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By P. O. Parfitt

At the McIntyre mine, there are two distinct operations: a gold mine with narrow veins, mined by cut-and-fill methods, and a copper mine with large, open, long-hole stopes. The application of the Critical Path Method to scheduling work in the copper mine, where it has been used successfully for several years, is de-scribed briefly. This application is relatively simple. Use of C.P.M. has now been extended to the gold mine. To replace the former method of scheduling from bar-charts, a procedure was developed for scheduling automatically. To handle an operation of this size and complexity, a computer was essential. Improved schedules are now being produced, with a saving in time.

Jan 1, 1967

By R. R. Godard

The practice of dust abatement or control is not new to any operation of United States Steel Corporation. This report will review those activities, past and present, within the five operating districts of United States Steel-Coal Operations with specific reference to mechanical and continuous mining, and including both the health and safety aspects of the problem. Obviously, the first principle of dust control is to inhibit its formation If this is not practical, steps may be taken to prevent its becoming airborne. Airborne dust control can be realized by either collecting it at the point of generation, diluting it with large volumes of air to reduce concentration, settling it by various means, or with reference to ignition hazard only, render it incombustible by neutralization with an inert material. These basic principles have been verified by the work of many, including the Bureau of Mines, U. S. Department of Interior, Bituminous Coal Research, Inc., and the Mining Research Establishment of the National Coal Board of Great Britain. Their application to every day mining problems is best illustrated by the following examples.

Jan 1, 1967

By J. S. Coffman

Wyoming is estimated to have more than 700 million tons and Utah more than 2.5 billion tons of +10 percent P2O6 phosphate rock considered to have some future economic potential. In Wyoming, the +24 and +18 percent P205 rock potential resources total nearly 250 and 450 million tons, respectively. In Utah, the +31, +24, and +18 percent rock total approximately 33 million, 222 million, and 2.2 billion tons, respectively. These resources are all located above the local drainage levels and do not include latent resources. All of the mining and beneficiation of phosphate rock in the two States is done by San Francisco Chemical Co. The facilities include open pit mines at Vernal, Utah, and Leefe, Wyo.; an underground mine in the Crawford Mountains, Utah, and beneficiation plants at Leefe and Vernal. One of the principal markets for the phosphate rock is Western Phosphates, Inc., fertilizer plant at Garfield, Utah. Recent exploration and development has been under-taken by different companies in the Southeastern Wind River Range, Sublette Range, and Crawford Mountains. The facilities at Leefe and Vernal are in the process of expansion. Some of the areas of western Wyoming contain vast quantities of phosphate rock in minable units, but, because of their remote location, are classed as latent areas. In these areas, there are estimated to be about 700 million, 2 billion, and 3 billion tons of phosphate rock in the +24, +18, and +10 percent P205 grade classes, respectively. The Snake River Range of Idaho and Wyoming is also estimated to contain roughly 21, 106, 177, and 214 million tons of potential resources in the +31, +24, +18, and +10 grade categories, respectively. This area also contains a large amount of latent rock in the more remote areas.

Jan 1, 1967

By S. W. Mao

Hydrologic and economic criteria figure in many obvious ways in water resources development, but they are rarely linked quantitatively, and most of the applications are pertinent only to the case-in-point. In the preparation of the Regional Plan for the massive program of ground water development in the Punjab, situations have arisen where the choice among two or more alternatives was made by analyzing the economic implications of critical hydrologic parameters. Two of these situations which are of more-or-less general interest are described herein. The first involves basic development policy -- whether ground water development should be based on the demand of the economy, or the conservation concept of safe-yield. The analysis demonstrated that mining of ground water is clearly indicated for areas where alternative supplies are unavailable. The second problem involves integrating hydrologic data into an economic model to determine optimum well design, From an analysis of all pertinent factors, a simple nomograph was derived which can be used to determine well specifications on-site during construction. The nomograph can be modified for use in any alluvial terrain.

