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Structural optimization and experimental investigation of supersonic ejectors for boosting low pressure natural gas
Applied Thermal Engineering 29 (2009) 2799–2807
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Structural optimization and experimental investigation of supersonic ejectors for boosting low pressure natural gas DaoTong Chong a, JunJie Yan a,*, GeSheng Wu b, JiPing Liu a a b
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an City 710049, PR China Research Institute of Oil and Gas Technology, PetroChina Changqing Oilfield Company, Xi’an City 710049, PR China
a r t i c l e
i n f o
Article history: Received 17 September 2008 Accepted 29 January 2009 Available online 4 February 2009 Keywords: Supersonic ejector Natural gas production Structural optimization Entrainment ratio Pressure ratio
a b s t r a c t The supersonic ejector was introduced into boosting the production of low pressure natural gas wells. The energy of high pressure gas wells, which was usually wasted through choke valves, was used as its power supply to boost the low gas production. The operating performance of natural gas ejectors was determined not only by the operating parameters but also by the structural parameters. This study focused on the structural optimization and operating performance of natural gas ejectors. The optimal structural parameters were obtained by numerical simulation when the maximum pressure ratio was obtained, and the numerical results were validated by experimental investigation. The numerical results showed that the optimal diameter ratio of mixing tube to primary nozzle throat was 1.6, the optimal length to diameter ratio of mixing tube was 4.0 and the optimal inclination angle of mixing chamber was 28°. The entrainment ratios and pressure ratios from the numerical simulation agreed well with the field experimental data, with the maximum value of pressure ratio up to 60%. The operating performance of the supersonic ejector was also investigated by the field experiment, and the results showed that the induced gas flowrate and entrainment ratio showed nonlinear characteristics with peak values when the motive pressure ranged from 8 MPa to 13 MPa. These experimental results have proved the optimized structural parameters of the supersonic ejector. The investigation will help to the further application in boosting natural gas production of supersonic ejector. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Natural gas production from satellite fields or fragmentation of gas reservoir often results in some wells having high pressure, while others may have low pressure. In many fields, the natural gas from wells flows to a manifold, then is transported by pipeline to a processing plant. However, the low well pressure (may be due to the drop in well pressure during its production life) results in restricting production and, in some cases, abandonment of the field. Getting the maximum total recovery from all gas wells and maintaining its production are highly desired when the reservoir pressure drops and the gas well reaches the end of its economic life. As the well production pressure declines, there are still demands for transporting the produced gas to the processing system and delivering the gas at required pressure for the export. Both technical and economical challenges are brought about when the pressure of the gas is lower than the pipeline pressure, e.g. many of the low pressure gas is to be flared for being uneconomical. However, the flaring of waste gas is becoming more and more unfavor* Corresponding author. Tel./fax: +86 29 82665741. E-mail address: [email protected] (J. Yan). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2009.01.014
able and unacceptable because of the environmental issues. Therefore, a production boosting system, which can maintain production of low pressure wells at an optimum level and maximize recovery from the field, is often required. The conventional method is to boost the gas pressure by compressors, which are bulky and highly costly for operating and maintenance. In view of the problems with the compressors, a much simpler and cheaper system or equipment known as the supersonic ejector has been introduced, which has been shown to be able to achieve the same duties of compressors in many cases. The utilization of supersonic ejector is an artificial lift method and the supersonic ejector has several benefits compared with other boosting systems, including: (1) it does not require any extra power supply and is simple, absent of moving parts and small dimensions; (2) it allows easy installation and management procedures during fields operations, therefore, the reliability is high and the cost of installation is low; (3) the most important benefit is to use the energy of high pressure gas wells as its power supply, which is usually wasted through choke valves, to boost the natural gas production from low pressure wells.
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Nomenclature A d G L m N P S t
flow area (m2) diameter (m) natural gas volume flowrate under standard condition (104 m3/d) length (m) natural gas mass flowrate (kg/s) pressure ratio, see Eq. (3) pressure (MPa) generalized source time (s)
Greek symbols a entrainment ratio (%), see Eq. (2) / generalized parameters j isentropic index
1.1. Application of ejectors in gas and oil industry Ejectors, also known as jet pumps or educators, are not new and can be dated back to as early as 1852 in England, with J. Thomson believed to be the inventor [7]. Since then, ejectors have been widely used in engineering industries, such as aerospace, refrigeration and district-heating system, for mixing two fluids of different pressure. In these industries the ejectors may be used to augment the thrust on aircraft propulsion systems [1,2], perform the refrigeration cycle [3,4] or lift the pressure [5]. But the production boost in the low pressure fluid in these industries is less important compared with the demands of the gas and oil industry. Although the supersonic ejector has been known for about one century, it is not long ago that the ejector was used to boost the production of natural gas. The investigations on the supersonic ejector of natural gas are relatively sparse. The application of ejectors for gas production dates back to 1987 when a group CALTEC developed and designed two units that were installed on two platforms for the Hewett field, North Sea [6]. Differing from applications in other industries, the pressure of mixture at the outlet of natural gas ejectors was desired to meet the pipeline and transportation requirements. Sarshar et al. developed a system to increase the production and recovery from low pressure gas and oil wells [7– 10]. They mainly introduced the system components and its application in gas and oil production. The system has been applied in some fields of North Sea and other places. The performance of their system has been investigated experimentally, which showed that the entrainment ratio could reach up to 78% when the high pressure, low pressure and discharged pressure were 5.5 MPa, 1.6 MPa and 2.0 MPa, respectively. Melancon also introduced an ejector system [11], where the operational mechanism and its economics were reported. Andreussi investigated the multiphase ejector to boost production in the gulf of Mexico [12]. Their experimental results showed the maximum pressure ratio was less than 45% when the entrainment ratio remained 10%. 1.2. Aims and structure of this paper In the studies mentioned above, several ejectors systems have been developed and applied in the natural gas production, where the main emphasis was put on the corresponding boosting system and application. The performance of natural gas ejectors is determined not only by the operating parameters, such as motive pressure, induced pressure and discharged pressure, but also by the structural parameters, e.g. a small deviation of the structural
m h
q C
specific volume (m3/kg) inclination angle (deg) density (kg/m3) generalized diffusion coefficient
Subscripts c throat of primary nozzle d discharged pressure H high/motive pressure L low/induced pressure mc mixing chamber mt mixing tube
parameter may even badly decline the performance of the natural gas ejectors. Although the influence of operating parameters on the performance of natural gas ejectors was briefly investigated [8,12], no structural optimization on the natural gas ejectors has been reported. To improve the performance of natural gas ejectors, it is necessary to re-think the method that marks out the design of conventional supersonic ejectors. In the present paper, the structural parameters of natural gas ejectors will be optimized numerically, and the numerical results will be validated by the field experimental data. Moreover, the performance of optimized ejectors will be investigated numerically and experimentally. All the work will benefit the design and application of the supersonic natural gas ejectors. 2. Mechanism of supersonic ejector for boosting production Supersonic ejectors of natural gas are simple and reliable devices, which use energy from a high pressure well to boost the production of low pressure well. The main components of the ejector is shown in Fig. 1, which involve five parts: primary nozzle (A), secondary nozzle (B), mixing chamber (C), mixing tube (D) and diffuser (E). The natural gas with high pressure PH is the motive or primary stream, while the other with low pressure PL is the induced or secondary stream. Operation of such systems is quite simple, as described now. High pressure natural gas passes through the primary nozzle which generates a high velocity. This results in the conversion of part of its potential (pressure) energy to kinetic (velocity) energy. As a result, the pressure of natural gas through the primary nozzle drops significantly. It is at this point where low pressure natural gas is introduced through the secondary nozzle, where it is initially exposed to the back pressure imposed by the pipeline in the system without the ejector. The mixture then passes through the mixing chamber and mixing tube where transfer of energy and momentum takes place between high and low pressure streams. The gas mixture then passes through the diffuser where the mixture velocity is gradually reduced and the pressure is further recovered. The pressure of the gas at the outlet of the ejector is at an intermediate level between the high and low pressures. Therefore, the supersonic ejector enables low pressure natural gas to operate at a lower pressure than the back pressure imposed by the pipeline. This results in the production and recovery increase of low pressure natural gas. As shown in Fig. 1, the supersonic ejector consists of five main parts. The flow in the primary and secondary nozzles can be treated as isentropic flow, and the primary and secondary nozzles can be designed empirically. However, the mixing process in the mix-
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Fig. 1. Supersonic ejectors of low pressure natural gas.
