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By G. D. Just

INTRODUCTION Large scale underground mining involves the bulk handling of fragmented material. The cost and efficiency of the mining systems is there- fore significantly influenced by material flow characteristics. Flow problems may occur in the form of ore pass blockages which interrupt the free flow at extraction openings. The costs of such delays can be readily assessed and compared to the costs incurred in reducing blockages by improved fragmentation or larger ore passes. In practice the problem is more complex than this statement suggests because it is generally un- economic to design for zero ore blockages. Another major flow problem occurs in the form of relative movement of ore and waste as the fragmented material is extracted. This produces waste dilution in the recovered ore and influences total ore recovery. This flow problem is much more complex than the ore block- age phenomena. Many questions concerning the precise flow characteristics remain unanswered because of the variability of size distributions, particle shapes, material properties and the total extraction layout and design. Model studies can provide a visual and quantitative illustration of probable flow characteristics but full scale data collection is necessary to evaluate the precision of such information. The methods and types of data obtained must be carefully selected to recover the maximum volume of useful information for operational control and future design. It is essential that honest precision levels are assigned to the data and any subsequent analyses. Grade control data may give misleading short term information on flow characteristics because of the difficulty in knowing the true grade of the mass of material before extraction commences. However, in the long term control of extraction grades is vital to the profitable operation of the mining system. The most efficient extraction design and operational schedule can only be determined after all of the facts and variables are known. This is usually only possible after the orebody has been completely extracted. However, if design and operational personnel have a full appreciation of the nature and variability of material flow under different conditions the best possible results should be achieved. The most significant features of material flow are out- lined in this paper in order to provide mine planning and mine management personnel with some of the necessary information relating to material flow. Available facts and reliable figures from selected publications are noted in association with unbiased and hopefully accurate opinions of the relevance of the data to mine design and mine system control. Possible future developments and profitable areas for research into material flow problems are also detailed. MATERIAL FLOW AND MINING METHODS The effects of material flow on the design and operation of an integrated underground ore handling system is one factor which is common to most mining methods. Analysis of the system as detailed by Just, 1980, permits the identification of unit process objectives. For example, a typical underground ore handling system as illustrated in Figure 1, involves the following unit operations:- (i) Gravity flow of ore in stope (ii) Ore extraction at base of stope (iii) Ore haulage on the production level (iv) Dumping of ore into ore pass system (v) Gravity flow of ore in the ore pass (vi) Underground crushing of ore (vii) Haulage of crushed ore to shaft (viii) Hoisting of ore to the surface. Average flow rates in each of these unit operations can be misleading due to variability in incremental capacity caused by flow blockages and machine delays. Thus to effectively analyse the probable performance of the system, it is necessary to have a measure of the flow loading and haulage rate variability. Mechanical equipment performance specifications can be used to provide such information for loading, haulage and crushing; however, in the case of the gravity flow of material field measurements are required to relate the probability of "hang-ups" to the degree of fragmentation. Factors affecting the frequency of flow stoppages are, size, distribution and cohesiveness of broken material and the geometry and size of the flow channel. Ore pass channel design is relatively simple since regular cross-sectional shapes are used

