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An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle
Accepted Manuscript Title: An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle Authors: Xuewen Cao, Xiaodan Song, Qi Chu, Linsheng Mu, Yuxuan Li, Jiang Bian PII: DOI: Reference:
S0957-5820(19)30876-6 https://doi.org/10.1016/j.psep.2019.07.008 PSEP 1848
To appear in:
Process Safety and Environment Protection
Received date: Revised date: Accepted date:
13 May 2019 7 July 2019 15 July 2019
Please cite this article as: Cao X, Song X, Chu Q, Mu L, Li Y, Bian J, An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle, Process Safety and Environmental Protection (2019), https://doi.org/10.1016/j.psep.2019.07.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle Xuewen Cao a,b, Xiaodan Song a,b, Qi Chu a,b, Linsheng Mu a,b, Yuxuan Li a,b, Jiang Bian a,b* (aCollege of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China; bShandong Provincial Key Laboratory of Oil & Gas Storage and Transportation Safety, Qingdao 266580, China) *Corresponding author at: College of Pipeline and Civil Engineering, China University of
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Petroleum (East China), Qingdao 266580, China. E-mail address: [email protected] (J. Bian).
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Highlights
A new method for hydrogen sulfide removal using Laval nozzle is proposed.
Mathematical model for the supersonic condensation of binary mixture is established.
The condensation characteristics of methane-hydrogen sulfide mixture is analyzed.
The influence of different inlet parameters on condensation process is investigated.
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Abstract
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A new method was proposed for hydrogen sulfide removal from natural gas through the utilization of supersonic flow in a Laval nozzle. For this purpose, a mathematical model was
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established for the supersonic non-equilibrium condensation flow of the binary methane-hydrogen sulfide mixture. The condensation parameters were numerically calculated
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and described in detail, and a sensitivity analysis was carried out to investigate the influence of the inlet parameters on the supersonic condensation flow. The results show that when the
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inlet temperature and pressure were 290 K and 5 MPa respectively, and the mole fraction of hydrogen sulfide was 15%, the removal efficiency of hydrogen sulfide was 64.83%, which indicates that the use of supersonic separation technology for this application is indeed feasible. It was also found that with the decrease of inlet temperature or the increase of inlet
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pressure, the nucleation site moved forward (i.e. closer to the throat), and the maximum droplet radius and liquid mass fraction of hydrogen sulfide increased. When the mole fraction of hydrogen sulfide was less than 5%, however, the liquid mass fraction of hydrogen sulfide was almost zero. Therefore, it appears that using a reasonable hydrogen sulfide fraction, a lower inlet temperature, and a higher inlet pressure can promote the supersonic condensation of hydrogen sulfide in the Laval nozzle and improve the efficiency of the removal process. 1
These results suggest that supersonic separation technology can provide an efficient and environment-friendly way to remove hydrogen sulfide from natural gas, thereby reducing emissions. Keywords: Hydrogen sulfide; Laval nozzle; Condensation characteristics; Removal
Nomenclature a0——molecular surface area (m2) D——the diameter at x (m)
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drd/dt——droplet growth rate (m s-1) E——total energy (J kg-1)
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h——total enthalpy (J kg -1) hlv—— latent heat of condensation (J kg -1) J——nucleation rate (m-3 s-1) Kn——Kundsen number (–)
L——length of the convergent section (m)
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kr——heat transfer coefficient (–)
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keff——effective thermal conductivity (W m-1 K-1)
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kB——Boltzmann constant (J K-1)
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mv——mass of droplets per unit volume condensation in unit time (kg m-3 s-1) mo——mass of the single molecular (kg)
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N——droplet number (kg-1) Prv——Prandtl number (–)
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p——pressure (pa)
RM——gas constant (J kg-1 K-1) rc——critical radius (m)
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rd——droplet radius (m)
S——degree of supersaturation (–) Sh——source term of energy equation (J m-3 s-1)
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Sm——source term of continuity equation (kg m-3 s-1) Su——source term of momentum equation (kg m-2 s-2) SY——source term of liquid continuity equation (kg m-3 s-1) t——time (s) T——temperature (K) Ts——saturation temperature of vapor (K) 2
u——velocity (m s-1) u’——velocity fluctuation (m s-1) vl——volume of a single droplet (m3) x——arbitrary length along the axis of the nozzle (m) Xm——relative coordinate of the junction point (–) Y——liquid fraction (–)
Greek symbols
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γ——specific heat ratio (–) δij——Kronecker delta (–)
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ε——correction factor proposed by Lamanna θ——dimensionless surface tension (–) λv——gas thermal conductivity (W m-1 K-1)
——viscosity (kg m-1 s-1)
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ρ——density (kg m-3)
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σ——droplet surface tension (N m-1)
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τeff——effective stress tensor (–)
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Subscripts i——axial parameter
j——radial direction l——liquid phase
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t——throat parameter
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in——inlet parameter
v——vapor phase
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1 Introduction
In the process of rapid industrialization and urbanization worldwide, air pollution has
emerged as a prominent environmental problem, with hydrogen sulfide being a major pollutant. Hydrogen sulfide is a toxic compound that is commonly found as an impurity in
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natural gas, coal gas, and synthesis gas, and is extremely harmful to the natural environment [1,2]. It not only causes corrosion to transport pipelines and equipment, but can also lead to catalyst poisoning and seriously threatens human health in areas where it is present [3-5]. Currently, many countries are in the process of strengthening environmental legislation in order to reduce hydrogen sulfide emissions and protect the natural environment. In the transport pipelines and refining facilities, the maximum allowable concentration of hydrogen 3
sulfide in natural gas is 4 ppm [6]. The removal of hydrogen sulfide therefore has important practical significance for both industrial production and environmental protection. Traditionally, commonly-used techniques for the industrial treatment of hydrogen sulfide include absorption [7,8], adsorption [9,10], and cryogenics [11], whereas newer techniques include biological oxidation combined processes purification, and electrochemistry. However, all of these techniques suffer from various disadvantages such as large capital costs, serious secondary pollution to the environment, and cumbersome equipment.
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Supersonic separation is a revolutionary technique that has been successfully applied
towards the dehydration of natural gas and the removal of heavy hydrocarbons [12-14]. It
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offers many advantages compared to traditional separation technologies, such as low capital costs, environmental friendliness, and flexible structure [15,16]. The supersonic separation technology is eco-friendly since it relies purely on physical separation without any consequent pollution generation due to the addition of chemicals [17]. Therefore, in the preset study, the
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use of supersonic separation technology for hydrogen sulfide removal is proposed as an
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alternative way to reduce hydrogen sulfide emissions from natural gas to the environment. In recent years, the supersonic condensation flow of gas in Laval nozzles, which is the
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key step in the supersonic separation process, has been extensively studied. Matsuo et al. [18]
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and Setoguchi et al. [19] developed a two-dimensional mathematical model for supersonic condensation considering the viscosity, and used this model to study spontaneous
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condensation of moist air in the nozzle boundary layer, the results show that the condensation of water vapor has large influence on temperature and velocity profiles. Jassim et al. [20,21]
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investigated the influence of real gas effects, nozzle structure, and vorticity on supersonic natural gas flow in Laval nozzles at high pressures. They found that the position of the shock wave can change significantly if the actual gas effect, nozzle structure and vorticity are taken
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into account. Ali et al. [22,23] studied the effect of thermal conductivity and tube geometry on the condensation heat transfer. Cao et al. [24] conducted a numerical simulation study on the supersonic condensation processes of binary gas mixtures in Laval nozzles, the conclusions
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are low inlet temperature and high inlet pressure can promote the condensation of binary gas. Zhang et al. [25,26] carried out a numerical study of condensing flow on the base of modified model and a novel dehumidification structure, comparing the simulation results with the experimental data, it is found that the Wilson point and thermal parameters prediction results of the modified model are more accurate. Niknam et al. [27] designed a supersonic separator with a set of tilted fixed blades and a swirl stabilizer at the nozzle inlet for dehydration processes. The experimental data of dehydration efficiency agree well with the simulation 4
results, and the error is within 3%. Bian et al. [28-30] studied the liquefaction characteristics of natural gas in Laval nozzles, and analyzed the effects of different temperatures, pressures, and the addition of external cores on condensation parameters and process efficiency. The author suggested that the natural gas can be liquefied in Laval nozzle which has good adaptability for condensation of natural gas under different conditions. More recently, supersonic separation technology has been introduced into the field of CO2 removal. Jiang et al. [31] and Bian et al. [32] investigated the use of supersonic
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condensation to separate CO2 from natural gas via a modified surface tension model for CO 2. It is found that the CO2 removal efficiency can be improved with higher inlet pressure and
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lower inlet temperature. Arinelli et al. [33] and Teixeira et al. [34] studied the CO2 removal performance in by supersonic separation for wet natural gas containing 44 mol% CO 2 in an offshore drilling platform and compared it with traditional natural gas CO2 removal techniques, the conclusions are the CO2 removal efficiency of supersonic separation is higher
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than traditional techniques under same conditions.
