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By R. S. Wagner, H. Brown

Criteria for nucleation with the aid of twin planes during crystal growth from the melt are discussed. It is shown experimentally that bismuth crystals can grow from a subercooled melt in a twinned bismdtic form. A mechanism of growth based on the presence of at least me twin plane is proposed. It is well known that faceted growth can be observed in crystals grown from the vapor phase, dilute solutions, or from the melt. Faceted growth, in which the crystal is bounded by its slowest growing faces, will occur if the growth rate is strongly orientation dependent. The addition of atom layers on a facet plane can only occur by two-dimensional surface nucleation or with the aid of an imperfection. Nucleation with the aid of dislocations was proposed by rank' and observed to be of particular importance in crystal growth from the vapor phase. Nucleation with the aid of two-dimensional imperfections, notably twin planes, was suggested by stranski2,3 and Frank.4 A twin plane, terminating at the growth interface, can form a reentrant step at which nucleation can occur at a much smaller super-saturation (or supercooling) than required for two-dimensional surface nucleation. Nucleation by a twin plane usually results in a fast growth rate along a crystallographic direction parallel to the twin plane. Such a nucleation mechanism, based on the presence of a twin plane, has been used by Dawson5 to explain the growth and morphology of sheet-like crystals of paraffin n-hectane. In recent years more evidence was found that nucleation by twin planes occurs frequently in crystal growth from the vapor phase and from dilute solutions, for example, in cadmium,' barium titanate,7 silver,8 silicon9 and gallium arsenide.10 In crystal growth from a supercooled melt, however, nucleation by twin planes has so far only been observed in materials with the diamond or zinc blende structure. Bennett and Longini11 were the first to recognize the important role a single twin plane plays in the growth of germanium dendrites. Subsequently, it was found that a prerequisite for continued propagation of germanium dendrites is the presence of two parallel twin planes which form a self-perpetuating system of nucleation sites.12 Sili- con and some III-V compounds such as InSb also grow dendritically by twin plane nucleation. It appears that the following criteria must be satisfied in order that nucleation with the aid of twin planes can occur: A) The growth form of the material must be faceted." B) The formation of twin boundaries, by a fault in layer sequence during growth, by plastic deformation, or by an accidental meeting of properly oriented crystals, must be possible. C) Twinning must form a reentrant step where the twin boundary terminates at the faceted growth interface. D) These three conditions are necessary, but in certain cases not sufficient for continued crystal growth with the aid of a twin plane. Depending on interface morphology, a combination of more twin planes is sometimes required to form a self-perpetuating system of nucleation sites. This investigation was carried out with the idea in mind that nucleation with the aid of twin planes is a more general phenomenon and should occur in those materials, grown from a supercooled melt, which satisfy the criteria outlined above. It has been found that crystals of high-purity bismuth grown from a supercooled melt can grow by the aid of a twin plane. In the first two sections the faceted growth form and the twinning elements of bismuth are discussed. In the last section prismatic crystals of bismuth, which appear to grow with the aid of a deformation twin are discussed.

Jan 1, 1962

By Y. Kondo, A. M. Gaudin

A combined method for sizing in the sub-micron range was developed using centrifugation and gamma emission. Its essential features are: 1) Centrifugation of suspended mineral in water carried out at 4°C where water has its maximal density and zero temperature gradient of density 2) Gamma activition of the sample suspension induced by irradiating it in a nuclear reactor prior to centrifugation 3) Measurement of the activity of a beam of suspension as it is sedimenting in the centrifuge, using a scintillation counter provided with a discriminator. Albite, the sodium feldspar, was used as feed to the comminution step, and the induced gamma activity of Na24 was measured. Dissolved sodium ion caused a a non-settling activity in the measurement. Other "noise" is due to scattered gamma radiation from albite particles in the centrifuge outside of the line of sight. These two activities were obtained sep arately and subtracted from the total activity counted. The relative solid concentration in the suspension under the collimating slit is proportional to this net activity. The cumulative weight per cent of undersize particles was calculated and plotted against size on logarithmic scales. The relationship was found to be linear down to about 30 mµ. The specific surfaces calculated from particle size distribution agree with those measured by krypton gas adsorption. The measurement of particle size distribution of comminution products has been of interest in clarifying the mechanism of the process. The Gaudin-Schuhmann equation1,2 relates the cumulative percentage undersize, y, to relative particle size x/k. The particle size, x, and the size modulus, k, together with the distribution modulus, m, characterize the particle size distribution, m is the slope of a plot of log (y) against log (x/k). This equation has been verified for ground particles down to 1 micron in size.3'4 For particle sizes smaller than a few microns, the precision and facility of sedimentation and microscope techniques become questionable. Use of a centrifuge which shortens settling time from weeks to hours is attractive. Many centrifugal methods have been proposed; however, determination of the solid concentration of the suspension at a reference level as a function of time is difficult, and sampling the suspension is likely to introduce errors. Measurement of particle size distribution by X-ray absorption in gravitational5 and in centrifugal6 sedimentation have also been tried. In these methods, the absorption coefficient for the solid is independent of size, since the wave lengths of the X-rays and gamma-rays are orders of magnitude smaller than the particles. Radiometric techniques7 in size distribution measurement have been developed within the last several years. They offer advantages over usual gravimetric and optical methods. PRINCIPLE OF METHOD The combined method of centrifugation and gamma emission for sizing in submicron range described in the present paper has the following essential features. 1) Centrifugation is carried out at 4 ± 0.1°C. Convection currents in the water phase due to density changes caused by temperature variation may disturb completely the settling system. To avoid this difficulty, the unique property of water having zero temperature gradient of density at 4°C is used. 2) Prior to size measurement the sample suspension is irradiated in a nuclear reactor and gamma activity induced. The gamma activity of the particles sedi-mented radially is measured by a scintillation counter provided with a discriminator. By this method, interruption of centrifugation by withdrawing samples is avoided and the counting rate at any time represents the solid concentration in the suspension at the level of the collimating slit of the centrifuge at the particular time at which the measurement is made. 3) By proper selection of the feed material and of the comminution device, gamma activities of foreign