Jan 1, 1967

By Forrest T. Moyer

The overall disabling work injury experience, excluding office- workers, at nometal mines and mills during the period 1961-63, as reported to the Bureau of Mines by operators, was 77 fatal and 7,201 nonfatal injuries during an aggregate worktime of 335,029,685 man- hours. These injuries, fatal and nonfatal combined, occurred at a frequency rate of 21.72 per million man-hours, comprising 0.23 for the fatal and 21.49 for the nonfatal injuries. The combined severity rate of the disabilities was 2,312 days lost or charged per million man-hours, consisting of 1,379 for the fatal and 933 of the nonfatal injuries, The average severity of all disabilities during 1961-63, was 106 days per injury, The number of days lost or charged, excluding officeworkers, at nonmetal mines and mills during 1961-63, was 462,000 days charged to fatal injuries and 312,461 days lost from nonfatal injuries. The outstanding causes for fatal injuries were explosions (18 fatalities occurred in a major mine-explosion disaster in a potash mine in Utah in 1963) and falls of rock or ore from back or side, while most nonfatal injuries were caused by handling materials, slips or falls of persons, haulage, and machinery. The parts of the body most frequently injured during the period 1961-63 were the trunk, hand and finger, and foot and toe, An average of 52,810 men were at work daily, There were 20 nonfatal disabling injuries reported for office- workers at nonmetal mines and mills during the period 1961-63 during an aggregate worktime of 23,088,496 man-hours, These injuries occur- red at a frequency rate of 0.87 per million man-hours, There were no fatal injuries reported.

Jan 1, 1967

There was a time, in the memory of some here tonight, when the annual meeting of The Institute was a nostalgic occasion. Often, in the 1920s, there was comment on the decline of Australian mining and on the lack of new mineral discoveries. When some of our Presidents prayed then for a new Bendigo, and instead were given a Mount Isa, they were justifiably disappointed because of the vastly different capital requirements.In 1967 the mining picture is very different. The recent mining developments in Australia are certainly as important as several Bendigos and several Kalgoorlies. The mining industry in Australia has never been more dynamic than today (Table 1). And if we ask why it is so dynamic, the answer lies in the role which overseas capital is playing in the industry. The contribution of overseas capital should concern us not only because we are members of the mining and metallurgical profession, but also because we have a duty to make our profession contribute as much as possible to the well-being of Australians. It is not sufficient to argue that overseas capital is good for the mining industry; we must also examine whether it is good for the economy and the nation. In this context the current criticism of the inflow of overseas capital into Australian mining is useful, for it gives us an opportunity to see what has resulted from the inflow.In discussing this question I do not suggest that we emulate Captain Hancock, that legendary Moonta mine manager who, according to Oswald Pryor's cartoon, used to say to his miners: "When I say a thing is, it is, even if it isn't". The question can only be discussed on a factual basis; and I would submit that many of the important facts relating to overseas capital in our mining industry are often overlooked or ignored. I would further submit, on the basis of these facts, that Australia's present day mining industry has been largely built on overseas capital and that the overall benefits of that capital to Australia have been enormous.

Jan 1, 1967

By J. W. Wolfe

The Benedict-Webb-Rmbin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predrcted component K-vallles, mixture enthalpies and phase aensities within tile accuracy of available correlations for rune-component mixtures: significant deviations were noted when mixtures contained components heavier than heptune. INTRODUCTION Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas proccssing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently. the best equation of state for describing the behavior of pure, light hydrocarbons over single-and two-phase regions, both below and above critical pressure, is that of Benedict. Webb and Rubin.' The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the clevelopment of their equation as early as 1940.2 The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a serics of articles in 1951,' showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed,'-',"'-':' the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state." Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases. Consequent-

Jan 1, 1967

By Howard N. Egan

EASTERN COAL CORPORATION is located in the heart of the Appalachian Mountain area of extreme Eastern Kentucky, The mountains are of sedimentary origin, and have been deeply eroded by streams as the area has been thrust up during geologic time. There are many seams of coal interspersed between beds of shale and sandstone. While some of the seams are thin, there are a number that can be economically mined. We are mining the Pond Creek, or No. 2 Gas Seam, at a rate in excess of 6,000 tons per day. Our central preparation plant utilizes tromp baths for the plus 3/8" size and Rheolaveur for the minus 3/8" portion. No provision was made to recover the fine coal, which was included with the plant effluent pumped to a 12 acre refuse pond. The pond is impounded behind the coarse refuse dump. This pond rose 15 feet last year. Obviously, no pond could stand many years at this rate. Limited pond space in this rugged area of steep hills and narrow valleys dictated a revised disposal method. Our first thought was that it would be necessary to dry the fine refuse sufficiently to permit inclusion with the coarse refuse, which is hauled uphill by monitor and then trucked to final disposal.

