Low Fluid Velocities Research Articles

低流速域での水平管内空気輸送特性（第２報） 粒子速度と固気速度比

The transportation of solids at low fluid velocities has recently begun with the object of reducing the pressure drop and power consumption in a pneumatic conveying system. Therefore, it is important to investigate flow characteristics at low fluid velocities. One of them is the solid particle velocity. Thus, in this paper a basic equation for the velocity ratio of particles to fluid was derived on the basis of the observation of solid flow patterns in Part I for the established flow at low fluid velocities in horizontal pipes. On the other hand, measurements of the solid particle velocity for the flow were conducted by measuring the impulsive force of the solids fluid two phase flow by the use of a ballistic pendulum. The unknown quantities in the equation were determined by analyzing of the experimental data, and an empirical equation was obtained. More than 95% of the values calculated by the equation fall within ±12% of the experimental values.

The hydrothermal system at Newberry Volcano, Oregon

Results of recent geological and geophysical studies at Newberry Volcano have been incorporated into conceptual and numerical models of a magma‐based hydrothermal system. Numerical simulations begin with emplacement of a small magma body, the presumed source of silicic eruptions at Newberry that began about 10,000 B.P., into a thermal regime representing 100,000 years of cooling of a large underlying intrusion. Simulated flow patterns and thermal histories for three sets of hypothetical permeability values are compatible with data from four geothermal drill holes on the volcano. Meteoric recharge cools the caldera‐fill deposits, but thermal water moving up a central conduit representing a permeable volcanic vent produces temperatures close to those observed in drill holes within the caldera. Meteoric recharge from the caldera moves down the flanks and creates a near‐isothermal zone that extends several hundred meters below the water table, producing temperature profiles similar to those observed in drill holes on the flanks. The temperatures observed in drill holes on the flanks are not influenced by the postulated Holocene magma body. The elevated temperature gradients measured in the lower portions of these holes may be related to the cumulative effect of older intrusions. The models also indicate that meteoric recharge to the deep hydrothermal system probably originates within or near the caldera. Relatively low fluid velocities at depth suggest that at least a significant fraction of the thermal fluid may be very old.

Simulation of granular layer inversion in liquid fluidized beds

A hydrodynamic computer model for describing multiparticle fluidization has been developed. Each group of particles, identical in density and in diameter, is treated as a particulate phase in this model. The computer code solves the mass and momentum balance equations for the fluidizing fluid and for the required number of particulate phases. The model has been used to simulate granular layer inversion in a liquid fluidized bed. This phenomenon occurs during the fluidization of a binary mixture of particles in which the denser particles are smaller. In such a system at low fluid velocities, the larger particles segregate into a top layer; at higher fluid velocities, they sink to form a bottom layer. At intermediate fluid velocities, the extent to which the particles mix is determined by the fluid velocity. The simulation results using the multiparticle code are in good agreement with experimental data on granular layer inversion. It is also shown that under some conditions, a radial segregation pattern exists in addition to the experimentally observed axial segregation pattern.

Axial dispersion in coiled tubular reactors : The Effect of Curvature at Low Dean Numbers

Deforming tubing (e.g., coiling) reduces axial dispersion in flow-injection systems and post-column reactors. An improvement is presented for a previous theoretical treatment of axial dispersion in coiled tubes. New experimental data are also presented for different coil radii. Changes were necessary because smaller-than-predicted dispersion improvements were observed. This contradicts earlier treatments that predict a linear dependence on the aspect ratio of the coil. Evidence is presented that this is explained by assuming a boundary layer thickness much smaller than the radius of the tube and proportional to the ratio of radial velocities. This is a special case of earlier theory and it predicts an almost curvature-independent change in dispersion. The inclusion of the critical Reynolds number, Re c, to form a reduced parameter, ( Re/Re c), accounts for all observations, including some previously-defined empirical constants. The dispersion is found to increase as ( Re/Re c) 2/3 Sc at low fluid velocities and to decrease as ( Re 1/6 c/( Re/Re c) 4/3 Sc 0.08) at higher velocities. Experiments are reported for several coil radii and with a range of proteins and protein mixtures.

