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By P. E. Chapman, J. E. Worthington, I. T. Kiff

Increases in the price of gold starting about six years ago, and rapid fluctuations since then, have created a substantial popular interest in the noble metal. Gold prospecting had been at a low ebb since the end of World War II in most of the United States, except for a flurry of activity in Nevada after the Carlin and Cortez discoveries. The last few years, however, have seen a great awakening of interest in gold exploration as well as an opportunity for education for many explorationists in the geology and other vagaries of gold deposits. The writers have participated over the last few years in a search for gold deposits throughout the United States. This search was greatly influenced by the geologic studies of Dr. William Spence at the Haile gold mine in South Carolina, as reported in a companion paper. Spence's studies resulted in definition of a geologic model that has proven useful in a number of other geologic environments in the United States. These programs were all carried out under the auspices of Cyprus Mines Corp. and permission by Cyprus to present these results is gratefully acknowledged. The writers, however, reserve for themselves all responsibility for the results and conclusions. The exploration program to be described began in the southeastern United States. Spence's studies provided a reasonable basis for interpreting and understanding the geology of the Haile deposit, and also provided a means for predicting additional occurrences. This concept was then expanded to other gold occurrences in the Piedmont, and became an effective tool for evaluating other prospects. Finally, it became evident that the concept could be applied in some western gold districts. The following discussion will then include descriptions of other Piedmont examples and a few western districts that also appear to fit the pattern.

Jan 1, 1981

By Frank Firmstone

Discussion of the paper of John B. Dilworth, presented at the Pittsburg meeting, March, 1910, and printed in Bulletin No. 35, November, 1909, pp. 1041 to 1043. FRANK FIRMSTONE, Easton, Pa. (communication to the Secretary*) :-Mr. Dilworth's formulas and tables are of course correct, and the extinction will occur as calculated, provided the money periodically set aside for sinking-fund be really invested. and the interest compounded as assumed in the calculation. Actually, in almost all cases, such funds are used "in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must be made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varying and continually increasing one until the date of extinction. On many accounts it seems more natural and convenient to make the extinction by a fixed periodical charge under the legal rule for partial payments, namely, that each payment should apply first to the interest due at the date of payment;: and any remainder, after this is satisfied, be deducted from the principal before the interest for the next period is calculated. The formula below is convenient for such calculations S, Principal to be extinguished. Q, Periodical payment or charge for sinking-fund. B, Balance unpaid at date of nth payment, but before that payment is made. r, Rate of interest per period per cent. n, Number of payments or periods. Then, B=S(1+r)n-Q(1+ r)n-(1+r) Received July 27, 1910.

Apr 1, 1911

Jan 1, 1886

AS I told you before in the treatise on ores, once these are found (whether they are ores of metals or semiminerals) it is necessary to assay them in order to know what is in them, since the judgment of the sight is not sufficient for recognizing the quantity or even what substance they contain. For this reason, it is necessary to come to assaying and, with the knowledge of experience, to weigh their virtues and to proceed with the work or withdraw from it and its expense; and also through knowledge to make provision for their defects if some evilness harms the ores. For if you should have need of a thing that would help them and should not find it, all that you have done would be lost; and, on the other hand, if you should find that the ores are abundant and rich and easy to smelt, you take courage to continue without respect for anything. Therefore, in the following book I shall tell you first in general how the assay of all the metals should be made. I shall enlarge in particular on silver more than on any of the others since it is more important. Then I shall tell you how the ores should be prepared for smelting and also how blast furnaces and other furnaces for smelting such ores should be constructed, and finally how all elemental mixtures of metals are to be separated one from the other with the ability and power of art, and how they are reduced to their final perfection and fineness according to their species.

Jan 1, 1942

By William Schriever

The flow of a gas-free liquid through a spherical-grain sand has been investigated by S1ichter.l By theoretical considerations involving a rather large number of approximations he arrives at the following flow-formula: V = CPd2At NLB{1 - m) where V is the volume of liquid delivered in time t through a cylindrical column of sand of length L and cross-sectional area A by a pressure-drop P when the sand grains of diameter d are packed to a porosity m and the coefficient of viscosity of the liquid is n. C and B are constants which were determined from geometrical relations; B was in reality a function of . Values of B(l — m) for various values of m were given in a table. In the same Annual Report of the U. S. Geological Survey, King reported the results of his experiments on the flow of water through porous media. He found that there was a departure of about 86 per cent. from a linear relationship between rate of flow and pressure, for a specimen of Dunnville sandstone for pressure drops not exceeding 60 cm. of mercury. The specimen was approximately 4 cm. in diameter and 5.1 cm. in length. Over the same range of pressure he found a departure of 45 per cent. for a specimen of Madison sandstone. For unconsolidated sands he found departures as great as 49 per cent. for pressure drops of 70 cm. of mercury; for pressure drops not exceeding a few inches of water he obtained a close approximation to a linear relation. He also investi-

