Influence of Natural Gas Composition and Operating Conditions on the Steady-State Performance of Dry Gas Seals for Pipeline Compressors

Abstract

A dry gas seal (DGS) is one of the key basic components of natural gas transmission pipeline compressors, and the sealing performance of a DGS dealing with complex multi-component pipeline natural gas is different from that dealing with conventional nitrogen medium. In this paper, a spiral groove DGS of the compressor in natural gas transmission pipeline systems is taken as the research object. The thermal hydrodynamic lubrication model of the DGS is established considering turbulence effect and choking effect. Based on the finite difference method, the temperature and pressure distributions and the steady-state performance of the DGS are obtained by simulating. The influence of unitary impurity compositions such as light hydrocarbon, heavy hydrocarbon, non-hydrocarbon, and their contents on the steady-state performance of the DGS is analyzed. The steady-state performance of the DGS dealing with multi-impurity natural gas such as in the West-East gas transmission is investigated under different operating conditions. The results show that turbulence had a significant effect on the DGS, while choking had a weak effect. Increasing the content of light hydrocarbon such as C₂H₆ and heavy hydrocarbon such as C₅H₁₀ resulted in an increase in the gas film stiffness, leakage rate, and the temperature difference between the inlet and outlet, while non-hydrocarbon, such as N₂, reduced the temperature difference between the inlet and outlet. The greatest impact on seal performance was produced by the heavy hydrocarbon, followed by the light hydrocarbon, and the least was produced by the non-hydrocarbon.

1. Introduction

As a relatively clean and low-carbon energy, natural gas plays an important role in the transition from fossil energy to renewable energy to achieve the “dual carbon” target in China. It is expected that the proportion of natural gas in primary energy consumption will continue to grow in the short term [1,2]. At present, natural gas transmission lines from the supply side to the user side are mainly based on pipeline transportation. Centrifugal compressors are the “heart” of natural gas transmission pipelines in China. And a DGS is one of the key components for the safe and stable operation of a centrifugal compressor. Since most of the compressor stations in long-distance natural gas pipeline systems were built in the field, the cost of using external pure gas as buffer gas or seal gas is very high. Generally, high-pressure natural gas from the compressor outlet is used as seal gas or buffer gas after treatment. Natural gas is a typical multi-component gas. Gas components and contents will affect the sealing performance of a DGS. It will be different from that of a DGS with a conventional nitrogen medium.

The DGS of compressor in natural gas transmission pipeline system is a typical seal with high pressure and high speed. Under high parameter conditions, the real fluid effects of a DGS are highlighted. The assumptions such as ideal gas, laminar flow model, and forced pressure boundary condition in the traditional design may no longer be applicable [3,4]. In recent years, many scholars have studied the influence of real fluid effects in the DGS. Glienicke et al. showed that the turbulence effect is particularly significant at high speed and high pressure [5]. When the seal clearance and speed were increased, the fluid flow state changed from laminar flow to turbulent flow, and the sealing performance would change significantly [6]. Xu et al. analyzed the influence of real fluid effects on the performance of spiral groove and T-groove DGS [7]. It presented that the real gas effect increased the opening force, leakage rate, outlet pressure and other parameters of CO₂ DGS. While the medium 2as H₂, the results were opposite to CO₂. The choking effect increased the opening force but decreased the leakage rate and the temperature difference between the inlet and outlet [8]. Fairuz et al. found that the real gas effect of supercritical CO₂(SCO₂) was more significant near the critical point [9]. The leakage rate was significantly reduced under high-speed conditions by the real gas effect working together with the centrifugal inertia effect. However, the influence of the real fluid effects for the DGS dealing with high-pressure multi-component natural gas is still unclear, which needs to be further studied.

Factors affecting the performance of a DGS include not only the seal structure and working conditions [10] but also the seal medium. When impurities are mixed with the pure seal gas, resulting in a change in the composition of the seal medium, the temperature and pressure distributions between the end faces may also be affected, which, in turn, affect the stable operation of the seal [11,12]. Seevam et al. pointed out that the type, combination, and content of impurities will change the physical properties and transmission characteristics of CO₂ [13], which directly affect the design and normal operation of pipelines, compressors, pumps, and other equipment [14]. For example, Martynov et al. showed that compressor power decreased with the increase of CO₂ purity [15]. Okezue et al. had investigated the influence of chemical impurities on the performance of SCO₂ compressors [16]. The results showed that the addition of any impurities reduced the overall fluid density causing the discharge pressure to drop. However, regarding natural gas, as a typical gas mixture, there have been few studies about the influence of its component variation on the performance of pipeline transportation equipment. Therefore, research is necessary to determine the performance of natural gas DGS with different components.

Taking the West-East Gas Pipeline as an example, the failure of the dry gas seal can account for 10–20% of the failure of the entire unit. The reasons for this phenomenon may include the following aspects: First, it may be attributed to high transmission pressure. The flowing heat transfer characteristics of natural gas DGS at high pressure is different from that at low pressure, which requires special consideration in the design of the seal. Second, the large temperature difference may be a factor. DGS may experience different climatic conditions, and temperature changes may have an impact on the sealing performance. Third, the complex composition of natural gas, which can lead to changes in its physical properties, affects the design and operation of dry gas seals.

Aiming at the features of high-pressure and high-speed conditions and the complex composition of the seal gas, the influence of real fluid effects, such as the choking effect and turbulence effect, is considered. The influence of unitary and actual multi-component impurities on the steady-state performance of the natural gas DGS is compared. In addition, the variation of flowing heat transfer and sealing performance under different conditions is analyzed.

