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.

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.

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.

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.

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.

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.

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.

沥青质颗粒在垂直井筒中的运移特征流速

为防止沥青质沉积堵塞油井,需明确垂直井筒内流体携沥青质颗粒运移特性。通过静态沉降试验探究不规则形状沥青质颗粒沉降末速规律,采用垂直井筒液携固流动试验装置研究不同因素对沥青质运移临界流速的影响程度,建立沥青质颗粒沉降末速和运移临界流速计算公式。结果表明:沥青质表面不均匀性增大了沉降阻力,使沉降等效直径小于颗粒实测粒径;运移临界流速与颗粒粒径成正比、与液相黏度成反比,颗粒体积分数对运移临界流速影响较小;相同条件下流体携沥青质运移临界流速为沉降末速的1.182倍。

考虑滤失的页岩裂缝内支撑剂自由沉降速度计算模型

为了研究滤失因素对支撑剂沉降速度的影响,将R-Z模型、阻力系数模型和页岩孔隙内滤失速度模型进行耦合,建立了在裂缝中受滤失影响的支撑剂沉降速度计算模型,研究黏度、孔隙半径、滑移长度和砂比对支撑剂沉降规律的影响。结果表明:随着滤失量的增加,支撑剂沉降速度在200~400 s内迅速降低;滤失会导致不同黏度下的支撑剂沉降速度发生交汇,之后黏度与沉降速度呈正相关;文中模型预测结果与前人数据相比平均误差为13.88%,验证了该模型的准确性。

黄河流域黏性泥沙群体沉速计算分析

针对黄河流域由黏性矿物组成的黏性泥沙群体沉降特征展开研究。基于泥沙颗粒受力分析和能量守恒定律,以处于稳态的泥沙颗粒为参照物,构建了泥沙颗粒水沙界面能量耗散物理图形;建立了考虑挟沙水流运动黏性系数和紊动黏性系数的泥沙群体沉速显式表达式,并采用黄河流域典型黏性泥沙红色砒砂岩颗粒开展了泥沙群体沉速试验研究。结果表明:红色砒砂岩组成的含沙水体中泥沙群体沉速整体随含沙量增大而减小并逐渐趋于定值;当垂向平均含沙量为0.34~0.45 kg/m^(3)时,泥沙群体沉速表现为随含沙量的增加而增大。采用试验数据对建立的公式进行验证,公式能较合理地表达水流黏性和尾流分离对泥沙颗粒沉降阻力的影响。研究结果可为黄河流域黏性泥沙淤积和输移规律研究提供参考。

环形异向流浅层流场油滴流动及分离特性研究

目前关于环形多层异向流浅层流道内液滴流动和油水分离特性的研究尚不够深入。为此,借助流体动力学方法,对环形异向流浅层流道内分散油滴运移分离特性和多层浅层流道速度分布特性进行分析。研究结果表明:环形异向流浅层流道内油滴浮升至斜板表面所需板长为96 mm,小于理论计算所需板长122 mm;浅层通道内层间速度分布对分离效率影响较大,下层流道入口速度峰值为0.00805 m/s,环形多层浅层通道内油相浮升过程中会遇到交叉流,显著影响浅层通道分离效率;滑移距离是影响浅层通道间分离效率的重要因素,当板长为350 mm、油滴粒径为50μm时,滑移距离占板长38.35%。所得结论可为基于浅层沉降强化分离理论的紧凑型采出水处理设备结构创新优化设计提供理论支撑。

研山铁矿选矿厂尾矿絮凝沉降试验及实践

研山铁矿选矿厂为了提高尾矿浓缩大井溢流水水质,针对当前尾矿浓缩大井存在的给矿量大导致溢流水浑浊、环水泵池清淤周期短等问题,开展了尾矿絮凝沉降试验研究。试验结果表明:在絮凝剂用量相同的条件下,随着矿浆浓度的升高,矿浆中固体颗粒的沉降速度随之变慢,澄清液变浑浊,结合现场实际生产情况,确定浓缩大井给矿浓度为8%;在矿浆给矿浓度为8%的条件下,当絮凝剂用量为8~10 g/t时,尾矿絮凝沉降效果较好,同时澄清液澄清,絮凝剂用量较原来降低50%,环水泵池清淤周期延长,周边环境卫生得到有效改善,同时大幅减少了人力、物力,年可创造经济效益约900万元。

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.

纤维状海洋微塑料静水沉降实验研究

近年来海洋微塑料污染治理受到了学者们的广泛关注.海洋微塑料的种类包括纤维、碎片、薄膜和颗粒,其中纤维状微塑料在水体中含量最高.然而纤维状微塑料的沉降形态和沉降速度目前研究还存在不足,已有的一些半经验沉降速度公式需要更多的实验数据进行验证.对不同密度、直径和长径比的聚酰胺和聚酯纤维状微塑料进行了室内静水沉降实验,利用高精度颗粒沉降观测系统对微塑料颗粒沉降过程进行直接测量,并统计了纤维状微塑料颗粒的沉降速度和沉降形态.实验结果表明,当纤维状微塑料的长径比固定时,微塑料颗粒的无量纲沉降速度随无量纲颗粒等效粒径的增大而增大.根据实验测量值和公式计算值的比较,当纤维状微塑料的长径比L d≤6.0时,Khatmullina-Isachenko公式的计算结果较为准确,各组次平均相对误差小于23.61%;而当长径比L d>6.0时,Waldschläger-Schüttrumpf公式的计算结果较为准确,各组次平均相对误差小于20.18%.此外,实验中85.51%的纤维状微塑料的沉降状态是沿着长轴方向的,纤维状微塑料在下沉过程中有旋转形成最大阻力形态的趋势.实验所采用的纤维状微塑料为理想材料,实际海洋中的微塑料颗粒可能因长期光照老化导致表面粗糙度和比表面积增大,应用公式时应注意这些因素对沉降速度造成的影响.本文为微塑料沉降速度的公式选择提供了参考,并为海洋微塑料治理提供了科学依据.