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By Walter Kauzmann

ALL viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.[t] Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem -i.e., the dependence of shear rates on temperature, stress, etc.-from the standpoint of recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of applications1 RESOLUTION OF MACROSCOPIC SHEAR INTO MICROSCOPIC MOVEMENTS; RESEMBLANCE TO CHEMICAL REACTIONS Just as any large body is made up of many small units, or atoms, so macroscopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for nonturbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove. In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker,4 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the

Jan 1, 1941

By Walter Kauzman

ALL viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.[t] Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem -i.e., the dependence of shear rates on temperature, stress, etc.-from the standpoint of recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of applications.1 RESOLUTION OF MACROSCOPIC SHEAR INTO MICROSCOPIC MOVEMENTS; RESEMBLANCE TO CHEMICAL REACTIONS Just as any large body is made up of many small units, or atoms, so macroscopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for nonturbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove. In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker,4 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the

Jan 1, 1941

By J. D. Miller

Fluid flow phenomena and therefore the flotation efficiency of air-sparged hydrocyclone (ASH) flotation are strongly dependent on operating and design variables such as air and slurry flow rates, underflow and overflow opening areas, percent solids of the feed, reagent levels, particle size and ASH length. Time-averaged multiphase flow characteristics, as determined by X-ray CT (described in a previous publication), are used to understand and explain the steady-state ASH flotation of quartz. A detailed parametric study of quartz flotation by a nominal 2in. diam. air-sparged hydrocyclone (ASH-2C) revealed the influence of these variables on the flotation response, which is discussed in terms of the multiphase flow characteristics. Thus, a phenomenological description of quartz flotation has been established to assist in the further development and utilization of the ASH technology.

Jan 1, 1996

By J. D. Miller

Fluid flow phenomena and therefore the flotation efficiency of air-sparged hydrocyclone (ASH) flotation are strongly dependent on the operating and design variables such as air flow rate, slurry flow rate, underflow and overflow opening areas, percent solids in the feed, reagent levels, particle size, ASH length, etc. Time-averaged multiphase flow characteristics, as deter-mined by x-ray CT and described in a previous publication, are used to understand and explain the steady-state ASH flotation of quartz. A detailed parametric study of quartz flotation by a nominal 2-inch diameter air-sparged hydrocyclone (ASH-2C) revealed the influence of these variables on the flotation response which is discussed in terms of the multiphase flow characteristics. Thus, a phenomenological description of quartz flotation has been established to assist in the further development and utilization of the ASH technology.

Jan 1, 1995

By R. Haldenwang, R. Erasmus, P. T. Slatter, R. P. Chhabra

Notches are used routinely for measuring the flow rate of water with free surface flows. As far as can be ascertained, no work has been done to investigate the performance of these flow rate measurement devices for non-Newtonian suspensions. The Flow Process Research Centre at the Cape Peninsula University of Technology has investigated the flow rate of kaolin and bentonite suspensions from a tank for two notch shapes, namely rectangular and triangular, and for 3 different concentrations of each suspension. The notches were calibrated using water and then the kaolin and bentonite suspensions were tested in them. The rheological characterisation of the fluids was done with a Paar Physica MC-1 rotary viscometer fitted with a cup and roughened bob. Analysis of the results shows a significant increase in discharge coefficient with increase in concentration, and the discharge coefficient has been correlated to the yield stress. This is the first such study, and further investigation is needed to confirm and extend these findings.

Jan 1, 2007

By L. C. Uren

THE resistance to flow of mixtures of gas and oil in passing up through the flow tubing of oil wells operated by gas-lift or by natural flow is a factor in oil-recovery technic that has received but little attention. Yet accurate design of a tubing installation for a particular set of conditions, where operation is by either of 'these methods, is impossible without quantitative data on the pressure loss suffered by the oil-gas mixture in its passage through the well tubing to the surface. Because of lack of such information, petroleum production technologists have been compelled to approach this problem by "cut-and-try" methods, which, doubtless in many cases, has resulted in the installation and use of tubing too large or too small for most efficient utilization of the expansive force of the gas used in lifting the oil. Impressed with the necessity for information of this character, the authors have conducted a series of tests with large-scale apparatus in the petroleum engineering laboratories of the University of California, designed to be productive of data that would afford a means of attacking the problem of flow-tubing design on a more scientific basis.