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As the studies cited so far show, supersonic separation techniques are overwhelmingly used for applications such as dehydration and removal of heavy hydrocarbons and CO2 from
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natural gas at present. Little research has been conducted on the removal of hydrogen sulfide
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from natural gas using this technology, despite its obvious advantages. Against this backdrop, the present study aims to evaluate the potential of supersonic separation technology for
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hydrogen sulfide removal from natural gas, which is not yet comprehensively understood. To this end, a supersonic non-equilibrium condensation model of the binary methane-hydrogen
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sulfide mixture in a Laval nozzle was established, and the model was validated using experimental data from Wyslouzil [43,44]. The key condensation parameters of hydrogen sulfide were simulated and analyzed in detail, and the influences of inlet temperature, inlet
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pressure, and inlet mole fraction of hydrogen sulfide on the condensation flow parameters of the binary mixture was investigated.
2 Simulation methodology
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2.1 Design of Laval nozzle It can be seen from Fig. 1 that the main structure of the supersonic separator includes a
Laval nozzle and a cyclone separation section. When gas flows through the Laval nozzle, its high-speed expansion causes a low-temperature effect resulting in gas condensation and droplet formation. These droplets flow through the swirling blade under supersonic conditions, and are thrown towards the wall under centrifugal force, before being discharged to the 5
collecting tank. The dry gas is discharged from the dry gas outlet after pressure recovery in the diffuser section. Thereinto the Laval nozzle is the key component to realize low-temperature condensation in the separator. In this study, an axially symmetric Laval nozzle was used—consisting of a straight section, a convergent section, a throat and a divergent section. The structure of the Laval nozzle is shown in Fig. 2. The convergent section, which uniformly accelerates the gas flow and improves the stability of the flow field, was designed using Eq. (1), which is a cubic
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polynomial expression. The divergent section of the nozzle was designed using an arc-and-straight-line method to simultaneously achieve expansion and ensure uniform gas
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flow at the nozzle outlet. The structural dimensions of designed Laval nozzle are calculated by MATLAB software, as shown in Table 1.
x Xm L
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x Xm L
(1)
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3 1 x 1 2 D Dt X m L 3 Din Dt 1 x 1 1 X 2 L m
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Fig. 1. Schematic diagram of the supersonic separator.
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Fig. 2. Structure of the designed Laval nozzle.
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Table 1. Geometry size of designed Laval nozzle
2.2 Governing equations of the mathematical model The governing equations of gas-liquid two phase flow for the methane-hydrogen sulfide
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mixture under supersonic spontaneous condensation conditions were developed based on the Euler-Euler model. Since the droplet size formed by spontaneous condensation is very small, the velocity slip between the gas and liquid phases can be ignored. The governing equations
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for the gas phase include the mass, momentum and energy equations (Eqs. (2)-(4)): v + vu j =Sm t x j
(2)
p u u 2 u v uiuj Su (3) vui + vu j ui = v j i ij j t x j xi x j xi x j 3 x j x j
v E + vu j E u j pv = t x j x j
T ui eff Sh keff x j 6
(4)
where
v uiuj
is the Reynolds stress term, and the turbulence model is needed for
calculation. The source terms of governing equations are defined to reflect the condensation phenomenon, expressed as Eqs. (5)-(7):
Sm = mv
(5)
Su = mvu
(6)
Sh = mv h hlv
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(7)
The supersonic flow characteristics of the liquid phase are described by the humidity, vY + vu jY =SY t x j
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condensation nucleation rate and droplet radius, defined as follows (Eqs. (8)-(10)): (8)
v N + vu j N =J t x j
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(9)
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3Y 3 rd = 4l N
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(10)
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2.3 Condensation model 2.3.1 Nucleation model
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Zeldovich [35] modified the Volmer and Weber formulas according to the kinetic theory, and subsequently derived the classical nucleation theory (CNT). Girshick and Chiu [36,37]
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solved the inconsistency in the CNT free energy calculation formula to derive the internally consistent classical nucleation theory (ICCT). Rudek [38] and Lamanna [39] demonstrated that ICCT can be used to obtain more accurate results than CNT. In this work, the ICCT
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model modified by Lamanna was used to calculate the condensation nucleation rate, as follows (Eqs. (11)-(13)):
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J
=
1 v 2
2
S l
mo
a0
3
exp 3kB l RM T ln S
exp
16 3
2
2
2
2
(12)
kBT 1
2
a0 = 36 3 vl 3
(13)
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(11)
2.3.2 Droplet growth model The number of critical condensation nuclei which move at the same speed as the gas flow is much smaller than the total number of gas molecules, and the probability of collisions between these nuclei is extremely small; hence, the collision and coalescence of droplets were neglected in this work. Here, the widely-used Gyarmathy droplet growth model [40] was utilized due to its good performance in calculating droplet growth rates. Using this model, the heat transfer coefficient may be calculated according to: v rd
1 1
2 8 Kn 1.5 Prv 1
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kr
(14)
hence, the droplet growth model can be expressed as: 4 rd2 l hlv
drd 4 rd2 kr (Ts T ) dt
(15)
rc Ts T drd rd dt 2 8 l hlv rd 1 Kn 1.5 Prv 1
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The mass transfer over the droplet growth process is accompanied by heat transfer;
v 1
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(16)
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The droplet radius is very small and the droplets are distributed in the gas flow at the same speed, the collision probability with other droplets is very low, so the collision and
2.4 Numerical schemes
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coalescence between different droplets is ignored in the above models.
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The model governing equations described in sections 2.1–2.3 were solved using the CFD software package ANSYS® Fluent 15.0, which was extended to take into account the
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condensation process. Considering the influence of condensation on flow governing equations, the source terms generated by condensation were added to FLUENT via UDF (User-Defined Functions) written by C language. The DEFINE_ADJUST macro and DEFINE_SOURECE are included in the UDF. The DEFINE_ADJUST macro was applied to define the
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condensation parameters such as gas supercooling, degree of supersaturation, nucleation rate, droplet growth rate and droplet radius; DEFINE_SOURECE macro was applied to define the source terms generated by condensation. Furthermore, the variations of droplet radius based on Gyarmathy droplet growth model [40] are written in UDF. The UDS (User-Defined Scalar) was used to establish governing equation of liquid phase flow with defining two scalars of droplet number and liquid mass fraction. 8
The flow of the methane-hydrogen sulfide mixture in Laval nozzles is a high-speed compressible flow, which was solved on a density basis. The structured grid was adopted in mesh of the Laval nozzle. The second-order upwind scheme was used to discretize the equations. The k-ω turbulence model was applied as it is applicable for wall-bonded flow and compressible flow [41,42]. 2.5 Grid independence verification and boundary conditions GAMBIT geometry and mesh generation software was utilized for generating structured
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meshes of the Laval nozzle, and the meshes of the throat and boundary layer were encrypted. The independence of the grids, which contained 4902 cells, 12015 cells, 28044 cells, and
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47175 cells, respectively, was validated using liquid mass fraction as a criterion. As Fig. 3
shows, the liquid mass fraction tends to be stable when the number of cells is greater than or equal to 28044. Therefore, the mesh with 28044 cells was selected to obtain accurate results
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while lowering the computation time as much as possible.
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Fig. 3. Simulation results of liquid mass fraction corresponding to different cells.
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The boundary conditions at the inlet and outlet were set as pressure boundary conditions.
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The range of inlet temperatures, inlet pressures and mole fractions of hydrogen sulfide used were 280–300 K, 4.5–5.5 MPa and 5–25%, respectively. The wall was subject to non-slip,
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non-seepage, and adiabatic boundary conditions.
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2.6 Experimental validation
The experimental data and nozzle structure from Wyslouzil et al. [43,44] were used to validate the accuracy of the simulation results, with experimental conditions as follows: inlet
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temperature of 287.6 K, inlet pressure of 60 kPa, and 1 kPa partial pressure of water. Fig. 4 shows the experimental data along with numerical simulation results for the static pressure distribution along the axial direction of the Laval nozzle. The experimental data of
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temperature difference distribution caused by condensation along the axial direction of the Laval nozzle was compared with numerical simulation results in the Fig. 5. As the Fig. 4 and Fig. 5 show, there are some deviations between the experimental and numerical simulation results. The relative error of pressure between the model and the experimental data does not exceed 6.4% and the relative error of temperature difference caused by condensation between the simulation and the experimental results is less than 7.2%, presented in Table 2. The main reasons for the deviations are as follows. (1) Under the condition of supersonic flow, the 9
parameters are difficult to be accurately measured by the test device, and there will be some changes in the actual results. (2) It is hard to control the partial pressure of water vapor at nozzle inlet exactly, moreover, there is a certain pressure fluctuation at the nozzle inlet. (3) Some assumptions are made to simplify the numerical simulations; for example the nozzle wall is specified as a no-slip, no seepage and adiabatic boundary, which is different from the real situation. Therefore, considering the uncertainties of experimental test equipment and the limitation of numerical model, the deviation between experimental data and simulation results
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is within a reasonable range. In addition, the simulated results of pressure and temperature difference distribution along the nozzle axis direction are consistent with the trend of
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experimental data, and the model also succeeded in accurately predicting the condensation
position; hence, these results validate the model and demonstrate that the simulation methods applied in this study are applicable to the supersonic condensation flow of the
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methane-hydrogen sulfide mixture in Laval nozzles.