ing chamber and tube is very complicated, and it has not been well understood. The structures of mixing chamber and mixing tube greatly influence the mixing process, which affects the boost production of the low pressure natural gas well, the most important function of the natural gas ejector. It is thus very necessary to optimize the structural parameters of the mixing chamber and mixing tube. 3. Structural optimization of natural gas ejector To optimize the structure of the mixing chamber and mixing tube, the flow of natural gas in the supersonic ejector was numerically simulated by PHOENICS 3.4. The flow and heat transfer in the ejector was governed by the compressible steady-state axisymmetric form of the fluid flow conservation equations. Although the whole process also involved heat transfer between the natural gas and solid surface, it was ignored here as the velocity in the supersonic ejector is very large (1500 m/s), and the natural gas passed through the ejector very quickly. Therefore, only the heat transfer between the high and low pressure streams has been considered in the present simulation. The RNG k–e model was employed to simulate the turbulent flow. To accurately simulate the flow of natural gas, the physical properties, such as density, compressibility factor, viscosity, enthalpy, were based on the real natural gas [13]. The general equation was written in the following form [14]:
oðq/Þ þ divðqV/Þ ¼ divðCgrad/Þ þ S ot
ð1Þ
where / may denote different parameters, such as velocity, temperature, k, epsilon. For different /, the generalized diffusion coefficient C has different expression, and the generalized source S also has different expression. Because of its irregular structure of the flow channel in the supersonic ejector, the body fitted grid in two-dimensional circular cylindrical coordinate was applied. The mesh and simulated region are shown in Fig. 2. The mesh was generated in three separated regions: the primary nozzle (A), the second nozzle (B), and the others (C–E). In each region, the mesh was denser for high velocity region, and relatively sparse for low velocity region. The independence of the mesh has been checked, and finally the meshes with 150 30 in primary nozzle (A), 50 10 in secondary nozzle (B) and 400 44 in others (C–E) were adopted. The boundary conditions were determined on the basis of corresponding field operation conditions. The primary nozzle inlet, secondary nozzle inlet and diffuser outlet were all defined as fixed pressure conditions. The pressures at the primary nozzle inlet, secondary nozzle inlet and diffuser outlet was subjected to the motive gas pressure, induced gas pressure and the back pressure imposed
by the pipeline, respectively. The bottom of the primary nozzle, mixing chamber, mixing tube and diffuser was treated as symmetric axis. The upper plate of primary nozzle, upper and bottom plate of secondary nozzle, and upper plates of the mixing chamber, mixing tube and diffuser were all adiabatic solid plates. The physical properties of natural gas were introduced into the PHOENICS by Ground (a FORTRAN subroutine in PHOENICS). For the present study, the ejector geometric design and operating conditions have been essentially established [15]. The flow and heat transfer were simulated under different operating conditions. As noted in the mechanism of supersonic ejector, it is necessary to optimize the structures of mixing chamber and mixing tube to improve the performance of the supersonic ejector. From Fig. 1, the mixing chamber is subjected to the inclination angle h and the length from the primary nozzle exit to the mixing tube inlet Lmc , and the mixing tube is subjected to the tube length Lmt and tube diameter dmt . On the other hand, the mixing chamber and mixing tube are correlated with each other, and the diameter of mixing tube dmt is correlated with parameters of mixing chamber h and Lmc . In other words, the length from the primary nozzle exit to the mixing tube inlet Lmc can be expressed by inclination angle of mixing chamber h and diameter of mixing tube dmt . Therefore, the mixing chamber and tube are subjected to three independent parameters dmt , Lmt and h, and the following optimization will be performed on the three independent parameters. In the application of the supersonic ejector, the parameters, namely the entrainment ratio and the pressure ratio, are the most important indexes, with the definitions as follows:
entrainment ratio a ¼ mL =mH pressure ratio N ¼ ðPd PL Þ=ðPH Pd Þ
ð2aÞ ð3Þ
The structural optimization may be carried out in two different ways: (1) maximum entrainment ratio and (2) maximum pressure ratio. The first is to get the maximum entrainment ratio when the structural parameters change under constant pressures (motive pressure, induced pressure and discharged pressure). This may be employed in the industry with constant induced pressure. However, in the natural gas production, the pressure of induced gas wells will decrease as time passes by. The supersonic ejectors are also supposed to be used under as low induced pressure as possible, and therefore the optimization can be performed by getting the lowest induced pressure. According to Eq. (3), under constant motive pressure and constant discharged pressure, the lowest induced pressure leads to the largest pressure ratio. Therefore, the structural optimization of the natural gas supersonic ejector was performed by the second method (maximum pressure ratio) under constant motive pressure and constant discharged pressure.
Fig. 2. Mesh generation of supersonic ejector.
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Fig. 3. Natural gas flow in the supersonic ejector (a) downstream, (b) stationary and (c) upstream.
In the operation of the supersonic ejector, the low pressure natural gas was induced through the secondary nozzle, and the flow direction is shown in Fig. 3a. When the induced pressure was lower than a certain value, the low pressure gas could not enter into the secondary nozzle. In this case, the high pressure gas could flow into the secondary nozzle in the opposite direction, as indicated by Fig. 3c. The lowest induced pressure was obtained when the induced flowrate approximately equaled zero under the constant motive pressure and constant discharged pressure, as shown in Fig. 3b. Then the critical pressure ratio could be obtained under the lowest induced pressure according to Eq. (3). In the process of the structural optimization, the motive pressure and discharged pressure were always kept at constant values of 12 MPa and 5.2 MPa, respectively. In the structure optimization, the independent parameter dmt was optimized first, followed by Lmt and h in turn. The optimization of the diameter of mixing tube dmt was performed when the inclination angles of mixing chamber and diffuser were kept constant. The ratio of mixing tube diameter to primary nozzle throat diameter dmt =dc was defined as the evaluation index in order to make the optimization universal. Under different diameter ratios, the corresponding critical pressure ratios have been obtained and are shown in Fig. 4. The maximum diameter ratio got to 1.86 when the length of the mixing chamber decreased to zero. From the figure, the critical pressure ratio first increased and then decreased with the increase of the diameter ratio. The maximum critical pressure ratio was 55.2% when the diameter ratio was about 1.6. In other words, the optimal diameter ratio of the mixing tube to primary nozzle throat was about 1.6 for the supersonic ejector. On the basis of the optimization of mixing tube diameter, the mixing tube length was further optimized, which was performed with constant values of the inclination angle of mixing chamber, inclination angle of diffuser and mixing tube diameter. To make
Fig. 4. Optimization of mixing tube diameter.
the results universal, the length to diameter ratio of the mixing tube Lmt =dmt was chosen as the evaluation index. The critical pressure ratios are illustrated in Fig. 5 with the length to diameter ratio ranging from 0 to 6.0. According to the figure, the critical pressure ratio increased with the length to diameter ratio increasing from 0 to 4.0. When the length to diameter ratio further increased, the critical pressure ratio changed little. Considering the field application, the cost would increase and the machining property would become more difficult as the length to diameter ratio increased. Therefore, the optimal length to diameter ratio of mixing tube was considered to be 4.0 with the maximum critical pressure ratio being 55.7%.
