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By Vard H. Johnson

IN 1943 the U. S. Bureau of Mines undertook drilling in an effort to develop new reserves of coking coal in an area near Paonia, Colo., as a part of an attempt to alleviate the shortage of known coking coal of good quality in the western United States. Geologic mapping of the area was undertaken by the U. S. Geological Survey with the purpose of first furnishing guidance in location of drillholes and later aiding in interpreting the results of the drilling. The drilling program was under the general supervision of A. L. Toenges of the U. S. Bureau of Mines. J. J. Dowd and R. G. Travis were in charge of-the work in the field. Geologic mapping was started by D. A. Andrews of the Geological Survey in the summer of 1943 and was continued from the spring of 1944 to 1949 by the writer. The first few holes drilled failed to locate coking coal, but in the summer of 1944 coking coal was discovered by drilling 6 miles east of Somerset, Colo., the site of present mining. In the succeeding years, 1945 to 1948, 100 to 150 million tons of coal suitable for coking were blocked out by drilling. The ensuing discussion of the geologic controls on the distribution of coking coal in the area is based on the geologic mapping as well as the drilling done in the Paonia area, more complete descriptions of which have appeared or are in process of publication.1-5 In order that the possible geologic controls affecting the present distribution of coking coal may be considered, it is necessary to discuss briefly the indicators. of coking quality coals. Coking Coal Coal that cokes has the property of softening to form a pastelike mass at high temperatures under reducing conditions in the coke oven. This softening is accompanied by the release of the volatile constituents as bubbles of gas. After release of the contained gases and upon cooling, a hard gray coherent but spongelike mass remains that is referred to as coke. This substance varies greatly in physical properties and, to be suitable for industrial use, must be sufficiently dense and strong to withstand the crushing pressure of heavy furnace loads. Western coals have a generally high volatile content and therefore form a satisfactory coke only when they attain a rather high fluidity during the process of heating and distillation in-the coke oven. When this high degree of fluidity is developed, the volatile constituents escape and leave a finely porous coke. On the other hand, when the degree of fluidity is low the product is an excessively porous and therefore physically weak mass that is called char.6 Small quantities of oxygen present in coal are believed to decrease the fluidity of the material during the coking process and to favor the development of char rather than coke. In consequence, coal chemists have for some time considered the possibility of developing an index to coking. qualities by inspection of chemical analyses of coals.7 A formula has now been developed that does permit a rough preliminary estimate of the cokability of coal on the basis of the analysis on an ash and moisture-free basis. Coals may be eliminated as possible coking fuels if the oxygen content is greater than 11 pct. Similarly the ratio of hydrogen to oxygen must be greater than 0.5 and the ratio of fixed carbon to volatile constituents must be greater than 1.3. If the coal, on the basis of these limiting factors, appears to have possible coking qualities, the following formula permits determination of the coking index: Coking index =[ a+b+c+d 5] a equals 22/oxygen content on ash and moisture- free basis, . b equals two times the hydrogen content divided by oxygen content on moisture and ash-free basis, c equals fixed carbon/1.3 x volatile matter, and d equals the heating value on moist, ash-free basis/13,600. Coking indices higher than 1.0 suggest that the coal will coke, and indices above 1.1 indicate good coking tendencies. Although generally usable, this formula is not completely satisfactory because the percentage of oxygen shown in ultimate analyses is derived only by difference; i.e., by subtracting the sum of the percentages of the constituents determined analytically from 100 pct.8,9 Although the coking index indicates the coking tendencies of coal, it is necessary to make physical tests of coke before its industrial value can be determined. The U. S. Bureau of Mines has developed a standard procedure for determining the approximate strength of coke that would be formed from a given coal. In this test one part of ground coal, mixed with 15 parts of carborundum, is baked to form a standard briquette. The weight, in kilograms, necessary to crush the briquette is termed the agglutinating index. This test determines the relative fluidity attained in the coking process by measuring the cementing strength of the coal in the briquette. A

Jan 1, 1952

By G. J. Dickman, W. N. Thomas

The factors involved in selecting, a drive system for a grinding mill, including gearing arrangement, motor selection, and electric-supply system limitations are reviewed. Equipment costs are evaluated on a dollar per horsepower basis and starting performance is analyzed, the latter making use of a recently developed computer program. The present interest in large-diameter grinding mills and the rapidly rising cost of the drive in proportion to the cost of the mill establishes a need to explore the drive system in detail. The drive for a 7 to 8,000 hp mill will cost from $350 to $600,000 which represents nearly half the total cost of the mill package, and requires as much building space as the mill proper. Some of the drive components require a longer time to manufacture and the installation time and costs are equal to those for the mill. It is apparent that the drive has become a dominant factor in the overall mill design consideration. A new plant requires a tremendous investment in both time and money. With the high degree of competition in the mining industry, low capital cost is an exceedingly important factor in the development of a project. It is just as important, however, to insure that the equipment is going to perform satisfactorily for the anticipated life of the project without adding unplanned operating, maintenance, and replacement costs. This is the position in which the engineer or designer usually finds himself and is really one of his primary functionsestablishing a realistic compromise between cost and performance. Large primary grinding mills can represent a major portion of the cost of a plant and the drive system accounts for a substantial part of this cost. These facts justify a careful analysis of the drive requirements and all of the factors involved in ultimately arriving at the best system for the lowest cost. A number of excellent papers have been published on various aspects of mill drives. The authors have used information from these papers in making a study of a drive for a 7600-hp, 32 x 12-ft autogenous mill. This was a broad investigation, including mechanical and electrical design, layout, performance, and maintenance considerations, and overall economics leading to the selection of the optimum system for that mill. This paper was developed from the study and includes information applicable to large mills in general. For a successful and economical application, the drive must be considered as a system and all of the components analyzed to determine their effect on the system. This requires the participation of the mill designer, gear, and other mechanical component manufacturers, motor manufacturer, plant designer, and operator. A careful analysis of the mill torque requirements is first necessary to provide a basis for selection of the mechanical and electrical drive components. Because of manufacturing limitations on the size and capacity of gearing available for these low-speed applications, an evaluation of costs for various gear ratios and configurations in conjunction with motor speeds is required. Consultation with the power-supply company is necessary to determine limitations on motor-starting disturbances and to analyze operating costs on the basis of existing rate structures and low characteristics. Finally, consideration must be given to the drive arrangement and its affect on plant layout, space requirements, and location of auxiliary equipment for the selected process. There are presently three basic schemes for driving a mill. The first is a direct drive by a motor operating at mill speed with no gearing. The second is by a higher-speed motor through a trunnion-connected gear drive. The third is by a motor through the more conventional pinion and ring-gear with the option of an interposing gear box to permit greater motor speed than pinion shaft speed. [(Fig. 1.)] Several manufacturers have or are presently developing motors which drive the mill directly without the use of gears. One arrangement has the motor armature intimately surrounding the mill shell-discharge spout or extension of the trunnion journal. The motor stator is then supported independently and surrounds the shell or trunnion-mounted rotor. Another variation utilizes an independent mill-speed motor connected to the trunnion by a drive shaft and flexible couplings.