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Fig. 4. Comparison between the experimental and simulation results for the static pressure
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distribution along the axial direction in Wyslouzil et al.’s [43,44] nozzle.
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Fig. 5. Comparison between the experimental and simulation results for the temperature difference distribution caused by condensation along the axial direction in Wyslouzil et al.’s
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[43,44] nozzle.
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Table 2. The relative error of pressure and temperature difference between experimental data and simulation data.
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3 Results and discussion
3.1 Flow and condensation characteristics of the methane-hydrogen sulfide mixture in the Laval nozzle
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Based on the spontaneous condensation model outlined in section 2, numerical
simulations were carried out. The operating parameters used in the simulation model are presented in Table 3. The simulation results of the spatial distributions for the main flow and condensation parameters in the Laval nozzle are shown in Fig. 6.
Table 3. Inlet conditions of the Laval nozzle 10
Fig. 6. Distributions of flow and condensation parameters in the Laval nozzle.
The distributions of the flow parameters are shown in Fig. 6(a)-(d). When the methane-hydrogen sulfide gas mixture enters the Laval nozzle, the Mach number increases steadily with the shrinking of the nozzle diameter, reaching a value of 1 at the throat. Subsequently, the mixture gas expands rapidly (with the Mach number increasing to 2.06),
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accompanied by significant decreases in the temperature and pressure and a corresponding
increase in the degree of supercooling. Once the degree of supercooling reaches its maximum
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value, condensation occurs, causing latent heat to be released. This is accompanied by a slight rise in temperature and pressure due to the condensation shock phenomenon.
Fig. 6(e) and (f) show the distributions of nucleation rate and droplet number in the Laval nozzle, wherein it can be seen that the hydrogen sulfide nucleation rate is zero over a
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certain distance after entering Laval nozzle. The condensation occurs at approximately x =
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0.456 m after the throat, whereupon the nucleation rate of hydrogen sulfide rapidly increases up to a maximum of 3.53×1021 m−3·s−1 over an extremely short distance of 0.004 m. However,
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the latent heat released by the condensation process eventually causes the temperature and
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pressure in the Laval nozzle to deviate from the conditions required for nucleation, and the nucleation rate sharply decreases to zero. The already-condensed nuclei grow into droplets,
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with the droplet number sharply rising to 3.62 × 1015 kg−1 and remaining at a stable value up to the outlet.
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Fig. 6(g) and (h) show the distributions of droplet radius and liquid mass fraction in the Laval nozzle. When the nucleation rate reaches its peak value, a large number of hydrogen sulfide vapor molecules gather on the droplet surfaces, leading to a rapid increase in droplet
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radius. After the degree of supercooling decreases, the hydrogen sulfide vapor is still in a state of supersaturation; therefore, the growth rate of the droplet radius and liquid phase mass fraction slows down. At the outlet of the Laval nozzle, the droplet radius reached a maximum
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of 2.23×10−7 m, and the liquid mass fraction and removal efficiency of hydrogen sulfide were 17.68% and 64.83%, respectively. As these results show, most of the parameters showed large gradients along the axial direction but changed very little in the radial direction, except for the nucleation rate and the number of droplets. Therefore, nephograms of these two parameters, and one-dimensional plots of the other parameters, are subsequently used in sections 3.2–3.4 to investigate the influence of different inlet conditions on flow and condensation in the Laval nozzle. 11
3.2 Effect of inlet temperature on the condensation process To investigate the temperature sensitivity of the condensation process, the inlet temperature was varied from 280 K to 300 K while maintaining the inlet pressure at 5 MPa and the hydrogen sulfide mole fraction at 15% (Fig. 7). As the figure shows, the pressures and Mach numbers at different inlet temperatures were consistent prior to the onset of supersonic condensation. The reason for this as the change of specific heat ratio in the temperature range
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studied is too small to make the pressure and March number distribution change significantly.
Once condensation started, however, the Mach number decreased due to the latent heat of
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condensation. The maximum degree of supercooling of the mixture increased at higher inlet temperatures, rising from 35.1 K to 39.8 K over the inlet temperature range.
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Fig. 7. Effect of different inlet temperatures on the condensation parameters.
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The initial position of condensation moved 28 mm towards the outlet over the inlet temperature range, due to the fact that the higher maximum degree of supercooling needed by
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condensation is more difficult to reach and more supersaturation is required for condensation.
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Additionally, the nucleation area became wider, the maximum droplet number grew significantly (from 3.91 × 1015 kg−1 to 5.68 × 1015 kg−1) because of higher degree of
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supercooling, and the maximum droplet radius decreased (from 2.45x10−7 m to 1.89×10−7 m) due to the fact that droplet growth rate is lower with higher inlet temperature.
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The mass fraction of hydrogen sulfide condensed into liquid increased from 15.41% to 23.26%, while the hydrogen sulfide fraction in the gas phase decreased from 8.36% to 5.91% as the inlet temperature decreased from 300 K to 280 K. The reason for this as the
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temperature is lowered, the nucleation position moves forward, the droplet growth process becomes longer, and more hydrogen sulfide molecules agglomerate around the droplets to condense out of the gas phase.
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These results show that the inlet temperatures have a significant influence on the degree
of supercooling and the liquid mass fraction of hydrogen sulfide, and that higher temperatures lead to greater fluctuations in liquid mass fraction. The reduction of inlet temperature from 300 K to 280 K causes 28.58% increase in removal efficiency of hydrogen sulfide, as presented in Table 4. Hence, a lower inlet temperature may facilitate the condensation of hydrogen sulfide from the gas mixture in the Laval nozzle, thereby improving the efficiency of the removal process. 12
Table 4. Hydrogen sulfide outlet concentration and removal efficiency at different inlet temperatures
3.3 Effect of inlet pressure on the condensation process To investigate the pressure sensitivity of the condensation process, the inlet pressure was varied from 4.5 MPa to 5.5 MPa while maintaining the inlet temperature at 290 K and the
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hydrogen sulfide mole fraction at 15% (Fig. 8). As the figure shows, the temperatures and Mach numbers at different inlet pressures were consistent prior to the onset of supersonic
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condensation. The reason for this as the change of specific heat ratio in the temperature range
studied is too small to make the temperature and March number distribution change significantly. Once condensation started, however, the Mach number decreased slightly. Under different inlet pressure conditions, the pressure difference at the nozzle outlet is very
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small. With increasing inlet pressure, the maximum sub-cooling degree of the mixture
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decreases due to the partial pressure of hydrogen sulfide being higher when the inlet pressure
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is higher; hence, a lower sub-cooling degree is required for large-scale nucleation.
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Fig. 8. Effect of different inlet pressures on the condensation parameters.
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The initial position of condensation moved 16 mm towards the throat over the inlet pressure range. This is due to the fact that the maximum degree of supercooling needed by
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condensation is lower, which can be achieved more easily at higher inlet pressures. Meanwhile, the nucleation area became narrower and the maximum nucleation rate deviated from the central axis and even approached the wall. The reason for this is that the central flow
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velocity of the nozzle is the largest, while the pressure and temperature are the lowest, the nucleation process occurs fastest and the latent heat released by the nucleation process has heating effect on the flow, causing the nucleation rate in the central region is reduced.
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Additionally, the maximum droplet number decreased significantly (from 5.54×1015 kg−1 to 4.15×1015 kg−1) because of lower degree of supercoiling, and the maximum droplet radius increased (from 1.95×10−7 m to 2.73×10−7 m) due to the fact that droplet growth rate is higher with higher inlet pressure. With increasing inlet pressure, the liquid mass fraction of hydrogen sulfide increased (from 16.62% to 17.94%), and the hydrogen sulfide fraction in the gas phase decreased (from 7.83% to 6.74%). This is because the nucleation occurs earlier as the entrance pressure 13
increases, meaning that the more hydrogen sulfide vapor molecules condense to form the droplets. These results show that while the effects of different inlet pressures on the condensation parameters are not as marked as that of different inlet temperatures, increasing the inlet pressure may facilitate the condensation of hydrogen sulfide. The increase of inlet pressure from 4.5 MPa to 5.5 MPa causes 4.46% increase in removal efficiency of hydrogen sulfide, as
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shown in Table 5. However, excessive inlet pressure will result in more pressure energy loss.
Table 5. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
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pressures
3.4 Effect of inlet hydrogen sulfide mole fraction on the condensation process
To investigate the sensitivity of the condensation process to the overall mixture
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composition, the inlet mole fraction of hydrogen sulfide was varied between 5% and 25%
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while maintaining the inlet temperature and pressure at 290 K and 5 MPa, respectively (Fig. 9). As the figure shows, the temperature, pressure, and Mach number distributions were
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consistent prior to the onset of supersonic condensation. Once condensation started, however,
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the temperature and Mach number clearly changed following the formation of a large number of condensation nuclei. This is because condensation releases great amount latent heat. When
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the inlet hydrogen sulfide mole fraction was 5%, the temperature and pressure curves hardly recovered, and the degree of supercooling did not come down after reaching its peak value.
