– 0.15613ω2, where ω is the acentric
factor.For the natural gas–hydrogen mixture, the above
coefficients a and b in eq are obtained by mixing
the corresponding coefficients of included components. The commonly
used mixing rules are defined as followswhere C is the total
number
of components; y is
the mole fraction of component i; and k is the binary interaction coefficient
between components i and j, k =k and k = 0. The value of k for different components can be obtained in refs (7, 27).For the convenience of calculation,
the molar volume υ in eq can be expressed by molar
density. Substituting υ = 1/ρ into eq yieldsAccording to eq ,
the partial derivative of SKR-EOS (eq ) to temperature T and density ρ
should be derived to calculate the J–T coefficient of the natural
gas mixture. However, it should be pointed out that the attraction
parameter a of SRK-EOS is a function of system temperature T; thus, special attention should be paid to the partial
derivative of SRK-EOS, eq , to Twhere .Substituting eqs and 11 into eq yields
the J–T coefficient μSRK of the natural gas–hydrogen
mixture by SRK-EOS.
Joule–Thomson Coefficient
by PR-EOS
Similar to SRK-EOS, PR-EOS is a kind of cubic equation
of state
developed in 1976 at the University of Alberta by Peng and Robinson.[28] It is commonly used to describe the state of
natural gas and can be written as followswhere p is the
system pressure,
kPa; T is the system temperature, K; υ is the
molar volume, m3/kmol; the attraction parameter , where ; ; T and p are the
critical temperature and critical pressure, respectively; κ
= 0.37464 + 1.54226ω – 0.26992ω2, where
ω is the acentric factor defined as ; T is the boiling temperature; and patm denotes the atmospheric pressure.For the natural
gas–hydrogen
mixture, the mixing rules of PR-EOS for calculating parameters a and b are the same as those of SRK-EOS.
However, it should be noted that the binary interaction coefficient k for PR-EOS is different
from that of SRK-EOS.[7,27] For the convenience of calculation,
the molar volume can be expressed by molar density, and eq can be reformulated asSimilarly, the partial derivative
of PR-EOS (eq ) to
temperature T and density
ρ can be derived as followswhere .Finally, substituting eqs and 15 into eq yields the J–T coefficient μPR of the natural gas–hydrogen mixture by PR-EOS.
Joule–Thomson Coefficient by BWRS-EOS
BWRS-EOS[29] is currently the most widely
used real gas model for describing the state of natural gas in engineering
practice. It is a multiparameter equation of state, which is commonly
written aswhere p is the system pressure,
kPa; T is the system temperature, K; ρ is the
molar density of natural gas, kmol/m3; R is the universal gas constant, R = 8.3145 kJ/(kmol·K);
and A0, B0, C0, D0, E0, a, b, c, d, α, and γ are coefficients
of BWRS-EOS, which can be calculated based on the critical temperature,
critical density, and the acentric factor for a pure component iwhere A and B are the
universal gas constants of component i; ρ is the critical density of component i; and ω is the acentric
factor of component i. The value of the above parameters
for different components can be obtained in refs (7, 27).For the natural gas–hydrogen
mixture, the above 11 coefficients of BWRS-EOS are obtained by mixing
the corresponding coefficients of included components. The mixing
rules are defined bywhere C, y, and k have similar meanings as in SRK-EOS and PR-EOS.Different from SRK-EOS and PR-EOS, the coefficients of BWRS-EOS
depend only on the critical parameters and acentric factors, and they
have nothing to do with the system temperature and density. Therefore,
the partial derivative of BWRS-EOS (eq ) for natural gas to temperature T and density ρ is the same as that for the pure component.
The only distinction is that the coefficients of the partial derivative
of BWRS-EOS are obtained according to the mixing rules. The partial
derivative of BWRS-EOS for the natural gas–hydrogen mixture
to T and ρ can be, respectively, derived asBased on the above analysis,
substituting eqs and 20 into eq yields the J–T
coefficient μBWRS of the natural gas–hydrogen
mixture by BWRS-EOS.
Validation
Experimental Conditions
In this study,
the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS are applied to
investigate the influences of hydrogen blending on the J–T
coefficient of the natural gas–hydrogen mixture. However, due
to the distinctions in model assumption and basic theory, the J–T
coefficients calculated by these methods possess different accuracies.
Here, the calculation accuracy of the J–T coefficient is validated
and analyzed. First, J–T coefficients of three different samples
experimentally measured by Ernst et al.[16] are used to validate the calculation results of empirical formula,
SRK-EOS, PR-EOS, and BWRS-EOS. Table presents the experimental conditions, compositions
of sample gases, purity, and mole fraction of each substance in the
experiments by Ernst et al.[16] In this experiment,
the J–T coefficients of pure methane, methane–ethane
mixture, and natural gas were measured at various pressures and temperatures.
Due to the limitation of the measuring accuracy, the uncertainty of
the mole fraction of different substances is also provided in Table .
