- Email: [email protected]
Drilling characteristics of combinations of different high pressure jet nozzles
384
2011,23(3):384-390 DOI: 10.1016/S1001-6058(10)60127-8
DRILLING CHARACTERISTICS OF COMBINATIONS OF DIFFERENT HIGH PRESSURE JET NOZZLES* ZHANG Yu-ying, LIU Yong-wang, XU Yi-ji, REN Jian-hua College of Petroleum Engineering, China University of Petroleum (East China), Dongying 257061, China, E-mail: [email protected] (Received October 12, 2010, Revised January 22, 2011) Abstract: The high speed fluid jet for directly or indirectly breaking rock is one of the most effective ways to improve the deep penetration rate. In order to maximize the efficiency of energy use, the flow characteristics of different combinations of high pressure jet nozzles are analyzed through numerical simulations. According to the velocity vectors at the bottom and the bottom hole pressure diagram, the effects of the high pressure nozzle combinations on the flow structure and the penetration rate are analyzed. It is shown that the combination of three vertical edge nozzles is very efficient, but inefficient in cleaning the bottom hole and eroding the wall. The jet velocity is 400 m/s and the radius is 5 mm, with a center nozzle added, the problem can be solved, but the high-pressure fluid displacement would increase. The center nozzle’s jet velocity is 200 m/s and the radius is 8 mm, the combination of two vertical edge nozzles and a center tilt nozzle or that of a vertical edge nozzle and a center tilt nozzle would provide a flow structure favorable for drilling. The angle of inclination is 10o. To take advantage of high pressure jet energy to improve the efficiency of drilling, it is important to select a suitable nozzle combination according real conditions. Key words: Rate Of Penetration (ROP), rock breaking, high pressure jet, nozzle, combination, numerical simulation, energy use
Introduction High pressure jet assisted drilling technology is an effective way to improve deep penetration rate[1-3]. In recent years, China National Petroleum Corporation (CNPC), Sinopec, China University of Petroleum (East China) and a number of other institutions devoted their effort on studies of pressure intensifier, with research installations including static pressure pressurezing unit, centrifugal down-hole pressurizing unit, jet flow type pressurizing unit, and anti-vibration pressurizing unit, involving a great number of technological breakthroughs. In a near future, the domestic pressure intensifier will be available for industrial applications[4-11]. But now, further studies are necessary to improve the efficiency of direct cutting or assisted rock breaking, where the submerged jet flow structure under high pressure is an important issue.
* Biography: ZHANG Yu-ying (1961-), Male, Ph. D. Candidate, Senior Engineer Corresponding author: REN Jian-hua, E-mail: [email protected]
Ultra-high pressure dual channel bit is an indispensable tool, where the conventional drilling fluid may be combined with high pressure drilling fluid to break hard rock. A high pressure tube is added to the conventional bit, with its upper end connecting to the pressure booster pump and the lower end connecting to the high pressure channel and nozzle. A high pressure jet can be generated to cut the rock, assisting the process of breaking rock. How to combine the high pressure nozzle with the conventional nozzle is an important factor which affects the efficiency of high pressure jet. In order to make full use of the high pressure jet to break the rock, a good understanding of the characteristics of the flow is necessary. Due to the high pressure, it is difficult to directly measure the flow field. Based on theoretical models, numerical simulations and analyses are effecttive[12,13]. This article proposes a bottom-hole flowing field calculating model for different nozzle combinations. Based on the analysis of simulated results, some significant conclusions are obtained, which can serve as a useful reference for nozzle design.
385
1. Mathematical model and numerical method 1.1 Governing equations Steady flow is assumed and the effect of fluid viscosity outside the boundary layer is ignored, because under the high-speed condition, the fluid viscocity is not a main concern. The change of fluid density is also ignored[14-20], as in ultra-high pressure condition, when the pressure reaches 100 MPa, water density is 1050 kg/m3, which is no more than 5% increase and can be ignored. Therefore the constant incompressible flow can be described by basic equations as follows. p = p( ρ , S )
(1)
and the equation of continuity
∂p + ρ a 2 ∇ui = 0 ∂t
(2)
The standard k − ε turbulence two-equation model is used, where Boussinesq assumption can simplify the calculation. Using the standard k − ε equation, the turbulent kinetic energy and the dissipation rate can be obtained by the following equations:
ρ
μt Dk ∂ ª§ = «¨ μ + σk Dt ∂xi «¬©
· ∂k º » + Gk + Gb − ρε − Ym ¸ ¹ ∂xi ¼»
ρ
μt Dε ∂ ª§ = «¨ μ + Dt ∂xi «¬© σε
· ∂ε º ε » + C1ε ( Gk + C3ε Gb ) − ¸ x k ∂ ¹ i ¼»
C2 ε ρ
ε2 k
in Eq.(3) is the same as before. In Eq.(4), C1ε , C2ε , Cμ , σ k and σ ε are empirical constants, determined by testing: C1ε = 1.43 ,
C2ε = 1.92 , Cμ = 0.09 , σ k = 1.0 and σ ε = 1.3 . 1.2 Numerical calculation methods The SIMPLE method proposed by Patankar and Splading is used to solve the coupling equations of the semi-implicit method, with the pressure correction term removed. For volume discretization, the finite volume method is used. The basic idea is as follows. The entire computational domain is divided into a number of control volumes, so that each node is surrounded by a control volume. Carrying on the integration for all differential equations, the equations for a set of nodes are obtained. The discrete equation on the control volume for the dependent variables is then obtained. 1.3 Calculation model Supposing that the bit bottom surface and the bottom hole are in two parallel planes, and the bit body has four holes. 2 to 4 nozzles can be arranged at the bit. The ratio of the diameter of the edge nozzle to that of the center nozzle is 0.62. The diameter of the center nozzle is 8 mm and that of the edge nozzle is 5 mm. The angle between edge nozzles is 120o, evenly distributed in the bit body, as shown in Fig.1.
