Flow-field distribution and parametric-optimisation analysis of spiral-tube separators

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1011–1018

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Flow-field distribution and parametric-optimisation analysis of spiral-tube separators Lixin Zhao a,∗ , Baorui Xu a , Minghu Jiang a , Feng Li a , Zhengrong Hua b a b

Northeast Petroleum University, Daqing 163318, Heilongjiang, China Daqing Oilfield Company Ltd., Daqing 163513, Heilongjiang, China

a b s t r a c t Here we focus on the analysis of spiral-tube separators; model selection and the basic parameters for numerical simulation are described. Flow-field simulation analyses were performed for spiral-tube separators both with and without holes. The effects of gyration radius, inlet flowrate, the number of spiral coils, and oil-droplet diameter on flow-field distribution and the separation performance of spiral-tube separators were analysed in detail. The simulation results showed that the gyration radius and inlet velocity are the two main factors affecting the separation characteristics of spiral-tube separators. In addition, the size of the holes in a spiral-tube separator also affects the separation results. Some simulation results were verified through experimental studies. This study provides a basis for the flow-field analysis and structural optimisation of spiral-tube separators. © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Oil–water separation; Separator; Spiral tube; Flow field; Parametric optimisation

1.

Introduction

Oily wastewater is a typical organic industrial wastewater that is widely produced and does great environmental harm. At present, a large number of the oilfields in China have moved into a period of high-water-cut crude-oil exploitation. In the process, the water content of the product fluid reaches up to 80–90 percent. A large amount of oily water remains after the oil–water separation (Wang et al., 2005; Chen, 2000), which has resulted in the pollution of water resources and a waste of oil; furthermore, the ecological harm and human health hazards caused by this oily pollutant have aroused serious concern. Therefore, the development of an effective and economical oily wastewater treatment technology to achieve the goals of energy conservation, environmental protection, and water reuse has become a key problem in oilfield operations (Zhao and Li, 2006; Zhao et al., 2008b). The treatment methods (Gao and Gu, 1999) for oily wastewater can be classified into the following according to their principles: (1) physical methods, e.g. gravity settling, mechanical separation, centrifugal separation, filtration,

and membrane separation; (2) physical–chemical processes, e.g. flotation, adsorption, and ionic exchange; (3) chemical processes, e.g. agglomeration, acidification, and electrolysis; and (4) biochemical process, e.g. activated-sludge processes, biological-filtration processes, and oxidation-pond methods. With respect to environmental protection, physical methods are preferred. The spiral-tube separator has advantageous structural characteristics. It can produce a centrifugal force field and form a secondary flow. Although its structure is relatively simple, the interior flow field is quite complicated. The flow-field distribution of spiral-tube separators and its parametric governing equations were studied in this work.

2. Structure and working principles of spiral-tube separators A geometric model of a spiral-tube separator is shown in Fig. 1(a), and a geometric parameter sketch is shown in Fig. 1(b). Here the inner diameter, d, is 25.4 mm. The pitch is marked as t, and R is the gyration radius.

∗ Corresponding author at: College of Mechanical Science and Engineering, Northeast Petroleum University, 199 Fazhan Rd., High-Tech Zone, Daqing 163318, Heilongjiang, China. Tel.: +86 459 6503853; fax: +86 459 6503853. E-mail address: lx [email protected] (L. Zhao). Received 7 December 2010; Received in revised form 14 November 2011; Accepted 18 November 2011 0263-8762/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2011.11.014

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Nomenclature Ai C1 , C2 Ci E Qi R a d d1 dh g k n pd r t v vi z ε  o w   w o

inlet section area (m2 ) empirical constants inlet oil concentration (%) separation efficiency (%) inlet flowrate (m3 /h) gyration radius (mm) centrifugal acceleration (m/s2 ) inner diameter (mm) oil-droplet diameter (mm) hole diameter (mm) gravitational acceleration (m/s2 ) turbulent kinetic energy (J) number of spiral coils pressure drop (Pa) cylindrical coordinates (m) pitch (mm) velocity (m/s) inlet velocity (m/s) cylindrical coordinates (m) turbulent energy-dissipation rate (J/kg s) phase dynamic viscosity (mPa s) dynamic viscosity of oil (mPa s) dynamic viscosity of water (mPa s) cylindrical coordinates (rad) phase density (kg/m3 ) density of water phase (kg/m3 ) density of oil phase (kg/m3 )

