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By Ramon Augusto Moretti, Henrique da Rocha Severino, Renato Nascimento de Castro, Fernando Cesar Sousa

Rolling stand 12 (LTx) of long steel, installed in the company A, Piracicaba - SP unit, had presented high levels of vibration, which affected its internal components, such as: shaft, gears and bearings, generating downtime. To evaluate this equipment a study was proposed by the following engineering techniques: Conventional Vibration Analysis, Operational Deflection Shape (ODS) and numerical simulation by the Finite Element Method (FEM). In the Conventional Vibration Analysis, high levels of vibration were observed during manufacturing process, especially when the material reaches the equipment. Impacts generate high values in acceleration, on average 80 m/s² peak to peak. In the moment of impact, misalignment of internal components was observed by ODS. Field results were correlated to those obtained by the Finite Element Method, which allowed to calibrate FEM model. Thus, the most effective structural modification already numerically evaluated was implemented in the system. Afterwards, new measurements by vibration and ODS techniques were performed, and attenuation of vibrational levels and operational mode, which overloaded the internal components rolling stand, were verified.

Oct 1, 2019

By Jeremy Butkovich

Dynamic soil-structure interaction (DSSI) analyses are becoming more common in bridge designs, especially in seismically active areas. Because of its proximity to two active fault zones, the Evergreen Point west approach bridge replacement will be base isolated, and will be designed using DSSI. The project team completed two independent bridge designs to satisfy peer review requirements. The designs required substantial characterization of the soil dynamic behavior using both laboratory and in-situ testing. The analyses made use of earthquake time histories spectrally matched to conditional mean spectra. This led to reduced, and more realistic seismic demands on the structure, compared to conventional uniform hazard spectrum matching. The bridge analyses suggest that the preliminary bridge design is relatively conservative. This will allow the design team to potentially reduce shaft/column diameters and reinforcement. The design team estimates that the dynamic analysis design could represent a net savings of around $60 to $90 million compared to a conventional design.

By Greg Nutson, Jeremy Butkovich, Bill Perkins, Hollie Ellis, Paul Bott

"Dynamic soil-structure interaction (DSSI) analyses are becoming more common in bridge designs, especially in seismically active areas. Because of its proximity to two active fault zones, the Evergreen Point west approach bridge replacement will be base isolated, and will be designed using DSSI. The project team completed two independent bridge designs to satisfy peer review requirements. The designs required substantial characterization of the soil dynamic behavior using both laboratory and in-situ testing. The analyses made use of earthquake time histories spectrally matched to conditional mean spectra. This led to reduced, and more realistic seismic demands on the structure, compared to conventional uniform hazard spectrum matching. The bridge analyses suggest that the preliminary bridge design is relatively conservative. This will allow the design team to potentially reduce shaft/column diameters and reinforcement. The design team estimates that the dynamic analysis design could represent a net savings of around $60 to $90 million compared to a conventional design.INTRODUCTIONThe Evergreen Point Bridge conveys State Route (SR) 520 2.6 miles (4.2 kilometers [km]) from Seattle to Medina across Lake Washington. The bridge is located in a seismically active area, and the Washington State Department of Transportation (WSDOT) has determined that the western half of the 1960s-era bridge (the “west approach”) is vulnerable to earthquake damage. WSDOT has begun preliminary design to replace the west approach bridge.The west approach extends about 6,100 feet (1,900 meters [m]) east from Seattle’s Montlake neighborhood, over Union Bay and Foster Island, then into Lake Washington proper (Figure 1). Approximately 5,600 feet (1,700 m) of the replacement bridge would be constructed over water. Subsurface conditions along the bridge alignment consist of 5 to 80 feet (2 to 24 m) of very soft peat and clay, over very dense/hard sand and clay. Multiple pile supported columns support the existing bridge. The new bridge would be supported by 8- to 10- foot-diameter (2.4 to 3.0 m) drilled shafts that extend about 50 feet (15 m) into the underlying very dense/hard soil. To reduce seismic demands on the bridge superstructure, WSDOT has decided to incorporate a base-isolation system into the bridge design."

