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By Joseph M. Chelini

Today, the two major operating costs of rubber tired off-road equipment are diesel fuel and tires. Mine Management has minimal control over the ever accelerating diesel fuel costs. However, they can exercise control over abnormal tire costs. Fortunately, with available technology and cost analysis methods, experience shows us the outlook for controlling tire costs is encouraging. Most earthmoving operations using off-road, rubber tired haulage and support equipment have abnormally high total tire costs. These costs, utilizing Tire Information Management, have been reduced more than 30%; 20% can often be guaranteed. Management Apathy on the subject of tires in a complex mining operation perhaps can be understood, but management apathy applied to an abnormally high operating cost, of which tires are, begs for a solution.' Tires have been professionally neglected for many years in most mine operations. This is exemplified in the January, 1982 issue of Mining Engineering by Charlie Son in his article Reducing Earthmoving Tire Costs. He compared the efforts to improve diesel engine costs to the same efforts given to earthmover tires.

Jan 1, 1983

By S S. Kanchibotla, I Brunton

Most blast fragmentation models assume the rock mass properties, explosive properties and blast design variables to be constants and uniformly distributed within a blast. However, in reality all these input variables vary within a blast resulting in variation in the resulting fragmentation size distribution. A stochastic modelling approach is introduced in this paper to quantify this variation. This technique takes the input variables as statistical distributions rather than constants and through several thousand iterations, generates a statistical representation of the expected fragmentation resulting from a production blast. A case study of three production blasts from a large open pit mine are presented and the modelled fragmentation æenvelopeÆ shows good agreement with the fragmentation æenvelopeÆ estimated from Split image analysis. The various blast-related parameters influence different parts of the fragmentation distribution, eg rock strength and explosive velocity of detonation have most impact on the fines. The technique is used to identify the parameters that have the greatest influence on various size fractions. Such an analysis will be useful to direct resources to efficiently minimise the variation.

Jan 1, 2001

By Z. E. Arlin, R. D. Lynn

A deep well injection system is used by The Anaconda Co. for the disposal of uranium mill tailing water near Grants, N. M. A 2511-ft hole was cored and tested through Triassic, Permian, and Pennsylvanian (?) sediments and bottomed in Precambrian granite gneiss. The disposal well was plugged back to 1830 ft and completed in 563 ft of sandstones in the Yeso formation. The reservoir sandstones contain water similar to the injected waste water, and are isolated from overlying fresh-water aquifers by an evaporite barrier zone. Mill tailing water is decanted, filtered, and introduced into the well by gravity at an average rate of 400 gpm. The reservoir has a life expectancy of 10 years. The Anaconda Co. began uranium milling operations near Grants, N. M. in 1953 with a small mill that processed limestone ores. A larger second mill was built in 1955 to treat sandstone ores. In 1956 it became apparent that a large tailing pond would be required to contain the increased discharge of mill waste water. Research was begun on supplementary methods of disposal by which a minimal pond size could be maintained to avert excessive seepage losses. An intensive sampling program was begun to monitor the fresh-water wells in the area. The original limestone mill ceased operation in 1959. The present mill treats sandstone ores by sulfuric acid leach and a resin-in-pulp ion exchange recovery circuit that uses chloride elution. Process waste water is discharged to a tailing pond where, after evaporation losses, an annual average of about 400 gpm are available for injection into the disposal well. The waste water is a mildly acid solution that contains large amounts of manganese, iron, and the sulfate and chloride salts of sodium, calcium, and magnesium. It is a low-level radioactive fluid that contains small amounts of Uranium-natural, Thorium-230, and Radium-226. The average chemical and radioactive analyses of the waste water injected into the disposal well are shown in Column B of Table I. Disposal of the excess mill waste water by deep well injection was investigated after extensive research had proved that alternate methods were not satisfactory. A study of the regional geology and hydrology indicated that a disposal well was feasible, and a test well to basement rock was planned. Tentative plans for the test well and the results of the geologic and hydrologic studies were submitted to the New Mexico Dept. of Public Health, the New Mexico State Engineer's Office, the U.S. Atomic