Jan 1, 1964

By A. D. Mutch

IT has long been known that there are wide variations in the thermo-electric potential of pyrite. In the last few years a study of this variation and other properties of pyrite was carried out at the University of Toronto by F. G. Smith on specimens of pyrite from many loyalities. As a result of these studies the pyrite geothermometer was developed by Professor Smith. The calibration of the pyrite geothermometer is based on the assumption that "crystals of any one electronically conducting mineral species deposited at a high temperature have a more positive thermoelectric potential than crystals deposited at a low temperature, and the thermo-electric potential varies continuously between any given limits of the temperature of deposition." The cause of the variation was postulated to be crystal discontinuities, such as lineage boundaries. As yet this postulated relationship has not been established as fact. On theoretical grounds it is indicated that the thermo-electric potential of pyrite or any other partial conductor is dependent upon a number of factors as well as the temperature of formation. For this and other reasons there is ground for doubt as to the validity of the relationship postulated above. To date a large number of readings have been made with the pyrite geothermometer which have been recorded in terms of the calibration of the instrument in degrees centigrade. So far most of the pyrite tested by this technique has been in association with gold ore. The values for the temperature of formation obtained in these tests appear to be reasonable and, in relation to geological problems, to vary in the right sense. Determinations on some specimens not in association with gold ore have given readings that appear to be much too high, taking into account the probable maximum temperature of the host rock. To sum up, although many determinations made with the pyrite geothermometer appear to give reasonable values for the temperature of formation of the pyrite, there are at the same time other readings which seem anomalous. On the basis of an examination of available results of work with the pyrite geothermometer, two problems must be considered: 1—the validity of the calibration of the pyrite geothermometer; and 2— the nature of the distribution of the thermo-electric potentials of pyrite in relation to the specific problems that have been examined. In this paper the academic problem relating to the validity of the calibration of the pyrite geothermometer will not be discussed. Instead, the variations of thermo-electric potential of pyrite in association with gold veins will be discussed with regard to specific examinations. The first of these two examinations deals with the distribution of thermo-electric potentials of pyrite in association with a gold vein and was carried out in the McIntyre Porcupine Mine, Schumacher, Ont., in the summer of 1949 as part of a study with this technique. The second problem deals with variations of thermo-electric potential of pyrite in gold ore specimens from all over the world. The specimens used in this study were part of the private collection of Frank Ebbutt, geologist for Howe Sound Exploration Co. Results of Detailed and Reconnaissance Studies In discussion of the results of determinations made in these two studies the values of thermo-electric potential in millivolts will be used. It will be noted that in some of the diagrams the determinations are recorded in terms of pyrite geothermometer temperatures. Fig. 1 is a calibration chart relating pyrite geothermometer temperatures and thermoelectric potentials. A full discussion of the technique is given in the original paper by F. G. Smith.' Briefly, the determinations are made by placing two stainless steel probes, one hot and the other cold, against the surface of the pyrite crystal being tested. The thermoelectric potential that is developed is read with a null-point potentiometer that is calibrated in what

Jan 1, 1953

By R. T. DeHoff

A general method for determining the geometric properties of structures composed of particles which are all the same shape and size is presented. The application of the method requires a knowledge of' the qualitative shape of the particles in the structure, ad a maximum of three simple counting measurenzents, which are made on a representative plane section taken through the structure. It is also shown that the number of different kinds of measurements necessary JOY the complete description of the structure can be decreased if some independent information about individual particles is available. The geometric properties that can be determined quantitatiz~ely from counting measurements for susch structures are size, shape, number, surface area, vlolume, ad such extensive properties as volume Mction and surface area per unit volume. THE simplest kinds of measurements that may be made on a metallographic section are counting measurements. There are three such simple counting measurements, which are determined by sampling the microstructure with a point, a line, and an area. The first of these, the point count, is probably the most familiar among metallographers. The second count, the number of intersections a test line makes with particle outline, is somewhat more recent in its origin and application. The third counting measurement, the number of particle sections observed in unit area of the plane of polish, has long been used in the estimation of grain sizes. The real utility of these three counting measurements lies in the fact that they are rigorously and unambiguously related to certain extensive geometric properties of the three-dimensional structure of which the metallographic section is a sample. These relationships will be reviewed briefly below. Of somewhat secondary importance to the fundamental relationships is the observation that, if some simplifying assumptions about the geometry of the three-dimensional structure are introduced, manipulation of the counting measurements gives a more complete description of the structure. Specifically, in addition to the extensive properties which these measurements rigorously estimate, the number of particles, their size, and their shape may be determined. The purpose of the present paper is to explore the consequences of introducing the assumption of constant size and shape. A later paper will deal with the estimation of geometric properties of structures which may be characterized by a two-parameter size distribution. It should be mentioned that the introduction of this simplest of assumptions, while clearly not generally justified in metallurgical structures, is not without precedent. For example, many estimates of the number of particles per unit volume of structure, based upon a single counting measurement, are scattered throughout the literature.13 Virtually all of these developments assume a constant particle shape, e.g., spherical or polyhydral, and constant size. That such an assumption is necessary is evident from the fact that, for more general structures, more than a single parameter is required to describe the three-dimensional structure, so that the determination of a single parameter on a section would be insufficient to specify the structure. Similar developments for the estimation of particle size from a single counting measurement, e.g., routine grain-size determinations, make the same very limiting assumption,435 but have nonetheless proven of practical value. The present paper embodies a generalized approach to the development of relationships among the two-dimensional counting measurements and the three-dimensional geometry of the structure, subject to the assumption of constant particle size and shape. It is the hope of the author that by presenting the relationships and the assumptions involved in dealing with this approximation, in a single, unified treatment, the reader may be impressed with the usefulness of the counting measurements, may be guided in their application to the estimation of details of the geometry in specific structures in which he may be interested, and may be moved to apply the results, with understanding, to new structural problems. Several authors6, 7 have demonstrated independently that it is possible to obtain unbiased estimates

Jan 1, 1964

By G. K. Dumbauld, B. E. Morgan

Kesults of laboratory investigations of the effects of drilling muds on oil well cements are presented which show that relatively large quantities of untreated muds do not seriously interfere with the setting of cement slurries, but that relalively small quantities of treated muds seriously retard the setting of cement slurries. Laboratory results also indicate that the harmful effects of contamination with treated muds can he counteracted by the addition of activated charcoal to cements. Also described is the successful use of cement containing activated charcoal for the placement of plugs in oPel hole after previous attempts with ordinary cement had been unsuccessful. INTRODUCTION The contamination of cement slurry by dilution with drilling mud has long been considered a cause of failure in oil well cementing. The cement slurry must displace the drilling mud from the annulus between the casing and the walls of the borehole. and it is probable that some mixing of the slurry and the mud occurs even under the most nearly ideal displacement conditions. Hole enlargement, failure to center the casing in the hole, and formation of gel structure in the drilling mud increase the probability of contamination. In some cementing operations, such as the placement of a cement plug in open hole, considerable mixing of the mud and slurry is likely. Many cement failures which can be attributed logically to no cause other than contamination of the cement slurry by the mud attest the need of a better understanding of this problem. Considerable attention was given to the problem of mud contamination of cements about 20 years ago.The effects of field mud upon cement slurries prepared with different amounts of mix water were investigated thoroughly, and the data obtained were invaluable in determining the causes of the high percentage of failure in oil-well cementing at that time and in bringing about improved cementing results. Since then, many aspects of the problem have changed, due primarily to advancements in cement and drilling mud technology. Today, several types of portland cement are used in well cementing and numerous chemical additives are used in drilling muds. An excellent report on the effects of drilling mud additives on oil-well cements was issued during 1951 by the American Petroleum Institute. Data in the report revealed that many mud additives, notably organic materials in relatively small amounts, produce a marked effect on the properties of cements. Prior to this time, little information has been available on the effects of chemicals commonly used in the treatment of drilling muds upon the properties of cements. Another aspect of the problem of mud contamination of cements, which has received no attention heretofore, is the possibility of producing a cement having properties unaffected by a reasonable amount of mud contamination. In view of the need for additional information on the contamination of present-day cements by currently-used drilling Muds, the investigation described herein was initiated Several years ago with a two-fold purpose: first, to determine the capacity of cement slurries to tolerate contamination by both untreated and treated muds without loss of ability to set and develop strength within a reasonable time; and, second, to investigate the possibility of enhancing the ability of cement slurries to withstand mud contamination by incorporating additives in the cement. The data for this study were obtained by mixing drilling mud with cement slurry and testing the resulting slurry-mud mixture for rate of set and development of strength. Also, several materials were tested for their possible improvement of the property of cement slurry to withstand mud contamination; these materials were tested in both contaminated and uncontaminated cement slurries.