Taking an oil–water mixture as an example fluid, the mixed fluid moves along the curved spiral tube, and the heavier phase is forced outward and the lighter phase inward to achieve a phase separation. Two methods are usually adopted for separating oil from water. One is designing an adjustable streamline baffle, i.e. a fluid-split board, at the outlet (Fig. 2); the other way is to make holes along the outer or inner radius of the spiral tube so as to drain oil or water into corresponding tanks (Zhao et al., 2008a); open holes on the outside of the spiral tube were used to drain the separated oil in this study.

3. Numerical simulation model and basic parameters To reflect the nature of fluid flow, stable, isothermal, and incompressible fluid characteristics were assumed. Two solvers are provided in the FLUENT soft pack: a segregated solver and a coupled solver. The segregated solver was used

Fig. 1 – Model of a spiral-tube separator.

Fig. 2 – Fluid-split design in a spiral-tube separator. in this study. The RNG k–ε model (Speziale and Thangam, 1992; Smith and Reynolds, 1992), a renormalisation-group k–ε model, was proposed by Yakhot and Orszag (1986). This model is suitable not only for the calculation of rotational flow and near-wall turbulent flow (Chen et al., 2003) but also for curvedtube flow (Ding and Weng, 2003) and impinging-jet flow (He et al., 2002), so our calculations were expected to be in accordance with the experimental data. The equation for turbulent kinetic energy and the equation for the turbulent energy-dissipation rate, the k and ε equations, respectively, of the RNG k–ε model in cylindrical coordinates are as follows: vz

∂k ∂k 1 ∂ +vr = ∂z ∂z r ∂z

vz

∂ε ∂ε 1 ∂ +vr = ∂z ∂z r ∂z



+



+

 ∂k  1 ∂ 

zz k

+

∂z

zz ε

r ∂r

+

 ∂ε  1 ∂  +

∂z

r ∂r

+

rr k rr ε

 ∂k  r

∂r

 ∂ε  r

∂r

+Sk ,

+Sz ,

where Sk = G − ε, Sz = ε/k(C1 G − C2 ε), and

 G = 2 zz + z

 ∂v 2 z

∂z

 ∂v

t

∂z

+

+rr

∂vz r∂

 ∂v 2

2

r

∂r + r

+

 ∂v

t

∂r

 ∂v 2 

+

t

r∂ ∂vr r∂

+rz

 ∂v

z

∂r

+

∂vr ∂z

2

2

For oil–water spiral-tube separators, relative motion exists between oil and water phases. For this reason, an Eulerian model was selected as multi-phase model. It can well reveal the separation process of oil from water in the spiral-tube separators. Considering the stability of the segregated solver and calculational economy, a second-order upwind difference scheme was adopted for the convection segregation and dissipation terms, respectively, in these equations. The pressure-andvelocity coupling method uses the PC-SIMPLE algorithm (Vasquez and Ivanov, 2000). Oil–water separation in a gravitational field is based on the density difference between oil and water. In unaided settling, the main factor determining the speed of oil flotation and water settling is gravitational acceleration. The structure of a spiral-tube separator promotes oil–water separation due to the centrifugal force produced. The gravitational force acts together with the centrifugal force field in a spiral-tube separator to achieve high-efficiency oil–water separation. This separation is dominated by the dimensionless parameters w /o and v2 /Rg (Zheng and Zhang, 2006). Although the structure of spiral-tube separator is relatively simple, the interaction of geometric and operating parameters greatly influences separation performance. Therefore, the effects of gyration radius, inlet flowrate, the number of

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1011–1018

numerical simulation results as far as possible. Four sets of grid numbers of 1,560,261, 2,683,093, 4,025,711 and 5,377,019 are carried on the computations for a 10-coil/100 mm-pitch separator under an inlet flowrate of 0.7 m3 /h. Fig. 3 shows the comparison effect of different grid quantity on pressure drop pd . It can be found that when the meshing grid was denser than 2,683,093, the computational error caused by the grid number is smaller. Therefore, following studies use 2,683,093-grid meshing scheme to achieve the most economical computation output.