Jan 1, 1929

By M S. Henderson, R D. Alorro, L G. Dyer

An alternative leaching system for rare earth element recovery from monazite is under development. The initial stage utilises oxalic acid to convert the rare earth phosphate into an oxalate salt through dissolution and reprecipitation and it is the efficiency of this stage that governs the overall recovery achieved. It has previously been proposed that lixiviant consumption is the primary limitation in this process. This work further investigates a range of conditions in an attempt to further elucidate the factors influencing the achievable conversion in this stage. It has been shown that the pH may be governed by multiple reactions both consuming and producing acid (thus the mild change over time). The importance of proper mixing and potential to operate at lower temperature with only moderate impact on kinetics has also been demonstrated. Staged/sequential leaching is more effective in fresh solution as opposed to restoring the lixiviant concentration with subsequent reagent addition, suggesting some impact of solution composition. However, contrary to previous findings, subjecting the leach residue to fresh solution resulted in significant decline in leach rate and overall dissolution. This may be because a greater proportion of conversion was achieved in stage 1 in this work than in previous investigation. This may indicate that eventual passivation or the presence of some more refractory REE minerals limits dissolution. Iron dissolution was relatively consistent upon exposure to fresh solution, displaying the ability of the solution to continue to leach the goethite component of the concentrate.

Aug 24, 2022

Flow Sheet Development of Three Geographically Distinct Chromium-Bearing Ores

Sep 13, 2010

Flow Sheet Simulation of Municipal Waste Treatment Processes

Sep 13, 2010

By C. Dan Kealy

Recent antipollution legislation for the control of mine tailings and waste-water has required an increasing number of tailings ponds. Many of these new waste-retention ponds are being constructed in congested locations, or the older ponds have reached such a size that--if failure occurs--they pose a threat to human life and public property. Although the typical tailings-disposal embankment represents--to the casual-, observer or the economy-minded mine official--a rather ugly but benign and stable pile of waste, they are in fact an extremely sensitive structural mass, retained behind the frailest of dikes. Failure of the waste mass requires only a minor change in water retention or weather conditions, erosion or piping of the ground strata, shifts in load or slight earth tremors. When failures occur, the results can be disastrous. In the U.S., we have been fortunate that, so far, pond failures have not caused loss of life. Thus, failures in this country have attracted little public attention. Present tailings-pond construction methods used by the mining industry require the barest money investment, and little engineering effort. Unfortunately, this superficial approach may increase short-term profits, but the practice may be conducive to the construction of needlessly weak structures. In coming years many of these designs will probaly become corporate liabilities. A typical pond is portrayed in Figure IA. This particular pond in Arizona is 1 mile long and 3/4 mile wide. Illustrated in Figure lB is a representative pond in cross section. This paper in concerned with two basic features common to all tailings disposal: (1) location of the phreatic surface within a tailings-pond embankment because of its influence on embankment-slope stability, and (2) prediction of

Jan 1, 1971

By Adrian C. Deneys, David G. C. Robertson

"Fluid flow phenomena on the surface of a molten slag have been documented using video photography in a laboratory scale D.C. arc furnace. The flow on the surface of the slag appeared to be electromagnetically influenced. This was confirmed by varying the position of the anode, which changed the direction of flow on the surface of the slag. Temperature measurements in the bath also confirmed the change in the directional nature of the fluid flow induced by the arc.During some periods, solids were fed into the arc attachment zone (AAZ) down the center of the hollow graphite electrode. Significant movement of the arc around the basal annular surface of the hollow electrode takes place. The point of attachment of an arc on a hollow electrode was more variable than an arc attached to a solid graphite electrode. Video images showed that the solids were rapidly incorporated into the bulk of the slag. Temperature measurements confirmed the existence of a superheated slag layer at the slag-gas interface, which allowed the solids to be rapidly incorporated into the melt.This work has been conducted to study fluid flow, temperatures, and solid behavior during feeding, in the arc attachment zone of a D.C. arc furnace. The work also has relevance to optimizing furnace design for pyrometallurgical slag cleaning processes."

