The transportation in vertical pipelines of particle slurry of oil shale has important applications in several fields (marine mining, hydraulic mining, dredging of river reservoir, etc.). However, there is still a lack of information about the behavior of coarse particles in comparison to that of fine particles. For this reason, experiments on the fluidization and hydraulic lifting of coarse oil shale particles have been carried out. The experimental data for three kinds of particles with an average size of 5 mm, 15 mm and 25 mm clearly demonstrate that vortices can be formed behind the particles. On this basis, a vortex resistance factor K is proposed here to describe this effect. A possible correlation law is defined by means of a data fitting method accordingly. This law is validated by an experiment employing particles with an average size of 3.4 mm. The vortex resistance factor K results in a reduction of the speed of solid particles and an increase in the sliding speed as well as a decrease in the hydraulic gradient. As a result, using this factor, the calculation of the solid particle speed and hydraulic gradient can be made more accurate with respect to measured values.

Due to the significance of energy, many countries around the world are exploring the safe and high efficient mining and transportation methods. Oil and gas resources buried in underground and submarine are the future energy for human beings. The vertical lifting technology with multiphase flow of these fuels has become a hot research topic for many scholars [

The general layout of the tested loop pipeline is shown in

In the loop pipe line, the fluidization section is acrylic transparent pipe with a length of 1.8 m and a diameter of 0.1 m. A piece of metal screen is set at the upper and lower parts respectively. The diameter of the hydraulic rising section is 0.036 m and the length is 4 m. There is a transparent acrylic pipe of 1.5 m within this hydraulic rising section to facilitate the use of high-speed camera to take particle motion images. Magnetic flow meter is used to measure water velocity before liquid and solid are mixed.

The coarse oil shale particles with density ranging from 1895 kg/m^{3} to 1900 kg/m^{3} are used in the fluidization and hydraulic lifting experiment. The average compressive strength of oil shale is 49.2 MPa, while the proctor hardness coefficient is 4.7. The particles have tough surface and are not easy to be broken. The average oil content is about 5.5%. The organic components of oil shale are mainly C, H, O. The main inorganic components and elements of N and S are clay and siltstone. Oil shale particles were processed by a sand mill to be approximately spherical shape. These particles prepared for fluidization experiment were divided into three groups by self-made metal sieve. Each group is narrow graded particles, and particle size ranges were 4.8 mm~5.2 mm, 14.2 mm~16.4 mm and 24.1 mm~26.2 mm with average particle size of 5 mm, 15 mm and 25 mm respectively. In hydraulic lift pipe section in

Firstly, the fluidization experiment is carried out. The coarse oil shale particles of 80 mm–100 mm thickness are placed on the metal screen, and the water speed is gradually increased through the frequency conversion motor driving centrifugal pump. When the particle layer on the metal screen disappears, the flow state changes from granular bed to movable bed. At this point, fluidization is achieved. After the flow state stabilizes for 15 min, the height of solid particles and the velocity water are recorded. This process should be repeated for 3~4 times. Then, the average value will be taken. The flow rate of water is raised gradually to achieve the fluidization at different particle concentrations. The corresponding water speed _{m} and height of suspended bed _{b} are recorded. Through the above steps, 21 groups of experimental data of coarse oil shale particle fluidization with an average particle size of 5 mm, 15 mm and 25 mm were obtained.

Secondly, the coarse oil shale particles hydraulic lifting experiment is carried out. The test pipe section is shown in vertical pipe lifting section of _{s} and concentration _{s} are obtained by integrating concentration _{s}. The average water velocity _{m} can be achieved from the magnetic flow meter.

In the fluidization experiment, the average local concentration of particles ranges from 3%~30%, and the average water velocity ranges from 0.172 m/s~0.763 m/s. In the vertical lifting experiment, the average local concentration of particles ranges 3.08%~25.7%, and the flow velocity of pump outlet ranges 1.84 m/s~2.6 m/s. As shown in

_{m} |
_{b} |
_{b} |
_{Di}_{hi} |
_{b} − (_{Di} + _{hi}) |
|||
---|---|---|---|---|---|---|---|