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The reason for this is that the partial pressure of hydrogen sulfide is too small to reach both a state of supersaturation and also the degree of supercooling required for condensation; hence, the latent heat of condensation is small, and nucleation rate and the droplet number are much
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lower than those at higher inlet partial pressures of hydrogen sulfide.
Fig. 9. Effect of different inlet hydrogen sulfide mole fractions on the condensation
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parameters.
The initial condensation position is closer to the throat of the Laval nozzle at higher mole fractions of hydrogen sulfide. This is due to an increase in the inlet partial pressure of hydrogen sulfide at higher mole fractions, which is more conducive to condensation. The increase in the inlet mole fraction of hydrogen sulfide from 5% to 25% caused the maximum nucleation rate to increase by two orders of magnitude. The maximum droplet radius 14
increased significantly, (from 4.21 × 10−8 m to 2.85 × 10−7 m, respectively) over the hydrogen sulfide mole fraction range, as the hydrogen sulfide vapor in mixture is more likely to achieve the supercooling and supersaturation required for large-scale nucleation, meanwhile, the droplet growth rate is higher due to a larger amount of vapor molecules condense on surface of nuclei. With the increase of hydrogen sulfide mole fraction, the liquid mass fraction of hydrogen sulfide increased by four orders of magnitude (from 0.00494% to 27.43%) and the hydrogen
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sulfide fraction in the gas phase increased (from 4.91% to 14.30%), which indicates that most
of the hydrogen sulfide molecules still remained in the gas phase even at higher overall
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concentrations.
These results show that the varying the inlet hydrogen sulfide mole fraction has a significant effect on the condensation parameters. As the Table 6 shows, the efficiency of hydrogen sulfide removal stayed fairly steady over most of this range, at 64–66%, but when
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the hydrogen sulfide mole fraction was less than 5%, the removal efficiency of hydrogen
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for natural gas with high hydrogen sulfide content.
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sulfide became close to zero. It is indicated that the supersonic Laval nozzle is more suitable
4 Conclusions
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hydrogen sulfide mole fraction
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Table 6. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
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In this study, a new method for the supersonic removal of hydrogen sulfide from natural gas was proposed. A Laval nozzle structure was designed, and a mathematical model of the
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supersonic condensation flow of methane-hydrogen sulfide mixture gas in the Laval nozzle was established to enable prediction of the condensation parameters of hydrogen sulfide vapor. The sensitivity of the model to inlet temperature and pressure and hydrogen sulfide mole fraction was investigated.
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The results showed that in the Laval nozzle, the number of condensation nuclei rises
sharply from zero to the maximum value over in an extremely short distance following the start of condensation, with the nucleation rate subsequently falling to zero due to the release of latent heat of condensation. At the outlet of the Laval nozzle, the droplet radius and liquid fraction of hydrogen sulfide are at their maximum values. When the inlet temperature and pressure were set to 290 K and 5 MPa, respectively, and the inlet mole fraction of hydrogen 15
sulfide was 15%, the outlet liquid fraction of hydrogen sulfide was 17.68% and the its removal efficiency was 64.83%. With a decrease in inlet temperature or an increase in inlet pressure, the initial nucleation position moves towards the throat and the droplet radius and liquid fraction of hydrogen sulfide increase, while the mole fraction of hydrogen sulfide in the gas phase decreases. When the inlet hydrogen sulfide mole fraction falls below the threshold value of 5%, the outlet liquid fraction of hydrogen sulfide and the removal efficiency of hydrogen sulfide drop to almost zero, however, above this value, increasing the mole fraction
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of hydrogen sulfide does not appear to change the removal efficiency very much. These results suggest that a reasonable hydrogen sulfide mole fraction, a lower inlet temperature and
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a higher inlet pressure are required for improving supersonic condensation of hydrogen sulfide gas in the Laval nozzle.
This study represents the first step towards the development of an effective and environment-friendly method for the removal of hydrogen sulfide from natural gas under a
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variety of inlet conditions, with the ultimate goal of reducing environmental pollution and
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reducing its negative impact on industrial processes. It is hoped that this investigation will also provide useful insights for the design and optimization of the supersonic separation
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technique for future applications.
Acknowledgements
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This study was supported by the National Key R&D Program of China (Grant No. 2016YFC0802302 and No. 2016YFC0802304) and the National Natural Science Foundation
References
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Fig. 1. Schematic diagram of the supersonic separator.
20
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Fig. 2. Structure of the designed Laval nozzle.
A
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Fig. 3. Simulation results of liquid mass fraction corresponding to different cells.
21
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Fig. 4. Comparison between the experimental and simulation results for the static
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A
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pressure distribution along the axial direction in Wyslouzil et al.’s [43,44] nozzle.
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Fig. 5. Comparison between the experimental and simulation results for the temperature
difference distribution caused by condensation along the axial direction in Wyslouzil et al.’s
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[43,44] nozzle.
22
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(b) Pressure /Pa
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A
N
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(a) Temperature /K
(d) degree of supercoiling /K
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(c) Mach number /Dimensionless
(e) Nucleation rate /m−3·s−1
(f) droplet number /kg-1
23
(g) droplet radius /m
(h) liquid mass fraction / Dimensionless
(b) Pressure distribution
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(a) Temperature distribution
A
N
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Fig. 6. Distribution of flow and condensation parameters in the Laval nozzle.
(d) Degree of supercooling distribution
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(c) Ma distribution
24
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(f) Droplet number distribution
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A
N
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(e) Nucleation rate distribution
(h) Liquid mass fraction distribution
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(g) Droplet radius distribution
25
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(i) Hydrogen sulfide fraction in gas phase distribution
A
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A
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Fig. 7. Effect of different inlet temperatures on the condensation parameters.
(a) Temperature distribution
(b) Pressure distribution
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(d) Degree of supercooling distribution
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(c) Ma distribution
(f) Droplet number distribution
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(e) Nucleation rate distribution
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(h) Liquid mass fraction distribution
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(g) Droplet radius distribution
(i) Hydrogen sulfide fraction in gas phase distribution
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Fig. 8. Effect of different inlet pressures on the condensation parameters.
28
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(a) Temperature distribution
29
(b) Pressure distribution
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(d) Degree of supercooling distribution
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A
N
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(c) Ma distribution
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(e) Nucleation rate distribution
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(f) Droplet number distribution
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(h) Liquid mass fraction distribution
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(g) Droplet radius distribution
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(i) Hydrogen sulfide fraction in gas phase distribution Fig. 9. Effect of different inlet hydrogen sulfide mole fraction on the condensation
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parameters.
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Table 1. Geometry size of designed Laval nozzle Geometry structure
Size /mm
Inlet diameter
148
Throat diameter
18.52
Outlet diameter
34.6
Straight section
185
convergent section
232.4
divergent section
130.9
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Table 2. The relative error of pressure and temperature difference between experimental data and simulation data.
x1=0.
ation 30458.6
2 x2=11
23866.2
.4 x3=21
21864.1
.5 x4=31
21424.6
.7 x5=41
19227.2
.9 x6=52
17176.2
.1 x7=62
15711.3
.9
x8=72
14490.4
23231 .4
0.02 7
21896 .1
0.00 2
20740 .9
0.03 2
18348 .2
0.04 6
16785 .5
0.02
3
15418 .3
0.01
9
14343
.9
ation 0.10
0.10
0.20
0.21
10.48
10.59
25.91
27.78
26.86
27.81
27.02
27.94
26.97
28.01
0.01
26.70
27.96
0
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.5
0.06 4
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.4
ment 32407
Simul tive error
Experi
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ment
tive error
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Table 3. Inlet conditions of the Laval nozzle Parameter
Unit
Value
Inlet temperature
K
290
Inlet pressure
MPa
5.0
Mole fraction
0.15
Mole fraction
0.85
Hydrogen
sulfide
composition Methane composition
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0
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Simul
Rela
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Experi
difference/K
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throat/mm
Rela
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from
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nce
Temperature
Pressure/Pa
Dista
0.05 0.01
1 0.07 2 0.03 5 0.03 4 0.03 9 0.04 7
Table 4. Hydrogen sulfide outlet concentration and removal efficiency at different inlet temperatures Hydrogen
sulfide
outlet concentration
Removal
efficiency
(%)
280
0.0591
85.21
290
0.0727
64.83
300
0.0836
56.63
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Inlet temperature (K)
pressures Hydrogen sulfide outlet
Inlet pressure (MPa)
5.0
0.0727
5.5
0.0675
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0.0783
Removal efficiency (%) 61.16 64.83 65.62
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4.5
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concentration
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Table 5. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
hydrogen sulfide mole fraction
concentration
0.15
Hydrogen sulfide outlet
concentration
Removal efficiency (%)
0.0499
0.05
0.0727
64.83
0.1368
65.97
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0.25
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0.05
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Hydrogen sulfide inlet
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Table 6. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
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S0957-5820(19)30876-6 https://doi.org/10.1016/j.psep.2019.07.008 PSEP 1848
To appear in:
Process Safety and Environment Protection
Received date: Revised date: Accepted date:
13 May 2019 7 July 2019 15 July 2019
Please cite this article as: Cao X, Song X, Chu Q, Mu L, Li Y, Bian J, An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle, Process Safety and Environmental Protection (2019), https://doi.org/10.1016/j.psep.2019.07.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
An efficient method for removing hydrogen sulfide from natural gas using supersonic Laval nozzle Xuewen Cao a,b, Xiaodan Song a,b, Qi Chu a,b, Linsheng Mu a,b, Yuxuan Li a,b, Jiang Bian a,b* (aCollege of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China; bShandong Provincial Key Laboratory of Oil & Gas Storage and Transportation Safety, Qingdao 266580, China) *Corresponding author at: College of Pipeline and Civil Engineering, China University of
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Petroleum (East China), Qingdao 266580, China. E-mail address: [email protected] (J. Bian).