Jan 1, 1930

By R. S. Shoemaker, D. L. Harris

PST investigations into the possibility of concentrating the low-grade iron ores of the Gogebic Range in Wisconsin have been hampered by the complex association of the constituent minerals. In part the problem arises from the fact that the iron occurs essentially as two minerals, hematite and goethite, having nearly the same chemical composition but exhibiting different physical properties. Individual grains of these minerals are usually so small that the ore must be ground to a size finer than 325 mesh if substantial liberation of the minerals is to be secured. Appraisal of beneficiation tests on this iron ore requires, therefore, some method of determining quantitatively the contents of constituent minerals in the various products of the beneficiation. Because of the chemical similarity of the two iron minerals, chemical analyses do not provide a means of differentiation. Although the minerals are different physically, they are both opaque and friable, and as the ore must be ground to a very fine size for liberation to be secured, quantitative microscopic methods of analysis are extremely difficult at best. In an effort to overcome these analytical problems, a quantitative X-ray diffraction analysis method has been developed at the University of Wisconsin for the research program on iron ore beneficiation. The X-ray diffraction analysis of chemical compounds of crystalline form has proved of inestimable value for structure studies and rapid qualitative analytical purposes in a number of fields.' In some cases X-ray diffraction analysis has been found suitable for quantitative determinations. H. P. Klug2 found that quantitative procedures for quartz powders when mixed with calcium fluoride were reproducible within ±1.0 pct. Talvenheimo and White3 reported quantitative analyses of clay minerals to be accurate within 10 pct and also detected 1 pct of bentonite in 99 pct illite. In other investigations,'" powders of quartz and mica have been analyzed quantitatively with accuracies from 1 to 5 pct. A powder of tungsten carbide was analyzed similarly by Redmond7 and Rooksby8 reported the determination of small amounts (0.11 pct) of calcium oxide in magnesium oxide. In the most generally practiced use of X-ray diffraction, traces of the diffracted beam are recorded as lines on a film much as lines of elements are recorded on an optical spectrograph film. As with the spectrograph, the darkness of the lines denotes the amount of the constituent in the sample. If the film is replaced by a Geiger tube assembly and a graphic recorder or a scaling unit, the intensity of the diffracted beam can be registered as a peak on a chart or energy impulses per unit of time on the scaler. Several methods of quantitative measurement have been investigated and reported in literature. Klug2 used manual operation of the goniometer and a counting technique to determine the difference in counting rates at the diffracted angle and for the background. In another case3 the area under the recorded diffracted peak was the basis for the determination. In other instances the height of the recorded diffraction peak above background, measured while the goniometer was moving, has been the basis for the measurement. The sizes of particles most suitable for diffraction techniques are reported in the literature as follows: for tungsten carbide a maximum of 40 microns7 and for quartz a maximum of 5 microns.' Very fine sizes of crystals are known to cause a broadening of the diffused beams; hence some workers have set a lower limit of 0.1 micron for quantitative results. Guinier10 has indicated that broadening of the diffracted X-ray beam is not appreciable for crystallites larger than 0.02 to 0.03