Table 1
Compositions of Investigated Samples[16]
sample
substance
purity
mole fraction
CH4
CH4
0.999995
1
CH4 + C2H6
CH4
0.999995
0.84874 ± 0.0001
C2H6
0.9995
0.15126 ± 0.001
natural gas
CH4
0.99995
0.79942 ± 0.00004
C2H6
0.9995
0.05029 ± 0.00001
C3H8
0.9995
0.03000 ± 0.00001
CO2
0.999993
0.02090 ± 0.00001
N2
0.999999
0.09939 ± 0.00001
Analysis of Validation Results
The
J–T coefficients of three investigated samples in Table are calculated using
empirical formula (EF), SRK-EOS, PR-EOS, and BWRS-EOS at different
experimental temperatures and pressures. The calculation results are
compared with the experimental measurement data (EX) from Ernst et
al.,[16] and the relative error e between calculation results and the experimental data is also obtained
(e is defined as ), as shown
in Figures –3 and Tables –4.
Figure 1
Relative error of the J–T coefficient of CH4 using
the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS compared with
the experimental data.[16]
Figure 3
Relative error of the
J–T coefficient of the natural gas
mixture using the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS
compared with the experimental data.[16]
Table 2
Comparison of J–T Coefficients
of CH4
experiment
empirical formula
SRK-EOS
PR-EOS
BWRS-EOS
p (MPa)
T (K)
μEX (K/MPa)
μEF (K/MPa)
eEF (%)
μSRK (K/MPa)
eSRK (%)
μPR (K/MPa)
ePR (%)
μBWRS (K/MPa)
eBWRS (%)
1.0
250
6.139
6.621
7.85
7.205
17.36
6.819
11.08
6.276
2.23
275
5.155
5.443
5.59
6.067
17.69
5.744
11.43
5.150
0.10
300
4.354
4.518
3.77
5.147
18.21
4.874
11.94
4.285
1.58
350
3.085
3.200
3.73
3.763
21.98
3.565
15.56
3.058
0.88
3.0
250
6.013
5.777
3.92
6.796
13.02
6.580
9.43
6.193
2.99
275
5.012
4.896
2.31
5.657
12.87
5.474
9.22
5.048
0.72
300
4.193
4.131
1.48
4.765
13.64
4.613
10.02
4.178
0.36
350
2.958
2.962
0.14
3.455
16.80
3.351
13.29
2.954
0.14
5.0
250
5.710
4.898
14.22
6.204
8.65
6.138
7.50
5.942
4.06
275
4.781
4.349
9.04
5.168
8.09
5.098
6.63
4.840
1.23
300
3.994
3.752
6.06
4.351
8.94
4.293
7.49
4.000
0.15
350
2.811
2.733
2.77
3.153
12.17
3.119
10.96
2.817
0.21
10.0
250
4.048
3.097
23.49
3.959
2.20
4.051
0.07
4.066
0.44
275
3.713
3.192
14.03
3.686
0.73
3.748
0.94
3.736
0.62
300
3.244
2.920
9.99
3.249
0.15
3.306
1.91
3.236
0.25
350
2.353
2.214
5.91
2.443
3.82
2.504
6.42
2.384
1.32
15.0
250
2.043 ± 0.01
2.649
29.03
2.036
0.00
2.095
2.05
2.083
1.46
275
2.389
2.553
6.86
2.299
3.77
2.361
1.17
2.360
1.21
300
2.327
2.358
1.33
2.239
3.78
2.307
0.86
2.285
1.80
350
1.854
1.789
3.51
1.833
1.13
1.915
3.29
1.822
1.73
17.5
275
1.82 ± 0.03
2.397
29.57
1.788
0.61
1.837
0.00
1.846
0.00
300
1.91 ± 0.03
2.166
11.65
1.828
2.77
1.889
0.00
1.874
0.32
20.0
300
1.544 ± 0.023
2.011
28.33
1.489
2.10
1.538
0.00
1.536
0.00
350
1.398 ± 0.021
1.445
1.83
1.346
2.25
1.418
0.00
1.350
1.96
eave
9.43
8.03
5.89
1.07
Table 4
Comparison of J–T Coefficients
of Natural Gas
experiment
empirical formula
SRK-EOS
PR-EOS
BWRS-EOS
p (MPa)
T (K)
μEX (K/MPa)
μEF (K/MPa)
eEF (%)
μSRK (K/MPa)
eSRK (%)
μPR (K/MPa)
ePR (%)
μBWRS (K/MPa)
eBWRS (%)
1.0
250
6.922
7.704
11.30
7.767
12.25
7.372
6.50
7.017
1.37
275
5.671
6.328
11.59
6.524
14.97
6.174
8.87
5.688
0.30
300
4.743
5.245
10.58
5.512
16.17
5.216
9.97
4.685
1.22
350
3.333
3.703
11.10
4.013
20.31
3.791
13.74
3.293
1.20
3.0
250
6.841
6.564
4.05
7.356
7.59
7.146
4.46
6.883
0.61
275
5.511
5.610
1.80
6.078
10.32
5.898
7.02
5.553
0.76
300
4.585
4.750
3.60
5.102
11.23
4.941
7.76
4.555
0.65
350
3.205
3.411
6.43
3.656
14.20
3.562
11.14
3.178
0.84
5.0
250
6.431
5.381
16.33
6.691
4.03
6.653
3.45
6.524
1.45
275
5.241
4.898
6.54
5.533
5.51
5.484
4.64
5.284
0.82
300
4.339
4.269
1.61
4.633
6.71
4.591
5.81
4.340
0.02
350
3.032
3.130
3.23
3.321
9.50
3.310
9.17
3.024
0.26
10.0
250
4.082
3.238
20.68
3.903
4.46
4.050
0.78
3.948
3.28
275
3.851
3.443
10.59
3.769
1.58
3.898
1.22
3.862
0.29
300
3.436
3.244
5.59
3.367
1.92
3.468
0.93
3.406
0.87
350
2.504
2.504
0.00
2.533
1.04
2.629
4.99
2.495
0.36
15.0
250
1.774 ± 0.012
2.980
66.85
1.813
1.34
1.916
7.28
1.864
4.37
275
2.283 ± 0.011
2.817
22.80
2.214
2.73
2.318
1.05
2.270
0.09
300
2.358 ± 0.012
2.612
10.21
2.235
4.94
2.337
0.38
2.293
2.26
350
1.926 ± 0.010
2.007
3.67
1.846
2.92
1.978
2.17
1.892
1.25
20.0
300
1.520 ± 0.015
2.249
46.51
1.423
5.65