(3)
(4)
In Eq.(3), Gk means the turbulent kinetic energy, as an additional item caused by the average velocity gradient Gk = μt S 2
where 1 § ∂u ∂u j · S ≡ 2Sij Sij , Sij = ¨ i + ¸ 2 ¨© ∂x j ∂xi ¸¹
Gb represents buoyancy generated additional items and the compressible turbulence dissipation rate Ym
Fig.1 Flow calculation diagram of the bottom
Because the model is not symmetrical, the entire flow field is considered. The calculated region ranges from the nozzle inlet to the annular outlet. Except a dense grid at the nozzle entrance, the grids in other regions are uniformly distributed. Cooper method is used to generate a non-structural grid system. The entire flow field in the region is divided into 48 000 hexahedral cells with a total of 53 000 nodes. Simulation cases for nozzle combinations are shown in Table 1. In the combinations, the edge nozzle is used for rock breaking and the center nozzle is mainly used for increasing drilling fluid displacement, and cleaning bottom hole and bit.
386
Table 1 List of composite structures of nozzles Combinations (a)
Nozzle diameter (mm)
Jet velocity (m/s)
Angle (o)
Serial number
Center
Side
Center
Side
Center
Side
Center
Side
Spray distance (mm)
1
-
3
-
5
-
400
-
0
50
2
1
3
8
5
400
400
0
0
50
3
1
3
8
5
200
400
0
0
50
4
1
2
8
5
200
400
0
0
50
5
1
2
8
5
200
400
10
0
50
6
1
1
8
5
200
400
10
0
50
7
1
1
8
5
200
400
0
0
50
8
-
2
-
5
-
400
-
0
50
1.4 Boundary conditions The fluid boundary is the outlets of nozzles. The annular space between the bit and the wall is the outlet boundary for the flow field. The entire flow within the solid boundary allows no heat transfer, the roughness is 0.5, and the wall is assumed to be smooth[21]. The bit body does not rotate, so the bit boundary is the same as other solid-wall boundaries and is a non-slip solid wall boundary. The direct impact by the jet in the bottom boundaries generates a thin overflow layer in the bottom hole. The velocity distribution is not easy to be obtained. Meanwhile, different combinations of the nozzles make the flow more complex. Therefore, based on a reasonable division of the grid, the side wall velocity on the bottom is assumed to have the logarithmic distribution. U∗ =
1 ln ( Ey ∗ ) k
and speed coincidence items, the SIMPLE algorithm is used, and for the turbulent flow kinetic energy and the turbulent flow dissipation rating, the first-order upwind scheme is used. On this basis, the calculation remainders are monitored in the calculation process by ploting curves, such as for continuity equation, velocities in x , y , z directions, k and ε . The calculation remainder curve should tend to an equilibrium point, or reach a preset value, which means that the results converge.