Jan 1, 1972

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By A. W. Bethune, L. M. Pidgeon

The equilibrium vapor pressure of zinc has been determined over the systems: ZnS(s) + Fe(s) = FeS(s) + Zn (vapor) and ZnS(s) + 2Cu(s) = Cu2S(s) + Zn (vapor) by reacting the components in an evacuated tube containing a thin copper fiber, and allowing equilibrium to be established with respect to the brass formed and the zinc in the vapor phase. The composition of the brass formed was determined and equilibrium vapor pressure values obtained from existing data. Between 850' and 1000°C, values for the first reaction ranged from 8 to 58 mm Hg; for the second reaction from 1.8 to 22 mm Hg. THE direct reduction of metallic sulphides may be indicated by an equation of the form MS + X = XS + M [1] where X is some suitable reducing agent. In the case where M is a metal of relatively high volatility, the use of vacuum will displace the equilibrium to the right at comparatively low temperatures in the face of the usually unfavorable thermochemistry. For this technique to be feasible, MS, X, and XS, must of course be nonvolatile compared to M. In this regard, zinc becomes an obvious metal both from the point of view of its volatility and the fact that most commercial ore deposits of this metal occur as the sulphide, and its direct reduction would avoid the expensive roasting process necessary prior to present day reduction methods. Two reducing agents are of interest, namely copper and iron, with the former having the added attraction of being relatively easily regenerated by oxidation in the copper converter. The possibility of these reactions has been considered before. Imbert1 patented a process whereby zinc sulphide was reduced by either copper or iron. The process as described took place at atmospheric pressure and, at the high temperatures required, the system was molten, resulting in the formation of a matte with the consequent reduction in the activities of the reactants. Peterson2 did further experimental work on these reactions and, although promising results were obtained on a small scale, attempts to increase the size of the furnace led to excessive "blue powder" formation. The early workers failed to realize the large reduction in temperature afforded by the use of vacuum and its desirable results. More recently, the direct reduction of zinc sulphide by iron has been the subject of a thermody-namic investigation by Kelley,3 and Gross and War-rington' have studied the kinetics of the reaction in the temperature range 900" to 1000°C, their experiments being conducted using vacuum and indicating that the reaction would proceed practically to completion in 1 to 3 hr, depending on the temperature. A qualitative examination of the system ZnS-Cu carried out at this University indicated that 98 pct of the theoretical zinc in the charge could be recovered in 1 hr at 1000°C when operating under reduced pressure. The purpose of this research program was to study the equilibrium of the two reactions. During the investigation, reference to the experimental work of Schenk5 was found but, due to lack of detail in the report, it was felt that it would be desirable to continue the equilibrium measurements. Selection of Method The measurement of vapor pressure of metals presents obvious problems resulting from the high temperatures which must be employed. In the present case, the production of the "reaction pressure" introduces a further difficulty since a chemical reaction must proceed before any metal vapor pressure is produced, resulting in depletion of the re-

Jan 1, 1954

By L. A. Bromley, A. W. Petersen

The van Arkel-deBoer method for producing ductile titanium by thermal decomposition of Til, vapor and deposition on an electrically heated filament is modified by film boiling Til liquid on a heated filament, resulting in similar titanium deposition on the filament and liberation of gaseous iodine. The deposition rate is higher and the energy requirement smaller than in the van Arkel process. Many problems must be solved before the process is commercially feasible. TITANIUM of 99.9 pct purity, called ductile titanium, has been produced by a modification of the van Arkel-deBoer&apos; method. In the van Arkel-deBoer method, an electrically heated wire is suspended from two electrodes, which are placed in a container holding TiI, vapor at a low&apos; vapor pressure (usually <5 mm Hg). The vapor diffuses to the hot wire, usually maintained at 1100" to 1600°C,&apos; and decomposes according to the reaction liberating gaseous atomic iodine and depositing solid crystalline titanium on the wire. Estimations based on the data of Runnalls and Pidgeon,&apos; indicate that the rate-control ling step is the diffusion of atomic iodine away from the wire. There appears to be nearly thermodynamic equilibrium at the wire with TiI, and iodine as the main gaseous species. TiI, is almost certainly an important gaseous species in the cooler regions.&apos; The liberated iodine diffuses to a heated source of crude titanium and reacts to form more TiI, vapor, which again diffuses to the hot wire and completes the cyclic process. The foregoing process may be modified by suspending the hot wire in liquid TiI,, instead of the vapor, and obtaining film boiling. This type of boiling is characterized by the formation of a continuous film of vapor over the wire surface. Since only vapor contacts the wire sul.face, the temperature of this surface may be raised as high as desirable, within the limit of mechanical strength requirements for the wire. By properly adjusting the input voltage. the temperature of the wire may be maintained above U0C"C; and by evacuating the vessel holding the liquid TiI, and maintaining a suitable condenser temperature, the vapor pressure of TiI, may be held low. Thus, the conditions of operation of the van Arkel-deBoer method may be approximated with film boiling; and hence, it is postulated that ductile titanium may be produced by this method. Preparation of Til, There are many methods available for the preparation of TiI,; that used in this research was prepared by the direct reaction of titanium sponge in controlled amounts with liquid iodine. Although no difficulty was encountered with this reaction, it has since been pointed out that this method is sometimes dangerous and should be used with caution. The resulting TiI, was purified by distillation. First Film Boiling Experiments Apparatus: The apparatus shown in Fig. 1 was used for film boiling TiI, on short wire filaments. The current to the filament was supplied through a bank of three 5 kva transformers connected in parallel. The current was controlled by adjusting the voltage over a 0 to 67.5 v range with a 7 kva variable transformer on the low voltage side of the bank of transformers. The current and voltage were measured by Weston meters. The sealed-in-glass tungsten electrodes were hard-soldered to the filament for the film boiling of TiI,. The bottom part of the reactor, containing TiI,, was wrapped with ni-chrome heating wires to maintain the TiI, in the liquid state. An ice or liquid nitrogen trap, for solidifying I, vapor and any TiI, not condensed, was attached to the low pressure side of the air-cooled condenser. A Megavac vacuum pump was used. Procedure: A 0.010 in. diam tungsten filament was hard-soldered to the tungsten electrodes. TiI, was melted (mp 156°C) and poured into the reactor chamber; the top of the reactor chamber, containing the electrodes, was replaced. Freezing of the TiI, was prevented by controlling the current to the ni-chrome wires wrapped around the reactor with a 1 kva variable transformer. The mechanical vacuum pump was started and the system evacuated to about 2 mm Hg TiI, vapor pressure. The current to the filament was turned on and the impressed voltage slowly increased with the variable transformer. A sudden drop in current at nearly constant im-

