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By R. Dawson Hall

Discussion of the paper of R. DAWSON HALL, presented at the San Francisco meeting, September, 1915, and at the New York meeting, February, 1916, and printed in Bulletin No. 105, September, 1915, pp. 2013 to 2021. R. DAWSON HALL, New York, N. Y.-The general practice in the past has been to view the roof as being somewhat subject only to shear. In fact the action of the roof under the stress of its own weight has been but little considered, not because the matter is unimportant but because it is so complicated that it has been felt that an analysis of it would not result in any conclusions definite enough to justify the inquiry. The result has been that the consideration of the subject has fallen into the hands of persons who are not experts in the study of beam and plate stress. They have been disposed naturally to view the destruction of the roof as the outcome of the simplest of stresses-vertical shear. In the lack of a careful consideration of the conditions of roof fracture it was thought that the roof consisted of a number of horizontal layers, which were each of them weak, because, no matter how strong they might be they usually lacked sufficient depth. This view of the condition of the roof would naturally lead one to expect that it would yield to bending moment, the various layers succumbing one by one to their lack of the necessary radius of gyration to meet such severe stresses. But,

Jan 5, 1916

Discussion of the paper of Leonard Waldo, presented at the New York meeting, February, 1911, and printed in Bulletin No. 76, April, 1913, pp. 555 to 559. HERBERT HAAS, San Francisco, Cal. (communication to the Secretary*):-Referring to Leonard Waldo's paper on Temperature Conversion Tables, I believe the following formulas can be easily remembered, and by reference to the thermomter scales of Fahrenheit (F.), Celsius (C.), and Réaumur (R.), their derivation and relation are at once understood n° F. = 4/9 (n°-32) R. = (n°-32) C. n° C.=(9/5 n° + 32) F. = 4/5 n° R. n° R.=(9/4 n° + 32) F. = 5/4 n° C. As the freezing point of water is at 32° F., corresponding to 0° C. and 0° R., 32 must be deducted from the Fahrenheit degrees when these are converted into C. or R. degrees. Likewise, to C. or R. degrees converted into F. degrees 32 must be added. The fractions 4/9 and 5/9 and their reciprocals are obtained thus:

Jan 5, 1913

By R. A. Pallanch

PROBABLY one of the most perplexing problems with which a mill operator contends is the proper evaluation of his mill results. True, he accurately determines his recoveries of metals and grades of products monthly, weekly, and often daily. These figures do not of themselves directly translate to mill economics. When one figure is unusually good there may be an offsetting circumstance. The advantage of high lead or zinc concentrate grade may be offset by poorer recovery; high lead recovery may be offset by poorer zinc recovery, or vice versa; and so on. Besides, grades or recoveries may not of themselves mean more than a reflection of the grade and character of the ore during the period under study. What the operator sorely needs is some one measuring stick that tells him when he has achieved his greatest return, regardless of grades or recoveries-for if he knows his methods and practices are yielding the optimum return he need no longer concern himself with the assays of products and tailings, or the corresponding distribution of metal values. At first blush it would appear that the obvious answer to this is the actual money return to the mill. Paradoxical as it may seem, however, money return does not make a dependable yardstick any more than do grades and recoveries, as ore conditions would vary enough to bring about greater money return during periods when the actual metallurgical work is not as good. The mill operator, of course, should always aim for the greatest return on the ore, once it is in the mill bins, with proper attention always to mill treatment cost. The need of a proper yardstick becomes more imperative with the increasing complexity of the problem. In the case of a simple, single-product operation on a fairly uniform ore, in which only one metal is of significant importance, the need is not great, as grade and recovery pretty well tell their own story. At the other extreme is the operation that makes three or four separate marketable products from a complex mixture of heterogeneous ores that vary tremendously in individual metal contents and ratios, degree of oxidation, and other characteristics, and in which gold, silver, copper, lead and zinc are all significant values. ECONOMIC RECOVERY The first attempt at obtaining a proper single yardstick for a fairly complex ore with which I am familiar is the use of the "Economic Recovery" term at the leadzinc flotation mill of the Sunnyside Mining and Milling Co., Eureka, Colorado. This method had been applied there early in Sunnyside flotation-mill history (not later than 1920) and credit for the innovation I believe belongs to Messrs. Kuryla and Marquand. The term "Economic Re-