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Highlights
A new method for hydrogen sulfide removal using Laval nozzle is proposed.
Mathematical model for the supersonic condensation of binary mixture is established.
The condensation characteristics of methane-hydrogen sulfide mixture is analyzed.
The influence of different inlet parameters on condensation process is investigated.
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Abstract
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A new method was proposed for hydrogen sulfide removal from natural gas through the utilization of supersonic flow in a Laval nozzle. For this purpose, a mathematical model was
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established for the supersonic non-equilibrium condensation flow of the binary methane-hydrogen sulfide mixture. The condensation parameters were numerically calculated
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and described in detail, and a sensitivity analysis was carried out to investigate the influence of the inlet parameters on the supersonic condensation flow. The results show that when the
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inlet temperature and pressure were 290 K and 5 MPa respectively, and the mole fraction of hydrogen sulfide was 15%, the removal efficiency of hydrogen sulfide was 64.83%, which indicates that the use of supersonic separation technology for this application is indeed feasible. It was also found that with the decrease of inlet temperature or the increase of inlet
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pressure, the nucleation site moved forward (i.e. closer to the throat), and the maximum droplet radius and liquid mass fraction of hydrogen sulfide increased. When the mole fraction of hydrogen sulfide was less than 5%, however, the liquid mass fraction of hydrogen sulfide was almost zero. Therefore, it appears that using a reasonable hydrogen sulfide fraction, a lower inlet temperature, and a higher inlet pressure can promote the supersonic condensation of hydrogen sulfide in the Laval nozzle and improve the efficiency of the removal process. 1
These results suggest that supersonic separation technology can provide an efficient and environment-friendly way to remove hydrogen sulfide from natural gas, thereby reducing emissions. Keywords: Hydrogen sulfide; Laval nozzle; Condensation characteristics; Removal
Nomenclature a0——molecular surface area (m2) D——the diameter at x (m)
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drd/dt——droplet growth rate (m s-1) E——total energy (J kg-1)
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h——total enthalpy (J kg -1) hlv—— latent heat of condensation (J kg -1) J——nucleation rate (m-3 s-1) Kn——Kundsen number (–)
L——length of the convergent section (m)
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kr——heat transfer coefficient (–)
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keff——effective thermal conductivity (W m-1 K-1)
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kB——Boltzmann constant (J K-1)
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mv——mass of droplets per unit volume condensation in unit time (kg m-3 s-1) mo——mass of the single molecular (kg)
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N——droplet number (kg-1) Prv——Prandtl number (–)
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p——pressure (pa)
RM——gas constant (J kg-1 K-1) rc——critical radius (m)
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rd——droplet radius (m)
S——degree of supersaturation (–) Sh——source term of energy equation (J m-3 s-1)
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Sm——source term of continuity equation (kg m-3 s-1) Su——source term of momentum equation (kg m-2 s-2) SY——source term of liquid continuity equation (kg m-3 s-1) t——time (s) T——temperature (K) Ts——saturation temperature of vapor (K) 2
u——velocity (m s-1) u’——velocity fluctuation (m s-1) vl——volume of a single droplet (m3) x——arbitrary length along the axis of the nozzle (m) Xm——relative coordinate of the junction point (–) Y——liquid fraction (–)
Greek symbols
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γ——specific heat ratio (–) δij——Kronecker delta (–)
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ε——correction factor proposed by Lamanna θ——dimensionless surface tension (–) λv——gas thermal conductivity (W m-1 K-1)
——viscosity (kg m-1 s-1)
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ρ——density (kg m-3)
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σ——droplet surface tension (N m-1)
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τeff——effective stress tensor (–)
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Subscripts i——axial parameter
j——radial direction l——liquid phase
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t——throat parameter
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in——inlet parameter
v——vapor phase
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1 Introduction
In the process of rapid industrialization and urbanization worldwide, air pollution has
emerged as a prominent environmental problem, with hydrogen sulfide being a major pollutant. Hydrogen sulfide is a toxic compound that is commonly found as an impurity in
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natural gas, coal gas, and synthesis gas, and is extremely harmful to the natural environment [1,2]. It not only causes corrosion to transport pipelines and equipment, but can also lead to catalyst poisoning and seriously threatens human health in areas where it is present [3-5]. Currently, many countries are in the process of strengthening environmental legislation in order to reduce hydrogen sulfide emissions and protect the natural environment. In the transport pipelines and refining facilities, the maximum allowable concentration of hydrogen 3
sulfide in natural gas is 4 ppm [6]. The removal of hydrogen sulfide therefore has important practical significance for both industrial production and environmental protection. Traditionally, commonly-used techniques for the industrial treatment of hydrogen sulfide include absorption [7,8], adsorption [9,10], and cryogenics [11], whereas newer techniques include biological oxidation combined processes purification, and electrochemistry. However, all of these techniques suffer from various disadvantages such as large capital costs, serious secondary pollution to the environment, and cumbersome equipment.
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Supersonic separation is a revolutionary technique that has been successfully applied
towards the dehydration of natural gas and the removal of heavy hydrocarbons [12-14]. It
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offers many advantages compared to traditional separation technologies, such as low capital costs, environmental friendliness, and flexible structure [15,16]. The supersonic separation technology is eco-friendly since it relies purely on physical separation without any consequent pollution generation due to the addition of chemicals [17]. Therefore, in the preset study, the
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use of supersonic separation technology for hydrogen sulfide removal is proposed as an
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alternative way to reduce hydrogen sulfide emissions from natural gas to the environment. In recent years, the supersonic condensation flow of gas in Laval nozzles, which is the
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key step in the supersonic separation process, has been extensively studied. Matsuo et al. [18]
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and Setoguchi et al. [19] developed a two-dimensional mathematical model for supersonic condensation considering the viscosity, and used this model to study spontaneous
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condensation of moist air in the nozzle boundary layer, the results show that the condensation of water vapor has large influence on temperature and velocity profiles. Jassim et al. [20,21]
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investigated the influence of real gas effects, nozzle structure, and vorticity on supersonic natural gas flow in Laval nozzles at high pressures. They found that the position of the shock wave can change significantly if the actual gas effect, nozzle structure and vorticity are taken
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into account. Ali et al. [22,23] studied the effect of thermal conductivity and tube geometry on the condensation heat transfer. Cao et al. [24] conducted a numerical simulation study on the supersonic condensation processes of binary gas mixtures in Laval nozzles, the conclusions
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are low inlet temperature and high inlet pressure can promote the condensation of binary gas. Zhang et al. [25,26] carried out a numerical study of condensing flow on the base of modified model and a novel dehumidification structure, comparing the simulation results with the experimental data, it is found that the Wilson point and thermal parameters prediction results of the modified model are more accurate. Niknam et al. [27] designed a supersonic separator with a set of tilted fixed blades and a swirl stabilizer at the nozzle inlet for dehydration processes. The experimental data of dehydration efficiency agree well with the simulation 4
results, and the error is within 3%. Bian et al. [28-30] studied the liquefaction characteristics of natural gas in Laval nozzles, and analyzed the effects of different temperatures, pressures, and the addition of external cores on condensation parameters and process efficiency. The author suggested that the natural gas can be liquefied in Laval nozzle which has good adaptability for condensation of natural gas under different conditions. More recently, supersonic separation technology has been introduced into the field of CO2 removal. Jiang et al. [31] and Bian et al. [32] investigated the use of supersonic
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condensation to separate CO2 from natural gas via a modified surface tension model for CO 2. It is found that the CO2 removal efficiency can be improved with higher inlet pressure and
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lower inlet temperature. Arinelli et al. [33] and Teixeira et al. [34] studied the CO2 removal performance in by supersonic separation for wet natural gas containing 44 mol% CO 2 in an offshore drilling platform and compared it with traditional natural gas CO2 removal techniques, the conclusions are the CO2 removal efficiency of supersonic separation is higher
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than traditional techniques under same conditions.
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As the studies cited so far show, supersonic separation techniques are overwhelmingly used for applications such as dehydration and removal of heavy hydrocarbons and CO2 from
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natural gas at present. Little research has been conducted on the removal of hydrogen sulfide
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from natural gas using this technology, despite its obvious advantages. Against this backdrop, the present study aims to evaluate the potential of supersonic separation technology for
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hydrogen sulfide removal from natural gas, which is not yet comprehensively understood. To this end, a supersonic non-equilibrium condensation model of the binary methane-hydrogen
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sulfide mixture in a Laval nozzle was established, and the model was validated using experimental data from Wyslouzil [43,44]. The key condensation parameters of hydrogen sulfide were simulated and analyzed in detail, and the influences of inlet temperature, inlet
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pressure, and inlet mole fraction of hydrogen sulfide on the condensation flow parameters of the binary mixture was investigated.
