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By James Harding

THE usual method of sampling mineral deposits is to drill holes and assay the sludge or core. Though the results thus obtained may not represent the true average value of the deposit, it is on these results that estimates of practically all large orebodies are made. In a large number of cases, the results of exploitation fall far short of the estimated value of the orebody. The standard method of making these estimates is to find the cubic contents of triangular prisms, in the apexes of which the drill holes are placed, .by multiplying the surface area by the average depth of the ore in the three drill holes and then multiplying the cubic contents by the specific gravity of the ore or rock to find the tonnage. The assay value is found by dividing the sum of the products of the depth of ore in each hole and the corresponding assay value by the sum of the depths of the ore in the three holes. As the latter part of this method is subject to many mathematical errors, it should not be depended on.. Some engineers, therefore, use a discount factor, but as this factor is either arbitrarily selected or is obtained by obscure methods, the results are no better than guesswork. The standard method is correct when the drill holes are so laid out that the triangular prisms are equilateral in cross-section. But as ore deposits cannot always be drilled into at regular intervals and because of the human factor, if many holes are drilled, triangular prisms of all degrees of angularity are produced. In such cases, it is necessary to assume that the influence of the different holes is not the same in all directions, which assumption of course is absurd.

Jan 1, 1921

By Z. Zhang, Cuihuan Huang, Zongshu Zou, Nan Wang, Xueqian Xin

"Vitrification is considered as an attractive procedure for municipal solid waste incineration ash, which can realize the volume reduction and innocent treatment of incineration ash, as well as reuse of bottom ash. The main oxide components of molten ash slag are CaO, Al2O3, SiO2, Fe2O3, MgO, and Na2O, accounting for more than 90% of the total mass. The phase relations and thermodynamic properties of the CaO-Al2O3-SiO2-FeOx-MgO-Na2O oxide system is highly required, and is of great scientific significance for optimization of vitrification processing and sustainable resource utilization of melting slag. A study on the equilibria phase relations of CaO-SiO2-MgO-FeOx system was done by using CALPHAD method based on FactSage in this paper. The modeling parameters for the thermodynamic properties of liquid phase in CaO-SiO2-MgO-FeOx system were established and the equilibrium phase relations of MgO-SiO2-FeOx and CaO-SiO2-FeOx-MgO systems were calculated for different temperatures and oxygen partial pressures.IntroductionThe main oxide components of vitrified bottom ash slag are CaO, Al2O3, SiO2, Fe2O3, MgO, and Na2O, accounting for more than 90% of the bottom ash by weight [1]. During slag processing and modification, the knowledge of thermodynamic properties and liquidus temperature in the related slag system is highly required [2-5], which is not yet available. Through literature survey [6-9], it is clear that the systematic information on the concerned complex slag system is scarce. Most binary subsystems except FeOx-Na2O have been investigated well. Among ternary subsystems, few phase relations of the Na2O-MgO-SiO2 ternary system are available. For the phase relations of the system Na2O-MgO-Al2O3, all the studies are focused on the Al2O3-rich region. Investigation on the CaO-Al2O3-FeOx system is limited to Fe2O3-containing system with relatively higher oxygen potential. Most quaternary systems are not studied well except the CaO-MgO-Al2O3-SiO2 system, mainly due to their metallurgical importance. Figure 1 demonstrates the research status of the vitrified bottom ash slag with almost zero effort [10]. The effort here is defined based on the published literature by considering the number of publications, the investigated composition ranges, and the research details. So far the engineers in the field have to make assumptions of the thermodynamic properties of the simplified oxide system, without taking into consideration the interactions of the different oxide components, which hinders the development of the slag valorization and utilization. In order to provide thermodynamic properties for the application of the vitrified bottom ash, the six-component oxide system (CaO-MgO-Al2O3-SiO2-FeOx-Na2O) will be investigated through both experimental approach and computer modeling."