(ms^{-1}) |
(m) | (^{-1}) |
(10^{-4}N) |
(10^{-4}N) |
(10^{-4}N) |
||

0.05 | 0.172 | 0.182 | 0.2457 | 7.5622 | 7.9230 | –0.3608 | 0.9308 |

0.05 | 0.236 | 0.309 | 0.2868 | 7.5622 | 7.0100 | 0.54516 | 1.1749 |

0.05 | 0.30 | 0.557 | 0.3326 | 7.5622 | 6.8507 | 0.7034 | 1.3801 |

0.05 | 0.313 | 0.627 | 0.3428 | 7.5622 | 6.9180 | 0.6447 | 1.4002 |

0.05 | 0.341 | 0.929 | 0.3236 | 7.5622 | 7.0420 | 0.5204 | 1.4678 |

0.05 | 0.361 | 1.129 | 0.3792 | 7.5622 | 7.1120 | –7.2789 | 1.5238 |

0.05 | 0.382 | 1.778 | 0.3942 | 7.5622 | 6.4578 | 0.10438 | 1.5812 |

0.15 | 0.205 | 0.150 | 0.3477 | 204 | 300 | –96 | 0.6605 |

0.15 | 0.302 | 0.206 | 0.4409 | 204 | 204 | 0 | 1.0051 |

0.15 | 0.381 | 0.355 | 0.4663 | 204 | 176 | 28 | 1.3300 |

0.15 | 0.464 | 0.481 | 0.5376 | 204 | 176 | 28 | 1.4923 |

0.15 | 0.487 | 0.584 | 0.5490 | 204 | 174 | 30 | 1.5949 |

0.15 | 0.535 | 0.719 | 0.5872 | 204 | 176 | 28 | 1.7078 |

0.15 | 0.642 | 1.784 | 0.6667 | 204 | 188 | 16 | 1.9518 |

0.25 | 0.294 | 0.160 | 0.3053 | 945 | 926 | 19 | 1.0282 |

0.25 | 0.362 | 0.205 | 0.5042 | 945 | 827 | 118 | 1.2141 |

0.25 | 0.453 | 0.275 | 0.5741 | 945 | 747 | 198 | 1.5195 |

0.25 | 0.492 | 0.330 | 0.5985 | 945 | 732 | 213 | 1.6040 |

0.25 | 0.687 | 1.030 | 0.7285 | 945 | 731 | 214 | 2.5682 |

0.25 | 0.732 | 1.230 | 0.7689 | 945 | 746 | 199 | 2.6576 |

0.25 | 0.763 | 1.780 | 0.7890 | 945 | 694 | 91 | 2.8528 |

It is considered that the frequency stands the probability of particle appearance-the volume ratio of particle at this position. The specific method is to sample the particle binary image along the radial position, count the number of particles appearing, and get the frequency of particles in each radial position.

In this experiment, the water isolation piercing device is used to avoid excessive particles from entering the plastic pipe. The pressure difference between two points can be directly read by the U-type differential meter. When a certain amount of solid particles is deposited in water tank, particles can be released through the particle exit. The formula of hydraulic gradient _{m} can be defined as follows:

where _{m} and

In the test, the oil shale particles do not need to pass through pump. The particle size remains unchanged in the test.

According to the existing results of relevant scholars, there are four forces acting on a single particle when the particles in the slurry are in fluidization state within the experimental tube in _{G}), the buoyancy of fluid on particle (_{B}), resistance from liquids (_{Di}) and interference force from other particles (_{hi}). Usually, the difference between particle gravity and buoyancy (_{G}_{B}) is called particle effective gravity (_{b}). When the particles are in a stable state, the force balance equation can be expressed as follows:

The formulas of the three forces in

Submitting the experimental data into _{m}) show a positive correlation, meanwhile the former is obviously larger than the latter. The calculation results listed in _{b} − (_{Di} + _{hi}) is positive in most cases, which shows that the factors considered in

The fluidization force of the particles is shown in _{vi}) behind the particle, playing a resistance role on the particle, as shown in _{vi}) is more complicated. In order to simplify the problem, _{hi} is used to replace the interference force (_{hi}) and vortex resistance (_{vi}), which is shown in _{hi} is slightly different from that of fluidization stage. The coefficient

Therefore, the particle force balance equation for the stable fluidization state is defined as [

Thus,

The vortex force factor in _{m}) show a positive correlation.

According _{b}, _{Di} and _{hi}) are the particle size (_{m}), water density (_{s}). The particle density of oil shale in this experiment is almost constant. Hence, it can be concluded that the vortex force resistance factor (_{m}/(g^{0.5}),

Therefore, the expression of the vortex force resistance factor (

The value of

The confidence for fitting of

Combining

During the vertical transport process of coarse-grained slurry as shown in

The _{D} and _{hi} will become _{D} and _{h} in the mean sense, which are functions of slip velocity _{slip} and average concentration

where _{h}_{Dr} is resistance coefficient based on _{w} − _{s} [_{;} _{w} and _{s} are the velocities of water and particles after momentum exchange between water and particles, respectively.