2. Numerical Analysis Models

2.1. Geometrical Model

Figure 1 shows the geometrical model of the spiral groove DGS. The main seal pair consisted of a rotating ring and a stationary ring, which moved relatively. One of the rings was provided with logarithmic spiral grooves uniformly in the circumferential direction. The number of grooves was N_g, and the depth was h_g. The root radius of the groove was r_g, and the downstream side was the dam region without groove to limit seal leakage. A fluid film with micrometer thickness was formed between the end faces under the combined action of the hydrostatic and hydrodynamic pressure effects to avoid contact between two seal rings. The polar equation of the logarithmic helix is as follows:

$$r=r_g\exp \left(\theta \tan \beta \right)$$

(1)

where, θ is the polar angle and β is the helix angle.

2.2. Governing Equations

This paper focuses on the flowing heat transfer characteristics of natural gas DGS without considering the thermal and pressure-induced deformation of the seal ring. The effects of pressure-induced deformation and thermal deformation on sealing performance can cancel other out [17]. During the machining of the seal ring, the flatness of the end face can be changed so that the two seal rings can form an approximate parallel gap under the action of pressure-induced and thermal deformation. In order to facilitate the simulation and analysis of the flowing heat transfer of seal medium, the following assumptions were made: the volume force of the ring and fluid was ignored; the surfaces of two rings was smooth; the pressure and physical properties of the fluid did not change along the direction of film thickness; there was no slippage of the fluid on the contact surfaces. Based on the mass conservation equation of compressible fluid:

$$\frac{\partial \left(\rho r{u}_{\mathrm{r}}\right)}{r\partial r}+\frac{\partial \left(\rho u_{\mathsf{\theta }}\right)}{r\partial \theta }+\frac{\partial \left(\rho u_{\mathrm{z}}\right)}{\partial z}=0$$

(2)

Derivation of the above assumptions leads to the circumferential, radial, and axial expressions of the simplified momentum conservation equations, respectively:

$$\rho \left(u_{\mathrm{r}}\frac{\partial u_{\mathsf{\theta }}}{\partial r}+\frac{u_{\mathsf{\theta }}}{r}\frac{\partial u_{\mathsf{\theta }}}{\partial \theta }+u_{\mathrm{z}}\frac{\partial u_{\mathsf{\theta }}}{\partial z}+\frac{u_{\mathrm{r}}{u}_{\mathsf{\theta }}}{r}\right)=-\frac{1}{r}\frac{\partial p}{\partial \theta }+\frac{\partial }{\partial z}\left({\mu }_{\mathrm{eff}}\frac{\partial u_{\mathsf{\theta }}}{\partial z}\right)$$

(3)

$$\rho \left(u_{\mathrm{r}}\frac{\partial u_{\mathrm{r}}}{\partial r}+\frac{u_{\mathsf{\theta }}}{r}\frac{\partial u_{\mathrm{r}}}{\partial \theta }+u_{\mathrm{z}}\frac{\partial u_{\mathrm{r}}}{\partial z}-\frac{u_{\mathsf{\theta }}^2}{r}\right)=-\frac{\partial p}{\partial r}+\frac{\partial }{\partial z}\left({\mu }_{\mathrm{eff}}\frac{\partial u_{\mathrm{r}}}{\partial z}\right)$$

(4)

$$\frac{\partial p}{\partial z}=0$$

(5)

where p is the pressure; $\rho$ is the fluid density; u_r, u_θ, and u_z are the radial, circumferential, and axial fluid velocities, respectively. And μ_eff is the effective viscosity of the fluid while the turbulence effect is considered, which is expressed as follows [18,19]:

$${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}=\mu \left(1+{\delta }_{\mathsf{\epsilon }}\cdot \frac{{\epsilon }_{\mathrm{t}}}{\upsilon }\right)$$

(6)

where μ and υ are the dynamic and kinematic viscosity of the fluid. ε_t is the eddy viscosity, and δ_ε is the interpolation factor. The fluid is in laminar flow at δ_ε = 0, in turbulent flow at δ_ε = 1, and in transitional flow at 0 < δ_ε < 1. The expression of δ_ε is as follows:

$${\delta }_{\mathsf{\epsilon }}=\left\{\begin{array}{ll}0& A<9/16\\ \frac{1}{2}\left[1-\cos \left(\frac{A-9/16}{1-9/16}\pi \right)\right]& 9/16\le A\le 1\\ 1& A>1\end{array}\right.$$

(7)

The mass conservation Equation (2) is integrated along the film thickness direction to obtain the modified Reynolds equation [20]:

$$\begin{array}{l}\frac{\partial }{r\partial r}\left(\rho r{G}_{\mathrm{h}}\frac{\partial p}{\partial r}\right)+\frac{\partial }{r\partial \theta }\left(\rho G_{\mathrm{h}}\frac{\partial p}{r\partial \theta }\right)\\ =\frac{\partial }{r\partial \theta }\left(\frac{\rho \omega r{I}_{\mathrm{h}}}{J_{\mathrm{h}}}\right)-\frac{\partial }{r\partial r}\left(\frac{\rho r{G}_{\mathrm{h}}}{h}{I}_{\mathrm{r}}\right)-\frac{\partial }{r\partial \theta }\left(\frac{\rho G_{\mathrm{h}}}{h}{I}_{\mathsf{\theta }}\right)\end{array}$$

(8)

where ω is the angular velocity; h is the thickness of the fluid film; I_h, J_h and G_h reflect the influence of the flow state; I_r and I_θ reflect the influence of the fluid inertia. The expressions are as follows:

$$I_{\mathrm{h}}={\displaystyle {\int }_0^h\frac{\xi }{{\mu }_{\mathrm{eff}}}d\xi }; J_{\mathrm{h}}={\displaystyle {\int }_0^h\frac{1}{{\mu }_{\mathrm{eff}}}d\xi }; G_{\mathrm{h}}={\displaystyle {\int }_0^h\frac{\xi }{{\mu }_{\mathrm{eff}}}\left(\xi -\frac{I_{\mathrm{h}}}{J_{\mathrm{h}}}\right)d\xi }$$