Jan 1, 1957

By E. A. Steigerwald, G. L. Hanna

The influence of work-hardening exponent on the variation of fracture toughness with material thickness was studied for high-strength steel, aluminum, and titanium alloys. The results indicate that, when materials are compared at similar fracture toughness to yield strength ratios, the material with the lower work-hardening exponent undergoes the transition from flat to slant fracture at a larger thickness than material with a high work-hardening exponent. In the thickness range where complete slant fracture is obtained the reverse is true and a lower work-hardening exponent results in a lower fracture toughness. The influence of work-hardening exponent on fracture toughness is, therefore, dependent on the particular fracture mode. In the transition region a low work-hardening exponent is beneficial for fracture toughness while in the 100 pct slant region it is detrimental. THROUGH the use of fracture mechanics analyses, the influence of geometric variables on the crack propagation resistance of structures can be interpreted with reasonable consistency. However, in order to gain a more complete understanding of the fracture process, the influence of material parameters on crack propagation must be defined and coupled to the macroscopic fracture mechanics approach. The work-hardening exponent, which characterizes specific material behavior, may serve as an effective parameter to allow some degree of coupling to be accomplished. In the extension of a crack in a specimen of suitable dimensions the propagation process occurs in a stable manner when the crack extension force is balanced by the resistance to crack extension, which exists in the material at the crack tip. As the applied stress, and therefore the crack extension force, on the specimen increases, the resistance also increases primarily because the effective plastic zone at the crack tip, which is the main energy absorption process, becomes larger. Since the work-hardening rate of a material influences the stress-strain relationship, it will also influence the energy absorption process in the plastic enclave at the crack tip and hence should have an effect on crack propagation. A number of studies have been made correlating the strain-hardening exponent or the strain to tensile instability with the ability of a material to resist fracture. Gensamer1 concluded that a low-strain-hardening exponent would result in a steep strain gradient at the base of a notch. He reasoned that a large work-hardening coefficient would result in high-energy ab- sorption due to the increased area under the stress-strain curve. Larson and Nunes2 experimentally observed in Charpy tests on steels heat-treated to below 200,000 psi yield strength that the energy to failure in the fibrous mode, i.e., above the brittle-to-ductile transition temperature, was logarithmically related to the strain-hardening exponent. In order to avoid the complicating effects present in studying materials which undergo a brittle-to-ductile transition, Ripling evaluated the notch sensitivity of a variety of fcc metals with varying work-hardening exponents.3 The results indicated that the relative notch sensitivity, as determined from tests on specimens with a sharp notch, decreased with increasing values of strain hardening. Although the energy required for ductile or fibrous fracture increases with increasing work hardening, high-strength steels often exhibit improved crack propagation resistance when heat-treated to obtain low values of strain hardening.4,5 An analysis of whether low strain hardening is beneficial or detrimental to crack propagation resistance must depend on the particular fracture criterion involved. At temperatures where the material is relatively ductile and the development of a critical strain is required for fracture, high strain hardening increases the energy required to produce failure. In the transition region and below, however, a critical stress law appears to be valid6 and a low rate of work hardening may produce superior resistance to semibrittle crack propagation. The experimental program is aimed at studying these possibilities and determining the specific influence of strain hardening on the crack propagation resistance of several high-strength materials. MATERIALS AND PROCEDURE The alloys, chosen as representative of various classes of high-strength materials, are summarized in Table I. The heat treatments evaluated along with the smooth tensile properties are presented in Table 11. Pin-loaded sheet tensile specimens were employed to determine the smooth tensile properties. A strain gage extensometer (measuring range 0.200 in.) was used at a strain rate of 0.02 in. per in. per min. The work-hardening exponents were determined from the stress-strain curves generated in the smooth tensile tests and the assumption that the portion of the stress-strain curve beyond the yield point can be described by the power relationship: where a is the true stress, P is the true plastic strain,