Jan 1, 1981

By MARIUS R. CIMPBELL, Edward W. Parker

DESCRIPTION. ACCORDING to the estimates prepared by the U. S. Geological Survey, the area underlain by workable coal-beds in the United States is 496,776 sq. miles. Of this total area, 480 sq. miles contain the entire anthracite coal-fields of Pennsylvania. The bituminous coal-fields are estimated to be contained in areas aggregating 250,051 sq. miles. The grade of coal between bituminous and lignite, and which is designated by the Geological Survey as " sub-bituminous," is estimated to be contained within areas aggregating 97,636 sq. miles, while the areas containing lignite aggregate 148,609 sq. miles. The coal-fields are divided, for the sake of convenience in classification, into six main provinces, as follows: 1. The Eastern. Province, containing the anthracite coal-fields of Pennsylvania and the bituminous coal-fields of the Appalachian region-namely, those of western Pennsylvania, Ohio, Virginia, West Virginia, Kentucky, Tennessee, Georgia, Alabama, and small outlying areas in North Carolina. 2. The Interior .Province, containing the bituminous coal-producing regions of Michigan, Illinois, Indiana, western Kentucky, Iowa, Kansas, Missouri, Oklahoma, Arkansas, and Texas. 3. The Gulf Province, containing the lignite-areas of Alabama, Mississippi, Louisiana, Arkansas, and Texas. 4. The Northern or Great Plains Province, containing the lignite and sub-bituminous areas of North and South Dakota, eastern Montana, and northeastern Wyoming. 5. The Rocky Mountain Province, containing the bituminous and sub-bituminous areas of western Montana and western Wyoming, Colorado, Utah, and New Mexico. 6. The Pacific Coast Province, containing-the areas of Washington, Oregon, and California.

Apr 1, 1909

By Mohamed Mortada

A practical analytical method is developed in this paper which provides the practicing reservoir engineer with a handy method for analyzing oilfield interference problems. The procedure employed entails the principle of superposition of individual eflects. A set of charts has been developed and can be used to evaluate the individual effects. The charts represent non-steady state pressure distribution in an extensive aquifer due to a constant rate of production from an oilfield which can be approximated by circular geometry; they are constructed from solutions to the diffusivity equation considering a circular sink as distinguished from a point sink. The solutions are obtained partially from mathenlatical considerations and partially from analog and digital computations. By virtue of the method of images, the charts can be used also to treat the case of production near a fault. In addition, provisions are made for treating oil fields, which are produced by partial water-drive. Treating an actual field case is deferred to a subyequent writing; however, illustrative example is presented to demonstrate the method of application. The pressure distribution in linear and limited radial aquifers is currently under study. INTRODUCTION With the increasing difficulty of discovering new oil reserves, attention is necessarily focused on the efficient development and production of existing reservoirs. Efficient production depends on the availability of reliable means for predicting the pressure-production behavior of oil fields. The prediction is usually performed by analytical methods or computers. Analytical methods are often limited to systems which can be approximated by simple geometry. However, analytical methods have the distinct advantage of being readily performed without special equipment. Analog and digital computers lend themselves to a variety of problems, but are not always locally available and consequently their use is limited. One particular situation in which analytical techniques are needed involves studies of multiple, water-drive oil fields sharing a common aquifer. Such oil fields are in hydrodynamic communication. Therefore, production from any of the oil fields is accompanied by a pressure decline which is transmitted through the aquifer to the other oil fields and manifested as pressure interference. The rate of propagation of the pressure decline is such that the pressure may be significantly reduced many miles away from a producing pool. An example of pressure interference is found in the Woodbine formation in East Texas. There. a dozen or more pools, including several of major size, draw on the Woodbine formation for water drive. The pressure in the water-bearing portion of the formation has been significantly reduced over an area of several thousand square miles. This reduction of pressure has been such that when the Hawkins pool was discovered in 1940, the pressure in it had already been reduced 280 psi below the initial value in the aquifer. This resulted from prior production from other Woodbine sand pools, including, in particular, the East Texas field some 20 miles to the east of Hawkins.' The above example indicates that the interference effect can be significant and should be taken into con-