Jan 1, 1967

By W. C. Ellis

Growth directions of tin, zinc, and cadmiun whisker crystals grown spontaneously fi-om the solid are summarized. In tin the edge and diagonal directions of the unit cell are jound with the exception oj- the [110] diagonal. In cadmiurn and zinc the usual dip-ections are a or a + c. The c direction has not been ohserwed. The gvouth directions from the solid are for the most part the same as those found for vapor-grozun crystals and are the ohserz:ed glide directions in plastic j-lou. Whisker crystals of these elements grown from the solid are not twinned. Specular lateral reflections are associated with planes of snall crystallographic indices. WHISKER crystals of tin, zinc, or cadmium grow spontaneously at room temperature in periods from months to years from thin electroplates and other prepared films of the respective metals.''2 It has been established that these crystals are single, but the question of twinning, such as occurs in whisker crystals of silicon,3'4 has not been resolved. Studies of morphology have been restricted to determinations of growth directions.5-' Whisker crystals are both straight and kinked. A few studies have been made on kinked whiskers including measurements of kink anglesa and determinations of growth directions,' but unfortunately not both on the same crystals. The kink angles, for the most part, for each species are grouped closely about a few unique values, but these values are not always those between observed growth directions in a single crystal. To supplement existing data, the growth directions, identification of lateral features, and presence or absence of twinning were determined with a Weissenberg goniometer by a method described elsewhereg on eight whisker crystals of tin, five of zinc, and five of cadmium. One kinked cadmium whisker was examined in detail. The specimens were needlelike, a few microns in cross section, and of the order of a millimeter in length. They were removed from electroplated substrates on laboratory specimens and commercial equipment after several years of growth as described in Table I. Since the specimens were less than 10 p in cross section they were ideally strong with no attendant risk of plastic deformation or damage in handling. Only deformation twinning has been reported for these elements. Therefore, twinning probably should not be expected in whisker crystals of these metals, particularly a twin plane containing the growth direction. A twin plane oriented in this direction was the one sought in this study. No examination was made for twinning at the boundary between kink segments except for one cadmium crystal. Well-defined reflections occur as a whisker crystal of tin, zinc, or cadmium is rotated about its growth direction when illuminated by a beam of light Although these reflections had been noted in earlier investigations, no study of them was made, probably because the earlier studies had disclosed also that

Jan 1, 1967

By G. S. Cole, G. F. Bolling

ThE exact type of fluid flow which occurs in a solidifying ingot is important in determining subsequent grain structure. This has been shown in studies of natural Convection" and of forced stirring or other disturbances of the melt."16 We shall explicitly argue that a complement to the existing natural flow in an ingot should be more effective than other types of flow in promoting the columnar-to-equiaxed transition. The ultimate effects of fluid flow upon structure is one of the topics of solidification that we have investigated in the alloy system Pb-Sb, under conditions simulating casting. In Fig. 1, the essential features of a bidirectional growth apparatus are shown; horizontal freezing from water-cooled faces within a low-thermal-conductivity lavite boat is a reasonable simulation of an ingot section. Details such as the furnace and thermocouples are omitted in order to show the location of four permanent. magnets, each with a pole separation of 21 in. providing a central field of about 1000 Gauss. When coupled with a dc current imposed through appropriate connections made at the cooled faces, a flow of fluid is produced as shown schematically. This technique described by Pfann and ~orsi" is ideal for our purpose since the flow indicated is the same as that we observe to occur naturally in this system. Components of 99.999 pct purity were used for study and all due precautions were taken in alloy preparation to avoid contaminants. Sections of the specimens were taken to ensure results representative of the interior as well as the surface of specimens. All proportions of equiaxed and columnar regions were measured by tracing the etched grain structures onto graph paper and simply counting squares. Four alloys were examined at superheats of 40" * 5°C and 100" * 9°C. Preliminary tests had shown that no appreciable enhancement of structure was obtained with magnetic field alone, so that this condition is not reported; it should nevertheless be noted that other configurations of magnetic field will reduce convection and thus enhance columnar growth.'8 For the tests reported the magnetic field was applied to a specimen by bringing the four preassembled magnets to a position 2 mm from an outer tube immediately after the ingot was poured. The dc current of 30 amps passed through the sample throughout the entire solidification cycle, resulting in a power dissipation of 9 w per sq cm of interface. This may be compared to the evolution of latent heat of approximately 18 w per sq cm. Table I contains the results of this experiment in terms of the total area ratio, equiaxed/columnar grains, as a function of the field interactions, solute concentrations, and superheats employed. The total structure of the ingot is seen to be most influenced when both the field and current are applied simultaneously; when current acts separately, little effect may be noted in spite of the heat supplied. In addition, the change in structure from the no field-no current case to the field-current condition is more pronounced at the higher superheat, and the higher the concentration of antimony. An example of the grain refinement, as well as the increased equiaxed zone, is shown in Fig. 2. It is now important to prove that there is indeed an increase in fluid flow due to the presence of the field-current interaction; this is done by temperature measurements in the liquid metal. Let us consider a bidirectional casting in which heat is applied to and removed from the system, in such a way that rate of solidification is zero.* When a sensitive thermocouple

