Fig 1.
The wellbore model of helical flow cleanout in horizontal wells.
Fig 2.
Nozzle assembly and jet orientations of the cleanout bit.
Fig 3.
The mesh near the nozzle exits are deliberately refined so that convergence can be accelerated and more precise simulation of the flow field can be achieved.
Table 1.
Orifice Diameters of Ten Nozzle Assemblies.
Table 2.
Data Set: Simulation Conditions.
Fig 4.
Numerical simulation process.
Fig 5.
The topology of three-layer BP-ANN.
This three-layer BP-ANN has 7 inputs (operation parameters) and 2 outputs (characteristic velocity Vt and Va). The transfer functions in the hidden layer are sigmoid. And the number of neurons in the hidden layer is 10.
Fig 6.
This process is accomplished in MATLAB.
Fig 7.
Pathlines of SC-CO2 helical flow field and separate jets.
(A) Pathlines are colored by turbulent kinetic energy. The turbulent kinetic reaches maximum near the nozzle exits and attenuates as SC-CO2 flow spreads further into the annulus. The flow is from right to left at the left side of the cleaning bit, while it is left to right at the right side of the bit. (B) Pathlines are colored by particle groups. The left figure shows the process that lateral jets reach the casing wall and turn into rotational flow. The right figure displays the tracks of other three jets.
Fig 8.
Velocity contours at different axial cross sections.
(A) The flow field featured by velocity is still heterogeneous and unsteady at 0.1 m from the right side of the bit. (B) The velocity contour is annularly symmetric and thus the flow field is steady and uniformly helical.
Fig 9.
The radial distribution of Vt for SC-CO2/water flow at different cross sections.
No.8 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K. In cross sections, dimensionless radius is the distance from the inner wall to the measure point divided by the total length between inner and outer wall. The tangential velocity has large gradients near both sides of inner and outer walls.
Fig 10.
The radial distribution of Va for SC-CO2/water flow at different cross sections.
No.8 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K.
Fig 11.
The distributions of Va,avg and Vt,avg for SC-CO2/water flow along the wellbore.
No.8 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K.
Fig 12.
The distribution of Vt and Vt,avg with respect to different lateral nozzle sizes.
Lateral nozzle diameter 3mm~5mm; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K. Cleaning distance is 0.6m in the left figure.
Fig 13.
The distribution of Vt and Vt,avg with respect to different rear nozzle sizes.
Rear nozzle diameter 3mm~5mm; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K. Cleaning distance is 0.6m in the left figure.
Fig 14.
The distribution of Vt and Vt,avg with respect to different forward nozzle sizes.
Forward nozzle diameter 3mm~5mm; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K. Cleaning distance is 0.6m in the left figure.
Fig 15.
The distribution of Va and Vt,avg with respect to different flow rates.
Nozzle assembly No.1; flow rate 10 L/s~20 L/s; ambient pressure 30 MPa; ambient temperature = jet temperature = 373 K.
Fig 16.
The distribution of Vt,avg with respect to different ambient pressures.
No.1 nozzle assembly; flow rate 15 L/s; ambient pressure 10 MPa~30 MPa; ambient temperature = jet temperature = 373 K.
Fig 17.
The distribution of Vt,avg with respect to different ambient temperatures.
No.1 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; jet temperature 373 K; ambient temperature 333 K~433 K.
Fig 18.
The distribution of Vt,avg with respect to different jet temperatures.
No.1 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; ambient temperature 373 K; jet temperature 353 K~433 K.
Fig 19.
Vt, Va, Vt,avg and Va,avg with the same ambient/jet temperature difference.
No.1 nozzle assembly; flow rate 15 L/s; ambient pressure 30 MPa; AT is ambient temperature; JT is jet temperature.
Fig 20.
The plots of train, validation and test process are quite close, indicating good performance of ANN. The smallest MSE during validation is 0.0059 at epoch 206. Validation stops when MSE keeps invariable for some epochs.
Fig 21.
Error histogram.
Fig 22.
R is coefficient of determination. Target is the true velocities of the simulated flow field while output is the results of the ANN model that should approach target. Points far away from the diagonal are ‘noise’ points.
Fig 23.
Shematic diagram of BP-ANN optimization strategies.
Fig 24.
Distributions of Vt,avg, Va,avg, Vt,max and Va,max along the horizontal wellbore.
No.3 nozzle assembly; flow rate 15.4 L/s; ambient pressure 35 MPa; ambient temperature is 363 K; jet temperature is 373 K.
Fig 25.
Vt,avg and Va,avg with respect to different nozzle assemblies.
Flow rate 12 L/s; ambient pressure 25.2 MPa; ambient temperature is 336.8 K; jet temperature is 360 K; cleaning distance 1.7 m.