Jan 1, 1969

By W. T. Roberts, N. G. Turner

A study of the fatigue properties of several grades of commercially pure titanium has established that the strain-aging process is of minor importance in the development of a fatigue limit and a relatively high fatigue strength ratio. Metallographic observations and damping measurements at room temperature indicate that striations are able to spread from grain to grain only at stress levels above the fatigue limit. This suggests that the fatigue limit represents the stress above which large-scale dislocation unlocking takes place. Fatigue tests on annealed material at - 60" and - 196" c showed that under conditions when a thermally activated diffusion process would be suppressed the fatigue limit is not eliminated. Prestraining at room temperature did not have a detrimental effect on fatigue strength at room temperature but a decrease was recorded at — 60°C. This is further evidence that initial dislocation locking is a important strengthening mechanism. TITANIUM and titanium alloys have S-N curves with a definite fatigue limit, and a high ratio of fatigue limit to UTS can be attained. Other materials which show similar fatigue characteristics are mild steel and some Al-Mg alloys. The fatigue limit of these materials has been associated with their strain-aging capacity. It is well-known that commercial-purity titanium contains interstitial impurities which can give rise to a sharp yield point, and a small strain-aging effect following static strain has been demonstrated.7 This type of aging reaction is differentiated from the dynamic aging process when aging occurs during plastic deformation, and which is generally observed at elevated temperatures. In a titanium at room temperature, dislocation locking is associated with the interaction of interstitial oxygen, nitrogen, and carbon atoms with dislocations. Ehr-lich has shown that the distortion produced by introduction of these atoms into the hcp lattice has no shear stress component and hence there is no interaction between the stress field and the screw component of a dislocation. Thus the dislocations as a whole are only weakly locked. It is clear that strain-aging effects in hcp a titanium will be much less pronounced than those observed in bcc iron and steel. In recent years, the attribution of the fatigue limit solely to strain aging has been questioned. It has been pointed out that a definite fatigue limit is observed at temperatures as low as -196°C in some titanium alloys,&apos; and strain aging is not expected to be effective at this temperature. The role of initial locking of dislocations in determining fatigue behavior has been examined in low-carbon steel by Oates and Wilson. They showed that under conditions in which the aging potential is low the factors which control the buildup of local stresses and hence affect dislocation unlocking, e.g., grain size, are important. There are indications that other metals can have a definite fatigue limit with no established strain-aging capacity, an example being magnesium12 which has the same crystal structure as a titanium. The spread of plasticity from grain to grain in hexagonal metals may be more difficult than in cubic metals because of the limited number of slip systems in the former, and this may account in part for their fatigue behavior. The present work was undertaken to elucidate the relative importance of crystal structure, strain aging, and initial dislocation locking in determining the properties of commercially pure titanium when subjected to cyclic stressing. 1) EXPERIMENTAL METHODS Three grades of commercial-purity titanium were used and a material of lower interstitial content was prepared by melting high-purity Japanese sponge titanium (referred to as H.P. Ti). The compositions and typical mechanical properties of the materials are shown in Table I. Fatigue tests were made in push-pull (zero mean stress) using an Amsler Vibraphore machine at a frequency of about 160 cps. Two types of fatigue specimen were used—one with a waisted gage length for determination of S-N curves and the other with a parallel gage length for metallographic studies and damping measurements. After careful machining and mechanical polishing, all specimens were electropolished prior to fatigue testing. The electrolyte consisted of 10 parts methyl alcohol, 6 parts 2-butoxyethanol, and 1 part perchloric acid (SG 1.54) and it was maintained at a temperature of -10" to -20°C during polishing. Tests at room temperature were normally carried out with the specimen immersed in a silicone oil bath which could be heated for elevated-temperature tests.

Jan 1, 1969

By H. S. Thomsen, W. C. Duesterhoeft, R. E. Hartline

The attenuation and phase shift which formations produce in the electromagnetic field of an induction-type electrical well-logging instrument are great enough to substantially affect the response of the tool to formation conductivity under normal logging conditions. The application of the general equations for the propagation of an electromagnetic field in a conductive medium to the transmitter-receiver coil pair of an induction-logging-tool coil system gives an expression for the response which properly takes the propagation effects into account. A comparison of a calculation of this type with the response computed from the commonly used geometric factor concept, which does not include the propagation effect, leads to a factor Go representing the ratio of the responses computed by the two methods. The value of Go decreases not only with increasing formation conductivity, but also with increasing transmitter-to-detector coil spacing. For a single coil pair with a 40-in. spacing, the value of Go is 0.972 in a 20-millimho/m formation. The value is reduced to 0.915 and 0.812 for conductivities of 200 and 1,000 millimhos/m. As a result, the basic signal generated by the induction-logging coil system is not linearly related to formation conductivity as expected from the geometric factor concept. A uniform conductivity scale can be obtained only by adding a suitable nonlinear element to the recording system. The addition of auxiliary coils, having spacings less than the main-coil span, to achieve focusing results in an even greater departure of the basic signal from linearity with conductivity. The solution of the field equations near the interface between two formations of different conductivity gives the curve shape on an induction logging tool in crossing the interface. The addition of auxiliary coils to achieve focusing can add anomalous character to the curve shape in crossing the interface, which might be mistaken for lithological detail. Preliminary calculations which include the propagation effects in the determination of the conductivity correction for thin beds lead to correction factors which are substantially smaller than those obtained from geometric factor considerations. It is apparent that thin-bed corrections derived from geometric factor calculations are of doubtful validity. INTRODUCTION Although the electromagnetic induction type of electrical well log has been used for a number of years and has gained general acceptance in quantitative well-log interpretation, no technically complete investigation of the mechanism and of its operation has been published. The studies which have been presented are based upon the premise that neither the shape nor the intensity of the induction field of the logging tool is in any way affected by the electrical characteristics of the formation. From the inception of induction logging it has been recognized that under some formation conditions the performance of the instrument could be expected to be substantially different from that predicted by the simplified analysis. This anomalous performance has been called "skin effect" since it is the result of the same phenomenon which causes high-frequency alternating currents to flow only near the surface of metallic conductors. In the range of conductivities encountered in the sediments, the formation actually does not exhibit the sharply defined conducting "skin" shown by metals. The gradual modification of the distribution of the currents in the formation, produced by the induction field of the logging tool, is the direct result of phenomena associated with the propagation of the electromagnetic field through the formation. Therefore, it can be much more appropriately described as the "propagation effect". One purpose of this paper is to review the results of a solution of the equations for the performance of a single transmitter-receiver coil pair induction-logging system which takes into account the propagation effect, showing the manner in which the tool performance established by this analysis differs from that derived from the less comprehensive analyses currently in use. PRINCIPLE OF OPERATION OF THE INDUCTION LOGGING INSTRUMENT The high-frequency alternating current which is maintained at a constant value in the transmitter coil