Jan 1, 1956

By J. P. Dunlop

The fact is not.ablc though probably little known that thc Unitcd Statcls is the only nation obtaining and distributing through its Govcrn-ment burcaus any data pertaining to waste metals and drosses. Some foreign goverrlnlents do issuc reports relating to rnine or smelter production of prirrlar~ metals, but none gives in scope and detail t'he information published now by the U. S. Bureau of Mines and formerly by the U. S. Geological Survey; and this is despite the fact that the funds annually allotted for those purposes are insignificant in comparison with allotments for the preparation of data relating to other industries of like importance. The earliest data on the production of metals from secondary sources in the United States were contained in a press bulletin issued by the U. S. Geological Survey on Jan. 4, 1909. The information published was that for thc year 1907 obtained ant1 compiled by C. E. Siebenthal, who was one of the first to visualize the growing importance of the scrap-letal indust,ry. Thc Nationd Conscrvation Commission had emphasized its opinion that the known domestic supply of certain kinds of the morc important irietals was being rapidly marketed and that while there was no immediate cause for concern it was best to conserve such resources. Not only had there been a lanlentable lack of any data regarding the quantity of scrap inetals available or used but also gross carelessness and indifference in the segregation, collection, and effective use of scrap material. Siebenthal realized that even approximately correct statistics of recoveries from the more important base-metal scrap and drosses wcrc nearly as essential t,o both producers and consumers as the stat'istics of the output of primary metals. There were not then nor are there now sufficient funds for complete collection of data, nor was it considered the province of the Geological Survey t'o do more than determine approximately the recovery of secondary metals for use in supplementing those given for the primary metals. Undoubtedly the first bulletins issued did not give the full output, for it takes time to establish contacts for an inquiry covering so

By E. H. Hamilton

WHEN starting a series of experiments on the use of powdered coal in lead blast furnaces to replace coke, I realized that in copper smelting the problem is simpler because the sulfur recovers the copper in the form of matte. In lead smelting there are greater difficulties because a reducing atmosphere must be maintained in the active, zone corresponding to each tuyere in order to get the best recovery of lead. Therefore, the feed of powdered coal must be quite regular, uniform and under control. The molten products issuing from the taphole are the resultant of the work of all the tuyeres and it can readily be con-ceived that one part of the furnace may be forming slag with a higher lead content than the slag formed in other parts of the furnace. At first, we used only one tuyere situated on the back of the furnace. This was for the purpose of getting all of our regulations under the regular operating conditions. We tried every known system of feed and found they were not dependable and our present system was finally worked out, and so far as we know, is the only working system that will give uniformly good saving in lead blast furnaces. We placed a Bristol self-recording thermometer on the feed floor. This gives a 24-hr. continuous record of the temperature of the gases leaving the furnace. We put a self-recording gage on the "15-lb." air used in the injector. A second recording Bristol gage was put on the low-pressure air (40 oz.). I realized that it was necessary that we should know the exact weight of coal going into each tuyere and that it should 'be under observation at all times. L. W. Kirk was assigned to the problem and developed the open sight feed and the distributor, so that we now have the coal being fed into each tuyere in sight of the men in charge. We have an apothecary's balance beside the furnace, and the operator takes the pan and inserts it under the stream of falling powdered coal for one minute, and places the pan on the scale, the other scale pan having weights indicating the desired amount to be fed to each tuyere per minute.

Jan 10, 1922

By DR. RICHARD RATHBUN

ON behalf of the Regents and the Secretary of the Smithsonian Institution, it gives me great pleasure to welcome you to the National Museum; but it is to your own museum, since it belongs to you in common with all the people of the country. Still young in a life which has been beset with many difficulties, it has gathered strength and attained a growth quite unprecedented. In fact, it is this very growth which has been the chief cause of trouble, always leading far and away beyond the capacity for storage ; and to-day there is nearly as much material contained in outside buildings as is displayed in this one. You will, accordingly, find the collections crowded, the cases so close together that their contents are often difficult to view, and the arrangement generally lacking symmetry. You may, therefore, be inclined to regard us as poor custodians of the collections of a great nation, but I beg you to withhold your judgment for a while. From the beginning there has been abundant zeal and activity and a proper direction of affairs, but space and money have been lacking. There is now a prospect of better times. All about you here is a beautiful park, but without. a covering it is not adapted to museum purposes. Upon it, however, a new large building is going up, so extensive in its dimensions that technology can soon be given a fitting home, thus realizing one of the earliest aspirations of the Regents. Some sixty-five years ago the extensive returns of specimens from the famous Wilkes Exploring Expedition around the world began to reach Washington, where they were deposited in the Patent Office Building, and formed practically the first of the National Collections. Six years later the Smithsonian Institution, based upon the bequest of James Smithson, was