Jan 1, 1956

By B. J. Kochanowsky

The idea of a portable crusher is not new. Many such crushers are available but they are small and designed for construction work. For many years the author has suggested, both in this country and in Europe, the building of larger portable crushers intended expressly for use in quarries or open pits. Although not applicable under all conditions, there are mining operations where a mobile crusher arrangement could be more profitable than the facilities now used. The primary use of a portable crusher, i.e., a crusher mounted on crawlers or tires, in the rock and mining industries is to reduce costs by permitting the substitution of conveyor belt haulage for truck or track haulage. The usual sequence of operations in surface mining is drilling, blasting, loading, haulage, and crushing. Haulage is normally accomplished by truck or track-mounted cars, the latter method being used for the longer distances. However, by using a portable crusher in the pit, the sequence of operations would be changed so that the crushing stage would occur before haulage (Fig. 1). Such a sequence would permit the use of conveyors to replace the more expensive truck or track haulage methods. Since most quarry and open pit operations normally require a crushing stage, the only additional costs incurred will be due to the investment required to purchase or construct a mobile arrangement for a crusher. But this factor has to be weighed against the advantages to be gained by conveyor haulage. As shown in Fig. 2, transportation of material by belt conveyor over short distances is less expensive than by truck. The inclination of the belt has no effect on belt speed; consequently, the hourly tonnage moved remains the same. Conversely, the output rate of trucks as expressed in tons or ton-miles per shift decreases proportionally to the haulage speed, which is considerably slowed by the steepness of the road (Fig. 3, left). Although maximum possible grades and maximum economic grades of haulage are greater for a belt than for a truck (over the same total lift), the longer haulage distances favor the use of trucks. Although power consumption for hauling on a grade increases for both conveyances, the rate of power consumption increases faster for trucks than for conveyor belts (Fig. 3, right). Since the output rate and related fixed costs are affected by the travel speed, total haulage costs with trucks would increase with the grade more rapidly than the similar costs of conveyor belts (Fig. 4). Travel distance, road grade, speed, size and number of pieces of equipment, efficiency of operation, and many other factors affect such haulage costs. In general terms it can be said that the shorter the distance, the steeper the grade, and the greater the output, the more advantageous the belt becomes in comparison to truck or track haulage. In addition to potential cost savings in haulage procedures, a portable crusher would allow better utilization and performance of shovels. Loading operations would not be interrupted as often by the necessity of waiting for cars or trucks. Unfortunately, the application of belts in open pits for haulage from bench sites is generally not practical under existing conditions because a belt fed directly by a mechanical shovel can be torn, damaged, or worn out quickly by the large rock fragments falling on it during loading. However, by using a mobile crusher this situation can be avoided. As shown in Fig. 1 (b), the shovel feeds rock into the crusher located behind it. The crushed material is initially transported by an extensible and/or movable belt, thence by a longer stationary conveyor to the plant where the material is subjected to further treatment by secondary crushing, screening, etc. The first-mentioned conveyor, needed to bridge the distance between the shovel and the stationary conveyor, is necessarily variable in length owing to the continuous movement of the shovel and the desire to keep the stationary belt at a safe distance from the bench during blasting operations. The remarkable part of mobile crusher operations is the extra-ordinarily high output per man-shift, the low maintenance and power requirements for haulage, and the increased output of the loading shovel. A cement quarry which has been using a portable crusher and conveyor since 1956 requires only three men to operate the shovel and crusher and to transport the crushed rock by belt from the quarry face to the screening plant. If truck haulage

Jan 1, 1961

By R. C. Hyslop

The object of this experiment was to obtain a usable set of field curves for determining the susceptibility of rocks with the vertical magnetometer. The need often arises for determining the susceptibility of rocks in the field in order to interpret magnetic anomalies obtained. This is particularly true when diamond drilling has been done and the relation to the surface rocks of the samples taken is desired. Many methods of measuring rock susceptibility have been developed, but in general they require careful shaping of the sample or pulverizing it in addition to delicate laboratory measuring instruments designed for the purpose. The requirements for a practical method for the determination of susceptibilities are as follows: 1. There should be as little alteration as possible of the specimen. 2. A minimum of time should be required in the preparation of the specimen and the calibration of the equipment. 3. Theequipment used should be portable. 4. An accuracy within the limits of the survey at hand should be obtainable. 5. A means of measuring the remnant magnetism should be available. Laboratory Procedure With these ideas in mind, the problem was approached in the manner in which Koenigsbergerl developed his method using the principle of the electrical theory of images of Lord Kelvin and applying it to the magnetic case. This solution of the problem states that the apparent change in the magnetic field intensity AZ due to the proximity of a specimen is given by: mk AZ = 2a2 Where k is the susceptibility of the specimen, m the strength of the pole of the needle, and a its distance from the surface of the specimen, as shown in Fig. r.2 This relation is true only for an infinite body and corrections are necessary for a finite body. Koenigsberger used in his work a variometer of special design. He suggested that a Schmidt vertical balance or horizontal magnetometer, as well as some other instrument, might be used. The Colorado School of Mines horizontal torsion magnetometer operates on this principle. In the