1.509
0.00
1.492
0.86
350
1.417 ± 0.014
1.614
12.79
1.334
5.69
1.439
0.56
1.372
2.21
eave
13.08
7.50
5.09
1.15
Relative error of the J–T coefficient of CH4 using
the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS compared with
the experimental data.[16]Relative error of the J–T coefficient of the CH4–C2H6 mixture using the empirical formula,
SRK-EOS, R-EOS, and BWRS-EOS compared with the experimental data.[16]Relative error of the
J–T coefficient of the natural gas
mixture using the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS
compared with the experimental data.[16]In Figures –3, the different colors denote
the different methods
adopted to calculate the J–T coefficient, and the symbol height
stands for the relative error. It can be clearly seen from Figures –3 that for all samples, i.e., pure CH4, CH4 + C2H6, and natural gas, the
height of BWRS-EOS is the smallest in almost all of the conditions,
indicating that the relative error of BWRS-EOS is the smallest, and
the J–T coefficient calculated using BWRS-EOS agrees best with
the experimental data under the same condition. From Tables –4, it is seen that the average relative error eave of the J–T coefficient between BWRS-EOS and the
experimental data is only 1.07, 1.05, and 1.15% for the three investigated
samples, respectively. It is inferred that BWRS-EOS is the most accurate
among these methods in predicting the J–T coefficient. Figures –3 and Tables –4 also imply that the calculation
accuracy of PR-EOS is slightly lower than that of BWRS-EOS, and the
average relative error for the three investigated samples is 5.89,
4.0, and 5.09%, respectively. Compared with BWRS-EOS and PR-EOS, SRK-EOS
and empirical formula have relatively low calculation accuracies;
especially, the average relative error of the empirical formula for
the three investigated samples is around 10% on the whole. Furthermore,
as the carbon number of the sample increases, the calculation accuracy
of the empirical formula decreases obviously.As with the influences
of temperature and pressure on the calculation
accuracy, Tables –4 demonstrate that for SRK-EOS and PR-EOS, under
the same pressure, a higher temperature provides a larger relative
error of the J–T coefficient, while at the same temperature,
the relative error of the J–T coefficient is much larger at
low pressure than that at high pressure. This indicates that SRK-EOS
and PR-EOS can provide a much better prediction of the J–T
coefficient at high pressure and low temperature. By contrast, the
calculated J–T coefficient is more accurate at low-pressure
and high-temperature conditions for BWRS-EOS and the empirical formula.
Thus, BWRS-EOS and the empirical formula are favorable for predicting
the J–T coefficient at low-pressure and high-temperature conditions.
But, overall, BWRS-EOS still delivers results of better accuracy compared
to the other two EOSs and the empirical formula at the same given
pressure and temperature.Based on the above comparison, it
can be concluded that BWRS-EOS
is most accurate in predicting the J–T coefficient within a
wide range of thermodynamic conditions (a temperature range of 250–350
K and a pressure range of 1–30 MPa), while PR-EOS, SRK-EOS,
and the empirical formula can only deliver good results in a limited
range of temperature and pressure. Overall, the calculation accuracy
of PR-EOS is still acceptable in most practical engineering problems.
Although the performance of the empirical formula is not so good,
it is much simpler for engineering applications and can save appreciable
computation resources. To ensure the completeness of our investigation
and reveal the influences of hydrogen blending on the J–T coefficient
of the natural gas mixture by different EOSs, all of the above four
methods are adopted in the following study.
Further
Validation by the Methane–Hydrogen
Mixture at Low Temperature
In Section , the calculation accuracy of the empirical
formula, SRK-EOS, PR-EOS, and BWRS-EOS is validated by the experimentally
measured J–T coefficients of three different samples in the
work of Ernst et al.[16] It should be noted
that in the above comparisons, there is no hydrogen in the three samples.