Jan 1, 2017

By Frank Rausche

Without doubt, driven piles are the most economical deep foundation element for a nearshore environment, providing for high bearing capacities and stiffness, quick installation times, assured quality by simple monitoring and inexpensive dynamic load testing during restrike testing. However, when the pile top elevation is several meters below water surface, questions often arise as to the most reliable and economical pile installation method. Frequently encountered, yet relatively expensive, solutions include driving inside a dewatered cofferdam, driving long piles that are later cut off below water surface, or using an underwater hammer. Arguably, the most economical solution is driving the piles with a follower or chaser. However, many foundation engineers shy away from this solution because of the uncertainty associated with the transfer of energy through the interface between follower and pile, the associated potential driveability problems and maybe the limited fatigue life of the follower. This paper will demonstrate how the driveability of a hammer-follower-pile-soil system should be analyzed prior to installation and how to model the pile-follower interface both for steel and concrete piles. As an example, results will be presented which were obtained for both steel pipe piles and precast concrete piles, driven by a single-acting diesel hammer through a steel follower for a pre-construction test pile program in Venice, Italy. While analysis of the steel pile-follower system was straightforward, for the concrete piles, the presence of a soft cushion material whose material properties changed continuously posed some difficulty. Pile Driving Analyzer® measurements and CAPWAP® analysis yielded not only realistic stresses and transferred energy values in the pile, but also reasonable model parameters for further use in a pure wave equation analysis. As a side note for clarity, the dynamic measurements and analysis results herein presented are based on the GRLWEAP and CAPWAP software. GRLWEAP is commonly used all around the world for the preparation of pile driving jobs. The program either yields a bearing graph that relates bearing capacity and pile stresses to blow count or set per blow or it predicts blow counts and pile stresses as a function of pile penetration. These results allow the contractor to estimate driving time and select an economical hammer and driving system for a safe and efficient installation. CAPWAP on the other hand is the analysis of choice once a pile has been installed and records of pile top force and velocity have been acquired during installation or during a restrike test. CAPWAP is a signal matching program which calculates for one particular impact (for example at the end of driving) the static and dynamic soil parameters. Its final results include the calculated resistance distribution, the complete stress history in the pile and also a simulated load set curve. The CAPWAP calculated dynamic soil parameters can also be used in a Refined GRLWEAP analysis to generate a calibrated bearing graph."

Jan 1, 2006

By M. C. Williams

The dynamic behavior of batch mill, CSTR mill, and a closed grinding network consisting of a mill, sump, and cyclone was analyzed using the dynamic population balance model (PBM). The dynamic solution of the PBM of a batch, CSTR and a closed grinding network consisting of a mill, sump, and cyclone forms the basis of the dynamic analysis presented here. Two numerical dynamic solution approaches were used. These are: 1) providing additional constraints on breakage selection functions or 2) performing the Arbiter-Bhrany (or other) normalization of the selection functions. Actual experimental anthracite batch grinding data was used to obtain the functionality of the batch dynamic mill selection and breakage functions for a real physical system. The Levenberg-Marquardt algorithm for systems of constrained non-linear equations is used to solve the batch dynamic PBM grinding equations to obtain the grinding selection and breakage rate functions. The mill, sump and hydrocyclone were modeled as a CSTR operating at various retention times. Batch dynamic PBM data was used to provide the mill kinetic and breakage selection function data. Different dynamic solutions were obtained depending on the numerical approach used. Each solution approach to a dynamic PBM with transport, while giving the same prediction for a single batch grinding time, gives different solutions or predictions for mill composition for other grinding times. This fact makes dynamic nodal analysis and control problematic. The fact that the constraint solution approach gives a solution may suggest that normalization for closed networks is not necessary. Differences in solutions to the PBM cannot be excused away by inaccuracies in the data used to model the grinding phenomenon.

Jan 1, 1995

By Jorge Castillo

This paper presents a dynamic analyses of heap leach pad stability under high phreatic levels and various levels of seismic loading. The dynamic analysis were conducted as fully non-linear two dimensional analyses with fully coupled liquefaction triggering using the Fast Lagrangian Analysis of Continua (FLAC) computer code. Also, the geotechnical parameters, appropriate earthquake record selection and modification, model calibration, numerical analyses and results are discussed.

Sep 12, 2005

By Douglas Lindsey, Glenn Hazen, Shad Sargand

"With the innovation of computational equipment, an exact analysis of structures as dynamic systems is more approachable. Accordingly, the dynamic system can be established, if the natural characteristics such as the natural frequency and the damping fraction of a system are known. Through dynamic analysis, the response of a structure can be predicted from ground vibration, and it becomes possible to forecast the damage potential to the structure with reasonable accuracy. Most vibration will appear as single harmonic or superposition of waves that consists of several harmonics with different frequencies. A vibration signal can be expressed, therefore, as the function of sine waves. If a signal is periodic, the particular harmonic with the smallest frequency will befundamental and frequency of the others will be multiples of the fundamental frequency."