Velocity Effects on Dispersion in Porous Media With a Single Heterogeneity

Regime changes during multifluid miscible displacement through a porous medium, containing a single heterogeneity were simulated. At very low fluid velocities (approximately 5 × 10−5 cm/s), the displacement is predominantly controlled by diffusion. Increasing the fluid velocity causes inter pore convection to become a factor. The third regime is at even higher velocities (0.5 × 10−3 to 5 ×103cm/s) and is predominantly controlled by mechanical dispersion. Analysis of simulations for heterogeneous flow fields reveals a fourth regime where flow is governed by megascopic dispersion caused by heterogeneity. Flow in this regime appears to be non‐Fickian. A maximum Fickian velocity was determined for various parameters of the heterogeneous flow field. Permeability rato had the greatest effect on overall dispersivity. The greater the length ratio, the greater the overall dispersivity, and the greater the chance of the flow exhibiting non‐Fickian behavior. Changing the size ratio did not significantly change the overall dispersivity but did affect the megascopic regime occurrence.

Momentum and heat flux in a swirl-stabilized combustor

The use of a fine-wire compensated thermocouple probe and two-color laser anemometry to measure both heat and momentum fluxes in the axial and azimuthal directions is assessed for a complex flow, swirl-stabilized laboratory combustor. Thermocouple probe perturbation and time constant variation are evaluated and the former is found to be significant in the central region of the recirculation zone. To minimize the effect of perturbation, the configuration of the probe is varied. In the recirculating region, the mean temperature is uniform with peak, instantaneous temperatures approximating the maximum adiabatic flame temperature. The maximum rms temperature approaches 250°C and occurs off-axis, just downstream of the recirculation zone. The heat flux on the centerline is negative and becomes more negative with downstream distance. Correspondingly, the temperature time series and the probability density function of the fluctuating temperature indicate that neither is cool dilution air present near the centerline nor are hot fluid particles present near the wall. This is attributed to the preferential transport of hot, low velocity fluid particles towards the centerline and cool dense gas, towards the wall by the swirl.

Drillpipe Eccentricity Effect on Drilled Cuttings Behavior in Vertical Wellbores

Summary Effects of drill pipe eccentricity and rotation of the eccentric drill pipe on the carrying capacity of drilling muds in a vertical wellbore have been observed on a simulated wellbore test apparatus under steady-state conditions at laminar fluid flow. The applicability of the semiempirical cuttings transport model developed by Zeidler to the experimental conditions also was tested. Experimental parameters included two velocity values 30.48 and 45.72 cm/s, four eccentric positions, and four rotary speeds, with a transparent simulated drilling fluid whose rheological properties were kept constant. Results show that drill pipe eccentricity has a minor influence on annular cuttings volumetric concentration and that the effect appears to be oscillatory in nature. Although increasing rotary speed generally improves particle transport, it is more pronounced at lower annular fluid velocities and appears to be negligible at high velocities. Also, there is a threshold value of rotary speed above which there is little change in transport behavior. Inspection of the equation developed by Zeidler I to predict the volumetric cuttings concentration in a vertical wellbore during drilling will show that the predicted concentration may be erroneously high at low fluid velocities. Experimental results indicate that the equation will yield accurate values of cuttings concentration, provided that the annular fluid velocity is at least twice the particle settling velocity. Otherwise, the equation should not be used. Introduction In the past, extensive work has been carried out in pursuit of a complete understanding of drilled cuttings behavior in vertical wellbores during drilling and during the hole-cleaning process after drilling has stopped. Perhaps the earliest study conducted on the problem of cuttings removal was that of Pigott in 1941, which considered fluid flow in mud pits, pipes, and wellbores. He discussed the application of Stokes' law for laminar flow and Rittinger's formula for turbulent flow to drilled particle settling velocity calculations. He concluded that high fluid viscosity was not necessary and suggested that laminar flow in the annulus would lead to more efficient cleaning. For trouble-free operation, he also recommended that the volumetric cuttings concentration in the annulus be kept less than 5%. Both field and laboratory tests were conducted in 1950 by Hall et al. with drilled cuttings settling velocities computed through estimates of cuttings circulation time from bottom. Among their results, the observed discontinuity in transport at the transition from laminar to turbulent flow was significant. A similar study conducted the following year by Williams and Bruce led to the conclusion that low viscosity and low get strength were advantageous in removing cuttings. However, their results indicated that turbulent flow in the annulus was preferable for cuttings transport, in apparent disagreement with Pigott's conclusions. Hopkin devoted considerable attention to particle slip velocity and presented correlations between slip velocity and funnel viscosity and Bingham yield value. Among his conclusions were that inducing laminar annular mud flow and rotating the drill string will improve drilling mud carrying capacity. Later, analytical relationships involving annular velocity, penetration rate, hole size, and drilling fluid properties with the problem of hole cleaning were developed by Chien, which included the influence of non-Newtonian viscosity on settling velocity. He found that there is an optimal annular velocity that varies with penetration rate, for any given pipe and hole size, and fluid properties. Results and conclusions from particle transport tests conducted in full-scale vertical annuli were reported by Sifferman et al., who studied various types of fluids. JPT P. 1929^