To further verify the applied methods for a hydrogen-enriched system,
the experimental data of the J–T coefficient of the CH4 + H2 mixture from Randelman and Wenzel[30] are used for comparison with our numerical results.
In the experiment of ref (30), the purity of hydrogen is 99.97%, with the impurity being
predominantly nitrogen. The mole fraction of hydrogen and methane
in the mixture is 56.57 and 43.43%, respectively. Interested readers
can refer to ref (30) for more experimental details. However, it is worth mentioning that
the experimental temperature in ref (30) is very low (around 200 K), and BWRS-EOS is
inapplicable at this condition. Thus, in Table , only the calculated J–T coefficients
of the CH4 + H2 mixture by the empirical formula,
SRK-EOS, and PR-EOS are compared with the experimentally measured
J–T coefficients in ref (30).
Table 5
Comparison of the J–T Coefficients
of the CH4 + H2 Mixture
experiment
empirical formula
SRK-EOS
PR-EOS
p (atm)
T (K)
μEX (K/atm)
μEF (K/atm)
eEF (%)
μSRK (K/atm)
eSRK (%)
μPR (K/atm)
ePR (%)
68.03
199.54
0.2617
0.1979
24.38
0.2367
9.57
0.2551
2.52
61.57
198.68
0.2715
0.2100
22.65
0.2491
8.26
0.2678
1.36
57.47
196.09
0.2807
0.2330
16.99
0.2606
7.17
0.2802
0.18
50.15
194.96
0.3023
0.2379
21.30
0.2699
10.7
0.2955
2.25
43.89
192.59
0.3264
0.2553
21.78
0.2815
13.7
0.3119
4.44
38.82
191.21
0.3496
0.2690
23.05
0.3122
10.7
0.3241
7.29
71.43
181.63
0.2846
0.2283
19.78
0.2633
7.49
0.2827
0.67
63.27
178.71
0.3094
0.2491
19.49
0.2887
6.69
0.3076
0.58
55.45
176.62
0.3383
0.2694
20.37
0.2978
11.9
0.3309
2.19
47.62
173.86
0.3723
0.2934
21.19
0.3423
8.07
0.3566
4.22
40.15
170.96
0.4095
0.3200
21.86
0.3723
9.09
0.3823
6.64
51.02
204.00
0.2735
0.2169
20.69
0.2584
5.53
0.2743
0.29
43.21
202.00
0.3001
0.2349
21.73
0.2706
9.83
0.2908
3.10
35.38
199.12
0.3268
0.2564
21.54
0.2891
11.5
0.3096
5.26
30.28
197.61
0.3442
0.2703
21.47
0.3006
–12.6
0.3211
6.71
24.15
195.72
0.3652
0.2883
21.06
0.3150
13.7
0.3350
8.27
18.37
193.17
0.3850
0.3326
13.61
0.3309
14.0
0.3501
9.06
eave
20.76
10.03
3.79
It can be clearly seen from Table that at the same
experimental pressure and temperature,
PR-EOS can give a much better prediction of the J–T coefficient
than the empirical formula and SRK-EOS. The average relative error
of PR-EOS is only −3.79%, which is much smaller than −10.03%
of SRK-EOS and −20.76% of the empirical formula. Compared with Tables –4, it can also be found in Table that the relative errors of the empirical
formula, SRK-EOS, and PR-EOS are all larger than those at a relatively
high-temperature range of 250–350 K. Thus, the thermodynamic
condition has a significant influence on the calculation accuracy
of the applied EOSs and the empirical formula. Overall, the comparisons
of the experimental measurement data with the calculated results as
shown in Tables –5 indicate that PR-EOS and BWRS-EOS are capable of
accurately predicting the J–T coefficient, and BWRS-EOS can
perform much better if the temperature is not very low (≥250
K in this study).
Results and Discussion
In this section, the effects of hydrogen blending on the Joule–Thomson
coefficient of the natural gas–hydrogen mixture are discussed
in detail.
Natural Gas–Hydrogen Mixture
Table depicts the
components of the natural gas for the study below.[7] The J–T coefficients of the natural gas at six different
thermodynamic conditions and six different hydrogen blending ratios
are calculated and analyzed. According to the transportation condition
using natural gas pipelines or pipe networks, the six thermodynamic
conditions are, respectively, set as (1) p = 0.1
MPa and T = 283.15 K; (2) p = 1.0
MPa and T = 283.15 K; (3) p = 1.0
MPa and T = 293.15 K; (4) p = 5.0
MPa and T = 293.15 K; (5) p = 5.0
MPa and T = 308.15 K; and (6) p =
10.0 MPa and T = 323.15 K. The six hydrogen blending
ratios (mole fraction) are, respectively, set as 5, 10, 15, 20, 25,
and 30%.