(9)

$$I_{\mathrm{r}}=-h\frac{\partial p}{\partial r}+hU; I_{\mathsf{\theta }}=-h\frac{\partial p}{r\partial \theta }+hV$$

(10)

$$U=\frac{1}{h}{\displaystyle {\int }_0^h\left(\rho u_r\frac{\partial u_r}{\partial r}+\rho \frac{u_{\theta }}{r}\frac{\partial u_r}{\partial \theta }+\rho u_z\frac{\partial u_r}{\partial z}-\rho \frac{u_{\theta }^2}{r}\right)dz+\frac{\partial p}{\partial r}}$$

(11)

$$V=\frac{1}{h}{\displaystyle {\int }_0^h\left(\rho u_r\frac{\partial u_{\theta }}{\partial r}+\rho \frac{u_{\theta }}{r}\frac{\partial u_{\theta }}{\partial \theta }+\rho u_z\frac{\partial u_{\theta }}{\partial z}+\rho \frac{u_r{u}_{\theta }}{r}\right)dz+\frac{1}{r}\frac{\partial p}{\partial \theta }}$$

(12)

The energy equation in enthalpy form is [21]:

$$\rho h{u}_{\mathsf{\theta }\mathrm{m}}\frac{\partial H}{r\partial \theta }+\rho rh{u}_{\mathrm{rm}}\frac{\partial H}{r\partial r}=-{\left.{\tau }_{\mathsf{\theta }}\right|}_{z=0}\cdot \omega r+Q_{\mathrm{R}}+Q_{\mathrm{S}}$$

(13)

where u_θm and u_rm are the average values of the circumferential velocity and radial velocity in the direction of film thickness, H is the enthalpy of the fluid, τ_θ is the circumferential shear stress, and Q_R and Q_S are the heat fluxes on the surfaces of the rotating ring and stationary ring, respectively.

Heat conduction equation of stationary ring:

$$\frac{\partial }{r\partial \theta }\left(k_{\mathrm{S}}\frac{\partial T}{r\partial \theta }\right)+\frac{\partial }{r\partial r}\left(r{k}_{\mathrm{S}}\frac{\partial T}{\partial r}\right)+\frac{\partial }{\partial z}\left(k_{\mathrm{S}}\frac{\partial T}{\partial z}\right)=0$$

(14)

where k_S is the thermal conductivity of the stationary ring.

The rotating ring is affected by the moment of inertia, and its heat conduction equation is as follows:

$$\frac{\partial }{r\partial \theta }\left(k_{\mathrm{R}}\frac{\partial T}{r\partial \theta }\right)+\frac{\partial }{r\partial r}\left(r{k}_{\mathrm{R}}\frac{\partial T}{\partial r}\right)+\frac{\partial }{\partial z}\left(k_{\mathrm{R}}\frac{\partial T}{\partial z}\right)=\rho c\omega \frac{\partial T}{\partial \theta }$$

(15)

where k_R is the thermal conductivity of the rotating ring, and c is the specific heat capacity of the rotating ring.

2.3. Boundary Conditions

In order to facilitate modeling and calculation, the inner and outer diameters of the end faces are equal to the inner and outer diameters of the seal ring. The section of the seal ring was regarded as a regular structure. A periodic part of the DGS was selected as the computational domain. The circumferential boundary conditions of the rotating ring, the stationary ring and the fluid film satisfiy the periodic boundary conditions. The pressure boundary conditions in the radial direction are as follows:

$$p\left(r=r_{\mathrm{i}}\right)=p_{\mathrm{exit}};p\left(r=r_{\mathrm{o}}\right)=p_{\mathrm{o}}$$

(16)

$$p_{\mathrm{exit}}=p_{\mathrm{i}}+\Delta p$$

(17)

When the forced pressure boundary condition is adopted, p_exit is equal to p_i. But if the radial pressure difference of the seal is very large, it is difficult for the seal medium to drop to atmospheric pressure at the outlet of the seal. In this case, if the forced pressure boundary is still adopted, the flow rate of gas near the inner diameter may exceed the local sound velocity, which is inconsistent with the actual situation. Therefore, the choking pressure boundary condition should be adopted at the inner diameter to avoid supersonic flow. Under this condition, the outlet pressure of the seal is not constant. Until the outlet Mach number is equal to 1, it needs to be continuously corrected by adding Δp, which is obtained by the secant method. Figure 2 shows the thermal boundary conditions of the DGS. Coupled boundary conditions are adopted on the contact surfaces between the end faces and the fluid film. The adiabatic boundary conditions are set for the backside and the inner diameter side of the rings because of the weak fluidity of the fluid [22]. The outer diameter side of the seal rings generates convective heat transfer with the fluid. Boundary conditions of the rotating and stationary ring are calculated as follows:

$$-k_{\mathrm{S}}\frac{\partial T}{\partial r}=h_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}\left(T_{\mathrm{S}}-T_{\mathrm{i}}\right)$$

(18)

$$-k_{\mathrm{R}}\frac{\partial T}{\partial r}=h_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}\left(T_{\mathrm{R}}-T_{\mathrm{i}}\right)$$

(19)

where T_i is the inlet temperature of the fluid. T_S and T_R are the temperature of rotating and stationary ring, respectively. And h_conv is the convective heat transfer coefficient, which is calculated as follows [23]:

$$h_{\mathrm{conv}}=0.133\frac{\lambda }{D_0}{\left(\frac{\rho \omega D_0^2}{2\mu }\right)}^{2/3}P{r}^{1/3}$$

(20)

where λ is the thermal conductivity, D₀ is the outer diameter of the seal ring, and Pr is the Prandtl number of the seal medium.