By Allan E. Martin, Harold M. Feder, Irving Johnson

The cadmium-uranium system was studied by thermal, metallographic, X-7-ay and sampling techniques; special emphasis was placed on the establishment of the liquidus lines, The single inter metallic phase, identified as the compound UCd11 melts peritectically at 473°C to form a-umnium and melt containing 2.5 wt pct uranium. The cadmium-rich eutectic (0.07 wt pct uranium) freezes at 320.6°C. Solid solubilities in uraizium and cadmium appear to be negligible. Between 473°C and 600°C the liquidus line is retograde. NO publication relating to the cadmium-uranium phase diagram was found in the literature. The establishment of this diagram was of considerable interest to us because of a possible application of the system to the pyrometallurgical reprocessing of nuclear fuels. Analysis of liquid samples, metallographic examination, thermal analysis, and X-ray diffraction analysis were used to establish the phase diagram from about 300° to 670°C. Particular emphasis was placed on the establishment of the liquidus lines. The same system was concurrently studied in this laboratory by the galvanic cell method.&apos; Both studies benefited from a continual interchange of information. MATERIALS AND EXPERIMENTAL PROCEDURES Stick cadmium (99.95 pct Cd, American Smelting and Refining Co.) contained 140 ppm lead as the major impurity. Reactor grade uranium (99.9 pct U, National Lead Co.) was most often used in the form of 20-meshspheres. This form was particularly suitable because it does not oxidize as readily as finer powder. The liquidus lines were determined by chemical analysis of filtered samples of the saturated melts. The liquid sampling technique is described elsewhere2 alumina crucibles (Morganite Triangle RR), tantalum stirring rods, tantalum thermocouple protecthecadmiumtion tubes, Vycor or Pyrex sampling tubes, and grades 60 or 80 porous graphite filters were used. Uranium dissolves in liquid cadmium rather slowly. In order to achieve saturation of the melts it was necessary to modify the procedure of Ref. 2 by the use of more vigorous stirring and longer holding periods (at least 3 hr) at each sampling temperature. The samples were analyzed for uranium by spectro-photometry (dibenzoyl methane method) or by polar- ography. The analyses are estimated to be accurate to 2 pct. Thermal analysis was performed on alloys contained in Morganite alumina crucibles in helium atmospheres. Standard techniques were employed; heating and cooling rates were about 1°C per min. For the determination of the peritectic temperature, Cd-10 pct U charges were first held for at least 50 hr at temperatures in the range 435° to 460°C to form substantial amounts of the intermediate phase. For the determination of the effect of cadmium on the a-p transformation temperature of uranium, charges of Cd-25 pct U (-140+100 mesh uranium spheres) were first held near the transformation temperature, with stirring, to promote solution of cadmium in the solid uranium. The holding times and temperatures for these treatments were 18 hr at 680°C for the cooling run and 28 hr at 630°C for the heating run. Alloy specimens for X-ray diffraction and metallographic examination of the intermediate phase were prepared in sealed, helium-filled Vycor or Pyrex tubes. Ingots from solubility runs and thermal analysis experiments also were examined metallographically. Crystals of the intermediate phase were recovered from certain cadmium-rich alloys by selective dissolution of the matrix in 20 pct ammonium nitrate solution at room temperature. Temperatures were measured with calibrated Pt/Pt-10 pct Rh thermocouples to an estimated accuracy of 0.3°C. However, the depression of the freezing point of cadmium at the eutectic is estimated to be accurate to 0.05°C because a special calibration of the thermocouple was made in place in the equipment with pure cadmium just prior to the measurement. EXPERIMENTAL RESULTS The results of this study were used to construct the cadmium-uranium phase diagram shown in Fig. 1. This diagram is relatively simple; it is characterized by a single intermediate phase, 6 (UCd11), which decomposes peritectically, and which forms a eutectic system with cadmium. The solid solubilities in the terminal phases appear to be negligible. An unusual feature of the diagram is the retrograde slope of the liquidus line above the peritectic temperature. The Liquidus Lines. The liquidus lines above and below the peritectic temperature are based on three separate solubility experiments. The data are shown in Fig. 1 and are given in Table I. It is apparent from the figure that the solubility data obtained by the approach to saturation from higher temperatures fall on substantially the same lines as those obtained

Jan 1, 1962

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity&apos; factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse

By R. A. Fitch, J. D. Griffith

A performance calculation method was used in conjunction with experimental studies to develop means of predicting and interpreting miscible floods and to explore possible methods. of improving their efficiency. The calculation method is based upon the division of reservoirs into multiple independent zones or strata. Comparison was made with some experimental floods and with a field project to obtain some measure of the applicability of the method. Two aspects of miscible flooding were considered: (I) the displacement of a miscible front through a reservoir, and (2) the distribution and utilization of the solvent volume injected to maintain miscibility. Calculations and experihental observations indicate that alternate gas-water injection behind a miscible front significantly improves miscible flood performance, both within a single stratum and in a multistrata reservoir. Calculations were made on the extent to which miscibiliry is maintained by a given solvent volume in a stratified reservoir. Two alternate criteria for determining the optimum volume of solvent for injection are discussed. The preinjection of a small volume of water ahead of the solvent is suggested as a method of obtaining more efficient utilization of solvent. Calculations and experiments were made to investigate the effects of water preinjection. INTRODUCTION Miscible fluid displacement as a possible means of recovering oil has been the subject of extensive research and numerous field tests over the past several years. This work has brought out both favorable and unfavorable features of the miscible recovery methods. Many tests have shown that a miscible fluid can displace all of the oil contacted, leaving no high residual oil saturation, as is characteristic of immiscible displacements. The miscible methods have proven dificult to control, however, as evidenced by early breakthrough of the displacing fluid and poor sweep efficiency in several field projects. It became apparent early in the investigation of miscible displacement that the development of improved techniques and better methods of control would be required to extend the range of applicability to any significant portion of our petroleum reservoirs. The purpose of this study was to consider the problem of designing miscible floods to obtain better performance. A performance calculation was used in conjunction with experimental studies to develop means of predicting and interpreting miscible floods and to explore possible methods of improving their efficiency. Two aspects of miscible floods were considered separately in this study and the results are presented in two parts. The first part concerns the manner in which the miscible front is displaced through the reservoir. In these calculations the condition of miscibility between the reservoir oil and the displacing fluid is assumed. In the second portion the distribution and utilization of the preinjected solvent in maintaining rniscibility is considered. This portion dealing with solvent utilization applies only to the enriched gas or LPG slug processes. CALCULATION METHOD AND EXPERIMENTAL STUDIES COMPUTATIONAL MODEL The calculations for expected reservoir performance are based upon the multi-strata concept of reservoir properties. The method assumes multiple, independent strata (no crossflow between strata) and explicitly includes variations in patterns, injectivity, areal sweep and displacement efficiency. Lateral variation in permeability within the strata (for example, directional permeability) may be considered in the calculations, provided the variations are similar in all strata. The calculations based on this model furnish the rates of injection and rates of production of both oil and the displacing fluid for the composite system of strata. To carry out calculations on the mathematical model described, information is required on the performance of the displacement process under consideration in a single stratum element of the pattern to be used. In particular, for a given pattern and displacement process, data are required relating injectivity and composition of the produced stream to the volume of fluid injected. Data on the variations in areal sweep must also be available if it is desired to track the areal sweeps in the multi-strata model. These data may be obtained from experimental work such as model studies or other suitable methods. This representation of reservoir properties is, of course, an approximation and may be inappropriate in some cases. But the representation is not an arbitrary one since most oil reservoirs are essentially successive layers of sediment with the net producing pay zone often comprising but a fraction of the gross formation thickness. The fact that permeabilities measured in the vertical direction are frequently but a fraction of the horizontal permeability adds some evidence to the validity of this model. This type cal-