Jan 1, 2011

By M. Muskat, H. H. Evinger

A METHOD of calculating productivity factors for oil, gas, and water systems in the steady state is presented as an illustration of the quantitative application of the fundamental data on the flow properties of heterogeneous- fluid systems. While the numerical results of the calculations cannot be applied directly to field conditions, because they are based on permeability data for unconsolidated sands and involve specific assumptions regarding the nature of the reservoir fluids, the methods of analysis and interpretation should have significance in considering certain specific field situations when the necessary field and laboratory data become available. Moreover, it is felt that even under the idealized conditions to which the numerical calculations refer they should serve to give at least the orders of magnitude of the effects of gas-oil ratio and connate water on observed productivity factors. Within the indicated limitations, the computations imply that the foregoing factors can explain only a part of the apparent discrepancy between the homogeneous fluid productivity factors and those obtained recently in field measurements on the West Coast.

Jan 1, 1942

By Elaine Gorham-Bergeron

CAROM is a distinct element, dynamic code developed at Sandia National Laboratories to calculate the motion of rock fragments during blasting.[1] It has recently been improved to incorporate a mechanism for its elements to mimic non-circular rock fragments. With this option, elements stack and move in ways that are characteristic of irregular boulders of blasted rock. In bench geometry, CAROM has been used to examine the possibility of producing variations in muckpile shape due to variations in detonation-time delays between rows. Surprisingly, the shape of the muckpile was predicted to be insensitive to time delays between detonation of rows of explosive, except where the rock fracturing was affected by the time delays.

Jan 1, 1987

An established method exists for the computation of rope lifetimes for shaft hoisting applications in the mining industry. In an earlier study, during the 1990s, an initial comparison of the calculated and actual rope life for various types of hoisting plants showed reasonably good correlation. In the meantime the calculation method has been developed further. The rotation behaviour of the rope during hoisting and the effects of multilayer spooling on drums are now considered in the assessment of expected rope lifetimes. The ability to determine an estimate of rope life in advance is particularly useful for mining companies. Such analysis allows them to predict the effects of rope choice in their particular application and thereby reduce the total cost of rope ownership. Such calculation techniques also allow designers of winding plants to identify aspects of the hoisting configuration that may negatively affect rope life. Often small (low-cost) changes, like increasing the diameter of head sheaves, can result in considerable improvements in rope performance. This paper describes the extended lifetime calculation method and gives further examples of the comparison between actual and calculated rope lives for operational double-drum mine hoists.

Jan 1, 2005

By Jorgen Elbrond

In a stream of ore in an underground mine or in a beneficiation plant bins are installed between machines or machine system. When the upstream machine is stopped the downstream machine can continue operation for a while and vice versa. The paper describes a procedure for calculating the total capacity of a system consisting of two machines with an intermediary bin as a function of the bin's live volume and of the installed machine capacities and their production variations, which are defined. Extensions to several machines in parallel and in series are shown as well as practical examples.

Jan 1, 1982

By Gen-Hua Shi, William Boyle, Richard E. Goodman

This keynote paper calls attention to two critically important issues relating to selecting supports for excavations in hard rock. The first is the proportion of the ultimate sliding volume that needs to be stabilized by the support system. Some excavations can be imagined to liberate very large rock volumes, whose weight can not be assigned to supports without severe economic penalty. Using the keyblock principle, it is argued that only the most critically oriented and finite blocks right on the periphery of the opening have to be supported; if these are retained by the support system, or by self resistance due to friction on the sliding faces, then the blocks behind will remain in place. As all concepts, this one has bounds and limits. Since the keyblock analysis for rock engineering is very new, these limits are not yet understood ... The second issue is the degree to which possibly stabilizing forces associated with the in-situ stress field ought to be accepted as support for potential keyblocks. It is shown that the initial stress can be effective in stabilizing rock wedges whose faces are nearly perpendicular to the excavation surface. It is too early to decide this issue but important to consider it.