Jan 1, 1993

By J. Jay Jacobsen

A dynamic regional coal development model is constructed for the Eastern Powder River Basin of Wyoming. Using this model, alternative development schedules from a recent environmental impact statement submitted to the Department of the Interior are simulated (Ref. 1). These alternatives include different mixes of export capacity, different coal conversion techniques within the region, as well as various levels of coal production. Exportation of 70 to 80 percent of an ultimate coal production of 180 million tons (163.3 x l09 kg) per year and the careful phasing of additional public services with population growth effectively reduce the social and environmental impacts of coal development. The alternative involving the addition of 43,000 megawatts of electrical generation capacity has very significant adverse social and environmental impacts on the region.

Jan 1, 1977

By Thomas Hyatt, Brandon Phetteplace, Camilo Alvarez

A test pile program was undertaken at a project site in Ain Sukhna, Egypt for an import/export oil jetty. Two 1219 mm diameter open ended steel pipe piles were evaluated at two separate test locations. Each test pile was dynamically tested during initial drive utilizing a Pile Driving Analyzer (PDA). Restrike testing was also performed to evaluate the time dependent soil setup. One static compression test and one static tension test was performed at each test location. A correlation of the static and dynamic load test results was established to develop a driving criteria for the piling across the two kilometer project. The constructability benefits of shorter piles will be discussed in more detail, given that the pile lengths were shortened by 9 to 10 meters on average. Lastly, the use of a four pile linear layout to perform both compression and tension tests will be covered. INTRODUCTION With the increased number of Very Large Crude Carriers (VLCC) & Ultra Large Crude Carriers (ULCC) being used to transport oil products around the world, companies and/or nations are presented with the challenge of transferring these products to and from the carriers in deep water scenarios, typically 15 to 20 meter depths, to accommodate the vessels draft. One option for loading/unloading the oil products from a VLCC or ULCC would be to transfer to/from smaller vessels several miles offshore, whereas the most economical option is to unload directly to a pipeline via a berth/jetty platform near shore. These berth platforms must be designed to withstand multiple loading scenarios while these carriers are moored and transferring their products. The use of Large Diameter Open Ended Pipes (LDOEP) piles are a common foundation choice for this offshore application. One of the drawbacks of LDOEP piles, especially across a large project site, is that there can be extreme variability in the pile driving behavior. This can be caused by either a change in soil conditions or the performance of the soil plug. Due to this variability, it is important to verify throughout the duration of the project that the piling is being installed to the correct criteria as established during the load test program. A well designed driven pile load test program, preferably with the combination of Static Load Testing (SLT) and Pile Driving Analysis (PDA), should develop a driving criteria that can allow the contractor and owner to monitor any change in driving behavior.

Jan 1, 2019

By Terrence M. Carroll, Chu E. Ho

"A pile installation and load testing program on driven tapered piles was undertaken at John F. Kennedy International Airport in New York City for the extension of the existing Terminal 4. As part of the program, dynamic testing by means of the Pile Driving Analyzer (PDA) was performed on several preliminary test piles as well as production piles. The results of the dynamic tests and subsequent static load tests were reviewed to develop an understanding of the pile-soil response of a tapered pile during driving and after setup. Pile setup occurred as a result of increase in shaft resistance with virtually no increase in toe resistance. More than 150 tons of additional capacity was gained after the setup time.The capacities measured during driving from the PDA are typically used as the basis for determining the pile driving set criteria, with the required initial driving capacities determined largely by the contractor’s experience. An improved appreciation of the setup phenomenon is required to better refine the driving criteria at the end of initial driving such that the required ultimate capacities can be obtained, with reasonable confidence, after a period of setup.This paper presents interpretation of pile-soil behavior from Case Pile Wave Analysis Program (CAPWAP) analyses and discusses the mechanism of increased capacity as a result of setup effects. Time-dependent capacity gain as a result of setup effects should be based on the extrapolation of the shaft resistance component rather than the total pile capacity as is commonly practiced. Prediction of pile performance using this approach was in good agreement with observed static and dynamic load test results.IntroductionTapered piles have been adopted for various projects at John F. Kennedy International Airport (JFKIA) since the late 1940’s. Initially timber piles were used exclusively, with steel Monotube piles being used from at least the 1980’s (Horvath and Trochalides, 2004). The steel Tapertube pile was developed in the mid-1990’s and has commonly been used in recent construction (Brusey and Yin, 2008). The Tapertube piles used for this project consisted of a 25 foot long tapered section that was 8 inches in diameter at the tip and 18 inches in diameter at the top. An 18 inch diameter straight pipe was welded above the tapered section."