Jan 1, 1946

By R. C. Hyslop

The object of this experiment was to obtain a usable set of field curves for determining the susceptibility of rocks with the vertical magnetometer. The need often arises for determining the susceptibility of rocks in the field in order to interpret magnetic anomalies obtained. This is particularly true when diamond drilling has been done and the relation to the surface rocks of the samples taken is desired. Many methods of measuring rock susceptibility have been developed, but in general they require careful shaping of the sample or pulverizing it in addition to delicate laboratory measuring instruments designed for the purpose. The requirements for a practical method for the determination of susceptibilities are as follows: 1. There should be as little alteration as possible of the specimen. 2. A minimum of time should be required in the preparation of the specimen and the calibration of the equipment. 3. Theequipment used should be portable. 4. An accuracy within the limits of the survey at hand should be obtainable. 5. A means of measuring the remnant magnetism should be available. Laboratory Procedure With these ideas in mind, the problem was approached in the manner in which Koenigsbergerl developed his method using the principle of the electrical theory of images of Lord Kelvin and applying it to the magnetic case. This solution of the problem states that the apparent change in the magnetic field intensity AZ due to the proximity of a specimen is given by: mk AZ = 2a2 Where k is the susceptibility of the specimen, m the strength of the pole of the needle, and a its distance from the surface of the specimen, as shown in Fig. r.2 This relation is true only for an infinite body and corrections are necessary for a finite body. Koenigsberger used in his work a variometer of special design. He suggested that a Schmidt vertical balance or horizontal magnetometer, as well as some other instrument, might be used. The Colorado School of Mines horizontal torsion magnetometer operates on this principle. In the

Jan 1, 1946

By E. F. Johnson, F. H. Brinkman, H. J. Welge, A. L. Hicks

A method is presented for predicting the character of gas or water displacement in a radial system, which can be either horizontal or inclined. The latter case would comprise cone-shaped or dome-shaped symmetry. The method conriders the one dimension of radial distance, taken parallel to the bedding planes. Approximate allowance can be made for segregation of the two fluids perpendicular to the bedding planes. A complete saturation history can be obtained in about a day's time with the use of a desk calculator. Results of an example calculation agree well with the performance of simulated gas drive in a large model representing a section of a cone. This pie-shaped, sand-packed model was 8-ft long and 4-in. thick. The method of solution is useful in handling other partial differential equations of first order and first degree. INTRODUCTION A new analytical method has been developed for predicting the performance of gas or water drive in a reservoir having radial or cone-shaped symmetry (see Fig. 1). In addition, this new development offers a general method of handling partial differential equations of first order and first degree. This work extends those methods developed previously'- "or predicting the displacement of oil by gas or water in linear systems. The method of calculating oil recovery in a radial system involves two major parts. The first part is a calculation of the distribution of saturations at various times of depletion. The second part is the calculation of oil recovery and producing gas-oil or water-oil ratios through volumetric balance on the saturation distributions obtained in the first part. This second part differs only slightly in principle from similar calculations made with linear systems, for instance. The basic assumptions used in the calculations are as follows. 1. One-dimensional radial flow. An approach is explained later for approximating a second vertical dimension. (With- drawals of oil, and of the driving fluid after breakthrough, are assumed uniform around the periphery of the dome.) 2. Constant-volume fluid flow. Thus, in a gas drive there is no change in gas solubility, or in oil or gas volume due to viscous and gravity pressure drops. 3. Capillary forces are negligible. 4. Constant rate of injection. A program has been written for carrying out the calculations needed on a digital computer. However, a prediction can also be arrived at using a desk calculator; this latter method of work requires about a day's time for each prediction made. CALCULATION OF SATURATION DISTRIBUTION For definiteness, we describe the development of our method for the case of gas drive from the crest of the structure. The reader will note, however, that the method is just as applicable to an advancing radial water drive. The equation describing gas flow over an infinitesimal

By Robert W. Bartlett

A computer model for predicting the rate of oxidative leaching of copper from fragmented low grade sulfide ores is presented. The model involves the kinetics of the dissolution of chalcopyrite grains and solution diffusion of oxygen within rock pores. Adjustable curve fitting parameters are not used. The model was tested by comparing computed extraction curves with experimental results for a -11 inch ore obtained by block caving and leached at 90°C and 400 psi oxygen for one year at the Lawrence Livermore Laboratories.