Table 6
Composition of the Investigated Natural
Gas
substance
CH4
C2H6
C3H8
i-C4
n-C4
i-C5
n-C5
n-C6
n-C7
n-C8
N2
CO2
mole fraction (%)
92.45
3.64
1.37
0.16
0.13
0.20
0.05
0.05
0.09
0.02
1.30
0.54
It should be mentioned that the reason
why the maximum hydrogen
blending ratio is set as 30% is that the present reports in the literature
show that when the hydrogen blending ratio is not higher than 30%,
the mixed hydrogen does not significantly affect the combustion characteristics
of natural gas, and there is no need to reform the domestic gas appliances
of end users.[31] The hydraulic and thermal
characteristics of natural gas pipelines will not be influenced appreciably
as well.[32,33] Therefore, the upper limit of the hydrogen
blending ratio is set as 30% in this study.
Analysis
of the Calculated Joule–Thomson
Coefficient
Figures –7 display the variation of the J–T coefficient of the
natural gas–hydrogen mixture at different hydrogen blending
ratios and thermodynamic conditions by the empirical formula, SRK-EOS,
PR-EOS, and BWRS-EOS, respectively. It can be obviously seen that
under the same thermodynamic conditions, the J–T coefficient
of the natural gas–hydrogen mixture approximately linearly
decreases with the increase of the hydrogen blending ratio. For instance, Figures –7 show that the slope of the μJT–H2% curve (the J–T coefficient
versus the hydrogen blending ratio) obtained by the empirical formula,
SRK-EOS, PR-EOS, and BWRS-EOS is, respectively, −0.066, −0.085,
−0.073, and −0.077 (K/MPa)/% at 0.1 MPa and 283.15 K.
Moreover, for the same EOS at the thermodynamic conditions of 0.1–5.0
MPa and 283.15–308.15 K, the decrease range of the J–T
coefficient against the increase of the hydrogen blending ratio is
approximately the same. That is, the slope of the J–T coefficient
curve changing with the hydrogen blending ratio is nearly the same,
and the curves under different thermodynamic conditions (except for
10 MPa and 323.15 K) are approximately parallel to each other. For
example, the slope of the μJT–H2% curve obtained by PR-EOS at 0.1 MPa/283.15 K and 1.0 MPa/283.15
K is −0.073 and −0.074 (K/MPa)/%, respectively. It indicates
that the impact of the hydrogen blending ratio on the J–T coefficient
is almost the same under different thermodynamic conditions, except
for the high-pressure and -temperature conditions, such as 10 MPa
and 323.15 K.
Figure 4
J–T coefficient of the natural gas–hydrogen
mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using the empirical formula.
Figure 7
J–T coefficient
of the natural gas–hydrogen mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using BWRS-EOS.
J–T coefficient of the natural gas–hydrogen
mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using the empirical formula.J–T
coefficient of the natural gas–hydrogen mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using SRK-EOS.J–T
coefficient of the natural gas–hydrogen mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using PR-EOS.J–T coefficient
of the natural gas–hydrogen mixture
at different hydrogen blending ratios and thermodynamic conditions
calculated using BWRS-EOS.In addition, Figures –7 also demonstrate that at the same
temperature and hydrogen blending ratio, the J–T coefficient
of the natural gas–hydrogen mixture decreases with increasing
pressure, such as the two curves corresponding to 1.0 and 5.0 MPa
at 293.15 K. Similarly, at the same pressure and hydrogen blending
ratio, the J–T coefficient of the natural gas–hydrogen
mixture decreases with the increase of temperature, such as the two
curves corresponding to 293.15 and 308.15 K at 5.0 MPa. Thus, either
higher pressure or temperature leads to a smaller J–T coefficient
of the natural gas–hydrogen mixture. The hydrogen-mixed natural
gas and natural gas without hydrogen (the hydrogen blending ratio
is 0% in Figures –7) show the same variation trend, implying that hydrogen
blending does not affect the variation trend of the J–T coefficient
with pressure and temperature. The underlying reason for this phenomenon
can be attributed to the influences of temperature and pressure on
the physical and thermal properties of the natural gas–hydrogen
mixture, such as the density and the specific heat capacity.To sum up, hydrogen blending has great influences on the J–T
coefficient of the natural gas–hydrogen mixture. With the increase
of the hydrogen blending ratio, the J–T coefficient of the
natural gas–hydrogen mixture decreases approximately linearly.
In addition, the decreasing trend of the J–T coefficient with
the increasing hydrogen blending ratio is similar under different
thermodynamic conditions. In engineering practice, the effect of hydrogen
blending on the J–T coefficient is actually a double-edged
sword. For example, in pipeline transportation of the natural gas–hydrogen
mixture, the influence of hydrogen blending on the J–T coefficient
is favorable. Due to this, the J–T coefficient of the natural
gas–hydrogen mixture becomes smaller than that of natural gas,
the cooling effect is weakened, and thus the risk of gas hydrate blockage
at the pipeline valve can be reduced. However, in the liquefaction
of hydrogen-enriched natural gas, it is disadvantageous that the J–T
cooling of the natural gas–hydrogen mixture is weakened compared
with that without hydrogen. Under the same pressure drop, the temperature
drop of the natural gas–hydrogen mixture produced by the J–T
cooling is lower than that of natural gas without hydrogen. To obtain
the same cooling effect, it is necessary to increase the pressure
drop, which consumes much more energy. For the convenience of quantitative
comparison, Tables –10 present detailed data of the J–T coefficient of the
natural gas–hydrogen mixture calculated using the empirical
formula, SRK-EOS, PR-EOS, and BWRS-EOS at six thermodynamic conditions
and six hydrogen blending ratios for reference.