Jan 1, 1947

By R. A. Pallanch

Probably one of the most perplexing problems with which a mill operator contends is the proper evaluation of his mill results. True, he accurately determines his recoveries of metals and grades of products monthly, weekly, and often daily. These figures do not of themselves directly translate to mill economics. When one figure is unusually good there may be an offsetting circumstance. The advantage of high lead or zinc concentrate grade may be offset by poorer recovery; high lead recovery may be offset by poorer zinc recovery, or vice versa; and so on. Besides, grades or recoveries may not of themselves mean more than a reflection of the grade and character of the ore during the period under study. What the operator sorely needs is some one measuring stick that tells him when he has achieved his greatest return, regardless of grades or recoveries—for if he knows his methods and practices are yielding the optimum return he need no longer concern himself with the assays of products and tailings, or the corresponding distribution of metal values. At first blush it would appear that the obvious answer to this is the actual money return to the mill. Paradoxical as it may seem, however, money return does not make a dependable yardstick any more than do grades and recoveries, as ore condi- tions would vary enough to bring about greater money return during periods when the actual metallurgical work is not as good. The mill operator, of course, should always aim for the greatest return on the ore, once it is in the mill bins, with proper attention always to mill treatment cost. The need of a proper yardstick becomes more imperative with the increasing complexity of the problem. In the case of a simple, single-product operation on a fairly uniform ore, in which only one metal is of significant importance, the need is not great, as grade and recovery pretty well tell their own story. At the other extreme is the operation that makes three or four separate marketable products from a complex mixture of heterogeneous ores that vary tremendously in individual metal contents and ratios, degree of oxidation, and other characteristics, and in which gold, silver, copper, lead and zinc are all significant values. Economic Recovery The first attempt at obtaining a proper single yardstick for a fairly complex ore with which I am familiar is the use of the ''Economic Recovery" term at the lead-zinc flotation mill of the Sunnyside Mining and Milling Co., Eureka, Colorado. This method had been applied there early in Sunnyside flotation-mill history (not later than 1920) and credit for the innovation I believe belongs to Messrs. Kuryla and Marquand. The term "Economic Re-