Jan 1, 1952

By Goldye Leeds, Marian Balicki

A SURVEY of literature reveals the scarcity of experimental evidence relating to work hardening and reannealing of silver.'-'" With the exception of the well-known X-ray investigation of silver and other metals by W. A. Wood? the effect of progressive cold working has not been studied. The determination of thermal stability of silver in the work-hardened state by means of isochronal or isothermal annealing has been confined apparently to very high reductions only. In the survey made, no study was encountered which endeavored to produce a complete picture of the changes in various properties due to cold working and subsequent reannealing. To fill these gaps and to assemble data that could be used for the determination of activation energies and of frequency coefficients of primary recrystallization, a systematic experimental approach, which was developed by one of the authors, has been applied to pure silver. Material and Processing The silver used was Handy and Harman fine silver, with a spectroscopic analysis at the testing stage of Cu, 0.0001 to 0.001 pct; Te, 0.0001; Pb, Si, Ca, Mg, and Mn, traces. The material was supplied in the form of a rod 0.406 in. diam and was converted into test samples according to the procedure condensed in Table I. It should be mentioned that air annealing was adopted to simulate industrial practice, though it was realized that annealing in a neutral gas or in a vacuum would be preferred. The usual precautions have been taken to eliminate any structural changes and property changes resulting from the storage of the samples prior to annealing or testing. Thus the wires were kept at the fully annealed stage, and the final wire drawing, which produced the desired degree of work hardening, was done just prior to the final annealing or testing. During the short waiting period, the samples were kept in a thermosflask filled with ice. Even with these precautions some strain-age-hardening or self-annealing could occur. To test such a possibility, wires of different reductions were prepared in the manner adopted and portions of them were immediately tested. The remaining portions were similiarly tested after different periods of storage, both at room and melting-ice temperature. Within experimental error, all samples obtained from a wire of a given percentage of reduction yielded identical values. This result qualified the material for further tests and interpretations, because it showed that either strain-age-hardening and self-annealing were absent, or that these effects fully balanced each other. The final annealing was carried out in an electric resistance furnace automatically controlled to within a 10°F. It was realized that the temperature fluctuations were greater than desired for this type of work. TO diminish the errors due to fluctuations of temperature, the hot junction of the thermocouple was placed as close to the samples as possible; the time of soaking was reduced to 15 min; and the number of samples annealed at different temperatures was increased. It will be seen from Table I that some tests were performed on the same material at rising temperature. These will be discussed elsewhere. Room temperature testing was limited to the determination of some of the mechanical properties that are known to be additive in a degree sufficient to be used for indirect study of the kinetics of the reannealing process, Tensile tests, carried out on a manually operated J. Camillon machine, accurate to within permitted the determination of the ultimate stress (U.S.1 and of the 2 in. elongation, (A,). The proof stress (d,e) has been determined from a series of bend tests carried out on a Tinius Olsen Stiffness Tester by using the offset method. This involved accurate determination for each sample of load-angular deflection curves, finding a

Jan 1, 1952

By J. R. Lucas, H. E. Rutherford

The primary objective of this research was to evaluate the feasibility of ultrasonic testing for the purpose of analyzing the structure and properties of rock material. A secondary objective of this study was to determine experimentally the elastic wnstants of various rock specimens with the use of ultrasonic equipment. Elastic constants can definitely be determined quickly and accurately by ultrasonic investigation. With proper equipment there are indications that ultrasonic waves could be utilized in the detection of flaws, such as fractures and planes of weakness, measurement of thickness, and the study of structure of rock material. Ultrasonic principles have been applied in many industries for the purpose of determining the structural characteristics of various materials. The principal applications of interest here are detecting flaws, measuring thicknesses, and determining elastic constants. The main advantage of ultrasonic analysis is that it is nondestructive. It also has extreme sensitivity, high penetrability, good accuracy, rapid response, and the necessity to have access to only one side of the specimen. These various applications and advantages lead one to think that ultrasonic principles might be applied to rock material in situ for purposes of analyzing its structural characteristics. Therefore, the primary objective of this research was to evaluate the feasibility of ultrasonic testing for the purpose of analyzing the structure and properties of rock material. A secondary objective of this research was to determine experimentally the elastic constants of various rock specimens with the use of ultrasonic equipment. The term ultrasonics is given to that branch of acoustics dealing with periodic sounds whose fre- quencies are above the audible range or above approximately 15,.000 to 20,000 cps. The first practical production of this high frequency sound was made possible after World War I due to developments of electronically controlled sound wave sources. At the present, the maximum practically attainable ultrasonic frequency is approximately 1000 megacycles per sec. Sound waves of sufficiently high frequency can be made to travel in a beam with little spreading. Therefore, such a beam can explore a material and detect nonhomogeneities in it by reflection. This is the principle of the ultrasonic reflectoscope invented by F. A. Firestone' in 1942. An ultrasonic beam, on pulse-penetratink a solid material medium, produces an echo when it strikes a flaw which has different acoustical properties than the surrounding medium. This echo can be detected by the same transducer which sends out the original pulse. This principle is the basis of the important industrial techniques of nondestructive ultrasonic testing of metals and other solid material. Later developments in the field of ultrasonic testing of solid material have been mostly improvements in equipment and instrumentation. To date, most of the industrial applications of ultrasonic analysis of solid bodies have been in the aircraft, electrical, and nuclear energy fields on the nondestructive testing of metal. The one solid material similar somewhat to rock material, upon which some work has been done to apply ultrasonic testing techniques to study structural integrity, is concrete. Jones and Gatfield3 briefly summarize this work on concrete. Their basic conclusion was that the strength of concrete was a function of the change of the longitudinal sound wave velocity in the concrete. Only recently has any extensive study been made to apply ultrasonic testing techniques to rock material. Lutsch studied rock material by an ultrasonic pulse method to determine the extent and degree of fracture of rock faces. Lutsch states that the number of observed reflections is a measure of the degree of fracture and that only ultrasonic waves are able to detect fractured zones subjected to high pressure. Suzuki, Sasaki, and Siohara5 studied the characteristics of the sonic wave in rock for propagation over a wide range of wave lengths. They indicated that, in rock, the propagation constant and attenuation of the

