A simple formula for predicting settling velocity of sediment particles

Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is proposed. Using a trial-and-error procedure to minimize errors, the coefficients were determined and a formula was developed for predicting the settling velocity of natural sediment particles. This formula has higher prediction accuracy than other published formulas and it is applicable to all Reynolds numbers less than 2× 10^5.

Observations and analyses of floc size and floc settling velocity in coastal salt marsh of Luoyuan Bay, Fujian Province, China

In coastal environments, fine-grain sediments often aggregate into large and porous flocs. ElectroMagnetic Current Meters （EMCM） and Laser In Situ Scattering and Transmissometry （LISST-ST） have been deployed within a Spartina alterniflora marsh of the Luoyuan Bay in Fujian Province, China, to measure the current velocity, the floc size and the settling velocity between 15 and 22 January 2008. During the observations, the near-bed water was collected in order to obtain the suspended sediment concentration （SSC） and constituent grain size. Data show that： （1） the nearbed current velocities vary from 0.1 to 5.6 cm/s in the central Spartina alterniflora marsh and 0.1–12.5 cm/s at the edge; （2） the SSCs vary from 47 to 188 mg/dm 3 . The mean grain size of constituent grains varies from 7.0 to 9.6 μm, and the mean floc sizes （MFS） vary from 30.4 to 69.4 μm. The relationship between the mean floc size and settling velocity can be described as： w s =ad b , in which w s is the floc settling velocity （mm/s）, a and b are coefficients. The floc settling velocity varies from 0.17 to 0.32 mm/s, with a mean value of 0.26 mm/s, and the floc settling velocity during the flood tide is higher than that during the ebb tide. The current velocity and the SSC are the main factors controlling the flocculation processes and the floc settling velocity.

Settling velocity of equiaxed dendrites in a tube

The settling velocity of equiaxed dendrites can cause macrosegregation and influence the structure of the equiaxed zone during the casting solidification process. So an understanding of the settling characteristics is needed to predict the structure and segregation in castings. The settling velocity of NH4Cl equiaxed dendrites of non-spherical geometry was studied experimentally in an NH4Cl-70wt.%H2O solution. A calculation formula was proposed to calculate the settling velocity of sediment equiaxed dendrites in a tube filled with saturated solution at a moderate Reynolds number region. The retardation effects of the wall and morphology of the equiaxed dendrite on the settling velocity were taken into account in the development of the calculation formula, and the correction function B of the drag coefficient with consideration of the retardation effects of the wall and morphology of the equiaxed dendrite on the settling velocity of the equiaxed dendrite was calibrated according to the experimental results. A comparison showed that the formula has a good accordance with the experimental results.

General formulas for drag coefficient and settling velocity of sphere based on theoretical law

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.

Determining suspended sediment concentration and settling velocity from PC-ADP measurements in the Beibu Gulf, China

Modeling sediment transport depends on several parameters, such as suspended sediment concentration （SSC）, shear stress, and settling velocity. To assess the ability of Pulse-Coherent Acoustic Doppler Profiling （PC-ADP） to non-intrusively quantify spatial and temporal SSC and settling velocity at seabed, a field experiment was conducted in the Beibu Gulf （Tonkin Gulf）, in the South China Sea. The spatial profiles and temporal variations in SSC at 1 m above bottom were derived from PC-ADP acoustic backscatter intensity determinations after being calibrated with the optical backscatter sensor （OBS） measurements at the same elevation. The PC-ADP and OBS results agreed well. The temporal settling velocity obtained from Rouse profiles agreed well with the Soulsby formula based on size information by LISST （laser in situ scattering and transmissometry）. Tides and tidal currents are diurnal in the gulf. SSC increased with increasing ebb and flood flow, and it rapidly decreased with the increase of distance from the seabed. The maximum SSC at 0.16 m and 1.3 m above bottom reached 816 mg/L and 490 mg/L during spring tides, respectively. The sediments consisted of mineral particles 23-162 μm in diameter and 0.05-2.04 crn/s in settling velocity. Generally, both the SSC and settling velocity followed variations in the bottom friction. Results suggest that PC-ADP is able to provide reasonable SSC and settling velocity measurements of both profiles and time series for a long study period.

A novel predictive model of drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids

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.