35000 1 560 261 2 683 093 4 025 711 5 377 019

30000

pd , Pa

25000

1013

20000 15000 10000 5000 0 100

200

300

400

500

600

700

4. Numerical simulation and experimental study

R , mm

Fig. 3 – Grid independency check. spiral coils, and oil-droplet diameter on flow-field distribution and the separation performance of spiral-tube separators were analysed. One boundary condition in a spiral-tube separator is the inlet fluid velocity, defined as vi =

Qi , Ai

where vi is inlet velocity, m/s; Qi is inlet flowrate, m3 /h; and Ai is inlet cross-sectional area, m2 . The outlet pressure is another boundary condition, here, 1.0 × 105 Pa. Completing the boundary conditions, a no-slip condition is assumed at the wall. The physical parameters are as follows: the density of water, w , is 0.9982 × 103 kg/m3 ; the dynamic viscosity of water, w , is 1.003 mPa s; the density of the dispersed phase oil, o , is 0.889 × 103 kg/m3 ; and the dynamic viscosity of oil, o , is 1.06 × 103 mPa s. Meshing is very important for numerical simulation. Due to the specific structure of spiral-tube separators, unstructuredgrid meshing and body-fitted coordinates (BFC) were adopted for Fluent analysis. Considering wall effect, the meshing near inner wall was denser. Grid independency check was carried out to determine appropriate computational grids, and then ensure obtaining reasonable simulation results. This part of work can reduce the effect of grid resolution on

To eliminate the influence of outflow holes on the flow-field distribution analysis, the simulation of a spiral-tube separator without outflow holes was first performed.

4.1.

Study on spiral-tube separator without holes

Here, the effects of varying gyration radius R, inlet flowrate Qi , number of spiral coils n, and oil-droplet diameter d1 were analysed.

4.1.1.

Effect of gyration radius on separation performance

The analysed gyration radius values were 200, 300, 400, 500, 600, 800, 1000, and 1100 mm. Some simulation results are shown in Fig. 4; it displays the oil-phase volume-ratio distributions of a 0◦ cross-section of a spiral-tube separator. We found that with the increase of gyration radius, centrifugal acceleration decreases, whereas the oil–water separation effect is improved, although it could not be improved indefinitely. When R = 1100 mm, the oil–water boundary area becomes larger, and the separation effect becomes worse than at lower radii. It is well known that centrifugal acceleration a is proportional to 1/R. In theory, a lower gyration radius should yield a larger acceleration, improving oil and water phase separation. In practice, with a low-viscosity oil, the droplets are likely to be sheared when the acceleration is too large, resulting in emulsification, which is detrimental to oil–water separation. In this study, the simulation results for a gyration radius of 1000 mm

Fig. 4 – Oil-phase volume-ratio distributions with different gyration radius values.

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100

E, %

80 60 Simulated data 40

Experimental data

20 0 100

200

300

400

500

600

R , mm Fig. 5 – Contrast between simulated and measured efficiency values with varying gyration radius. were the best. With this best parameter, simulations for other parameter optimisation were carried out. But it was hard to make contrasts for most situations due to the perfect separation effect under the condition of 1000 mm gyration radius. So, a 500 mm gyration radius was adopted for subsequent simulation analyses, allowing the results to be conveniently contrasted for analysis. Fig. 5 shows the contrast between the simulated values and the experimentally measured data for the variation in separation efficiency with a changing gyration radius. It indicates that the difference between simulated and experimental data is larger when gyration radius is smaller, and the difference becomes little with the rise of gyration radius. It also shows clearly that the changing trends of both simulated data and experimental data are nearly the same.

4.1.2.