2.4. Numerical Procedure

Figure 3 depicts the numerical procedure employed in this work. The governing equations were discretized and solved based on finite difference method and over-relaxation iteration. The boundary conditions and parameters were initialized, and the REFPROP database was invoked to obtain the physical properties of natural gas at different temperatures and pressures. Then, the modified Reynolds equation, heat conduction equations, and energy equation were solved by iterative coupling to obtain the distributions of fluid temperature, pressure and other flow field parameters between the end faces. The program also included iterative calculations of μ_eff and Mach number M_a, taking into account the influence of real fluid effects on the sealing performance at high pressure. In the program, the average relative error of each parameter was taken as the convergence criterion. The convergence residuals were ε₁ = 10⁻³, ε₂ = 10⁻⁵, respectively. When considering the choking effect, it was necessary to determine whether M_a is less than 1 at the inner diameter with the highest flow rate in the seal clearance. Otherwise, a tiny pressure was added on the basis of the original outlet pressure until M_a ≤ 1.

Once the flow parameter distributions were obtained by the program, the steady-state performance parameters of the seal could be calculated. Opening force (F_o), mass leakage rate (Q) and gas film stiffness (k_z) were broken down by the following formulas [24]:

$$F_{\mathrm{o}}={\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_{r_{\mathrm{i}}}^{r_{\mathrm{o}}}prdrd\theta }}$$

(21)

$$Q={\displaystyle {\int }_0^{2\pi }\rho u_{r}hrd\theta }$$

(22)

$$k_{\mathrm{z}}=-\frac{F_{\mathrm{o}}\left(h_0+\Delta h_0\right)-F_{\mathrm{o}}\left(h_0\right)}{\Delta h_0}$$

(23)

3. Result Discussion and Analysis

As the seal gas or buffer gas, the composition of pipeline natural gas is complex. In addition to the main component CH₄, it also contains light hydrocarbon, heavy hydrocarbon, non-hydrocarbon and so on. On the basis of considering the influence of real fluid effects, the influence of binary and multi-component natural gas mixtures with different compositions on the flow field distribution and steady-state performance of the DGS is calculated. The sensitivity of sealing performance with different compositions and contents of the natural gas to the change of working conditions is analyzed.

Table 1. Operating conditions and groove structure parameters of the DGS.

Item and Symbol	Value	Item and Symbol	Value
Groove root radius rg/mm	66.65	Outer diameter pressure po/MPa	15
Groove depth hg/μm	5	Rotational speed n/rpm	6000
Spiral angle β/°	15	Outer diameter temperature To/K	333
Slot width ratio δ	1	Gas film thickness h0/μm	3
Groove number Ng	12

presents the operating conditions and groove structure parameters of the DGS, which are regarded as the default working conditions without any special description. The rotating and stationary rings are made of pressure-less sintering SiC. The structural and material parameters are shown in

Table 2. Structural parameters and material parameters of the seal rings.

Item and Symbol	Value	Item and Symbol	Value
Inner radius ri/mm	55.85	Density ρ/kg·m−3	3150
Outer radius ro/mm	78	Thermal conductivity λ/W·m−1·K−1	57
Stationary ring thickness Hs/mm	12	Specific Heat Capacity Cp/J·kg−1·K−1	710
Rotating ring thickness Hr/mm	12

.

The design pressure of major natural gas pipelines is 10 or 12 MPa. To ensure the reliability of the seal, the design pressure of DGS is mostly 15 MPa. The newly developed DGS pressure of a few pipelines can reach 20 MPa. The rotational speed of the compressor is about 6000~8700 rpm. The inlet temperature of the seal gas is about 333 K by a heating system. Under such conditions, the film thickness of the DGS is generally 2.5~6.5 μm [5]. Therefore, in order not to loss generality, the gas film thickness in the subsequent analysis was taken as 3.0~6.0 μm.

3.1. Numerical Model Validation

Figure 4 shows the results of the grid independence validation. Compared to the results with the grid number of 120 × 120, the relative errors of the opening force were 0.07%, 0.03%, and 0%, respectively, when the grid numbers were 60 × 60, 80 × 80, and 100 × 100. The relative errors of the leakage rate were 1.3%, 0.8%, and 0.3% respectively. Considering both computation cost and the accuracy of the results, the calculation domain was divided into 80 × 80 structural grids. The number of axial grids of both seal rings was 10, and the number of axial grids of fluid film was 15.

In order to validate the correctness of the numerical model and calculation program in this paper, the numerical calculation results were compared with those in the literature [25,26]. Figure 5 shows the calculated and literature values of the radial mean film pressure (p) and temperature (T) on the end face. It can be seen that the calculated values of p at different radial positions are basically consistent with the literature values, and the maximum error is less than 3%. The distribution of T is well consistent at large film thicknesses, and the error on the outer diameter side will increase slightly when h₀ decreases. But the maximum error is less than 3 K of T at h₀ = 3 μm. The reason for the error is that, with the increase of rotational speed, the viscous shear heat increases, resulting in the temperature of the end face is significantly higher than that of the seal chamber, whereas the temperature near the outer diameter of the seal ring is closer to that of the seal chamber. So, the temperature of fluid film near the outer diameter decreases due to the effect of stronger convective heat transfer with the seal ring.