Jan 1, 1949

By Mark J. Klein, A. H. Clauer

The Snoek peak induced by solute nitrogen in chromium was studied. A rapid quenching rate is required to maintain nitvogen in solution in sufficient concentrations to be detectable by internal-friction techniques. An expression for the tertninal solubility, c, of nitrogen in weight pevcent is log,,c = -4130/T + 1.05. The diffusion of nitrogen in zhromium determined by internal friction is SNOEK&apos;S theory1 of the stress-induced ordering of interstitial solute elements in the bcc lattice has been used to deduce information on the behavior of interstitials in a number of bcc metals. Under the proper conditions, internal-friction studies of "Snoek peaks" permit a determination of diffu-sivities, solubilities, and precipitation kinetics of interstitial elements. Internal-friction studies of this type have been reviewed by Nowick,&apos; Wert,= Powers and Doyle,4 and others. The behavior of interstitial atoms in Group V-A metals and iron has been rather extensively studied in this way, and results are reasonably self-consistent. However, the study of interstitial elements using internal friction in the Group VI-A metals—tungsten, molybdenum, and chromium—is much less clear. Thus far, internal-friction studies have revealed a peak in tungsten tentatively attributed to carbon5 and a peak in chromium associated with nitrogen. In chromium, Bungardt and Preisendanz6 observed a peak at 180°C for a frequency of -1 cps which they associated with nitrogen. More recently, de Morton7 determined the diffusivity of nitrogen in chromium from studies of a nitrogen peak at 160°c for a frequency of -1 cps and from elastic aftereffect measurements. The objective of this investigation was to study the nitrogen peak in greater detail, to obtain information on the behavior of nitrogen in chromium. This information is of interest because nitrogen is known to have an embrittling effect on chromium. However, efforts to deduce the role played by nitrogen in influencing the mechanical behavior of chromium are handicapped by lack of information on its behavior and distribution in chromium. EXPERIMENTAL PROCEDURES The chromium wires used in these studies were drawn from arc-melted iodide-chromium stock that had been extruded, swaged, and centerless-ground to 0.25 in.-diameter rods. Internal-friction measurements were made in an evacuated torsional pendulum similar to the one described by Kê,8 utilizing wires 0.048 to 0.030 in. in diameter. A series of analyses of the fabricated wires showed that the major impurities were approximately 100 ppm Fe and a combined interstitial content of 50 to 100 ppm C, O, N, and H. A typical interstitial analysis of the wires after processing is 15 ppm C, 2 ppm H, 50 ppm O, and < 5 ppm N. Interstitial concentrations were determined by vacuum-fusion, combustion-conductimetric, and micro-Kjeldahl analyses. In general, vacuum-fusion analysis yielded a lower nitrogen concentration than did micro-Kjeldahl analysis. For consistency, the nitrogen concentrations reported in this investigation were determined by the former method. Heat treatments were carried out by encapsulating the specimens in quartz tubes containing argon. The fabricated wires were annealed at 1150°C for 1 hr to produce uniform recrystallized grain size of about 0.015 mm. Nitrogen and carbon were added to the fabricated wires by encapsulating them in a quartz tube containing ammonia or methane, and annealing them at 1150°C for 48 hr. In some instances, carbon was also introduced by coating the wires with carbon black prior to annealing.

Jan 1, 1965

By C. A. Bruch, W. E. McHugh, R. W. Hockenbury

Commercially pure molybdenum specimens were irradiated in the Materials Testing Reactor for an estimated exposure of 1.9 to 5.9x10 20 thermal nvt. Prior to irradiation, the material was ductile in the tension test; whereas after irradiation, it was brittle. The results of tension tests conducted at various temperatures revealed that the transition temperature for this material had been increased from —30&apos; to +70°C as a result of the radiation exposure. From metallographic studies, it is concluded that the embrittlement is due to submicroscopic changes which raise the flow stress-temperature curve of the material. PRIOR to ten years ago, the bombardment of metals with high speed heavy particles such as protons, deuterons, a particles, and neutrons was primarily of academic interest. These particles existed in extremely small numbers in a few laboratories and only under very special conditions. With the introduction of the nuclear power reactors, these particles are now available in enormous quantities and it has become important from a practical standpoint to learn how well metals withstand severe reactor radiations. The principal radiations of concern in reactors are neutrons and y rays, since the heavier charged particles exist only in limited regions of reactors. Seitz,&apos; in a theoretical approach, has shown that all of these high energy particles, except y rays, have enough energy to knock atoms from lattice sites and that these knocked-on atoms have enough energy to cause additional displacements of neighboring atoms. The result of this process would be a lattice containing many imperfections in the form of interstitial atoms and vacancies. Hence, it would be expected that the properties of metals can be changed by reactor radiations, and such has been found to be the case. Only a limited amount of data have been published in the open literature,2,3 and these data have been for relatively low integrated-neutron-flux exposures. In general, one effect of reactor radiations on the mechanical properties of metals has been to increase strength and decrease ductility. It is now possible to irradiate specimens in the Materials Testing reactor at much higher fluxes and to higher integrated exposures than previously possible.&apos; The data which are being presented here describe the effects of a relatively high exposure on some mechanical properties of molybdenum. Experimental Procedures Material: The molybdenum used in this investigation was obtained from the Climax Molybdenum Co. The two heats from which the material originated were melted under a vacuum of 5 to 30 microns and cast in 7 in. diam water-cooled copper molds. One ingot contained 0.061 pct C and the other 0.066 pct. Both ingots were hot worked by extrusion and rolling into % in. diam rods, after which they were annealed and straightened. The rods were subsequently heated to 1100°C in a hydrogen atmosphere and swaged to ½ in. diam rods at the Research Laboratory of the General Electric Co. The resulting material had an average hardness of 264 VPN, or 99.2 Rb, and had an average of 5000 grains per sq ml in the transverse section, Test Specimens: Substandard-size tensile specimens were prepared according to the specifications shown in Fig. 1. These specimens were used also for hardness measurements. The metallographic specimens were small disks which were polished, etched, and photographed at X1000 prior to irradiation. The field studied was