Group Settling Velocity of Non-Cohesive Sediment Mixtures

Settling velocity is a fundamental parameter in sediment transport dynamics. For uniform particles, there are abundant formulas for calculation of their settling velocities. But in natural fields, sediment consists of non-uniform particles. The interaction among particles is complex and should not be neglected. In this paper, based on the analysis of settling mechanism of non-cohesive and non-uniform particles, a theoretical model to describe settling mechanism is proposed. Besides suspension concentration and upward turbulent flow caused by other particles, collision among particles is another main factor influencing settling velocity. By introducing the collision theory, equations of fall velocity before collision, collision probability, and fall velocity after collision are established. Finally, a formula used to calculate the settling velocity of non-cohesive particles with wide grain gradation is presented, which agrees well with the experimental data.

Hydrostatic settling velocity of sediments

The settling of sediments is an accelerative process in which the concentration of the main sediments zone will heavily influence settling velocity,but the explicit relationship between the concentration and settling velocity has not been reported in literature. Here a theoretical function was built for the time dependent concentration and time dependent settling velocity of sediments;then the entire settling process reflecting concentration was shown on the basis of sediments instant\|settlement theory and mathematical method. Agreement of computed results and experimental data was found. Several governing parameters,including particle size,particle density,initial suspended sediments concentration and suspension height,were discussed with a series of calculated velocity curves. The research indicated that ⑴ the presented concentration\|velocity time relationship is rational,⑵ settling process of the sediments group with variation of concentration consists of acceleration stage,uniform motion stage and deceleration stage,and ⑶ particle size,particle density and initial suspended sediments concentration have more influence on the settling velocity than the suspension height and water temperature.

Influence of MBBR carrier geometrical properties and biofilm thickness restraint on biofilm properties,effluent particle size distribution,settling velocity distribution,and settling behaviour

The relatively poor settling characteristics of particles produced in moving bed biofilm reactor(MBBR)outline the importance of developing a fundamental understanding of the characterization and settleability of MBBR-produced solids.The influence of carrier geometric properties and different levels of biofilm thickness on biofilm characteristics,solids production,particle size distribution(PSD),and particle settling velocity distribution(PSVD)is evaluated in this study.The analytical Vi CAs method is applied to the MBBR effluent to assess the distribution of particle settling velocities.This method is combined with microscopy imaging to relate particle size distribution to settling velocity.Three conventionally loaded MBBR systems are studied at a similar loading rate of 6.0 g/(m^(2)·day)and with different carrier types.The AnoxK^(TM)K5 carrier,a commonly used carrier,is compared to so-called thickness-restraint carriers,AnoxK^(TM)Z-carriers that are newly designed carriers to limit the biofilm thickness.Moreover,two levels of biofilm thickness,200μm and 400μm,are studied using AnoxK^(TM)Z-200 and Z-400 carriers.Statistical analysis confirms that K5 carriers demonstrated a significantly different biofilm mass,thickness,and density,in addition to distinct trends in PSD and PSVD in comparison with Z-carriers.However,in comparison of thickness-restraint carriers,Z-200 carrier results did not vary significantly compared to the Z-400 carrier.The K5 carriers showed the lowest production of suspended solids(0.7±0.3 gTSS/day),thickest biofilm(281.1±8.7μm)and lowest biofilm density(65.0±1.5 kg/m^(3)).The K5 effluent solids also showed enhanced settling behaviour,consisting of larger particles with faster settling velocities.