Jan 1, 1962

By E. A. Hopkin

Laboratory tests conducted by the author. together with actual field experience in Canada. have indicated the magnitudc of some of the factors affecting ability of drilling mud to clean the hole. A correlation was observed between funnel viscosity and particle slip velocity. A relationship was also observed between the Bingham yield value of the mud and the particle .slip velocity. Laburatury tests indicated little change in slip velocity with funnel viscosities up to ahout 80 sec/qt or to yield values of aboul 15 lb/100 .sq ft. The lip velocity of the partic1e.s. studied vuried from 160 ft/min with water to neerly zero for high mud viscositie. lncreasing the mud density, creating laminar annular mud flow or rotating the drill pipe Mlay also improve the carrying capacity of mud. Field tests indicated that during fast upper-hole drilling, the rate of cutting removal must he sufficien to maintain the concentration of cuttings in the annulus at less than 5 percent by volume to prevernt balled-up drill collars and .stuck drill pipe. INTRODUCTION In the Mid-Continent area, hole cleaning during rotary drilling normally involves the use of low-density drilling muds with funnel viscosities varying from 26 to 80 sec/qt. However, frequently it is necessary to raise the mud viscosity in excess of 200 sec/qt to clean the hole. In addition, field experience has indicated that during very fast upper-hole drilling, annular mud velocities considerably in excess of the maximum slip velocity of the cuttings (normally considered to be 120 to 150 ft/min) are necessary to prevent balling the bit and drill collars. In view of these variations in mud properties and circulation rates necessary to clean the wellbore, a study of factors affecting hole cleaning and the relative magnitude of each was undertaken. The study was also prompted by the knowledge that a drilling mud with properties close to those of water would drill at rates several times that of a viscous mud. The carrying capacity of these near-water muds was not clearly understood, however, and many drillers were reluctant to use them. DISCUSSION EFFECT OF MUD PROPERTIES ON DRILLING RATE The effect of mud properties on drilling rate has been studied by a number of investigators. 1t is clear from their work that mud properties close to those of water will significantly improve drilling rate and bit life. If the water-type mud will also effectively clean the hole and cause no logging or formation impairment problems, the choice of an appropriate drilling fluid is clear—use water. Often, however, a water-type drilling fluid is not capable of effectively cleaning the hole. THEORY OF PARTICLE SETTLING The forces acting on a particle that is allowed to settle through a fluid quickly reach equilibrium, and the particle settles at some constant velocity referred to as the slip velocity. The slip velocity of any particle depends upon a number of factors such as density and viscosity of the fluid, the volume, specific gravity, shape and roughness of the particle, and upon the shape and area of the projected face of the particle at right angles to the direction of relative fluid solid movement. Brown' expressed this relationship for spheres in Newtonian fluids in the following equation. where v, = slip velocity D, — diameter of sphere p, = density of spheye p, = density of liquid /a = friction factor g = constant. The friction factor f, varies as the size, shape, surface roughness and slip velocity of the body, and as the density and viscosity of the fluid varies. WaddelV ound experimentally that where dynamic similarity exists. f, was a function of the particle Reynolds number (NRe) of the sphere (Fig. 1). Fig. 1 shows that f, for spheres varies from over 10 for low NKe numbers to 0.44 for N,,. over 600.

By J. Washburn

Two simple types of dislocation distribution were introduced into zinc crystal specimens and the effect of each on the stress-strain curve was investigated. Quantitative results were obtained for simple edge dislocation arrays and for an array of screw dislocations lying in the slip plane. A CCORDING to present knowledge, the disloca-tions present in large annealed metal crystals can be divided into two somewhat arbitrary groups: 1—single dislocation lines distributed more or less at random or forming elements of a three-dimensional network in which the distance between adjacent dislocations is of the order of 10 2 to lo-' cm and 2— widely separated planar arrays of edge dislocations forming dislocation walls or small angle boundaries within which adjacent dislocation lines are spaced at much smaller distances (lo-' to 10- hm). The former can be considered as a dislocation interpretation of the mosaic crystal proposed by Darwin and Ewaldl, ' 40 years ago to account for anomalously high integrated intensities of X-ray diffraction maxima. Small angle boundaries, although now known to be present in most single crystals used for mechanical testing, were not generally recognized by the early workers. This was partly due to the fact that only recently have improved X-ray and metal-lographic techniques been available for checking the macroscopic perfection of crystals."" It has long been known that changes in growth conditions and in annealing procedure, which might logically be expected to cause variations in the structural details of both the dislocation network and of dislocation boundaries, produce marked variations in some mechanical properties such as yield strength." However, no quantitative experimental correlations between changes in dislocation distribution and changes in mechanical properties have yet been made. Such a correlation has been difficult to obtain because, even when great care is exercised to keep the histories of a number of single crystal specimens identical, it usually has not been possible to avoid considerable variation in macroscopic per- fection.' The number and orientation of dislocation boundaries vary from specimen to specimen. This has probably been an important contributing factor to the large scatter in the results of most mechanical measurements on pure single crystals. Some recent experiments"% ith single crystals of zinc have shown that the presence of dislocation boundaries in a specimen can increase its resistance to deformation by slip. With polycrystalline aluminum and nickel, there is also evidence that dislocation boundaries within the individual grains of the aggregate can increase the resistance of the material to plastic deformation, either as measured by tension tests at room temperature or by creep tests at higher temperatures.'" " Although the foregoing observations seem to have established the fact that substructure can have a strengthening effect, the test conditions were too complex to give much information concerning the mechanism. In the foregoing cases, a network of intersecting boundaries having various orientations and boundary angles were present. Before their apparent strengthening effect can be understood, it will be necessary to isolate and study separately the effect of a number of variables: 1—boundary angle, 2—boundary orientation with respect to the active slip direction, 3—number of boundaries, 4—intersections of boundaries, 5—detailed structure of the boundaries, and 6—interaction of impurity atoms with dislocations in boundaries. The object of the present work was to study the effect of dislocation boundaries on flow stress under the following simple experimental conditions: 1— substantially pure shear deformation and 2—boundaries of controlled angle, orientation, and number. In this way, it might be possible to distinguish the important variables from the relatively unimportant ones. Experimental Procedure Stress-strain curves of hexagonal metals are generally nearly linear even out to very large strains."