Jan 1, 1956

By J. E. Tobey, David R. Mitchell, J. H. Kerrick

DETAILED knowledge of purchase specifications established by coal consumers is essential to the successful design and operation of a coal-preparation plant. ANTHRACITE Specifications should be considered by both the consumer and the producer as guide posts outlining a certain path for both to follow. Plants differ, therefore specifications must differ to meet the varied requirements. Specifications are not of themselves a "cure all" or an assurance of complete satisfaction in fuel utilization. Specifications should not be regarded as a license to engage in an orgy of buying any and all coals that may happen to fall within their limits. This would lead to the indiscriminate mixing of coals which may vary in their burning characteristics. Different coals of equal grade tend to be individualistic in their burning characteristics. Rather, specifications should be used to help simplify coal selection, to reduce the actual number of coals used over a given period; in other words, to have a stabilizing influence on coal or customer turnover. In the final analysis, the use of too many coals per year in a plant is costly to both the consumer and the producer. Too many sources usually result in higher operating and maintenance costs for the consumer and higher sales costs for the producer. Finally, the statement included in the report accompanying the com¬prehensive Coal Selection Charts prepared by the Coal Committee of the National Association of Purchasing Agents, and released in 1938, is significant. This Committee worked diligently for a period of 15 years seeking to find a scientific and reliable method for selecting coals. The two following paragraphs are quoted from its report: More important is the fact that no ready-made classification or set of specifications can possibly replace the judgment and resourcefulness of an experienced combustion engineer or fuel technologist, nor the usual need for full scale plant tests under the exact conditions of use before a final decision is made ...

Jan 1, 1943

ONE of the perplexing problems that face the translator of an old technical treatise is the question of terms for units of weight and measure. We have used an English word only when it is linguistically equivalent to the Italian one and is a unit of approximately the same size. Libbra and oncia thus become pound and ounce, for the actual weights were within 10 per cent of the modem Troy weights. On, the other hand, the length measures braccio, palmo, and dito, which could be rendered literally as arm, palm, and finger or digit, respectively, have no good English metrological equivalents and it has seemed best to retain the Italian words. The exact transfer of Biringuccio&apos;s weights and measures into modern terms is impossible because of the uncertainty as to his standards. Even as late as 1803, when the metric system was first introduced into Italy, practically every city had its own standards. There were, for example, at least eight different palmi, varying from 22.3 to 29.2 centimeters. The values listed below for the various units mentioned by Biringuccio are the Florentine ones, which were also used in Siena and Tuscany: [ ]

Jan 1, 1942

By R. E. Allen

One of the most unusual oil-field engineering accomplishments of the past two years is the development and rapid advance in the directed drilling of wells. Directed drilling as referred to herein is the controlled steering of the drill stem in the required direction to a given location in the oil sand. The deliberate drifting of holes is an act so far removed from what has been considered good drilling practice that all of the old questions of correlation, drillability and production difficulties are revived. Only a few years ago, during the boom days of Seminole and Santa Fé Springs, the crooked-hole problem, as it was then called, occupied a primary position among the topics of the day in the fields of California and the Mid-Continent. The net result of all the discussion and study at that time was the conclusion that oil wells should be drilled with as little deviation from the vertical as possible and that crooked holes with elbows and dog legs were to be avoided because of the drilling and producing difficulties encountered therein, but that many nonvertical holes were slanting or angling rather than crooked and were not a serious problem.