Jan 1, 1982

By P. D. Gorsuch, D. L. Newhouse, Irvin R. Kramer

ALTHOUGH many methods have been suggested for the calculation of tensile strength and yield point from chemical composition, their usefulness has been limited to a particular cooling rate or section size. Further limitations have been imposed by failure to take into account many of the alloying elements that exert a considerable influence on the tensile strength or yield point. These systems, nevertheless, have filled an important need in many instances. The value of a system for the calculation of the tensile properties from the chemical composition and cooling rate is that it permits the prediction of the effect of alloying elements and heat-treatment on the mechanical, properties, so that more efficient use of alloying elements may be made. Furthermore, it aids in the choice of steel for a given application and tends to decrease the number of steels that otherwise would have to be tested. It is the purpose of this work to present a method of calculating tensile strength and yield point from the chemical composition and to suggest a method of correlating the tensile-strength and yield-point factors and cooling rate. Steelmakers have been interested for many years in the calculation of the tensile strength of hot-rolled steels. Quest and Washburn' summarize several of the attempts that have been made to devise formulas. They show the inadequacy of each of these formulas and present one of their own. It is apparent from their work that a simple additive equation of the type TS = A + BX + Cy + DZ + ? ? ? , where A, B, C, D, etc. are experimentally determined constants and x, y, z, etc., are the percentages of alloying elements present in the steel, is not adequate to analyze fully the situation encountered in the calculation of tensile strength. For example, it was found that the difference between the calculated and observed values became progressively greater as the carbon and manganese contents were increased. Therefore, the effect of manganese was given as a function of the carbon content. Grossmann,2 in his work on the hardenability of quenched steels, and Walters,3 in his method of calculation of tensile strength of normalized steels, present two cases in which multiplying factors were successfully used to express the combined effect of alloying elements. The factors in both cases were obtained from the fractional increase in hardenability or tensile strength with increase of alloy content. Yield point often is more important in design than tensile strength. For quenched and tempered steels a linear correlation exists between yield and tensile strength .4 This is not true, however, for normalized

Jan 1, 1946

By J. den Drijver, M. Opahle, R. Inderst

Safety reasons render necessary the advanced calculation of the amount of methane degassing from a longwall in the scope of the ventilation planning of mines. Today empirical methods, which are based on observations of operational procedures, are used for the calculation of the amount of methane. Despite of constant improvement those calculations are not always sufficient. In particular calculations which are based on operational facts but not proved by experience are not reliable. Most of all these calculation procedures lack physical-analytical descriptions of the procedure itself, presenting only the effects on important parameters such as the distance between seams in the roof or floor or gas pressure. Tschersich [Tschersich 961 developed an analytical model for an advanced calculation by analysing the degassing of seams in the roof and floor and the physical parameters of gasflow. This model might correct the lacks of existing procedures and improve the precision and reliability of additional calculations. The model simulates the emission record in seams of the roof and the floor. It takes into account not only a multitude of parameters such as the distance to adjacent seams and gas pressure but also the depth of seams, gas content, rank of carbonification, rock temperature, face advance rate, initial and succeeding mining and the face length. In order to comprehend and to verify those correlations we extended the model of Tschersich and programmed this enlarged model using the computer language C++. Aim of this research is to guarantee a much higher accuracy in calculating methane emission caused by mining. The improved planning is expected to result in more safety and better prevention of high methane con- tent in ventilation as well as in a better use of the capacity of the mining equipment. The application [Drijver, lnderst 961 of the ex- tended model will also be very useful in the course of research projects as it allows computer simulation, i.e. in-situ research can be extensively limited or even replaced.