Jul 1, 1905

By B. Silliman

The experiments detailed by Dr. Hunt,* having demonstrated the fact that the copper contained in the "clay ore" of Jones's Mine, was rendered completely soluble in the bath of ferrous chloride, used in the Hunt and Douglas process, after heating in contact with carbonaceous matter in a close vessel, I set myself to devise a form of muffle furnace adapted to the treatment of large quantities of these and similar ores by a continuous process. The result is shown in the diagrams on Plate X, reduced from the working drawings, after which this furnace was built early in 1876, at Phœnixville, by the Chemical Copper Company on their works at this place. The peculiar character of this ore determined the form, dimensions, and position, with reference to charging and discharging of these muffles. The ore arrived from the mine with from 20 to 25 per cent. of moisture, and when dried at 21o F., or more slowly at lower temperature, it falls to a light incoherent powder, with occasional lumps of undecomposed rock. In this condition it is readily mingled with coal-dust or any like reducing agent, and requires no other preparation for the muffle than the use of the shovel, to mix it well with the reducing agent. As it is a remarkably good non-conductor of heat, it was obvious that the mass, to be heated through in a reasonable time, must not be too thick, while the weight of the mass must be sustained in a way to avoid undue strain upon the walls of the muffle. These walls must be as thin as practicable, to favor the more rapid transmission of heat, and must, therefore, be so constructed as to admit of being stayed on the sides at frequent intervals to resist the lateral thrust of the very mobile mass of pulverulent ore, which, for obvious reasons, must be charged at the top and drawn from the bottom of each chamber. These considerations led to the form adopted, viz., two vertical muffles, standing upon very strong bridge tiles, seen in longitudinal section, on the line E, F, and in plan in Fig. 3, on the same plane. (Plate X.) The vertical section of the muffle is seen in Fig. 4, drawn in the plane G, H, of the longitudinal section, Fig. 6, which is the key to all sections. The walls of the muffles are built of the best firebrick, very care-

