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By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

The formation density logging tool provides a radioactivity measurement that yields formation densities in situ. The relationship between bulk density and porosity is well understood. With knowledge of grain and fluid densities, porosity may be computed from the indicated formation bulk densities in shale-free formations. The porosities thus determined may be used with a resistivity log for water-saturation determinations. One technique utilizes a density vs resistivity plut. A plot of density vs Sonic-log transit time is used for porosity determinations in shaly sands. This method is particularly suited to wells drilled with oil-base or salt muds. In shale-free formations, comparisons of density values nnd neutron-log readings are used to identify lithologr and, thus, to select appropriate values of grain density for porosity computations. Through the use of Formation Density, Sonic and neutron logs, the interpretation problems caused by complex matrix lithologies are simplified. Other applications of the Formation Density log are found in the identification of minerals in evaporite deposits and in yield determinations of "oil shales". INTRODUCTION Widespread field application has demonstrated that the measurement of formation density is a useful and revealing technique for well logging. Responding to the bulk density variations of the formation, the Formation Density log affords valuable data on the porosity, lithology and fluid content of the formations. Although not without its own limitations, the Formation Density tool may provide effective interpretation under conditions that hamper or preclude the use of other porosity devices. When used in conjunction with other devices, such as the Sonic or neutron, complex matrix conditions may be better understood, defined and evaluated. A previous paper' described the valuable contribution of the Formation Density tool in the logging of empty, or gas-filled, holes. The purpose of the present paper is to describe applications of the device in liquid-filled holes. THE FORMATION DENSITY TOOL The Formation Density tool was devised to measure the bulk densities of formations in situ. Actually, the device responds to electron density, but in the overwhelming majority of cases of interest, the electron density is very closely proportional to the bulk density. In other cases appropriate corrections can be made if necessary. Comparisons of log-derived densities with true densities for the more common matrix minerals are shown in Table 1. The tool consists of a gamma-ray source and detector mounted in a skid which, during the logging operation, is in contact with the borehole wall (see Ref. 1 for schematic). Gamma rays are emitted by the source and diffused through the formation. The number of diffused gamma rays reaching the detector at a fixed spacing from the source are counted. An increase in counting rate by the detector indicates a decrease in bulk density in front of the skid. Conversely, a decreased counting rate signifies an increase in bulk density. A measurement of hole diameter, between the face of the skid and that of the eccentering arm, is recorded simultaneously with the measurement of diffused gamma rays. Since the tool is a wall-contact device, the size of the borehole has little influence, provided good contact is maintained with the wall of the hole. Only in extremely large or small boreholes does the actual diameter become significant. However, for most accurate measurements the borehole size should be taken into account. Fig. 1 presents the departure curves for the conversion of counting rate to bulk density for liquid-filled holes of various sizes. It is of utmost importance that the skid maintain good contact with the wall of the hole. If, due to roughness or caving, there is mud between the skid and the formation, the tool will include in its response the relatively low-density mud, and the apparent density reading will be too low. Normally, permeable beds do not cave appreciably, so that reliable readings are usually available for zones of interest. Nevertheless, the caliper reading over the zone of interest should be examined for any wall roughness. When mud cake exists between the skid and the formation, the Formation Density log sees it as part of the formation. When thick mud cakes exist, a correction is required. For best results in wells having thick mud cakes,

By A. Kenneth Schellinger

THE terms surface tension .and surface energy are well known when applied to liquids and are generally described by referring to the excess energy of the air: liquid interface as a result of unsaturated molecular forces surrounding the surface molecules of the liquid due to the presence of the air phase on one side. Such unbalanced forces produce the familiar water droplet of spherical form and are generally summed up as a surface tension measured in dynes per centimeter which can be shown mathematically to be equal numerically to a corresponding surface energy expressed in ergs per square centimeter. A specific surface energy, however, is best thought of as the energy necessary to produce one unit of new surface on a substance. Hence, in producing a bubble in a flotation cell the impeller must supply surface energy corresponding to the air: liquid interfacial area on the interior of the bubble. Inasmuch as it is relatively easy to extend or contract the surface of a liquid, there are a number of successful methods for liquid surface tension, or energy, measurement based upon surface deformation. This happy state of affairs does not, however, extend to solids, which are considered to possess surface energies for the same reasons as do liquids, i.e. because of unsaturated ionic bonds at the solid gas interface. As in the case of the flotation cell producing surface on liquids as new bubbles, it takes energy to produce new surface on solids as new particles. As every mill man knows, this surface is produced on mineral solids in a grinding mill by the action of a tumbling mass of iron balls. But here so much energy usually is wasted by the inefficient action of these balls that a large amount of heat is generated, and the surface energy production may be easily confused with the energy necessary to produce this ineffective heat. The tumbling balls and fracturing minerals ultimately take their energy from a rather large electric motor. It has been variously estimated that from 10 to 20 pct" only of this energy from the motor does not appear as heat and may be presumed to appear as surface energy on the minerals present.. Such a production of new surface on the mineral phases is accompanied, of course, by a size reduction that is inevitable as more and more mineral interior molecules become surface molecules by the fracture exposure. This size reduction of mineral particles, although the most obvious feature and perhaps the sole object of the milling operation, is from this energy viewpoint the outward manifestation of the production of surface energy only. Measurement of the characteristic surface energies of pure minerals and their various mixtures in ores would be a step towards understanding of the energetics of the commercial grinding operation. In addition, the characteristic surface energy of a mineral is probably a physical property specific for that mineral, and therefore, from a scientific standpoint, should be measured. It is interesting to note that, in contrast to the large body of work on the surface tensions of liquid systems and biological systems, the field of solid surface energies has been neglected. Prior to. 1920 it is difficult to find more than one or two references to work on solid surface energies in Chemical Abstracts. Since 1920 such references number somewhat less than 100, while those on liquid systems are numbered in the thousands. Much of this apparent neglect of the field of solid surface energies (the term is intended to be somewhat inclusive at this point and refers both to the solid: gas, and the solid: liquid interface) is because of the lack of a reliable method of measurement rather than any lack of scientific curiosity. It was, and still is, difficult to produce new surface on a solid without the simultaneous production of interior changes in the same solid which may consume part of the energy used. The extension in the surface area can be measured, but the interior crystal-