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mixing process. In the supersonic ejector, the induced and mixing processes were mainly caused by the shearing force between two different pressure streams. But the processes were also influenced by the reversed force caused by the convergent face of the mixing chamber, and the reversed force increased with the inclination angle. Therefore, a critical inclination angle could be got when the reversed force was neglected compared with the shearing force. When the inclination angle of the mixing chamber was less than a critical value, the pressure ratio was independent on the inclination angle. As the inclination angle further increased, the processes was impaired and therefore the pressure ratio decreased. In the numerical simulation, the optimal inclination angle of the mixing chamber was obtained as 28° with the critical pressure ratio being 55.9%. 4. Field experimental investigation Fig. 5. Optimization of mixing tube length.
When the optimization of diameter and length of mixing tube has been finished, the optimal mixing tube of supersonic ejector could be derived. Subsequently, the mixing chamber was to be optimized. As noted above, the mixing chamber was dependent on the inclination angle h and the length from the primary nozzle exit to the mixing tube inlet Lmc , where the length Lmc was a function of the inclination angle h and mixing tube diameter dmt . On the basis of the optimization of mixing tube diameter dmt , the optimal mixing chamber could be obtained when optimal inclination angle was obtained. The critical pressure ratios are shown in Fig. 6 with the inclination angle of mixing chamber h increased from 22° to 38°. As the secondary nozzle was the negative throat nozzle, the inclination angle of the upper surface should be larger than that of the lower surface. Moreover, the outer surface of mixing chamber was the extension of the upper surface of the secondary nozzle, which could be derived from Fig. 1. Because the inclination angle of the lower surface of the secondary nozzle was chosen to be 22°, the inclination angle of the mixing chamber should be larger than 22°. From Fig. 6, the critical pressure ratio decreased with the inclination angle ranging from 28° to 38°. But when the inclination angle increased from 22° to 28°, the critical pressure ratio was almost a constant value. This can be deduced from the mechanism of the
Based on the structural optimization on the mixing chamber and mixing tube, an optimized supersonic ejector of natural gas was designed, with the design operation parameters and structural parameters given in Table 1. The supersonic ejector was applied in Changqing gas field, China and the schematic experimental system is shown in Fig. 7. The natural gas in the experimental gas wells was composed of CH4, C2H6, C3H8, CO2, H2S and so on. But CH4 was the main component, with the proportion larger than 97%, and all the other components were less than 3%.The motive natural gas from the high pressure well was first heated by the heater and then entered into the supersonic ejector through the primary nozzle. The induced natural gas from the low pressure well was also first heated and then sucked into the supersonic ejector through the secondary nozzle. The two different pressure streams were mixed in the mixing chamber and mixing tube, and then the pressure was lifted in the diffuser to match the pipeline and transportation requirements. As the pressures of motive gas were very high (even >20 MPa), it was very difficult to measure the flux safely and economically. Thus, the flowrates of induced and discharged gas (GL, Gd), which are less than 10 MPa, were measured in the field experiment. Then the flowrate of motive gas could be calculated as follows:
GH ¼ Gd GL
ð4Þ
As the flowrates measured have been transferred to volume flowrates under the standard condition (0.1 MPa, 273.15 K), therefore the mass entrainment ratio could be calculated as
a ¼ mL =mH ¼ GL =GH
ð2bÞ
The uncertainty analysis was performed by applying the estimation method proposed by Moffat [16]. In the experiment, the pressures, temperatures and flowrates were measured. The temperature was measured by K type thermocouples (nickel chromium–nickel silicon), with the accuracy of 0.5 K. The gas flowrate was measured by Tancy vortex precession flowmeters.
Table 1 Design operation parameters and structural parameters.
Fig. 6. Optimization of inclination angle of mixing chamber.
Parameters
Symbols
Unit
Result
Motive pressure Motive gas flowrate Induced pressure Induced gas flowrate Discharged pressure Throat diameter of primary nozzle Diameter of mixing tube Length of mixing lube Inclination angle of mixing chamber
PH GH PL GL Pd de dmt Lmt h
MPa 104 m3/d MPa 104 m3/d MPa mm mm mm deg
12.0 8.0 3.0 2.4 5.2 6.0 9.6 38.4 28
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Fig. 7. Installation diagram of supersonic ejector of natural gas.
The accuracy of each flowmeter used in the experiment was 1%, but different flowmeter had different measuring range. The range of the gas flowmeter measuring the induced gas was 0– 6 104 m3/d. In the experiment, the induced gas flowrate varied from 0.45–4.69 104 m3/d, therefore, the uncertainty of induced gas flowrate was 1.3–13.3%. The range of the gas flowmeter measuring the discharged gas was 0–20 104 m3/d, with the discharged gas flowrate varying from 4.87–12.20 104 m3/d, therefore, the uncertainty of induced gas flowrate was 1.6– 3.7%. All the pressure transducers had the same accuracy of 1%, but different measuring ranges. The range of the pressure transducer measuring the discharged gas and induced gas was 0–10 MPa, with the discharged gas pressure almost keeping constant at 5.4 MPa and the induced gas pressure varying from 1.1– 5.0 MPa. Therefore, the uncertainty of discharged pressure and induced pressure was 1.9% and 2–9.1%, respectively. The range of the pressure transducer measuring the motive gas was 0– 20 MPa, with the motive pressure varying from 8.0–13.0 MPa, therefore the uncertainty was 1.5–2.5%. In the experiment, the motive gas flowrate, pressure ratio and entrainment ratio were calculated by Eqs. (4), (3) and (2), respectively. Accordingly, the uncertainty of motive gas flowrate, entrainment ratio and pressure ratio was 2.7–4.5%, 2.9–14.1% and 3.7–27.6%, respectively. The supersonic ejectors of natural gas was used to boost the low pressure gas, therefore the performance of the ejector could be mainly indicated by the induced gas flowrate and the entrainment ratio. Moreover, the motive gas flowrate also needed to be kept at the normal value. Therefore, the three parameters were investigated. The variation of motive natural gas flowrate with motive pressure and induced pressure are shown in Fig. 8. As shown in the Fig. 8a, the motive pressure had great influence on the motive gas flowrate and there was a linear relationship between them (given as the solid line in Fig. 8a). From Fig. 8b, the motive gas flowrate had little dependent on the induced pressure under the same motive pressure: it almost remained unchanged as the induced pressure increased. As the primary nozzle was a convergent–divergent channel, the flowrate was subjected to the inlet parameters and area of throat. When the pressure ratio was less than the critical value, the flowrate could be described as:
Fig. 8. Variation of motive gas flowrate (a) with motive pressure and (b) with induced pressure.
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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k1 P k 2 H mH ¼ Ac 2 kþ1 kþ1 mH
ð5Þ
where k is the isentropic exponent, for the natural gas (mainly composed of CH4), k ¼ 1:32; Ac is the area of throat, m2. For the fixed Ac , the motive gas flowrate was determined only by parameters of the inlet motive gas, and independent of the induced gas. The induced gas flowrate was influenced not only by the motive pressure but also by the induced pressure, as shown in Fig. 9. From Fig. 9a, the induced gas flowrate changed non-monotonically with the motive pressure when the induced pressure was less than 5.0 MPa, and it first increased and then decreased with the increase of the motive pressure. When the motive pressure was about 11– 12 MPa, the induced gas flowrate reached up to the peak value. But when the induced pressure was about 5.0 MPa, the induced gas flowrate changed little with the increase of the motive pressure. Generally, with the increasing motive pressure, the motive gas flowrate increased and the corresponding induced gas flowrate increased. On the other hand, the mixing process in the mixing chamber and tube was greatly influenced by the shear stress between the motive stream and induced stream. When the motive pressure increased, the pressure at the exit of primary nozzle increased, and the pressure difference between the pressures of primary nozzle exit and secondary nozzle exit decreased, which
Fig. 9. Variation of induced gas flowrate (a) with motive pressure and (b) with induced pressure.