Jan 1, 1967

By Russell G. Hood

Rock bolting or anchoring are methods of stabilization which are not being fully utilized in California and probably in other parts of the world due to lack of understanding of the principles, or due to poor results in actual installation. The problem is greater in California because so much of the rock is either soft or badly fractured and broken. Almost any recognized type of rock bolt or anchor will perform successfully is hard, fresh rock, but the problems become many-fold when working in decomposed granites, shales, soft sandstones or other soft, highly-broken rock. There has been an enormous amount of research by manufacturers, consultants, private organizations, and governmental agencies on rock bolting. It would be impossible to discuss all the methods and philosophies of rock bolting in this paper. Therefore, with the indulgence of the experts, I will give only a very generalized coverage on rock bolting techniques. However, My main purpose is to point out some of the problems of rock bolting in soft rock.

Jan 1, 1967

By J. M. Blank, V. A. Russell

When the nucleation of silicon on a sapphire substrate is accomplished by gradually decreasing the substrate temperature while subjecting it to a constant impingement rate of hydrogen and silicon tetrachloride, the resulting deposit is characterized by widely separated islands of silicon scattered over an "open sea" of sapphire. Analysis shows that nucleation takes place mainly on sites of large adsorption energy, about 85 kcal per mole, and small surface concentration, about 108 cm-2. Crystal growth proceeds rapidly on these nuclei and results in enough depletion of Sicl4 from the ambient gas to suppress further nucleation. The technological importance of single-crystal films on dielectric substrates has prompted considerable work on the deposition of silicon on sapphire. This paper is concerned with the deposition of silicon, by the reduction of silicon tetrachloride with hydrogen, onto heated sapphire substrates. The apparatus consisted of a temperature-controlled container for the silicon tetrachloride along with gas lines and flow meters necessary to convey a hydrogen-silicon tetrachloride mixture to a reaction chamber constructed of quartz tubing. Heat for the substrate was provided by means of an inductively heated graphite susceptor. The observations pertinent to the present discussion were made with an American Optical Co. high-temperature microscope which allowed us to make motion pictures of the deposition process at a magnification of approximately 50 times. Two main categories of experiments were carried out: one on determination of critical condensation temperatures and the other on the deposition of epitaxial silicon films on the sapphire substrates. Critical condensation temperatures were determined in the traditional way by raising the substrate temperature well above that at which condensation could be expected at the impingement rates being studied and then gradually lowering the temperature until the condensation of the first silicon was observed. This was done initially with ellipsometry-type detection but it was soon discovered that the deposits were occurring as widely separated islands and groups of islands scattered over an "open sea" of sapphire. We have called these archipelago formations. They were most easily detected by optical microscopy. Data gathered from experiments of this type have been collected in Table I. Motion pictures of the formation of archipelago patterns show that the nucleation period lasts about 10 sec if the substrate temperature and impingement rate are kept constant. Essentially all of the nuclei are formed in a few seconds and all subsequent silicon deposition merely adds to the size of the established nuclei. After an archipelago formation has matured at a given substrate temperature and impingement rate, it is very difficult to stimulate any further nucleation in the open space between islands. Lowering the substrate temperature will occasionally stimulate nucleation but increasing the impingement rate hardly ever produces any more new nuclei. It should also be emphasized that the nucleation rates appear to be very small, about 104 cm-2 sec-1. They will receive special attention in the analysis section. Another series of experiments was performed employing a systematic variation of substrate temperatures and impingement rates approximating those expected to produce epitaxy. Sapphire substrates with surfaces normal to the 2233 direction were used. In contrast to the procedure that produces archipelago patterns, these films were deposited by raising the substrate temperature to a desired value at which time the silicon tetrachloride and hydrogen flow was begun. Of course, these depositions produced mainly films that were continuous. After removal from the deposition chamber, the substrate and silicon film were examined microscopically to determine the nature of the deposit and by X-ray diffraction to determine the extent to which a single-crystal film had been achieved. Results of these experiments are summarized in Table 11. Of interest for the present analysis is the fact that epitaxy appears to be confined to a fairly narrow temperature range between about 1050" and 1150°C. This also will be discussed in the analysis section. ANALYSIS In this section we shall apply nucleation theory to the data presented above with the objective of testing

