Study on the Physical Properties of Hydrogen-Doped Natural Gas Based on Equation of State

As a zero-emission green clean energy, hydrogen energy is an important means to achieve the strategic goal of carbon neutrality and an important part of the energy Internet. Hydrogen-doped natural gas transportation is an economical and feasible scheme to realize long-distance transportation of hydrogen by using the existing natural gas pipeline network. However, the addition of hydrogen to natural gas will cause obvious changes in the physical properties of the transport medium, which will have a certain impact on the transport characteristics and flow measurement of the pipeline. The main problem is that we need to understand the changes of physical properties after natural gas mixed with hydrogen to ensure the safe operation of natural gas pipe network mixed with hydrogen. Based on this situation, this paper takes BWRS equation as the theoretical basis, selects typical natural gas temperament, calculates and solves the physical parameters of natural gas under different hydrogen blending ratios, and compares them with the standard physical reference values. After verification, the results are used to explore the physical properties of hydrogen-doped natural gas with hydrogen blending ratio, temperature and pressure as variables. The relative average absolute value error (RAAD) of the calculated physical properties of hydrogen-doped natural gas in this paper is less than 2% compared with the reference value of standard physical properties, which can provide theoretical data basis for studying hydrogen-doped pipeline transportation, ensuring pipeline transportation safety and hydrogen-doped natural gas metering.


Introduction
Under the background of "dual carbon", China's energy structure is accelerating its transformation towards diversification, cleanliness, and low-carbon [1].Hydrogen energy has the characteristics of clean and carbon free, green and efficient, renewable, and rich application scenarios.The active and orderly development of hydrogen energy is an important direction for promoting China's energy transformation and upgrading, and an important way to achieve the dual carbon strategic goals.From the perspective of hydrogen energy preparation, it mainly benefits from the rapid progress of "Power to Gas" conversion (P2G) and by-product hydrogen purification technology in industries such as petroleum and petrochemical.The development of the hydrogen energy industry is a complete industrial chain that includes production, storage, transportation, and utilization.Among them, "transportation" connects the upstream hydrogen energy production, storage, and downstream hydrogen energy utilization, which is an important link in the development of the hydrogen energy industry [3].According to the current technological level, the cost of hydrogen energy storage and transportation accounts for over 30% of the final hydrogen consumption cost [2,4].Mixing hydrogen into natural gas and utilizing existing natural gas pipelines for transportation is an important way to achieve large-scale and efficient hydrogen transportation [5,6].
In recent years, many countries have carried out pilot projects for the transportation of hydrogenated natural gas, including the NATURALHY and Ameland projects in the Netherlands, the HyDeploy project in the UK, the GRHYD project in France, and the ARENA project in Australia.At present, there is a lack of research on the changes in physical parameters of natural gas mixed with hydrogen in China, and some achievements have been made in foreign research.Kuczys ń Ki et al. [7,8] and Blacharski [9] studied the influence of different hydrogen doping ratios on the hydraulic parameters of high-pressure gas pipelines.As the hydrogen doping ratio increases, the gas density inside the tube decreases, the calorific value per unit mass of gas increases, and the compression factor of the mixed gas significantly increases.Accurately predicting the physical parameters of pipeline gas can ensure the accuracy of the design.AliAA et al. studied the effect of hydrogen concentration in natural gas on flow performance and natural gas properties, and found that the presence of hydrogen in the mixture increased critical pressure and decreased critical temperature [10].ElaoudS et al. pointed out that injecting hydrogen into natural gas has a significant impact on transient pressure, thereby affecting flow characteristics [11].GuandaliniG et al. found that the influence of hydrogen addition on the physical properties of pipeline gas such as calorific value, Wobbe index, and density cannot be ignored [12].This article is based on the BWRS state equation to study the changes in the physical properties of hydrogen doped natural gas, with a focus on analyzing the changes in physical state parameters such as density, compression factor, sound velocity, and specific heat capacity under 0-30% hydrogen doping conditions.The aim is to provide data support for the safe transportation of hydrogen doped natural gas pipelines.

Hydrogen Doped Natural Gas Model and Variation Pattern
At present, it has been analyzed from a large number of literature and some engineering practices that the commonly used equations for calculating the physical properties of natural gas include SRK, PR, BWRS, AGA8, etc.Among them, the BWRS equation of state can not only be applied to the calculation of the thermal properties of light hydrocarbons and their mixtures, but also expand its application range to mixtures with higher non-hydrocarbon gas content, heavier hydrocarbon components (C6+), and comparison temperatures less than 0.6.It is the preferred choice for calculating the physical properties of hydrogenated natural gas.The BWRS equation of state is a multi-parameter equation of state [13], whose basic form is:   2.1.1.Temperament and Operating Point Selection.Select the typical natural gas quality 1 of a longdistance natural gas pipeline from the calibration file of an ultrasonic flowmeter, as shown in table 1. Add 10%, 20%, and 30% hydrogen by volume to obtain temperament 2, temperament 3, and temperament 4 (see table 1).Calculate the physical parameters of the gas quality under four different hydrogen doping ratios using the BWRS equation, and analyze the error in solving the BWRS equation.
The operating conditions are based on the commonly used temperature and pressure for natural gas transportation in the pipeline network, with a temperature range of 273.15K-323.15Kand a pressure range of 1MPa-15MPa, totaling 1551 (11 * 141) operating points.

Error
Analysis.This article uses relative absolute value error (RAD) and relative average absolute value error (RAAD) for error analysis, and the error calculation formula is as follows: In the formula, X represents the compressibility factor, density (kmol • m -3 ) or specific heat at constant pressure (kj • (kmol • K) -1 ), and sound velocity (m • s -1 ); NP represents the operating point, number; The subscript i represents the i-th operating point; The subscript cal represents the calculated value of the BWRS equation; The subscript st represents the standard value.