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resulted in the decrease of the shear stress between the two streams and thus the decrease of induced gas flowrate. When the motive pressure was larger than a certain value (about 11– 12 MPa), the decreasing induced gas flowrate due to the decrease of the shear stress was larger than the increasing value due to the increase of the motive gas flowrate This resulted in that the appearance of a maximum value. In the field application of natural gas ejector, it is thus not economic to increase the motive pressure blindly, and this is very important for the operators. The induced gas flowrate was linear with the induced pressure under different motive pressure, as shown in Fig. 9b. Under the same induced pressure, the higher the motive pressure, the higher the induced gas flowrate. As the induced pressure increased and the motive pressure was kept constant, the pressure difference between the exits of the primary nozzle and secondary nozzle increased, which resulted in the increase of the shear stress between the two streams and thus the increase of induced gas production. The entrainment ratio was the most important parameter for the supersonic ejector of natural gas, and it was also affected by both the motive pressure and the induced pressure, as shown in Fig. 10. From Fig. 10a, the entrainment ratio first increased with the increase of the motive pressure and then decreased when the induced pressure was less than 5.0 MPa. The entrainment ratio increased up to the peak value when the motive pressure ranged
Fig. 10. Variation of entrainment ratio (a) with motive pressure and (b) with induced pressure.
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from 10 MPa to 12 MPa, similar to the variation trend of the induced gas flowrate. But when the induced pressure was 5.0 MPa, the entrainment ratio decreased with the increase of motive pressure, which was different from the variation trend of the induced gas flowrate. This could be explained from the results of Figs. 8a and 9a, where the motive gas flowrate increased with the increase of the motive pressure and the induced gas flowrate was kept constant. Therefore, it could be deduced that the entrainment ratio decreased with the increased of motive pressure according to Eq. (2). The entrainment ratios increase linearly with the rise of induced pressure for the same motive pressure, as shown in Fig. 10b. Differing from the variation trends of induced gas flowrate, the entrainment ratio was higher for smaller motive pressure when the induced pressures were about 5.0 MPa, while the induced gas flowrates were kept constant under the same operating conditions. The maximum entrainment ratio reached up to about 100% when the motive pressure was 8.0 MPa and the induced pressure was 5.0 MPa. Besides the experimental investigation as described above, the performance of the optimized supersonic ejector was also simulated by PHOENICS. In the numerical simulation, the motive pressure ranged from 8.0 MPa to 13.0 MPa, and the induced pressure from 3.0 MPa to 5.0 MPa. The comparisons between numerical and experimental results showed that the changes of motive gas flowrates, induced gas flowrates and entrainment ratios with motive pressure and induced pressure all had the same trends. The entrainment ratios obtained from experiment and numerical simulation were illustrated in Fig. 11. From Fig. 11a, the numerical
entrainment ratios agreed with the experimental data. When the motive pressure was no more than 11 MPa, the numerical and experimental entrainment ratios almost overlapped each other. When the motive pressure was larger than 11 MPa, the numerical entrainment ratios were slightly larger than the experimental data, which was due to the difference between the motive gas flowrates from the simulation and those from the experiment. In the field experimental system, some impurities, which could be oil, condensate, water and sand, might be produced with the natural gas. When the motive pressure increased, more impurities would be produced, which resulted in the lower experimental motive gas flowrates. Therefore, the numerical entrainment ratios were smaller than the experimental data for higher motive pressure. The deviations of entrainment ratios were shown in Fig. 11b, it can be seen that the deviations were less than 10.0% when the motive pressure was no more than 11 MPa, and less than 24.0% when the motive pressure was larger than 11 MPa. The pressure ratio in the experiment was also calculated according to Eq. (4), and given in Fig. 12 as a function of the entrainment ratio. It can be seen that the pressure ratio generally decreased with the increase of the entrainment ratio. The maximum pressure ratio was approximately 60%, which was in agreement with the optimized results (55.9%). From the figure, the maximum value for entrainment ratio may be deduced to be 90%, which was higher than the value from Sarshar et al. [8] for the same pressure ratio (about 11%), where a maximum value of 78% was obtained by Sarshar. Moreover, the pressure ratio obtained in the present experiment (about 55%) was also higher than Andreussi’s investigation (45%) for the same entrainment ratio (10%) [12]. The comparisons indicated that the performance of the present supersonic ejector of natural gas was better than the ejectors that have been reported by Sarshar and Andreussi. 5. Conclusions The structural parameters of natural gas ejector for boosting low pressure natural gas production were optimized numerically. The performance under different operation parameters was studied by field experiment and numerical simulation. The supersonic ejector was characterized by a simple structural design, absence of moving parts and small dimensions. The main benefit of the ejectors was its ability to use the energy of high pressure gas wells, which was usually wasted through choke valves, to boost production from low pressure wells. The field experiment was carried out with the motive pressure ranging from 8 MPa to 13 MPa, induced
Fig. 11. Comparison of entrainment ratios between experiment and simulation (a) variation trend comparison and (b) deviation of experiment and simulation.
Fig. 12. Pressure ratio variations under different entrainment ratios.
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pressure ranging from 1.0 MPa to 5.0 MPa and discharged pressure being 5.2 MPa. According to the numerical and experimental results, the following conclusions can be made: (1) The structural optimization was performed on the mixing chamber and mixing tube. The numerical results showed that the optimal diameter ratio of mixing tube to primary nozzle throat was 1.6, the optimal length to diameter ratio of mixing tube was 4.0 and the optimal inclination angle of mixing chamber was 28°. (2) The pressure ratio generally decreased with the increase of the entrainment ratio. The maximum pressure ratio was approximately 60%, which was in agreement with the optimized results. The entrainment ratio may be deduced to be up to 90% when the pressure ratio was about 11%, and the entrainment ratio was 55% when the entrainment ratio was 10%. (3) The motive gas flowrate, induced gas flowrate and entrainment ratio was also investigated experimentally and numerically. The entrainment ratios from experiment agreed with those from simulation, with the deviations less than 10.0% when the motive pressure was no more than 11 MPa, and less than 24.0% when the motive pressure was larger than 11 MPa. The motive natural gas flowrate increased linearly with the rise of the motive pressure and was independent of the induced pressure. The induced flowrate and entrainment ratio of natural gas were both increased linearly with the rise of induced pressure under each motive pressure, and the two parameters revealed nonlinear characteristics with the peak values when the motive pressure ranged from 8 MPa to 13 MPa.
Acknowledgements This work was supported by National 863 Scientific Program of China (Grant No. 2006AA05Z230).