Research Needs in Low Reynolds Number Flow Heat Exchangers

Low Reynolds number flows prevail in some process, power, automotive, aircraft, and other industrial heat exchangers such as shell-and-tube, plate, and compact heat exchangers. Laminar or low Reynolds number turbulent flows are the results of either high viscosity fluids, compact flow passages (i.e., small hydraulic diameter), or low fluid velocities. Significant advancements have been made in the past 100 years in understanding and predicting flow and heat transfer in such internal flows. This paper summarizes the research needs to further advance the science of low Reynolds number flow heat exchangers. Emphasis is primarily given to the thermal design aspects; research needs related to mechanical design, manufacturing, material selection, and other nonthermal design aspects are not covered. Also the coverage is restricted primarily to single-phase applications. The outlined research needs are based on the input from invited lecturers and some participants, experts in the field, at the Fourth NATO Advanced Study Institure in Ankara, Turkey, July 1981.

Observations of fouling biofilm formation.

Fouling biofilm development was monitored in a completely mixed tubular recycle reactor. A unique sampling system allowed direct (brightfield, epifluorescence, and scanning electron photomicroscopy) and indirect (increased fluid frictional resistance) observations of biofilms. Low fluid velocity (138.5 cm/s) experiments had shorter induction times and biofilm matrixes which included firmly adherent filamentous bacteria. High fluid velocity (265.4 cm/s) experiments had longer induction times with firmly adherent filamentous bacteria present only after the accumulation of extracellular materials. In both cases the fluid frictional resistance increased after filamentous bacteria became a permanent part of the biofilm.

Application of a two-component LDV to the measurement of flows induced by flames propagating over condensed fuels

In the early stages of a fire, the two mechanisms by which heat transfer occurs are conduction and convection ahead of the flame through gas and fuel phases. The convective flows induced are characterized by low-fluid velocities with changes in magnitude and direction occurring over small distances accompanied by sharp temperature changes. These characteristics make quantitative measurements of fluid velocities difficult using conventional techniques. With the advent of LDV techniques, a nonperturbing means of making high resolution measurements of 2-D flows now exists. In this paper the details of the LDV facility and the results of some recent experiments on the flame spread problem are presented.

Bedforms produced by fine, cohesionless, granular and flakey sediments under subcritical water flows

ABSTRACTExperiments have been conducted in a 10 m long laboratory flume to investigate the bedforms which develop from fine, cohesionless sediment beds. Two grades of near uniformly sized silica grains (of median nominal diameters 15 and 66 μm) and six grades of micaceous flakes (ranging in median nominal diameter from 15.5 to 76 μm) were used. A steady subcritical water discharge, which was increased in steps after several hours, was applied to a flat bed of each grade. The developing bedform sequence for fine granular beds was identified as many small‐sized primary ripples, isolated primary, transverse primary, secondary ripples and then possibly dunes; this development was almost the same as that observed for coarser grains. The sequence for fine flake beds differed from grains. Only the single bedform type of parting lineations was observed; with increased discharge, the lineations began to oscillate and eventually enter into fluid suspension. The low discharge parallel lineations were thought to be generated by ‘streaks’ or lanes of transversely alternate high and low velocity fluid which have been reported to exist in the viscous sub‐layer of a turbulent‐smooth boundary, whilst the higher discharge wandering lineations were attributed to low velocity streak ‘bursts’.

Moment theory of breakthrough curves for fixed-bed adsorbers and reactors

For linear rate expressions in isothermal fixed-bed adsorbers or reactors, an approximate expression for the breakthrough curve (BTC) is obtained by applying the convolution theorem and integrating a Hermite polynomial series expansion for the pulse response of the column. The approximate solution is compared with exact solutions such as that of the Goldstein J function model and a dispersed-flow column with homogeneous first order reaction. If the series is truncated so that only two moments appear, i.e. the first absolute moment μ' 1 and the second central moment μ 2, then the approximate model gives BTCs which are in good agreement with the exact solutions when μ' 1 / (2μ 2) 1/2⩾ 2.5. The agreement is improved for longer columns and lower fluid velocities. For a model describing mass transfer to porous particles and intraparticle diffusion as well as adsorption, the approximate solution compares well with experimental data except for very short columns. The semi-empirical method of combining mass-transfer resistances is evaluated and is found to be quite accurate. An economic study of pumping cost and product value is developed to optimize flow rates in adsorption processes.