Jan 1, 1934

By Donald M. Liddell

From a commercial standpoint, the only beryllium mineral warranting attention is beryl, 3Be.Al2O3.6SiO2, which is of fairly widespread occurrence. The chief deposits are in Brazil, Argentina, India, Canada and Portugal. When pure this contains about 14 per cent of beryllium oxide. The mineral richest in beryllium is phenacite, (BeO)2SiO2, or beryllium orth-osilicate, which contains 45.55 per cent beryllium oxide when pure, and if anyone is ever fortunate enough to discover a large deposit of it, it will revolutionize beryllium metallurgy. Gadoljnite, zBe0.Fe0.2Yz0~.zSi0~, is also often referred to as a beryllium mineral, though the occurrences are comparatively scant and it is of more interest as a source of yttrium than it is of beryllium. There has been a good deal of talk recently regarding some occurrences of helvite in the United States. Helvite is a complex manganese-iron beryllium silicate and, apart from difficulties that would arise in its treatment because of its compo-sition, the beryllium content of the known deposits is not high. Early Metallurgy The elemcnt beryllium was first isolated by L. N. Vauquelin in 1797.~ He crushed and heated beryl, having the idea that this heating made it more readily amenable to attack by chemicals, and then mixed the mineral with three times its weight of caustic potash and fused the mixture. The melt after cooling was dissolved in hydrochloric acid: dehydrated, and again taken up with hydrochloric acid and filtered to separate the silica. The filtrate was treated with an excess of potassium carbonate and the precipitate after draining was leached with a solution of caustic potash, which dissolved the alumina. The undissolved material was, in Vauquelin&apos;s own words, "une terre nouvelle." He dissolved the precipitate with nitric acid and evaporated it to dryness, took up with hydrochloric acid and threw the iron out with potassium hydrosulphide, though he found that to make a complete separation of the iron involved a second treatment. The solution, after throwing out of the iron, had a pronounced sweet taste, and though Vauquelin always speaks of working on "terre du beril" he suggests that the new element should be known as "glucine" (glucinum) from the Greek word for sweet, because of this outstanding property. Vauquelin did considerable work on the comparison of aluminum and beryllium, working out a separation of most of the aluminum based on its precipitation as alum. His work is reviewed at some length, since ordinarily his procedure is incorrectly stated. It will also be recognized by those who have studied beryllium metallurgy that a good many technicians have followed his ideas since, including preheating the beryl before treatment. The fusion with

Jan 1, 1944

By D. R. Uhlmann, T. P. Seward, O. Chalmers

A magnetic field has been used to damp out liquid convection during the solidification of castings. Ingots of Al-2 pct Cu were poured from various sperheats (10" to 65°C) into a room-temperature graphite mold located between the poles of an electromagnet. The effect on ingot structure of varying the strength and time of application of the magnetic field was investigated, and the results are interpreted in light 01- current theories of ingot structure. In the solidification of alloy systems, thermal gradients in the melt and differences in density of the constituents are expected to produce convective motion in the liquid. The thermal convection caused by temperature gradients should be present during the freezing of both alloys and pure materials, while the solute convection caused by density differences should be of concern only for alloys. The possible influence of this natural convection on the structure of castings has been discussed by Ruddle,&apos; Chalmers, and Tiller. More recently, an experimental investigation of such effects was carried out by Cole and Bolling. These workers took stationary molds containing lead- and tin-based alloys and. using a brine solution. quenched them from various superheats above their respective liquidus temperatures. When grids were placed across the mold diameter to suppress convection, the grid region was later observed to contain a larger percentage of columnar grains than other parts of the casting or than similar castings poured without the grids present. From thermocouple measurements, they found the temperature in the grid region to be higher than that in the region outside the grids throughout the freezing process, and concluded that convection should be an important mode of heat transfer in normal castings. In addition to such convection arising from thermal gradients or differences in density of the constituents, a further source of convective motion, which we shall call "momentum convection", may be particularly important in small (laboratory-size) castings. By this term we refer to the convective motion produced in the initial pouring process, a motion which is damped out as the linear momentum and angular momentum of the liquid are dissipated. Besides these sources of convection, which are present to some extent in all castings. external influences may also be effective in producing convective motion. Examples of such "forced" convection which have been discussed in the literature include stirring the melt, shaking the mold, rotating the mold, and so forth The purpose of the present study was to examine the effect of convection on the structure of castings poured into a cold mold. In this work, a magnetic field was employed to damp out the convective motions within the liquid, and hence control the extent of con- The effect of a magnetic field on convective currents in a conducting liquid is to induce eddy currents which oppose and damp out the convective motion. vection. The technique of magnetic damping was previously used by Utech and F1emings" in their study of convective effects on impurity banding and other substructure in alloy crystals grown unidirectionally from the melt. In their investigation, fields as small as 200 gauss were found to be effective in damping the convection currents which influence the banding. I) EXPERIMENTAL TECHNIQUE In the present study, alloys of A1-2 wt pct Cu were poured into a room-temperature graphite mold. The mold, in the shape of a circular cylinder, 2 in. ID, 2-3/4 in. OD, 5 in. inside height, and 5-1/2 in. outside