By J. F. Myers, F. M. Lewis

DISCUSSION L. E. Djingheuzian (Canadian Dept. of Mines and Technical Surveys, Ottawa)—In their Summary the authors say: "Reconciling the grinding efficiency with good metallurgy is still a problem." In the discussion of the first paper8 in his reply to W. I. Garms, Mr. Myers states: "Our grinding process with smooth I-in. balls has reduced by nearly one half the metallic losses in the fine micron sizes of the tailing. This is simply because less of the fine micron sizes are produced. Since the + 65 mesh size is the same as formerly, a higher percentage of the intermediate sizes are developed. These sizes have the highest floatability, require the least reagents, and use less floating time. "These factors contribute so heavily to the overall economies that dropping our power grinding gain from 28 pct back to 19 pct is a small detail. However, we feel that this is only a momentary situation and that eventually the best features of the grinding and flotation processes can be brought together, which is as it should be." Italics are mine. The above statements, to me, appear to be the answer to the opening statement in the Summary. Denoting the costs at different power grinding gains as: Power Grinding Power Grinding Gain, 28 Pct Gala, 19 Pct Cost of grinding G G1 Cost of flotation F F1 Value of metallic losses T T1 where G1 > G2 F3 < F, and T1 < T, we have: G1+Fl+T1<G +F+T. Since the authors accept the idea that "grinding in flotation plants becomes part of the &apos;conditioning&apos; of the feed to flotation",4 i.e., that in flotation the ball mill is primarily a conditioning machine, it can be postulated that Tennessee Copper grinding at cost G1 is more efficient than grinding at lower cost G. This can be directly inferred from the Conclusion of the paper. Mr. Myers also emphasizes this at the end of his reply to Mr. Garms: "that grinding is for the purpose of preparing flotation feed and not grinding per se." This, to me, in the final analysis means that when the efficiency of grinding is weighted against the conditioning factor, the former becomes a function of efficient conditioning, hence, within the system in which proper conditioning is the dominant factor, the best grinding efficiency is provided by grinding which will contribute towards the optimum conditioning. This brings us again to the statement: "that if every grinding unit were considered as a conditioner for each following step, efficient grinding plants would become much easier to design."&apos; In other words, grinding equipment should be balanced against the flotation equipment and against chemical reactions taking place in the system. F. C. Bond (Allis-Chalmers Mfg. Co., Milwaukee)— The authors&apos; discussion of the probable ball motion in a slow speed high dilution mill is very interesting. When the 1-in. balls have worn down to about one fourth of their original weight they apparently first develop a flat surface; as wear progresses this flat face becomes concave, and other concave faces appear. It seems more probable that the first flat face may form at the softest part of the ball surface, and that each succeeding contact tends to force this flat face into sliding contact with a larger round ball; than that the flat faced ball tends to pair off with a particular round ball and to travel with it continuously. When the small worn ball has a flat face and is in sliding contact with a large round ball, the surrounding large balls will assume a more or less definite pattern, and slide against the worn ball, thus producing secondary concave faces. The primary concave face seems to be larger and better developed than the secondary faces. The ball charge can be divided into "concaves" which show at least one concave surface, "intermediates" which have developed flats or incipient concaves, and "rounds." Ball slippage is always present in a tumbling mill, and the mutual ball movement is necessarily a combination of rolling and sliding. The sliding motion is apparently concentrated upon the smaller worn balls which nest between the surrounding larger round balls. When each worn ball starts its upward path in the mill its primary flat or concave surface fits against a larger round ball, and the round ball slides upon it. The action may be something like that of the ball separator in a ball bearing, except that the worn sliding balls are always under considerable pressure. The material is ground under the combined influence of breakage 1—by impacts between falling balls and between falling and supported balls, 2—by being nipped between rolling balls, and 3—by being rubbed between the sliding balls. The rubbing action will be increased in the presence of worn balls with concave surfaces. The rubbing action probably produces a considerable portion of the finely ground slimes in the product. The worn balls commonly approach tetrahedrons in shape, and are very different from concavex, each of which has two equal opposed concave surfaces. Concavex were designed only to grind upon themselves, and not for use in combination with grinding balls. Their action in a grinding charge is very different from

Jan 1, 1952

By Jay A. Carpenter

IN six years the construction of Hoover Dam and the power plants probably will have reached the operating stage and this vast new source of power will then be continuously available for industry. The height of the darn will be 580 ft. and the average annual flow of the Colorado River is calculated at approximately 24,000 cu.ft. per sec. If this full head and average flow can be maintained the year round, about one million horsepower will be generated. The U. S. Reclamation engineers, taking into consideration the probable range in flow and head, have set the figure for power contracts at 660,000 firm horsepower, which can be assured at all times of the year. During the months of heavy run-off of water from the Colorado River Basin the power plants should be able to generate the full 1,000,000 hp. capacity of the power plants, so there will be 340,000 excess or secondary horsepower. The cost of firm power at the switchboard will be close to 2.15 mills per kw.-hr., equal to $14.05 per hp.-yr., and the cost of the secondary or off-peak power will be close to 0.8 mills per kw.-hr., or $5.22 per hp.-yr. In no place in the country can such cheap power be obtained today. The electrochemical industry is in a state of flux because the power costs from its old sources have increased so much (to $30 per hp.-yr. at Niagara) that the industries have had to seek new sources, so they have gone to Canada and Norway and built new plants.