Artificial neural network model for predicting drill cuttings settling velocity

The traditional method of using the coefficient of drag–Reynolds number relationship to predict cuttings settling velocity involves an implicit procedure that requires repeated,time-consuming and tedious iterations using Newtonian or mostly non-Newtonian correlations.Usually,these correlations are limited to certain fluid flow regimes.Besides,most of the explicit and direct cuttings settling velocity models that exist are based on the assumption that the cuttings are spherical particles.However,in the field,the cuttings are a mixture of various shapes and are hardly spherical,hence these models when applied to field conditions come off with huge errors.The objective of this work was to use a nature-inspired algorithm(artificial neural network-ANN)to develop a model for estimating cuttings settling velocity that would be robust and useful in the field that would take into account the shape of the cuttings.The data used for this work was obtained from research experiments in the literature.The model was then evaluated using four performance metrics namely:mean squared error(MSE),root mean square error(RMSE),sum of squares error(SSE)and goodness of fit(R2).It was found that the model's predictions obtained in this work agreed with experimental evidence.Furthermore,the developed model possesses the capacity to generalize across new input datasets and can be applied to particles of any shape,hence,defining the novelty of this research and bridging the gap between theory and practice.When compared with state-of-the-art models,the developed models show a high degree of robustness,as the ANN model performed reasonably well with an MSE of 7.5×10−4,an R2 of 0.978,RMSE of 0.0274 and SSE of 0.25.To generalize the results across new input datasets,the developed model was cross-validated with new data that was not part of the training process.It was found that the ANN model had an MSE value 0.00807,RMSE of 0.0898,MAE of 0.065,SSE of 2.74 and MAPE of 0.675%.To ensure the replicability of the ANN model,the weights and biases for the inputs,hidden and output layers are presented in this work unlike other artificial intelligence-based models in the literature.The range of application for the developed ANN model is 0.0001<Particle Reynolds's number<100 and 0.471<cuttings sphericity<1.With the model developed in this work,the cuttings settling velocity can be predicted with minimal errors in a quick,less cumbersome,non-iterative manner and is not limited by cuttings shapes'factor and fluid flow regimes.

A high precision model for the terminal settling velocity of drops in fluid medium

The terminal settling velocity(TSV)calcula-tion of drops and other spherical objects in fluid medium is a classical problem,which has important application values in many fields such as the study of cloud and precipitation processes,the evaluation of soil erosion,and the determination of fluid viscosity coefficient etc.In this paper,a new explicit approximation model of TSV is established,which combines the theoretical solution of N-S equation about fluid motion around spherical objects and the statistical regression of solution dimensionless coeffi-cients with measurement data.This new model can adapt to different values of drop parameters and medium parameters in a large range of Re.By this model,the relative and absolute calculation errors of TSV are in range of 3.42%+4.34%and 0.271 m/s-+0.128 m/s respec-tively for drop radius 0.005-2.9 mm.Their corresponding root mean square values are 1.77%and 0.084 rn/s respectively,which are much smaller than that of past theoretical and empirical models.

Predicting wall drag coefficient and settling velocity of particle in parallel plates filled with Newtonian fluids

The hindrance of boundary to particle transport exists widely in various industrial applications.In this study,the wall drag force of parallel plates on settling particles was revealed through settling experiment.High-speed camera was used to record and analyze the settling process of particles in parallel plates that are filled with Newtonian fluids.A total of 600 experiments were carried out,involving the range of relative diameter and particle Reynolds number of 0.01-0.95 and 0.004-14.30,respectively.The wall drag coefficient was defined to quantitatively analyze the wall drag force of the parallel plates.The influence of relative diameter,particle properties,rheological properties,and the settling dynamic process on the wall drag coefficient was revealed,and the wall drag coefficient model with mean relative error of 5.90% was established.Furthermore,an explicit settling velocity model with mean relative error of 8.96% for the particle in parallel plates was developed by introducing a dimensionless variable independent of settling velocity,the Archimedes number.Finally,a calculation example was provided to clarify the using process of the explicit model.This research is expected to provide guidance for optimizing water hydraulic fracturing in the oil and gas industry.

Investigation on Settling Characteristics of Floes in the Changjiang Estuary, China

Settling characteristics of floes, including relative settling velocity, relative flocculation coefficient and flocculation exponent, are obtained by the suspended load equations for different size fractions. Data of the Changjiang Estuary suggest that level of flocculation changes from river section, river mouth (turbidity maximum) to offshore area in sequence of low, very high and high. The settling characteristics of floes reflected by in situ estimation performs a similar feature as that obtained from still water experiment.

Settling behavior of spherical particles in eccentric annulus filled with viscous inelastic fluid