Heat transfer in a multi-stage flash/ fluidized bed evaporator (MSF/FBE).

The MSF/FBE process in which a fluidized bed heat exchanger is used represents an attractive process for water distillation. High heat transfer coefficients obtained at low fluid velocities allow for vertical long-tube condenser configuration with short stage heights. In an MSF/FBE vapour production takes place in the vapour space and causes a high interfacial heat transfer. Flash chamber volume is reduced with a factor 6 comparing with the conventional MSF. Fouling factor is drastically reduced by the mechanical abrasive action of the solid fluidized particles. Hence there is a more urgent need to know the wall-to-liquid heat transfer coefficient in fluidized beds. Correlations from literature are in some cases contradictory. Ruckenstein's correlation agreed best with indirect measuring of the coefficient. A test programme was started to investigate heat transfer and to measure values in a direct method test module. Data-aquisition is reported. Independent variables as particle size, porosity, particle density and tube diameter allow for application of a large variety in heat and mass transfer. This enables a optimum unit design based on thermo-economic considerations. Such an optimum design is only possible with the aid of a flexible computer program. Part of this paper is devoted to calculation procedures, while in the last part the test module for determination of the wall-to-liquid heat transfer is reflected.

The MSF/FBE: An improved multi-stage flash distillation process

A new type of flash evaporator is discussed which avoids certain limitations of the conventional horizontal flash evaporator. The main characteristic of the plant is its vertical concept with short flash chambers accommodating a large number of parallel tubes. Heat transfer in the tubes takes place by means of a fluidized bed. Due to this fluidized bed the heat transfer coefficient is enhanced in particular during operation at low superficial fluid velocity. Heat transfer data, stability of the multiple parallel fluidized beds, flash-off, entrainment separation, allowable vapour space loading of the flash chamber as well as the possibilities to design the plant for lower specific heat consumption and to operate at higher maximum brine temperatures are discussed. Delft University of Technology developed a 50 m 3/day plant for the production of feed water for the University's central boiler house. Construction and operating experiences of this plant are presented. Results of easy start-up and part-load procedures due to the non-flooding precautions in this design will be discussed. A comparative cost study between a 10,800 m 3/day horizontal flash evaporator of the Rotterdam Municipal Water Department and a MSF/FBE for the same production as the conventional plant will be mentioned in this paper. Further extensive studies on determination of heat transfer coefficients, fouling and scale removing capabilities of the fluidized bed are briefly mentioned.

The Measurement of Low Fluid Velocities with the Aid of a Tethered Sphere

Two‐ or three‐dimensional velocity fields in hydraulic models can be measured with the aid of a tethered sphere if the absolute velocity values are very small. The apparatus is relatively simple and quite sensitive. Experimental data can be handled numerically, taking into account all effects, and print‐out is readily available in useful tabular or graphical form. The greatest disadvantage at present seems to be that the position of the tethered sphere is not stable, and it is difficult to define when turbulence is present in the flow. The average position of the sphere will most probably not correspond to the velocity average in this case. This disadvantage is, however, shared by most velocity measuring devices with low frequency response. The second inaccuracy is that the program presently available is based on the assumption that the velocity is uniform over the height of the probe. The development of a new program taking into account continuously varying velocity and temperature profiles is in progress. It is of particular importance for small spheres on long support lines. The instrument may also be inverted by using a sphere slightly heavier than water. Such an instrument would be suitable for velocity measurements near the bottom of a channel. (Key words: Data; density currents; instruments; low velocity)

The Void Fraction in Subcooled Boiling—Prediction of the Initial Point of Net Vapor Generation

The satisfactory prediction of the vapor volume fraction in subcooled boiling depends in large part on the ability to predict the point where a significant amount of net vapor is first formed. A method for the prediction of this point is derived here and compared with experimental measurements at both low and high fluid velocities. The derived relationships for this point include the effect of fluid properties, geometry, and the liquid velocity. A comparison with the empirical formula of Bowring [2] for water is given.