Jan 1, 1956

By J. N. Ong, J. P. Ratledge, J. H. Boyce

SINCE German operators opened the Tsumeb mine in the early 1900's, continuous operation has been interrupted only by enforced shutdowns during two world wars and the depression of the 1930's. Original metallurgical practice was blast furnace smelting. This was applicable only to low zinc ore, leaving large tonnages of high zinc ore to be stockpiled on the surface. A gravity concentrator using tables, buddles, and jigs operated for several years, but differential flotation of the ore did not get beyond the experimental stage. When the property was put up for sale by the South African Custodian of Enemy Property there was an estimated 434,000 tons of ore on surface dumps. The dump material, assaying 4.48 pct Cu, 15.8 pct Pb, and 10.9 pct Zn, had become highly oxidized during a stay of many years on the surface. But these dump ores had to be used in evaluating possible metallurgy because the shaft became flooded after the 1940 shutdown and underground ore was unavailable. Many companies examined Tsumeb but quickly lost enthusiasm because of the formidable metallurgical problems presented by the dump ore. However, on the basis of extensive test work, the present company decided that differential flotation would be successful and purchased the property after competitive bidding. Geology and Mineral Association is Complex The Tsumeb mine lies near the northern boundary of South West Africa at an altitude of 4200 ft. The village of Tsumeb is 335 air miles northeast of Wal-vis Bay, territorial port of entry. The orebody is a hydrothermal replacement deposit associated with an irregular intrusion of aplite cutting folded pre-Cambrian dolomite beds. In plan the deposit is a lens of 250x600 ft maximum dimensions. In section the orebody dips 55" south from the surface to 2000 ft, below which there is a reversal in dip to 75" north. Mineralization is localized in the aplite and in the adjoining brecciated dolomite. In the upper levels the ore is largely confined to a single lens, but below the 1890 level massive sulphide ore forms north and south lenses that partially enclose a pipelike body of medium to low grade disseminated ore, part of which is of too poor a grade to mine. Drilling below the 24th, or bottom level, has disclosed that a high percentage of the mineralization from the 3000 to 3300-ft horizons is comprised of copper and lead oxides. The deep oxidation may be local, since it appears due to circulating waters in a major fault cutting the orebody. Tsumeb ranks as one of the highest grade base metal deposits in the world. It is geologically and mineralogically famous for 41 copper, lead, zinc, vanadium, and germanium ore minerals, but its complex mineral assemblage is not attractive to metallurgists. In addition, there is a gradual change in oxidation intensity from the upper levels to the lowest level now operating, which is the 24th. This is well illustrated by the copper minerals. In the upper levels malachite and azurite are predominant, in the intermediate levels chalcocite, and in the lower levels tennantite. Throughout the mine there are sufficient heavy metal soluble salts to activate zinc, and large amounts of depressants are required even for so-called clean sulphide ores. When the same sulphide ore is exposed to prolonged oxidation aboveground, as was the case with the dump ores, reagent requirements become fantastic. Plant Construction First staff members arrived at Tsumeb in March 1947, and by May essential services had been restored and mine unwatering began. In 2 1/2 months company employees built a temporary jig and sorting plant for treating existing dumps to provide a saleable product during high metal prices. Meanwhile, concentrator design and construction was contracted to a South African firm, with subcon-

Jan 1, 1956

By W. W. Mullins

The development, by the mechanism of volume diffusion, of a grain boundary groove on an interface separating a solid phase and a saturated fluid phase is calculated under the following assumptions: 1) isotropy of the interfacial free energy 's, 2) applicability of the Gibbs-Thompson formula relating curvature and chemical potential, 3) a nearly planar groove surface. The groove profile is found to have a .fixed shape and linear dimensions that are proportional to (time)1/3. The constant of proportionality is evaluated and involves ?s in such a way that the latter my be evaluated from grooving kinetics. A grain boundary that intersects an interphase interface will tend to produce a groove along the line of intersection (Fig. 1). The ultimate motivation for the formation of the groove is the reduction in interfacial free energ that occurs as the grain boundary contracts. Smith has discussed the way in which the free energy of the interfaces determines their dihedral angles at the groove root and has given a detailed analysis of the effect of the dihedral angles upon the nature the microstructures developed in polyphase alloys. Herring2 has extended the considerations to the case in which the free energy of an interface depends on its orientation and has thus added torque terms to the condition for interface equilibrium. Although the grain boundary and the interphase interface may quickly achieve the proper equilibrium angles where they intersect, as determined by the balance of equivalent tensions and torques,"2 the groove will generally continue to grow (though with decreasing speed). Thermodynamically, this continued growth reflects the fact that the lowest free energy cannot be achieved until the entire grain boundary has been eliminated; mechanistically, the growth occurs in response to inhomogeneities of chemical potential that are caused by the constraint of fixed dihedral angles at the groove root. The latter point is illustrated in Fig. 1, which shows that atoms* near the groove are on the convex side of a cylindrically curved surface and therefore have a higher chemical potential than atoms on the flat interface beyond. Thus atoms tend to leave the curved groove shoulders and force the groove to deepen. When both phases are solid additional chemical potential gradient may arise from whatever strain fields are necessary to insure continuity of material across the interface. In the discussion that follows, this complication due to strain will not occur since we always assume one phase to be a fluid and the other a solid. The transport processes that may operate to permit growth of the groove are surface (interface)* diffusion, volume diffusion in the phase on either side of the interface, and evaporation-condensation when one phase is gaseous. (Also a melting-freezing process is responsible for groove enlargement on a solid-melt interface as discussed in Sec. VI). The theory of grain boundary grooving has been discussed in detail for the processes of surface diffusion and of one type of evaporation-condensation.3'4 The theoretical predictions for the mechanism of surface diffusion have been confirmed in an experimental study of grooving kinetics in copper.5 In this paper, the theory of groove development by volume diffusion will be presented. Volume diffusion can occur either by atomic migration in the solid S or by diffusion of S atoms in the fluid phase, or solvent, adjacent to the groove surface. As discussed in Sec. V, volume diffusion in the solid should be less important than surface diffusion in forming a groove. Apart from verifying this statement then, the main interest of the present analysis centers on diffusion in an external solvent. The solvent may be either a liquid (e.g., water, or-