Jan 1, 1999

By F. Shen

Qualitative and quantitative results obtained during the physical modeling of the molten aluminum flow in a tundish using an aqueous system are presented. Surface tuft, free-surface powder and laser sheet visualization techniques were utilized for qualitative studies, whereas laser Doppler velocimetry was used to elucidate the 3-D flow regimes quantitatively. The results of the study are used for validation of the CFD codes, and to explore the effect of the alterations below the nozzle in order to: (1) decrease turbulence levels, and (2) collect the inclusions. Near the nozzle, the interaction of the impinging jet and the inclined walls gives rise to vortex structures. Downstream of the nozzle, two counter-rotating secondary cells diminish in strength. As flow turns through the bend, a separation region is created. The flow heading into the closed duct is seen to be nonsymmetric. A video tape highlighting the major findings is presented.

Jan 1, 1993

By D. Bouchard, M. Forté, A. Charette

A transparent replica of a casting die was built to achieve a better understanding of the filling mechanisms of aluminum in high pressure die casting. Water and tomato paste were respectively used as analogues for the Newtonian liquid aluminum and the non-Newtonian semi-solid aluminum. The transparent die was installed on an industrial casting press and filling was filmed with a high-speed camera. Differences between the Newtonian and non-Newtonian fluids are presented and discussed.

Jan 1, 2006

By Frances Jane Cromwell, D. J. McAdam, G. W. Geil

INTRODUCTION IN a series of papers, the authors and their associates have shown that the technical cohesion limit is affected by the same four factors that affect the flow stress, namely, the stress system, plastic deformation, temperature, and the strain rate.16-28 Moreover, each of these factors affects the technical cohesion limit in the same way that it affects the flow stress.‡ The influence of any one of these factors may be represented by a curve of cohesion limits, although only one point on the curve may represent actual fracture. As the term "fracture stress" has come into use with the same significance as "technical cohesion limit," the authors are here using the shorter term with the understanding that it does not always refer to actual fracture. This paper presents the results of an investigation of the flow of notched and unnotched specimens between yield and fracture. A study has thus been made of the flow and fracture of metals as affected by the stress system, and of the ductility of metals as affected by the stress system throughout plastic deformation. Since two of the principal stresses were equal (S2 = S3), the stress systems can be represented in terms of the radial stress ratio, the ratio of the transverse radial stress S3 to the longitudinal stress Sl.* The results of the experiments are represented by a series of complete flow-stress curves for each of the metals investigated, and these diagrams have been used for the development of other diagrams of various types. Ludwik was the first to suggest that fracture occurs when the flow stress becomes equal to a technical cohesion limit. Although Ludwik was incorrect in his view that the technical cohesion limit depends only on the amount of plastic deformation and not on the stress system, he was correct in his view that the flow-stress curve for any stress system terminates at a point representing a technical cohesion limit. The authors have seen some recent references to assertions by other investigators that a point representing the fracture stress need not be on the flow-stress curve. The Ludwik principle, however, would seem to be axiomatic, provided that the flow stress and fracture stress are properly defined and that the fracture stress is properly determined. Disregard of this principle has led to some untenable theories of criteria for fracture. When a metal is very ductile, the conventional method of determining the ductility and fracture stress by dividing the breaking load by the sectional area after fracture, generally gives values that are much too high. With some metals and in some conditions, the fracture stress thus determined may be two or more times the