Hole cleaning is a complex process as there are many variables affecting cuttings removal(e.g.drilling fluid type,density,flow rate and rheological properties,cuttings size,drill pipe rotation speed).With the increasing number of drilling small diameter wells(e.g.coiled tubing drilling applications,ultra-deep wells drilled for exploitations of unconventional oil and gas resources),the wall resistance of the micro annulus also emerges as one of the most critical factors affecting the cuttings accumulation in wellbore.The eccentricity of drill pipes commonly observed during the drilling process of ultra-deep well and coiled tubing well makes the wall resistance effect on the cuttings transport even more prominent.Understanding the wall resistance effect on the particle settling behavior in eccentric annuli is,therefore,crucial for hydraulic design of efficient cuttings transport operations in these wells.In this study,a total of 196 sets of particle settling experiments were carried out to investigate the particle settling behavior in eccentric annuli filled with power-law fluids.The test matrix included the eccentricity ranges of 0-0.80,the dimensionless diameter ranges of 0.13-0.75 and the particle Reynolds number ranges of 0.09-32.34.A high-speed camera was used to record the particle settling process and determine the influences of the eccentricity,the dimensionless diameter,the fluid rheological properties,and the solid particle characteristics on the wall factor and the particle settling velocity.The functional relationship among the dimensionless diameter,the particle Reynolds number,and the wall factor was determined by using the method of controlling variables.An eccentric annulus wall factor model with average relative error of 5.16%was established.Moreover,by introducing Archimedes number,an explicit model of particle settling velocity in the eccentric annulus with average relative error of 10.17%was established.A sample calculation of particle settling velocity was provided to show the application of the explicit model.Results of this study can be used as a guideline by field engineers to improve hydraulic design of cuttings transport operations in concentric and eccentric annuli.

Siltation Prediction for Navigation Channels and Harbour Basins on Muddy Beach

This paper, after briefly reviewing the experimental research on sediment transport on muddy beach since the 1950s, improves and perfects the method for forecasting siltation in navigation channels and harbour basins which was first put forward in China by the authors. In consideration of silty sediment and sand, some factors in forecasting methods have been changed and modified. Consequently, the modified methods can be used either to compute siltation in navigation channels and harbour basins on muddy beach or to compute siltation and scouring in navigation channels and harbour basins on both silty beach and sandy beach. The verification of field data from eleven large, medium and small natural harbours shows a good agreement between the forecasting by the modified method and the natural conditions. Finally, the paper deals with the rational utilization of water area after the construction of the West Dyke in Lianyungang, the maintenance of water depth of the navigation channel at the entrance, siltation distribution, siltation in the navigation channel and harbour basin for ships of 100 thousand tonnnage. Results once again prove that the prospect of constructing Lianyungang Harbour into a deepwater harbour is bright.

Moving Behavior of an Object in Gas-Solid Fluidized Beds

The settling behavior of coarse particles in a gas-solid fluidized bed was experimentally studied by using magnetic tracer. It is well known that the calculation of terminal velocity is of interest in dense medium separation. However, this problem has not been completely solved up to now. In this work, the terminal velocity of an object mov-ing in a gas-solid fluidized bed was experimentally measured and theoretically calculated. The experimental results in-dicated that the plastic viscosity and yield stress of the bed increase as the size of fluidized particles increases, but it varies little when some coarser particles are mixed with the fluidized particles. The resistance to a rising object was an order magnitude greater than that to a settling object. The efficient buoyancy on a flaky object, which lies flatly on the gas distributor, was much less than that calculated by the Archimedes principle. The object does not always rise or set-tle with minimal projective area owing to radial motion of the fluidized particles. But in the lower part of the bed, the bar-shaped objects were likely with minimal projective area rising or settling.

Preparation and properties of gradient Al_2O_3-ZrO_2 ceramic foam by centrifugal slip casting method

The aim of the present research is to provide a novel technique for preparing gradient Al 2 O 3-ZrO 2 ceramic foams.This technique used epispastic polystyrene spheres to array templates and centrifugal slip casting to obtain cell struts with gradient distribution of Al 2 O 3 and ZrO 2 particles and high packing density.Aqueous Al 2 O 3-20vol.% ZrO 2 slurries with 20vol.% solid contents were prepared and the dispersion and rheological characteristics of the slurries were investigated.The settling velocity and mass segregation of Al 2 O 3 and ZrO 2 particles at different centrifugal accelerations were calculated and studied.The drying behavior,macrostructure,microstructure,compressive property and resistance to thermal shock of the sintered products were also investigated.The results show that the difference of settling velocity of Al 2 O 3 and ZrO 2 particles increases and mass segregation becomes acute with an increase in centrifugal acceleration.The cell struts prepared at a centrifugal acceleration of 1,690 g have high sintered density(99.0% TD) and continuous gradient distribution of Al 2 O 3 and ZrO 2 particles.When sintered at 1,550 o C for 2 h,the cell size of gradient Al 2 O 3-ZrO 2 foam is approximately uniform,about 1.1 mm.With the porosity of gradient Al 2 O 3-ZrO 2 ceramic foams increasing from 75.3% to 83.0%,the compressive strength decreases from 4.4 to 2.4 MPa,and the ceramic foams can resist 8-11 repeated thermal shock from 1,100 o C to room temperature.

