Effect of different port diameter and cone angle at various conditions was calculated to evaluate the optimum design for higher pressure at outlet.
Effects of different port diameters and cone angles
The various port diameters which are analysed are 0.09 inch, 0.125 inch and 0.155 inch. The cone angles used are 45°, 30° and 15°. The effects of these parameters on the outlet pressure, outlet mass flow rate and outlet velocities are studied for all the three design configurations.
Outlet pressure comparison
Figure 8 shows the plot to compact the results for all the nozzle configurations (i.e. 1port@0°_6ports@30°, 1port@0°_4ports@90°, 1port@0°_4ports@45°) with port diameter on the x-axis, the outlet pressure on the y-axis and the cone angle on the secondary y-axis. The yellow-coloured line indicates the cone angle, and the grey, orange and blue plot lines differentiate between the different port angles, i.e. 30°, 90° and 45°. After observing the results, it is noted that at the highest port diameter of 0.155 inch the pressure at the outlet is the highest, whereas the outlet pressures are in the same range in the lower 0.125 inch and 0.009 inch port diameters. Cone angle of 45° gives the best pressure results at the outlet. Cone angle of 30° gave intermediate results. Low pressure at outlets is recorded at a cone angle of 15°. Therefore, as we increase the cone angle the outlet pressure increases. Looking at the nozzle performances, 1port@0°_6ports@30° configuration performs exceedingly well and gives the highest pressures at outlet followed by 1port@0°_4ports@90° configuration, and 1port@0°_4ports@45° configuration records the lowest outlet pressures.
Table 5 shows the evaluation of various combinations of design for obtaining the required outlet pressure at various inlet pressures. Analysis of different designs shows that optimum pressure is obtained for a 0.155 inch port diameter, 45° cone angle and 30° port angle, while the performance of the nozzle decreases with a port diameter of 0.009 inch, a cone angle of 15° and a port angle of 45°. As the port angle increases to 90°, the port diameter of 0.125 inch and the cone angle of 30° cause an intermediate upsurge in the outlet pressure.
Table 5 Effects of port diameter, cone angle and port angle on outlet pressure Outlet velocity comparison
Figure 9 shows the plot for all the nozzle configurations (i.e. 1port@0°_6ports@30°, 1port@0°_4ports@90° and 1port@0°_4ports@45°) with port diameter on the x-axis, the outlet velocity on the y-axis and the cone angle on the secondary y-axis. The yellow-coloured line indicates the cone angle, and the grey, orange and blue plot lines differentiate between the different port angles, i.e. 30°, 90° and 45°. As can be seen that the outlet velocity decreases from 0.009 inch port diameter to 0.155 inch port diameter, nozzles with port angle of 45° undergo an increase in velocity with an increase in the port diameter. But, on the whole there is a clear fall in the outlet velocity with an increase in the port diameter. Cone angle of 15° records a low outlet velocity throughout, whereas the outlet velocities for 30° and 45° cone angles are in close approximation to each other. On an average, the nozzles with 60° port angles give the highest velocities. The plot indicates that the outlet velocity for 60° port angle decreases below the nozzles with 45°/90° port angles as the port diameter increases from 0.125 to 0.155 inch. In totality, the 1port@0°_6ports@30° configuration with an outlet velocity range of 1100–400 m/s gives the best results, followed by 1port@0°_4ports@90° configuration ranging from 1000 to 300 m/s, and a low 800–200 m/s range is obtained for the 1port@0°_4ports@45° configuration.
There are some cases during fill removal where higher velocity is required rather than higher pressure. Table 6 shows the evaluation of various combinations of design for obtaining the required outlet velocity at 4000–8000 psi pump pressure. Analysis of different designs shows that optimum velocity is obtained for a 0.009 inch port diameter, 30° and 45° cone angles and 30° port angle, while the performance of the nozzle decreases with a port diameter of 0.155 inch, a cone angle of 15° and port angles of 45° and 90°.
Table 6 Effects of port diameter, cone angle and port angle on outlet velocity Outlet mass flow rate comparison
Figure 10 shows the plot for all the nozzle configurations (i.e. 1port@0°_6ports@30°, 1port@0°_4ports@90° and 1port@0°_4ports@45°) with the port diameter on the x-axis, the outlet mass flow rate on the y-axis and the cone angle on the secondary y-axis. The yellow-coloured line indicates the cone angle, and the grey, orange and blue plot lines differentiate between the different port angles, i.e. 30°, 90° and 45°.