Jan 1, 1952

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By R. A. Greenkorn

This project originated in a practical problem—we needed five tracers that could be used together to locate flow paths in a pilot flood. While tracers for subsurface liquids have been used since the turn of the century,1-15 none of those reported in the literature appeared to be either consistent or quantitative enough for our purposes. Most were used in field systems without controlled experiments to determine the accuracy and precision of analysis, and many were tracers that could not be used collectively. The ideal tracer, of course, would follow the fiuid of interest exactly, traveling at the same velocity as the fluid front. But the ideal is impractical to attain because adsorption-desorption effects cause the tracer to lag behind the front; these effects, plus diffusion-dispersion effects, cause the tracer front to spread more than the fluid front. Thus, our objective was not to locate a tracer that would be ideal for all circumstances but rather, to find one that would approximately follow the fluid, or one that under controlled conditions could be corrected to calculate the movement of the fluid front. We considered tracers satisfactory—(1) if they were easy to analyze; (2) if their breakthrough-elution curves were not too different from those for the chloride ion, a tracer believed to follow the fluid front closely; and (3) if we could calculate from the curves a material balance, at 1.25-PV (pore volume) injected, within 5 per cent of that calculated from chloride curves. Of a possible 35 materials, we selected 13 tracers that could be quickly and easily identified and whose analysis was claimed to be accurate within 5 per cent. Only one of these, tritiated water, was a radioactive tracer. Radioactive tracers are easy to detect even in small quantities, but they require special handling and special equipment. Also, those that can be used together are limited because special equipment is required to separate emissions from the various tracers. Two of the original 13 tracers were eliminated in static tests to determine how accurately and precisely they could be analyzed, and to check on gross adsorption. The remaining 11 were flowed through a 9-ft linear sandstone model, and breakthrough-elution curves were obtained. Finally, three tracers were field-tested as breakthrough tracers. These tests are described in the following sections. The 13 tracers considered in these experiments were EDTA (ethylene diamine tetra acetic acid), fluo-rescein, picric acid, salicylic acid and ammonium, boron (as borate), bromide, dichromate, iodide, nitrate and thiocyanate ions, plus chloride ion and tritiated water. All but the chloride ion and tritiated water were subjected to static sand tests to eliminate the tracers that could not be analyzed quickly and accurately and to eliminate those that showed excessive adsorption. All but two of the tracers, EDTA and salicylic acid, qualified for flow tests on this basis. The procedures used in the static tests (see Appendix A for analytical details) were as follows. Each tracer (in the amount shown in Table 1) was dissolved in 1,000 ml of water. Then, 800 ml of this solution was added to 500 gm of sand, and the remaining 200 ml was reserved as a control standard. The sand-tracer mixture was agitated once a day over a 10-week period, and during this period we analyzed five duplicate samples from this mixture, along with five duplicate samples from the control solution. From the control-sample analyses, we constructed a control chart on which the sand-tracer analysis results were plotted. The control chart, and its use to determine accuracy and precision of analytical results, as well as the amount of adsorption, is described in Appendix B. The results of the static tests are summarized in Table 1, which lists the concentration c (concentration at time t) divided by c, (initial concentration). If there was no adsorption, c/c, = 1. The acceptable deviation from this value varied from tracer to tracer, depending upon the limits of analytical precision established for the different tracers. The best results were obtained with boron, bromide and dichromate, with all values falling within limits of accuracy and precision. Ammonium, iodide, nitrate and picric acid also were satisfactory, although the ammonium results were erratic. Flourescein and thiocyanate were unsatisfactory ini-

By Charles P. Berkey, Joseph H. Sinclair

This paper describes the results of a visit to the Santa Elena Peninsula, Ecuador, in January and February, 1921. On account of the complicated folding and faulting of the rocks and the peculiar occurrence of petroleum, field work was possible on only a few of the many geological problems and the results here published are only a contribution to the solution of the general problem. We know of nothing published on the geology of the district, except one account, in Spanish and German, by Theodor Wolf. The Santa Elena peninsula, the most important headland of the coast of Ecuador, lies two degrees south of the equator. The chief town, Santa Elena, is about 75 miles west of Guayaquil, the main seaport of Ecuador. The nearest developed oil field is the Zorritos of northern Peru, 120 miles south across the Gulf of Guayaquil. If newspaper reports are true, viz. that the Anglo-Ecuadorian Oilfields, Ltd., has recently brought in a 700-bbl. well on the coast of the peninsula near Ancon, the district may become important in the production of petroleum. At the time of our visit, the best way to reach the peninsula was by a steamer of the Pacific Steam Navigation Go., southward from Panama and northward from Guayaquil. About once a week, one of these steamers anchored 1/2 mile off shore near the village of Salinas, an important cable station. An alternative route, in the dry season, is by automobile from Guayaquil. In February, 1921, a railway bed had been graded part way between Guayaquil and Salinas, but this was detcriorating rapidly because of lack of funds to continue construction or to keep in repair that portion already completed.