Jan 1, 1965

By John L. Ham, Robert M. Parke

The melting point of molybdenum is 2625° + 50°C. Heretofore the metal has been considered too refractory to be melted in commercial quantities; hence, it has been formed into rod, wire, and sheet by the methods of powder metallurgy, wherein the temperatures do not exceed 90 per cent of the melting temperature. The manipulation of liquid metals at temperatures of about 2000°C. and above presents some difficult problems in heat transfer, in purification, and in container materials. For metals melting at such high temperatures, it is generally regarded as expedient to circumvent the more common melting and casting process by resorting to powder metallurgy. This circumvention is not accomplished without some penalties, the more notable of which are the relatively high cost of the powder metallurgy method and particularly the size limitations of its product. In an effort to overcome the inherent disadvantages of the powder metallurgy method, especially in respect to the limit of size, a project was begun in 1943 at the Climax Molybdenum Co. laboratory to develop a method of melting and casting molybdenum capable of producing larger bodies of molybdenum than were then obtainable. Later, from Feb. I, 1944, to Aug. 31, 1945, the project was under the supervision of the National Research Committee, Division One. In peacetime, too, there are needs for molybdenurn, which make consideration of another process desirable; for example, large parts for heat engines generally, the omnipresent demand for metal of higher quality and lower cost, and the development of molybdenum-base alloys. This paper describes methods for melting and casting molybdenum, with details of the special process needed to make molybdenum castings ductile, and reports some of the properties of what may be regarded as a new, or at least modified, form of the metal. First Process for Melting and Casting Molybdenum The maintenance of a temperature greater than 2625°C. in a &apos;pace large enough to melt several pounds of molybdenum may involve the loss of heat at a Very considerable rate. For melting molybdenum, therefore, the source of heat must be of high potential and of fairly high power. Evidently, also, the source of heat must not impair the purity of the product. The electric arc operating in vacuum appeared to meet these requirements and was accordingly the first choice as a source of energy. A number of arc devices for melting molybdenum were examined, and several were tried. In the first experiment, a 20-kw., 60-cycle-per-second alternating-current arc was operated between two horizontal and opposed electrodes of molybdenum- In this arrangement the falling droplets of molybdenum solidified below the arc in an irregular mass. This experiment did not produce a useful casting, but the data obtained indicated that

Jan 1, 1947

By R. F. Mehl, J. K. Stanley

THE recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are employed.1 Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystallization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress .4,5† The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed .27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert measurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now

Jan 1, 1942

By N. J. Grant, E. Gregory

The creep rupture properties of wrought aluminum powder products made from five grades of sintered aluminum powder were investigated at temperatures from 400° to 900°F for rupture times up to 1000 hr. The effect of stress concentrations on materials of this type was investigated by means of notched creep rupture tests. A tentative correlation was obtained between the creep rupture properties and the structure as revealed by electron micrographs. SEVERAL papers have been published recently concerning the production and properties of wrought aluminum powder products and their possible high temperature applications. Most of the published work in this field has come from abroad, notably Switzerland, and articles by Irmann and his colleagues were summarized in English recently.&apos;.&apos; Most of the papers published by Dr. Irmann are principally concerned with the retention of properties (by a product which is produced from extremely fine flake powder and is subsequently hot extruded) after heating to high temperature for prolonged times. The powder may be in atomized or flake form, and during hot working the applied pressure is reported to plastically deform the aluminum powder, thus breaking the oxide skin and welding the particles together. Irmann attributes the remarkable properties to the dispersion of oxide inclusions. Specifically, the product described by Irmann is one labeled SAP (Sintered Aluminum Powder) in which the initial flake powder is so fine that at least 50 pct of the flakes have one dimension of 2 microns or less. The composition of the starting aluminum shows in percent, Fe, 0.18; Si, 0.19; Zn, 0.06; Ti, 0.03; Cu, Mn, Mg, all nil; balance Al, approximately 99.5 pct. Aluminum is not the only material that has been found to have increased resistance to deformation at elevated temperatures when produced by powder metallurgy. It has been reported by Middleton, Pf eil, and Rhodes- hat platinum has a higher recrys-tallization temperature when produced by powder metallurgy and exhibits peculiar properties, many of which are similar to those of the aluminum powder products. Difficulties were encountered in explaining the reason for the strengthening in the case of platinum since the existence of the oxide is doubtful. The authors attributed the special properties to "a small amount of suitably dispersed porosity." This theory was supported by von -~eer-leder4 in the discussion to the paper, and the similarity between this method of hardening and that suggested by Rohner in his theory of age hardening was pointed out. R. de Fleury5 attempted to explain some of the properties in terms of the modulus of elasticity and elastic limit of alumina and aluminum while von Zeerleder examined the relationship between the yield strength and the reciprocal of the powder particle size. Boenisch and WiderholtQ dealt mainly with the corrosion resistance of the powder aluminum material and compared it with other aluminum alloys. The diffusion rates of other metals in SAP and pure aluminum have been compared by Seith and Lop-mann.&apos; They showed that the alloying metals diffuse particularly quickly in SAP possibly due to the very fine grain size. The properties of the Alcoa products were given by Lyle.&apos; The creep rupture properties of SAP and two of the Alcoa experimental powder products were compared by Gregory and Grant hnd it was shown that these products are vastly stronger at 900°F than are the best cast and wrought alloys at 600°F. Since the publication of these data, the authors have investigated two further aluminum powder products and it is the object of this paper to show how the high temperature creep rupture properties of the five materials vary with oxide content and with the structure as revealed by electron microscopy. Materials One of the five products, SAP, a sintered aluminum product, was supplied by the Societe Anonyme pourl Industrie de l,Aluminium, Neuhausen a/RHF, Switzerland, through Dr. R. Irmann, while the others, M276, M257, M293, and M255 were supplied by the Aluminum Company of America as experimental powder metallurgical products. M255- and M293 were made from coarse and fine atomized powders, respectively. The other materials were made from flake powders with significant differences in oxide content, the details of the type of powders used in the manufacture of these materials