Jan 1, 1967

By Geoffrey Purcell

Improvements which have been made in commericial flotation systems during the past fifty years have resulted more from trial and error methods in the mill than from research in the laboratory. Research has often provided explanations of why mill changes have improved the metallurgical process. Hopefully, in the next fifty years, changes in mill flowsheets will come about, primarily, as a result of research work. However, since minerals, in their infinite variety, cannot be reduced to a standard state, research on commercial ores will have only a local utility, and research on pure minerals will have little commercial application. What will emerge from research on pure systems are mechanisms of adsorption, and this in turn may throw some light on the very much more complex adsorption processes taking place in the pulps of commercial ores. Quartz, without a doubt, has been the subject of more research effort than any other mineral, but we are still a long way from completely understanding its behavior in flo¬tation. Hematite and calcite have received considerably less attention. Ores containing a mixture of all three minerals, however, are commercially important, and the iron deposits in Alabama have been extensively studied by the United States Bureau of Mines (1). The literature reveals no reports of research on synthetic mixtures of all three.

Jan 1, 1967

By R. E. Evans

This paper contains an analysis of the geography and geology of the Black Lake area, Eastern Townships of Quebec, an outline of the work to be performed, an explanation of the design concept and how it was developed, and a discussion of the actual stripping operation, including details of the machinery being used, etc.

Jan 1, 1967

By W. V. Swarzenski

In its, effort to combat waterlogging and coil salinity, the later and Soils Investigation Division of WAPDA (West Pakistan's Water and Power Development Authority) has carried out an extensive program of test drilling and water sampling, since 1954. Data collected during the past ten years have permitted the delineation of fresh and saline ground-water-zones in the Punjab Plain. Fresh ground water containing generally, less than 500 ppm (parts per million) of total dissolved solids is found in wide belts paralleling the major rivers and in other areas of fresh-water recharge. Locally, fresh ground water extends to depths of 1,500 feet and more. Saline ground water occurs downgradient from sources of recharge, particularly in the lower central parts of the interfluvial areas and, presumably, underlies most of the Punjab Plain. The ground waters of the Punjab are characterized by their evolution from calcium, magnesium bicarbonate waters, near sources of recharge, to waters containing a dominant proportion of sodium. The highly mineralized waters of the Punjab are generally of the sodium chloride type, whereas in Dera Ismail Khan District sodium sulfate waters predominate. The pattern of distribution of saline ground-water zones and the observed gradual increase in mineral content, downgradient from sources of recharge, can be explained best by a hypothesis stressing the processes of evaporation from the water table and solution of minerals within the alluvial aquifer.