Jan 1, 1948

By G. W. Zhang

Ultra-fine Stirred Mill is a kind of high energy efficient equipment for ultra-fine grinding, and has been the mainstream equipment in the submicron powder and slurry industry. This paper mainly describes flow-field numerical simulation of the three popular ultra-fine grinding mills: (respective-ly as) Disc Stirred Mill, Pin Stirred Mill and Spiral Stirred Mill, by means of the software Computational Fluid Dynamics (CFD). In the flow-field numerical simulation, the velocity gradient, shear rate dispersion of the flow-field, the viscosity dissipation rate were analyzed with CFD. It is discovered that Pin Stirred Mill has the highest velocity gradient in circular directions and the most homogeneous distribution of shear rate among the three. Flow-field numerical simulation provides a new way (and means to) for the parameter optimization design and project enlargement of Ultra-fine Stirred Mill. The experiments were also carried out, the results are consistent with the results of the simulation analysis. For example, in GCC grinding experiments under the same conditions, the specific energy consumption of Pin Stirred Mill with 3600L in volume is 15%~17% less, and its processing capability is 13%~15% better than Disc Stirred Mill. Now with its optimized structure and excellent performances, more than ten sets Pin Stirred Mill with 3600L in volume have been used in industrial production in Shandong, Guangdong and Hunan province.

Jan 1, 2014

By Robert B. Parsons

"Recent amendments to the so-called ""flow-through share"" rules in our income tax legislation have given a new lease on life to this once popular investment vehicle.The original ""Dome funds"" for exploration in the Beaufort sea recognized the usefulness of flow-through share arrangements, but, by and large, flow-through shares have until recently not been able to compete effectively with other tax shelter instruments-mainly , limited partnership interests.This month, Tax Notes examines the new tax rules for investing in flow-through shares.IntroductionRecent income tax amendments have helped to rekindle investor and industry interest in so-called ""flow-through shares"" as a mechanism for mobilizing funds toward mineral exploration and development activities. In competing for investment funds, flow-through shares have historically placed a distant second in terms of investor popularity, being unable to compete with the more attractive features of limited partnership arrangements. However, primarily as a result of favourable changes to the income tax law, flow-through shares may be well poised for a comeback.This article examines the income tax considerations pertaining to issuing and investing in flow-through shares, and compares the former and the new income tax rules relating thereto. Of course, inasmuch as a flow-through share issue can involve various contractual arrangements between the investor and the issuer, there is a wide range of legal and business factors that generally have to be taken into account. A discussion of these matter s is beyond the scope of this paper, which is restricted to a summary of the special income tax factors attributable to flow-through shares."

Jan 1, 1983

By Roy J. Leonard

Two small diameter sewer tunnel projects being hand dug under major highways in the Greater Kansas City area encountered problems which were unforeseen from the geotechnical engineering information supplied with the contract documents. Both tunnels were being excavated by experienced crews using steel liner plates. One required the use of compressed air for completion, while the other required poling boards. Both contractors overran their budgets and filed changed condition claims, and this promoted further geotechnical engineering investigations. Fissured clays beneath a water table were encountered at both sites, but the character of these clays differed; however, both were inadequately described in the original geotechnical engineering reports.