Jan 1, 1923

By J. R. Long, R. S. Dean, F. S. Wartman, E. T. Hayes

The production of titanium in I5-lb. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,&apos; has provided adequate material for a study of the physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited&apos; and all efforts were centered on fabrication methods for those powders and the proper- ties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. Consolidation of the PowdeR The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at 50 tons per

Jan 1, 1946

By J. R. Long, E. T. Hayes, R. S. Dean, F. S. Wartman

The production of titanium in I5-lb. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,&apos; has provided adequate material for a study of the physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited&apos; and all efforts were centered on fabrication methods for those powders and the proper- ties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. Consolidation of the PowdeR The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at 50 tons per

Jan 1, 1946

By H J. Ross, R K. Beatson, T J, W R. Fright

Traditional method of explicitly defining three-dimensional (3D) ore-waste and geological boundaries relies heavily on a time-consuming process of manual digitisation. This method of modelling can be best described as surface modelling, as complex surface geometry is built up by digitising points that lie on the surface. With the advent of fast 3D interpolation methods, however, construction of geological surfaces using volume functions is now a practical alternative to explicit modelling of surfaces. Unlike explicit modelling, surfaces contained in volume functions are not explicitly defined or digitised. Instead the existence of surfaces in the volume function is implicit, thus the process of modelling surfaces from volume function is called æimplicit modellingÆ. Based on recent advances in fast scattered data interpolation methods, implicit modelling first defines a continuous three-dimensional function that describes the grade or rock distribution. This volumetric function is interrogated for a grade value, or a geological surface, thus allowing the extraction of the 3D object to be automated and eliminating the need to manually digitise surfaces. Since the function is continuous throughout space and does not depend on a mesh or grid for its definition, the extracted geological or grade wireframes can be constructed at any desired resolution in the specific volume of interest. The volume modelling method can work on scattered drillhole data of any data density, including processing combined information from dense grade control data as well as sparse resource drilling. It offers distinct advantages over surface modelling, including: being able to wireframe geological objects that may take days to digitise in tens of minutes; substantial improvement in modelling accuracy; and the ability to generate conditional models rapidly allowing mining risks inherent in geological modelling to be examined.

Jan 1, 2003

By Philip Bucky

THE general conception of a mine model is that of a three-dimensional object representing the mine workings, the orebody and the country rock of a particular property. Its chief uses have been to make it easier to understand the mine and to serve as a basis for the arguing of legal questions. Fayol endeavored to use mine models in a different way and to all students of subsidence "Fayol&apos;s dome theory" is of decided interest. We have more recently the suggestion of Young and Stoek of the University of Illinois, who1 suggest the use of models as a means of studying the problem. Prof. Henry Briggs, of the University of Edinburgh and Herriott Watt College, also makes use of models to determine the effects of bending at the edges of extensive workings.2 It is interesting to note that civil engineers are taking a decided interest in the application of models and the principles of dynamic similarity to the solution of their problems. The Proceedings of the American Society of Civil Engineers for 1930 contain an elaborate article by Benjamin F. Groat,3 who says, in his opening remarks: "Every engineer should know and understand that a model constructed in accordance with Newton&apos;s theory of similarity is not only the means for reproducing the complexities of flow, or other mechanical action, on a small scale, but that models may be made the best means of designing works of great magnitude. In the present state of knowledge, a properly constructed and properly tested model will answer the difficult questions of hydrodynamics much more quickly and accurately than the most profound mathematical analyses." A study of P. W. Bridgman&apos;s book on Dimensional Analyses leads one to arrive at the same conclusion.

Jan 1, 1931

By L. Xu, A. Vazirnegad, R. Bhaskar

"Respirable dust samples are collected by the U.S. Mine Safety and Health Administration (MSHA) and mine operators as part of the requirements of the Federal Coal Mine Health and Safety Act of 1969. About 1.85 million respirable dust samples collected by MSHA were analyzed for the period 197/ to 1990 f or the states of Alabama, Colorado, Illinois, Kentucky, Ohio, Pennsylvania, Utah, Virginia, and West Virginia. Trends in coal dust exposure of continuous miner operators, helpers, and roof bolters were analyzed. The reported production in each of the nine states was analyzed. The relationship between average dust exposure and coal production was evaluated. In addition, the differences between mine operator and MSHA inspector collected data were examined for each state. The average exposure levels for the three occupations - miner operator, miner helper, and roof bolter were also compared.The data indicate that the dust exposure levels have significantly dropped over the last twenty years, while at the same time production has increased, attesting to the ability of the U.S. mining industry to adapt successfully to the stringent dust control regulations. In terms of coal production, it appears that some states, such as Utah, Illinois, and Kentucky, were able to increase their production significantly relative to others, such as Pennsylvania and Virginia. The relationship between dust concentration and coal production is, at best, tenuous. 11 implies that existing dust control technology has assisted several mine operators to meet dust standards, while, at the same time, enabling mines to produce more coal than before. Comparison of data collected by MSHA and mine operators indicate that MSHA inspectors recorded higher dust levels and lower shift production relative to mine operators."

Jan 1, 1993

By Charles P. Berkey, Joseph H. Sinclair

This paper describes the results of a visit to the Santa Elena Peninsula, Ecuador, in January and February, 1921. On account of the complicated folding and faulting of the rocks and the peculiar occurrence of petroleum, field work was possible on only a few of the many geological problems and the results here published are only a contribution to the solution of the general problem. We know of nothing published on the geology of the district, except one account, in Spanish and German, by Theodor Wolf. The Santa Elena peninsula, the most important headland of the coast of Ecuador, lies two degrees south of the equator. The chief town, Santa Elena, is about 75 miles west of Guayaquil, the main seaport of Ecuador. The nearest developed oil field is the Zorritos of northern Peru, 120 miles south across the Gulf of Guayaquil. If newspaper reports are true, viz. that the Anglo-Ecuadorian Oilfields, Ltd., has recently brought in a 700-bbl. well on the coast of the peninsula near Ancon, the district may become important in the production of petroleum. At the time of our visit, the best way to reach the peninsula was by a steamer of the Pacific Steam Navigation Go., southward from Panama and northward from Guayaquil. About once a week, one of these steamers anchored 1/2 mile off shore near the village of Salinas, an important cable station. An alternative route, in the dry season, is by automobile from Guayaquil. In February, 1921, a railway bed had been graded part way between Guayaquil and Salinas, but this was detcriorating rapidly because of lack of funds to continue construction or to keep in repair that portion already completed.