Jan 1, 2015

By W. J. van Niekerk

Ballast Nedam is in Surinam constructing two bridges that will improve communications in the coastal region. The bridges will cross the Coppenam and Surinam rivers and will be founded on open-ended steel piles over 60 meters in length. The majority of piles are inclined and support prefabricated concrete girders forming the roadway. In most locations the stratum is consolidated cohesive layers extending to a depth in excess of 60 meters. For this reason, before pile driving operations commenced, it was decided that a number of test loads would be carried out determine the capacity of the piles. Loading tests were carried out on specially installed piles as well as on piles that would be used as working piles to support the structure. Working piles were dynamically tested using Pile Driving Analysis (PDA) equipment. This decision was based on the inclination of the piles, the cohesive nature of the soil and the increase of strength after the piles are driven. A good insight has been obtained into the real strength of the soil by comparing dynamic and static loading tests on vertical test piles. This made it possible to determine the required length of pile.

Jan 1, 2000

By Yingcai Han

The dynamic behavior of pile foundations is investigated in both theory and practice. The computation method for vibration of pile foundations and DYNAN computer program are introduced comprehensively. With a model of non-reflective boundary between the near field and far field, the Novak's method of soil-pile interaction is improved. The dynamic analysis and design of foundation for a reciprocation compressor with driver power 15,000 HP are described to illustrate the computation method of soil-pile interaction. Different design options for the piles are compared to limit the vibration of foundation and produce a safe, economic system. The design with 16 - 0.9 m piles is adopted rather than that with 25-0.5 m piles, since the larger damping is provided by the piles with larger diameter. Both field and laboratory tests were carried out to investigate the soil properties including down hole seismic tests to provide soil shear wave velocities at different depths. The method and procedure used in this study can be applied to the design of pile foundations for tall buildings, bridges and offshore platform with soil-pile interaction under seismic, blast, sea wave and other dynamic loads.

Jan 1, 2002

By A. K. Kyllo, N. B. Gray, B. N. McCurry

"Dynamic control of the formation of a solidified layer between a pipe wall and a flowing melt enables the flow rate to be adjusted in real time. This solidified layer can be generated by using a coolant on the outside of the pipe wall to remove the required heat. The coolant, and hence the solidified layer, can be controlled remotely. The dynamic behaviour of the solidified layer was investigated by both physical experiments and mathematical modelling. The mathematical model has been developed using a finite difference technique to describe conduction through the pipe wall and solidified layer. Results from the model were consistent with previous steadystate experimental results using molten lead. Experiments are currently being carried out using molten tin in a recirculating circuit with a cooling system that is instrumented for accurate computer control to validate the model. The circuit is designed for flowrates of up to 24 kg/s (86 tph) of molten tin. Steady-state and dynamic predictions were made for the current rig.Industrial SignificanceThe current method of choice for tapping slags, metals and mattes from many metallurgical furnaces is using an oxygen lance to open the taphole and using a clay plug to close it. There are, however, some significant drawbacks in this method. The heat generated by the oxygen lance erodes the refractory lining of the taphole, as well as the clay plug, and the furnace products themselves corrode the taphole. Using an oxygen lance is also a significant safety hazard to the operators as they must work in close proximity to the furnace and be subjected to a shower of sparks while opening the taphole. Also, the flowrate of material through the taphole cannot be controlled online as the diameter of the opening cannot be varied easily. This feature means that the level of product in a furnace cannot be kept constant."