(5)
In this article, when the dimensionless wall distance y ∗ > 11.225 , the logarithmic distribution is used. When y ∗ < 11.225 , the stress-strain relationship of laminar flow is used with U ∗ = y ∗ . 1.5 Numerical solutions In the iterative calculation process, the pressure operations are to keep the pressure within the annular wall always an atmospheric pressure, that is, the flow field under normal pressure. Jet exit sections are circular. Because the submerged jet structure is independent, the jet Reynolds number has no effect on the jet structure. The governing equation is the explicit steady-state three-dimensional navier-stokes equation. In order to obtain an accurate result, the relaxation factor method is used for the pressure, momentum, turbulent kinetic energy and turbulent dissipation rate. Different discretization methods are used for different arameters. For the momentum item the first-order upwind scheme is used, for the pressure
Fig.2 Velocity vector diagram (b) and pressure contours (c) on the bottom section
2. Analyses of simulation results The velocity distribution, which is related to the efficiency of rock breaking, bottom hole cleaning and wall stabilization, is an important indicator in the study. Jet impacts the bottom hole to produce a high pressure gradient. Under the unbalanced force moment, the debris turns over and trundles and then is carried into the annulus. The force of the bottom
387
overflow on the debris is also helpful for bottom hole cleaning[15]. Therefore, the pressure distribution on the bottom hole is important in the whole process. The study of different combinations of nozzles will be based on the flow velocity distribution and the pressure distribution. 2.1 The combination of three vertical edge nozzles In this combination, three straight nozzles are on the bottom of the bit. The angle between the nozzles is 120o. The nozzles are located in the middle of radii with diameter of 5 mm. Jet velocity is 400 m/s. From Figs.2(a), 2(b) and 2(c), it can be seen that three jets flow into the bottom to generate three distinct fan-shaped regions. The tangential velocity at the boundary is 0. But the fluid keeps flowing, therefore, is forced to spread out. At the bottom center, the overflow stops. In the region between the edge nozzle and the wall, the overflow velocity is large, but without much indication of vortex. In the bottom center, three jets impact the bottom and spread out. The jets in the bottom push one another, so that the fluid is forced upward to form a strong vortex area. Rock debris will be in a repeated movement in the region, unable to leave the bottom and go into the annular space, which is not good for cleaning the borehole. Vortex is not clearly seen in the region between the edge nozzle and the wall. A high overflow rate will produce a strong wall erosion effect. In view of rock breaking, the jets with ultrahigh pressure deal with the outer edge of the bottom, because for a large amount of rock, a large amount of hydroelectric energy is required[16], where high pressure edge nozzle structure is appropriate. 2.2 The combination of three vertical edge nozzles and a center nozzle In this combination, a center nozzle is added besides of the edge nozzles, with diameter of 8 mm. It was shown that the velocity of the center nozzle would influence the bottom flow field[17]. Figure 3 is a comparison of the bottom hole pressure distribution under different central nozzle jet velocities, where D is the radial distance, P is the bottom hole pressure.
Fig.3 Radial bottom pressure distributions
As can be seen from the figure, the center nozzle jet velocity has a great influence on the pressure distribution of the bottom hole flow field. When the center nozzle jet velocity is increased from 200 m/s to 400 m/s, the pressure of the bottom center increases from 20 MPa to 80 MPa and the edge nozzle pressure drops from 70 MPa to 60 MPa. It is because the pressures produced by the center nozzle and the edge nozzle’s jet diffusion towards the center are interacted. When the center nozzle velocity is decreased, the jet diffusion offsets a part of the bottom hole pressure, when the center nozzle velocity is increased, the overflow layer disappears and the overflow layer produced by the center nozzle would interfere with the pressure of the edge nozzle. This indicates that the increase of the center nozzle outlet pressure would reduce the edge nozzle pressure. In view of rock breaking, the outer boundary volume is to be larger than that at the center and would consume more energy. Therefore, the jet of the center nozzle should go the same way as that of the edge nozzle. The jet velocity of the central nozzle should be smaller than that of the edge nozzle. The main purpose is to increase the displacement to clean the bottom hole. Based on this consideration, the center jet nozzle outlet velocity is 200 m/s. Figures 4(a) and 4(b) show the velocity vectors and the pressure isoclines of the bottom cross section. A comparison with Fig.2 shows that the presence of the center nozzle makes a great difference for the bottom center flow field. The center nozzle jet pushes the fan-shaped dividing line in the fluid obviously outward. The pressure isoclines of the bottom center obviously bend outward. This is mainly because the center nozzle jet prevents the diffusion of the edge nozzle jet, which makes its energy concentrated in the boundary part.
Fig.4 For the combination of four nozzles, the bottom horizontal velocity vector profile (b) and pressure contours (c)
388
Figure 4(b) shows that the center nozzle and the edge nozzle jointly produce strong vortexes, in the complex flow field, which can also be found in the middle of both sides of the nozzle jet, due to the role of the central suction nozzle, where the fluid does not reach the boundary. The flow structure can reduce the erosion of the wall to avoid the well eyes expansion, which is beneficial. But for the kind of high-pressure fluid flow under a large displacement, a high pressure pump is required. 2.3 The combination of two edge nozzles and a central nozzle For the combination of two edge nozzles and a vertical center nozzle, as well as that of two edge nozzles and a inclined center nozzle, the bottom hole pressure distribution is shown in Fig.5.
and longitudinal section and the pressure contour map are shown in Fig.6.