2 Simulation methodology
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2.1 Design of Laval nozzle It can be seen from Fig. 1 that the main structure of the supersonic separator includes a
Laval nozzle and a cyclone separation section. When gas flows through the Laval nozzle, its high-speed expansion causes a low-temperature effect resulting in gas condensation and droplet formation. These droplets flow through the swirling blade under supersonic conditions, and are thrown towards the wall under centrifugal force, before being discharged to the 5
collecting tank. The dry gas is discharged from the dry gas outlet after pressure recovery in the diffuser section. Thereinto the Laval nozzle is the key component to realize low-temperature condensation in the separator. In this study, an axially symmetric Laval nozzle was used—consisting of a straight section, a convergent section, a throat and a divergent section. The structure of the Laval nozzle is shown in Fig. 2. The convergent section, which uniformly accelerates the gas flow and improves the stability of the flow field, was designed using Eq. (1), which is a cubic
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polynomial expression. The divergent section of the nozzle was designed using an arc-and-straight-line method to simultaneously achieve expansion and ensure uniform gas
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flow at the nozzle outlet. The structural dimensions of designed Laval nozzle are calculated by MATLAB software, as shown in Table 1.
x Xm L
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x Xm L
(1)
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3 1 x 1 2 D Dt X m L 3 Din Dt 1 x 1 1 X 2 L m
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Fig. 1. Schematic diagram of the supersonic separator.
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Fig. 2. Structure of the designed Laval nozzle.
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Table 1. Geometry size of designed Laval nozzle
2.2 Governing equations of the mathematical model The governing equations of gas-liquid two phase flow for the methane-hydrogen sulfide
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mixture under supersonic spontaneous condensation conditions were developed based on the Euler-Euler model. Since the droplet size formed by spontaneous condensation is very small, the velocity slip between the gas and liquid phases can be ignored. The governing equations
A
for the gas phase include the mass, momentum and energy equations (Eqs. (2)-(4)): v + vu j =Sm t x j
(2)
p u u 2 u v uiuj Su (3) vui + vu j ui = v j i ij j t x j xi x j xi x j 3 x j x j
v E + vu j E u j pv = t x j x j
T ui eff Sh keff x j 6
(4)
where
v uiuj
is the Reynolds stress term, and the turbulence model is needed for
calculation. The source terms of governing equations are defined to reflect the condensation phenomenon, expressed as Eqs. (5)-(7):
Sm = mv
(5)
Su = mvu
(6)
Sh = mv h hlv
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(7)
The supersonic flow characteristics of the liquid phase are described by the humidity, vY + vu jY =SY t x j
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condensation nucleation rate and droplet radius, defined as follows (Eqs. (8)-(10)): (8)
v N + vu j N =J t x j
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(9)
1
3Y 3 rd = 4l N
A
N
(10)
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2.3 Condensation model 2.3.1 Nucleation model
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Zeldovich [35] modified the Volmer and Weber formulas according to the kinetic theory, and subsequently derived the classical nucleation theory (CNT). Girshick and Chiu [36,37]
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solved the inconsistency in the CNT free energy calculation formula to derive the internally consistent classical nucleation theory (ICCT). Rudek [38] and Lamanna [39] demonstrated that ICCT can be used to obtain more accurate results than CNT. In this work, the ICCT
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model modified by Lamanna was used to calculate the condensation nucleation rate, as follows (Eqs. (11)-(13)):
A
J
=
1 v 2
2
S l
mo
a0
3
exp 3kB l RM T ln S
exp
16 3
2
2
2
2
(12)
kBT 1
2
a0 = 36 3 vl 3
(13)
7
(11)
2.3.2 Droplet growth model The number of critical condensation nuclei which move at the same speed as the gas flow is much smaller than the total number of gas molecules, and the probability of collisions between these nuclei is extremely small; hence, the collision and coalescence of droplets were neglected in this work. Here, the widely-used Gyarmathy droplet growth model [40] was utilized due to its good performance in calculating droplet growth rates. Using this model, the heat transfer coefficient may be calculated according to: v rd
1 1
2 8 Kn 1.5 Prv 1
IP T
kr
(14)
hence, the droplet growth model can be expressed as: 4 rd2 l hlv
drd 4 rd2 kr (Ts T ) dt
(15)
rc Ts T drd rd dt 2 8 l hlv rd 1 Kn 1.5 Prv 1
U
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The mass transfer over the droplet growth process is accompanied by heat transfer;
v 1
A
N
(16)
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The droplet radius is very small and the droplets are distributed in the gas flow at the same speed, the collision probability with other droplets is very low, so the collision and
2.4 Numerical schemes
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coalescence between different droplets is ignored in the above models.
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The model governing equations described in sections 2.1–2.3 were solved using the CFD software package ANSYS® Fluent 15.0, which was extended to take into account the
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condensation process. Considering the influence of condensation on flow governing equations, the source terms generated by condensation were added to FLUENT via UDF (User-Defined Functions) written by C language. The DEFINE_ADJUST macro and DEFINE_SOURECE are included in the UDF. The DEFINE_ADJUST macro was applied to define the
A
condensation parameters such as gas supercooling, degree of supersaturation, nucleation rate, droplet growth rate and droplet radius; DEFINE_SOURECE macro was applied to define the source terms generated by condensation. Furthermore, the variations of droplet radius based on Gyarmathy droplet growth model [40] are written in UDF. The UDS (User-Defined Scalar) was used to establish governing equation of liquid phase flow with defining two scalars of droplet number and liquid mass fraction. 8
The flow of the methane-hydrogen sulfide mixture in Laval nozzles is a high-speed compressible flow, which was solved on a density basis. The structured grid was adopted in mesh of the Laval nozzle. The second-order upwind scheme was used to discretize the equations. The k-ω turbulence model was applied as it is applicable for wall-bonded flow and compressible flow [41,42]. 2.5 Grid independence verification and boundary conditions GAMBIT geometry and mesh generation software was utilized for generating structured
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meshes of the Laval nozzle, and the meshes of the throat and boundary layer were encrypted. The independence of the grids, which contained 4902 cells, 12015 cells, 28044 cells, and
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47175 cells, respectively, was validated using liquid mass fraction as a criterion. As Fig. 3
shows, the liquid mass fraction tends to be stable when the number of cells is greater than or equal to 28044. Therefore, the mesh with 28044 cells was selected to obtain accurate results
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while lowering the computation time as much as possible.
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Fig. 3. Simulation results of liquid mass fraction corresponding to different cells.
A
The boundary conditions at the inlet and outlet were set as pressure boundary conditions.
M
The range of inlet temperatures, inlet pressures and mole fractions of hydrogen sulfide used were 280–300 K, 4.5–5.5 MPa and 5–25%, respectively. The wall was subject to non-slip,
ED
non-seepage, and adiabatic boundary conditions.
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2.6 Experimental validation
The experimental data and nozzle structure from Wyslouzil et al. [43,44] were used to validate the accuracy of the simulation results, with experimental conditions as follows: inlet
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temperature of 287.6 K, inlet pressure of 60 kPa, and 1 kPa partial pressure of water. Fig. 4 shows the experimental data along with numerical simulation results for the static pressure distribution along the axial direction of the Laval nozzle. The experimental data of
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temperature difference distribution caused by condensation along the axial direction of the Laval nozzle was compared with numerical simulation results in the Fig. 5. As the Fig. 4 and Fig. 5 show, there are some deviations between the experimental and numerical simulation results. The relative error of pressure between the model and the experimental data does not exceed 6.4% and the relative error of temperature difference caused by condensation between the simulation and the experimental results is less than 7.2%, presented in Table 2. The main reasons for the deviations are as follows. (1) Under the condition of supersonic flow, the 9
parameters are difficult to be accurately measured by the test device, and there will be some changes in the actual results. (2) It is hard to control the partial pressure of water vapor at nozzle inlet exactly, moreover, there is a certain pressure fluctuation at the nozzle inlet. (3) Some assumptions are made to simplify the numerical simulations; for example the nozzle wall is specified as a no-slip, no seepage and adiabatic boundary, which is different from the real situation. Therefore, considering the uncertainties of experimental test equipment and the limitation of numerical model, the deviation between experimental data and simulation results
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is within a reasonable range. In addition, the simulated results of pressure and temperature difference distribution along the nozzle axis direction are consistent with the trend of
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experimental data, and the model also succeeded in accurately predicting the condensation
position; hence, these results validate the model and demonstrate that the simulation methods applied in this study are applicable to the supersonic condensation flow of the
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methane-hydrogen sulfide mixture in Laval nozzles.
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Fig. 4. Comparison between the experimental and simulation results for the static pressure
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distribution along the axial direction in Wyslouzil et al.’s [43,44] nozzle.
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Fig. 5. Comparison between the experimental and simulation results for the temperature difference distribution caused by condensation along the axial direction in Wyslouzil et al.’s
ED
[43,44] nozzle.
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Table 2. The relative error of pressure and temperature difference between experimental data and simulation data.