Jan 1, 1967

By Nicholas J. Grant, Rolf Nordheim, Bill C. Gissen

The system Cb-Re was examined in detail utilizing pure metals, careful melting techniques, and heat treatments. Metallographic and X-my methods were utilized for phase identification. In addition to soli-dus determinations, the composition limits and mode of formation of the intermetallic compounds 0 and X were determined. The binary constitution diagram Cb-Re has been the subject of a number of investigations.&apos;-7 Two intermetallic phases have been described and tentative diagrams have been proposed. It was the aim of this investigation to obtain a complete and more accurate diagram through the use of purer alloys and improved techniques. The diagram worked out by Knapton7 was published after our experiments were concluded. EXPERIMENTAL METHODS The starting materials were Re powder of 99.95 pct purity, supplied by the Chase Brass and Copper Co., and Cb rondelles of 99.6 pct purity, supplied by the Electro Metallurgical Co. Typical analyses are given in Table I. The alloys were prepared from compacted Re powder and Cb rondelles; for critical compositions master alloys were used. The melts varied from 5 to 50 g and were melted nonconsumably in an Heraeus arc furnace, under ti-tanium-gettered laboratory grade argon. It was necessary to invert the buttons and remelt, followed by crushing and further remeltings, the number of which depended on the nature of the fracture of the alloy. The weight of each alloy was carefully checked after each melting operation. It was found that significant weight losses occurred only when loose Re powder was used. These losses amounted to a maximum of 3 wt pct in such instances, but did not occur after the charge was once molten, regardless of the composition. Typical loss of weight after 4 remelts, including crushing, amounted to 0.2 wt pct. Oxygen pickup during successive melting cycles did not appear to be significant, since the weight gain values never exceeded 0.01 wt pct. Control of the composition of the alloys was not too difficult; however, the problem of homogenization was a far greater one. Optimum alloying conditions were finally achieved by a combination of master alloy production and repeated crushing and remelting cycles. The compositions of the alloys utilized to determine the constitution diagram are listed in Table 11. The weight balance method was used ultimately as the sole analytical method, since repeated checks indicated that it was accurate to 0.2 pct, if the weight losses were small. The results were double-checked by a metallographic study of the homogeneity of the samples, since this was presumed to be the more serious factor. Heat treatments at 1200°C or lower were accomplished by sealing the specimens in Vycor tubes, heating in a Globar furnace, followed by air cooling. This was considered to be an adequate quench because of the very low temperatures involved. For temperatures of 1200" to 1900°, alloys were homogenized and heat treated in a tungsten-filament resistance vacuum furnace. From 1900" to 2750" a tantalum-tube resistance furnace was utilized, operating under a vacuum of 105 mm Hg. The temperature measurements up to 1200" were made by means of platinum-platinum 10 pct Rh thermocouples, with an accuracy of 5°C. For temperature measurements greater than 1200°C, optical pyrometers were used. They were calibrated against a standardized instru-