Fig.6 Bottom profile horizontal velocity vector (b) and pressure contour map (c)
Fig.5 Bottom hole pressure distribution under different nozzle angles
The inclined nozzle pressure is smaller than that of the vertical nozzle. This is mainly because the overflow increases the thickness of the bottom layer and the maximum overflow velocity is increased. Therefore, with the decrease of the vertical impact velocity, the impact pressure is reduced. Also, the pressure on the wall near the inclined central nozzle will increase. The interpretation of the phenomenon may be as follows: after the overflow impacts the wall, the overflow rate around the wall is decreased, to generate a pressure stagnation zone and thus increase the pressure. The inclined nozzle tends to increase the overflow rate, which is beneficial for the bottom hole cleaning, but not good for the well-bore stability. When the actual bottom wall is not perpendicular to the plane, this disadvantage can be avoided and wall stability problem no longer exists. From the point of view of bottom hole cleaning, the inclined center nozzle is better than the vertical one. Therefore, the combination of two edge nozzles and a center tilt nozzle is worth a further study. The diameter of the center nozzle is 8 mm, with the outlet velocity of 200 m/s, and the diameter of the edge nozzles is 5 mm, with the outlet velocity of 400 m/s. The horizontal velocity vectors on the bottom well crosswise section
It can be seen that the bottom flow field is divided into three irregular fan-shaped regions. The pressure contours also tend to one side. The tilt center nozzle’s overflow area is increased, which is beneficial to cleaning the bottom hole. From the point of view of rock breaking, two high pressure edge nozzles can break the rock, at the same time, can also clean the bottom and cool the bit. From Fig.6(c), it can be seen that for the inclined center nozzle, the vortex is not obvious on the tilt side. Fluid moves quickly into the annular, reducing the fluid circulation path. Therefore, the combination of two edge nozzles and a center tilt nozzle is ideal.
Fig.7 Bottom hole pressure distribution with different nozzle number
2.4 Other nozzle combinations Because of the limitation of the down-hole flow boosting device, it is not practical to use too many nozzles. It would be desirable to reduce the nozzle number and at the same time to achieve the same
389
effect. Therefore, we will consider the bottom-hole flow field of a combination of the two nozzles. Figure 7 gives a comparison of the pressure distribution between the combinations of two nozzles and that of two edge nozzles and a center nozzle. Figure 7(a) is the combination of two edge nozzles and a center nozzle. Figure 7(b) is the combination of an edge nozzle and a center nozzle. Figure 7(c) is the combination of two edge nozzles. Curves are for pressure values at the bottom center of the edge nozzle. As can be seen from the figure, the pressure distribution curves of 7(a) and 7(b) are similar. But the pressure of two edge nozzles is slightly lower than that of one edge nozzle, whereas the bottom center pressure does not change significantly. It is because that two edge nozzles locate a certain distance apart, and the initial jet segments do not overlap each other. But the overflows have some mutual interference so that the jet’s impact is decreased, reducing the efficiency of rock breaking. From this point of view, using one edge nozzle is better than using two. The impact pressure of the combination of one edge nozzle and one center nozzle is basically the same as that of a center nozzle and two edge nozzles. 3. Conclusions (1) Different combinations have different bottom high pressure flow fields. The process of breaking rock is also different. (2) The combination of three edge nozzles has a good efficiency in rock breaking. The jet velocity is 400 m/s with the radius of 5 mm. But it is inefficient in cleaning the bottom hole, which would result in serious erosion. The combination can be used for hard ground, where there is no problem of instability formation such as hole enlargement and chipping. (3) The combination of three edge nozzles and a center nozzle is good for cleaning and reducing the erosion of sidewall. The added noozle’s jet velocity is 200 m/s with the radius of 8 mm. But it requires a large high-pressure displacement, a high demand on the equipment. (4) For the combination of two edge nozzles and a center nozzle, the center nozzle tilted 10o is beneficial for bottom cleaning and breaking rock efficiency. It will not affect the stability of wall. The flow field structure is ideal. (5) For the combination of two nozzles, an edge nozzle and a center nozzle tilted 10o is more efficient than the combination of two edge nozzles in rock cleaning and wall stability. (6) Making a full use of high pressure jet energy improves the efficiency of drilling, with an appropriate choice of the nozzle combination according to the actual conditions.
References [1] [2]
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characteristics of oscillating hydrofoil[J]. Journa of Hydrodynamics, 2008, 20(3): 280-287. LAO Yi-jia, WANG Zhi-dong and ZHANG Zhen-shan et al. Experimental measurement and analysis on the wake vortex of oscillating flexible caudal fin[J]. Journal of Hydrodynamics, Ser. A, 2009, 24(1): 106112(in Chinese). CHEN Ting-gen, GUAN Zhi-chuan. Theory and technology of drilling engineering[M]. Dongying: The Press of the University of Petroleum, 2006, 166-211(in Chinese). KUBRAK E., KUBRAK J. and ROWINSK P. M. Vertical velocity distributions through and above submerged, flexible vegetation[J]. Hydrological Sciences, 2008, 53(4): 905-920.