Jan 1, 1923

By J. B. Wagstaff, R. A. Buchanan, J. F. Elliott

High speed photography through blast-furnace tuyeres showed coke particles moving rapidly. Model studies showed a raceway was formed and gave quantitative results which were correlated with actual blast furnaces. Another study showed the similarity between hanging and the flooding of a packed column. This was explored by models. THE combustion zone before the tuyere in an iron blast furnace is a vital region because here are generated: 1—most of the gases on which the furnace depends to carry out its basic operation of reducing iron ore to the metallic state, and 2—the major fraction of the heat required in the nearby regions of the furnace for the various reduction reactions, the fusion of the slag, and the melting of the iron. Since the greater part of the coke is consumed in this region, the descent of the burden must be greatly affected by the characteristics of the tuyere zone. This region then would seem to be a profitable field for study. Fortunately, a view into this important zone is available to the operator through the tuyere peep sight. Here he sees relatively dark pieces of coke "dancing" in the blast. What he sees is of considerable help in interpreting the behavior of the furnace at a given time but the very rapidly moving particles and the intense radiation obscures what is happening very deep in the zone. This investigation was initiated in the hope that a better understanding of the combustion region could be obtained by using a high speed camera with a maximum speed of 3000 frames per sec. It seemed the best practical method of "slowing down" this characteristically violent action within the highly luminous field. Model studies and tuyere probing also have been used to aid in explaining the observed phenomena. Above the combustion zone, but below the fusion zone, there is probably a region in which the coke is comparatively stationary. Here are zones in which the gases must flow up through the granular bed counter to descending liquid slag and metal. There is no easy way to observe this zone in a blast furnace, but model studies have been of some help in explaining the nature of the zone and the laws governing the flow of the fluids involved. The whole problem is difficult and involved and any approach to a complete solution may require long investigation. This preliminary report has been written, therefore, because it is believed that appreciable progress has already been made that would be of interest to others. Tuyere Studies, Chemistry and Kinetics It is well known from the early work of Kinney and coworkers1,2 that combustion of carbon before the tuyeres appears to occur in two zones: Zone A: C + O, = CO2; AH77°F. = — 14,108 Btu per lb of carbon [I] Zone B: CO2 + C = 2CO; H77°F = + 6,183 Btu per lb of carbon [2] Zone A (Fig. 1) is close to the tip of the tuyere and zone B is somewhat farther back; there being a transition region in which both reactions occur. It is interesting to estimate the rate at which coke is burned before a tuyere with a wind rate of 90,000 cfm in a modern furnace having 18 tuyeres. Approximately 0.55 lb of carbon is consumed by eq 1 per tuyere per sec. A like amount disappears by eq 2 for a total consumption of 1.11 Ib per sec per tuyere. Assuming the coke is 85 pct C and has a bulk density of 30 lb per cu ft, this figure can be converted to a total of 1.30 lb of coke with a bulk volume of 0.043 cu ft disappearing per sec per tuyere. At the temperatures prevailing in the combustion zone (according to Kozlovich,³ he maximum is about 3400°F), the rate at which carbon is con-

Jan 1, 1953

By B. H. Caudle, B. M. Hickman, I. H. Silberberg

Secondary recovery projects often are not started in oil reservoirs until dictated by rising GOR&apos;s or declining oil production. Such circumstances require a well dispersed injection pattern to prevent the oil bank from bypassing the production wells. Many times this purpose is served by using the five-spot or line-drive patterns, in which half of the wells are made injection wells. A regular injection pattern is proposed that is based on the same well spacing as the five-spot but in which only a third of the wells need be converted to injection wells. Fluid flow model studies on this proposed pattern show that production histories will be as good as those for a five-spot pattern at mobility ratios of three and above. The model data are presented in a form that may be used to predict recoveries from both homogeneous and stratified formations. Introduction The injection of fluid into a petroleum reservoir usually is prompted by an actual, or predicted, loss in the productivity of the reservoir. Often, an oil reservoir is produced by pressure depletion until high GOR&apos;s dictate a change in policy. Fluid injection also causes increased ultimate recovery, but this usually is of less importance to the operator than is the maintenance of the production rate. It is a fact that the ultimate recovery in any particular fluid injection project is relatively independent of the number and spacing of the injection wells as long as the reservoir voidage through the production wells is balanced by the total injection rate. However, the response of a production well is directly affected by the distance it lies from an injection well. In places where the well productivities are declining, the injection wells should be spaced as evenly as possible among the producing wells ("dispersed" injection pattern). More particularly, if the production response depends upon the formation (and subsequent production) of an oil bank, each production well should be surrounded by injection wells. Otherwise, the oil productivity will increase very little as the oil bank moves past the well.&apos;.&apos; An evenly spaced injection pattern has the best chance of generating an oil kick in the production wells. If reservoir voidage and injection rates are to be equal, the ratio of injection wells to production wells must be equal to the ratio of the average injectivity to the average productivity (in reservoir volumes). This ratio is in strumental in choosing the injection pattern. Table 1 shows the production well to injection well ratio for the dispersed injection patterns that have been described in the literature.&apos;-&apos; All of these patterns will have comparable recoveries and response times (for the same basic distance between wells). The choice of pattern there fore depends upon the relative injectivity and productivity of the wells and upon the type of drilling pattern employed. Another important factor may be the ability of the proposed production wells to make up the lost productivity from those wells converted to injectors. These factors become more pronounced at the higher oil viscosities (low gravity oils). All other things being equal, the probable ratio of single well injectivity to single well productivity will be equal to the water-oil mobility ratio of the proposed flood. Thus, high mobility ratios (due to low gravity oil) should call for fewer injection wells — as long as these injection wells are "dispersed" to obtain more even pro duction response for the remaining wells. Secondary re covery projects in oil reservoirs seldom, if ever, will have mobility ratios requiring more injection wells than production wells. Thus, only the last five of the patterns listed in Table 1 will be of significant interest in oil recovery. Almost every development drilling program calls for the wells to be drilled along equally spaced rows and