Jan 1, 1999

By J. Seo

We propose a dynamic biomechanical simulation method that uses motion capture to evaluate the risk of Work-related Musculoskeletal Disorders (WMSDs). Statistics show that WMSDs accounted for 33% of all non-fatal occupational injuries and illness in construction in 2009, and were a leading cause of temporary and permanent disability. Present methods rely largely on self-reports from workers, observational techniques, and direct measurements of motion and muscle activity to assess awkward postures, physical loads, repetitiveness, and the duration of exposure. While these methods have helped to prevent WMSDs in construction work, they may not be suitable for estimating the internal tissue loads associated with WMSDs. We propose a dynamic biomechanical simulation method to estimate internal forces and moments at each body joint of construction workers with motion capture data. Particularly, we explore the biomechanical loads by simulating active 3D musculoskeletal models based on measured postures and movements. To demonstrate the feasibility of this approach, we studied a ladder climbing task using a portable ladder under controlled laboratory conditions. Postures and motions were determined with a commercial motion capture system (e.g., VICON). The results were analyzed to investigate the feasibility of identifying risk factors based on biomechanical simulation. The results show that the proposed approach allows us to determine the biomechanical basis for WMSDs, and to identify postures and movements associated with excessive physical demands on each body joint. When combined with marker-less motion capture which is our ongoing work, the proposed approach has the potential to assess an individual?s motions and to provide personalized feedback for the purpose of reducing biomechanical loads and WMSD risk in real workplaces.

Aug 1, 2013

By J R. "Dick" Daniel

One of the more common tasks in blast management is the adjustment of: shot geometry, explosive energy, and shot timing parameters to achieve changes in blast outcomes and costs. Many of these shot parameters, once a delayed blast is initiated, are modified by the development of new free faces which change the original or static input values to dynamic values. These newly generated dynamic values are easily calculated and find use in fine tuning shot adjustments and in rationalizing blast outcomes in a systematic manner.

Jan 1, 1996

By J R. "Dick" Daniel

One of the more common tasks in blast management is the adjustment of: shot geometry, explosive energy, and shot timing parameters to achieve changes in blast outcomes and costs. Many of these shot parameters, once a delayed blast is initiated, are modified by the development of new free faces which change the original or static input values to dynamic values. These newly generated dynamic values are easily calculated and find use in fine tuning shot adjustments and in rationalizing blast outcomes in a systematic manner.

Jan 1, 1996

By P. Cleyle, J. H. Masliyah, R. S. Chow, Z. H. Xu, Z. A. Zhou

Bubble nucleation in water under dynamic conditions was investigated using an autoclave at an air saturation pressure of 7 atm. Agitation during air saturation of water was found to be crucial in enhancing tiny bubble formation. More bubbles nucleated on hydrophobic surfaces at a higher agitation rate, due to cavity formation by the more intense hydrodynamic conditions. Flotation recovery of bitumen from oil sands demonstrated a significant role of bubbles nucleated in water: more than 50-170% increase in bitumen recovery from different oil sands was obtained by using air supersaturated than the regular water.

Jan 1, 2009

By Tsuda Wakaki, Naoki Takahashi, Natsuki Okuno, Hidenori Takahashi, Ikuo Towhata, Yoshiyuki Morikawa

"Deep mixing (DM) method has been increasingly employed as a countermeasure against subsoil liquefaction in recent years. Pile-type DM, however, is considered to have little effect as a liquefaction countermeasure, because the shear deformation of unimproved soil around the piles cannot be reduced. However, experimental results, which imply that shear deformation of unimproved soil around DM piles can be reduced, were reported. Furthermore, a new plane-arrangement of DM piles has been proposed to mitigate lateral flow induced by liquefaction. The DM piles in this arrangement confront the lateral flow in any direction, compared with the piles arranged in conventional pattern such as square and triangular arrangements. In this study, a series of dynamic centrifuge model tests was conducted to verify the lateral flow resistance of DM plies in the new arrangement. The results indicate that the DM plies can reduce the lateral flow of liquefied ground when the pile displacement and the pile head rotation are restricted. In addition, lateral load acting on DM pile from liquefied ground, which is required for design strength of the DM pile, was investigated.INTRODUCTIONDeep mixing (DM) method has been increasingly employed as a countermeasure against subsoil liquefaction in recent years. The solidified body formed by the deep mixing method is usually block or lattice shape, composed of solidified columns that overlap each other horizontally. Lattice-type solidification has been shown to be effective as a liquefaction countermeasure despite the presence of unimproved soil inside the lattice wall, because the shear deformation of the interior soil is restrained by the wall (Suzuki et al., 1989). On the other hand, it has been thought that pile-type DM cannot reduce shear deformation of unimproved soil around the piles, because the displacement of the pile is less restricted than that of the lattice wall. DM piles have been reported to have little effect as a liquefaction countermeasure, but to be superior in terms of construction cost and applicability around existing underground structures (Koga et al., 1986). However, there are experimental results implying that DM piles have reduced the shear deformation of unimproved soil and mitigated its liquefaction (Yasuda et al., 2003; Tanaka et al., 2003). Yamamoto et al. (2006) conducted dynamic analyses of ground improved with lattice- and pile-type DM. Their results showed that pile-type DM with an improvement ratio of more than 35% reduces excess pore water pressure generated by earthquakes. Furthermore, the new pile arrangement shown in Fig. 1(a) has been proposed to mitigate lateral flow induced by liquefaction. It was developed and has been verified using dynamic model testing in a 1 g field (Takahashi et al., 2010a; 2010b; 2013; Towhata et al., 2010, Morikawa et al., 2014). The DM piles in this configuration interrupt lateral flow in any direction, unlike those placed in square and triangular arrangements."