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ERIC G. P., LEONARD J. P. Detached-eddy simulation of high-Reynolds-number beveled-trailing-edge boundary layers and wakes[J]. Journal of Fluids Engineering, 2005, 127(3): 897-906. LIEFVENDAHL M., FUREBY C. LES and DES of high Reynolds number wall bounded flows[C]. The 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, USA, 2006, 121-126. BENSOW R. E. Large eddy simulation of the viscous flow around submarine hulls[C]. The 25th Symposium on Naval Hydrodynamics. Newfoundland and Labrador, Canada, 2004, 212-219.
2011,23(3):384-390 DOI: 10.1016/S1001-6058(10)60127-8
DRILLING CHARACTERISTICS OF COMBINATIONS OF DIFFERENT HIGH PRESSURE JET NOZZLES* ZHANG Yu-ying, LIU Yong-wang, XU Yi-ji, REN Jian-hua College of Petroleum Engineering, China University of Petroleum (East China), Dongying 257061, China, E-mail: [email protected] (Received October 12, 2010, Revised January 22, 2011) Abstract: The high speed fluid jet for directly or indirectly breaking rock is one of the most effective ways to improve the deep penetration rate. In order to maximize the efficiency of energy use, the flow characteristics of different combinations of high pressure jet nozzles are analyzed through numerical simulations. According to the velocity vectors at the bottom and the bottom hole pressure diagram, the effects of the high pressure nozzle combinations on the flow structure and the penetration rate are analyzed. It is shown that the combination of three vertical edge nozzles is very efficient, but inefficient in cleaning the bottom hole and eroding the wall. The jet velocity is 400 m/s and the radius is 5 mm, with a center nozzle added, the problem can be solved, but the high-pressure fluid displacement would increase. The center nozzle’s jet velocity is 200 m/s and the radius is 8 mm, the combination of two vertical edge nozzles and a center tilt nozzle or that of a vertical edge nozzle and a center tilt nozzle would provide a flow structure favorable for drilling. The angle of inclination is 10o. To take advantage of high pressure jet energy to improve the efficiency of drilling, it is important to select a suitable nozzle combination according real conditions. Key words: Rate Of Penetration (ROP), rock breaking, high pressure jet, nozzle, combination, numerical simulation, energy use
Introduction High pressure jet assisted drilling technology is an effective way to improve deep penetration rate[1-3]. In recent years, China National Petroleum Corporation (CNPC), Sinopec, China University of Petroleum (East China) and a number of other institutions devoted their effort on studies of pressure intensifier, with research installations including static pressure pressurezing unit, centrifugal down-hole pressurizing unit, jet flow type pressurizing unit, and anti-vibration pressurizing unit, involving a great number of technological breakthroughs. In a near future, the domestic pressure intensifier will be available for industrial applications[4-11]. But now, further studies are necessary to improve the efficiency of direct cutting or assisted rock breaking, where the submerged jet flow structure under high pressure is an important issue.
* Biography: ZHANG Yu-ying (1961-), Male, Ph. D. Candidate, Senior Engineer Corresponding author: REN Jian-hua, E-mail: [email protected]
Ultra-high pressure dual channel bit is an indispensable tool, where the conventional drilling fluid may be combined with high pressure drilling fluid to break hard rock. A high pressure tube is added to the conventional bit, with its upper end connecting to the pressure booster pump and the lower end connecting to the high pressure channel and nozzle. A high pressure jet can be generated to cut the rock, assisting the process of breaking rock. How to combine the high pressure nozzle with the conventional nozzle is an important factor which affects the efficiency of high pressure jet. In order to make full use of the high pressure jet to break the rock, a good understanding of the characteristics of the flow is necessary. Due to the high pressure, it is difficult to directly measure the flow field. Based on theoretical models, numerical simulations and analyses are effecttive[12,13]. This article proposes a bottom-hole flowing field calculating model for different nozzle combinations. Based on the analysis of simulated results, some significant conclusions are obtained, which can serve as a useful reference for nozzle design.