Jan 1, 1962

TO THE BOARD OF DIRECTORS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-The following report covers briefly some of the more important activities of the Institute during the year 1923. In my report for the year 1922, I drew attention to the falling off in membership of the Institute due to the depressed condition of the mining industry in several lines and the inability of many of our members to find profitable employment in mining or its associated branches. A number who were unemployed during 1922 established connections during 1923, but a still greater number have been forced to resign or drop their membership during 1923. Fortunately, the number dropped is not so great as in the previous year. The Employment Service conducted by the four Founder Societies bears witness to the trend in business. For the young men just out of college, there are plenty of opportunities at small salaries, there are plenty of opportunities for them as laborers; but for the mature members, those of experience, there are few calls. During the last eighteen months, our Employment Service has been able to place only six of our members out of every hundred engineers for whom it has found work. Another loss which this Society has suffered, but which is not felt so keenly by our sister societies, is in its foreign members. The A. I. M. E. has always had a large foreign membership, but of recent years exchange has been so heavily against many European and South American countries that a large number of members residing abroad have been compelled to relinquish their membership. Almost invariably these members express keen regret because of the necessity that confronts them, and almost invariably the writers express hope that present conditions will not last long and that they will soon be able to ask-for reinstatement. Having stated the darkest side of the picture first, it may now be drawn to your attention that in spite of these losses the number of persons applying for membership was decidedly encouraging.

Jan 2, 1924

By D. P. Harris

The construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area is postulated. The questions (1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and (2) can this geology be related mathematically to mineral wealth and probability are answered in a case study of 97,000 square miles in Arizona and New Mexico. Measurements on mineral wealth and geologic variables of 243 cells were made. The geologic variables, valued in counts, percentages and lengths, quantified the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. The cells of explored area must be allotted the value class indicated by their cumulative production and estimate reserves (given well-defined geological relationships in a mineral wealth area), and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. This determines whether high value cells can be distinguished from low value cells by their geology as well as indicating those cells misclassified by the model into a higher value group than warranted by their known mineral wealth. The second use of the model is for extrapolation. It is demonstrated how geologic information on an explored area can be utilized in guiding exploration in an unexplored area. Exploration decisions can be predicted on explicitly determined measures of uncertainty (the probabilities). SUMMARY This study postulates the construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area. Such a model will distinguish those cells deserving further exploration on the basis of their geology: The basic postulates of this study are as follows: v = Q(R,S,F,A) P(V) = G(R,S,F,A,V), where V = a measure of mineral wealth P(V) = the probability of occurrence of V R = age and type of rock F = rock fracturing A =age of igneous activity and contact relationships. There are really two questions to be answered: 1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and 2) can this geology be related mathematically to mineral wealth and probability? In order to answer these questions, an area of about 97,000 square miles situated chiefly in Arizona and New Mexico was selected as a case study. This case study area was divided into 243 cells, each 20 miles square, and measurements were made on mineral wealth and geologic variables. Crude geologic variables valued in counts, percentages and lengths are constructed to reflect the above postulated variables. These measurement variables thus provide quantified values defining the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and the multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. Given the availability of an area that is well explored and upon which the relationships of mineral wealth to geology can be adequately defined, there are two ways in which the analysis outlined in this paper can prove beneficial. First, the cells of the explored area must be allotted the value class indicated by their cumulative production and estimated reserves, and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. Such an analysis determines whether cells of high