Jan 1, 1969

By J. A. Stachura

Continuous mining machinery provides the coal industry with one way to compete for a larger share of the total energy market. Various types of machines are discussed and some of the problems with continuous miners, encountered by operators, are reviewed. Equipment manufacturers are working with mine personnel to provide solutions for problems that arise. While coal production over the past 25 or 30 years has been on a horizontal plane, coal&apos;s share of the total energy market has declined. To participate more effectively in this total energy market, it is necessary to produce coal more efficiently. It is the obligation of all management, employes, and mining departments to gear the deep mining industry to the rapid progress and changing of today&apos;s modern industry. This can be accomplished in the near future with the selection of the proper type of continuous miner best suited to each operator&apos;s individual situation. In most mining operations there is tremendous incentive to undertake the continuous mining program. It can reduce the size of the mine greatly by permitting a minimum of working places; it makes pillar recovery work more efficient from the standpoint of overall cost, amount of coal recovered, and safety. The work force can be reduced materially permitting closer and more efficient supervision. It simplifies maintenance because equipment can be more readily standardized. The trend of the coal market favors the use of continuous mining machines. Although there appears to be a general feeling that continuous mining is still a relatively new program and will be slow in replacing conventional mechanical equipment, the fact is that tremendous strides have been made since the first machines were installed in 1948. This program is advancing at approximately the same rate that mobile loading machines replaced hand loading. From 1948 to 1955 there were approximately 450 continuous mining machines in service. In October 1959, a survey revealed that there were more than 700 continuous mining machines in service. Many operators have expressed a desire to undertake this program, but they feel that they could not do so at this time because of one or more of the following reasons: 1) the thickness of their coal seams, 2) seam characteristics, 3) soft bottoms, 4) bad roof conditions, 5) size consist, 6) insufficient flexibility in machines, 7) difficult ventilation problems, and 8) high maintenance costs. With the realization on coal about the same today as it was in 1948, or slightly less and since coal is still failing to participate to a greater degree in the total energy market, it is not surprising that the coal industry is desperately exploring more economical methods for deep mining. The manufacturers are aware that the coal industry is willing to invest in continuous miners if the equipment is built for maximum flexibility, will produce higher tons per man, and assure long life between overhaul programs. CONTINUOUS MINING MACHINES Before discussing details regarding the selection of a continuous miner, let us have a preview of some of the continuous mining machines which are available to the coal industry today. Jeffrey Manufacturing Co.: The machine shown is the Jeffrey 76 A.M. Colmol. This is their most widely used miner, and has been particularly successful in central Pennsylvania and in high-wall mining in western Kentucky. One of the outstanding features of this auger-type miner is its portability. The entire mining range can be changed from its lowest point to the maximum height without stopping the mining operation. Jeffrey 76 B.M. Colmol: This machine is similar to the 76 A.M. model; however, it is built bigger and stronger for a mining range of 50 1/2 to 72 in. This is the model that is now available (Fig. 2). Jeffrey has added two arms to the top row, omitted the odd arm in the bottom row, thus permitting a 50 pct larger throat opening. This eliminates one

Jan 1, 1961

By Margaret N. Maxey

Man&apos;s capacity far fretting is endless, and no matter what difficulties we surmount, how many ideals we realize, there is a stealthy pleasure in rejecting mankind or the universe as unworthy of our approval. - Will Durant Until recently, reasons for favoring one or another energy alternative were advanced on the basis of technical considerations and economic realities. However, it is an indication of the cultural climate of our society and growing realization of why energy is our master resource that many citizens have begun to express concern about the social and ethical implications of our energy deci¬sion-making. A vivid indication of this shift toward ethical concerns is reflected in the attention being focused on conservation - even to the point of regarding it as a virtual panacea equivalent to a "free energy resource." Among others, the authors of a publication by Resources for the Future cautions us about the difficulties of defining conservation. They also point out that unrealistic expectations for achieving the high levels of conservation claimed by true believers may boomerang if, at the same time, we are morally required to maintain economic growth and robust productivity for the basic well-being of more people. In its economic meaning, conservation signifies the most economic or cost-effective applications of energy, together with other resources, in a given process or activity. To achieve conservation that is cost-effective, saving energy alone is not sufficient; the cost involved in saving the energy must be no greater than the cost of the energy that is saved. Using its thermodynamic meaning, conservation and efficiency are viewed as constrained by physical laws and measured against ideal limits set by these laws and processes. Since achieving higher levels of technical performance is not without costs, the economic meaning of conservation must be factored into technical possibilities. It is the ethical, equity and environmental meaning of conservation that concerns us here. In its third meaning, conservation consists in moderation as a value which appears inherently worthwhile both in itself and in relation to social choices dedicated to achieving distributive justice. The value of moderation seems predicated on the assumption that natural resources and the environment have fixed, finite, exhaustible capacities for satisfying human needs. Hence norms for moderating human behavior appear to require prescriptions by some authority. Such norms presuppose some agreement on "essential" uses of energy. However, the difficulties of setting behavioral norms loom large, because "... it is as difficult to determine essential energy consumption as to determine what is essential in any other phase of consumption, whether it involves food, clothing, shelter, or recreation." The ethical meaning of conversation is further complicated by a centuries-old argument over the proper exercise of stewardship - i.e., how best to develop natural resources. On the one hand, the preservationist position insists on an inviolate, "hands-off" policy and stands opposed to ongoing development of wilderness areas and mineral resources. On the other hand, the "scientific conservationist" who preaches the "gospel of efficiency" insists on development of resources based on principles of sustained-yield, multiple use and - in the case of competing claims - reserving resources or land for their "higher use." Current confusion reigns among opinion leaders in the environmental movement because they appear to have lost the genius of the original Conservation ethic, developed in the 19th century. They seem to think that conservation is preservation. The question I wish to explore is whether a single-minded, exclusive pursuit of "conservation" in its economic, thermodynamic and preservationist meanings may actually do more harm than good in serving the ethical goals of conservation. There