385
1. Mathematical model and numerical method 1.1 Governing equations Steady flow is assumed and the effect of fluid viscosity outside the boundary layer is ignored, because under the high-speed condition, the fluid viscocity is not a main concern. The change of fluid density is also ignored[14-20], as in ultra-high pressure condition, when the pressure reaches 100 MPa, water density is 1050 kg/m3, which is no more than 5% increase and can be ignored. Therefore the constant incompressible flow can be described by basic equations as follows. p = p( ρ , S )
(1)
and the equation of continuity
∂p + ρ a 2 ∇ui = 0 ∂t
(2)
The standard k − ε turbulence two-equation model is used, where Boussinesq assumption can simplify the calculation. Using the standard k − ε equation, the turbulent kinetic energy and the dissipation rate can be obtained by the following equations:
ρ
μt Dk ∂ ª§ = «¨ μ + σk Dt ∂xi «¬©
· ∂k º » + Gk + Gb − ρε − Ym ¸ ¹ ∂xi ¼»
ρ
μt Dε ∂ ª§ = «¨ μ + Dt ∂xi «¬© σε
· ∂ε º ε » + C1ε ( Gk + C3ε Gb ) − ¸ x k ∂ ¹ i ¼»
C2 ε ρ
ε2 k
in Eq.(3) is the same as before. In Eq.(4), C1ε , C2ε , Cμ , σ k and σ ε are empirical constants, determined by testing: C1ε = 1.43 ,
C2ε = 1.92 , Cμ = 0.09 , σ k = 1.0 and σ ε = 1.3 . 1.2 Numerical calculation methods The SIMPLE method proposed by Patankar and Splading is used to solve the coupling equations of the semi-implicit method, with the pressure correction term removed. For volume discretization, the finite volume method is used. The basic idea is as follows. The entire computational domain is divided into a number of control volumes, so that each node is surrounded by a control volume. Carrying on the integration for all differential equations, the equations for a set of nodes are obtained. The discrete equation on the control volume for the dependent variables is then obtained. 1.3 Calculation model Supposing that the bit bottom surface and the bottom hole are in two parallel planes, and the bit body has four holes. 2 to 4 nozzles can be arranged at the bit. The ratio of the diameter of the edge nozzle to that of the center nozzle is 0.62. The diameter of the center nozzle is 8 mm and that of the edge nozzle is 5 mm. The angle between edge nozzles is 120o, evenly distributed in the bit body, as shown in Fig.1.
(3)
(4)
In Eq.(3), Gk means the turbulent kinetic energy, as an additional item caused by the average velocity gradient Gk = μt S 2
where 1 § ∂u ∂u j · S ≡ 2Sij Sij , Sij = ¨ i + ¸ 2 ¨© ∂x j ∂xi ¸¹
Gb represents buoyancy generated additional items and the compressible turbulence dissipation rate Ym
Fig.1 Flow calculation diagram of the bottom
Because the model is not symmetrical, the entire flow field is considered. The calculated region ranges from the nozzle inlet to the annular outlet. Except a dense grid at the nozzle entrance, the grids in other regions are uniformly distributed. Cooper method is used to generate a non-structural grid system. The entire flow field in the region is divided into 48 000 hexahedral cells with a total of 53 000 nodes. Simulation cases for nozzle combinations are shown in Table 1. In the combinations, the edge nozzle is used for rock breaking and the center nozzle is mainly used for increasing drilling fluid displacement, and cleaning bottom hole and bit.
386
Table 1 List of composite structures of nozzles Combinations (a)
Nozzle diameter (mm)
Jet velocity (m/s)
Angle (o)
Serial number
Center
Side
Center
Side
Center
Side
Center
Side
Spray distance (mm)
1
-
3
-
5
-
400
-
0
50
2
1
3
8
5
400
400
0
0
50
3
1
3
8
5
200
400
0
0
50
4
1
2
8
5
200
400
0
0
50
5
1
2
8
5
200
400
10
0
50
6
1
1
8
5
200
400
10
0
50
7
1
1
8
5
200
400
0
0
50
8
-
2
-
5
-
400
-
0
50
1.4 Boundary conditions The fluid boundary is the outlets of nozzles. The annular space between the bit and the wall is the outlet boundary for the flow field. The entire flow within the solid boundary allows no heat transfer, the roughness is 0.5, and the wall is assumed to be smooth[21]. The bit body does not rotate, so the bit boundary is the same as other solid-wall boundaries and is a non-slip solid wall boundary. The direct impact by the jet in the bottom boundaries generates a thin overflow layer in the bottom hole. The velocity distribution is not easy to be obtained. Meanwhile, different combinations of the nozzles make the flow more complex. Therefore, based on a reasonable division of the grid, the side wall velocity on the bottom is assumed to have the logarithmic distribution. U∗ =
1 ln ( Ey ∗ ) k
and speed coincidence items, the SIMPLE algorithm is used, and for the turbulent flow kinetic energy and the turbulent flow dissipation rating, the first-order upwind scheme is used. On this basis, the calculation remainders are monitored in the calculation process by ploting curves, such as for continuity equation, velocities in x , y , z directions, k and ε . The calculation remainder curve should tend to an equilibrium point, or reach a preset value, which means that the results converge.