Jan 1, 1961

By H. R. Hose

The total crude fluorspar reserves in Western Europe, including the USSR and the Soviet sphere, Thetotalare estimated to exceed 17 million metric tons. The total fluorspar production in 1951 in Western Europe, excluding the USSR and Soviet sphere, amounted to 371,109 metric tons. The chief fluorspar-producing countries in Europe, excluding Russia and the Soviet sphere, are France, Western Germany, Italy, Spain, and the United Kingdom. TOTAL crude fluorspar reserves in western Europe, containing more than 35 pct CaF2, are estimated at 12 million metric tons, while reserves in the USSR and Soviet sphere may exceed 5 million metric tons. The bulk of these reserves are concentrated in the USSR, Spain, United Kingdom, Western Germany, and Italy. Since published estimates of the tonnages of individual mines and explored deposits are not available for most countries in Europe, the estimates given in Table I for individual countries are necessarily approximate, as they have been compiled from various sources and modified and combined according to the author's judgment. The majority of fluorspar deposits in Europe belong to the late Paleozoic metallogenetic epochs and have been found within or along the borders of the Hercynian massifs. Deposits in the Central and Esterel massifs of France, those of Western and Eastern Germany, Sardinia, the Catalonian coastal range and the Sierra de los Santos in Spain, and those of Devonshire and Cornwall belong to the Hercynian metallogenetic epochs. The deposits in southern Norway and Sweden belong to the middle Paleozoic or later, those of northern England to the late Paleozoic or later, those of northern Spain and Greece to the late Mesozoic, and those of northern and probably central Italy and Switzerland to the early Tertiary. Fluorspar occurs typically in veins, lenses, and stringers, but also in bedded replacement deposits and pockets, and may be colorless to white, yellow, green, pink, brown, blue, or purple to almost black. Except for the colorless variety, the only kind which can be used for the optical industry, the color of the fluorspar does not affect its ultimate use. Crystalline cubic or octahedral fluorite of CaF2 composition, with 48.9 pct fluorine and 51.1 pct calcium, has a specific gravity of 3.18. The ore in place, however, usually averages 3.0 metric tons per cubic meter owing to the quantity of other minerals asso- ciated with the fluorspar in the veins and the physical state of the fluorspar, which may vary from sugary to massive crystalline or microscopic inter-growths with barite or quartz. Barite of 4.5 sp gr, quartz of 2.66 sp gr, and chert and calcite are commonly associated with fluorspar. Other minerals usually present in lesser amounts are celestite, wad, silver, lead, zinc, copper, iron, and uranium minerals. In some cavity fillings the rhythmic deposition of the fluorspar, barite, and quartz into successive crusts may make it possible to handpick the crude ore on belts or to separate the fluorspar from other minerals while the actual mining is carried on. Where metallurgical grade lump spar is required for foundries, separation of quartz and barite may be made also by jigs and heavy media, and in some mines the lead and zinc sulphides may be separated and recovered by vibrating tables. However, except in the case of unusually high grade deposits, acid grade fluorspar is obtained by flotation. By this process fluorspar deposits grading down to 35 pct CaF2 in the crude ore can be worked at a profit when fluorspar, lead, zinc, and silver prices are high, as the sulphides of these ores can be separated from the fluorspar by flotation and concentrated.

Jan 1, 1956

By Dennis H. Laubscher

INTRODUCTION The selection of mass mining methods is the situation facing not only planners of new operations, but also those involved with cur- rent operations, including the eventual change from open-pit to underground. Increasing ground control problems on many mines, plus a better understanding of dilution and ore loss problems have meant a review of current mining methods and support techniques. Experiments are only successful if conducted in the right mining environment and on the right scale. Mining personnel have been known for their conservatism and will tend to persevere with an established method rather than change; often, hidden costs will obscure the correct economic assessment. An established mining sequence is not necessarily correct in the long term. However, recommendations to change are usually met with opposition because of inconvenience, temporary production problems and the desire for a trouble-free guarantee. In any planning exercise, care must be taken that time and money are not wasted in trying to achieve the unattainable. During the decision-making period, production personnel must be involved, and, if possible, they should visit similar omrations to that proposed. Co-operative production personnel will help ensure success. Descriptions of mining methods are available in technical papers and books, and it is not intended to discuss this aspect, but, rather, the various factors which must be recognised before arriving at a final selection. In another paper presented at this Conference (Heslop and Laubscher, 1981) factors affecting ore recovery and dilution are discussed in greater detail for various cave mining methods. PRELIMINARY CONSIDERATIONS Comprehensive Geological Data. Geological information is available during the exploration stage, but, often, core from exploration drilling is not analysed with the selection of a mining method in mind. Drilling costs are high, therefore the maximum benefits must be derived from this operation. Holes which have not intersected ore may provide data on possible shaft sites, and 35 mm colour slides of core, sound logging and geomechanics classification, will provide a record which can be used with confidence at a later date. Intersections of the various rock types should be kept for future study; for example, is weathering likely to be a problem, bearing in mind that this can be accelerated in the warm, humid atmosphere of an underground mine. The accumulation of data required to select a mining method starts with initial geological work in the target area, whether this be surface mapping or a diamond drill hole. Publications. As technical papers, reports and books are used in the selection of mining methods, an appeal is made to authors to describe the geological environment so that readers can relate to their own conditions. Not enough emphasis is given to the problems experienced and the techniques employed to overcome them. Follow-up papers are seldom written and we should be prepared to discuss our failures. Diagrams are often misleading, as the ideal and not actual situations are depicted. The caved ore/waste interface is not a straight line, and whereas this may not be significant in a diagram of a 200-117 draw height, it certainly is in sub-level caving with draw zones only 1 - 2 m width but up to 20 m high. SUMMARY OF FACTORS AFFECTING THE SELECTION OF UNDERGROUND MASS MINING METHODS (a) Regional rock stresses and mining geometry. (b) The geomechanics rock mass classification of the orebody and surrounding rock mass. (c) Ratio of the surface area of the ore/unpay interface to the contained ore which determines ore losses and dilution. (d) The cavability and fragmentation data of the ore and hangingwall. (e) The mineral distribution in the orebody and its dilution zone.

Jan 1, 1981

By M. R. Geer, H. F. Yancey

John Grifien (Pittsburgh)—I wish to congratulate the authors on this paper, which, I am sure, will promote a clearer conception of the various criteria which have been advanced as measures of coal-cleaning performance. Their clear descriptions of the more important criteria that have been advanced and explanations of their meaning and application have been sorely needed and, if widely promulgated and followed, should remove much of the confusion which, heretofore, has been evident. I suggest that much of this confusion has also arisen from lack of common agreement as to the exact meaning of the words and terms used in our discussions of this subject. I am sure I have been equally guilty in this respect and suggest it is time that we select a committee to study vocabulary as well as criteria, so that common understanding and agreement can be had. Thus, I suggest, that the title of this paper should have used the words "coal-cleaning performance" and not "coal-washery performance." My understanding is that "washery" refers to a complete plant and it has additional functions to that of coal-cleaning, such as control of size, moisture, etc. Also, I do not agree with the authors that the formulas given in their paper, the Fraser and Yancey formulas, are necessarily the only ones that can be called efficiency formulas. When a dictionary is consulted one realizes that the words "efficiency" and "efficient" have not precise meanings but only very general ones and must be further defined for each particular use, if they are to have any precise meaning. To my mind, the first of the Fraser and Yancey formulas given should never be used as expressing "efficiency" alone but only by the fuller phrase which truly expresses the kind of efficiency it states, which is "coal recovery efficiency." For complete clarity we then need only define "coal" for the particular circumstances under which the formula is used. This would recognize the fact, fully explained by the authors, that the limits in coal qualities imposed by the market have imposed a factor—and a variable factor—which has influenced any answer obtained by this formula. Such a procedure makes it entirely practical and logical to use the values of any of the qualities of coal—ash, sulphur, phosphorus, specific gravity—or a combination of them to define what is coal for that particular use of the formula. Further, it is clear to me that the criteria to be used must be dictated by the objective in view and the use for which the data are obtained. The authors clearly point out that the Fraser and Yancey coal-recovery efficiency formula is influenced by three factors, "one is determined by the coal, one is dictated by market or use conditions, and one is an inherent characteristic of the cleaning unit itself." The formula which uses the inverse of misplaced material as a measure of efficiency is also a coal recovery efficiency formula and is influenced in like manner by these three factors. As the authors point out, both are useless in obtaining data which enables a direct and valid comparison of the performance of a given cleaning unit on two coals where the other two factors vary or of the performance of two or more cleaning units of different types unless the values of the other two factors are identical. Much of the confusion in our discussions of and literature on coal cleaning has come from failure to understand clearly this fact. Many such comparisons have been made from which erroneous conclusions have been drawn. I am, therefore, particularly glad to see the authors' emphasis on 4?-1e criteria which indicate the "sharpness of separation. I feel that these are the essential criteria