Table 7
J–T Coefficient of the Natural
Gas–Hydrogen Mixture Using the Empirical Formula; Unit, K/MPa
p/T
0%
5%
10%
15%
20%
25%
30%
0.1 MPa/283.15 K
5.85
5.60
5.17
4.84
4.51
4.18
3.87
1.0 MPa/283.15 K
5.59
5.34
4.94
4.62
4.30
3.98
3.66
1.0 MPa/293.15 K
5.18
4.95
4.59
4.29
3.99
3.69
3.40
5.0 MPa/293.15 K
4.19
4.01
3.74
3.48
3.21
2.93
2.63
5.0 MPa/308.15 K
3.84
3.66
3.39
3.15
2.89
2.63
2.34
10 MPa/323.15 K
2.77
2.63
2.40
2.18
1.94
1.66
1.36
Table 10
J–T Coefficient
of the Natural
Gas–Hydrogen Mixture Using BWRS-EOS; Unit, K/MPa
p/T
0%
5%
10%
15%
20%
25%
30%
0.1 MPa/283.15 K
5.41
5.01
4.62
4.23
3.85
3.47
3.10
1.0 MPa/283.15 K
5.38
4.97
4.57
4.18
3.79
3.41
3.04
1.0 MPa/293.15 K
4.98
4.60
4.23
3.86
3.50
3.15
2.80
5.0 MPa/293.15 K
4.66
4.27
3.89
3.53
3.19
2.86
2.54
5.0 MPa/308.15 K
4.16
3.81
3.48
3.16
2.85
2.55
2.26
10 MPa/323.15 K
3.03
2.82
2.61
2.39
2.17
1.96
1.74
Relative Deviation of
the Calculated Joule–Thomson
Coefficient
To quantitatively reveal the influences of hydrogen
blending on the J–T effect of natural gas, the relative deviation
between the J–T coefficient of hydrogen-enriched natural gas
and that of natural gas without hydrogen is displayed and analyzed
in this section. Figures –11 show the relative deviation of the J–T
coefficient at six thermodynamic conditions and six hydrogen blending
ratios calculated using the empirical formula (eEF), SRK-EOS (eSRK), PR-EOS (ePR), and BWRS-EOS (eBWRS), respectively.
Figure 8
Relative deviation of the J–T coefficient between
the hydrogen-blended
natural gas and natural gas without hydrogen under different conditions
using the empirical formula.
Figure 11
Relative deviation of the J–T
coefficient between the hydrogen-enriched
natural gas and natural gas without hydrogen under different conditions
using BWRS-EOS.
Relative deviation of the J–T coefficient between
the hydrogen-blended
natural gas and natural gas without hydrogen under different conditions
using the empirical formula.Relative
deviation of the J–T coefficient between the hydrogen-enriched
natural gas and natural gas without hydrogen under different conditions
using SRK-EOS.Relative deviation of the J–T
coefficient between the hydrogen-enriched
natural gas and natural gas without hydrogen under different conditions
using PR-EOS.Relative deviation of the J–T
coefficient between the hydrogen-enriched
natural gas and natural gas without hydrogen under different conditions
using BWRS-EOS.It can be clearly observed
from Figures –11 that with
the increase of the hydrogen blending ratio, the relative deviation
of the J–T coefficient between the natural gas–hydrogen
mixture and natural gas without hydrogen increases gradually. When
the hydrogen blending ratio is up to 30%, the relative deviations
of the J–T coefficient calculated using the empirical formula,
SRK-EOS, PR-EOS, and BWRS-EOS are as high as 50.9, 40.2, 39.4, and
45.7%, respectively, compared with those of natural gas without hydrogen.
This indicates that the hydrogen blending ratio has important impacts
on the J–T effect of natural gas. That is to say, when the
hydrogen blending ratio reaches 30%, the temperature drop caused by
the J–T effect is decreased by 40–50% under the same
pressure drop. This phenomenon exerts negative effects on the process
of liquefaction of natural gas; the same pressure drop of the hydrogen-blended
natural gas can only yield a 50–60% cooling effect compared
with that of natural gas without hydrogen. It is suggested that if
the end user of the hydrogen-enriched natural gas is a natural gas
liquefaction plant, the throttling process that induces the cooling
effect should be improved accordingly. For pipeline transportation
of the natural gas–hydrogen mixture, it is also essential to
carefully consider the impact of hydrogen blending on downstream end
users.