Jan 1, 1967

By Harraway D. H, Draper N

The association of graphite with a fine grained pyrite in the Mount Isa lead-zinc ore was investigated from mineralogical and metallurgical standpoints. The pyrite has been partially or completely replaced by galena and to a less extent by sphalerite, pyrrhotiteand chalcopyrite with the retention of graphite films or inclusions. During lead flotation the graphite imparts a spontaneous flotability to all associated minerals, resulting in a low grade fraction, which we call the carbonaceous fraction, floating with and diluting the lead concentrate. In times of low metal prices this fraction seriously reduces the economic value of the lead concentrate. A flotation procedure was developed to upgrade the carbonaceous fraction separately, producing an economic concentrate and a tailing.INTRODUCTIONThe lead concentrate produced from Mount Isa ores can vary from 20 to 50 per cent lead, depending on the locality in the mine from which the ore is obtained. Variations of this order are independent of ore grade and lead recovery. The large variation is related to the presence in the ore of a variable fast floating low grade fraction known locally as the carbonaceous fraction because of its association with graphite. During conventional lead flotation with sodium ethyl xanthate the carbonaceous fraction floats rapidly and unselectively with normal Mount Isa galena.The paper discusses mainly the examination and treatment of an average carbonaceous fraction, defined here as the fast floating material in the mill feed of late 1956. The ore was drawn from the Mount Isa Black Star orebodies. The fraction represented about 5 per cent of the total ore...

Jan 1, 1961

By S. R. Zimmerley, John Gross

The method of measurement of surface on quartz particles was given in a previous paper.' With such a method the relation of surface produced in crushing quartz can be compared to the work in crushing without recourse to sieve sizing or microscopic measurement. In crushing, the work input must be known with a fair degree of accuracy. With crushers, rolls, ball mills, and similar apparatus the measurement of the work in crushing is subject to possible errors, due to friction in the transmission as well as in the machine itself. Moreover, relatively large quantities of material must be crushed to get an average figure. In the selection of a method of crushing, simplicity in design and operation was desired and this was most readily obtained by the use of a free-falling body. A description of the apparatus embodying this principle is given herewith. The Crushing Device The apparatus used is shown in Fig. 1 and in cross-section in Fig. 2. The material to be crushed is placed in the crushing chamber C in the steel mortar M. The mortar is 3 in. dia. by 3 in. high. Two mortars are used, one having a crushing chamber 1 in. dia. by 36 in. deep, with a capacity of 4 g. of quartz, the other having a crushing chamber 1 1/2-in. dia. by % in. deep, with a capacity of 12 g. of quartz. The position of the mortar is adjusted by means of three centering screws A. The steel plunger P, which fits neatly into the chamber, is placed on top of the material to be crushed. Plungers of different lengths were tried and as they were found to give practically identical results the length adopted was equal to the depth of -the chamber. The mortar rests on a solid steel base B but is separated therefrom

Jan 1, 1930

By C. J. Fleisch, C. P. Clingerman

THE recent installation of a combination dust catcher, gas washer and precipitator at Carrie blast furnaces of the Homestead Steel Works has given very satisfactory results. The following description of the gas-cleaning installation is based on actual operating experience. When Carrie blast furnace No. 3 was rebuilt the decision was made to fine-clean all the gas produced by the furnace, because the management wanted fine-cleaned gas for fuel in the stoves and boilers. In order to keep the installation cost as low as possible, the gas-cleaning system was streamlined. All by-pass lines and goggle valves for bypass lines were eliminated from the system. A radical departure from the use of 8-in. tubes in the Cottrell-type precipitators was made by using 12-in. diameter tubes in a single compartment, the single compartment being divided into two units by a single partition wall in the top header. THE FURNACE PROPER A few of the characteristic points and dimensions of the furnace proper are: [Hearth diameter 26 ft. o in. Bosh diameter 29 ft. 1 3/4 in. Stock-line diameter 20 ft. o in. Large-bell diameter 114 ft. 8 in. Small-bell diameter 6 ft. 6 in. Height of furnace from center of iron notch to bottom of large bell, closed 94 ft. 4 in. Height of furnace from center of iron notch to main platform 105 ft. o in.] The furnace top is equipped with a McKee revolving distributor, the operation of which is electrically interlocked with the skips, bell hoists, and coke-weighing and charging apparatus through a Freyn automatic charging control. The gas leaves the furnace first through four offtakes, 5 ft. g in. in diameter, then through uptakes that are approximately 85 ft. high, which feed into a single down-comer that is 9 ft. in diameter. DUST CATCHER The primary dust catcher installed (Fig. I) may be described as a single-cone type. The inlet pipe at the top of the dust catcher is g ft. in diameter; it is flared to a conical shape as it extends down inside the dust-catcher shell, which is 35 ft. in diameter, 37 ft. high on the straight side, and has a conical top and bottom. The slope of the bottom is 50° with the horizontal. The cone-shaped pipe inside the dust-catcher shell is 42 ft. high and is 19 ft. 7 in. in diameter at its bottom lip where it releases the gas in-