Jan 1, 1986

By Gary Beerkirkcher

INTRODUCTION The mine hoisting equipment that is selected and installed at a mine is for the lifetime of the mine and, therefore, it is extremely important that a proper choice be made. Several types of mine hoist designs, including double drum hoists, single drum hoists, friction hoists, and various special designs of these, are available to¬day. Each has advantages and disadvantages and they should only be used in suitable applications. Drive systems for mine hoists must be evaluated together with the mechanical systems for each hoist application. It does not make sense to properly select the hoist mechanical system and then choose a drive system that turns out to be a bottleneck. MINE HOIST TYPES There are two basic types of mine hoists available in the world today: the drum hoist, on which the hoist rope is actually stored during the hoisting cycle, and the friction (Koepe) hoist, which merely passes the rope over the wheel during the hoisting process. Drum Hoists Single Drum Hoist: A single drum hoist (shown diagrammatically in Fig. 1) can be used as a service or production hoist with the cage or skip in balance with a counterweight (Figs. 2 and 3). It can efficiently service one or more levels, since the location of the counterweight at any time is not important. As a pro¬duction hoist with skips in balance, the single drum hoist is best used for single level hoisting. All rope adjustments for proper spotting must be done manually for the single drum hoist. This has to be done periodi¬cally to compensate for rope stretch. A variation of the single drum hoist is the divided drum hoist. If multilayer winding is necessary, the single drum hoist must have a divider to allow a sep¬arate compartment for each rope. If a counterweight is used with a divided drum application, the counter¬ weight rope can be wound on a smaller diameter (Fig. 4). Consequently, it moves a lesser distance than the main conveyance and rope adjustment problems are re¬duced. Double Drum Hoist: A double drum hoist in oper¬ation is shown in Fig. 5. Double Drum Hoist With One Drum Clutched: As a service hoist with cage and counterweight, a double drum hoist with one drum clutched (Fig. 6) can serve several levels efficiently. The advantage of having the clutched drum is that it allows rapid adjustment of ropes due to initial stretch. Some users may prefer the single drum hoist with manual rope adjustment, while others consider the added expense of the second drum and clutch is justified to make rope adjustments quickly. The value of this feature for a particular application should be discussed with the hoist manufacturer. As a production hoist with skips in balance for a multi¬level operation, the clutch can be adjusted for efficient hoisting from any level. Double Drum Hoists with Both Drums Clutched: There are also double drum hoists that have both drums clutched (Fig. 7). The main advantage claimed for this type of hoist is that if something happens in one of the two compartments, the hoist can operate in the other compartment to raise and lower men and sup¬plies. This feature is particularly favorable if there is only one shaft entrance to the mine. Multiple Drum Hoist: The multiple drum hoist, a South African innovation, is a type of drum hoist about which everyone should be aware. Basically, it uses two hoist ropes per conveyance which at great depths per¬mits use of smaller ropes and smaller drums. There are none in use in the United States today. However, they should be considered in very deep mines. Friction (Koepe) Hoists This hoist (Fig. 8) was introduced to the mining world by Frederick Koepe in 1877. The basic prin¬ciple of the friction hoist is that the hoist rope passing