3.2. Influence Analysis of Real Fluid Effects

The gas in the seal chamber of the natural gas compressor adopts the high-pressure natural gas from the outlet of the compressor, and the pressure can generally be as high as 15 MPa. The real fluid effects, such as the choking effect and turbulence effect, may have a significant impact on the sealing performance. The properties of the real gas are acquiescently considered, which are very different from the ideal gas at high pressures. The typical natural gas consisting of 92%CH₄, 2%C₂H₆, 1%C₃H₈, and 5%N₂ was used as an example to focus on analyzing the influence of the choking effect and turbulence effect on the steady-state performance of the DGS.

3.2.1. Influence of the Choking Effect

Due to the large pressure difference between both ends of the end face, the flow rate of the gas continued to increase. However, the flow channel gradually decreased with the radius, and the flow rate of the seal gas could not exceed the sound velocity, resulting in the choking phenomenon, which caused the outlet pressure of the seal to be higher than the ambient pressure. Figure 6 shows the distributions of the M_a and p on the end face under the choking pressure boundary condition and the forced pressure boundary condition. It can be seen that there was no obvious difference between the two conditions at the grooved area, and there was only little localized difference at the sealing dam region near the inner diameter. When the forced pressure boundary condition was adopted, the p_i was always equal to 0.1 MPa. The M_a at the inner diameter was much higher than 1, and even up to 10, resulting in a supersonic region. However, when the actual flow rate reached the sound velocity, it could not continue to increase due to the choking effect. Therefore, the forced pressure boundary condition could not be applied to the case of choking occurring. When the choking pressure boundary condition was adopted, the maximum Mach number of the fluid in the seal clearance was less than 1 by constantly adjusting the value of the outlet pressure. The final value of the outlet pressure was 1.04 MPa after calculation.

Figure 7 shows the relative error of the steady-state performance of the DGS with or without considering the choking effect at different film thicknesses. As can be seen from the Figure 7, the choking effect had almost no influence on F_o of the seal, because the choking effect can only change the pressure distribution in a small region at the leakage port of the end face. The choking effect had a relatively large influence on Q and k_z, but the maximum relative error was no more than 1.5%. Therefore, to save calculation cost, the pressure at the leakage port was set directly to 1.04 MPa for subsequent calculations.

3.2.2. Influence of the Turbulence Effect

The flow state of the fluid will change from laminar flow to turbulent flow under high-pressure conditions. Figure 8 shows the Reynolds number R_e distribution of the leakage fluid with different film thicknesses and fluid flow models. It can be considered as turbulent flow at R_e > 977 [27]. It can be seen that R_e > 1000 only in the groove region at h₀ = 3 μm. When h₀ increased to 6 μm, R_e > 1000 on the whole end face of the two models, which means that the fluid flow state on the whole end face was turbulent. Therefore, it was more reasonable to choose a turbulent flow model to calculate the performance of the natural gas DGS. And the laminar flow state or turbulent state could be simultaneously characterized by the δ_ε [18]. Further analysis reveals that the Reynolds number calculated by the laminar flow model was significantly higher than that obtained by the turbulent flow model, which was caused by the relatively small effective viscosity due to the absence of turbulent viscosity in the laminar flow model.

Figure 9 shows the relative deviation of the sealing performance at different film thicknesses under the laminar flow model based on the sealing performance obtained by turbulent flow model. It can be seen that the relative deviations of F_o and k_z corresponding to the laminar flow model were small, always within 2%. And both F_o and k_z were slightly larger when h₀ was 3 μm and 4 μm, while the F_o and k_z corresponding to the turbulent flow model were larger with the increase of h₀. This is because the F_o under high-pressure conditions mainly depends on the hydrostatic pressure. The effect of turbulence on the hydrodynamic pressure was not obvious. From the perspective of Q, there was a significant difference under the two different flow models. The Q under the laminar flow model was significantly higher than that of the turbulent flow model. Moreover, the relative deviation of the two increased rapidly with the increase of h₀. For example, when h₀ was 3 μm and 6 μm, the relative deviation of Q was 4% and 110%, respectively. It can be seen that the turbulent flow model should be selected in the flow field analysis of high-pressure natural gas DGS. Otherwise, it will cause a large deviation in the prediction of seal leakage rate.

To further find out the reason for the large deviation of Q, the radial distributions of the flow field parameters of the natural gas DGS with different fluid flow models at h₀ = 6 μm were analyzed, as shown in Figure 10. The mass flow rate of the medium was proportional to the density of the medium, the radial flow rate, and the flow area. When h₀ and the structural parameters were consistent, the flow regions corresponding to the two fluid flow models were consistent. The mass flow rate was only related to the density and the radial flow rate at this point. It can be seen that the turbulent flow model had little influence on the distribution of temperature and pressure, indicating that the corresponding medium density distributions of the two flow models were similar. The fluid flow model had a great influence on the radial velocity of the medium. The radial velocity obtained by the laminar flow model was approximately twice that of the turbulent flow model. This was due to the fact that the effective viscosity of the medium was greater than the dynamic viscosity when the turbulent flow model was adopted. The hydrostatic flow resistance of the fluid driven by the differential pressure of the medium increased, resulting in a reduction of the radial velocity, and hence a significant reduction of Q.

3.3. Influence of Unitary Component and Content of Impurity on Sealing Performance

The main components of natural gas are CH₄, light hydrocarbon (C2~C4), heavy hydrocarbon (C5 and above), and non-hydrocarbon, of which CH₄ was the main component, and the content of other components or impurities was low. We took C₂H₆, C₅H₁₂, and N₂ as the representative components of light hydrocarbon, heavy hydrocarbon, and non-hydrocarbon, respectively, to form binary mixtures with CH₄. Their contents were changed to form seven different mixtures of four categories, as shown in

Table 3. Composition of unitary impurity natural gas samples.