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3 Results and discussion
3.1 Flow and condensation characteristics of the methane-hydrogen sulfide mixture in the Laval nozzle
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Based on the spontaneous condensation model outlined in section 2, numerical
simulations were carried out. The operating parameters used in the simulation model are presented in Table 3. The simulation results of the spatial distributions for the main flow and condensation parameters in the Laval nozzle are shown in Fig. 6.
Table 3. Inlet conditions of the Laval nozzle 10
Fig. 6. Distributions of flow and condensation parameters in the Laval nozzle.
The distributions of the flow parameters are shown in Fig. 6(a)-(d). When the methane-hydrogen sulfide gas mixture enters the Laval nozzle, the Mach number increases steadily with the shrinking of the nozzle diameter, reaching a value of 1 at the throat. Subsequently, the mixture gas expands rapidly (with the Mach number increasing to 2.06),
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accompanied by significant decreases in the temperature and pressure and a corresponding
increase in the degree of supercooling. Once the degree of supercooling reaches its maximum
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value, condensation occurs, causing latent heat to be released. This is accompanied by a slight rise in temperature and pressure due to the condensation shock phenomenon.
Fig. 6(e) and (f) show the distributions of nucleation rate and droplet number in the Laval nozzle, wherein it can be seen that the hydrogen sulfide nucleation rate is zero over a
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certain distance after entering Laval nozzle. The condensation occurs at approximately x =
N
0.456 m after the throat, whereupon the nucleation rate of hydrogen sulfide rapidly increases up to a maximum of 3.53×1021 m−3·s−1 over an extremely short distance of 0.004 m. However,
A
the latent heat released by the condensation process eventually causes the temperature and
M
pressure in the Laval nozzle to deviate from the conditions required for nucleation, and the nucleation rate sharply decreases to zero. The already-condensed nuclei grow into droplets,
ED
with the droplet number sharply rising to 3.62 × 1015 kg−1 and remaining at a stable value up to the outlet.
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Fig. 6(g) and (h) show the distributions of droplet radius and liquid mass fraction in the Laval nozzle. When the nucleation rate reaches its peak value, a large number of hydrogen sulfide vapor molecules gather on the droplet surfaces, leading to a rapid increase in droplet
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radius. After the degree of supercooling decreases, the hydrogen sulfide vapor is still in a state of supersaturation; therefore, the growth rate of the droplet radius and liquid phase mass fraction slows down. At the outlet of the Laval nozzle, the droplet radius reached a maximum
A
of 2.23×10−7 m, and the liquid mass fraction and removal efficiency of hydrogen sulfide were 17.68% and 64.83%, respectively. As these results show, most of the parameters showed large gradients along the axial direction but changed very little in the radial direction, except for the nucleation rate and the number of droplets. Therefore, nephograms of these two parameters, and one-dimensional plots of the other parameters, are subsequently used in sections 3.2–3.4 to investigate the influence of different inlet conditions on flow and condensation in the Laval nozzle. 11
3.2 Effect of inlet temperature on the condensation process To investigate the temperature sensitivity of the condensation process, the inlet temperature was varied from 280 K to 300 K while maintaining the inlet pressure at 5 MPa and the hydrogen sulfide mole fraction at 15% (Fig. 7). As the figure shows, the pressures and Mach numbers at different inlet temperatures were consistent prior to the onset of supersonic condensation. The reason for this as the change of specific heat ratio in the temperature range
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studied is too small to make the pressure and March number distribution change significantly.
Once condensation started, however, the Mach number decreased due to the latent heat of
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condensation. The maximum degree of supercooling of the mixture increased at higher inlet temperatures, rising from 35.1 K to 39.8 K over the inlet temperature range.
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Fig. 7. Effect of different inlet temperatures on the condensation parameters.
N
The initial position of condensation moved 28 mm towards the outlet over the inlet temperature range, due to the fact that the higher maximum degree of supercooling needed by
A
condensation is more difficult to reach and more supersaturation is required for condensation.
M
Additionally, the nucleation area became wider, the maximum droplet number grew significantly (from 3.91 × 1015 kg−1 to 5.68 × 1015 kg−1) because of higher degree of
ED
supercooling, and the maximum droplet radius decreased (from 2.45x10−7 m to 1.89×10−7 m) due to the fact that droplet growth rate is lower with higher inlet temperature.
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The mass fraction of hydrogen sulfide condensed into liquid increased from 15.41% to 23.26%, while the hydrogen sulfide fraction in the gas phase decreased from 8.36% to 5.91% as the inlet temperature decreased from 300 K to 280 K. The reason for this as the
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temperature is lowered, the nucleation position moves forward, the droplet growth process becomes longer, and more hydrogen sulfide molecules agglomerate around the droplets to condense out of the gas phase.
A
These results show that the inlet temperatures have a significant influence on the degree
of supercooling and the liquid mass fraction of hydrogen sulfide, and that higher temperatures lead to greater fluctuations in liquid mass fraction. The reduction of inlet temperature from 300 K to 280 K causes 28.58% increase in removal efficiency of hydrogen sulfide, as presented in Table 4. Hence, a lower inlet temperature may facilitate the condensation of hydrogen sulfide from the gas mixture in the Laval nozzle, thereby improving the efficiency of the removal process. 12
Table 4. Hydrogen sulfide outlet concentration and removal efficiency at different inlet temperatures
3.3 Effect of inlet pressure on the condensation process To investigate the pressure sensitivity of the condensation process, the inlet pressure was varied from 4.5 MPa to 5.5 MPa while maintaining the inlet temperature at 290 K and the
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hydrogen sulfide mole fraction at 15% (Fig. 8). As the figure shows, the temperatures and Mach numbers at different inlet pressures were consistent prior to the onset of supersonic
SC R
condensation. The reason for this as the change of specific heat ratio in the temperature range
studied is too small to make the temperature and March number distribution change significantly. Once condensation started, however, the Mach number decreased slightly. Under different inlet pressure conditions, the pressure difference at the nozzle outlet is very
U
small. With increasing inlet pressure, the maximum sub-cooling degree of the mixture
N
decreases due to the partial pressure of hydrogen sulfide being higher when the inlet pressure
A
is higher; hence, a lower sub-cooling degree is required for large-scale nucleation.
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Fig. 8. Effect of different inlet pressures on the condensation parameters.
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The initial position of condensation moved 16 mm towards the throat over the inlet pressure range. This is due to the fact that the maximum degree of supercooling needed by
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condensation is lower, which can be achieved more easily at higher inlet pressures. Meanwhile, the nucleation area became narrower and the maximum nucleation rate deviated from the central axis and even approached the wall. The reason for this is that the central flow
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velocity of the nozzle is the largest, while the pressure and temperature are the lowest, the nucleation process occurs fastest and the latent heat released by the nucleation process has heating effect on the flow, causing the nucleation rate in the central region is reduced.
A
Additionally, the maximum droplet number decreased significantly (from 5.54×1015 kg−1 to 4.15×1015 kg−1) because of lower degree of supercoiling, and the maximum droplet radius increased (from 1.95×10−7 m to 2.73×10−7 m) due to the fact that droplet growth rate is higher with higher inlet pressure. With increasing inlet pressure, the liquid mass fraction of hydrogen sulfide increased (from 16.62% to 17.94%), and the hydrogen sulfide fraction in the gas phase decreased (from 7.83% to 6.74%). This is because the nucleation occurs earlier as the entrance pressure 13
increases, meaning that the more hydrogen sulfide vapor molecules condense to form the droplets. These results show that while the effects of different inlet pressures on the condensation parameters are not as marked as that of different inlet temperatures, increasing the inlet pressure may facilitate the condensation of hydrogen sulfide. The increase of inlet pressure from 4.5 MPa to 5.5 MPa causes 4.46% increase in removal efficiency of hydrogen sulfide, as
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shown in Table 5. However, excessive inlet pressure will result in more pressure energy loss.
Table 5. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
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pressures
3.4 Effect of inlet hydrogen sulfide mole fraction on the condensation process
To investigate the sensitivity of the condensation process to the overall mixture
U
composition, the inlet mole fraction of hydrogen sulfide was varied between 5% and 25%
N
while maintaining the inlet temperature and pressure at 290 K and 5 MPa, respectively (Fig. 9). As the figure shows, the temperature, pressure, and Mach number distributions were
A
consistent prior to the onset of supersonic condensation. Once condensation started, however,
M
the temperature and Mach number clearly changed following the formation of a large number of condensation nuclei. This is because condensation releases great amount latent heat. When
ED
the inlet hydrogen sulfide mole fraction was 5%, the temperature and pressure curves hardly recovered, and the degree of supercooling did not come down after reaching its peak value.
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The reason for this is that the partial pressure of hydrogen sulfide is too small to reach both a state of supersaturation and also the degree of supercooling required for condensation; hence, the latent heat of condensation is small, and nucleation rate and the droplet number are much
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lower than those at higher inlet partial pressures of hydrogen sulfide.
Fig. 9. Effect of different inlet hydrogen sulfide mole fractions on the condensation
A
parameters.