Jan 1, 1962

By T. F. Mueller, P. A. Witherspoon

For the case of an infinite radial system operating at constant terminal rate, the reservoir engineer often uses the "point source" solution of the diffiusivity equation to study pressure interference effects. At early times and at short distances from the inner boundary these solutions are invalid. The amount of error is often not precisely defined because of mathematical difficulties. Work presented here shows that, if dimensionless time is defined appropriately, previous solutions of the pressure equation can be displayed .as a family of curves on one chart. These solutions include the point source solution (referred to in the field of hydrology as the Theis solution) and other solutions obtained with digital computer methods. With these curves, an exact evaluation of the pressure drop within a reservoir or an aquifer can be made by the engineer. Examples of field problem solutions are presented. In most reservoirs the error involved when the Theis solution is employed is often negligible; whereas, in the calculation of interference effects in an aquifer, a substantial error can occur through such an approach. INTRODUCTION Flow equations are used in petroleum engineering to study the behavior of individual wells and reservoirs. In the case of wells, the pressure response at the wellbore face is the major point of interest; whereas, in the case of reservoirs, the pressure response at the interface of the aquifer boundary is sought. To aid in such studies, the flow equations have been solved in terms of the behavior at these two inner boundaries. Only limited work has been published in regard to the pressure conditions away from these points, i.e., within the reservoir or aquifer. Theis and Mortada are among the few who have reported on this problem. The Theis approach employs the exponential integral and is valid for pressure conditions that occur some distance away from the flow disturbance. It is derived from the concept of a point source, as opposed to a flow across some finite area. The Mortada results, on the other hand, are valid at all points within the reservoir or aquifer. They are presented in terms of dimension less ratios of the radius where the pressure is desired to the radius where the flow rate is measured. Their main use, in the past, has been in aquifer studies. The published results are presented in the form of graphs that are limited to a maximum radius ratio of 64. These graphical results are cumbersome to interpolate at non-integral radius ratios, so that one may be forced to utilize a rather involved analytical expression presented by Mortada. BASIC EQUATIONS The solutions of Mortada and Theis are both based on the diffusivity equation as applied to the case of an infinite radial system subject to a constant terminal rate. The equation is obtained by combining the material balance equation with Darcy&apos;s flow equation. The assumptions implicit in the use of this equation are as follows: (1) a single fluid is present that occupies the entire pore volume; (2) the reservoir is horizontal, homogeneous, uniform in thickness, and of infinite radial extent; (3) compressibility and viscosity of the fluid remain constant at all pressures; and (4) fluid density obeys the equation Using the diffusivity equation in situations where the above conditions do not hold will result in errors. These errors (not discussed here) but only the errors which arise in the solution of the equation itself. The diffusivity equation for the homogeneous reservoir conditions cited above can be written in cylindrical coordinates, as To obtain a dimensionless equation, so a single solution can be used for applications of different porosity, permeability and fluid properties, the following transformations are usually made: After these transformations are made, Eq. 3 .can be written in dimensionless form, as MORTADA SOLUTION One solution of Eq. 6 has been given by Mortada.