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References [1] M. Alperin, J.J. Wu, Thrust augmenting ejector, Part I, AIAA Journal 21 (10) (1983) 1428–1436. [2] M. Alperin, J.J. Wu, Thrust augmenting ejector, Part II, AIAA Journal 21 (12) (1983) 1428–1698. [3] Z. Aidoun, M. Ouzzane, The effect of operating conditions on the performance of a supersonic ejector for refrigeration, International Journal of Refrigeration 27 (2004) 974–984. [4] Y. Bartosiewicz, Z. Aidoun, Y. Mercadier, Numerical assessment of ejector operation for refrigeration applications based on CFD, Applied Thermal Engineering 26 (2006) 604–612. [5] J.J. Yan, S.F. Shao, J.P. Liu, et al., Experiment and analysis on performance of steam-driven jet injector for district-heating system, Applied Thermal Engineering 25 (2005) 1153–1167. [6] K. Ashton, A.J. Green, A. Read, Gas production improvements using ejectors, Society of Petroleum Engineers, Offshore Europe, Aberdeen, 1993, SPE Paper # 26684. [7] M.M. Sarshar, Boosting production from low-pressure oil and gas fields: a revolution in hydrocarbon production, Philosophical Transactions of the Royal Society of London A 357 (1999) 921–941 (The Esso Energy Award Lecture, 1998). [8] M.M. Sarshar, N.A. Beg, Ian Andrews, The applications of jet pumps as a cost effective way to enhance gas production and recovery, in: Proceedings, Indonesian Petroleum Association Twenty-Ninth Annual Convention & Exhibition, October 2003, Paper # IPA03-E-059. [9] S. Sarshar, N. Beg, A novel application of jet pump technology to boost production-field experience and lessons learned, in: Offshore Gas Processing Technical Conference, 22nd and 23rd February 2006, London. [10] S. Sarshar, N. Beg, A cost effective way to boost production and recovery from the oil and gas fields, in: Multiphase flow 2006 conference 27th and 28th March, The Marcliffe at Pitfodels Aberdeen. [11] K. Melancon, J. Nunn, Ejector vapor recovery unit reliably and economically recovers vent and flash gas, World Oil 225 (11) (2004) 75–76. [12] P. Andreussi, S. Sodini, V. Faluomi, et al., Multiphase ejector to boost production: first application in the gulf of Mexico, Offshore Technology Conference held in Houston, Texas, USA, 2003, Paper # OTC 15170. [13] B.A. Younglove, J.F. Ely, Thermophysical properties of fluids. II. Methane, ethane, propane, isobutane and normal butane, Journal of Physical and Chemical Reference Data 6 (4) (1987) 577–798. [14] W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, 2001. [15] R.B. Power, Steam Jet Ejectors for The Process Industries, second ed., McGrawHill, 1994. [16] R.J. Moffat, Describing the uncertainties in experimental results, Experimental Thermal Fluid Science 1 (1) (1988) 3–17.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Structural optimization and experimental investigation of supersonic ejectors for boosting low pressure natural gas DaoTong Chong a, JunJie Yan a,*, GeSheng Wu b, JiPing Liu a a b
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an City 710049, PR China Research Institute of Oil and Gas Technology, PetroChina Changqing Oilfield Company, Xi’an City 710049, PR China
a r t i c l e
i n f o
Article history: Received 17 September 2008 Accepted 29 January 2009 Available online 4 February 2009 Keywords: Supersonic ejector Natural gas production Structural optimization Entrainment ratio Pressure ratio
a b s t r a c t The supersonic ejector was introduced into boosting the production of low pressure natural gas wells. The energy of high pressure gas wells, which was usually wasted through choke valves, was used as its power supply to boost the low gas production. The operating performance of natural gas ejectors was determined not only by the operating parameters but also by the structural parameters. This study focused on the structural optimization and operating performance of natural gas ejectors. The optimal structural parameters were obtained by numerical simulation when the maximum pressure ratio was obtained, and the numerical results were validated by experimental investigation. The numerical results showed that the optimal diameter ratio of mixing tube to primary nozzle throat was 1.6, the optimal length to diameter ratio of mixing tube was 4.0 and the optimal inclination angle of mixing chamber was 28°. The entrainment ratios and pressure ratios from the numerical simulation agreed well with the field experimental data, with the maximum value of pressure ratio up to 60%. The operating performance of the supersonic ejector was also investigated by the field experiment, and the results showed that the induced gas flowrate and entrainment ratio showed nonlinear characteristics with peak values when the motive pressure ranged from 8 MPa to 13 MPa. These experimental results have proved the optimized structural parameters of the supersonic ejector. The investigation will help to the further application in boosting natural gas production of supersonic ejector. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Natural gas production from satellite fields or fragmentation of gas reservoir often results in some wells having high pressure, while others may have low pressure. In many fields, the natural gas from wells flows to a manifold, then is transported by pipeline to a processing plant. However, the low well pressure (may be due to the drop in well pressure during its production life) results in restricting production and, in some cases, abandonment of the field. Getting the maximum total recovery from all gas wells and maintaining its production are highly desired when the reservoir pressure drops and the gas well reaches the end of its economic life. As the well production pressure declines, there are still demands for transporting the produced gas to the processing system and delivering the gas at required pressure for the export. Both technical and economical challenges are brought about when the pressure of the gas is lower than the pipeline pressure, e.g. many of the low pressure gas is to be flared for being uneconomical. However, the flaring of waste gas is becoming more and more unfavor* Corresponding author. Tel./fax: +86 29 82665741. E-mail address: [email protected] (J. Yan). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2009.01.014
able and unacceptable because of the environmental issues. Therefore, a production boosting system, which can maintain production of low pressure wells at an optimum level and maximize recovery from the field, is often required. The conventional method is to boost the gas pressure by compressors, which are bulky and highly costly for operating and maintenance. In view of the problems with the compressors, a much simpler and cheaper system or equipment known as the supersonic ejector has been introduced, which has been shown to be able to achieve the same duties of compressors in many cases. The utilization of supersonic ejector is an artificial lift method and the supersonic ejector has several benefits compared with other boosting systems, including: (1) it does not require any extra power supply and is simple, absent of moving parts and small dimensions; (2) it allows easy installation and management procedures during fields operations, therefore, the reliability is high and the cost of installation is low; (3) the most important benefit is to use the energy of high pressure gas wells as its power supply, which is usually wasted through choke valves, to boost the natural gas production from low pressure wells.
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Nomenclature A d G L m N P S t
flow area (m2) diameter (m) natural gas volume flowrate under standard condition (104 m3/d) length (m) natural gas mass flowrate (kg/s) pressure ratio, see Eq. (3) pressure (MPa) generalized source time (s)
Greek symbols a entrainment ratio (%), see Eq. (2) / generalized parameters j isentropic index
1.1. Application of ejectors in gas and oil industry Ejectors, also known as jet pumps or educators, are not new and can be dated back to as early as 1852 in England, with J. Thomson believed to be the inventor [7]. Since then, ejectors have been widely used in engineering industries, such as aerospace, refrigeration and district-heating system, for mixing two fluids of different pressure. In these industries the ejectors may be used to augment the thrust on aircraft propulsion systems [1,2], perform the refrigeration cycle [3,4] or lift the pressure [5]. But the production boost in the low pressure fluid in these industries is less important compared with the demands of the gas and oil industry. Although the supersonic ejector has been known for about one century, it is not long ago that the ejector was used to boost the production of natural gas. The investigations on the supersonic ejector of natural gas are relatively sparse. The application of ejectors for gas production dates back to 1987 when a group CALTEC developed and designed two units that were installed on two platforms for the Hewett field, North Sea [6]. Differing from applications in other industries, the pressure of mixture at the outlet of natural gas ejectors was desired to meet the pipeline and transportation requirements. Sarshar et al. developed a system to increase the production and recovery from low pressure gas and oil wells [7– 10]. They mainly introduced the system components and its application in gas and oil production. The system has been applied in some fields of North Sea and other places. The performance of their system has been investigated experimentally, which showed that the entrainment ratio could reach up to 78% when the high pressure, low pressure and discharged pressure were 5.5 MPa, 1.6 MPa and 2.0 MPa, respectively. Melancon also introduced an ejector system [11], where the operational mechanism and its economics were reported. Andreussi investigated the multiphase ejector to boost production in the gulf of Mexico [12]. Their experimental results showed the maximum pressure ratio was less than 45% when the entrainment ratio remained 10%. 1.2. Aims and structure of this paper In the studies mentioned above, several ejectors systems have been developed and applied in the natural gas production, where the main emphasis was put on the corresponding boosting system and application. The performance of natural gas ejectors is determined not only by the operating parameters, such as motive pressure, induced pressure and discharged pressure, but also by the structural parameters, e.g. a small deviation of the structural
m h
q C
specific volume (m3/kg) inclination angle (deg) density (kg/m3) generalized diffusion coefficient
Subscripts c throat of primary nozzle d discharged pressure H high/motive pressure L low/induced pressure mc mixing chamber mt mixing tube
parameter may even badly decline the performance of the natural gas ejectors. Although the influence of operating parameters on the performance of natural gas ejectors was briefly investigated [8,12], no structural optimization on the natural gas ejectors has been reported. To improve the performance of natural gas ejectors, it is necessary to re-think the method that marks out the design of conventional supersonic ejectors. In the present paper, the structural parameters of natural gas ejectors will be optimized numerically, and the numerical results will be validated by the field experimental data. Moreover, the performance of optimized ejectors will be investigated numerically and experimentally. All the work will benefit the design and application of the supersonic natural gas ejectors. 2. Mechanism of supersonic ejector for boosting production Supersonic ejectors of natural gas are simple and reliable devices, which use energy from a high pressure well to boost the production of low pressure well. The main components of the ejector is shown in Fig. 1, which involve five parts: primary nozzle (A), secondary nozzle (B), mixing chamber (C), mixing tube (D) and diffuser (E). The natural gas with high pressure PH is the motive or primary stream, while the other with low pressure PL is the induced or secondary stream. Operation of such systems is quite simple, as described now. High pressure natural gas passes through the primary nozzle which generates a high velocity. This results in the conversion of part of its potential (pressure) energy to kinetic (velocity) energy. As a result, the pressure of natural gas through the primary nozzle drops significantly. It is at this point where low pressure natural gas is introduced through the secondary nozzle, where it is initially exposed to the back pressure imposed by the pipeline in the system without the ejector. The mixture then passes through the mixing chamber and mixing tube where transfer of energy and momentum takes place between high and low pressure streams. The gas mixture then passes through the diffuser where the mixture velocity is gradually reduced and the pressure is further recovered. The pressure of the gas at the outlet of the ejector is at an intermediate level between the high and low pressures. Therefore, the supersonic ejector enables low pressure natural gas to operate at a lower pressure than the back pressure imposed by the pipeline. This results in the production and recovery increase of low pressure natural gas. As shown in Fig. 1, the supersonic ejector consists of five main parts. The flow in the primary and secondary nozzles can be treated as isentropic flow, and the primary and secondary nozzles can be designed empirically. However, the mixing process in the mix-
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Fig. 1. Supersonic ejectors of low pressure natural gas.