Jan 1, 1943

By Joseph Kelly, Christopher Kelsey

This revolutionary super-fine crusher has the unique capacity to generate fine and ultra-fine products from single stage reductions of coarse or fine mineral feeds. The crusher consists of a rotating compression chamber and an internal gyrating mandrel. The axis of rotation of the shell is displaced relative to the axis of the vertically mounted mandrel. The inner surface of the compression chamber is machined as double cone frustums at an angle equal to the displacement angle. Crusher feed is accelerated into a compacted particle bed, which lines the inside of the compression chamber. The depth of the compacted bed progressively increases until the mandrel is engaged. The mandrel is then free to rotate with the compression chamber. Continued feeding increases power draw and triggers the counter rotating mandrel gyration drive. The gyrating mandrel delivers multiple compressions at high pressure to the rotating particle bed. High concentrations of energy are harnessed within a small active volume over short retention times. The combination of extraordinarily high power intensity and extreme compressive force results in primary compressive fracture and induced secondary tensile failure. The axially displaced rotation of the compression chamber effectively distributes the breakage forces throughout the particle bed. This paper covers open circuit, pilot trials on magnetite, perlite, garnet, marble and a copper/pyrite concentrate. Particular emphasis is placed on the extraordinary results achieved with trials on zircon and highly refractory fly ash. The extreme duties were deliberately chosen to demonstrate the crusher’s application scope and potential to impact capital operating and maintenance costs as the technology matures. Super-fine crushing, once considered impracticable has the potential to offer compelling options for the generation of ultra-fine products.

Jan 1, 2014

By Andrzej Luszczkiewicz, Alicja Bakalarz

The application of new collectors is considered to improve the beneficiation of Polish sedimentary complex copper ores from the Legnica-Glogow Copper Basin (SW Poland), the upgradeability of which becomes more difficult because of ores grade declining. One group of potential collectors is represented by nonpolar reagents. According to the available literature data, only selected sulfides float in the presence of the nonpolar liquids. The paper presents laboratory scale flotation results for the main sulfide minerals occurring in the Polish copper ores applying either thiol (potassium ethyl xanthate) or nonpolar (aqueous emulsion of n-dodecane) collectors. The investigated feed contained 1.91 % Cu in the form of sulfide minerals such as bornite, chalcopyrite, chalcocite and covellite. Other sulfide minerals including galena, pyrite and sphalerite were also present in the samples. Several flotation tests with various doses of each collector were conducted. Mineralogical analyses of flotation products were carried out and the results compared. A comparison of the results indicated that all sulfide minerals floated well with high recoveries ranging from 91 % to 99 % in the presence of the thiol collector. The use of the nonpolar collector provided results in flotation of sulfide minerals with different terminal recoveries from 61 % for chalcopyrite to 100 % for sphalerite. The most significant differences in flotation in the presence of both types of collector under various conditions of upgrading were observed for chalcocite, chalcopyrite and covellite. Similar flotation results were observed for sphalerite and galena for both collectors. The studies confirmed selective flotation of sulfides from the copper sulfide ores of the Legnica-Glogow Copper Basin in the presence of nonpolar collectors.

