NUMERICAL SIMULATION OF PARTICLE FLOW IN A NATURAL GAS SUPERSONIC SEPARATOR

Transcription

1 Eeventh Internationa Conference on CFD in the Mineras and Process Industries CSIRO, Mebourne, Austraia 7-9 December 2015 NUMERICAL SIMULATION OF PARTICLE FLOW IN A NATURAL GAS SUPERSONIC SEPARATOR Yan YANG 1, Chuang WEN 1, *, Shui WANG 1 and Yuqing FENG 2 1 Schoo of Petroeum Engineering, Changzhou University, Changzhou, , CHINA 2 CSIRO Minera Resources, Cayton, VIC 3169, AUSTRALIA *Corresponding author, E-mai address: chuang.wen@cczu.edu.cn ABSTRACT The supersonic separator is a new device which can be used to condense and separate water and heavy hydrocarbons from natura gas. The partice fow, representing the motion of condensed iquid dropets, in a supersonic separator was numericay cacuated using the Discrete Partice Method (DPM) with the Reynods stress mode (RSM) being used to capture the strong swiring fow of the natura gas. The resuts showed that most of the partices either coided with the was or entered into the iquid-coection space directy, whie ony a few partices escaped together with the gas from the gas outet. The effect of the partice diameter on the coection efficiency was obtained in the newy designed supersonic separator. The separation efficiency coud be over 70% when the dropet diameter was more than 2μm, demonstrating a good performance of the newy designed separator. NOMENCLATURE Cc Cunningham correction coefficient C D drag coefficient. C m constant C s constant C t constant d ij deformation tensor d partice diameter D T g, thermophoretic force coefficient E tota energy F gas-partice interaction force F a additiona force F d drag force F s Saffman s ift force F t thermophoretic force g acceeration of gravity K conductivity ratio K n Knudsen number K s constant iquid phase m partice mass p pressure q j heat fux Re reative Reynods number t time T g oca temperature u g gas veocity partice veocity u V δ ij λ μ g μ ν g ρ g ρ τ ij partice voume Kronecker deta moecuar mean free path gas viscosity iquid viscosity gas dynamic viscosity gas density partice density viscous stress INTRODUCTION Supersonic gas separation is a nove technoogy, which has been used to remove the water vapor and higher hydrocarbons from natura gas (Okimoto and Brouwer, 2002; Aferov et a., 2005; Brouwer et a., 2004; Schinkeshoek and Epsom, 2006; Betting and Epsom, 2007; Kaikmanov et a., 2007; Wen et a., 2011a). A supersonic separator is usuay composed of a Lava nozze, a swir device and a diffuser, as shown in Figure 1 (Wen et a, 2012a). The Lava nozze is used to acceerate the natura gas to the supersonic veocity, resuting in a ow pressure and temperature. The swir device is empoyed to generate a strong swiring fow to separate and remove the condensed iquids from the gas-iquid mixture. The diffuser is designed for the purpose of the pressure recovery. The computationa fuid dynamics (CFD) modeing has been empoyed to study the fow behavior in a supersonic separator. Mayshkina (2008, 2010) obtained the distribution of gas dynamic parameters through a supersonic separator with a computationa method, and a procedure was deveoped to predict the separation capabiity of water vapor and higher hydrocarbons from natura gas by using a supersonic separator determined by the initia parameters. Karimi and Abdi (2009) predicted the effect of the dynamic parameters of the nozze entrance and exit on the seective dehydration of highpressure natura gas by using the MATLAB and HYSYS packages. The generaized radia basis function artificia neura networks were used to optimize the geometry of a supersonic separator by Vaziri and Shahsavand (2013). Shooshtari and Shahsavand deveoped a new theoretica approach based on mass transfer rates to cacuate the iquid dropet growth in supersonic conditions for binary mixtures (2013). In our previous studies, a new supersonic nozze was designed incorporating a centra body and the Copyright 2015 CSIRO Austraia 1