Jan 1, 1973

By B. G. Klugh

(New York Meeting, February, 1912). IN a paper before the Institute at Wilkes-Barre, Pa., June 1911,1 Mr. James Gayley discussed the application of this process to iron-bearing materials. The same author2 described the results of operations at the plant at Birdsboro, Pa. The purpose of the present paper is to present further discussion of some technical details involved in the operation of this plant, and of the theoretical and practical relations of this product to blast-furnace practice. Since Oct. 1, 1911, the Birdsboro plant has been in operation at the blast-furnace of the E. & G. Brooke Iron Co. The results have been highly satisfactory, although the material treated, being chiefly the flue-dust currently made by the furnace or taken from the accumulated stock-pile, was excessively high, and yet not uniform, in carbon, so that the desirable control or regularity of the amount of fuel in the mixture treated could not be maintained. Nothing could more forcibly demonstrate the flexibility of the process than the fact that, under these conditions, the sinter produced was, in all cases, of excellent quality. The Dwight & Lloyd process, as such, and its present highly-developed mechanical appliances were described by Mr. Gayley in the paper above mentioned. While the repetition of some particulars will be unavoidable in this paper, it will be confined to features bearing upon the metallurgical principles involved. According to the principle of the process, the finely-divided iron-bearing material to be sintered is intimately mixed with

May 1, 1912

By Stanford O. Grodd

The Sanford Lake district encompasses an area covering 24 square miles in the central Adirondack Mountains of northern New York State. Discovery of the titaniferous magnetite deposits dates back to 1826. Several attempts to exploit the ores for iron prior to 1942 proved uneconomical because of difficulties with the associated titanium, lack of transportation facilities, and the isolated location. Since 1942, the National Lead Company has produced ilmenite concentrates for the titanium pigment industry, and a magnetite by-product used in the steel and refractory industries. Rocks of the area are Precambrian in age and of igneous origin. The area has a history of erosion, deformation, and metamorphism, subsidence, and finally uplift and glaciation. The resulting topography is extremely rough with drainage patterns controlled by a combination of fault patterns and glacial modifications. The district is within the large anorthosite massif making up the central high peak area of the Adirondacks. All of the various lowsilica rock types associated with the massif are found within the boundaries of the district. These consist of both the Marcy and Whiteface types of anorthosite and of gabbroic anorthosite, gabbro, and different grades of titaniferous magnetite ores. All of the rocks contain the same minerals and differ only in their percentages of these consitituents. Gabbro, and ore associated with it, demonstrate flow structure as both have foliation and lineation. Anorthosite and its associated ores are massive and show very little primary structure. Minor pegmatites and diabase dikes provide evidence of remobilization in selected areas and of late intrusion as well. Faulting is prevalent and follows a regional pattern of major faults trending northeastsouthwest and of minor faults at nearly right angles to them. There are four mineralized areas where an economic grade of ore has been found. Three of these have both gabbroic-type ore and anorthositic-type ore. The fourth has only gabbroic ore. Ores are graded according to their TiO, content, and these range from 9.5 per cent to over 30.0 per cent TiO,. Ore bodies of both types are related to gabbro and conform to the configuration of the gabbro bodies within the anorthosite. At least three distinct theories of ore genesis have been expounded by different investigators. Others propose some variations of one or more of these. Although complete agreement probably never will be reached, it is certain that no one process of ore emplacement can explain the complicated picture as seen today. Further understanding of the ores and their origin will require detailed mapping, sampling, and mineralogical studies of the entire district, and then it may never be understood without qualification.