Jan 1, 1952

By P. B. Mee

The secondary re crystallization behavior of two vacuum-melted, nominally 3 pct Si-Fe alloys has been studied, one alloy being produced from pure electrolytic iron and semiconductor-grade silicon and the other from commercial-purity hot band. The vacuum-melted and vacuum-remelted alloys were found to develop {110}(hhl) and {lll)(hkl), respectively, on annealing in high vacuum and {100}(0kl) and {11l}(hkl), respectively on annealing in pure hydrogen of dew point, < — 60°C. H2S doping of the hydrogen or annealing in commercial argon was found to effect a reversal for the vacuum-remelted alloy from (111) to (100) secondary recrys-tallization, while prolonged vacuum annealing at 2 x 10-6 Tow resulted in a tertiary re crystallization from (111} to (110). The growth selection of the {lll}(hkl) component was found to be governed predominantly by the {111}/planar misorientation, the maximum deviation of the resulting secondaries being 5 deg. It is considered that the driving force for {111}(hkl) secondary recrystallization arises from the preferential lowering of ?111, possibly by phosphorus or nitrogen diffusion, just as oxygen and sulfur under certain conditions have been found to preferentially lower ?100. When heavily cold-rolled metals are annealed at high temperatures, primary recrystallization usually occurs rapidly and may be followed by considerable grain growth. However, in the presence of a fine dispersion of inclusions1"3 or with a strong matrix preferred orientation4&apos;&apos; the matrix may be stabilized and a secondary recrystallization may then be effected. Also, in vacuum-melted Si-Fe it has been shown possible to develop {100}(001) and {110}(001)6 surface energy driven secondary recrystallization textures. Further, it has been found that, on annealing very pure metals, grain growth normally ceases when a grain size approximately twice the strip thickness is acquired, due to the formation of V-shaped thermal grooves which result in an equilibrium being set up between surface and grain boundary stresses. If, however, a surface energy difference ??s, exists between adjacent grains (of the order of a few percent of the grain boundary energy ?b), then according to Mullins8 a secondary recrystallization may be effected, since the grains having lowest ?s would grow at the expense of their higher-energy neighbors. For clean bee metal surfaces ?110 should be lowest; however, for 3 pct Fe-Si (100) secondary structures have frequently been developed and have been attributed by Walter and Dunn9 to an alteration of the relative surface energies due to the preferential chemisorption of oxygen on (100) planes. Kohler,10 however, indicated that this reversal may be achieved by employing minute quantities of highly polar compounds in the annealing atmosphere, i.e., sulfur compounds, in par- ticular H2S being beneficial in (100) growth. This work has been verified by Kramer" using {100)/{110} bicrystals, while Mager12 demonstrated the importance of sulfur diffusion within the strip. Detert13 has intimated that carbon may be responsible for the preferential lowering of ?110 although no direct evidence has appeared yet to support this supposition. It must , be appreciated that the above-mentioned examples of surface energy driven secondary recrystallization were obtained with very pure vacuum-melted materials with oxygen contents (which is now known to be a critical factor") less than 35 ppm. During the course of a textural study on Si-Fe it has been found that under certain conditions (111) secondary recrystallization can be obtained by what is believed to be a surface energy growth selection mechanism. The purpose of the present paper is to briefly describe this result and to try and postulate the possible causes. EXPERIMENTAL Two vacuum-induction-melted, nominally 3 pct Si-Fe alloys were produced, one from pure electrolytic iron and semiconductor-grade silicon designated A and the other from commercial-purity hot band, designated B.

Jan 1, 1969

By W. F. Kieschnick, C. C. Miller, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By F. F. Skiba, J. E. Warren

An idealized miscible displacement process in a three-dimensional, heterogeneous porous medium has been studied via experimental computation based on a "Monte Carlo"&apos; model. The macroscopic dispersion which results solely from variations in the permeability of the porous system is related to the scale of the heterogeneity as well as the distribution function for the permeabilities. The interpretation of laboratory data is often subjective and may bt? misleading since ambiguities are not always recognized. Furthermore, an experiment performed on a conventional oil-field core does not yield a valid measure of Macroscopic dispersion for reservoir engineering purposes since the scale of heterogeneity that is significant in the laboratory is not significant in the reservoir. The analysis of field-performance data is discussed and it is shown that a unique characterization of the reservoir can not be obtained from this information alone. A possible method based on a minimum of data, for estimating the spatial distribution of permeabilities in a reservoir is postulated INTRODUCTION Many studies concerned with diffusion and dispersion in porous media have been undertaken because of the potential importance of miscible displacement processes for increasing the recovery of oil. The results from a large number of these studies have been published; in a recent paper Perkins and Johnstonl presented a comprehensive survey of the pertinent literature and excellent appraisal of the "state of the art". In this investigation, dispersion resulting from macroscopic variations in the properties of the porous medium is of primary interest. Dispersion, in this sense, is caused by fluctuations in the velocities of the individual fluid elements as they move through the porous system. This phenomenon is the result of inhomogeneities in the permeability and/or porosity, but it can be amplified by differences in the characteristics of the fluids involved. The objectives of this study are the following: (1) to determine the qualitative manner in which macroscopic rock properties affect the observed dispersion coefficient; (2) to evaluate the possible influence of macroscopic dispersion on laboratory experiments; and (3) to appraise the significance of macroscopic dispersion with regard to reservoir performance. Investigations of this type are essential since many miscible displacement processes, while seemingly understood from a mechanistic point of view, do not behave in a predictable manner under field conditions. Although a plausible explanation is that the process is dominated by the environment, little serious effort has been devoted either to describing the reservoir itself or to determining the probable effect of the reservoir properties on the process. This study is intended to be exploratory in nature; however, it is hoped that it will provide additional insight into the physical problem and that it will suggest areas suitable for further investigation. EXPERIMENTAL COMPUTATION MODEL To limit the observed dispersion to that which results solely from variations in the properties of the porous medium, an idealized process in which one incompressible fluid displaces another identical fluid is simulated. This simulation is achieved by means of a modified Monte Carlo method — by tracking a number of mathematical particles (tracer) through the system according to the steady-state, single-phase velocity distribution. Then the system is characterized by the distribution of the residence times of the particles. Since any number of particles can be injected simultaneously (a true delta-function distribution) and only pressure conditions are imposed on the boundaries, the model is completely determinate. Furthermore molecular diffusion, microscopic dispersion, adsorption and/or reaction are automatically precluded from the model. The heterogeneous medium is represented by a rectangular, three-dimensional array of uniform, homogeneous porous blocks which are randomly arranged; it is assumed that any two opposing faces of the system are held at fixed potentials