Jan 1, 1955

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The complicated nature of the property changes that accompany age-hardening has made it necessary to reconsider and to elaborate the simple dispersion theory.l It has been apparent for some time that more direct information is needed concerning the atomic mechanism of precipitation from solid solution if the theory of age-hardening is to be developed past a purely qualitative stage.‡ Fortunately, in recent years information has been developed which allows us to trace in detail the lattice changes accompanying the process of precipitation from solid solution. This information relates chiefly to the sequence of the several stages of lattice alteration by which the matrix lattice is transformed to the equilibrium precipitate lattice, and permits reasonable inferences to he drawn concerning the states of internal strain that accompany these stages. This information is most complete for the solid solution of copper in aluminum. The equilibrium precipitate is the 0 phase, "CuAl2." This forms in plates, parallel to the {100} matrix planes. The atom pattern and atom spacing on the plane in 0 lying parallel to this plane are roughly similar to those opposite it in the matrix.3 The formation of 0, however, is preceded by the formation of a transition lattice 0&apos;: which again lies parallel to the matrix {100} plane, but in this case the matching of atom pattern and spacing across the matrix-precipitate interface is nearly periect; thus there is lattice coherency across the interface and the interface is a plane of separation in only a very limited sense.&apos;8 Particles of 0&apos; may be recognized microscopically and form a well-defined Wid-manstatten figure.* The 0&apos; lattice is recognized by the occurrence of diffraction lines on powder photo-grams or of spots on Laue photograms which may be analyzed in the usual ways to determine the lattice type and the lattice spacings. Very recent research 6, 7, 1 has shown, however, that streaks occur on the Laue photogram at an earlier point in time during the aging process. These streaks have been attributed to a preferential clustering of copper atoms into small platelike elements of only a few atoms in thickness and a lew hundred atoms in diameter, probably of the composition of " CuA12," which may be designated as Guinier-Preston zones or aggregates.1 It is difficult if not impossible to determine the lattice type and lattice spacing in these aggregates. It is possible1 that these aggregates are in fact ?&apos; in a high State of dispersion; the inclination to argue this is strong, as we shall see later. Never-

Jan 1, 1941

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By G. P. Conard, R. C. Hall, J. F. Libsch

The 50 pct Fe-50 pct Co alloy undergoes a transformation from disorder to an ordered structure of the CsCl type reportedly in the vicinity of 732OC. During this process, the coercive force goes through a maximum, apparently as a result of strains associated with the coherent nucleation and growth reaction. This magnetic alloy also shows a marked increase in the ratio of residual to saturation induction, which is associated with annealing to a high degree of order with the continuous application of a magnetic field. The increase in ratio can be explained on the basis of a decrease in 90&apos; domain boundaries and, perhaps, by an increase in anisotropy resulting from lattice distortion. THE 50 pct Fe-50 pct Co alloy undergoes a disorder-order transformation which has been reported to occur in the vicinity of 732°C1,2 The ordered structure is the CsCl type.&apos; This magnetic alloy also shows a marked increase in the ratio of residual to saturation induction as a result of heat treatment in a magnetic field, sometimes called a response to magnetic anneal.&apos;-&apos; The purpose of this investigation was to study the course of the ordering reaction, the nature of the response to .heat treatment in a magnetic field, and the relation, if any, between ordering and the response. Procedure The method of approach in this investigation was to produce an initial structure as completely disordered as possible and then gradually to order the alloy by isothermal anneals at various temperatures under different conditions of the applied magnetic field. Magnetic, magnetostriction, and X-ray analyses were of primary importance in determining the property and structural changes resulting from the isothermal anneals. Rings of the 50 pct Fe-50 pct Co alloy were prepared from the elemental powders by a powder metallurgy technique, further details of which may be found in ref. 7. The initial structure was produced by annealing the specimens for ½ hr at 1000°C, cooling to and holding for ½ hr at 900°C (in the a range above the ordering temperature), and water quenching. Isothermal anneals were performed at 600°, 675°, 720°, and 740°C. For example, rings were heated to 600°C, held for a predetermined period of time, and cooled by natural cooling at a rate slightly slower than an air cool (average of 20" to 25°C per min). The tests (magnetic, etc.) were made after each heat treatment. All high temperature treatments were performed in a purified hydrogen atmosphere. The treatments at the various temperatures were carried out under one or more conditions of an applied field including 1—no field, 2—field of 20 oersteds applied on cooling only, and 3—field of 20 oersteds applied continuously during heating, holding, and cooling. Magnetic measurements were made using the standard Rowland ring technique8 with a maximum field strength of 100 oersteds. The magnetization curve, induction at 100 oersteds (B.), residual induction (Bt), and coercive force (Hc) were determined. All magnetic analysis data were based on an average of the results from three rings. A strain gage technique9 as used for the measurement of magnetostriction. The X-ray determination of the relative amount of ordered phase present was made on the ring specimen used for magnetic measurement. This was done by the back-reflection method using a rotating specimen (because of the large grain size) with unfiltered CoKa radiation and a 7 hr exposure time. Intensity measurements of the ordered line (300) were made by comparing visually the films so obtained with standard films prepared by exposing for different lengths of time a specimen given a long time anneal (high degree of order). Results In all instances the saturation induction (induction at 100 oersteds) was found to increase slightly with annealing time. This effect was small and appears to be the increase in saturation induction to be expected on ordering.10-13 The residual induction behavior was markedly influenced by the field condition during annealing, Figs. 1, 2. For the condition of no applied field, the ratio of residual to saturation induction remained essentially constant for short annealing times but showed a significant increase at longer times. With increasing annealing temperature, less time was required to produce this increase in the ratio. In the case of the 600°C anneals, the increase did not occur until approximately 20 hr, Fig. I, while on annealing at 740°C the increase was immediate, Fig. 2. Slight decreases in the ratio may be observed at 100 hr for specimens treated at 720°C and at 1 hr for those treated at 740°C. Specimens annealed in a field of 20 oersteds showed a residual to saturation induction ratio consistently higher than that for the specimens annealed without the field. The first anneal with the field (¼ hr) caused an abrupt increase in the ratio at all temperatures; thereafter, the increase in the ratio was generally similar for specimens annealed