2 Figure 1: Schematic diagram of a supersonic separator (Wen et a, 2012a). effect of the nozze geometric structure on the separation characteristics was anayzed by the numerica simuation (Wen et a., 2011b). A new swiring device composed of some vanes and an eipsoid was designed for the supersonic separator. The natura gas fows in diffusers were numericay cacuated using the Navier-Stokes equations with the Reynods Stress Mode (RSM) to account for the swiring turbuence effect (Wen et a., 2011c). The resuts show that the shock waves appear as bifurcation structures as a resut of the interaction between the shocks and the boundary ayer in the diffuser (Wen et a., 2012b). The experimenta studies aso have been conducted to test the dehydration performance of a supersonic separator. An indoor experiment oop was set up to test the dehydration characteristics of a designed supersonic swiring separator with the moist air by Liu et a. (2005). The dew point depression between the inet and outet of the separator was anayzed under various pressure oss ratios. A supersonic separator was compared to a Joue-Thomson vave with TEG and the resuts demonstrated the high economic performance and natura gas iquids recovery of a supersonic separator by Machado et a (2012). Wen et a. (2012c) designed a new type supersonic swiring separator based on the principe of conservation of anguar momentum. An experimenta oop was set up to test the dehydration characteristics of the new supersonic separator with a moist air. The effect of the pressure recovery coefficient on the dew point depression was anayzed experimentay. The above mentioned studies focused on the singe gas fow or condensation fow in a supersonic separator, and very itte attention was paid to the dropet fows. The purpose of this paper is to study the dropet motion in the newy designed supersonic separator by empoying the Discrete Partice Method (DPM), as we as the coection behavior of dropets at different region of the device. COMPUTATIONAL APPROACH Continuous Phase The natura gas can be acceerated to supersonic veocities within a supersonic separator, and accordingy ower pressure and temperature conditions are achieved for water vapor condensation. The fuid structure of natura gas fows can be described by the conservation equations of mass, momentum and energy. Without considering a condensation fow, a gas phase is simuated as a steady state, described as Eqs. (1) - (3). ( gugi ) 0 x ρ = i ( ρgugiugj + pδij τ ji ) = 0 x j ( ρgugje+ ugj p+ qj uiτij ) = 0 x j where ρ g, u g, p are the gas density, veocity, and pressure, respectivey. τ ij is the viscous stress; δ ij is the Kronecker deta; E is the tota energy; q j is the heat fux. An equation of state must be deveoped to cacuate the physica property of fuids in supersonic fows. In this simuation, the Redich-Kwong rea gas equation of state mode, derived from the van der Waas equation (Redich and Kwong, 1949), was empoyed to predict gas dynamic parameters. Discrete Phase A partice motion in a supersonic separator can be described as transation and rotation, which are competey determined by Newton's second aw of motion. During the movement, the partice may coide with the was at the contact points and interact with the surrounding fuid, through which the momentum and energy are exchanged. Assume that the force on a partice can be determined excusivey from its interaction with the vicina iquid by choosing a reasonabe time step, the governing equation for a discrete iquid partice is: (1) (2) (3) du m = mg ρggv + F (4) dt where m, u and V are, respectivey, the mass, veocity and voume of the iquid partice. g is the acceeration of gravity. t is the time. F is the gas-partice interaction force. In a supersonic separator, the centrifuga force pays a much more significant roe than the gravity force, therefore, the gravity force can be negected. Because the density of the iquid partice is usuay much arger than the gas density, the buoyancy force acting on a partice has been ignored in Eq. (4) as we. Copyright 2015 CSIRO Austraia 2