Jan 1, 1987

By F. B. Micheli

Introduction and Historical Background Although both sluices and devices using a simple flowing film are among the oldest known methods of concentration, they are still extensively employed in a variety of situations where they are not only efficient but also have a low operating cost. More particularly, they are valuable for making a bulk concentrate of high specific gravity minerals from alluvials and beach sand and in upgrading low value ores. The antiquity of some of the basic concepts can be seen in the fact that they are found in Agricola's De Re Metallica which was published at Basic in 1546, while in 1602, Carew114 gave a fairly clear account of tin ore dressing in Cornwall in which grass turves were used to catch the cassiterite. This is perhaps one of the forerun¬ners of the blanket strake. The planilla of Mexico, the lanchute of Malaysia and the old Cornish box huddle are also descended from these early strakes. In fact, a sluice with holes in the bottom for concentrate discharge was shown by Agricola, not unlike the principle used in the plane table and the lamflo sluice. The convex huddle for the treatment of sandy material appeared about 1848 and the concave form eight to ten years later. For the treatment of "slime" sizes, wooden dead frames which were manually worked were used in Cornwall for many years but gave way to the automatic water-operated type in 1860, and even a mechanically tilted frame was described by Henderson115 in 1857. Theoretical Considerations The behavior of solid particles in suspension depends to a great extent upon the pulp density and the size of the suspended particles. In a fairly dilute suspension, such as that normally used when dealing with small particle sizes, the behavior of particles in a flowing film results from two effects. These are the lateral displacement, which is determined by the time taken for each particle to penetrate the flowing film and reach the solid surface, and the resistance offered by each particle to further displacement after it has reached this surface. The initial penetration through the flowing film depends on the size and specific gravity of the particle and the thickness and viscosity of the film. As a result the smaller particles will migrate further before their movement is retarded relative to larger particles of the same specific gravity. The behavior on reaching the solid surface de¬pends on whether there is a single particle layer or, as is more often the case, a multiple layer or thin bed of material which is sufficiently dilated, permits the penetration of higher specific gravity grains. Thrust of Flowing Films. When a thin film of liquid flows over a plane solid surface, the layer next to the surface remains at rest but the velocity of the film increases with the distance from the surface and becomes a maximum near, but not quite at, the free surface. Therefore, a particle in suspension in such a film is acted upon by a greater force near the upper part of the film than at the lower part, resulting in an overturning effect. After a particle reaches the separating surface or an accumulated densely packed bed of other particles, the liquid flow causes it to move downstream by rolling, sliding, or by a movement involving alternating suspension and deposi¬tion (saltation). In rolling and sliding, which are brought about by a substantially noneddying stream, the large submerged particles are acted upon to the greatest extent and they move more rapidly than smaller ones, notwithstanding their greater mass. When two particles of the same size but of different specific gravity are considered, the higher density one moves more slowly by reason of its greater mass. As a result the particles tend to become arranged in the manner shown in Fig. 29. If any particle is so large as to stand above the water surface, the transporting force on such a particle, although the maximum available, will have less effect than that on a submerged one. Such large grains are therefore carried a lesser distance. Fluid Velocity in a Flowing Film It can be shown that if y is the distance within the flowing film from the interface, the fluid velocity v' at this point is given by IIn this equation p' is the fluid density, g the acceleration due to gravity, a the viscosity, a the angle made by the film to the horizontal, and 0 the film thickness (in cgs units). Furthermore, the volume Q of fluid per unit time and unit width is related to the film thickness and can be calculated, since which upon integration gives Consideration of the velocity v' (Eq. l) and the terminal falling velocity µ derived from Stokes law enables the horizontal travel dz in time dt to be calculated as follows: Again integration and substitution of Eq. 3 gives In this equation, z is the distance travelled before a particle of density p at the top of the fluid film has settled on the concentrating surface. From these expressions it can be seen that the depth of the flowing film varies as the cube root of the volume of fluid and inversely as the cube root of the sine of the plane surface inclination. Similarly the distance a particle can travel before reaching the surface is directly related to the quantity of fluid and its viscosity. The viscosity of pulp is greatly increased by the presence of near colloidal particles and consequently the penetration of the somewhat larger grains through the flowing film is retarded, resulting in them being carried further across the concentrator deck. Obviously this effect can be reduced by prior removal of some or all of the ultra¬fine particles. The detrimental effect of kaolin on the separation of fine ferrosilicon from quartz has also been demonstrated by Johnston,116 the relationship between viscosity and efficiency of separation being shown in Fig. 30. The pH value also has a very marked influence on the viscosity and the use of acid mine water, for example, can increase viscosity materially and thereby result in lower efficiency. Dilation of Multi-Particle Systems Except during washing (when a single particle layer may exist) concentration usually takes place in a bed of particles which is partially dilated or stirred by eddy currents. The extreme case is seen in various forms of the sluice where the flow of water and the presence of riffles combine to create a fluid bed in which reverse classification takes

