In oil and gas well drilling operations,it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids.In this paper,the free-falling of...In oil and gas well drilling operations,it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids.In this paper,the free-falling of 172 groups of spheres and 522 groups of irregular-shaped sand particles in Newtonian/non-Newtonian fluids were investigated experimentally.It was found that the drag coefficient calculated based on Newtonian correlations can result in a significant error when the particle settles in the non-Newtonian fluid.Therefore,predictive models of drag coefficient were established respectively for different types of fluids.The validity of the proposed drag coefficient model of spheres was verified by comparing it with the previous works.On this basis,the drag coefficient model of irregular-shaped sand particles was established by introducing a shape factor.The models do not use the shape factor that requires detailed threedimensional shape and size information.Instead,two-dimensional geometric information(circularity)is obtained via image analysis techniques.The present new models predict the settling velocity of sand particles in the power-law fluid and Herschel-Bulkley fluid accurately with a mean relative error of5.03%and 6.74%,respectively,which verifies the accuracy of the model.展开更多
The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of...The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.展开更多
The electron swarm parameters including the density-normalized effective ionization coefficients（α-η）/N and the electron drift velocities V e are calculated for a gas mixture of CF3I with N2 and CO2 by solving the...The electron swarm parameters including the density-normalized effective ionization coefficients（α-η）/N and the electron drift velocities V e are calculated for a gas mixture of CF3I with N2 and CO2 by solving the Boltzmann equation in the condition of a steady-state Townsend（SST） experiment.The overall density-reduced electric field strength is from 100 Td to 1000 Td（1 Td = 10-17V·cm2）,while the CF3I content k in the gas mixture can be varied over the range from 0% to 100%.From the variation of（αη）/N with the CF3I mixture ratio k,the limiting field strength（E/N） lim for each CF3I concentration is derived.It is found that for the mixtures with 70% CF3I,the values of（E/N） lim are essentially the same as that for pure SF 6.Additionally,the global warming potential（GWP） and the liquefaction temperature of the gas mixtures are also taken into account to evaluate the possibility of application in the gas insulation of power equipment.展开更多
The electron drift velocity, electron energy distribution function （EEDF）, densitynormalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SFs-A...The electron drift velocity, electron energy distribution function （EEDF）, densitynormalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SFs-Air mixtures. The experimental results from a pulsed Townsend discharge are plotted for comparison with the numerical results. The reduced field strength varies from 40 Td to 500 Td （1 Townsend=10-17 V.cm2） and the SF6 concentration ranges from 10% to 100%. A Boltzmann equation associated with the two-term spherical harmonic expansion approximation is utilized to gain the swarm parameters in steady-state Townsend. Results show that the accuracy of the Boltzlnann solution with a two-term expansion in calculating the electron drift velocity, electron energy distribution function, and density-normalized effective ionization coefficient is acceptable. The effective ionization coefficient presents a distinct relationship with the SF6 content in the mixtures. Moreover, the E/Ncr values in SF6-Air mixtures are higher than those in SF6-O2 mixtures and the calculated value E/Ncr in SF6-O2 and SF6-Air mixtures is lower than the measured value in SFB-N2. Parametric studies conducted on these parameters using the Boltzmann analysis offer substantial insight into the plasma physics, as well as a basis to explore the ozone generation process.展开更多
In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff p...In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity vth are naturally avoided. The probability function P（v, Av） for non- Maxwellian scattering is derived by the method of choosing velocity transfer Av, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.展开更多
This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic f...This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.展开更多
Acoustic wave velocity has been commonly utilized to predict subsurface geopressure using empirical relations.Acoustic wave velocity is, however, affected by many factors. To estimate pore pressure accurately, we here...Acoustic wave velocity has been commonly utilized to predict subsurface geopressure using empirical relations.Acoustic wave velocity is, however, affected by many factors. To estimate pore pressure accurately, we here propose to use elastic rock physics models to understand and analyze quantitatively the various contributions from these different factors affecting wave velocity. We report a closed-form relationship between the frame flexibility factor(γ) in a rock physics model and differential pressure, which presents the major control of pressure on elastic properties such as bulk modulus and compressional wave velocity. For a gas-bearing shale with abundant micro-cracks and fractures, its bulk modulus is much lower at abnormally high pore pressure(high γ values) where thin cracks and flat pores are open than that at normal hydrostatic pressure(low γ values) where pores are more rounded on average. The developed relations between bulk modulus and differential pressure have been successfully applied to the Upper Ordovician Wufeng and Lower Silurian Longmaxi formations in the Dingshan area of the Sichuan Basin to map the three-dimensional spatial distribution of pore pressure in the shale, integrating core, log and seismic data. The estimated results agree well with field measurements. Pressure coefficient is positively correlated to gas content. The relations and methods reported here could be useful for hydrocarbon exploration, production, and drilling safety in both unconventional and conventional fields.展开更多
The terminal velocity has been widely used in extensive fields, but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow （1 〈 Re ≤ 1000） with much more d...The terminal velocity has been widely used in extensive fields, but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow （1 〈 Re ≤ 1000） with much more difficulty than those in laminar flow （Re ≤ 1） and turbulent flow （Re ≥ 1000）. This paper summarized and compared 24 drag coefficient correlations, and developed an expression for calculating the terminal velocity in transitional flow, and also analyzed the effects of particle density and size, fluid density and viscosity on terminal velocity. The results show that 19 of 24 previously published correlations for drag coefficient have good prediction performance and can be used for calculating the terminal velocity in the entire transitional flow with higher accuracy. Adapting two dimensionless parameters （w＊, d＊）, a proposed explicit correlation, w＊=-25.68654 × exp （-d＊/77.02069）＋ 24.89826, is attained in transitional flow with good performance, which is helpful in calculating the terminal velocity.展开更多
In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional...In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant no.51674087,51974090)the National Science and Technology Major Project of the Ministry of Science and Technology of China(grant number 2017ZX05009003)。
文摘In oil and gas well drilling operations,it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids.In this paper,the free-falling of 172 groups of spheres and 522 groups of irregular-shaped sand particles in Newtonian/non-Newtonian fluids were investigated experimentally.It was found that the drag coefficient calculated based on Newtonian correlations can result in a significant error when the particle settles in the non-Newtonian fluid.Therefore,predictive models of drag coefficient were established respectively for different types of fluids.The validity of the proposed drag coefficient model of spheres was verified by comparing it with the previous works.On this basis,the drag coefficient model of irregular-shaped sand particles was established by introducing a shape factor.The models do not use the shape factor that requires detailed threedimensional shape and size information.Instead,two-dimensional geometric information(circularity)is obtained via image analysis techniques.The present new models predict the settling velocity of sand particles in the power-law fluid and Herschel-Bulkley fluid accurately with a mean relative error of5.03%and 6.74%,respectively,which verifies the accuracy of the model.