3 The gas-partice interaction force F incudes the drag force F d and the additiona force F a. That is: F = F + F (5) The F d is given by Ounis et a. (1991): D a 18µ g CDRe FD = ( u - ) 2 g u (6) ρ d 24 where ρ and d are the density and diameter of the iquid partice, respectivey. U g is the fuid phase veocity, μ g is the moecuar viscosity of the fuid, C D is the drag coefficient. Re is the reative Reynods number, which is defined as: Re ρ d u u µ g g = (7) The additiona force F d refers to the virtua mass force, pressure gradient force, thermophoretic force, and Saffman s ift force. In the supersonic separator, the virtua mass and pressure gradient forces can be ignored, because the density of the fuid (natura gas) is much ower than the density of the partices (water dropet). Therefore, these two kinds of additiona forces were not considered in the simuation of the partice behavior. In the supersonic swiring separator, sma iquid partice suspended in the gas which had a great temperature gradient, which caused a force in the direction opposite to that of the gradient. Therefore, the thermophoretic force F t was used to consider the sharp temperature gradient effect, which was given as: g 1 T F = (8) t g DT g, mt g x where T g is the oca fuid temperature, D T g is the, thermophoretic force coefficient, which can be given as (Tabot et a., 1980): D Tg, 2 6 πdmgcs( K + CtKn) = ρ (1+ 3 C Kn)(1+ 2K + 2 C Kn) g m t where K n is Knudsen number; K is the conductivity ratio between the fuid therma conductivity and partice therma conductivity; C s, C t, and C m are the constant, with vaues of 1.17, 2.18 and 1.14 respectivey. Due to the strong shear and swiring fow in the separator, the Saffman s ift force was incuded to account for the swiring fow effect on partice motions. The Saffman s ift force can be described as (Saffman, 1965): 2K ν ρ d s g g ij FS = ( u ) 0.25 g u (10) ρd ( dkdk ) where F S is the Saffman s ift force, K s =2.594, ν g is the gas dynamic viscosity, d ij is the deformation tensor. Computationa Method Numerica soution of the above equations was achieved with ANSYS/Fuent. In this case, we adopted the finite voume method to sove the governing equations, whie (9) the SIMPLE agorithm (Patankar, 1980) was empoyed to coupe the veocity fied and pressure. The Reynods stress mode (RSM) (Pope, 2000) was empoyed to predict the strong swiring fow. The Reynods stress mode is abe to capture the characteristics of anisotropic turbuence and requires the soution of transport equations for each of the Reynods stress components as we as for dissipation transport. The Speziae-Sarkar-Gatski Reynods stress mode was empoyed to appropriatey mode turbuent fow with a significant amount of swir in the supersonic separator. A structured grid was generated for the Lava nozze, the cyconic separation section and the diffuser, whie the deta wing section was meshed using a tetrahedra grid due to its compexity, as shown in Fig. 2. The grid independence was tested before the case studies were conducted. In this simuation, the Mach number at the Lava nozze exit was seected for grid independence. When the Mach numbers are consistent with different grid numbers, the grid independence coud be verified. The grid independence was investigated with the mesh ces of , and , respectivey. Even grids provided a sufficient grid independence. However, for judging the shock wave position exacty, the simuations were performed using the ces in the case studies. The pressure boundary conditions were assigned for the inet and outet of the supersonic separator. Non-sip and adiabatic boundary conditions are specified for the was. In addition, for the discrete phase, the escape boundary conditions are assigned for the inet and dry gas outet. The trap boundary conditions are used for the was of the cycone separation section and the iquid-coection space. We appoint the refect boundary conditions for a other was. RESULTS AND DISCUSSION The fow characteristics of a natura gas were numericay simuated in our newy designed supersonic separator based on the above mentioned mathematica methods. The muti-components gas mixture in a Baimiao gas we of the Zhongyuan Oi Fied was seected for the cacuation. The composition of the natura gas in moe fraction is shown in Tabe 1. Natura gas composition Moe fraction (%) CH C 2 H C 3 H i-c 4 H n-c 4 H i-c 5 H n-c 5 H H 2 O 0.03 CO N Tabe 1: Moe composition of the natura gas. Copyright 2015 CSIRO Austraia 3

4 Figure 2: Grid system of the newy designed supersonic separator (Wen et a, 2012a). Figure 3: Trajectories of three representative partices in the supersonic separator. Partice Trajectories In the present mode, the iquid partice formation process was not considered. Thus, the iquid partices were simpy injected from the nozze outet. Figure 3 showed the trajectories of three partices representing some typica partice moving states: a) the partice coiding with the wa, b) the partice entering into the iquid-coection space, and c) the partice passing through the diffuser. For the first kind partice (Fig.3 (a)), the partice was Copyright 2015 CSIRO Austraia 4