ing chamber and tube is very complicated, and it has not been well understood. The structures of mixing chamber and mixing tube greatly influence the mixing process, which affects the boost production of the low pressure natural gas well, the most important function of the natural gas ejector. It is thus very necessary to optimize the structural parameters of the mixing chamber and mixing tube. 3. Structural optimization of natural gas ejector To optimize the structure of the mixing chamber and mixing tube, the flow of natural gas in the supersonic ejector was numerically simulated by PHOENICS 3.4. The flow and heat transfer in the ejector was governed by the compressible steady-state axisymmetric form of the fluid flow conservation equations. Although the whole process also involved heat transfer between the natural gas and solid surface, it was ignored here as the velocity in the supersonic ejector is very large (1500 m/s), and the natural gas passed through the ejector very quickly. Therefore, only the heat transfer between the high and low pressure streams has been considered in the present simulation. The RNG k–e model was employed to simulate the turbulent flow. To accurately simulate the flow of natural gas, the physical properties, such as density, compressibility factor, viscosity, enthalpy, were based on the real natural gas [13]. The general equation was written in the following form [14]:
oðq/Þ þ divðqV/Þ ¼ divðCgrad/Þ þ S ot
ð1Þ
where / may denote different parameters, such as velocity, temperature, k, epsilon. For different /, the generalized diffusion coefficient C has different expression, and the generalized source S also has different expression. Because of its irregular structure of the flow channel in the supersonic ejector, the body fitted grid in two-dimensional circular cylindrical coordinate was applied. The mesh and simulated region are shown in Fig. 2. The mesh was generated in three separated regions: the primary nozzle (A), the second nozzle (B), and the others (C–E). In each region, the mesh was denser for high velocity region, and relatively sparse for low velocity region. The independence of the mesh has been checked, and finally the meshes with 150 30 in primary nozzle (A), 50 10 in secondary nozzle (B) and 400 44 in others (C–E) were adopted. The boundary conditions were determined on the basis of corresponding field operation conditions. The primary nozzle inlet, secondary nozzle inlet and diffuser outlet were all defined as fixed pressure conditions. The pressures at the primary nozzle inlet, secondary nozzle inlet and diffuser outlet was subjected to the motive gas pressure, induced gas pressure and the back pressure imposed
by the pipeline, respectively. The bottom of the primary nozzle, mixing chamber, mixing tube and diffuser was treated as symmetric axis. The upper plate of primary nozzle, upper and bottom plate of secondary nozzle, and upper plates of the mixing chamber, mixing tube and diffuser were all adiabatic solid plates. The physical properties of natural gas were introduced into the PHOENICS by Ground (a FORTRAN subroutine in PHOENICS). For the present study, the ejector geometric design and operating conditions have been essentially established [15]. The flow and heat transfer were simulated under different operating conditions. As noted in the mechanism of supersonic ejector, it is necessary to optimize the structures of mixing chamber and mixing tube to improve the performance of the supersonic ejector. From Fig. 1, the mixing chamber is subjected to the inclination angle h and the length from the primary nozzle exit to the mixing tube inlet Lmc , and the mixing tube is subjected to the tube length Lmt and tube diameter dmt . On the other hand, the mixing chamber and mixing tube are correlated with each other, and the diameter of mixing tube dmt is correlated with parameters of mixing chamber h and Lmc . In other words, the length from the primary nozzle exit to the mixing tube inlet Lmc can be expressed by inclination angle of mixing chamber h and diameter of mixing tube dmt . Therefore, the mixing chamber and tube are subjected to three independent parameters dmt , Lmt and h, and the following optimization will be performed on the three independent parameters. In the application of the supersonic ejector, the parameters, namely the entrainment ratio and the pressure ratio, are the most important indexes, with the definitions as follows:
entrainment ratio a ¼ mL =mH pressure ratio N ¼ ðPd PL Þ=ðPH Pd Þ
ð2aÞ ð3Þ
The structural optimization may be carried out in two different ways: (1) maximum entrainment ratio and (2) maximum pressure ratio. The first is to get the maximum entrainment ratio when the structural parameters change under constant pressures (motive pressure, induced pressure and discharged pressure). This may be employed in the industry with constant induced pressure. However, in the natural gas production, the pressure of induced gas wells will decrease as time passes by. The supersonic ejectors are also supposed to be used under as low induced pressure as possible, and therefore the optimization can be performed by getting the lowest induced pressure. According to Eq. (3), under constant motive pressure and constant discharged pressure, the lowest induced pressure leads to the largest pressure ratio. Therefore, the structural optimization of the natural gas supersonic ejector was performed by the second method (maximum pressure ratio) under constant motive pressure and constant discharged pressure.
Fig. 2. Mesh generation of supersonic ejector.
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Fig. 3. Natural gas flow in the supersonic ejector (a) downstream, (b) stationary and (c) upstream.