Jan 1, 1968

By T. S. Lundy, J. I. Federer

A graphical method has been developed and tested for separating the effects of grain boundary and lattice diffusion in polycrystalline materials. The method is based on the assumptions that for unidirectional diffusion from a plane source of radioactive material, the penetration of activity far into the specimen from the source is due solely to grain-boundary effects, and 2) pure grain-boundary penetration is described by a linear plot of log activity vs the perpendicular distance x from the source. The former is based on the fact that at any temperature the grain-boundary diffusion coefficient is always very large relative to the lattice diffusion coefficient; and the latter is based on the derivation of Fisher.1 Using these criteria along with appropriate penetration data (in this case, data for the diffusion of Cb95 in pressed and sintered UO2) one first plots the data as log activity vs x2 and as log activity vs x, as shown by curves 1 and 2, respectively, in Fig. 1. A tangent line to curve 2 for large x (curve 3) is then transferred to the x2 plot as curve 4. The subtraction of curve 4 from curve 1 yields curve 5 which represents only lattice diffusion and may therefore be related to the diffusion coefficient by using the appropriate solution to Fick's second law. It should be noted that the method has inherent inaccuracies for small and large values of x2 and only the subtraction at intermediate values can be used. For the illustrated specimen the calculated diffusion coefficient is 3.4 X 10-11 sq cm per sec at1445°C while data using a single crystal of UO2 at the same temperature yielded a value of 2.9 x 10-11 sq cm per sec.2 The same method of subtracting grain-boundary diffusion effects to obtain lattice diffusion coefficients has been successfully used to determine self-diffusion coefficients of Th230 in polycrystalline thoria.

Jan 1, 1962

By G. R. Fitterer

NonmEtallic inclusions in steel have received much attention by metallurgists during the past few years. Many investigators have been emphatic in stating their belief that these impurities are the chief causes of steel failures, while others think that their effects are negligible. One of the main reasons that definite information on the effects of these impurities is lacking is that no reliable method has been developed for the exact determination of the amounts of these different impurities in steel. Some valuable new information has been brought out by a reliable method for nonmetallic inclusions which has been developed at the Pittsburgh Experiment Station of the U. S. Bureau of Mines, in cooperation with the Carnegie Institute of Technology and the Metallurgical Advisory Board. This procedure satisfactorily extracts some of the more common inclusions from steels, thus enabling the investigator to correlate steel failures with inclusion content. Although the data given herein are the first to be published on the subject of the electrolytic extraction method, the interest in the subject is evidenced by the fact that it is already being used by some 20 to 30 steel companies for their various purposes. Some of the comments received from these laboratories indicate that the method is highly satisfactory: the unfavorable comments, when traced to their sources, have been found to be based on some small mistake made in either installation or operation. The chief discrepancy seems to have occurred in attempts to apply the method to the extraction of inclusions from alloy steels. The procedure can be used only for the plain carbon steels and for such low alloy steels as those containing the usual amount of copper (0.2 to 0.3 per cent). Steels containing the carbide-forming alloys such as chromium, tungsten, etc., present far too many difficulties for the accurate determination of inclusions. Luckily, the iron and manganese carbides do not offer any difficulties and no contamination of the oxide-sulfide residue results, It is highly probable that some modification of the following

Jan 1, 1931

By P. F. Gnirk, J. B. Cheatham

The results of combined analytical and experimental studies involving simulated multiple bit-tooth penetration into mck are incorporated into a drilling rate equation for roller-cone bits assuming rather idealized downhole conditions. In particular, it is assumed that the rock behaves statically in a ductile fashion during bit-tooth penetration and that the rock chips are instantaneously removed from the bottom of the drill hole. The general analysis demonstrates an application of plasticity theory for the rock/bit-tooth interaction to the formulation of an upper limit on rotary drilling rate. INTRODUCTION Extensive experimentation involving single and indexed bit-tooth penetration into rock in a confining pressure environment has demonstrated that the chip formation process is of a ductile, or pseudoplastic, nature at sufficiently low differential pressures so as to be of interest in rotary drilling. Coincident with the experimentation, analytical consideration has been given to the theoretical problems of single and indexed bit-tooth penetration into rock. In general, the analyses have assumed that the rock behaves statically in a rigid-plastic fashion and obeys the Mohr-Coulomb yield criterion. The quantitative comparison between experimental and calculated values of bit-tooth load required for chip formation has been remarkably good for a variety of rocks commonly encountered in drilling and at simulated differential pressures as low as 500 to 1,000 psi. Results obtained recently for indexed bit-tooth penetration indicate that the work (or energy) required to produce a unit volume of rock chip can be minimized by a proper combination of bit-tooth spacing and bit-tooth load for a given rock type and differential pressure. By utilizing this information, it is possible to formulate a drilling rate equation, at least in a preliminary fashion, for a roller-cone bit performing under rather idealized downhole conditions. In particular, through the use of characteristic dimensionless quantities pertinent to a roller-cone bit and to indexed bit-tooth penetration, interrelationships among bit weight, rotary speed, rotary power, bit diameter, rock strength and bit-tooth shape and spacing can be explicitly expressed. In the formulation of the equations, however, it is assumed that the rock chips are instantaneously removed from the bottom of the drill hole and- that the rock behaves in a ductile manner during bit-tooth penetration. In addition, the effects of bit-tooth load application and penetration by a yawed tooth at an oblique angle are neglected. Although the analysis is presented in the light of some rather restrictive conditions, it does demonstrate a method of applying fundamental rock/bit-tooth interaction data, obtained by combining the results of analysis and experiment to the formulation of a drilling rate equation for rotary drilling. JNDEXED BIT-TOOTH/ROCK INTERACTION PREVIOUS RESULTS The mechanics of bit-tooth/rock interaction under simulated conditions of borehole environment have been extensively described in a number of papers.l-ll In particular, the effects of differential pressure, mechanical properties of rock, pore fluid, bit-tooth shape and spacing, rate of bit-tooth load application and dynamic filtration below the bit-tooth have been investigated experimentally. From a sequence of experiments.1-4 it was demonstrated that, for dry rock at atmospheric pore pressure, the mode of chip formation exhibits a transition, with increasing confining pressure, from predominantly brittle to predominantly ductile. This transition