According to the _{w} − _{s}) in the pipeline can be obtained using the iterative method if _{m} are known.

Considering the momentum exchange between liquid and solid and additional pressure of solid particle acceleration, and the following equation exists [

where _{s/}_{a} is the acceleration distance of solid particles and _{a} and

According to the flow balance, there exists the following relationship:

In _{m} is the velocity of clear water, which equals average slurry velocity. It can be measured by magnetic flow meter in _{s} = 0 for fluidization experiment pipe section.

By using _{w}, _{s}, and

When the water flow in the pipeline is in a turbulent state, the hydraulic gradient can be expressed as:

where:

Obviously, _{m}) after the intervention of solid particles. Therefore, the hydraulic gradient caused by the slurry velocity of (_{m}) in the pipeline can be considered to be the hydraulic gradient of the clear water flowing in the pipeline at the speed of _{s} and _{w} can be achieved. Bring

Calculation process of flow parameters including _{w}, _{s,} _{slip} and _{m} is shown in

In above process, the initial value of _{slip} is 0.001 m/s and the step size is 0.001 m/s when calculating _{slip} by iterative calculation of

The calculated results of particle velocity (_{s}), slip velocity (_{slip}) and hydraulic gradient _{m} for coarse particle slurry in vertical pipe are shown in

The effect of vortex force resistance factor (

Effect of vortex force resistance factor (_{m}) without considering vortex force resistance factor is larger than that of measured value, and the maximum deviation of the two is 15.26%. The calculated hydraulic gradient (_{m}) considering vortex force resistance factor is also larger than that of measured value, and the maximum deviation of the two is 9.79%. It can be implied that the calculated value of hydraulic gradient without considering vortex force resistance factor is too large, while after considering vortex force resistance factor will be closer to the measured value.

In summary, the vortex resistance reduces the calculated value of particle velocity (_{s}) and hydraulic gradient, while increases the slip velocity (_{slip}). The calculated particle velocity and hydraulic gradient are closer to the measured ones when the vortex resistance is considered.

_{slip}) and resistance factor (_{m} = 1.84 m/s is higher than that of high water velocity _{m} = 2.15 m/s. The resistance factor (_{m}), which is consistent with the law in

_{slip}) and resistance factor (_{m}) is 2.3 m/s and 2.6 m/s, respectively. In the figure, the slip velocity of the two kinds of flow velocity is much close.

The above two figures illustrate that the smaller the water flow velocity (_{m}), the greater the slip velocity. When the flow velocity is greater than 2.3 m/s, the flow velocity has little effect on the slip velocity. The larger the flow velocity (_{m}), the greater the value of resistance factor (

_{m}) on slip velocity (_{slip}) and resistance factor (

The force state of the fluidized bed with coarse oil shale particles is calculated and analyzed. The traditional force balance is defective for coarse particle oil shale slurry. There is a vortex resistance behind the particle. The vortex resistance factor

Theoretical calculation models of several flow parameters with influence of vortex resistance are given. The calculated results of the proposed model show that after considering vortex force resistance factor

The author sincerely thanks the school colleagues and the leaders at all levels at Liaoning Technical University, as well as the help and collaboration of Pipeline Engineering Institute of Wuhan Design and Research Institute of China Coal Technology and Engineering Group in the pipeline experiment and writing process of this article.

Particle size, (m);

Pipe diameter (m);

_{G}:

Solid particle gravity, (N);

_{B}:

Buoyancy of fluid on particle, (N);

_{Di}:

Resistance on particle from liquids, (N);

_{hi}:

Interference force from other particles (N);

_{vi}:

Vortex resistance (N);

Froude number (-);

Acceleration of gravity (m/s²)

Pressure difference (m);

_{m}:

Friction resistance, (mH_{2}O/m);

Vortex force factor (-);

Distance between connection points of mercury differential pressure gauge (m);

_{a}:

Acceleration distance of solid particles (m);

Water density (kg/m^{-3});

_{s}:

Solid density (kg/m^{-3});

Local concentration,

Particle concentration in tube;

_{m}:

Average water velocity (m/s);

_{s}:

Mean Velocity of particle after momentum exchange between water and particles (m/s);

_{slip}:

Slip velocity (m/s);

_{w}:

Mean Velocity of water after momentum exchange between water and particles (m/s);

Coefficient;

Darcy resistance coefficient (-).