In the operation of the supersonic ejector, the low pressure natural gas was induced through the secondary nozzle, and the flow direction is shown in Fig. 3a. When the induced pressure was lower than a certain value, the low pressure gas could not enter into the secondary nozzle. In this case, the high pressure gas could flow into the secondary nozzle in the opposite direction, as indicated by Fig. 3c. The lowest induced pressure was obtained when the induced flowrate approximately equaled zero under the constant motive pressure and constant discharged pressure, as shown in Fig. 3b. Then the critical pressure ratio could be obtained under the lowest induced pressure according to Eq. (3). In the process of the structural optimization, the motive pressure and discharged pressure were always kept at constant values of 12 MPa and 5.2 MPa, respectively. In the structure optimization, the independent parameter dmt was optimized first, followed by Lmt and h in turn. The optimization of the diameter of mixing tube dmt was performed when the inclination angles of mixing chamber and diffuser were kept constant. The ratio of mixing tube diameter to primary nozzle throat diameter dmt =dc was defined as the evaluation index in order to make the optimization universal. Under different diameter ratios, the corresponding critical pressure ratios have been obtained and are shown in Fig. 4. The maximum diameter ratio got to 1.86 when the length of the mixing chamber decreased to zero. From the figure, the critical pressure ratio first increased and then decreased with the increase of the diameter ratio. The maximum critical pressure ratio was 55.2% when the diameter ratio was about 1.6. In other words, the optimal diameter ratio of the mixing tube to primary nozzle throat was about 1.6 for the supersonic ejector. On the basis of the optimization of mixing tube diameter, the mixing tube length was further optimized, which was performed with constant values of the inclination angle of mixing chamber, inclination angle of diffuser and mixing tube diameter. To make
Fig. 4. Optimization of mixing tube diameter.
the results universal, the length to diameter ratio of the mixing tube Lmt =dmt was chosen as the evaluation index. The critical pressure ratios are illustrated in Fig. 5 with the length to diameter ratio ranging from 0 to 6.0. According to the figure, the critical pressure ratio increased with the length to diameter ratio increasing from 0 to 4.0. When the length to diameter ratio further increased, the critical pressure ratio changed little. Considering the field application, the cost would increase and the machining property would become more difficult as the length to diameter ratio increased. Therefore, the optimal length to diameter ratio of mixing tube was considered to be 4.0 with the maximum critical pressure ratio being 55.7%.
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mixing process. In the supersonic ejector, the induced and mixing processes were mainly caused by the shearing force between two different pressure streams. But the processes were also influenced by the reversed force caused by the convergent face of the mixing chamber, and the reversed force increased with the inclination angle. Therefore, a critical inclination angle could be got when the reversed force was neglected compared with the shearing force. When the inclination angle of the mixing chamber was less than a critical value, the pressure ratio was independent on the inclination angle. As the inclination angle further increased, the processes was impaired and therefore the pressure ratio decreased. In the numerical simulation, the optimal inclination angle of the mixing chamber was obtained as 28° with the critical pressure ratio being 55.9%. 4. Field experimental investigation Fig. 5. Optimization of mixing tube length.
When the optimization of diameter and length of mixing tube has been finished, the optimal mixing tube of supersonic ejector could be derived. Subsequently, the mixing chamber was to be optimized. As noted above, the mixing chamber was dependent on the inclination angle h and the length from the primary nozzle exit to the mixing tube inlet Lmc , where the length Lmc was a function of the inclination angle h and mixing tube diameter dmt . On the basis of the optimization of mixing tube diameter dmt , the optimal mixing chamber could be obtained when optimal inclination angle was obtained. The critical pressure ratios are shown in Fig. 6 with the inclination angle of mixing chamber h increased from 22° to 38°. As the secondary nozzle was the negative throat nozzle, the inclination angle of the upper surface should be larger than that of the lower surface. Moreover, the outer surface of mixing chamber was the extension of the upper surface of the secondary nozzle, which could be derived from Fig. 1. Because the inclination angle of the lower surface of the secondary nozzle was chosen to be 22°, the inclination angle of the mixing chamber should be larger than 22°. From Fig. 6, the critical pressure ratio decreased with the inclination angle ranging from 28° to 38°. But when the inclination angle increased from 22° to 28°, the critical pressure ratio was almost a constant value. This can be deduced from the mechanism of the
Based on the structural optimization on the mixing chamber and mixing tube, an optimized supersonic ejector of natural gas was designed, with the design operation parameters and structural parameters given in Table 1. The supersonic ejector was applied in Changqing gas field, China and the schematic experimental system is shown in Fig. 7. The natural gas in the experimental gas wells was composed of CH4, C2H6, C3H8, CO2, H2S and so on. But CH4 was the main component, with the proportion larger than 97%, and all the other components were less than 3%.The motive natural gas from the high pressure well was first heated by the heater and then entered into the supersonic ejector through the primary nozzle. The induced natural gas from the low pressure well was also first heated and then sucked into the supersonic ejector through the secondary nozzle. The two different pressure streams were mixed in the mixing chamber and mixing tube, and then the pressure was lifted in the diffuser to match the pipeline and transportation requirements. As the pressures of motive gas were very high (even >20 MPa), it was very difficult to measure the flux safely and economically. Thus, the flowrates of induced and discharged gas (GL, Gd), which are less than 10 MPa, were measured in the field experiment. Then the flowrate of motive gas could be calculated as follows:
GH ¼ Gd GL
ð4Þ
As the flowrates measured have been transferred to volume flowrates under the standard condition (0.1 MPa, 273.15 K), therefore the mass entrainment ratio could be calculated as
a ¼ mL =mH ¼ GL =GH
ð2bÞ
The uncertainty analysis was performed by applying the estimation method proposed by Moffat [16]. In the experiment, the pressures, temperatures and flowrates were measured. The temperature was measured by K type thermocouples (nickel chromium–nickel silicon), with the accuracy of 0.5 K. The gas flowrate was measured by Tancy vortex precession flowmeters.
Table 1 Design operation parameters and structural parameters.
Fig. 6. Optimization of inclination angle of mixing chamber.
Parameters
Symbols
Unit
Result
Motive pressure Motive gas flowrate Induced pressure Induced gas flowrate Discharged pressure Throat diameter of primary nozzle Diameter of mixing tube Length of mixing lube Inclination angle of mixing chamber
PH GH PL GL Pd de dmt Lmt h
MPa 104 m3/d MPa 104 m3/d MPa mm mm mm deg
12.0 8.0 3.0 2.4 5.2 6.0 9.6 38.4 28
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Fig. 7. Installation diagram of supersonic ejector of natural gas.
The accuracy of each flowmeter used in the experiment was 1%, but different flowmeter had different measuring range. The range of the gas flowmeter measuring the induced gas was 0– 6 104 m3/d. In the experiment, the induced gas flowrate varied from 0.45–4.69 104 m3/d, therefore, the uncertainty of induced gas flowrate was 1.3–13.3%. The range of the gas flowmeter measuring the discharged gas was 0–20 104 m3/d, with the discharged gas flowrate varying from 4.87–12.20 104 m3/d, therefore, the uncertainty of induced gas flowrate was 1.6– 3.7%. All the pressure transducers had the same accuracy of 1%, but different measuring ranges. The range of the pressure transducer measuring the discharged gas and induced gas was 0–10 MPa, with the discharged gas pressure almost keeping constant at 5.4 MPa and the induced gas pressure varying from 1.1– 5.0 MPa. Therefore, the uncertainty of discharged pressure and induced pressure was 1.9% and 2–9.1%, respectively. The range of the pressure transducer measuring the motive gas was 0– 20 MPa, with the motive pressure varying from 8.0–13.0 MPa, therefore the uncertainty was 1.5–2.5%. In the experiment, the motive gas flowrate, pressure ratio and entrainment ratio were calculated by Eqs. (4), (3) and (2), respectively. Accordingly, the uncertainty of motive gas flowrate, entrainment ratio and pressure ratio was 2.7–4.5%, 2.9–14.1% and 3.7–27.6%, respectively. The supersonic ejectors of natural gas was used to boost the low pressure gas, therefore the performance of the ejector could be mainly indicated by the induced gas flowrate and the entrainment ratio. Moreover, the motive gas flowrate also needed to be kept at the normal value. Therefore, the three parameters were investigated. The variation of motive natural gas flowrate with motive pressure and induced pressure are shown in Fig. 8. As shown in the Fig. 8a, the motive pressure had great influence on the motive gas flowrate and there was a linear relationship between them (given as the solid line in Fig. 8a). From Fig. 8b, the motive gas flowrate had little dependent on the induced pressure under the same motive pressure: it almost remained unchanged as the induced pressure increased. As the primary nozzle was a convergent–divergent channel, the flowrate was subjected to the inlet parameters and area of throat. When the pressure ratio was less than the critical value, the flowrate could be described as:
Fig. 8. Variation of motive gas flowrate (a) with motive pressure and (b) with induced pressure.