There is an increase in the mass flow rate from about 50GPM to around 150GPM. This increment is due to the increase in port diameter from 0.009 to 0.155 inch. The larger the port area, the larger the volume flowing through it, which will increase the mass flow rate. Interestingly, the configuration 1port@0°_6ports@30° gives lower outlet flow rates (75–25 GPM) than the other two configurations. On an average, the highest flow rates are recorded by the nozzles with 90° port angle ranging from 175 to 25 GPM, followed by the 1port@0°_4ports@45° configuration ranging from 150 to 25 GPM. The cone angle of 45° gives the highest outlet flow rate followed by 30° and 15°, although cone angles of 45° and 30° have very close flow rate values. Once a large amount of fill material is accumulated in the wellbore, a higher mass flow is required to suspend that amount of material. Table 7 shows the evaluation of various combinations of design for obtaining the required outlet mass flow rate at various inlet pressures. Analysis of different designs shows that optimum mass flow rate is obtained for a 0.155 inch port diameter, 45° cone angle and 30°, 45° and 90° port angles.
Table 7 Effects of port diameter, cone angle and port angle on outlet mass flow rate Effects of different nozzle inner diameters and total nozzle length
Effect of various nozzle inner diameters (0.65 inch, 0.75 inch and 1 inch) is analysed. The total nozzle length is 1.562 inch, 2.125 inch and 3.125 inch. The effects of these parameters on the outlet pressure, outlet mass flow rate and outlet velocities are studied for all the three design configurations.
Outlet pressure
Figure 11 presents the results of outlet pressure at all nozzle configurations (i.e. 1port@0°_6ports@30°, 1port@0°_4ports@90° and 1port@0°_4ports@45°) with the total nozzle length (1.562 inch, 2.125 inch and 3.125 inch) on the x-axis, the outlet pressure on the y-axis and the nozzle inner diameter on the secondary y-axis. The yellow-coloured line indicates the nozzle inner diameter (0.65 inch, 0.75 inch and 1 inch), and the grey, orange and blue plot lines differentiate between the different port angles, i.e. 30°, 90° and 45°. Nozzles with port angle of 45° do not give high outlet pressures at 4000 PSI inlet pressure. It is clear that the 1port@0°_6ports@30° configuration achieves the highest outlet pressures out of the three, followed by nozzles with port angle of 90°. At a nozzle inner diameter of 1 inch, the pressure drops to a lower value, whereas as the nozzle ID decreases from 1 inch to 0.75 inch and 0.65 inch the outlet pressure rating increases. The outlet pressure values are evidently higher with smaller nozzle length of 1.562 inch, but there is a very less difference in the outlet pressure with 2.125 inch. The pressure recorded with 3.125 inch of nozzle length is the lowest, especially for nozzles with 45° and 90° port angles. The nozzle with 60° port angle has the best performance throughout.
As shown in Fig. 12, the high output pressures are achieved with a 60° port angle followed by nozzles with an output angle of 90°, with 45° port-oriented nozzles giving low pressure values at the output. The 1-inch ID nozzle gives low output pressures, while 0.625-inch ID nozzle gives a high dominant output pressure rating. The nozzle length of 1.562 inch gives the highest pressures at the outlet and is clearly represented on the graph. It is followed by a nozzle length of 2.125 inch, and the lowest values are reached by a nozzle length of 3.125 inch. This clarifies that the nozzles with a small nozzle length and the diameter of the nozzle with an orifice angle of 30° give the best nominal pressure at the outlet. Table 8 shows the evaluation of various combinations of design for obtaining the required outlet pressure by varying total nozzle length, nozzle ID and port angle at 4000–8000 psi pump pressure.
Table 8 Effects of total nozzle length, nozzle id and port angle on velocity Outlet velocity
Figure 13 shows the outlet velocity of all the nozzle configurations (i.e. 1port@0°_6ports@30°, 1port@0°_4ports@90° and 1port@0°_4ports@45°) with the total nozzle length (1.562 inch, 2.125 inch and 3.125 inch) on the x-axis, the outlet velocity on the y-axis, and the nozzle inner diameter on the secondary y-axis. The yellow-coloured line indicates the nozzle inner diameter (0.65 inch, 0.75 inch and 1 inch), and the grey, orange and blue plot lines differentiate between the different port angles, i.e. 30°, 90° and 45°. At an inlet pressure of 4000 PSI, nozzle length of 3.125 inch gives lower velocity as compared to nozzle length of 2.125 inch and 1.562 inch. Nozzle length of 3.125 inch gives a velocity in the range of 900–300 m/s. Nozzle length of 2.125 inch gives a cumulatively higher velocity at the outlet. Nozzle inner diameter of 1 inch does not deviate from the trend and gives low velocity rating, whereas ID of 0.65 inch and 0.75 inch gives high outlet velocity values in the range of 1100–400 m/s. The configuration 1port@0°_6ports@30° performs well followed by nozzles with 90° port angles with values very close to the former. Nozzles with port angle of 45° have outlet velocity in the range of 700–200 m/s. Figure 13 shows that a nozzle with port angle of 60° with a total nozzle length of 2.125 inch along with a 0.65-/0.75-inch nozzle ID would give the best possible performance.