Jan 1, 2014

By H. C. Verakis, M. L. Harris, M. J. Sapko, K. L. Cashdollar

In underground mines, coal dust explosions are prevented by the addition of rock dust sufficient to render the coal dust inert. The National Institute for Occupational Safety and Health (NIOSH) has developed a hand-held instrument that uses optical reflectance to measure the explosibility of a rock dust and coal dust mixture. This instrument is called the Coal Dust Explosibility Meter (CDEM). In this study, NIOSH personnel accompanied Mine Safety and Health Administration (MSHA) inspectors on their routine band surveys in five and three underground coal mines in MSHA District 2 (PA) and District 11 (AL), respectively. While underground, NIOSH personnel and MSHA inspectors used the CDEM to assess the explosibilities of the dust samples. The values of percent incombustible content (% IC) determined by the CDEM agreed well with those obtained later by low temperature ashing (LTA) in both MSHA and NIOSH laboratories. Further, the meter identified some samples as potentially explosible that LTA analysis had found to possess sufficient rock dust for inerting. The CDEM provides more information on the hazards in the mine. Rapid identification of areas with explosible dust mixtures using the CDEM allows for immediate intervention rather than a wait of several weeks for laboratory analysis.

By C. Gatlin, C. E. Nemir

A common cure of lost circulation is the introduction of granular bridging agents into the mud system. Many materials, such as ground nut shells, are used for this purpose. If the trouble causing void (fracture, fissure, vug, etc.) is not too large, the granular agent forms a "bridge" across or within the opening. Successively smaller particles in the mud stream then accumulate on and/or within this bridge until normal filtration is finally established. The efficiency of many bridging agents has been studied in the laboratory using various slot testers.',' Many investigators have remarked that a granular bridging material should have the proper particle size distribution. With the exception of the broad range specified in the patent of Goins and Nash,3 here is apparently no definition as to what this distribution should be. A bridge may be initiated when several particles of lost circulation material lodge against each other in a fracture or other void. Smaller particles then may bridge the openings between the larger, previously bridged particles. This process continues until the voids become quite small and the problem becomes one of filtration. It would seem logical that an optimum particle size distribution exists, i.e., one containing the proper quantity of properly sized material to fill the successively smaller voids of the bridge. The filtration characteristics of drilling fluids may be subject to a similar analysis. It has been clearly demonstrated by many workers that the filtration behavior of various muds can be altered by particle size control.'.' Slusser, et al, divided filtration into three periods and showed that particle sizes affecting a given period did not necessarily affect other portions of the filtration curve. An analagous problem is the proper sizing of gravel, liner slots and screen sizes in various sand-exclusion problems. Here the situation is reversed in that a proper "void" size, rather than the size of the bridging agent, is sought. The classic work of Coberly 9 forms the quantitative basis for most sand-exclusion processes. It is interesting to note that, in general, Coberly's work has been overlooked by most drilling-mud researchers. Other investigators have made various studies of the effect of particle size distribution .on drilling-mud properties. As a part of their studies, Fancher and Oliphant reported 30-minute filtration loss of a variety of mixtures of particle sizes.'' Gates and Bowie noted an effect of particle size distribution on filtration, as well as on other physical properties.' MAXIMUM DENSITY THEORY A maximum density mixture has been mentioned as the possible solution for both lost circulation and mud filtration problems. Furnas 12 derived mathematically a method for obtaining maximum density of beds of packed solids, having either a given number of component sizes or a continuous gradation of sizes. This work was verified experimentally by Anderegg.13 or mixtures having a continuous grading of sizes, the interval between sizes is taken as successive screen sizes of interval 2 The ratio of the quantity of each size and the next smaller size is given by the equation Fig. I, number of size intervals of ratio 2 taken from Furnas' paper, gives the value of n + 1 for any given values of + and K, where K is the ratio of the diameter of the smallest particles to the diameter of the largest particles. Measurement by weight assumes, of course, constant density for all particle sizes. Choosing the quantity of the smallest particle size as a unit weight, the required weights of the successively larger interials are then r1 r2 r3 . ®1,2,3. Thus, the grading curve of a maximum density mixture represents a geometric pro gression of ratio r.