Jan 1, 2015

By Martina Balic

Dynamic properties of the drilled shaft foundations supporting Doremus Avenue Bridge were determined by forced vibration testing. The main objectives of the substructure testing at Doremus Avenue Bridge were: (1) site evaluation with respect to the dynamic soil properties, and, (2) shaft evaluation for the purpose of definition of their dynamic stiffness. The site characterization entailed crosshole testing for the purpose of evaluation of the shear modulus profile. The drilled shaft impedance evaluation was done through forced excitation using an electromagnetic shaker. The responses of the tested shaft, as well as the response of adjacent shafts, were measured for the purpose of evaluation of the shaft interaction. To gain a better insight into the shaft dynamics, one of the shafts was instrumented with five triaxial geophones distributed along the full length of the shaft. The scope and results of the site characterization, shaft impedance and shaft interaction evaluation are presented.

Jan 1, 2004

By L. Vinnett, I. Panire, J. Yianatos, F. Ruiz

"The effect of operating variables on the flotation performance at steady-state has been extensively used for modelling and simulation of separation processes. However, the dynamic characterization of key variables such as gas dispersion (Sauter mean diameter of bubbles, D32, and bubble surface area flux, SB) and froth discharge rate is rather scarce. In this paper, an experimental design allowed identifying the dynamic response of the flotation process in a laboratory scale flotation cell, using a two-phase system, airwater. The installation included automatic control for the superficial gas rate, JG, and the pulp level. Gas dispersion was evaluated in terms of the Sauter mean diameter of a bubble population and the bubble surface area flux, SB = 6·JG/D32. The D32 was measured using the McGill Bubble Size Analyzer (MBSA) along with a semiautomated algorithm. In addition, the froth discharge velocity was measured in real-time using a Visiofroth system. The control variables were the superficial gas rate and the frother concentration (Teefroth). The dynamic characterization of the flotation process is useful to design algorithms that allow the direct or indirect control of metallurgical variables such as flotation rate, concentrate grade and mineral recovery.INTRODUCTIONGas dispersion indicates the way the gas entering a flotation machine is dispersed throughout the volume of the equipment (Schwarz & Alexander, 2006). The gas dispersion is typically characterized in terms of the bubble size (dB), gas holdup (eG), superficial gas rate (JG), and bubble surface area flux (SB =6·JG/dB) (Finch et al., 2000). All these variables have significant impact on the metallurgical performance of flotation machines. For example, Perez-Garibay et al. (2014) investigated the effect of the particle size, bubble size distribution, superficial gas rate and collector dosage on the flotation performance, for the separation of a sphalerite mineral. The authors observed that recovery increased with the superficial gas rate ranging from JG = 0.04 to JG = 0.08 cm/s and also a maximum recovery was obtained for bubble size close to 300 µm. Gorain et al. (1998) reported a strong correlation between the flotation rate constant and the bubble surface area flux in a zinc cleaner circuit. Both variables were directly proportional at three froth depths in the range of hF =7 - 45 cm. Dobby & Finch (1986) incorporated the effect of the superficial gas rate and the bubble size on the flotation efficiency by means of a kinetic model for the rate constants. Yianatos & Contreras (2010) developed a model to estimate the carrying capacity in large flotation cells by including the bubble surface area flux."

Jan 1, 2016