Propping Agent Transport in Horizontal Fractures

Abstract This laboratory flow study covers propping agent transport in horizontal fractures as influenced by the characteristics of the propping particles, fluid and fracture. Correlations are presented for the transport of particles, deposition and fingering through dunes. For particles moving individually, the particle velocity in some cases may be low compared to the bulk average fluid velocity; in other cases, the particle velocity may exceed the bulk average fluid velocity. At high propping agent concentration or low fluid velocity, the likelihood of particle deposition and dune formation increases. Fingering and channeling accompany dune formation. Dune formation can be limited to the outer region of the fracture by adjustment of pump rate, fluid viscosity and particle concentration. A method is presented by which pump rate and fluid viscosity may be selected to control dune formation for given propping agent concentrations. Introduction The area and flow capacity of a fracture predominantly control the stimulation derived from hydraulic fracturing. Generation of fracture area exposes the rock matrix to a flow channel; the flow capacity of the fracture controls the flow through the channel to the wellbore under a given pressure gradient. This paper pertains to an important factor that affects the flow capacity of a fracture: the transport of the propping particles in the fracturing during the hydraulic fracturing treatment. With a better understanding of particle transport, fracturing treatments may be designed to obtain more effective distribution of the propping agent. RELATED STUDIES In recent years, the approach to obtaining high fracture flow capacity has been partial monolayer propping. Three papers have dealt with various facets of this concept. However, in some papers dealing specifically with particle transport, the results generally indicate that packing the propping particles within a fracture is inevitable. In early work with a sand slurry flowing in a pie-shaped flow cell, qualitative results showed that particle deposition in a fracture during transport should be expected. In other studies correlations based on slurry flow in vertical linear flow cells showed particle deposition was primarily a function of fluid velocity. In a recent paper the rate of sand advance (movement of dunes) in a horizontal linear flow cell was discussed. Subsequently, a method was given for designing fracturing treatments, based on the extent of sand advance during a treatment. In this work, particles whose diameter was small relative to the fracture width (i.e., d/W less than 0.2) were primarily considered. The particle transport approaches that of sand transport in a stream bed. The industry trend. however, has been to use larger size propping agents. That is, particles with diameters approaching fracture widths predicted by Perkins and Kern. This trend has led to generally better fracturing treatments with particle relative sizes in the range 0.2 less than d/W less than 1.0. In all of the particle transport studies previously cited. the fluid characteristics were discussed. However, little or no attention was given to the particle characteristics. In this study the particles, as well as the fluid and fracture, are considered. VARIABLES AFFECTING PARTICLE TRANSPORT In the exploratory work to set up a program for this study, it was noted that particles within a batch moved at different velocities in a horizontal linear flow cell. In some cases the particles moved independently. In others there was particle interference. Also, particle deposition and fluid fingering occurred in some cases (Fig. 1). As a result of observing the easily distinguishable types of particle movement, the particle variables as well as the fluid variables were included. In addition, the fracture with was included because the fluid velocity profile surely must affect the movement of the larger particles differently than that of smaller particles. Particle variables were density, diameter (based on a sphere of equal volumetric displacement), long and short dimensions, drag coefficient and velocity, fluid variables were density, viscosity, yield shear strength and velocity. Fracture variables were the width and the angle between the plane of flow and a horizontal plane. Two factors which may prove to be important were omitted because of the complexity resulting from the parameters cited above. These are the fracture-surface roughness and gross irregularities that cause changes in the direction of flow. EXPERIMENTAL EQUIPMENT AND PROCEDURE A linear parallel-plate flow cell (Fig. 2) was used in the study. Lucite plates 1 in. thick formed the test section and permitted a viewing section 11 ft long and 10 in. wide. Spacing between the plates was adjusted with shims to give fracture widths of 1/16 to 1/2 in. The model could be tilted to an angle of 45 degrees with the horizontal plane. Fluid flow was maintained with a Moyno positive displacement pump. Single particles were placed in the flow stream with a particle injector. JPT P. 753ˆ

A new technique for the measurement of low fluid velocities

A new instrument for measuring the velocities of particles suspended in a flowing fluid is described. The instrument is linear and is therefore capable of measuring the mean velocity in a fluctuating stream, even when these fluctuations are greater than this mean value. This particular instrument was developed for free convection work where the velocities to be measured were in the range + k 0.2 in./sec to − 0.2 in./sec, but there seems to be no reason why this range could not be considerably extended.

Reply to measurement of low fluid velocities

Reply to measurement of low fluid velocities

An instrument for measuring low fluid velocities

An instrument is described with which the velocity of a slowly moving fluid can be determined in terms of the change in temperature of a heated copper body exposed to the fluid stream. The change in temperature is detected by a thermopile assembly whose output is recorded on a spot galvanometer. The useful range of the instrument for the measurement of water velocity is 0.1-1.0 ft sec-1 and for air velocity 1.5-15 ft sec-1.