Flocculation properties of cohesive fine-grained sediment in the Three Gorges Reservoir under variable turbulent shear

Sediment flocculation is a key process for the deposition of fine-grained sediments in the Three Gorges Reservoir(TGR)of China.Sediment flocculation influences the evolution of the river regime,but also hampers the smooth navigation in the long term.However,the flocculation process and its controlling factors are poorly understood.We experimentally determined the flocculation properties of cohesive sediment of samples from the TGR(predominantly a mixture of clay and silt)over a range of turbulent shear rates and sediment concentrations.The experiments were conducted in an almost isotropic turbulence field,which was simulated by an array of horizontal oscillating grids in a water tank.Sediment flocculation was recorded by a camera and investigated by image analysis.Our new data indicate that flocculation is generally a response in equilibrium median floc size(d_(f,50))to the increase of the shear rate G.The peak value is attained at G=16.5 s^(-1),where d_(f,50) is 81.3μm(for the suspended sediment concentration(ssc)=0.4 g/L)and 107μm(for ssc=0.7 g/L),respectively.At low shear rates(G<16.5 s^(-1)),the equilibrium floc sizes d_(f,50) increase with rising shear rate G and isinversely related to the Kolmogorov micro length scale η.We attribute this variability to an insufficient deposition time of the sediment flocs in the water tank.Settling velocities,calculated from our experimental data of the floc sizes,are almost consistent with in-situ measured settling velocities,and are ten times larger than the terminal settling velocity of primary particles as calculated from Stokes'law.

The estimation of a critical shear stress based on a bottom tripod observation in the southwest off Jeju Island,the East China Sea

The resuspension and deposition of sediment within a bottom boundary layer（BBL） is the main dynamic processes that control the fate of the suspended sediment in shelf seas.The numerical study of sediment transport patterns relies on the knowledge of some critical parameters that describe sediment erosion and deposition.A critical shear stress is estimated based on field observations at the edge of a mud area southwest off Jeju Island,the East China Sea.On the basis of the simultaneous observation of velocity and suspended sediment concentrations within the BBL by means of acoustic instruments including an acoustic Doppler velocimeter and an acoustic Doppler current profiler,the settling velocity is estimated by turbulent oscillations of the SSC under the assumption of inertial-dissipation balance.This method gives a mean value of 0.91 mm/s and standard deviation of 0.20 mm/s,which is an order of magnitude larger than the value obtained by an empirical method of Soulsby and by an in situ submersible particle size analyzer.The difference is possibly due to the distinct natures of two methodologies,the inertial-dissipation method is more indicative of the BBL dynamics and is thus believed to provide reasonable in situ estimates of the settling velocity,whereas Soulsby＇s method is usually suitable for still water.A novel method for estimating the critical stresses of erosion and deposition based on statistical analyses of the temporal variability of the SSC（which is defined as a derivative of the depth-averaged SSC with respect to time） and the corresponding bottom shear stress is proposed.Both critical stresses of erosion and deposition vary between 0.11 Pa and 0.25 Pa with corresponding median values of 0.20 Pa and 0.16 Pa,respectively,which confirms that the critical stresses of erosion is somewhat higher than the critical stresses of deposition.Another method of estimating the critical shear stress by means of the settling velocity is also employed,which yields reasonable critical shear stress values of 0.06-0.17 Pa.

A Sedimentation-Dispersion Model for both Non-attached and Attached Particles in Three-Phase Batchwise Fluidized Beds

The axial concentration distribution of both particles with betterwetting (forming non-attached system) and poorer wetting (formingattached system) was investigated in a vertical gas-liquid-solidfluidized bed of 4.2 cm in diameters and 130 cm in height with thesolids holdup less than 0.05. The one-dimensionalsedimentation-dispersion model could be used satisfactorily todescribe the axial distribution of solids holdup by modifying only amodel parameter, i.e. by means of the terminal settling velocityminus a certain value, which is a functions of gas velocity andconsiders the effect of an additional drag force resulted fromattached rising bubbles.