Jan 1, 1982

By H. V. Welch

In this paper, as prepared for delivery at the Southern California regional meeting on Oct. 14, 1948, it was thought best to interpret the term "economics" in a rather broad manner and to include, in addition to the material losses and recoveries and associated monetary values (Part I), a limited discussion of the increased difficulties or the particular problem and the special requirements, as the particle sizes of the suspended particles range down from the relatively coarse to 100, to 10, to 1 micron or even to a fraction of one micron (Part II). Further, it is not quite in order to overlook entirely the community and individual health problems, although space requires the economics of this to be considered only very incompletely. Therefore, Part III, covering this phase of the subject, is very limited. This paper, then, is divided into 5 parts or headings as follows: I Losses and/or values in suspended solids. II Particle size. III Dust and fumes in community and individual living. IV Means and Procedures for dust and fume collection. V Description or examples of specific equipment in service and of the several types used for dust and fume collection. Because of the wide extent and wealth of subject material available and the space and time limitation imposed, presentation and discussion are less than originally planned. I—Losses and/or Values in Suspended Solids The weight involved in moving streams of industrial plant gases is commonly not appreciated, neither is their carrying power in the weight of solids maintained in suspension and moved with the gas stream from a point of origin or pick-up to a point of dissipation or settlement. These, however, are major weight figures; for example, in a modern iron blast furnace there may be five tons of gas for every ton of iron produced and by the time this blast furnace gas has been burned in stoves or under boilers the weight of gas discharged to atmosphere is on the order of eight times the weight of iron produced. Similarly for nonferrous metallurgy there may readily be from 10 to 20 times the weight of gases discharged to atmosphere as there is metal produced. A cement kiln in operation or a kiln in service to produce metallurgical lime may have on the order of 5 to 6 times the weight of stack gases as of clinker or lime produced, and at least the cement kiln, because of the very fine nature of its feed, is a very heavy dust producer. It may be noted that there have been two developments in progress for nearly three decades. Both are extraordinary in the industrial economics effected and in their ready availability to ever larger units of operation and their ever widening importance in industry, and both are productive of great quantities of finely divided material in furnacing. The first of these is the flotation process for ores, especially the metallics such as copper, lead, and zinc; and the second, powdered fuel combustion for power plant, industrial plants and metallurgical operations. Today, new developments, for example, flotation for the nonmetallics such as higher grade limestone for cement manufacture which requires still finer grinding and the powdered-coal-fired boilers with production ratings of over 1,000,000 lb of steam per hr, bring still more concentrated and hugely increased quantities of stack emission. Perhaps the honors for the greatest interest in the quantities and values escaping in waste furnace and equipment gases belong to the nonferrous metallurgical operations. Their record of achievement in the installation of dust and fume collection equipment, largely baghouses or Cottrell electrical precipitators, is exceeded by no other industry. Something of the magnitude and variety of equipment utilized in such recovery systems was covered by the writer in two papers presented to the Institute some 10 years ago.1,2 It is not intended to repeat the material of those articles, but it is thought that they complement this offering and should be noted. COPPER ROASTERS As the copper roasters are the first of the series of furnaces handling the copper-bearing concentrates in the usual copper smelter of today, it is in order to make them the first consideration. Multiple hearth sulphide roasters, not hard driven, often maintain their dust loss through exit gases at 3 pet or below of feed to furnace; in hard-driven or maximum-driven furnaces, exit gas losses often approximate 7 pet of charge with a ±2 pet variation for special conditions prevailing at some plants. A 5 pet loss of feed in a roaster gas exit, unless reclaimed, often makes the difference between a profit and loss operation, and in many cases substantial recovery is the very basis of dividend payments. As there is available very practical and successful equipment for the collection of the

Jan 1, 1950

A Seminar to discuss &apos;Reactivity of Line in Steel Making&apos; was held in the auditorium of Iscor&apos;s Headquarters Building in Pretoria on the 5th August, 1971. The Institute organised this Seminar on the occasion of the visit of Dr Obst of the Rheinische Kalkstein Werke GMBH, Wuelfrath, West Germany. The latter is one of the largest lime companies in the world and Dr Obst is in charge of their research laboratory. He and his co-workers have earned a reputation for their research into reactivity of lime in steel making. This work is also of great importance to the steel industry in this country, particularly with the changes which are occurring with the introduction of basic oxygen furnaces. Some 80 persons representing most of the major steel companies attended this Seminar. Dr Obst presented his most interesting paper which he illustrated with projector slides. This paper is printed in full in this journal. This was followed by several contributions and active discussions. The first contribution was made by Dr T. B. Beeton of the Research and Development Department, Iscor. He gave a brief summary of the studies on reactive lime carried out at Iscor since 1968. Their work was particularly related to the selection and definition of the various reactivity tests and the correlation of these with plant results. He demonstrated that the DIN methods, particularly the Din (40°) test, gave the best results and reported that good agreement had been reached between Iscor, Highveld and Northern Lime on future test procedures. Mr B. Lowther of The Northern Lime Company then dealt with problems associated with the production of high reactive lime. The rotary kilns at The Northern Lime plant at Lime Acres are particularly suitable for the production of high-reactive lime, because this type of kiln lends itself to accurate control of temperatures and retention times. Several problems, however, exist. Because of the long haul distances and the deterioration of reactive lime by absorption of CO2 and water, high reactive lime is not suitable for most customers. To constantly be changing kiln conditions to produce relatively small quantities of high-reactive lime, therefore, causes problems. Highveld Steel at present is the only company requiring high-reactive lime and a satisfactory product is now being produced at a cost because kiln capacity is reduced and fuel costs are higher. Dr P. R. Jochens, of the National Institute for Metallurgy then submitted data to show how the reactivity of soft burnt reactive lime deteriorated due to long railage hauls. Detailed sampling of trucks had been carried out leaving the lime works and on receipt at Highveld and it was demonstrated that there was deterioration in the top layers of the truck. This top layer protected the balance of the lime which is still in good condition on arrival at Highveld. Exposure to atmosphere by further handling and storage into the bunkers at Highveld, however, resulted in further severe deterioration in the lime reactivity and the lime when finally fed to the Basic Oxygen Furnace is reduced to one third to one quarter of the original reactivity value. The same deterioration does not occur with normal run of kiln lime, which is burnt harder, but still has a satisfactory reactivity for most purposes. Mr A. A. Hejja of the Department of Metallurgy, Witwatersrand University then made a contribution on the metallurgical aspects of the use of lime of different reactivities in the Basic Oxygen Furnace and the effect on desulphurization efficiencies. He gave a wealth of data on actual tests which had been carried out and came up with the surprising conclusion that the deterioration of high-reactive lime due to transport did not have as serious an effect on the efficiency of desulphurization as one would have expected. The efficiency was good provided high-reactive lime in the first instance had been produced, irrespective of whether it had deteriorated thereafter. Poor efficiency was obtained only when the lime in the first instance was produced in an unreactive form. The temperature rise in the Basic Oxygen Furnace also has a definite effect. If lime is introduced when the temperature is too high, soft burnt reactive lime becomes hard burnt and unreactive before it can dissolve in the slag. Use of ferromanganese slag assists dissolution of lime. There was a great deal of discussion following these contributions. Particular interest was expres8ed in the special lime described by Dr Obst. This consists of a mixture of fine lime which is premixed with fluxes and either briquetted or pelletised. The question of injecting finely ground lime as an alternative was also discussed. Both these systems eliminate the necessity for highly reactive lime. With smaller lime particles, larger surfaces are exposed thereby ensuring more rapid dissolution in the molten slag. The discussions generally were lively and informative and all present derived benefit from learning of the experiences of others. The valuable contribution made by our German visitor, Dr Obst, was particularly appreciated. The instantaneous English-German translation service which was provided, greatly facilitated discussions.