Jan 1, 1970

By T. Smales, P. L. Wright, K. Barron

The results of field measurements using an air injection technique to investigate the integrity of three pillars in the Mclntyre Mines Ltd. 114 seam at Crande Cache, Alberta, are reported. These pillars are shown to be stable and an estimate is made of the strength of these pillars. Using these results, together with Hustrulid's pillar strength formulae, a general pillar strength equation for the 114 seam is developed. This equation takes into account the probability of failure that may be deemed tolerable within the design requirements. The variation of the minimum pillar dimensions with depth below surface for uniform pillar layouts is then examined for a range of tolerable failure probabilities. A general equation of the form B = 2.60 +B Z relates the minimum pillar design width, B metres, with the overburden depth, Z metres, where B is a parameter related to the tolerable failure probability. This equation only applies for 3.05m high pillars with 6.lm wide entries. Finally, the question of what failure probability is tolerable within the design of mine pillars is discussed. This will depend on the support role required of that pillar and the anticipated period over which the pillar must perform that role. Five categories of coal mine pillars are defined, each with a somewhat different role to perform. Tentative design criteria in the form of "tolerable probabilities of failure" are suggested for four of these five categories of pillar. The fifth category of pillar has no reliable support function to perform and support must be obtained by other means.

Jan 1, 1983

By R. W. Nelson

The theoretical basis is presented for energy dissipation methods of measuring permeability in saturated heterogeneous media. Analysis starts with the equation for single-phase flow in heterogeneous porous media which is a first-order partial differential equation in the unknown permeability. This equation is reduced to a system of characteristic equations useful in deriving a differential expression for the permeability as a function of the known potential distribution. For steady flow systems the expression is integrable, giving the permeability integral for direct calculation of the distribution along successive streamlines. The boundary condition in permeability is presented and includes a discussion of the special requirement to assure uniqueness. Theoretical results and necessary computations are incorporated into two general computer programs capable of determining the permeability distribution in two- and three-dimensional steady flow systems. Results are then presented for an energy dissipation analysis using the methods and soltware to determine a field permeability thickness distribution. INTRODUCTION Theoretical work leading to the description of fluid flow in heterogeneous porous media has developed slowly and somewhat sporadically, although the areas of engineering applications predominantly involve flow in nonhomogeneous media. The lack of accurate and economical methods for measuring field permeability distributions has been a major limitation to realistic description of natural flow systems. The economical measurement of permeability using energy dissipation methods may overcome this limitation. Among other things, any permeability measurement method involves consideration of energy dissipation; as used here, "energy dissipation method" denotes the following general approach. The areal energy distribution is measured on an existing flow system in porous media. Then through appropriate analysis of the dissipation of energy in the flow system, the permeability distribution is determined throughout the region using the minimum boundary conditions required to assure a mathematically unique result. This paper presents the theoretical basis for such a method, as well as the techniques and computer software needed to carry out the analysis. The method and techniques are then used in a preliminary field application. EQUATIONS DESCRIBING FLOW IN HETEROGENEOUS MEDLA Heterogeneous as used here implies differing in kind, having unlike quantities or possessing different characteristics. Accordingly, a heterogeneous porous medium has unlike quantities or differing characteristics at different locations. More precisely, if a porous medium is heterogeneous with respect to some property, then that property is functionally dependent on the spatial location. (Media properties are considered here as macroscopic.) Specifically considering permeability k,** then k = G(x, y, z) ,............(1) or the permeability is a scalar function G of the location (x, y, z). Spatial variation of several other properties, of which porosity, dispersivity and medium compressibility are but a few, is implied by the broad title of heterogeneous porous media. The term will be used hereafter to imply only heterogeneity with respect to permeability. The porous medium is considered isotropic as implied by G being only a scalar function. Anisotropy