Methane–Hydrogen
Mixture
It
is worth pointing out that due to the difference in the composition
of natural gas produced from different natural gas fields, the J–T
coefficient of different natural gas components at different hydrogen
blending ratios varies substantially, which is inconvenient for readers
to compare and benchmark. Therefore, the J–T coefficient of
the methane–hydrogen mixture at different hydrogen blending
ratios is presented in this study for readers’ reference and
benchmark. Since the prediction result of BWRS-EOS is most accurate,
only the J–T coefficient calculated using BWRS-EOS is presented
here. Table shows
the J–T coefficient of the methane–hydrogen mixture
at the hydrogen blending ratios (mole fraction) of 5, 10, 15, 20,
25, and 30%; pressure of 0.5–20 MPa; and a temperature of 275
K. Similarly, the J–T coefficients of the methane–hydrogen
mixture at the same hydrogen blending ratios and pressure and temperatures
of 300 and 350 K are presented in Tables and 13, respectively.
Table 11
J–T Coefficient of the Methane–Hydrogen
Mixture at 275 K; Unit, K/MPa
p (MPa)
5%
10%
15%
20%
25%
30%
0.5
4.76
4.38
4.00
3.64
3.28
2.95
1.0
4.74
4.35
3.97
3.60
3.25
2.91
2.0
4.69
4.28
3.89
3.52
3.16
2.82
3.0
4.61
4.20
3.80
3.42
3.06
2.72
5.0
4.39
3.96
3.57
3.19
2.84
2.50
7.5
3.96
3.56
3.19
2.84
2.51
2.20
10.0
3.39
3.06
2.75
2.45
2.16
1.89
12.5
2.78
2.54
2.30
2.06
1.82
1.59
15.0
2.23
2.07
1.89
1.71
1.52
1.33
17.5
1.78
1.68
1.55
1.41
1.25
1.10
20.0
1.43
1.36
1.27
1.16
1.03
0.91
Table 12
J–T Coefficient
of the Methane–Hydrogen
Mixture at 300 K; Unit, K/MPa
p (MPa)
5%
10%
15%
20%
25%
30%
0.5
3.97
3.64
3.33
3.02
2.73
2.44
1.0
3.95
3.62
3.30
2.99
2.69
2.40
2.0
3.89
3.55
3.23
2.91
2.61
2.33
3.0
3.82
3.48
3.15
2.83
2.53
2.24
5.0
3.63
3.28
2.95
2.64
2.34
2.06
7.5
3.31
2.98
2.66
2.37
2.09
1.82
10.0
2.92
2.62
2.34
2.07
1.82
1.58
12.5
2.50
2.25
2.01
1.78
1.56
1.34
15.0
2.09
1.90
1.70
1.51
1.32
1.13
17.5
1.74
1.59
1.43
1.27
1.11
0.95
20.0
1.44
1.32
1.19
1.06
0.93
0.80
Table 13
J–T Coefficient
of the Methane–Hydrogen
Mixture at 350 K; Unit, K/MPa
p (MPa)
5%
10%
15%
20%
25%
30%
0.5
2.84
2.60
2.37
2.14
1.92
1.71
1.0
2.81
2.57
2.34
2.11
1.89
1.68
2.0
2.76
2.52
2.28
2.05
1.83
1.62
3.0
2.70
2.45
2.22
1.99
1.77
1.55
5.0
2.56
2.31
2.07
1.85
1.63
1.42
7.5
2.35
2.11
1.88
1.66
1.50
1.25
10.0
2.11
1.89
1.67
1.46
1.27
1.08
12.5
1.87
1.66
1.47
1.28
1.10
0.93
15.0
1.63
1.45
1.27
1.10
0.94
0.78
17.5
1.41
1.25
1.09
0.95
0.80
0.66
20.0
1.21
1.07
0.94
0.81
0.68
0.55
Conclusions
Hydrogen blending has significant influences on the J–T
effect of natural gas. In this study, the equation of state of real
gas and a widely used empirical formula are applied to numerically
investigate the effects of hydrogen blending on the J–T coefficient
of a natural gas–hydrogen mixture in detail. The main work
and findings of this study can be summarized as follows.Theoretical formulas
for calculating
the J–T coefficient of the natural gas–hydrogen mixture
using the empirical formula, SRK-EOS, PR-EOS, and BWRS-EOS are mathematically
derived. The experimental measurement data of the J–T coefficient
of CH4, CH4 + C2H6, natural
gas, and CH4 + H2 are used to validate the calculated
J–T coefficient using the empirical formula, SRK-EOS, PR-EOS,
and BWRS-EOS. Relative errors of the J–T coefficient between
the experimentally measured data and these four methods indicate that
both PR-EOS and BWRS-EOS are accurate in predicting the J–T
coefficient, and BWRS-EOS can perform much better if the temperature
is not very low (≥250 K).The J–T coefficient of natural
gas at six different thermodynamic conditions and hydrogen blending
ratios is calculated using the empirical formula, SRK-EOS, PR-EOS,
and BWRS-EOS, respectively. Results indicate that under different
thermodynamic conditions and hydrogen mixing ratios, the J–T
coefficient of the natural gas–hydrogen mixture decreases approximately
linearly with the increasing hydrogen blending ratio. When the hydrogen
blending ratio reaches 30%, the J–T coefficient of the natural
gas–hydrogen mixture is 40–50% lower than that of natural
gas without hydrogen. In addition, the influence of the hydrogen blending
ratio on the J–T coefficient is nearly the same under different
thermodynamic conditions.The database for the J–T coefficient
of the methane–hydrogen mixture at 275, 300, and 350 K is presented
in this work to provide a reference and a benchmark for interested
readers, where the pressure is set as 0.5–20 MPa and the hydrogen
blending ratio of 5–30% is taken into account.This study also demonstrates that the impact of hydrogen
blending
on the J–T coefficient of natural gas is a double-edged sword.