Jan 1, 1932

By AIME AIME

OPPORTUNITY may not be knocking but it, at least, is waiting for you, your family and your friends in that amazing republic south of the Rio Grande. For the first time we are able to publish the official itinerary for the forth-coming Mexico City meeting of 1936. As shown on Page 351, the deluxe special train leaves St. Louis on Thursday. Nov. 5 at 5:30 p.m., returning to St. Louis on Nov. 18 at 8:15 a. m. The schedule provides seven days and six nights in Mexico City with numerous excursions to nearby towns and resorts. The oldest surviving city in&apos; North America is Mexico City, dating back at least to the twelfth century. It was the Aztec capital when Cortez arrived in 1519. The famous cathedral still standing was built on a foundation of sculptured Indian images and the remains of a great Aztec temple. Today it is a city of romance.

Jan 1, 1936

By Robert K. Warner

When a new mine is opened, and often when an operating mine must adapt itself to physical or economic changes, a mining system must be selected in complete detail. In the past the plan chosen was usually the product of the local staff alone, however limited the training and experience of that staff might be, which often resulted in the introduction of methods that were familiar to the staff, but not so well suited to the conditions as others unknown to the local men. A new management, noting the difficulties with the existing layout, might make modifications or complete changes, so that many mines in their history have seen a whole series of mining systems, each somewhat laboriously grafted on to its predecessor. This should not be interpreted as a condemnation of the older staffs for sticking to the tried systems, such as open square-sets in the early days at the Homestake, because they knew it would work after a fashion, nor does the statement apply to the technically trained, and usually broadly experienced staffs of most present-day properties. The older miners did not have the variety of tools and methods, nor the present freedom of transfer of information as to what the other man is doing, and so did the best they could under the circumstances. Finally, the higher grade of the ores made the choice less vital. The ever-increasing need to mine low-grade orebodies, with a fixed or even lower price for the metal produced, has caused an increasing need for low-cost mining. In most new mines this has simplified the problem of selection by eliminating from consideration all of the high-cost systems, but it has also complicated the choice by the necessity for refinement in detail and a close adjustment of the plan selected to all the conditions at the property. In these low-cost problems any textbook division of mining systems as applied to "beds, veins or masses" avails little as a guide. It should be realized at the outset that to be successful under modern competitive conditions a system of mining must be worked out with elaborate detail, with careful time scheduling and control of the various elemental operations, and that after it is introduced it must be run with a large amount of technical direction.

Jan 1, 1934

By George Langford

THE McIntyre mine is in the Pearl Lake section of the Porcupine gold area. The rocks are Keewatin lavas intruded by quartz porphyries and albitite dikes of Algoman age. Gold-bearing quartz veins are found in the Keewatin rocks near the porphyry stocks. The whole area has been highly compressed by forces acting along a N. 20°W. line. These forces folded the Keewatin rocks before the intrusion of the Algoman rocks, and later schisted both the Keewatin and Algoman rocks. Vein fractures were developed after the folding but before the development of the schist by the compres-sive forces being locally broken up into couples. These couples were set up by the differential resistance to deformation of porphyries and basalts, and also by the competency of the dacites and incompetency of the tuffs and fragmental rocks. During the important period of vein formation, two zones were developed-an inner productive zone in which the quartz veins are ankerite-bearing and an outer barren zone in which the quartz veins are calcite-bearing. The vein solutions originated in the same magma that supplied the albitite dikes.