Jan 1, 1956

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.&apos; Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.&apos;.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

By C. M. Loeb, T. E. Norman

The use of ball, rod and tube mills for grinding ore, cement and other materials has grown so rapidly during the past forty years that the world&apos;s annual consumption of ferrous grinding media for these mills is now estimated to be between one half million and one million tons per year. Ferrous grinding balls constitute the major portion of this tonnage. Obviously they represent suficient value to justify thorough studies of the factors governing their performance. The selection of grinding balls is governed principally by: I. Quality (wear resistance, impact resistance, soundness, and the like). 2. Sources of supply and delivered cost. 3. Grinding characteristics or efficiency in the ball mill. This paper deals principally with the quality of ferrous grinding balls. In the study of these factors certain data relative to the fundamental nature of ball wear in ball mills have been obtained. These data are also presented and discussed briefly. The Development of a Suitable Wear Test A study of the fundamental factors governing the quality of grinding balls has been hampered seriously by the fact that a competent test has, in the past, involvetd the purchase of several hundred tons of halls of a specific type which were then run in one or more ball mills for a period ranging from several months&apos; to several years&apos; duration. Often, during the period of test, it became necessary to change operating conditions or the character of the ore fed to the test mill with the result that the rate of ball consumption changed and the test figures became of little value. Under such circumstances, progress in the development of better grinding balls, has been necessarily slow. Economic factors and variations in the quality of balls produced by different sources of supply generally make it necessary for each mill operator to determine for himself the most suitable type of balls for his mills. In our own ball mill grinding operations at Climax, Colo., we were faced with this problem. After we had run a few large scale wear tests at considerable expense we decided to investigate the possibilities of a small scale wear test which would be capable of testing numerous types of balls within a relatively short time. The most important requirement of any test is, of course, that it give results which can be used to predict accurately the wear in full scale operations. It was known that Ellis and his associates1&apos;2 had developed a method of testing grinding balls by small scale tests run at the Ontario Research Foundation. Ellis&apos; method of testing was used as a starting point in our investigations. In the course of our tests a number of modifications of the original method were found to be desirable so that, by an evolutionary procedure, a method of small scale

Jan 1, 1949

By W. J. Millard

It is well known that the excellent mica from Brazil played a most vital role in World War 11. Increased production from Brazil was necessary and with the assent of the Brazilian Government engineers from the united&apos; States went down to study the problem. One of the means advocated by a former Chief of Metals and Minerals Branch of the Board of Economic Warfare, Mr. Carl Schwegler, was the use of stripping machinery. On a pegmatite dike favorable for stripping, a small number of miners could produce as much mica per day as an underground mine employing many times the same number of men. Type of Deposit Favorable The most favorable type of pegmatite for stripping is that which lies more or less parallel to the surface of the slope of a hill. Pegmatite dikes that cut directly into a hill are not suitable for stripping except where a long outcrop extends along the slope. Then just the outcrop could be stripped to some advantage. The ratio at no time should be greater than 1: 3; i.e., I cu. m. of pegmatite to 3 cu. m. of waste, unless the pegmatite was extremely rich throughout the dike. The Economics of Stripping When a mineral is badly needed to win a war, not too much heed can be paid to costs. The object is to produce rapidly and in quantity. Again, a deposit containing a superior grade of mica may be worked although the pegmatite is more costly to work than another deposit containing a considerably greater amount of poor-grade mica. For example: one deposit may have a little mica that will run 11 per cent good stain and better when trimmed and contain 2 kg, of crude mica per cubic meter of pegmatite, while another may run 0.2 per cent of good stain and better, and have a mica content of 10 kg. per cubic meter. A number of stripping projects were found in the vicinity of Raul Soares, Minas Gerais. These were sampled in the various old workings by cutting out a cubic meter of pegmatite and saving the usable mica. Because of the proximity to the surface of most stripping projects, about 34 per cent only of the mica is good for trimming. The other 66 per cent is too badly weathered to be of use. In Table I are given data collected on five properties near Raul Soares. In Table I, "value per cubic meter of pegmatite" means the value of the qualified mica obtainable. This does not include the half trimmed and splittings. By "value per cubic meter of matter" is meant the value of the qualified mica per cubic meter of material excavated; i.e. both waste and pegmatite. This is the figure that should be used to determine whether the operation will be profitable or not, as the cost of stripping is about $0.14 per cubic meter. With new machinery not subject to breakdowns, the cost per cubic meter should be around $0.10 to $0.15. To this should be

Jan 1, 1948