Natural Gas Category	Gas Sample	CH4	C2H6	C5H12	N2
Ⅰ	ng1	100%
Ⅱ	ng2	90%	10%
	ng3	95%	5%
Ⅲ	ng4	90%		10%
	ng5	95%		5%
Ⅳ	ng6	90%			10%
	ng7	95%			5%

, so as to analyze the influence of single impurity and its content on the sealing performance.

Figure 11 shows the influence of the composition and content of the unitary impurities on the steady-state performance of the seal. It can be seen that the impurities had little effect on the F_o. The relative deviation of the F_o for class Ⅱ, Ⅲ, and Ⅳ impurity-containing natural gas seals was not more than 0.5% compared with pure CH₄ or class I gas. For class IV natural gas containing non-hydrocarbon components such as N₂, the k_z and the Q of the seal were less affected. For example, when the content of N₂ reached 10%, the k_z and Q only increased by 0.79% and 1.06%, respectively. The temperature difference between the inlet and outlet (ΔT) increased by 1.76 K. The light and heavy hydrocarbon components represented by C₂H₆ and C₅H₁₂ increased the k_z and Q of the seal and further decreased the outlet temperature of the seal. Further analysis shows that light hydrocarbon and heavy hydrocarbon had similar effects on the Q and ΔT. For example, 10% of the components increased the Q by nearly 6.5%, and the outlet temperature decreased by 3 K. The influence of heavy hydrocarbon on the k_z was significantly greater than that of light hydrocarbon. For example, 10% of the heavy hydrocarbon and light hydrocarbon increased the k_z by 3.4% and 1.6%, respectively.

In order to further analyze the mechanism of the influence of impurity components and their contents on the steady-state performance of CH₄ DGS, the flow field parameters of pure CH₄ DGS were used as the basis. The difference of flow field parameters of the DGS with different gas samples ngi (i = 1, 2, …, 7) was defined as ΔΦ_1i, where Φ represents the fluid film pressure, temperature, density, viscosity, and other flow field parameters:

$$\Delta {\mathrm{\Phi }}_{1\mathrm{i}}={\mathrm{\Phi }}_{\mathrm{i}}-{\mathrm{\Phi }}_1$$

(24)

Figure 12 shows the radial distributions of the flow field parameters difference at the end face with the unitary impurity of natural gas. It can be seen that compared with pure CH₄ DGS, the introduction of N₂ into the seal gas slightly increased the radial pressure on the end face, and the maximum value was close to 20 kPa, while C₂H₆ and C₅H₁₂ decreased the radial pressure on the end face. The maximum values were approximately 60 kPa and 90 kPa, respectively. Therefore, the change of radial pressure distribution on the end face caused by different types of natural gas was very small compared to the total pressure difference on the end face. The reason is that the change of pressure distribution was mainly caused by the variable density effect and the hydrodynamic effect. But the fluid pressure generated by these two was not high. So, different types of impurities had little influence on the F_o of natural gas DGS.

The factors affecting the temperature difference between inlet and outlet of the end face include the temperature decrease caused by gas expansion, the heat generated by viscous shear, and the temperature change of the gas film caused by convective heat transfer with the seal rings, which work together to determine the temperature change law between the end faces. From the perspective of viscous shear heat, it can be seen from Figure 12d that the viscosity of the natural gas containing N₂ increased by about 0.3 μPa∙s as a whole compared to pure CH₄. The viscosity of natural gas containing C₂H₆ or C₅H₁₂ was slightly lower than that of pure CH₄ only at the outlet of end face, while the viscosity away from the outlet was gradually greater than that of pure CH₄. And the viscosity of C₅H₁₂ increased more obviously, which increased to 1.35 μPa∙s at the outer diameter. It can be seen that the inclusion of impurities will increase the viscous shear heat of CH₄, and the heat generated by the increase of heavy hydrocarbon was greater than that of light hydrocarbon. In terms of the convective heat transfer effect, because the temperature of the gas film was lower than that of the seal ring, heat was transferred from the seal ring to the gas film, resulting in an increase of the gas film temperature.

Table 4. The convective heat transfer coefficients of the 7 gas samples.

Gas Sample	hconv (kW·m−2·K−1)	Gas Sample	hconv (kW·m−2·K−1)
ng1	5.71	ng5	5.90
ng2	5.87	ng6	5.51
ng3	5.75	ng7	5.58
ng4	6.21

shows the convective heat transfer coefficients of the seven gas samples. As can be seen from the table, the impurity C₂H₆ and C₅H₁₂ increased the convective heat transfer coefficient of natural gas so that the heat exchange between the fluid and the seal rings increased and the temperature of the gas film increased. On the contrary, the impurity N₂ reduced the convective heat transfer coefficient and the heat transfer. From the perspective of gas expansion, the temperature decrease caused by gas expansion was related to pressure. As can be seen above, the pressure distributions between the end faces of various types of natural gas were ng6 > ng1 > ng2 > ng4. Therefore, the gas expansion effect of ng4 was more obvious. The temperature drop containing the impurity C₂H₆ or C₅H₁₂ of the natural gas was greater than that of pure CH₄, while the temperature drop containing the impurity N₂ was less than that of pure CH₄. In summary, the viscous shear heat of natural gas with impurity N₂ increased, the convective heat transfer decreased, and the temperature drop caused by gas expansion decreased, while the viscous shear heat of natural gas with impurity C₂H₆ or C₅H₁₂ increased, the convective heat transfer increased, and the temperature drop caused by gas expansion increased. As a result of the large pressure gradient under high-pressure conditions, the temperature drop caused by gas expansion was more obvious. So, the temperature of the gas film showed a downward trend on the whole.