Jan 1, 1967

By M. H. Harris

A solution has been obtained to the problem of calculating flow into a cased and perforated well. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. Computer experimentation indicated that the results are within 3 per cent of the exact solution. Computed results are presented as an apparent skin effect, on a series of dimensionless working curves. Productivity ratios can be rapidly calculated from these data for the wide range of wellbore and reservoir properties actually encountered in field practice. Any reasonable vertical unisotropy ratio can be included in the computation. Productivities can be calculated for wells perforated in a regular pattern, a single horizontal plane or a vertical line on one side of the casing. Solutions for asymmetrical perforation patterns can he easily obtained from the working curves. Solutions for flow into sells completed with a horizontal notch are also provided. Results show that productivity can be increased by extending perforation penetration. This is especially true for shallow penetrations. The highest productivity is obtained when perforations are arranged in horizontal planes, as opposed to a vertical line on one side of the casing. Four or five perforations in one plane will approach the maximum productivity. The effect of perforation hole diameter is small, and is rioticeable only in shallow penetrations. INTRODUCTION The perforating method of well completion has been successfully and widely used in most producing areas. In the past, the desired perforation results were achieved by simply shooting numerous large holes in the casing. A perforating scheme for an area, or particular well, was established by evaluating two types of experimental data: the well flow index and the productivity ratio.' 3 The well flow index test is a means of determining the relative flow capacity of perforations in a linear system. This test also gives information on the perforation size, shape and hole damage which can be expected under well-bore conditions. However, relative flow data from this test cannot be accurately tarnsformed into the radial wellbore system. Thus, no true indication of the productive capacity of a perforated well can be obtained from the well flow index test. A well productivity ratio is derived from electrolytic models built to simulate perforated wells. Available productivity ratio data 2,3 are limited in that all important variables are not extensively evaluated. For example, data are limited to well radii of 3 and 6 in., and to maximum perforation penetration of 1 ft. Practically no information is available on the pattern of flow into a perforation. The effect of various perforation patterns on well productivity has not yet been determined and the effect of perforation diameter has not been thoroughly studied. Also, it will be shown that this type of electrolytic model data is probably in error by as much as 10 per cent or more. Modern completion techniques such as limited-entry perforating, single-plane fracturing, steam and hot air injection and chemical consolidation of incompetent formations all rely on injection and/or production from a limited type of completion. These completions may consist of several high-capacity perforations or a horizontal notch which is equivalent to an infinite number of perforations in one plane. Proper design of these new completion techniques requires, in part, accurate estimates of a well's productive capacity. Data on perforated and notched well productivity have been determined in this investigation. Results are presented as a function of the pertinent variables. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. DESCRIPTION OF PROBLEM PRACTICAL APPLICATION The computed results can be applied to wells which meet several general specifications. An external drainage radius of the well must be known or assumed, but the well need not be drilled on a regular pattern. The well must be cased and cemented through the entire producing interval. And, the casing must be perforated with one or more horizontal planes of perforations. The perforation pattern itself must conform to three geometrical requirements. 1. The perforations in a plane must divide the plane into equal angular segments (Fig. 1). Four perforations per plane would be 90" apart. 2. Perforations in a plane must be directly above or beneath perforations in adjacent planes. For two shots per plane, perforations would lie in the BB' plane (Fig. 1). 3. Horizontal planes must have equal vertical spacing and be separated from the top and bottom of the formation by one half the spacing interval. Single planes of perforations should be in the middle of the formation. This is shown in Fig. 2 where h is the formation thickness in a single plane conlpletion or the spacnig interval in a multiple plane completion. The spacing interval at the top and bottom of the formation may vary somewhat without causing an appreciable error in the productivity calculation if the formation is reasonably thick and there are many horizontal planes of perforations. A special provision has been made to calculate the productivity ratios of wells with uneven spacing intervals, or for the case where a single plane of perfora-