Inlet pressure of 5000 PSI gives a more uniform outlet velocity as compared to the inlet pressure of 4000 PSI. The velocity lies in the range of 1100–300 m/s for both inlet pressures as shown in Figs. 13 and 14. The highest velocities at the outlet are recorded with a total nozzle length of 2.125 inch, ranging from 1100 to 500 m/s. Nozzle length of 1.562 inch (1100–300 m/s) and 3.125 inch (1000–300 m/s) gives nearly the same outlet velocity values with 1.562 inch length being a bit higher. Nozzle inner diameter of 0.75 inch and 0.65 inch gives nearly the same high values of outlet velocity, with 0.75 inch giving a bit higher outlet velocity value. Nozzle length of 1 inch creates a sudden dip in the recorded outlet velocity values as can be seen from the plot. Again, nozzles with 1port@0°_6ports@30° configuration perform well followed by 1port@0°_4ports@90° nozzle configuration. The nozzles with port angle of 45° perform better than before but, on an average, give lower velocities at the outlet. The best performing nozzle in this case would be a nozzle with a port angle of 30° with 2.125 inch nozzle length and a 0.65 inch or 0.75 inch nozzle inner diameter.
The performance of nozzles with 45° port angle increases with increase in inlet pressure from 5000 PSI to 8000 PSI as shown in Figs. 14 and 15. In totality, the best outlet velocities resulted from nozzles with a port angle of 30°, but 90° port angle nozzles were close. The middle nozzle length of 2.125 inch achieves the highest outlet velocities in the range of 1400–400 m/s, followed by nozzle length of 1.562 inch giving outlet velocities in the range of 1300–300 m/s. Lower outlet velocities in between 1200 and 300 m/s are achieved by nozzles with a total nozzle length of 3.125 inch. Nozzle inner diameter of 1 inch lowers the outlet velocities drastically, whereas 0.65-inch nozzle ID and 0.75-inch nozzle ID give consistently higher outlet velocities. Nozzles with port diameter of 30° perform exceedingly well, followed closely by 90° port angle nozzles. Therefore, a nozzle with a 60° port angle having a 2.125 inch nozzle length with a nozzle inner diameter of 0.75 inch or 0.65 inch gives exceptionally well performance. Table 9 shows the evaluation of various combinations of design for obtaining the required outlet velocity by varying total nozzle length, nozzle ID and port angle at 4000–8000 psi pump pressure.
Table 9 Effects of total nozzle length, nozzle id and port angle on outlet velocity Nozzle selection
After examining all the simulation results, it is clear that nozzles with a port angle of 30° achieve the best performance. Therefore, selecting an appropriate nozzle for sand removal is done by selecting all the parameters which have recorded high outlet velocity, flow rate and pressure values for the 1port@0°_6ports@30° configuration, while in the case of nozzle for scale removal nozzles with port angle of 90° give the second-best performance as shown in Table 10. It gives high values to intermediate pressure, velocity and mass flow rate at output. The selections made in the previous section for the 30° port angle nozzle give optimum performance for 90° port angle.
Table 10 Selection of nozzle for sand and scale removal The optimized dimensions of coiled tubing jetting nozzle parameters for sand transport from wellbore are as follows;
- i.
Port diameter To get a high outlet pressure and mass flow rate, 0.155 inch port diameters should be used, whereas high velocity is achieved by the smaller 0.09 inch port diameter. Therefore, it can be concluded that, to achieve high pressure and rate, a higher port diameter should be used. On the other hand, a smaller port diameter creates higher velocity at the outlet.
- ii.
Cone angle The larger cone angle of 45° gives a higher value of the outlet pressure, flow rate and velocity. Therefore, during selection the higher the cone angles the better the results.
- iii.
Total nozzle length The medium nozzle length of 2.125 inch has given consistently high results at the outlet, followed closely by the smaller 1.562-inch-long nozzles. Hence, the performance of a nozzle reduces with an increase in the nozzle length and also when the length is too short.
- iv.
Nozzle inner diameter The smaller nozzle inner diameters of 0.65 inch and 0.75 inch have performed equally well, and the 1-inch ID has given low performance. Therefore, the lower the nozzle diameter, the better the performance.