Jan 1, 1938

Jan 1, 1940

By J. H. Mallery, J. H. Keeler

THE crystal structure of Zral, the compound richest in zirconium (91.03 pct Zr by weight) in the system Zr-Al, has been found to be ordered face-centered-cubic. This compound is of particular interest, since it is encountered as the precipitated phase in potentially useful zirconium-rich alloys. It forms peritectoidally from body-centered-cubic zirconium and Zr,Al at about 975°C. The Zr-A1 constitution diagram has been reported by McPherson and Hansen.&apos; For the primary determination a 100 g ingot was prepared by arc-melting in a water-cooled copper crucible under purified argon. The raw materials were crystal-bar zirconium (a purity of better than 99.7 pct) and spectroscopically pure aluminum. The ingot was double melted, examined metallographi-cally, and found to be quite uniform as shown in Fig. 1. The hardness of the as-cast button was VHN 390 to 445. A 20 mil diam specimen was prepared from annealed (900°C) filings of Zr,Al. The specimen was mounted in a 5 cm radius powder camera and an 8 hr exposure was taken using copper radiation with a nickel filter. The structure of the compound Zral was found to be ordered face-centered-cubic of the Cuau type, with an a,, value of 4.37220.003A. Its calculated density is 5.976e0.013 g per cu cm. The relative intensities for the lines were calculated using the formula 1+cos2 20 I oc----------------- • p • /F7 sin2 0 cos 0 1 + COS&apos; 20 where----------------is the Lorentz polarization fac- sin2 0 cos 0 tor, p is the multiplicity factor, and F is the structure factor. The X-ray data are given in Table I. The compound has exhibited plasticity when present as particles in a matrix of a zirconium. During hot working at about 900°C, the compound has been found to deform plastically to the extent that some of the particles exhibit a length-to-width ratio greater than 4:1 as shown in Fig. 2. In answer to the discussion of ref. 1, McPherson and Hansen pointed out that the compound may be cold rolled and reduced as much as 33 pct. Zr,Al has also been found2 under certain conditions to precipitate in lamellar form at grain boundaries of the a phase of hexagonal-close-packed zirconium. Acknowledgment This work was carried out under Contract W-31-109-Eng 52 for the United States Atomic Energy Commission.

Jan 1, 1956

By Ross W. Smith, M. E. Wadsworth, T. James Smolik, A. S. Peck

Ross W. Smith (Acting Instructor, Department of Mineral Engineering, Stanford University, Stanford, Calif.) and T. James Smolik (Kennecott Copper Corp., Salt Lake City, Utah) - Professors Peck and Wads-worth have made an interesting contribution to the study of fluoride activation of beryl. We have a few comments to make regarding the paper and a question to ask of the authors. We note that glass containers were used in the study. Hydrofluoric acid should react with glass to produce SiFg2 in quantity which could adsorb onto the beryl surface (onto either beryllium or aluminum sites). The authors propose that individual F- ions actually go into the mineral surface lattice rather than onto the surface by adsorption of siFi2 ions. Based on infrared reverse bands with an untreated

Jan 1, 1969

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.&apos;-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.&apos; For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.&apos; Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.&apos;,&apos; However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By P. H. Mell

The little village, from which this formation receives its name, is situated on a bluff of the Alabama River, 175 feet above water level. This bluff is a portion of high table land that begins in the western portion of Choctaw and extends through Clarke and Monroe counties. We find points on this ridge more than 100 feet higher than Tuscaloosa, and nearly as high as the Tennessee River at Tuscumbia. Through this the Alabama River cuts its way, exposing a beautiful cross-section of the strata, of which the accompanying sketch may give some idea. The fossils are found about 75 feet below the surface and 100 feet above the level of the river. There are seven distinct strata. 1. The lowest, extending from the water&apos;s edge up the bluff 80 feet, is a soft calcareous rock containing about 15 per cent. of carbonate of lime, with occasional specks of mica. In this a few Ostrea, Turritellæ, and Flustræ were found, but so friable as to fall to pieces when handled. 2. Next comes a stratum varying from 2 to 8 feet, consisting of