Jan 1, 1967

By G. P. Conard, E. H. Rennhack

The creep behavior of hot-rolled, hypoeutectic Zn-Ti alloys was investigated in the temperature range from 0.43 to 0.53 TM. Secondary flow was found to originate primarily from strain-induced gvain growth where grain boundary )nigvation served to relieve the strain energy of distortion introduced by slip, grain boundary sliding, and subgvain formation. The extent to which this recovery mechanism operated was determined by the ratio of grain width to the spacing between planar fibers of TiZn,, compound particles generated in these alloys during rolling. When this ratio was unity, creep resistance demonstrated a marked improvement. In this condition, which was fulfilled by annealing following rolling, structural stability was enhanced with decreasing grain size below the equicohesive temperature (-0.5Tm), while the reverse was true above this temperature. TITANIUM concentrations approaching the eutectic composition of 0.23 wt pctl have been shown to promote a significant increase in the creep resistance of rolled zinc,2 The alloying effect created with titanium is somewhat unique; a structure closely resembling that of a fiber-reinforced metal composite can be developed which selectively modifies creep strength in preference to other mechanical properties. In an earlier investigation,~ the present authors found that, while the fiber network, composed of individual TiZn,, compound particles, had a distinct influence on rolled texture, the crystallographic variations produced were of minor importance with respect to creep. Rather, creep resistance seemingly increased when the grain size appeared to coincide with the in-terfiber spacing. The work described here was undertaken to explore this effect in greater detail. EXPERIMENTAL PROCEDURE Three zinc-base alloys containing 0.05, 0.12, and 0.16 wt pct Ti were prepared from CP zinc and iodide titanium in the form of 4 by 2 by f in. chill-cast ingots. The melting and casting procedures for these alloys have been detailed el~ewhere.~ Individual ingots of each alloy were hot-rolled at 200°C (392°F) to total reductions of 10, 25, 50, 75, and 90 pct in from one to five passes, respectively, employing a 10-min reheat prior to each rolling pass. With grain, tensile-type creep specimens with a 1-in.-long, -in.-wide gage section were machined from the rolled strips for test purposes. Annealing studies to explore the influence of grain size on secondary creep flow were carried out at 400°C (752°F) in argon for times extending up to 60 min. The grain-size effect was evaluated in terms of average grain width and length values statistically derived from lineal intersection measurements.4 A similar method was applied in establishing the average interfiber spacing, i.e., average perpendicular distance between adjacent planar fibers. The creep characteristics of the alloys were investigated by means of constant-load and constant-stress creep tests. The former tests were conducted at 25°C (77°F) under an initial stress of 10,000 psi, while the latter were performed in the range from 25°C (77°F) to 90°C (194°F) at stress levels varying from 8000 to 22,000 psi. Total specimen strain, as determined with Budd HE-1161-B strain gages, was in excess of 0.10. Maintenance of constant stress was achieved through periodic load reductions made at 0.01 strain intervals to compensate for the attendant incremental reduction in specimen cross-sectional area. The maximum indicated error in the applied stress at these strain intervals was less than 3.0 pct. RESULTS AND DISCUSSION Constant-Load Creep. In an effort to clarify the in-terrelation between interfiber spacing and grain size with respect to the creep resistance of the Zn-Ti alloys, their separate effects on secondary creep rate were determined as a function of titanium content and rolling reduction. These results are set forth in Figs. 1 and 2, respectively. The average grain diameter plotted in Fig. 2 was resolved from average grain width and length values. No data are presented for reductions of less than 50 pct because of the inability to obtain consistent measurements on these strips. The curves of Fig. 1 indicated that, for a given titanium content, a decrease in interfiber spacing, as produced with increasing reduction, promoted a decrease in creep rate. Depending on titanium content, however, wide variations in creep rate occurred at the same interfiber spacing suggesting that interfiber spacing, by itself, has little or no influence on creep resistance. Grain size, on the other hand, decreased progressively with both increasing rolling reduction and titanium content, the effect of which led to a pronounced decrease in creep rate, particularly when the average grain diameter became smaller than 3.0 x 10"4 in., Fig. 2. The continuity of this relationship tended to support the view that grain size rather than interfiber spacing was predominant in controlling secondary creep. Annealing Effect. The observed dependence of creep flow on grain size suggested that a further contribution to creep resistance would result when the alloys were annealed to effect a coincidence between grain width and interfiber spacing, see Fig. 3(b). ~eiides creating an immediate barrier to grain boundary movement, annealing offered the possibility of providing increased structural stability by eliminating many high-energy, mobile grain boundaries.= To test this hypothesis, specimens from the Zn-0.16 Ti strips reduced 75 and