Jan 1, 1997

By Donald Barton

THE purpose of this torsion balance survey and the quantitative calculations was to delimit the extension of the cap rock at the Hoskins Mound salt dome. The sulfur ore in the Gulf Coast sulfur-bearing salt domes occurs in the lime rock, which is the outer layer of the cap-rock mass, and also in the underlying gypsum zone. The status of the exploration and exploitation of the Hoskins Mound dome at the date of this survey is shown by Fig. 1. The mound had been covered by the very early prospect wells of the Mound Oil Co., and the later and more numerous prospect wells of The Texas Company. The Freeport Sulphur Co. was producing from the flank wells in the southwest quadrant. The limits of the cap were surmised to lie inside the centers of quad-rangles 4F, 3F, the center of the NE. ¼ of 2E, and the north line of 2D. That surmise was based partly on the data of Fig. 1 and partly on the position of the edge of the topographic mound. The management of the Freeport Sulphur Co. wished to block out the extent of its ore reserves with a minimum of expenditure. The management was informed by the writer that no geophysical method could map the presence or quantity of sulfur directly, or determine the presence and quantity of the lime-rock cap independently of the rest of the cap, but that a reasonable probability existed that the approximate position of the edge, the depth and the thickness of the cap-rock mass as a whole could be determined through quantitative calculations based on the data of a very careful torsion balance survey. Considerable lime rock would probably be present, of course, wherever much cap rock was present. This paper presents the data of the survey, our calculated prediction of the configuration of the cap rock, and the degree of confirmation by the subsequent drilling. The survey was made by the Geophysical Research Corporation, under the direction of the writer. The work of the calculations was done by Andrew Gilmour, then assistant to the writer.

Jan 1, 1936

By Janshi Sen

VERTICAL-INTENSITY magnetometers, such as the Hotchkiss Superdip and the Askania vertical field balance, are now [ ] widely used, because vertical-intensity charts give definite information for the location of upper pole, dip and strike, and approximate shape of the deposit. Again, a slow and steady increase of dip over a large area indicates a large deep-lying deposit, while a large dip limited to a small area and falling away rapidly suggests a small and shallow one. The complication comes more from the richness of the ore. A large body of lean ore near the surface might produce the same vertical-intensity chart as a rich ore at depth. This paper presents a method for calculating the maximum depth of a single-pole deposit and another for a two-pole mineral body, by utilizing data of both vertical and horizontal intensities as obtained by a Thalen-Tiberg magnetometer. As shown on the left side of Fig. 1, lean ore, rich ore and a single pole produce the same magnetic field. The depth of the pole, [ ] h, can be calculated from the following relation: [h=a=tan¢=G-F h=aXFy] where G is the vertical intensity at point A due to the pole; F, the horizontal intensity of the same; and a, the distance from the point of maximum vertical intensity or the vertical projection of the pole on the surface to the point of observation A. If an entirely covered deposit is indicated by magnetic measurements and boring cost estimated from the calculated depth is so reasonable as to encourage drilling, the ore should be struck somewhere within the limit of the calculated depth by the borehole. A number of such points as A should be taken for calculation, erratic results should be rejected and the average figure used for cost estimation.

Jan 1, 1944

By T. T. Natarajan, Nagy EI-Kaddah

"Numerical simulation of electromagnetic confinement systems generally requires large CPU time due to the strong coupling between the electromagnetic and the free boundary problems. The present paper examines the accuracy and the computational efficiency of the most common numerical schemes used in modeling such systems. Levitation melting was taken as a test case. In this study, a comparison was made between the finite element and surface integral methods for electromagnetic field calculations. The computational efficiency of Lagrange and the modified Hestenes methods for solving the free boundary problem were investigated. The convergence of the Lagrange method was found to be much faster than the modified Hestenes method. It was also found that finite element method not only gives accurate solutions, but faster convergence to the final equilibrium shape than the surface integral method. The applications and the limitations of these techniques in modeling electromagnetic confinement systems will be discussed.IntroductionIn recent years there has been a growing interest in the use of electromagnetic forces for confinement of molten metals as a means to eliminate molten metal contamination during melting and to improve surface quality of cast products. Continuous casting of metal without contact of a mold is now a reality, and is being commercially applied for casting of aluminum slabs /1/, and copper rods /2/. New applications of electromagnetic confinement in melting and casting include containerless melting (Magnetic Suspension Melting) /3/, edge containment in twin roll casting, and meniscus shape control in continuous casting of steel /4/.Modeling of confinement systems involves the determination of the electromagnetic field and the equilibrium shape. These two problems are strongly coupled due to the dependence of the field on the shape of the melt. While significant advances have been made in computational electromagnetics /5/, the application of developed computational techniques to electromagnetic confinement problems is not a simple task. The principal difficulty in using these methods is that the solution domain is not known a priori. due to coupling between the electromagnetic field and the free boundary problems. These two problems have to be solved simultaneously, leading to an iterative solution procedure. As a result, numerical simulation of electromagnetic confinement systems are computationally intensive with computational time at least an order of magnitude larger than the fixed domain problems."

