CFD Simulation in Helical Coiled Tubing

Journal of Applied Science and Engineering, Vol. 19, No. 3, pp. 267 272 (2016) DOI: 10.6180/jase.2016.19.3.04 CFD Simulation in Helical Coiled Tubing Z. Y. Zhu Department of Petroleum Engineering, China University of Petroleum, Beijing, P.R. China Abstract According to hydrodynamic theory, based on CFD software-fluent, the simulation for Newtonian fluid flow in helical coiled tubing was carried out to reveal the flow characteristics and pressure gradient of the helical section. Laminar and turbulent flow with different inlet velocities are considered. The results are compared with other published correlations. The results show that maximum velocity distributes in the outer side of the coiled tubing. The velocity in turbulent flow is more uniform than in laminar flow. It is shown that the faster the inlet velocity, the greater the pressure gradient increment. CFD simulation is in close agreement with the published correlations. Key Words: CFD, Helical Coiled Tubing, Pressure Gradient 1. Introduction Slimhole drilling and coiled tubing operations involve fluid flow in a long and narrow geometry. The main characteristic is the coiled tubing can be used as transportation and circulation drilling fluid. When the drilling technology is applied, the key point is to evaluate pressure loss reasonably. Coiled tubing pressure loss is mainly composed of two parts: one is coiled section twined on the drum on the ground; another is the straight pipe underground. Usually, on-site operation pays more attention to coiled tubing states in the wellbore. But less attention was put to coiled part on the ground. In addition, it is rather difficult to get precise results through the experiment. The objective of the present study is to use CFD software-fluent to simulate the flow and compute pressure gradient, and then compare the results with the previous correlations. 2. Model Geometry and Grid Generation In the present work, a 60.325 mm OD, 52 mm ID *Corresponding author. E-mail: zhiying_2008@hotmail.com coiled tubing on a reel of 2819.4 mm drum diameter is considered. In order to simplify the model, we make some assumptions as follows: Consider only one turn of the tubing string and the flow will reach fully-developed flow in this part. The coiled tubing has a long and thin geometry. Torsion is negligible because the value is very small. Therefore, the model geometry can be simplified as a torus. And in this work, gravity is not mentioned, so the flow in the coiled tubing can be viewed as symmetric about the central plane which is normal to the torus axis. Therefore, it is reasonable to model only half of the torus. But it is ill-defined half torus which has a slot to form the inlet and outlet, for example, the half ill-defined torus is 359, not 360. The schematic drawing is shown in Figure 1. Figure 2 is enlarged drawing of the inlet and outlet part. For meshing procedures are as follows. First of all, draw a half circle, mesh the circular edgewith intervals count (r, radial direction;, circumferential direction). Then, mesh the boundary layer for the edge by specifying the first row height, growth factor, and total rows for the boundary layer. After that, use the default interval size and apply Quad/Pave scheme to mesh the semicircle

268 Z. Y. Zhu face. Next, the semicircle face rotates 359 degrees with mesh to form a volume. And mesh the edge in the axial direction by specifying the number of intervals count (, axial direction). Finally, apply the Cooper scheme to the whole volume. The grid mentioned in this section is 23(r) 40( ) 720( ) mesh. The grid has a boundary layer of 6 row with the first row being 0.0005 mm and the growth factorof1.2[1].figure3isthegridofhalftubingcross section. 3. Simulation In regular straight pipe, different flow regime is distinguished by Reynolds number. But in Coiled Tubing, because of centrifugal forces the flow is featured by the secondary flow, Re is not suitable. W. R. Dean proposed Dean number (De) to analyze fluid in the curved pipe. De is ratio of centrifugal force and viscous force and defined as (1) where a = radius of coiled tubing (m), R =radiusof drum (m), Re = Reynoldsnumber [2]. And Re is defined as (2) Figure 1. The schematic drawing of one turn coiled tubing. where u = fluid average inlet velocity (m/s), d =diameter of coiled tubing (m), = fluid density (kg/m 3 ), = fluid dynamic viscosity coefficient (pa s). Figure 2. The enlarged drawing of the inlet and outlet part.

CFD Simulation in Helical Coiled Tubing 269 This will lead to secondary flow. The results of other velocity are similar to these, not mentioned here. Table 1 shows the CFD pressure gradient simulation results, Srinivasan correlation solution, Re, De according to different velocities. Here, all De are smaller than 750. The flow is laminar. Srinivasan et al. [3] and S. N. Shan et al. [4] point out when the flow is laminar, friction factor f can be calculated by Eq. (4) (4) Figure 3. The gird of the tubing cross section (half). The critical Dean number (De CT ) isdescribed as According to the law of fanning in the coiled tubing, pressure gradient is (5) (3) In this work, De CT equals 750. When De is smaller than De CT, the flow is laminar. On the contrary, the flow is turbulent. In other words, 0.115 m/s can be viewed as critical velocity. When the inlet velocity is smaller than 0.115 m/s, the flow regime is laminar, bigger than it, the flow regime is turbulent. In this part, water-liquid flow at inlet velocity of 0.02, 0.03, 0.05, 0.1, 0.5, 0.9, 1.2, 3.5 and 10 m/s is considered. The fluid density is 998.2 kg/m3; viscosity is 0.001003 pa s. Depending on De CT, it is concluded that the flow regime is laminar at inlet velocity of 0.02, 0.03, 0.05 and 0.1 m/s; the rest is turbulent. When laminar simulation, the viscous model chooses laminar; and when turbulent, the viscous model is set as k-epsilon, Realizable, Standard wall function. Figure 4. Contours of velocity (inlet velocity v = 0.02 m/s). 4. Results and Discussion 4.1 General Format Requirements Laminar Flow Figures 4 and 5 shows the contours of velocity and velocity profile on the outlet face when inlet velocity is 0.02 m/s. Because of centrifugal forces, maximum velocity distributes in the outer side of the coiled tubing. Figure 5. Velocity profile (inlet velocity v = 0.02 m/s).