Jan 1, 1880

Jan 1, 1940

By E. H. Rose

The question is often pondered whether the flotation process is still an art or has become a science. The fact is that flotation is a science in so many variables that only art can blend them. It is demonstrable that no less than one hundred variables are involved in any flotation operation, most of them immeasurable on a routine basis. The behavior of every one of them is always governed by orderly and unchanging law, as no man can doubt. There is nothing truly indefinite about that behavior; the only indefiniteness is in our knowledge of it, either in general or from hour to hour in the circuit. In dealing with a simultaneous equation in, say, one hundred variables, all not only affecting the outcome to some degree but many influencing each other as well, it is small wonder that the mineral-dressing profession presents a case history of debate and controversial opinion. The statement of the subject of this symposium—a symposium on flotation machines—seems to delimit and define the matters to be considered and at least the general nature of the conclusions sought. Nevertheless, in such a meeting it is not possible to meditate upon all the variables that do in one way or another affect performance of flotation machines. To attempt it would be much like trying to operate a hundred-ring circus. Perverse variables being what they are, one could expect the elephant in ring 36 to squirt a trunkful of water at the tightrope performer in ring 37 to ruin that artist&apos;s act, just as our learning to depress pyrite in the early 1920&apos;s ruined the act of the formerly faithful old Callows. Honest Disagreements Selective flotation dates from 1922 or 1923, when several plants established their regular flotation operations on a selective basis. Since then, two decades of efforr have gone into the development of better and better flotation machines. Many have come and gone. The competition has simmered down to perhaps a dozen machines, each one of which is staunchly defended by some operators as being the best for their particular jobs, and as scornfully dismissed by at least a few others elsewhere as being positively the poorest for theirs. These disagreements are honest disagreements, honestly arrived at after plenty of sweat. In many a flotation plant, one machine has been tried out against another under conditions as fair as they could possibly be made. Sometimes the results are on a par but more often one machine shows a consistent and unmistakable margin of superiority over the other. In equally honest and enlightened tests, machine A may win over machine B in one place, and machine B over machine A by as great a margin in another. This paper purposes to identify some of the more prominent reasons why this is so,

Jan 1, 1947

By E. H. Rose

The question is often pondered whether the flotation process is still an art or has become a science. The fact is that flotation is a science in so many variables that only art can blend them. It is demonstrable that no less than one hundred variables are involved in any flotation operation, most of them immeasurable on a routine basis. The behavior of every one of them is always governed by orderly and unchanging law, as no man can doubt. There is nothing truly indefinite about that behavior; the only indefiniteness is in our knowledge of it, either in general or from hour to hour in the circuit. In dealing with a simultaneous equation in, say, one hundred variables, all not only affecting the outcome to some degree but many influencing each other as well, it is small wonder that the mineral-dressing profession presents a case history of debate and controversial opinion. The statement of the subject of this symposium—a symposium on flotation machines—seems to delimit and define the matters to be considered and at least the general nature of the conclusions sought. Nevertheless, in such a meeting it is not possible to meditate upon all the variables that do in one way or another affect performance of flotation machines. To attempt it would be much like trying to operate a hundred-ring circus. Perverse variables being what they are, one could expect the elephant in ring 36 to squirt a trunkful of water at the tightrope performer in ring 37 to ruin that artist&apos;s act, just as our learning to depress pyrite in the early 1920&apos;s ruined the act of the formerly faithful old Callows. Honest Disagreements Selective flotation dates from 1922 or 1923, when several plants established their regular flotation operations on a selective basis. Since then, two decades of efforr have gone into the development of better and better flotation machines. Many have come and gone. The competition has simmered down to perhaps a dozen machines, each one of which is staunchly defended by some operators as being the best for their particular jobs, and as scornfully dismissed by at least a few others elsewhere as being positively the poorest for theirs. These disagreements are honest disagreements, honestly arrived at after plenty of sweat. In many a flotation plant, one machine has been tried out against another under conditions as fair as they could possibly be made. Sometimes the results are on a par but more often one machine shows a consistent and unmistakable margin of superiority over the other. In equally honest and enlightened tests, machine A may win over machine B in one place, and machine B over machine A by as great a margin in another. This paper purposes to identify some of the more prominent reasons why this is so,

Jan 1, 1947