By Arthur Lubinski, K. A. Blenkarn

It is explained why the bottom portion of freely suspended tubing in a pumping well buckles and straightens in succession during the pumping cycle. Field evidence of resulting rod-on-tubing wear, excessive polished rod load, and excessive horsepower are given. The possibility that buckling hastens pump wear is strongly suggested. Means for either prevention of buckling or for mini-mizing its effects are explained, their relative merits compared, and field results of their use given. These means are: tension anchors, tail pipe, sucker rod guides, and corrosion inhibitors. Charts and formulas for best use of tension anchors, tail pipe, and guides are given. Use of tension anchors, or compression anchors with a heavy tail pipe, prevents both buckling and breathing, thus improving volumetric efficiency. Without tail pipe, buckling above compression anchors precludes such improvement. INTRODUCTION It is well known that a column must be subjected to some compression in order to buckle; and also that a structural member does not buckle if subjected to a tension. When consideration is given to a tubular column, the question may be asked, "How is the buckling phenomenon affected by inside or outside pressure?&apos; At first, it seemingly should not be affected. However, this is not so. In order to arrive at a correct deduction one should first understand the basic reasons for buckling of a column under loading*. Then he should add to the effect of that loading the effect of pressure. Following this procedure, one may discover quite unexpected phenomena. In some cases, when subjected to more pressure inside than outside, a pipe may buckle under tension. In other cases, a pipe may remain straight, although subjected to a very large compression. In 1950 and 1951 it was explained why the bottom portion of a string of pipe freely suspended in a well does not buckle even when subjected to a large compression due to buoy- ancy.2,3 It was shown that the com-monly used concept of a neutral point, as being a point in the string with neither compression nor tension, is inadequate, and a more relevant definition of the neutral point was introduced. The findings were also generalized to cases of different pressures inside and outside a pipe.3a Later, in a further generalization, allowance was made for variations of stress and pressure with depth.&apos; The findings were applied to the new technique of hydrostatic high pressure testing of lengths of pipe in the mill.5 In 1952 it was observed that previous theoretical findings apply to tubing in pumping wells. The lower part of freely suspended tubing buckles during the upstroke portion of the pumping cycle. Later, it was ascertained that this phenomenon is responsible for wear and malfunctioning of the equipment. Various remedial measures were devised and successful field trials conducted. Only brief mentions on the subject have been published.6,7 In this paper, the phenomenon of tubing buckling is explained, field

Jan 1, 1958

By E. T. Turkdogan, P. Grieveson, J. F. Beisler

Experimental results are given for the rate of reduction of silica from silicate melts by paphite-saturated iron in the presence of carbon monoxide. It is shown that, when gas bubbles are present at the slag-metal interface, the interfacial chemical reaction is the rate-controlling process in the transfer of silicon from slag to metal. From the silicon-concentration profiles in the metal sample, the diffusivity of silicon in paphite-saturated iron is found to be (5.4 * 0.4) x 10 sq cm per sec at 1600°C. Some consideration is given to the transport of oxygen from the slug-metal interface to the walls of the gvaphite metal container as becoming the rate-controlling process in the absence of gas bubbles at the slag-metal interface. ATTEMPTS were made by Fulton and chipman1 to investigate the kinetics of reduction of silica from calcium alumino-silicate melts by graphite-saturated iron in an atmosphere of carbon monoxide. In these experiments with 400 to 500 g of metal and slag, both phases were stirred in such a manner that the interface was essentially undisturbed. Initially, the graphite-saturated iron contained about 15 pct Si and, after about 8 or 10 hr of reaction time at 1600°C, the silicon content of the metal in- creased by about 0.2 pct. In a written discussion on this paper of Fulton and Chipman, schuhmann2 pointed out the possibility that this observed slowness of the reduction of silica could be due to the transport of oxygen across the liquid metal boundary layer at the slag-metal interface. Although this explanation of Schuhmann is quite feasible for the experimental data of Fulton and Chipman on silica reduction, such a reasoning should not be extended to other rate data on slag-metal reactions unless sufficient evidence is available satisfying the boundary conditions for such a transport process. The hydrodynamics of stirred liquids are very complex and even for a simple method of stirring there is no exact mathematical solution which will predict the mass transfer coefficient accurately. The best available solution of this problem is that given by Lewis&apos; and later modified by mayers~ for a two-liquid system where liquids are stirred by counter-rotating stirrer blades without disturbing the interface. In such a system the mass transfer coefficient is estimated from an empirical relationship using the data on viscosity and density of the two liquids, rate of revolution, the length of stirrer blades, and the diffusivity of the element which is transferred from one phase to the other. It was found in these investigations&apos; that the estimated and observed mass transfer coefficients, in systems containing two immiscible aqueous solutions, agreed within *40 pct. Although this is not considered to be an unreasonable error for the study of industrial processes, uncertainties of this magnitude cannot be tolerated in any theoretical study of reaction kinetics. In view of the complexity of the

Jan 1, 1963