Jan 1, 1985

By A. Diaz, Minera Los Pelambres, C. G. Salinas, G. Leinenweber, F. Diaz, D. Rojas, R. Bernal, O. Jimenez

"Los Pelambres Mine (MLP) is located in the IV Region of Chile, a semi-arid region where water plays a key role in operations as a scarce resource and is vital for the sustainability of human life, animals and ecosystem. The conventional flow meters installed on pipes at MLP can fail to provide an accurate measurement due to corrosion and/or fouling on the inner wall or presence of elements in the water such as acids, salts and suspended solids. Conventional flow measurement methods require the inner diameter to be known, however it is not always possible to assess its real value due to scaling, fouling, corrosion, etc. Here we present a novel methodology to solve these problems, which consists of the measurement of flow by a method that does not require the internal area of the pipes: the fluorescent tracer dilution method. In addition, the fluid velocity can be determined by the transit time of a radioactive tracer method. With the flow rate and velocity, the equivalent area is determined and thus the equivalent internal pipe diameter as well. This methodology was applied in a recirculation pump station, for mineral processing from the El Mauro tailings dam.This work demonstrated adequate correlation between measurements from fluorescent tracers and velocity measurements from radioactive tracers, both of which lead to the assessment of the internal diameter of pipes with scaling. The results of both methods disagree with the data provided by the flowmeter installed on the line due to its miscalibration. This information is useful in validating and correcting the information provided by online flowmeters of all water and solutions transport processes in filled pipes.INTRODUCTIONPresently, the need to optimize water resources is increasingly ever important, due to various reasons such as water scarcity, community empowerment, an increased use of water for mining processes and environmental considerations. Taking into account those main considerations, Los Pelambres Mine decided to focus on water conservation to avoid losses of this vital element. They decided to demonstrate that all of the systems that used water (flow meters, pipes, pumping stations, lagoons, etc) were in good condition and that no evitable loses of this important resource occurred. A plan was proposed to conduct a “hydraulic assessment” of fluid flux and water speed at different points and courses at the mine, with the purpose of obtaining hard data to support, verify and correct the information provided online from specific instrumentation dedicated to those purposes. The final goal was to manage the water resource basin in a sustainable way, based on cross-checked information. The chosen points are representative of the processes present in the mine, such as recirculating water stations at different operating conditions and surface water courses, where the fresh water capture systems operate."

Jan 1, 2016

By James Wm. White

Calculation of consistent steady-state mass balances in operating metallurgical plants and pilot plants is of interest for many reasons. In general, enough data can - and should - be collected to overdefine the system, i.e., permit calculation of nonmeasured quantities via more than one path. In such cases, resulting steady-state metallurgical mass balances rarely close due to sampling, analysis and/ or instrument error. Indeed, determination of a valid calculational sequence for complicated process flowsheets with multiple recycle streams can prove quite difficult. Here we present and discuss a method that has proven useful in analysis of numerous grinding circuit flowsheets of varying-degrees of complexity our technique requires only a consistent process flowsheet with appropriate associated data and arbitrary numbering of streams and equipments. Process topology and user data are decoded to yield a set of "search" or base variables and a set of "calculated" variables in solids, water, particle size and splitter parameter space. This procedure greatly speeds subsequent actual mass balance adjustment calculations since perturing certain variables (e.g., a solids value) does not require recalculation of other variables (e.g., the water balance). Finally, internal search and calculated variables are back converted to User units and used in a Sum-of-Squares criterion. Global minimization of this performance functional then yields a consistent mass balance in a least, squares sense. Weighting factors of choice can be used. Examples illustrate application of these methods.

Jan 1, 1979