270 Z. Y. Zhu Table 1. Compares the results of pressure gradient by the CFD simulations and Srinivasan correlation Pressure gradient (Pa/m) Inlet velocity u (m/s) Deviation rate Re De CFD simulation Srinivasan correlation 0.02 0.396 0.404 0.2% 1035.02 140.563 0.03 0.652 0.712 8.4% 1552.53 210.845 0.05 1.417 1.456 2.7% 2584.55 351.408 0.1 3.978 3.841 3.6% 5175.10 702.817 here, L d is the length of the coiled tubing (m). Here one turn is mentioned.therefore L d equals the perimeter of the drum. It can be seen that the CFD result is in close agreement with the Srinivasan correlation. It is shown the faster the inlet velocity, the greater the pressure gradient increment. accounts for almost half of the whole plane, whereas the area of maximum velocity is less than quarter of the plane. Table 2 compares the results of pressure gradient by the CFD simulation and White correlation. White [5] and Vashisth et al. [6] make a conclusion for turbulent flow that the friction factor f is 4.2 Turbulent Flow Figures 6 and 7 shows the contours of velocity and velocity profile on the outlet face when inlet velocity is 0.9 m/s. Compare Figures 6 and 7 with Figures 4 and 5, it can be seen that the velocity in turbulent flow is more uniform than in laminar flow. Figure 5 is steep but Figure 7 is gentle. However, the location of the maximum velocity is nearly the same with each other, in the outer side of the coiled tubing. When inlet velocity is 10 m/s, the contours of velocity and velocity profile on the outlet are illustrated in Figures 8 and 9. We can find that Figures 8 and 9 are similar to Figures 6 and 7. The maximum velocity occurs in the outer side and the area of it (6) put Eq. (6) into Eq. (5), can get pressure gradient shown in the third column in Table 2. It can be seen that the CFD results are similar to White correlation except the last one. The reason for this probably because the applicability of Eq. (6) is Re (1.5 10 4,10 5 ). When the inlet velocity is 3.5 m/s and 10 m/s, Re are bigger than 10 5, Eq. (6) is not suitable for this situation at all. The same to laminar, the faster the inlet velocity is, the greater the pressure gradient increment. Figure 10 shows the contrast between CFD simulation and White correlation in pressure gradient vs. inlet velocity intuitively. Figure 6. Contours of velocity (inlet velocity v = 0.9 m/s). Figure 7. Velocity profile (inlet velocity v = 0.9 m/s).

CFD Simulation in Helical Coiled Tubing 271 Figure 8. Contours of velocity (inlet velocity v = 10 m/s). Figure 9. Velocity profile (inlet velocity v = 10 m/s). Table 2. Compares the results of pressure gradient by the CFD simulations and white correlation Pressure gradient (Pa/m) Inletvelocityu(m/s) Deviation rate Re De CFD simulation White correlation 0.5 00067.942 00062.666 8.4% 25875.5 03514.083 0.9 00186.974 0176.23 6.1% 46575.9 6325.35 1.2 00311.972 00292.406 6.7% 62101.2 8433.80 3.5 02109.395 01927.875 9.4% 181128.50 24598.584 10 14118.105 12301.005 14.8%0 517510 70281.670 (4) Regardless of the laminar flow and turbulent flow, the faster the inlet velocity, the greater the pressure gradient increment. (5) The pressure gradient values of CFD simulation is in close agreement with the published correlations. Acknowledgement Figure 10. Pressure gradient vs. inlet velocity (turbulent). 5. Conclusions (1) The flow of water in helical coiled tubing has been simulated by CFD successfully. (2) Because of centrifugal forces, maximum velocity distributes in the outer side of the coiled tubing. (3) The velocity in turbulent flow is more uniform than in laminar flow. The research reported herein is partly supported by China University of Petroleum (Beijing) (grants No. ZX20150195). These financial supports are gratefully acknowledged. References [1] Zhou, Y. and Shah, S. N., Fluid Flow in Coiled Tubing: CFD Simulation, Canadian International Petroleum Conference, Paper 2003-212 (2003). doi: 10.2118/ 2003-212 [2] Zhang, J. K., Li, G. S., Huang, Z. W., Tian, S. C., Shi,

272 Z. Y. Zhu H. Z. and Song, X. Z., Numerical Simulation on Friction Pressure Loss in Helical Coiled Tubing, Journal of China University of Petroleum, Vol. 36, No. 2, pp. 115 119 (2012). (in Chinese) [3] Srinivasan, P. S., Nandapurkar, S. S. and Holland, F. A., Friction Factors for Coil, Trans Instn Chem Eng, Vol. 48, pp. 156 161 (1970). [4] Shah, S. N. and Zhou, Y., Naval Goel, Flow Behavior of Fracturing Slurries in Coiled Tubing, SPE 74811 (2002). doi: 10.2118/74811-MS [5] White, C. M., Streamline Flow though Curved Pipes, Proc Roy Soc (London), Vol. 123 (ser A), pp. 645 663 (1929). doi: 10.1098/rspa.1929.0089 [6] Vashisth, S. and Nigam, K. D. P., Experimental Investigation of Pressure Drop during Two-phase Flow in a Coiled Flow Inverter, Ind Eng Res, Vol. 46, pp. 5043 5050 (2007). doi: 10.1021/ie061490s Manuscript Received: Jan. 25, 2016 Accepted: May 22, 2016