(5)
In this article, when the dimensionless wall distance y ∗ > 11.225 , the logarithmic distribution is used. When y ∗ < 11.225 , the stress-strain relationship of laminar flow is used with U ∗ = y ∗ . 1.5 Numerical solutions In the iterative calculation process, the pressure operations are to keep the pressure within the annular wall always an atmospheric pressure, that is, the flow field under normal pressure. Jet exit sections are circular. Because the submerged jet structure is independent, the jet Reynolds number has no effect on the jet structure. The governing equation is the explicit steady-state three-dimensional navier-stokes equation. In order to obtain an accurate result, the relaxation factor method is used for the pressure, momentum, turbulent kinetic energy and turbulent dissipation rate. Different discretization methods are used for different arameters. For the momentum item the first-order upwind scheme is used, for the pressure
Fig.2 Velocity vector diagram (b) and pressure contours (c) on the bottom section
2. Analyses of simulation results The velocity distribution, which is related to the efficiency of rock breaking, bottom hole cleaning and wall stabilization, is an important indicator in the study. Jet impacts the bottom hole to produce a high pressure gradient. Under the unbalanced force moment, the debris turns over and trundles and then is carried into the annulus. The force of the bottom
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overflow on the debris is also helpful for bottom hole cleaning[15]. Therefore, the pressure distribution on the bottom hole is important in the whole process. The study of different combinations of nozzles will be based on the flow velocity distribution and the pressure distribution. 2.1 The combination of three vertical edge nozzles In this combination, three straight nozzles are on the bottom of the bit. The angle between the nozzles is 120o. The nozzles are located in the middle of radii with diameter of 5 mm. Jet velocity is 400 m/s. From Figs.2(a), 2(b) and 2(c), it can be seen that three jets flow into the bottom to generate three distinct fan-shaped regions. The tangential velocity at the boundary is 0. But the fluid keeps flowing, therefore, is forced to spread out. At the bottom center, the overflow stops. In the region between the edge nozzle and the wall, the overflow velocity is large, but without much indication of vortex. In the bottom center, three jets impact the bottom and spread out. The jets in the bottom push one another, so that the fluid is forced upward to form a strong vortex area. Rock debris will be in a repeated movement in the region, unable to leave the bottom and go into the annular space, which is not good for cleaning the borehole. Vortex is not clearly seen in the region between the edge nozzle and the wall. A high overflow rate will produce a strong wall erosion effect. In view of rock breaking, the jets with ultrahigh pressure deal with the outer edge of the bottom, because for a large amount of rock, a large amount of hydroelectric energy is required[16], where high pressure edge nozzle structure is appropriate. 2.2 The combination of three vertical edge nozzles and a center nozzle In this combination, a center nozzle is added besides of the edge nozzles, with diameter of 8 mm. It was shown that the velocity of the center nozzle would influence the bottom flow field[17]. Figure 3 is a comparison of the bottom hole pressure distribution under different central nozzle jet velocities, where D is the radial distance, P is the bottom hole pressure.
Fig.3 Radial bottom pressure distributions
As can be seen from the figure, the center nozzle jet velocity has a great influence on the pressure distribution of the bottom hole flow field. When the center nozzle jet velocity is increased from 200 m/s to 400 m/s, the pressure of the bottom center increases from 20 MPa to 80 MPa and the edge nozzle pressure drops from 70 MPa to 60 MPa. It is because the pressures produced by the center nozzle and the edge nozzle’s jet diffusion towards the center are interacted. When the center nozzle velocity is decreased, the jet diffusion offsets a part of the bottom hole pressure, when the center nozzle velocity is increased, the overflow layer disappears and the overflow layer produced by the center nozzle would interfere with the pressure of the edge nozzle. This indicates that the increase of the center nozzle outlet pressure would reduce the edge nozzle pressure. In view of rock breaking, the outer boundary volume is to be larger than that at the center and would consume more energy. Therefore, the jet of the center nozzle should go the same way as that of the edge nozzle. The jet velocity of the central nozzle should be smaller than that of the edge nozzle. The main purpose is to increase the displacement to clean the bottom hole. Based on this consideration, the center jet nozzle outlet velocity is 200 m/s. Figures 4(a) and 4(b) show the velocity vectors and the pressure isoclines of the bottom cross section. A comparison with Fig.2 shows that the presence of the center nozzle makes a great difference for the bottom center flow field. The center nozzle jet pushes the fan-shaped dividing line in the fluid obviously outward. The pressure isoclines of the bottom center obviously bend outward. This is mainly because the center nozzle jet prevents the diffusion of the edge nozzle jet, which makes its energy concentrated in the boundary part.