Jan 1, 1994

By Wang Xuguang Shen Yingfeng

Structure is the main aspect affecting the performance of emulsion explosive. Calculation of such structure parameters as osmosis pressure, interface area per unit volume etc. must be helpful to the understanding of the structure of emulsion explosive. This paper has solved the Laplace-Young Equation for simplified monodisperse emulsion system by Galerkin method, and gained the relationship between mean curvature, contact angle, volume fraction, fractional film area and interface area per unit volume. The paper also presents a new expression of osmosis pressure at non zero contact angle.

Jan 1, 1998

By Andrzej Frycz

The development of the theory of reliability creates more and more possibilities of its application in different domains of technics. The methods evolved to date, both theoretical analysis of the engineering systems and investigations techniques in practice can be put in use a d translated from one science to another one [1,3,7J . It needs to consider the specific of the different sciences. But it is necessary to take account of the specific characteristic of each line of science. The reliability investigations needs, justified in technical and economical viewpoint appear too in mine ventilation technics and systems. The mine ventilation system is a complex of workings and ventilation plants, which serve to supply the networks with a sufficient quantity of fresh air from the atmosphere and then carry off the vitiated air. The condition necessary for a ventilation system to perform definite task is the correctness of all its elements, that is a capability to preserve in a expected range of tolerance, the values of basic parameters. The element of a system which ceases to work correctly is called failed. The basic parameter of all elements of a ventilation system is the characteristic curve, pressure loss - air quantity relation ?p = f(Q) (1) This curve concerning the workings and ventilation stoppings is given by the formula: ?p = R Q2 (2) thus the resistance R (of the workings or stoppings) may be taken as a characteristic parameter. The course of this characteristic f(Q) will be given in a complex form in concern with fans, ejectors, air curtains. The failure of a ventilation plant or working is therefore an event, relying on a change of its characteristic, thus for a definite time the losses of the plant's or working's capability set in for the fulfilment of its function in the ventilation system. The failures are divided in viewpoint of their nature on sudden and progressive. We are in concern with the sudden failures which are characterised by a violent change of the ventilation element parameter for example a fall of roof, or silt up of the working, opening or failure of the ventilation stopping, the stand-off of the fan or ejector etc. We distinguish two kinds of failures on the viewpoint of their action on the air flow: the "opening" failure and "closure" failure. The prevalence of factors, which causes the failures is in connection with the intersection in the mine of roads of haulage, roads of underground transport of materials and lining elements, roads of people motion with airways, as also depends on the rock pressure reaction on the workings lining and plants placed there. Other factors will yet be decisive upon supply decay of fans, ejectors and curtains. The appearance of failure of the ventilation element is therefore of random nature and determines the change of the element, when it is passing from operating state to unoperate. Qualifying the ventilation system element to one of these states is easy, when the characteristic change is clear and occurs suddenly, that was assumed. The investigations conducted by Patrushev and Karnaukh [91 in concern with the ventilation stoppings resistance change in the case of their opening, had shown the possibility of resistance value change in the range of several hundreds higher.

Jan 1, 1980

By F. M. Walters

IN order to isolate the effect of an element on some property of an alloy, the effect of the other alloying elements must be elimi- [ ] nated, either by reducing their quantity to the extent that they may be neglected or by determining the specific effect of each. The success of Grossmann1 in calculating [ ] hardenability from chemical composition by means of factors suggested such a

Jan 1, 1942

By M. Muskat, H. H. Evinger

A METHOD has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-pressure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. INTRODUCTION The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical properties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.1 Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of 0 to 100 bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* [ ] where k is the sand permeability, h its thickness, µ the liquid viscosity, [Ap] the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius [ro ]and [r ] is the well radius. This gives the productivity factor: [ ] which will have a numerical value for a liquid of I centipoise viscosity of 0.9316 or

Jan 1, 1941

The results of the washing of coal are often presented by using Partition Curves. By analogy, it is possible to express the results of screening by using similar partition curves. As in the coal washing processes, this method determines the accuracy of screening and is also suitable for different separations depending on the difference in size distribu- tion. This method compares the effectiveness of two screening operations and forecasts the performances.