Jan 1, 1969

By M. E. Hassan, J. C. Calhoun, R. F. Nielson

An apparatus was constructed for the measurement of inter-facial tensions over a range of temperatures and pressures. This apparatus utilized the pendent drop method, and resembles in construction similar apparatus recently described in the literature and in use in some petroleum research laboratories. The interfacial tensions of benzene, propane, n-pentane, n-hexane. n-octane. and iso-octane against water were measured at temperatures ranging from 26" to 82" C and at pressures ranging from 1 to 204 atm. Values of interfacial tensions for the henzene-water system and their variations with temperature and pressure are generally in good agreement with value? of previous investigations. The data in all cases showed a slight decrease of interfacial tension with pressure at constant temperature in the range studied. The effect of pressure became less as the pressure was increased, with an indication of a reversal of the effect at higher pressures. There was a decrease of interfacial tension with temperature at constant pressure in all cases, as would normally be expected. This rate of decrease became greater the higher the temperature. A general equation is presented for the interfacial tensions as a function of presPurp and temperature over the range studied, and the constants calculated for each system. A definite trend was found in the effect of molecular weight on the interfacial tension at a given temperature and pressure, for the homologous series from propane to n-octane. Data for n-decane from the literature fitted well into this trend. INTRODUCTION It has been recognized for many years that surface forces play an active part in the production history of an oil reservoir as well as in determining the amount of unrecoverable oil. The magnitudes of these forces are governed by the values of the interfacial tensions. These vary greatly with composition, pressure, and temperature. The effect of composition is greater than that of pressure and temperature over the ranges normally encountered. In fact, because of the variety of compounds present in a crude, no attempt has yet been made to correlate crude composition with its surface tension or with its interfacial tension against water. The amount of dissolved methane greatly affects the surface properties of an oil, and there are "surface-active" compounds in crudes which have a much greater effect on boundary tensions than do equal amounts of hydrocarbons. The purpose of the present work was partly to contribute data that would eventually be used in correlations applicable

Jan 1, 1953

By A. B. Hildebrandt

P. B. Baxendell is to be complimented for an exccllent piece of work. To our knowledge there has been no previous publication of field data on the flow of oil and gas through the annulus of a well. It is certainly gratifying to see this work on annular flow confirm the previous published correlation procedure on tubing flow. It extends considerably the range under which reliable gas-lift calculations can be made. Baxendell discussed this work with us about a year ago and was kind enough to send a large scale plot of his correlation. We had been designing gas-lift installations on flow through the annulus, assuming that the original correlation of the f factor based on tubing flow' was valid as long as we stayed within the same mass velocity range on which the correlation was based. Doing this work necessitated the use of an equivalent diameter for the annular flow. The equivalent diameter is defined as area' of stream cross section wetted perimeter and for the case of an annulus is D, — D,. Substituting this in the basic equation correlating energy loss along with the area to flow required to convert the velocity, to volumetric flow rate, D (Baxendell's Eq. 7) becomes dell's expression, D,). Similarly, the D in 1.4737 X 10 (M&/D) becomes (D, + D;) for annular flow. On receipt of Baxendell's data, we. of course, recalculated it to put it into the form we were using, and to see how well it agreed with the correlation based on tubing flow. Fig. 1 shows the results, which were certainly gratifying. For low values of (D, - D,) pv, the data coincide with the data on flow through tubing, whereas at high values the data on flow through the annuli appear to be leveling off to a constant value. For very high rates of flow where the turbulence is very high, one might expect the value f to level out and become constant. A bulletin published in 1914 by the U. of Wisconsin presented results of a large number of laboratory teats in air lifting water through short lengths of 1.25-in. tubing. It was possible to correlate a random sampling of