5 centrifuged and coided with the was, creating a thin iquid fim, which woud fow into the iquid-coection space aong the wa. Some partices entered into the iquid-coection space directy without coiding with the wa (Fig.3 (b)). These partices woud either coide with the was in the iquid coection region or fowed out through the iquid outet. For a few partices, the drag force payed a much more significant roe than other forces. Therefore, these partices passed through the diffuser together with the dry gas fow, which caused the gas phase entraining some iquids (Fig. 3 (c)). Coection Efficiency The coection efficiency is one of the most important technica parameters in assessing a supersonic separator s performance. In this work, the discrete partice mode was empoyed to track the dropet motion and anayze the effect of the dropet size on the coection efficiency at different partice diameters. We assumed that the dropets were trapped directy, when they reached the wa of the cycone separation section. As shown in Figure 4, the coection efficiency increased with the dropet size. When the dropet diameters were ess than 1μm, the coection efficiency was ower than 50%. It indicated that the smaer size dropets were easier to foow the fow of dry gas and escape with gas phase rather than to be separated. The coection efficiency was more than 70% with the dropet diameter of about 2 μm, which demonstrated a good separation performance of our designed supersonic separator. Figure 4: Coection efficiency in a supersonic separator. CONCLUSIONS The Discrete Partice Method (DPM) was empoyed to predict the partice trajectories and separation efficiency in a supersonic separator for natura gas dehydration. It was found that the partices woud mainy have three types of trajectories, namey coiding with the surrounding wa, entering into the iquid-coection space and passing through the diffuser. The separation efficiency was strongy affected by the dropet size, which increased as the partice size increases. The separation efficiency can be over 70% when the dropet diameter was more than 2μm, demonstrating a good performance of the newy designed separator. The simuation resuts demonstrated that the present CFD mode provided a reasonabe estimation of dropet coection in the newy designed separator. Further mode refinement wi be conducted to consider the detaied condensation process for a quantitative vaidation of the deveoped mode. ACKNOWLEDGEMENTS This work was supported in part by the Natura Science Foundation of Jiangsu Province, China (No. BK ), the Genera Program of Natura Science Research Project of Jiangsu Province Universities and Coeges (No. 15KJB440001), and the Scientific Research Project of Changzhou (No. CJ , CJ ). REFERENCES ALFEROV, V., BAGIROV, L., DMITRIEV, L., FEYGIN, V., IMAEV, S. and LACEY, J., (2005), Supersonic nozze efficienty separates natura gas components, Oi Gas J., 5, BETTING, M. and EPSOM, H., (2007), Supersonic separator gains market acceptance, Word oi, 254, BROUWER, J., BAKKER, G., VERSCHOOF, H. and EPSOM, H., (2004), Supersonic gas conditioning first commercia offshore experience, Proceedings of the 83rd Annua GPA Convention. KALIKMANOV, V., BETTING, M., BRUINING, J. and SMEULDERS, D., (2007), New deveopments in nuceation theory and their impact on natura gas separation, Proceedings of the 2007 SPE Annua Technica Conference and Exhibition. KARIMI, A. and ABDI, M., (2009), Seective dehydration of high-pressure natura gas using supersonic nozzes, Chem. Eng. Process., 48, LIU, H., LIU, Z., FENG, Y., GU, K. and YAN, T., (2005), Characteristic of a supersonic swiring dehydration system of natura gas, Chin. J. Chem. Eng., 13, MACHADO, P. B., MONTEIRO, J. G. M., MEDEIROS, J. L., EPSOM, H. D., ARAUJO, O. Q. F., (2012), Supersonic separation in onshore natura gas dew point pant, J. Nat. Gas. Sci. Eng., 6: MALYSHKINA, M. M., (2008). The structure of gas dynamic fow in a supersonic separator of natura gas, High Temperature, 46: MALYSHKINA, M. M., (2010). The procedure for investigation of the efficiency of purification of natura gases in a supersonic separator, High Temperature, 48: OKIMOTO, F. and BROUWER, J., (2002), Supersonic gas conditioning, Word Oi, 223, OUNIS, H., AHMADI, G., and MCLAUGHLIN, J. B., (1991), Brownian diffusion of sub-micrometer partices in the viscous sub-ayer, J. Cooid. Interf. Sci., 143, Patankar, S. V., (1980), Numerica heat transfer and fuid fow, New York. POPE, S., (2000), Turbuent Fows, Cambridge: Cambridge University Press. REDLICH, O. and KWONG, J., (1949), On the thermodynamics of soutions. V. an equation of state. fugacities of gaseous soutions, Chem. Rev., 44, Copyright 2015 CSIRO Austraia 5

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