By James J. Guesk, Robert W. Reisinger, Timothy C. Richmond

A high-altitude (2,900 m [9,500 ft]) historic underground copper mine in Wyoming is discharging copper-laden water with a neutral pH into an otherwise pristine creek. The Wyoming Abandoned Mine Land program is reclaiming the site under a CERCLA deferral agreement. The clean-up goal is to reduce copper in the mine discharge so that the creek can eventually support a trout fishery. A pilot-scale passive treatment test utilizing sulfate-reducing bacteria has been conducted at the site beginning in summer 1997. Test results show significant reduction in copper concentrations in near-freezing mine water at flow rates ranging to 19 liters per minute (5 gpm)

Jan 1, 2000

By H. Kobbè William

ARTHUR KNAPP, Ardmore, Pa. (communication to the Secretary*).¬On p. 2275 I find a quotation from Mr. Thompson regarding the fountains of the Baku field. I have seen a large number of these gushers or fountains. In every case where unusual amounts of sand were produced the wells caved in and shut off in a few clays and were an absolute loss Very often the formation had caved so far up as to allow the water to enter the oil strata, and not only was the well lost but the ground for many acres around the well was useless for drilling purposes because the disturbed ground had allowed the gas and oil to dissipate and the water to enter. On p. 2268, Mr. Thompson is again quoted regarding the Balakhany field. If the text is consulted further, it will be found that the oil at Balakhany is heavy only in contradistinction to the Bibi Eibat, field. The gravity of the oil at Balakhany is from 28 to 32. Also, it must be noted that the illustration is taken from the conditions in the older part of the field. This field was first chilled 40 years ago, and was a worn-out field 15 years ago. The wells which produce sand are wells in which the casings are practically gone and the formations are full of water. The sand must be bailed from these wells because the clays from the upper stratum have caved into the wells and are obstructing the passage of oil. On p. 2262 is the statement that the Russian wells cannot be pumped on account of the large amounts of free sand produced. They have never tried pumping in the Baku field to any extent. Wherever tried, it has proven a great success. If we take the author's theories as correct and wish to put them into practice, it would first be necessary to consider a few figures. Let us assume that we produce oil and sand together in the proportion in which they exist in the productive strata. It is not uncommon to have wells in the California field which are not gushers, but which, by pumping, produce 1,000 bbl. per clay the first 100 clays.

Jan 3, 1917

By Almon F. Robertson

The floor of Shady Valley, Johnson County, Tenn., is underlain by the Shady dolomite formation. In places the residual clay derived from this formation contains considerable manganese oxides. Nine properties in Shady Valley and two in Doe Valley were prospected by the Bureau of Mines from January 1943 to April 1943. The results obtained indicate that the ore bodies are small and spotty and, that the ore is not well-adapted to gravity concentration. The work of the Bureau was confined to the open end of the valley. One mile northeast of the Ham Greer property, Beaverdam Creek enters a rocky gorge, and it was believed that the few prospects in this area were of secondary impor-tance and, owing to the steep slope and general roughness of the terrain, that exploration with the rite', bucket-drill would be impracticable. A total of 4,398.5 feet was drilled in 131 holes. In addition, 235 lineal feet of bulldozer trenches were cut and 4.5 feet of test pits were sunk. The following nine properties were explored in Shady Valley: Bentley, Walker, Blevins, Scott, North Ham Greer, South Ham Greer, Lipford, Blackburn, and Steagall In Doe Valley, the Gerd Shoun and Brookshire properties were explored.

Jan 1, 1949

By Bruce E. Stauffer

The report recommends criteria for the design of safe surface mine haulage roads. Information relevant to road design at surface mine sites delineates vertical and horizontal alignment; subbase and surface materials; drainage; cross-slope, superelevation; runaway vehicle protection; and road and vehicle maintenance criteria. An appendix Is included which details the study methods used in compiling the final report information. A bibliography following the main text lists literature referenced for the report data and which is available as a valuable tool for use by individuals involved in haul road design.