Jan 1, 1984

By Paul H. Muller

The configuration of remote seal DP cells for specific gravity measurement is described and the calculations for calibration are presented. The error induced by ambient temperature change is investigated as it relates to capillary dynamics and electronic considerations. Instrument specifications are discussed in the light of accuracy requirements and the calculation of error vs. ambient temperature is described.

Jan 1, 1984

By C. W. Greenhalgh

THE accuracy with which grade and tonnage of a mineral deposit may be calculated from diamond-drill assays is dependent upon: (I) the reliability of core and sludge samples and (2) the validity of methods used in grade and tonnage calculations. Limitations imposed by drilling and sampling preclude elaborate methods of computation. In adjusting core and sludge assays the importance assigned the core and sludge samples may be based on either the respective weights recovered or the respective volumes represented by each. Only when core and sludge recoveries are poor do discrepancies between adjusted assays calculated by these two methods develop, in which case the "weight" method gives emphasis to the core sample and the "volume" method gives emphasis to the sludge sample. When the sludge suffers classification within the drill hole, the weight method gives more accurate results; when the sludge sample suffers no classification, the volume method gives more accurate results. Any drilling campaign offers a compromise between desired accuracy on the one hand and expediency, limited time, money, or facilities on the other. Since the determination of grade and tonnage is an approximation at best, a proper basis for their computation requires a knowledge of the limitations imposed by all phases of work upon which the calculations depend. A rational basis for coordination of these phases of work requires determination of: (I) the degree of accuracy desired, as a function of the object of examination; (2) the degree of accuracy attainable, as a function of the limitations imposed in the drilling and sampling program; and (3) the validity of method to be used in calculating grade and tonnage from core and sludge assays. This paper presents results of a comparison made between two commonly used methods of adjusting core and sludge assays, the assumptions upon which these methods are based, and the interrelationship of the phases of work upon which these calculations are dependent. OBJECT OF EXAMINATION The purpose of prospecting any mineral deposit is to secure sufficient samples from which ore grade and tonnage may be calculated. Any mine examination, preliminary or formal, has a definite purpose, although its scope may be limited or broad. The type of examination to be conducted is dependent, therefore, upon the reason for instituting the investigation; its scope and thoroughness are directly related to economic considerations. It is highly desirable, therefore, that before starting a drilling campaign a complete understanding of the extent of examination and desired degree of accuracy be determined as a means of simplifying the drilling program and unifying the relative degree of

Jan 1, 1946

By W. Luyken

A NUMBER of articles have been published, notably those by R. S. Handy, R. T. Hancock and A. P. Watt in Engineering and Mining Journal, dealing with the calculations involved in ore dressing.. These publications demonstrate both, the importance of the subject and the lack of success in developing a generally recognized method for comparing enrichment effects. Considering that we may wish -to compare enrichment results on similar or dissimilar ores, that we may desire to make the comparison on the basis of either the absolute or the economical efficiency, and that the number of factors upon which the result depends is large, the question arises whether it is possible to set up a positive method for such calculations. In the following pages it is our aim to show that a sure, complete and successful way to overcome existing difficulties has been found. GRAPHICAL ANALYSIS OF ORE-DRESSING PROCESSES The following is from Truscott's Text Book of Ore Dressing (London, 1923) x = assay of ore treated (feed). y = assay value of the concentrate. z = assay value of the tailing. a = weight of feed. b = weight of concentrate. c = weight of tailing. C = fractional concentration = b/a= x-z/y-z (1) K = ratio of concentration = 1/C = a/b =y-z/x-z (2) R = fractional recovery = yb/xa = Cy/x. (3) 100R = percentage recovery. Copt = theoretically best concentration. 100 - Copt = waste in the feed.

Jan 1, 1929