The difference of Q is discussed from the density and radial flow rate of different components of natural gas. As can be seen from Figure 12c, the radial velocity of natural gas containing impurity C₂H₆ had little difference from that of pure CH₄, while the radial velocity of natural gas containing impurity N₂ or C₅H₁₂ was about 10 m/s lower than that of pure CH₄ at the outlet of inner diameter. But the difference between the radial velocity and that of pure CH₄ at the inlet of outer diameter was less than 1 m/s. According to the law of mass conservation, the mass leakage rate of the medium is equal along the radial direction between the end faces. In order to facilitate the analysis, the fluid mass leakage rate can be calculated by taking a circumferential section per unit region near the outer diameter, and the difference of Q is determined by ΔQ₁:

$$\Delta Q_1=\left(\rho +\Delta \rho \right)\left(u_r+\Delta u_r\right)-\rho u_r=\rho \Delta u_r+u_r\Delta \rho +\Delta \rho \Delta u_r$$

(25)

Figure 13 shows the difference distribution of the density on the end face with different impurity-containing natural gases based on that of pure CH₄. As can be seen from the figure, the densities of ng2, ng4 and ng6 near the outer diameter were 7.1%, 11.2%, and 2.5% higher than those of ng1, and the values of u_r were 1.0%, 5.2%, and 1.9% lower, respectively. The corresponding relative deviations of the mass leakage rate were 6.0%, 5.4%, and 0.6%, respectively. On the side near the inner diameter, the densities of ng2, ng4, and ng6 were 6.2%, 10.0%, and 3.7% larger than that of ng1, and the values of u_r were −0.2%, 3.1%, and 2.5% lower, respectively. The corresponding relative deviations of the mass leakage rate were 6.4%, 6.6%, and 1.1%, respectively. It can be seen that the difference law of mass leakage rate at the inner and outer diameters of the end face based on the difference of medium density and radial velocity was basically consistent with the results in Figure 11c. In summary, it can be seen that different impurity components will increase the leakage rate. The influence of the density change on the leakage rate is more significant than that of the radial velocity, which is also related to the content of impurities.

3.4. Influence of Multi-Impurity Components and Working Conditions on the Sealing Performance

To analyze the influence of multi-impurity components on the sealing performance, natural gas extracted from the Mandong region of the Tarim Basin, a major gas region of the West-East gas transmission line, was taken as an example. And representative natural gas samples with CH₄ content in different intervals were selected, as shown in

Table 5. Composition of natural gas samples with multiple impurities.

Gas Sample	CH4	C2H6	C3H8	C4H10	C5H12	C6H14	N2
NG1	66%	8%	4%	2%			20%
NG2	66%	8.3%	3.5%	2%	0.7%	0.9%	18.6%
NG3	75%	7%	2%	1%			15%
NG4	82%	10%	3%	1%			4%
NG5	92%	2%	1%				5%

[28]. Among them, NG1 and NG3 are wet natural gases with a high N₂ content and different CH₄ contents. NG2 represents natural gas containing heavy hydrocarbon, which is not much due to the fact that the actual natural gas is prone to condensate when the content of heavy hydrocarbon is too high. NG4 is a wet natural gas with a high light hydrocarbon content. NG5 is a typical dry gas with CH₄ as its main component. Since most of the natural gas transported in pipelines is dry gas with CH₄ content greater than 90%, NG5 was used as the reference sample to analyze the influence of multiple impurities on the steady-state performance of the DGS.

3.4.1. Influence of Components on Opening Force and Gas Film Stiffness

Figure 14 shows the pressure difference distributions on end face of different natural gas samples under the default working condition, where Δp_i5 is the pressure difference of the gas sample Ngi (i = 1, …, 4) and NG5:

$$\Delta p_{\mathrm{i}5}=p_{\mathrm{i}}-p_5\left(\mathrm{kPa}\right)$$

(26)

It can be seen from the figure that different components of natural gas had little influence on the pressure distribution. Among them, the pressure difference of NG1~4 was negative compared to NG5, and the maximum value was 35, 50, 20, and 70 kPa, respectively. It can be seen from Section 2.3 that the N₂ increased the F_o, while the light hydrocarbon and heavy hydrocarbon decreased the F_o. Although NG1, NG2, and NG3 contained 15–20% N₂, the F_o still showed a decreasing trend, which indicates that light hydrocarbon and heavy hydrocarbon have slightly more significant influence on the opening force than non-hydrocarbon.

Figure 15 shows the variation curves of gas film stiffness of natural gas DGS with different working conditions. It can be seen from the figure that the k_z changed with the h₀ and n of all natural gas samples, which was basically the same. With the increase of the h₀, the k_z decreased first and then increased. The relative deviations of the k_z under different h₀ were less than 1.5%. The k_z had a tendency to decrease with the increase of n, and the maximum relative deviation of the k_z was less than 5% at different rotational speeds. The reason is that the F_o was composed of two parts: a hydrostatic opening force and hydrodynamic opening force. Under high-pressure conditions, the F_o mainly depends on the hydrostatic opening force, and the influence of working conditions on the hydrodynamic opening force will not significantly change the total opening force, so the k_z under different working conditions changes little. Furthermore, under different film thicknesses and rotational speeds, the k_z of DGS with NG1~4 was larger than that of NG5, with an increase of 3.3%, 3.9%, 1.6%, and 2.3%, respectively, which shows that the interaction law of multi-component impurities is the same as that of the unitary impurity, which will increase the k_z. It can be seen from Figure 15c that the k_z of all natural gas samples increased with the increase of p_o, but the increase rate of NG5 was relatively slow. At 10 MPa, the k_z of NG5 was the largest, while that of NG5 was the smallest when the pressure increased, which shows that the increase of impurity content will make the k_z more sensitive to the change of pressure. And NG2, containing lots of CO₂ and few heavy hydrocarbons, had the fastest increase. As shown in Figure 15d, the k_z changing with the T_o of NG5 was different from that of the other four types of natural gas. The k_z of NG5 was smaller at low temperatures and increased with the increase of T_o, while the k_z of the NG1~4 gas seal decreased monotonically with the increase of T_o. At 313 K; the k_z of NG1~4 was 23.5%, 25.7%, 17.4%, and 20.6% higher than that of NG5, respectively. It can be seen that increasing the impurity content at a lower temperature is more conducive to improve the k_z of the DGS.