Jan 1, 1976

By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966

By P. Stark, B. S. Lement

ACCORDING to Hanemann1 the hardness of retained austenite in a 1.7 pct C steel is increased by subsequent tempering. He reported that the hardness of this constituent increases only slightly on tempering to 300°F, rises more rapidly above this temperature, and attains the same value as the tempered martensite present in steel at approximately 480°F. The variation of hardness of both retained austenite and martensite with tempering temperature as obtained by Hanemann1 is shown in Fig. 1. Hanemann attributes the increase in hardness of the retained austenite essentially to continued formation of fine needles of martensite on tempering. Although he did not explain the actual mechanism involved, work hardening of retained austenite by the plastic deformation associated with such martensite formation appeared to be a possibility. Recently Lement, Averbach, and Cohen2 reported the existence of subgrains, about l000Å in diameter, in retained austenite and suggested that they may be delineated by a subboundary carbide. This raised the possibility that carbide precipitation might be responsible for the hardening reported by Hanemann. In view of these conflicting possibilities, an investigation" was carried out on a high purity, Fe-C alloy containing 1.7 pct C in order to clarify the nature of the phenomenon involved in the reported hardening of retained austenite. This investigation involved correlation of changes in microhardness and microstructure of the austenite as a result of tempering. Microhardness tests were made with a Tukon tester using a 25 gram load and a Vickers diamond. It was found that two groups of austenite hardness values were obtained after tempering at a series of temperatures up to 450°F, which was the highest temperature at which retained austenite regions could be identified microscopically. One group represents a high hardness level which in-

Jan 1, 1955

By P. H. Scott, Walter Rose

Recent papers by S. T. Yuster have called attention to the largely ignored concept that there will be a transfer of viscous forces across fluid-fluid interfaces during the flow of immiscible fluid phases through porous media. This leads to the implication that the relative permeability us saturation function, as applied to each of the fluid phases of the system, will in some way be dependent on the viscosities of all the other fluid phases which are contiguous to the flowing fluid of interest. In fact, Yuster has selected and analyzed the properties of a capillary-tube model of the reservoir-prototype flow systems and concludes from his studies that relative permeability values will be very markedly influenced by the viscosity ratio in two-phase systems. On the other hand, relative permeability data have been reported in the literature for more than 20 years; and where these data are consistent at all, they consistently how no dependence on viscosity ratio (cf. chapter 7 of Muskat3 for a resume of past experiniental work). This paradoxical situation has prompted us to re-evaluate Yuster's work. The major flaw we find has to do with the properties of the model Yuster employed to give qualitative support to his predictions. This model is defective in that important surface area parameters characteristic of the prototype-reservoir flow system have not been propertly scaled. Fig. 1 shows how we believe Yuster's model should be modified to circumvent this difficulty. It depicts the capillary tube of radius R and length L, comprised of two elements in series. The first part of length, L has the nonwetting phase flowing centrally out to a radius distance r, where an interfacial boundary exists with the wetting phase which flows in the concentric annular pace of the tube. The second part of length, L-L,. has the

Jan 1, 1953

By Frank H. Riddle, Wilfrid R. Foster

GENERAL treatment of the various minerals of importance in refractories appears in the chapter entitled "Refractories" elsewhere in this volume. The present chapter is restricted to a discussion of minerals of the sillimanite group and brings up to date the excellent information contributed by Prof. Paul F. Kerr to the first edition (1937). Since the appearance of that edition, the status of the group has changed some- what. Kyanite remains the preferred source material for mullite refractories but total consumption of kyanite has increased considerably.85 The exigencies of World War II forced an increased dependence on domestic sources and led to an intensification of the search for higher-grade deposits of kyanite and allied minerals. The first discovery of massive kyanite similar to that of India has been reported from Georgia.37 British East Africa has joined India as a substantial supplier of our imported kyanite, but that from India continues to hold preference.85 During World War II, prices of both domestic and foreign grades reached peaks unparalleled since the earliest years of the use of kyanite and as yet have shown no tendency to return to prewar levels. Topaz, by virtue of the deposit outlined in South Carolina, merits inclusion in the group.20,36,95 Large andalusite deposits, which threaten to rival our one large domestic occurrence, have been found in Russia.69,88 Sillimanite has not yet attained an important position among these useful minerals because of the lack of accessible deposits of high-quality material in adequate supply.37,50,58 Tests by the Bureau of Mines have indicated the possibilities of economically beneficiating low-grade sillimanite and kyanite.105.106,140 Government, university, and industrial

Jan 1, 1949