基金financial support of the Natural Science Foundation of China (NSFC,No.50974094)
文摘The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51177101)
文摘The electron swarm parameters including the density-normalized effective ionization coefficients（α-η）/N and the electron drift velocities V e are calculated for a gas mixture of CF3I with N2 and CO2 by solving the Boltzmann equation in the condition of a steady-state Townsend（SST） experiment.The overall density-reduced electric field strength is from 100 Td to 1000 Td（1 Td = 10-17V·cm2）,while the CF3I content k in the gas mixture can be varied over the range from 0% to 100%.From the variation of（αη）/N with the CF3I mixture ratio k,the limiting field strength（E/N） lim for each CF3I concentration is derived.It is found that for the mixtures with 70% CF3I,the values of（E/N） lim are essentially the same as that for pure SF 6.Additionally,the global warming potential（GWP） and the liquefaction temperature of the gas mixtures are also taken into account to evaluate the possibility of application in the gas insulation of power equipment.
基金supported by National Natural Science Foundation of China(Nos.11105067 and 51366012)Jiangxi Province Young Scientists(Jinggang Star)Cultivation Plan of China(No.2013BCB23008)
文摘The electron drift velocity, electron energy distribution function （EEDF）, densitynormalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SFs-Air mixtures. The experimental results from a pulsed Townsend discharge are plotted for comparison with the numerical results. The reduced field strength varies from 40 Td to 500 Td （1 Townsend=10-17 V.cm2） and the SF6 concentration ranges from 10% to 100%. A Boltzmann equation associated with the two-term spherical harmonic expansion approximation is utilized to gain the swarm parameters in steady-state Townsend. Results show that the accuracy of the Boltzlnann solution with a two-term expansion in calculating the electron drift velocity, electron energy distribution function, and density-normalized effective ionization coefficient is acceptable. The effective ionization coefficient presents a distinct relationship with the SF6 content in the mixtures. Moreover, the E/Ncr values in SF6-Air mixtures are higher than those in SF6-O2 mixtures and the calculated value E/Ncr in SF6-O2 and SF6-Air mixtures is lower than the measured value in SFB-N2. Parametric studies conducted on these parameters using the Boltzmann analysis offer substantial insight into the plasma physics, as well as a basis to explore the ozone generation process.
基金National High-Tech ICF(Inertial Confinement Fusion)Committee in ChinaNational Natural Science Foundation of China(Nos.10475076,10505021,40336052,and 10175065)
文摘In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity vth are naturally avoided. The probability function P（v, Av） for non- Maxwellian scattering is derived by the method of choosing velocity transfer Av, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.
文摘This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.
文摘Acoustic wave velocity has been commonly utilized to predict subsurface geopressure using empirical relations.Acoustic wave velocity is, however, affected by many factors. To estimate pore pressure accurately, we here propose to use elastic rock physics models to understand and analyze quantitatively the various contributions from these different factors affecting wave velocity. We report a closed-form relationship between the frame flexibility factor(γ) in a rock physics model and differential pressure, which presents the major control of pressure on elastic properties such as bulk modulus and compressional wave velocity. For a gas-bearing shale with abundant micro-cracks and fractures, its bulk modulus is much lower at abnormally high pore pressure(high γ values) where thin cracks and flat pores are open than that at normal hydrostatic pressure(low γ values) where pores are more rounded on average. The developed relations between bulk modulus and differential pressure have been successfully applied to the Upper Ordovician Wufeng and Lower Silurian Longmaxi formations in the Dingshan area of the Sichuan Basin to map the three-dimensional spatial distribution of pore pressure in the shale, integrating core, log and seismic data. The estimated results agree well with field measurements. Pressure coefficient is positively correlated to gas content. The relations and methods reported here could be useful for hydrocarbon exploration, production, and drilling safety in both unconventional and conventional fields.
文摘The terminal velocity has been widely used in extensive fields, but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow （1 〈 Re ≤ 1000） with much more difficulty than those in laminar flow （Re ≤ 1） and turbulent flow （Re ≥ 1000）. This paper summarized and compared 24 drag coefficient correlations, and developed an expression for calculating the terminal velocity in transitional flow, and also analyzed the effects of particle density and size, fluid density and viscosity on terminal velocity. The results show that 19 of 24 previously published correlations for drag coefficient have good prediction performance and can be used for calculating the terminal velocity in the entire transitional flow with higher accuracy. Adapting two dimensionless parameters （w＊, d＊）, a proposed explicit correlation, w＊=-25.68654 × exp （-d＊/77.02069）＋ 24.89826, is attained in transitional flow with good performance, which is helpful in calculating the terminal velocity.
文摘In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.