Jan 1, 1967

By J. B. Conway

Stress-vuptuve data for several of- the refractory metals are frequently found to yield a linear relationship between the Larson-Miller parameter and the logarithm of the applied stress. In such cases linear stress-rupture isotherms result with slopes bearing a definite relationship to the temperature. It also follows that the stress to produce rupture in a certain period of time will be linear in temperature. Data for several refractory metals have been reviewed and excellent linearity is shown in this type of isochronal plot. In addition, the af ore - mentioned lineavity leads to a linear relation between the log of the stress to produce rupture in a certain time and the homologous temperature. This has been illustrated for the Group VI-A metals, tungsten and molybdenum. EXTENSIVE use has been made of the Larson-Miller' parameter in the interpolation and extrapolation of stress-rupture and creep data. In those cases where this particular parametric approach is applicable a convenient and fairly straightforward procedure is made available for the correlation of experimental stress-rupture data. It is quite common to employ this parameter in the form of a master rupture plot in which the parameter, T(C + log tr), is expressed as a function of log stress. In many cases this functional relationship in log stress is linear within acceptable accuracy and hence the following relation results: where P is the parameter, C is the Larson-Miller constant, T is the absolute temperature, t~ is the rupture time, a is the stress, and a and b are constants. Examples of such a relationship are contained in the work of Green, Smith, and 01son2 dealing with high-temperature rupture behavior of molybdenum and in the work of Green' dealing with the high-temperature behavior of tungsten. In addition, pugh4 has shown a similar linearity for some fairly low-temperature data for molybdenum. It can be shown that when the relationship in Eq. [I] is exhibited certain generalizations can be made concerning the form of the stress-rupture isotherms. For example, rearranging yields: For a given material (constant C) at a given temperature the first term on the right-hand side of Eq. [2] is a constant and hence this equation defines a straight line when log stress is plotted as a function of log-rupture time. This is recognized as the standard form usually employed in this type of data presentation. Such linearity then suggests the linear form of the Larson-Miller parameter. Or, in other words, the linear parametric relationship in Eq. [2] results only when the stress-rupture data are linear on a log-log plot of stress vs rupture time. Another interesting observation can be made in regard to Eq. [2]. It can be noted that the slope of the stress-rupture isotherms is given by - T/b and hence a direct calculation of the constant b is available. It also follows that since the value of b is the same for all temperatures the slopes of the various isotherms on the log-log stress-rupture plot cannot be the same. Indeed, the existence of the relationship in Eq. [2] precludes a system of parallel lines on this common stress-rupture plot. As a matter of fact it further specifies that in addition to being nonparallel the slope of these isotherms must decrease (i.e., become more negative) with increasing temperature. Such a condition is indeed found to exist in the case of the stress-rupture data reported for molybdenum.' As a corollary to the above, it may be stated that stress-rupture data which do not lead to a linear log-log stress-rupture plot or whose isotherms do not exhibit a decrease in slope as the temperature increases will not yield the linear relationship of Eq. [I]. Applying Eq. [2] to two different temperatures and solving for C yields: Eq. [3] affords a simple and rapid method for calculating the Larson-Miller constant from the log-log stress-rupture plot. The slope of a given linear isotherm is measured and the value of "b" calculated based on Eq. [2] as: slope = - -Tb Then at an abscissa value of 1.0 hr (making log tr in Eq. [3] equal to zero) read the stress corresponding to rupture for two different temperatures. Substitution in [3] yields: A value of the Larson-Miller constant can thus be calculated from a few simple mathematical procedures employing data read directly from the log-log plot of the stress-rupture data. Of course, it is not to be overlooked that the above reasoning has been based on the linear relationship of Eq. [I] being applicable. However, if as mentioned above the log-log plot is

Jan 1, 1967

By Sidney Katell

This report, covering the period January 1966 through December 1966, is a continuation of a series that began with the publication of Information Circular 7516 in October 1944. It is the eighth in a series of reports prepared in cooperation with the American Association of Cost Engineers. The abstracted articles are concerned with all phases of cost engineering in the field of chemical and petroleum plants and related subjects. They are from the following sources: 1. American Association of Cost Engineers Bulletin. 2. Bureau of Mines Information Circulars. 3. Bureau of Mines Reports of Investigations. 4. Chemical Engineering.

Jan 1, 1967

By Millard M. Gilkey

This Bureau of Mines report presents results of a detailed study of water usage in the Wyoming mineral industry along with projections for the future In 1964, the mineral industries of Wyoming used 20 billion gallons of new water, nearly all self-supplied, and reused 72 billion gallons, a total usage of 92 billion gallons. Consumption amounted to 2.8 billion gallons. About one-half of the 20 billion gallons of new water was obtained from [srface] sources and the rest from ground water. Reported costs, covering power and maintenance, for the self-supplied new water at mineral industry operations ranged from less than 1 cent to 20 cents per thousand gallons and aver-aged 8 cents. At one mineral-related operation, water was hauled by truck to supplement a well supply. The cost was $2.00 per thousand gallons delivered. However, the supplemental requirement was only 10 gpm. Cost figures for the recirculation of water, covering power and maintenance, averaged 2 cents. In terms of water usage, the value of product for the entire industry was $25 per thousand gallons of new water intake and about $180 per thousand gallons consumed. The study revealed that Wyoming has a water deficiency but that the shortage is less severe than in the arid Southwest. Projection of the water needs of the Wyoming mineral industries indicates that the demand for new water will increase from the 20 billion gallons used in 1964 to 25 billion gallons in 1980, a 25-percent increase. The projected new-water requirement for the year 2000 is 40 billion gallons, a 100-percent increase compared with the 1964 figure.

Jan 1, 1967