Jan 1, 1965

By R. E. Cook

This work presents the development and application of equations of the form developed by Martin1 to describe gravity segregation performance during natural depletion. One-dimensional depletion analyses are applied to several hypothetical reservoirs. Considerable attention is given to the changes in saturation distribution in the dip direction resulting from depletion at various rates. Vertical gas saturation distribution within a sand having vertical permeability is studied to illustrate conditions which provide For low gus-oil ratio production from wells selectively completed away from sand tops, as observed from well performance. Results of performance calculations are shown graphically and illustrate the rate sensitivity of the gravity segregation mechanism and the influence of reservoir geometry and withdrawal distribution. It is shown that for sufficiently high depletion rates gas saturation distribution in the dip direction is characterized by the formation of two discontinuities, or saturation "fronts"; the updip front being the gas-oil contact of the secondary gas cap and the downdip front occurring at a position dependent upon the reservoir depletion rate, withdrawal distribution and reservoir geometry. The gas saturation in the region between fronts is shown to continually increase with time, while that downdip from the lower front remains very low and relatively stable. The effect of increased depletion rate is to reduce the region of stable gas saturation and thus enlarge the portion of the reservoir producing with continually increasing gas saturation. Special attention is given to the performance of reservoirs having sufficient vertical permeability to permit liberated gas to segregate vertically within the sand section before proceeding in the updip direction. It is shown that reservoirs of this type are far less sensitive to depletion rate due to the mechanical control of producing gas-oil ratios afforded by selective well completions away from sand tops. It is shown that gravity segregation performance is adversely af- fected by decreasing reservoir cross-section area in the updip direction. It is also shown that down-dip withdrawal concentrations can restrict gas segregation rates in the dip direction. INTRODUCTION The natural depletion performance of several large producing reservoirs in Western Venezuela has unmistakably shown the significant role that gravity forces play in governing the gas-oil ratio behavior of individual wells and the over - all pressure-production performance of the reservoirs. Analysis and prediction of the natural depletion performance of these reservoirs is of great importance in determining the economics of pressure maintenance operations. In 1957, a method for the analysis of pressure maintenance performance was presented by Martin1 which, in the original and more general form of the equations involved, provides a physically sound basis for the analysis of one-dimensional gravity segregation performance during natural depletion. The work reported herein is an application and extension of Martin&apos;s outstanding developments to a series of hypothetical reservoirs in an attempt to explain the general behavior of the gravity segregation mechanism and the influence of such parameters as depletion rate, reservoir geometry and withdrawal distribution. The study considers two types of flow: "distributed flow", where vertical permeability in the reservoir is zero and fluids flow only in the dip direction while uniformly distributed over the sand thickness; and "segregated flow", where vertical permeability is sufficient to permit gas to segregate against the sand top before proceeding updip. This latter type of flow has been recognized as an important mechanism active in the massive sand reservoirs of Western Venezuela. ANALYSIS OF ONE-DIMENSIONAL DISTRIBUTED FLOW SYSTEMS For an inclined reservoir having zero vertical permeability, the velocities of oil and gas flow at any point in the reservoir can be derived from Darcy&apos;s equations as

By C. C. Miller, W. F. Kieschnick, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By A. F. Colombo, R. T. Sorensen, D. W. Frommer

An analytical method has been developed and used in batch and continuous tests to provide initial insights into the effect of soluble calcium ion in anionic flotation of silica from iron ores. A deficiency or excess of calcium ion in pulps subjected to this type of flotation produces an impairment in flotation efficiency. Data developed in the investigation are from a single ore, but show that total calcium requirement is met from water, ore and reagent sources. In batch studies, starch additions were shown to exert no influence on the calcium level, but fatty acid and sodium hydroxide had subtractive effects. The investigation was next extended to continuous flotation testing where the general observations from batch testing were confirmed. Factorially designed experiments were performed showing that the relationship of calcium additions to flotation response was not a simple one, but tended to shift to higher additions with increased fatty acid. Nevertheless, the range of soluble calcium levels measured remained fairly constant in areas of good flotation response. It is concluded that techniques developed should be useful in removing empiricism from flotation operations in this and other systems requiring activation for success. Further development should aid in process control both through methods outlined and through investigations aimed at studying the effects of other soluble reagents. Of the major mineral commodities, iron ore was one of the last to succumb to flotation processing. Commenting on this fact, one of the speakers 1 at the convention celebrating the 50th Anniversary of flotation in the U.S.A., said ". . . in 1951 froth flotation as a means of beneficiating nonferrous minerals was a might giant and could be characterized by &apos;you name it, we float&apos; - but not iron ore". This tardiness in applying flotation to iron ores was the result of a number of factors, including economics and ready availability of direct shipping ores. Even now, when the need for beneficiation can no longer be denied, proposals for flotation of iron ores are apt to be viewed with some misgivings. This disquiet results from knowledge that wide variability, which would necessitate corresponding adjustments in reagents, often exist within even a single ore deposit. Coupled with ore variability is the fact that, at present, there is no way of quickly and precisely anticipating the direction and magnitude of reagent changes required for uninterrupted production of acceptable concentrates. Despite the long delay, iron ore flotation is now practiced commercially, although the chief applications2-4 are to specular hematites having relatively coarse liberation and low slime content. In addition, the application of flotation in upgrading magnetic concentrates seems assured. However, these flotation methods do not appear applicable to substantial tonnages of fine grained, earthy, and frequently more complex semitaconites and nonmagnetic taconites. The U.S. Bureau of Mines, in devoting its attention to the semitaconite and nonmagnetic taconite class of materials, has demonstrated that anionic flotation of calcium-activated silica can be utilized with an expected high frequency of success.&apos; Even so, it has been recognized that the flotation method is a complex one, and that the reagent suite must be carefully tailored to the feed. These conditions would be expected to offer difficulties in treating ores with the wide range of variability previously discussed. Accordingly, research was initiated to develop methods to remove much of the empiricism from the flotation operation by measuring the reagent variables within the pulp for a correlation with flotation response. A simple illustration of the technique sought would be in the well established use of pH meters to provide feedback control to reagent feeders and thereby limit acidity or alkalinity to a range producing optimum results. The first efforts in this area have been concerned with measurements of soluble calcium ion. Bureau experience in both laboratory and pilot plant over the past five years has proved that the amount of calcium

Jan 1, 1965