3.4.2. Influence of Components on Leakage Rate

Figure 16 shows the variation curves of leakage rate of natural gas DGS with different working conditions. It can be seen that the influence of working conditions on the Q of different natural gas samples was the same. The influence of h₀ and p_o on the Q was more significant than that of n and T_o. When h₀ increased, the flow channel increased, resulting in the increase of Q. The increase of p_o not only increased the density of the fluid but also increased the radial velocity. When n increased, the Reynolds number of the fluid and the turbulent viscosity increased, and the viscous shear heat caused by the increase of n increased the temperature of fluid, the dynamic viscosity, or effective viscosity, as well as decrease the density of the medium, causing the radial flow resistance driven by hydrostatic pressure to increase. The mass leakage rate decreased as a result of the decrease of the density and the flow rate of the medium. The increase of T_o increased the dynamic viscosity and decreased the density of natural gas, resulting in an effect similar to the decrease of Q with the increase of n.

Furthermore, by longitudinal comparison of the leakage rates of several natural gas samples, it was found that the leakage rates of NG1~4 with high impurity content were all higher than those of NG5. Under the default working condition, the leakage rates of NG1~4 were 10.1%, 11.4%, 6.0%, and 8.0% higher than those of NG5, respectively. The reason is that the relative molecular weight of any component of multiple impurities was larger than that of CH₄. So, an increase in the impurity content will increase the density of the natural gas, resulting in an increase in Q.

3.4.3. Influence of Components on the Temperature Difference between Inlet and Outlet

Figure 17 shows the variation curves of temperature difference between the inlet and outlet of natural gas DGS with different working conditions. It can be seen from the figure that ΔT increased with the increase of h₀ and p_o and decreased with the increase of n and T_o, which was basically consistent with the change law of Q. When h₀ and p_o increased, the gas expansion effect was more obvious, and the temperature reduction was greater. When n increased, the viscous shear heat of the fluid increased, and ΔT decreased. When T_o increased, the viscosity of natural gas increased, resulting in an increase of viscous shear heat, and the ΔT decreased.

In order to further study the influence of different components of natural gas on the ΔT of the end face, the temperature distribution of the end face under the same working conditions was analyzed. Figure 18 shows the temperature difference distributions on the end face of different natural gas samples under the default working condition, where ΔT_i5 is the temperature difference between Ngi (i = 1, …, 4) and NG5:

$$\Delta T_{\mathrm{i}5}=T_{\mathrm{i}}-T_5\left(\mathrm{K}\right)$$

(27)

It can be seen that the temperature difference between NG1, NG3, and NG5 was small, and the temperature difference at the outlet was −0.35 K and −0.08 K, respectively, while the temperature difference at the outlet of NG2 and NG4 was larger, which was −1.2 and −3.8 K, respectively. It can be seen that when multiple impurities coexisted, the influence of each impurity on ΔT was the same as that of unitary impurity. The effect of increasing ΔT by light hydrocarbon and heavy hydrocarbon could cancel out each other with the effect of decreasing ΔT by non-hydrocarbon, and the part of mutual cancellation was related to the impurity content. Therefore, the ΔT of NG1~3, which had both hydrocarbon and non-hydrocarbon, was much smaller than that of NG4, which had significantly lighter hydrocarbon.

4. Conclusions

Based on the finite difference method, the influence of real fluid effects, natural gas components, and operating conditions on the steady-state performance of dry gas seals was analyzed. The important conclusions are as follows:

(a)

For the DGS of a natural gas pipeline compressor operating at high pressures, the laminar flow assumption caused a significantly higher mass leakage rate, and the relative error of the leakage rate exceeded 100% when the film thickness was large. Therefore, the influence of the turbulence effect is significant and cannot be ignored, while the choking effect has little influence on the steady-state performance of a natural gas DGS.

(b)

The change of impurities, such as light hydrocarbon, heavy hydrocarbon, and non-hydrocarbon in the natural gas mixture and their contents, as well as the interactions between the components, made the thermal physical properties of natural gas different from those of pure CH₄ and further affected the flow and heat transfer behavior between the two faces of a DGS, resulting in the sealing performance of the natural gas DGS, which was different from that of the pure CH₄ DGS.

(c)

For natural gas containing unitary impurity component, increasing the content of light and heavy hydrocarbon resulted in the increase of sealing performance, such as the film stiffness, leakage rate, and the temperature difference of both the inlet and outlet of the DGS. When the content of light hydrocarbon or heavy hydrocarbon reached 8%, the influence of impurity could not be neglected. When the impurity content was 10%, the values of the above performance parameters increased by about 1.5~3.5%, 6.5%, and 3 K, respectively. For natural gas containing non-hydrocarbon, when the impurity content reached 10%, the temperature difference between the inlet and outlet of the DGS decreased by 1.8 K, but the influence on the opening force, gas film stiffness, and leakage rate was negligible.

(d)

The influence of multiple impurities on the sealing performance is basically the same as that of the unitary impurity, and increasing the content of light or heavy hydrocarbon at lower temperatures is more conducive to the improvement of the gas film stiffness. With the increase of the film thickness and inlet pressure, the leakage rate of the DGS and the temperature difference between inlet and outlet will increase. The increase of rotational speed or inlet temperature will decrease the leakage rate and the temperature difference between the inlet and outlet.