Effect of inlet flowrate on separation performance

For this simulation, n was 7, t was 100 mm, and d1 was 0.1 mm. The inlet flowrate values were 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, and 0.8 m3 /h. Some simulation results are shown in Fig. 6. As shown in Fig. 6, the inlet flowrate greatly influences separation performance. Starting at 0.4 m3 /h, with the rise of inlet flowrate, an obvious oil–water interface appeared in the sections, which indicates that oil–water separation was achieved.

When the flowrate was 0.55 m3 /h, the oil phase gathers nearly all in the top-left sector. The oil–water interface here was quite distinct, and it changed with regularity. As the flowrate was increased beyond 0.6 m3 /h, the separation effect was reduced with rising flowrate. Due to the constant tube cross-sectional area, the increase of flowrate enlarges inlet velocity, and the carrying force for the oil droplets is increased as well. In theory, a larger flow velocity should provide a better separation effect; however, again, the rise of velocity increases the shear force on oil droplets, which leads to a drop in separation efficiency (He et al., 2002). Additionally, if the velocity is too large, the residence time of the oil–water mixture in the tube separator is much shorter, increasing energy consumption, and the turbulence is increased, which can destroy the separation effect. This turbulence is the likely reason that the separation deteriorates at high flowrates, as shown in Fig. 6(e) and (f). However, the flowrate should not be too low because it could result in a decrease of the carrying force for the oil droplets and negatively affect separation efficiency (Vasquez and Ivanov, 2000). In theory, the effective measures for enhancing separation efficiency would be to increase the velocity inside the tube separator or to decrease the gyration radius, but a different conclusion can be drawn from the simulation results of 4.1.1. We also concluded from the simulation of 4.1.2 that a flowrate of 0.55 m3 /h is the best for our system. Therefore, the values of flowrate and gyration radius should be defined by comprehensively considering several factors. In this study, it was found that when R = 500 mm and vi = 0.3 m/s, the separation effect seems to be ideal. Fig. 7 shows the contrast between the simulated values and the experimentally measured data for the variation in separation efficiency with a changing inlet flowrate. In the experiments, the oil used was a machine oil (GL3-85W/9) with a density of 880 kg/m3 and a kinetic viscosity of 17–19 × 10−6 m2 /s (at 100 ◦ C). The oil content of the mixed fluid Ci was 0.4%. It was found that the trend in the measured values was the same as that of the simulated values. The measured values were slightly higher than the simulated values, and their difference was greater when the flowrate was at the

Fig. 6 – Oil-phase volume-ratio distributions at different inlet flowrate values.

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1011–1018

separator, the mixture should have a sufficient preseparation segment to ensure effective oil–water separation. Therefore, the number of spiral coils should be greater than five. The final number of coils will depend on the number, size, and distribution of the holes.

100 80 60

E, %

1015

Simulated data 40

4.1.4. Effect of oil-droplet diameter on separation performance

Experimental data

20 0 0.40

0.45

0.50

0.55

0.60

0.65

0.70

Q i , m3/h Fig. 7 – Contrast between simulated and measured efficiency values with varying inlet flowrate. higher and lower ends of the range because the setting of simulation boundary conditions differs from actual experimental conditions.

4.1.3. Effect of the number of spiral coils on separation performance The number of spiral coils is another important parameter affecting separation efficiency. Based on the results of 4.1.2, the inlet flowrate was fixed at 0.55 m3 /h, and a simulation was performed in which the number of coils was varied. In general, the distribution of the oil phase with different numbers of spiral coils was the same as that of the different coil sections in a multicoil spiral-tube separator. Fig. 8 shows the oil-phase distributions in cross-sections of the different coils in a 10-coil spiral-tube separator. It was found that the oil–water separation effect was strengthened on passing each coil of the separator until reaching Coil 5, after which the separation effect seemed to reach a limit, and no obvious improvement was observed. In addition, beginning in Coil 8, there was a remixing of the separated oil and water. The likely reason for this remixing is that the pressure drop increases with increasing coil number, decreasing the necessary centrifugal force for oil–water separation. For oil–water separation by opening holes in the studied tube

In theory, a larger oil-droplet diameter should yield a better separation effect. Fig. 9 shows the oil-phase distributions for different oil-droplet diameter values. It was found that a large oil area appeared with oil droplets 1 mm in diameter after one coil separation, whereas the separation effect was worse for 0.1 mm droplets; 0.05 mm droplets could hardly be separated. This result suggests that the larger size of the dispersed phase resulted in a faster separation process and better effect, which is in accordance with the anecdotal knowledge and indicated the correct selection of the RNG k–ε model for the simulation.