The initial condensation position is closer to the throat of the Laval nozzle at higher mole fractions of hydrogen sulfide. This is due to an increase in the inlet partial pressure of hydrogen sulfide at higher mole fractions, which is more conducive to condensation. The increase in the inlet mole fraction of hydrogen sulfide from 5% to 25% caused the maximum nucleation rate to increase by two orders of magnitude. The maximum droplet radius 14
increased significantly, (from 4.21 × 10−8 m to 2.85 × 10−7 m, respectively) over the hydrogen sulfide mole fraction range, as the hydrogen sulfide vapor in mixture is more likely to achieve the supercooling and supersaturation required for large-scale nucleation, meanwhile, the droplet growth rate is higher due to a larger amount of vapor molecules condense on surface of nuclei. With the increase of hydrogen sulfide mole fraction, the liquid mass fraction of hydrogen sulfide increased by four orders of magnitude (from 0.00494% to 27.43%) and the hydrogen
IP T
sulfide fraction in the gas phase increased (from 4.91% to 14.30%), which indicates that most
of the hydrogen sulfide molecules still remained in the gas phase even at higher overall
SC R
concentrations.
These results show that the varying the inlet hydrogen sulfide mole fraction has a significant effect on the condensation parameters. As the Table 6 shows, the efficiency of hydrogen sulfide removal stayed fairly steady over most of this range, at 64–66%, but when
U
the hydrogen sulfide mole fraction was less than 5%, the removal efficiency of hydrogen
A
for natural gas with high hydrogen sulfide content.
N
sulfide became close to zero. It is indicated that the supersonic Laval nozzle is more suitable
4 Conclusions
ED
hydrogen sulfide mole fraction
M
Table 6. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
PT
In this study, a new method for the supersonic removal of hydrogen sulfide from natural gas was proposed. A Laval nozzle structure was designed, and a mathematical model of the
CC E
supersonic condensation flow of methane-hydrogen sulfide mixture gas in the Laval nozzle was established to enable prediction of the condensation parameters of hydrogen sulfide vapor. The sensitivity of the model to inlet temperature and pressure and hydrogen sulfide mole fraction was investigated.
A
The results showed that in the Laval nozzle, the number of condensation nuclei rises
sharply from zero to the maximum value over in an extremely short distance following the start of condensation, with the nucleation rate subsequently falling to zero due to the release of latent heat of condensation. At the outlet of the Laval nozzle, the droplet radius and liquid fraction of hydrogen sulfide are at their maximum values. When the inlet temperature and pressure were set to 290 K and 5 MPa, respectively, and the inlet mole fraction of hydrogen 15
sulfide was 15%, the outlet liquid fraction of hydrogen sulfide was 17.68% and the its removal efficiency was 64.83%. With a decrease in inlet temperature or an increase in inlet pressure, the initial nucleation position moves towards the throat and the droplet radius and liquid fraction of hydrogen sulfide increase, while the mole fraction of hydrogen sulfide in the gas phase decreases. When the inlet hydrogen sulfide mole fraction falls below the threshold value of 5%, the outlet liquid fraction of hydrogen sulfide and the removal efficiency of hydrogen sulfide drop to almost zero, however, above this value, increasing the mole fraction
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of hydrogen sulfide does not appear to change the removal efficiency very much. These results suggest that a reasonable hydrogen sulfide mole fraction, a lower inlet temperature and
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a higher inlet pressure are required for improving supersonic condensation of hydrogen sulfide gas in the Laval nozzle.
This study represents the first step towards the development of an effective and environment-friendly method for the removal of hydrogen sulfide from natural gas under a
U
variety of inlet conditions, with the ultimate goal of reducing environmental pollution and
N
reducing its negative impact on industrial processes. It is hoped that this investigation will also provide useful insights for the design and optimization of the supersonic separation
M
A
technique for future applications.
Acknowledgements
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This study was supported by the National Key R&D Program of China (Grant No. 2016YFC0802302 and No. 2016YFC0802304) and the National Natural Science Foundation
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Fig. 1. Schematic diagram of the supersonic separator.
20
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IP T
M
A
N
U
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Fig. 2. Structure of the designed Laval nozzle.
A
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Fig. 3. Simulation results of liquid mass fraction corresponding to different cells.
21
IP T SC R
Fig. 4. Comparison between the experimental and simulation results for the static
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ED
M
A
N
U
pressure distribution along the axial direction in Wyslouzil et al.’s [43,44] nozzle.
CC E
Fig. 5. Comparison between the experimental and simulation results for the temperature
difference distribution caused by condensation along the axial direction in Wyslouzil et al.’s
A
[43,44] nozzle.
22
IP T
(b) Pressure /Pa
M
A
N
U
SC R
(a) Temperature /K
(d) degree of supercoiling /K
A
CC E
PT
ED
(c) Mach number /Dimensionless
(e) Nucleation rate /m−3·s−1
(f) droplet number /kg-1
23
(g) droplet radius /m
(h) liquid mass fraction / Dimensionless
(b) Pressure distribution
CC E
PT
ED
M
(a) Temperature distribution
A
N
U
SC R
IP T
Fig. 6. Distribution of flow and condensation parameters in the Laval nozzle.
(d) Degree of supercooling distribution
A
(c) Ma distribution
24
IP T
(f) Droplet number distribution
CC E
PT
ED
M
A
N
U
SC R
(e) Nucleation rate distribution
(h) Liquid mass fraction distribution
A
(g) Droplet radius distribution
25
IP T
(i) Hydrogen sulfide fraction in gas phase distribution
A
CC E
PT
ED
M
A
N
U
SC R
Fig. 7. Effect of different inlet temperatures on the condensation parameters.
(a) Temperature distribution
(b) Pressure distribution
26
IP T SC R U N A M
(d) Degree of supercooling distribution
CC E
PT
ED
(c) Ma distribution
(f) Droplet number distribution
A
(e) Nucleation rate distribution
27
IP T SC R U N A
(h) Liquid mass fraction distribution
CC E
PT
ED
M
(g) Droplet radius distribution
(i) Hydrogen sulfide fraction in gas phase distribution
A
Fig. 8. Effect of different inlet pressures on the condensation parameters.
28
IP T SC R U N A
A
CC E
PT
ED
M
(a) Temperature distribution
29
(b) Pressure distribution
IP T
(d) Degree of supercooling distribution
M
A
N
U
SC R
(c) Ma distribution
A
CC E
PT
ED
(e) Nucleation rate distribution
30
(f) Droplet number distribution
IP T
(h) Liquid mass fraction distribution
M
A
N
U
SC R
(g) Droplet radius distribution
ED
(i) Hydrogen sulfide fraction in gas phase distribution Fig. 9. Effect of different inlet hydrogen sulfide mole fraction on the condensation
CC E
PT
parameters.
A
Table 1. Geometry size of designed Laval nozzle Geometry structure
Size /mm
Inlet diameter
148
Throat diameter
18.52
Outlet diameter
34.6
Straight section
185
convergent section
232.4
divergent section
130.9
31
Table 2. The relative error of pressure and temperature difference between experimental data and simulation data.
x1=0.
ation 30458.6
2 x2=11
23866.2
.4 x3=21
21864.1
.5 x4=31
21424.6
.7 x5=41
19227.2
.9 x6=52
17176.2
.1 x7=62
15711.3
.9
x8=72
14490.4
23231 .4
0.02 7
21896 .1
0.00 2
20740 .9
0.03 2
18348 .2
0.04 6
16785 .5
0.02
3
15418 .3
0.01
9
14343
.9
ation 0.10
0.10
0.20
0.21
10.48
10.59
25.91
27.78
26.86
27.81
27.02
27.94
26.97
28.01
0.01
26.70
27.96
0
PT
.5
0.06 4
ED
.4
ment 32407
Simul tive error
Experi
SC R
ment
tive error
A
CC E
Table 3. Inlet conditions of the Laval nozzle Parameter
Unit
Value
Inlet temperature
K
290
Inlet pressure
MPa
5.0
Mole fraction
0.15
Mole fraction
0.85
Hydrogen
sulfide
composition Methane composition
32
0
IP T
Simul
Rela
U
Experi
difference/K
N
throat/mm
Rela
A
from
M
nce
Temperature
Pressure/Pa
Dista
0.05 0.01
1 0.07 2 0.03 5 0.03 4 0.03 9 0.04 7
Table 4. Hydrogen sulfide outlet concentration and removal efficiency at different inlet temperatures Hydrogen
sulfide
outlet concentration
Removal
efficiency
(%)
280
0.0591
85.21
290
0.0727
64.83
300
0.0836
56.63
IP T
Inlet temperature (K)
pressures Hydrogen sulfide outlet
Inlet pressure (MPa)
5.0
0.0727
5.5
0.0675
N
0.0783
Removal efficiency (%) 61.16 64.83 65.62
A
4.5
U
concentration
SC R
Table 5. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
hydrogen sulfide mole fraction
concentration
0.15
Hydrogen sulfide outlet
concentration
Removal efficiency (%)
0.0499
0.05
0.0727
64.83
0.1368
65.97
A
CC E
0.25
PT
0.05
ED
Hydrogen sulfide inlet
M
Table 6. Hydrogen sulfide outlet concentration and removal efficiency at different inlet
33