D.T. Chong et al. / Applied Thermal Engineering 29 (2009) 2799–2807
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k1 P k 2 H mH ¼ Ac 2 kþ1 kþ1 mH
ð5Þ
where k is the isentropic exponent, for the natural gas (mainly composed of CH4), k ¼ 1:32; Ac is the area of throat, m2. For the fixed Ac , the motive gas flowrate was determined only by parameters of the inlet motive gas, and independent of the induced gas. The induced gas flowrate was influenced not only by the motive pressure but also by the induced pressure, as shown in Fig. 9. From Fig. 9a, the induced gas flowrate changed non-monotonically with the motive pressure when the induced pressure was less than 5.0 MPa, and it first increased and then decreased with the increase of the motive pressure. When the motive pressure was about 11– 12 MPa, the induced gas flowrate reached up to the peak value. But when the induced pressure was about 5.0 MPa, the induced gas flowrate changed little with the increase of the motive pressure. Generally, with the increasing motive pressure, the motive gas flowrate increased and the corresponding induced gas flowrate increased. On the other hand, the mixing process in the mixing chamber and tube was greatly influenced by the shear stress between the motive stream and induced stream. When the motive pressure increased, the pressure at the exit of primary nozzle increased, and the pressure difference between the pressures of primary nozzle exit and secondary nozzle exit decreased, which
Fig. 9. Variation of induced gas flowrate (a) with motive pressure and (b) with induced pressure.
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resulted in the decrease of the shear stress between the two streams and thus the decrease of induced gas flowrate. When the motive pressure was larger than a certain value (about 11– 12 MPa), the decreasing induced gas flowrate due to the decrease of the shear stress was larger than the increasing value due to the increase of the motive gas flowrate This resulted in that the appearance of a maximum value. In the field application of natural gas ejector, it is thus not economic to increase the motive pressure blindly, and this is very important for the operators. The induced gas flowrate was linear with the induced pressure under different motive pressure, as shown in Fig. 9b. Under the same induced pressure, the higher the motive pressure, the higher the induced gas flowrate. As the induced pressure increased and the motive pressure was kept constant, the pressure difference between the exits of the primary nozzle and secondary nozzle increased, which resulted in the increase of the shear stress between the two streams and thus the increase of induced gas production. The entrainment ratio was the most important parameter for the supersonic ejector of natural gas, and it was also affected by both the motive pressure and the induced pressure, as shown in Fig. 10. From Fig. 10a, the entrainment ratio first increased with the increase of the motive pressure and then decreased when the induced pressure was less than 5.0 MPa. The entrainment ratio increased up to the peak value when the motive pressure ranged
Fig. 10. Variation of entrainment ratio (a) with motive pressure and (b) with induced pressure.
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from 10 MPa to 12 MPa, similar to the variation trend of the induced gas flowrate. But when the induced pressure was 5.0 MPa, the entrainment ratio decreased with the increase of motive pressure, which was different from the variation trend of the induced gas flowrate. This could be explained from the results of Figs. 8a and 9a, where the motive gas flowrate increased with the increase of the motive pressure and the induced gas flowrate was kept constant. Therefore, it could be deduced that the entrainment ratio decreased with the increased of motive pressure according to Eq. (2). The entrainment ratios increase linearly with the rise of induced pressure for the same motive pressure, as shown in Fig. 10b. Differing from the variation trends of induced gas flowrate, the entrainment ratio was higher for smaller motive pressure when the induced pressures were about 5.0 MPa, while the induced gas flowrates were kept constant under the same operating conditions. The maximum entrainment ratio reached up to about 100% when the motive pressure was 8.0 MPa and the induced pressure was 5.0 MPa. Besides the experimental investigation as described above, the performance of the optimized supersonic ejector was also simulated by PHOENICS. In the numerical simulation, the motive pressure ranged from 8.0 MPa to 13.0 MPa, and the induced pressure from 3.0 MPa to 5.0 MPa. The comparisons between numerical and experimental results showed that the changes of motive gas flowrates, induced gas flowrates and entrainment ratios with motive pressure and induced pressure all had the same trends. The entrainment ratios obtained from experiment and numerical simulation were illustrated in Fig. 11. From Fig. 11a, the numerical
entrainment ratios agreed with the experimental data. When the motive pressure was no more than 11 MPa, the numerical and experimental entrainment ratios almost overlapped each other. When the motive pressure was larger than 11 MPa, the numerical entrainment ratios were slightly larger than the experimental data, which was due to the difference between the motive gas flowrates from the simulation and those from the experiment. In the field experimental system, some impurities, which could be oil, condensate, water and sand, might be produced with the natural gas. When the motive pressure increased, more impurities would be produced, which resulted in the lower experimental motive gas flowrates. Therefore, the numerical entrainment ratios were smaller than the experimental data for higher motive pressure. The deviations of entrainment ratios were shown in Fig. 11b, it can be seen that the deviations were less than 10.0% when the motive pressure was no more than 11 MPa, and less than 24.0% when the motive pressure was larger than 11 MPa. The pressure ratio in the experiment was also calculated according to Eq. (4), and given in Fig. 12 as a function of the entrainment ratio. It can be seen that the pressure ratio generally decreased with the increase of the entrainment ratio. The maximum pressure ratio was approximately 60%, which was in agreement with the optimized results (55.9%). From the figure, the maximum value for entrainment ratio may be deduced to be 90%, which was higher than the value from Sarshar et al. [8] for the same pressure ratio (about 11%), where a maximum value of 78% was obtained by Sarshar. Moreover, the pressure ratio obtained in the present experiment (about 55%) was also higher than Andreussi’s investigation (45%) for the same entrainment ratio (10%) [12]. The comparisons indicated that the performance of the present supersonic ejector of natural gas was better than the ejectors that have been reported by Sarshar and Andreussi. 5. Conclusions The structural parameters of natural gas ejector for boosting low pressure natural gas production were optimized numerically. The performance under different operation parameters was studied by field experiment and numerical simulation. The supersonic ejector was characterized by a simple structural design, absence of moving parts and small dimensions. The main benefit of the ejectors was its ability to use the energy of high pressure gas wells, which was usually wasted through choke valves, to boost production from low pressure wells. The field experiment was carried out with the motive pressure ranging from 8 MPa to 13 MPa, induced
Fig. 11. Comparison of entrainment ratios between experiment and simulation (a) variation trend comparison and (b) deviation of experiment and simulation.
Fig. 12. Pressure ratio variations under different entrainment ratios.
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pressure ranging from 1.0 MPa to 5.0 MPa and discharged pressure being 5.2 MPa. According to the numerical and experimental results, the following conclusions can be made: (1) The structural optimization was performed on the mixing chamber and mixing tube. The numerical results showed that the optimal diameter ratio of mixing tube to primary nozzle throat was 1.6, the optimal length to diameter ratio of mixing tube was 4.0 and the optimal inclination angle of mixing chamber was 28°. (2) The pressure ratio generally decreased with the increase of the entrainment ratio. The maximum pressure ratio was approximately 60%, which was in agreement with the optimized results. The entrainment ratio may be deduced to be up to 90% when the pressure ratio was about 11%, and the entrainment ratio was 55% when the entrainment ratio was 10%. (3) The motive gas flowrate, induced gas flowrate and entrainment ratio was also investigated experimentally and numerically. The entrainment ratios from experiment agreed with those from simulation, with the deviations less than 10.0% when the motive pressure was no more than 11 MPa, and less than 24.0% when the motive pressure was larger than 11 MPa. The motive natural gas flowrate increased linearly with the rise of the motive pressure and was independent of the induced pressure. The induced flowrate and entrainment ratio of natural gas were both increased linearly with the rise of induced pressure under each motive pressure, and the two parameters revealed nonlinear characteristics with the peak values when the motive pressure ranged from 8 MPa to 13 MPa.
Acknowledgements This work was supported by National 863 Scientific Program of China (Grant No. 2006AA05Z230).
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