4.2.

Study on spiral-tube separator with holes

Referring to the simulation results of the spiral-tube separator without holes, the model of the separator with holes was then defined. Here the inner diameter d of the spiral-tube separator is again 25.4 mm. To conveniently contrast the experimental and simulation results, the model parameter selection for the spiral-tube separator with holes considered the design geometry of the experimental prototypes. The main parameters are defined as follows: R = 500 mm, t = 100 mm, and n = 10. For the boundary conditions, we set the inlet velocity vi at 0.3 m/s, the outflow pressure was given for the outflow holes on the separator wall, and the back pressure was set to atmospheric, i.e. 1.01325 × 105 Pa; the other parameters were the same as in the previous simulation. Considering that the separator was designed for deoiling, the outflow holes were made on the inner radius of the separator coil so as to drain the separated oil phase. The separation effect nearly reached a limit after passing through five coils. Considering the effect of the elbow at the inlet on the interior flow field, the first hole position was not before Coil 6. For the sake of high-efficiency oil–water

Fig. 8 – Oil-phase distributions of different coils in a 10-coil separator.

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Fig. 9 – Oil-phase distributions with different oil-droplet diameter values.

Fig. 10 – Oil-phase distributions at outflow holes (Model 1). separation, the number of spiral coils should be reduced as much as possible so as to reduce pressure drop and ensure that the separated oil can be drained from the holes, i.e. the separation efficiency can be enhanced. Therefore, the holes were located on Coils 7, 8, and 9, with two holes evenly spaced on each coil. The hole diameter dh was 3 mm (Model 1), and the holes were numbered 1–6. The holes were located at a position of 45◦ on the top-left side of the tube sections, as shown in Fig. 10. Thus, there is a half coil between every two holes, functioning to stabilise the flow field. Fig. 10 shows the respective oil-phase distributions at the cross-sections of Holes 1 through 6. The oil-phase velocity vectors at the outflow holes are also shown in the figure. It was found that the oil-phase content in the outflow at Holes 1 through 4 was relatively low, while the water phase congregated. Thus, a great deal of oil was drained from these holes. For outflow Holes 5 and 6, not only was the oil content higher but the oil–water interface was also weak. In addition, the velocities at these holes were lower due to the pressure losses when the mixture flows by each hole, resulting in the worse separation effect at Holes 5 and 6. Fig. 11 is the flow field sketch of Model 2 in which the hole diameter was 2.5 mm, and all other parameters were the same as in Model 1. Fig. 11 shows the respective oil-phase distributions at the cross-sections of Holes 1 through 6. It was found that with the mixture passing through these holes successively, the water content inside the tube increased.

Compared with the results of Model 1 (Fig. 10), the velocity values in Model 2 are larger, and obvious oil–water interfaces exist at Holes 5 and 6. The entire flow field is in good order. The oil and water flowrate report is shown in Table 1. Here, the oil flowrate at the outlet is 7.57% of that at the inlet, and that of the water is 76.59%, or, conversely, 23.41% of the entering water and 92.43% of the oil was drained through the outflow holes. Table 1 shows that the water flows at Holes 3 to 6 was greater than that at Holes 1 and 2, while the oil content at Holes 1 and 2, i.e. the separated oil, was relatively greater. The oil content at Holes 3–6 was reduced compared with that at Holes 1 and 2, whereas the water content was higher. To

Table 1 – Flowrate report (Model 2). Phase

Oil

Water (×10−2 m3 /h)

Inlet Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Hole 6 Outlet Ratio of outlet to inlet (%)