For long-distance pipeline transportation of the natural gas–hydrogen
mixture, hydrogen blending can reduce the risk of gas hydrate blockage
at the pipeline valves. For natural gas liquefaction, however, the
temperature drop of the hydrogen-mixed natural gas is smaller than
that of natural gas without hydrogen under the same pressure drop.
To produce the same cooling effect, a larger pressure drop is required
for the natural gas–hydrogen mixture.
Table 3
Comparison of J–T Coefficients
of the CH4 + C2H6 Mixture
experiment
empirical formula
SRK-EOS
PR-EOS
BWRS-EOS
p (MPa)
T (K)
μEX (K/MPa)
μEF (K/MPa)
eEF (%)
μSRK (K/MPa)
eSRK (%)
μPR (K/MPa)
ePR (%)
μBWRS (K/MPa)
eBWRS (%)
1.0
250
7.66
7.912
3.29
8.602
12.27
8.040
4.96
7.835
2.28
275
6.251
6.492
3.86
7.178
14.86
6.720
7.50
6.323
1.15
300
5.164
5.369
3.97
6.061
17.35
5.669
9.78
5.189
0.48
350
3.662
3.768
2.89
4.399
20.15
4.114
12.34
3.625
1.01
3.0
250
7.651
6.599
13.75
8.313
8.61
7.943
3.82
7.794
1.87
275
6.176
5.702
7.67
6.812
10.43
6.509
5.39
6.242
1.07
300
5.028
4.848
3.58
5.691
13.17
5.429
7.98
5.094
1.31
350
3.507
3.484
0.66
4.082
16.34
3.894
11.04
3.527
0.57
5.0
250
7.338
5.137
29.99
7.644
4.12
7.492
2.10
7.480
1.94
275
5.924
4.885
17.54
6.278
6.01
6.113
3.19
6.000
1.28
300
4.806
4.327
9.97
5.234
8.82
5.084
5.78
4.895
1.85
350
3.354
3.208
4.35
3.742
11.51
3.639
8.50
3.381
0.81
10.0
250
3.992 ± 0.02
2.715
31.65
3.740
5.79
3.944
0.70
3.750
5.59
275
4.280
3.197
25.30
4.145
3.04
4.202
1.82
4.210
1.64
300
3.789
3.200
15.54
3.804
0.29
3.809
0.53
3.816
0.71
350
2.804
2.590
7.63
2.879
3.07
2.899
3.39
2.814
0.36
12.5
250
2.34 ± 0.012
2.770
17.77
2.423
2.89
2.456
4.42
2.346
0.00
275
3.103 ± 0.016
2.846
7.81
3.041
1.52
3.118
0.00
3.074
0.42
300
3.113 ± 0.016
2.833
8.52
3.045
1.52
3.092
0.16
3.092
0.16
350
2.481
2.335
5.88
2.478
0.00
2.517
1.45
2.464
0.69
15.0
275
2.198 ± 0.015
2.714
22.64
2.202
0.00
2.270
2.58
2.225
0.54
300
2.445 ± 0.012
2.595
5.62
2.389
1.77
2.447
0.00
2.434
0.00
350
2.123
2.117
0.28
2.113
0.61
2.154
1.46
2.113
0.47
20.0
300
1.52 ± 0.04
2.325
49.04
1.463
1.35
1.505
0.00
1.522
0.00
350
1.48 ± 0.04
1.771
16.51
1.491
0.00
1.536
1.05
1.506
0.00
eave
12.63
6.62
4.00
1.05
Table 8
J–T Coefficient
of the Natural
Gas–Hydrogen Mixture Using SRK-EOS; Unit, K/MPa
p/T
0%
5%
10%
15%
20%
25%
30%
0.1 MPa/283.15 K
6.43
5.99
5.56
5.13
4.71
4.29
3.87
1.0 MPa/283.15 K
6.28
5.84
5.41
4.99
4.57
4.16
3.76
1.0 MPa/293.15 K
5.87
5.46
5.06
4.67
4.28
3.89
3.51
5.0 MPa/293.15 K
5.01
4.67
4.33
3.99
3.67
3.35
3.03
5.0 MPa/308.15 K
4.52
4.21
3.91
3.61
3.32
3.03
2.74
10 MPa/323.15 K
3.09
2.93
2.76
2.58
2.40
2.22
2.03
Table 9
J–T Coefficient
of the Natural
Gas–Hydrogen Mixture Using PR-EOS; Unit, K/MPa
Figure 1
Figure 3
Figure 4
Figure 7
Figure 8
Figure 11