Fig.4 For the combination of four nozzles, the bottom horizontal velocity vector profile (b) and pressure contours (c)
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Figure 4(b) shows that the center nozzle and the edge nozzle jointly produce strong vortexes, in the complex flow field, which can also be found in the middle of both sides of the nozzle jet, due to the role of the central suction nozzle, where the fluid does not reach the boundary. The flow structure can reduce the erosion of the wall to avoid the well eyes expansion, which is beneficial. But for the kind of high-pressure fluid flow under a large displacement, a high pressure pump is required. 2.3 The combination of two edge nozzles and a central nozzle For the combination of two edge nozzles and a vertical center nozzle, as well as that of two edge nozzles and a inclined center nozzle, the bottom hole pressure distribution is shown in Fig.5.
and longitudinal section and the pressure contour map are shown in Fig.6.
Fig.6 Bottom profile horizontal velocity vector (b) and pressure contour map (c)
Fig.5 Bottom hole pressure distribution under different nozzle angles
The inclined nozzle pressure is smaller than that of the vertical nozzle. This is mainly because the overflow increases the thickness of the bottom layer and the maximum overflow velocity is increased. Therefore, with the decrease of the vertical impact velocity, the impact pressure is reduced. Also, the pressure on the wall near the inclined central nozzle will increase. The interpretation of the phenomenon may be as follows: after the overflow impacts the wall, the overflow rate around the wall is decreased, to generate a pressure stagnation zone and thus increase the pressure. The inclined nozzle tends to increase the overflow rate, which is beneficial for the bottom hole cleaning, but not good for the well-bore stability. When the actual bottom wall is not perpendicular to the plane, this disadvantage can be avoided and wall stability problem no longer exists. From the point of view of bottom hole cleaning, the inclined center nozzle is better than the vertical one. Therefore, the combination of two edge nozzles and a center tilt nozzle is worth a further study. The diameter of the center nozzle is 8 mm, with the outlet velocity of 200 m/s, and the diameter of the edge nozzles is 5 mm, with the outlet velocity of 400 m/s. The horizontal velocity vectors on the bottom well crosswise section
It can be seen that the bottom flow field is divided into three irregular fan-shaped regions. The pressure contours also tend to one side. The tilt center nozzle’s overflow area is increased, which is beneficial to cleaning the bottom hole. From the point of view of rock breaking, two high pressure edge nozzles can break the rock, at the same time, can also clean the bottom and cool the bit. From Fig.6(c), it can be seen that for the inclined center nozzle, the vortex is not obvious on the tilt side. Fluid moves quickly into the annular, reducing the fluid circulation path. Therefore, the combination of two edge nozzles and a center tilt nozzle is ideal.
Fig.7 Bottom hole pressure distribution with different nozzle number
2.4 Other nozzle combinations Because of the limitation of the down-hole flow boosting device, it is not practical to use too many nozzles. It would be desirable to reduce the nozzle number and at the same time to achieve the same
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effect. Therefore, we will consider the bottom-hole flow field of a combination of the two nozzles. Figure 7 gives a comparison of the pressure distribution between the combinations of two nozzles and that of two edge nozzles and a center nozzle. Figure 7(a) is the combination of two edge nozzles and a center nozzle. Figure 7(b) is the combination of an edge nozzle and a center nozzle. Figure 7(c) is the combination of two edge nozzles. Curves are for pressure values at the bottom center of the edge nozzle. As can be seen from the figure, the pressure distribution curves of 7(a) and 7(b) are similar. But the pressure of two edge nozzles is slightly lower than that of one edge nozzle, whereas the bottom center pressure does not change significantly. It is because that two edge nozzles locate a certain distance apart, and the initial jet segments do not overlap each other. But the overflows have some mutual interference so that the jet’s impact is decreased, reducing the efficiency of rock breaking. From this point of view, using one edge nozzle is better than using two. The impact pressure of the combination of one edge nozzle and one center nozzle is basically the same as that of a center nozzle and two edge nozzles. 3. Conclusions (1) Different combinations have different bottom high pressure flow fields. The process of breaking rock is also different. (2) The combination of three edge nozzles has a good efficiency in rock breaking. The jet velocity is 400 m/s with the radius of 5 mm. But it is inefficient in cleaning the bottom hole, which would result in serious erosion. The combination can be used for hard ground, where there is no problem of instability formation such as hole enlargement and chipping. (3) The combination of three edge nozzles and a center nozzle is good for cleaning and reducing the erosion of sidewall. The added noozle’s jet velocity is 200 m/s with the radius of 8 mm. But it requires a large high-pressure displacement, a high demand on the equipment. (4) For the combination of two edge nozzles and a center nozzle, the center nozzle tilted 10o is beneficial for bottom cleaning and breaking rock efficiency. It will not affect the stability of wall. The flow field structure is ideal. (5) For the combination of two nozzles, an edge nozzle and a center nozzle tilted 10o is more efficient than the combination of two edge nozzles in rock cleaning and wall stability. (6) Making a full use of high pressure jet energy improves the efficiency of drilling, with an appropriate choice of the nozzle combination according to the actual conditions.
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