10.901 4.098 2.998 1.100 1.130 0.509 0.314 0.825 7.57

44.046 0.699 0.653 3.127 1.777 2.248 1.893 33.474 76.59

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Fig. 11 – Oil-phase distributions at outflow holes (Model 2). decrease the amount of water at Holes 3–6, the diameters of Holes 3–6 were reduced in next model analysed, Model 3. Fig. 12 shows the cross-sectional flow-field contours for Model 3, in which the hole diameters at Coils 7, 8, and 9 were 2.5, 2, and 2 mm, respectively. Fig. 12 shows the respective the oil-phase distributions at the cross-sections of Holes 1 through 6. Compared with the results of Model 2 (Fig. 10), the deoiling effect in Model 3 is more pronounced. Table 2 is the flowrate report for Model 3. Compared with that of Model 2, the water contents at the outflow holes increased, while the oil content remained nearly unchanged. A reasonable separation efficiency was obtained, and the water content flowing through the outflow holes is also better controlled, indicating that the design of Model 3 is the optimum model at this point in the study. Fig. 13 shows the contrast between the simulated flowrate values and the experimental data. Here “0” refers to the inlet, and “7” refers to the outlet; the consistency is quite good, indicating that oil–water separation

Table 2 – Flowrate report (Model 3). Phase

Oil

Water (×10−2 m3 /h)

Inlet Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Hole 6 Outlet Ratio of outlet to inlet (%)

10.901 4.453 2.791 0.939 0.768 0.530 0.391 0.825 7.57

44.046 0.579 1.918 1.705 1.573 1.342 2.742 36.077 81.91

is feasible by opening holes on the inner side of the spiral-tube separator. For carrying out a good numerical simulation, a precise physical model, a suitable turbulent model, and an independent meshing are all very essential. Only based on those can

Fig. 12 – Oil-phase distributions at outflow holes (Model 3).

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0.6 0.5 0.4

3

Qi , m /h

outflow holes was experimentally tested and compared with the simulation results. The results were very consistent, verifying the feasibility of studying the spiral-tube separator by CFD simulation. (4) This study provides a basis for flow-field analysis and the structural optimisation of spiral-tube separators.

Simulated data Experimental data

0.3 0.2

Acknowledgments

0.1 0

0

1

2

3

4

5

6

7

Sequence number of holes Fig. 13 – Simulated and experimental flowrate-distribution data. the simulation results be convincible. By having done it in this research, it is believed that the simulation results described here can well reflect internal behaviour of the spiral-tube separator to some extent. In addition, the experimental efficiency results with varying gyration radius and inlet flowrate, and those flowrate data of different holes (including inlet and outlet) verified the correlating simulation results well, which further supports our analysis. The closer combination of numerical simulation and experimental research can provide more accurate and more reliable data for a problem analysis.

5.

Conclusions

(1) The gyration radius and inlet velocity are the two main factors affecting the separation effect of a spiral-tube separator. In theory, a smaller gyration radius should provide a larger centrifugal force and better oil–water separation. In fact, for a low-viscosity oil, when the acceleration is too large, oil droplets are likely to be sheared, resulting in emulsification, which is not beneficial for oil–water separation. In this study, the simulated result of a 1000 mm gyration radius was the best; however, it was found that when R = 500 mm and vi = 0.3 m/s the separation effect was ideal. (2) The oil–water separation effect was strengthened after passing each coil of the separator up to Coil 5, after which the separation effect seemed to reach a limit, and no obvious improvement was observed. In addition, starting at Coil 8, there was a remixing of the separated oil and water. (3) The outflow-hole diameter of the spiral-tube separator greatly influenced the separation effect. Holes were opened at Coils 7, 8, and 9, with two holes in each coil. The subsequent modelling showed the optimum separation results with hole diameters of 2.5 mm for Coil 7 and 2 mm for Coils 8 and 9. The flowrates with the different

Thanks for the support by the Program for New Century Excellent Talents in Heilongjiang Provincial University, China (Contract No. 1155-NCET-003).

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