Precision Comparison Results
. Taking gas quality 3 (20% hydrogen doped) as an example, the relative absolute error distribution of hydrogen doped natural gas under different operating conditions is shown in figure 1-4.Figures 1-4 respectively show the specific heat, density, sound speed and compression factors of the gas.The maximum relative absolute value error and relative average absolute value error under other conditions are shown in table 2.     From figure 1, it can be clearly seen that under all operating conditions, using the BWRS equation to solve the density, constant pressure specific heat, compression factor, and sound velocity of 20% hydrogen doped natural gas, the maximum relative absolute value error (RAD_max) with the reference value does not exceed 2.49%, 1.88%, 2.55%, 4.54%, and the relative average absolute value error (RAAD) is 0.59%, 1.12%, 0.60%, and 1.28%, respectively.
From table 2, it can be seen that the higher the hydrogen doping ratio of natural gas, the smaller the relative average absolute error of density, compression factor, and sound velocity.The relative average absolute value error does not exceed 2%, indicating that the BWRS equation is accurate and reasonable in calculating the physical properties of hydrogen doped natural gas under pipeline transportation conditions.
The relatively large absolute error of some values is due to the harsh high-pressure and lowtemperature conditions.Based on data statistics, the relative average absolute error (RAAD) of the four physical parameters under different hydrogen doping ratios is less than 1% in the pressure range of 4-12MPa and temperature range of 283.15K-323.15K.

Changes in Physical Properties of Hydrogen Doped Natural Gas
After accuracy verification, the physical properties of hydrogen doped natural gas were studied using the BWRS equation.The volume of hydrogen doped natural gas was still based on gas quality 1, and gas quality 2, 3, and 4 were obtained after adding 10%, 20%, and 30% hydrogen.

Change Law of Density and Physical
Properties.The curve of density versus pressure at different hydrogen doping ratios and temperatures is shown in figure 5 for analysis based on molar density.From figure 5, it can be seen that as the proportion of hydrogen doping increases, the density of hydrogen doped natural gas shows a decreasing trend.Regardless of the proportion of hydrogen doping, the change trend of gas density with temperature and pressure is the same.Under the same hydrogen doping ratio, if the pressure is the same, the higher the temperature, the smaller the density of the mixed gas; If the temperature is the same, the higher the pressure, the higher the density of the mixed gas.This confirms the rationality of the physical property calculation of the BWRS equation of state.

Change Law of Specific Heat Physical
Properties at Constant Pressure.The constant pressure specific heat capacity Cp is an important parameter for describing the thermodynamic properties of gases.The curve of constant pressure specific heat versus pressure at different hydrogen doping ratios and temperatures is shown in figure 6.Under different hydrogen doping ratios, as the hydrogen doping ratio increases, the specific heat at constant pressure of hydrogen doped natural gas gradually decreases; Under the same hydrogen doping ratio, if the pressure is the same, in the low pressure region, the higher the temperature, the greater the specific heat at constant pressure; in the high pressure region, the higher the temperature, the smaller the specific heat at constant pressure; If the temperature is the same, the higher the pressure, the greater the specific heat at constant pressure.

Change Law of Specific Heat Physical
Properties at Constant Pressure.The compression factor of a gas can generally be represented by Z, and the curve of the compression factor changing with pressure at different hydrogen doping ratios and temperatures is shown in figure 7.Under different hydrogen doping ratios, the compression factor Z of hydrogen doped natural gas gradually increases with the increase of hydrogen doping ratio; Under the same hydrogen doping ratio, if the pressure is the same, the higher the temperature, the greater the compression factor.If the temperature is the same, the compression factor first decreases and then increases with the pressure.

Change Law of Sound Velocity and Physical Properties.
Gas sound velocity is an important influencing parameter for natural gas pipeline network simulation and ultrasonic flowmeter measurement.The curve of sound velocity changing with pressure at different hydrogen doping ratios and temperatures is shown in figure 8.Under different hydrogen doping ratios, as the hydrogen doping ratio increases, the sound velocity of hydrogen doped natural gas gradually increases.Under the same hydrogen doping ratio, if the pressure is the same, the higher the temperature, the greater the sound velocity.If the temperature is the same, the sound velocity first decreases and then increases with the increase of pressure, and the decreasing trend becomes weaker with the increase of hydrogen doping ratio.

Conclusion
Based on the BWRS equation of state, research on predicting the physical properties of hydrogen doped natural gas was carried out.Under different hydrogen doping ratios, as the hydrogen doping ratio increases, the density and specific heat at constant pressure of hydrogen doped natural gas gradually decrease, while the compression factor and sound velocity gradually increase.Under the same hydrogen doping ratio, if the pressure is the same and the temperature is higher, the density and specific heat at

Figure 1 .
Figure 1.The relative absolute value error of Cp.Figure 2. The relative absolute value error of density.

Figure 2 .
Figure 1.The relative absolute value error of Cp.Figure 2. The relative absolute value error of density.

Figure 3 .
Figure 3.The relative absolute value error of sound speed.

Figure 4 .
Figure 4.The relative absolute value error of Z.

Figure 5 .
Figure 5.The density change curve of hydrogen-mixed natural gas.

Figure 6 .
Figure 6.The Cp change curve of hydrogen-mixed natural gas.

Figure 7 .
Figure 7.The Z change curve of hydrogen-mixed natural gas.

Figure 8 .
Figure 8. Sound speed change curve of hydrogen-doped natural gas.

Table 1 .
Styles available in the Word template.

Table 2 .
Physical property error table of hydrogen-mixed natural gas.