Jan 1, 1966

By D. E. Etter, J. E. Selle

The Pu-Ce phase diagram was determined by differential thermal analysis, metallography, and elechm-nricroprobe analysis. The dingram is chararterized by a eutectic with extensive solid solubility in the cubic Phases of both cerium and plutonium. No intermediate phases were found. Cerium is soluble in e plutonium to 16.0 at. pet Ce at 626OC nnd in d plcltoniurn to 23.0 at. pet at 613 "C, decreasing to 17.5 at. pet at room temperature. No solubility in the a, ß, or ? phases was jound, and the mininum cerium required to stabilize 5 plutonium to room temperature is 3.2 at. pet. The maximum solubility of plutonium in 6 cerium is 19.5 at. pet at 721OC, and the maximum soluhility of plutonium in ? cerium is 34.5 at. pet. Invariant points in the system are: a) eutectic at 626oC, L16.5 = E Pu16.0 + y Ce65.5; b) peritectoid at613oC, e Pu13.5 -y Ce65.5- d Pu23.0. AS part of a program aimed at the determination of the phase equilibria in the Pu-Ce-Cu ternary system, preliminary investigations were made of the three binary systems. A survey of the Pu-Ce binary system by differential therma1 analysis indi- cated several areas of disagreement with the published diagram,&apos; primarily in the shape of the liquidus surface. Consequently, a thorough investigation of the system was undertaken, and this report presents the results of the study. EXPERIMENTAL PROCEDURE Three methods of investigation were used: differential thermal analysis (DTA), metallography, and analysis with electron-microprobe X-ray analyzer (EMX). The EMX analysis was particularly useful for the determination of solvus lines. The DTA method was most useful for the determination of the liquidus curves. Metallography complemented both of these techniques. Materials. The cerium metal used for most of this work had a freezing point of 805°C. This material showed 15°C premelting, and was found metallographically to contain some unidentified in~lusions.2 The temperature of premelting is defined as the point at which the DTA curve breaks away from the base line, analogous to a curve obtained from a solid-solution alloy. Several compositions were prepared near the cerium end of the diagram with higher-purity material which had a freezing point of 800°C. etallographic analysis showed this material to be relatively free of inclusions and only 8°C premelting was observed. Major impurities were found by spectrographic

Jan 1, 1964

By J. P. Heller, H. B. Bradley, A. S. Odeh

It is an accepted procedure to represent oil field displacement problems in which the pressure is relatively constant by a potentiometric model. Variations in reservoir permeability thickness product are represented in the model by proportional variations in electrolyte depth. It is shown that significant errors are present wherever these variations are of such magnitude that the consequent differences in the electrolyte depth in the model or any regions therein are appreciable in comparison with their respective horizontal dimensions. To demonstrate the order of magnitude of this error, a hypothetical linear oil field in which permeability varies linearly with distance was treated both analytic.ally and by potentiometric model. The results obtained from the model are compared with the exact solution for various configurations of linear geometry. Deviations in flow times up to 11 per cent were observed. It is confirmed that these discrepancies can be reduced by increasing the areal scale and/or decreasing the vertical scale of the model. It is the purpose of this work to assist in the design of potentiometric models by indicating the relationship between this error and the chosen scale factors. INTRODUCTION The fundamental geometrical criterion which determines whether the pressure distribution in an oil or gas reservoir may be simulated in a conventional potentiometric model is the requirement that all reservoir parameters be constant along any vertical line between its upper and lower boundaries. This situation never obtains exactly; nevertheless, it is usually assumed that there is no permeability stratification within the section of interest, that all wells completely penetrate the sand, that there are no gravitational effects, and that variations in thickness of the sand are small compared to the horizontal extent of the field. In these ways the reservoir problem is reduced to two dimensions in which there is no variation of pressure in the vertical direction within the limits of the sand. Variations in sand thickness and/or horizontal pesmeability may be taken into account as described by Muskat, by considering the fluid conductivity of the reservoir in its horizontal plane to be proportional to the product of permeability and sand thickness. If the variations in sand thickness are small compared to the horizontal dimensions of the reservoir, then it is a good approximation to consider the reservoir problem to be essentially two dimensional. The same approximation, however, is made in the simulation of the assumed two-dimensional reservoir by the electrolytic model. The model, if it is to take into account variations of permeability-thickness product, must of necessity be made in three dimensions, that is, with variable depth. Most potentiometric model studies and theoretical treatments reported in the literature to date2,3,4,5,6,7,8 are those in which either an average permeability was used or a constant permeability was assumed. This is understandable since detailed permeability data are not usually available for the majority of reservoirs. Many investigators have recognized that the failure to incorporate permeability variations within a reservoir in model studies leads to serious error in predictions made

Jan 1, 1957

By J. A. Jargon, H. K. van Poollen

Flow of slightly compressible fluids through porous media can be described by linear equations. Many mathematical solutions- are available for the boundary conditions of constant terminal pressures or constant flow rates, or a combination of both. Various techniques of formation evaluation use drastic rate changes, such as sudden shut-in. Other methods require that the well be produced at a constant rate. In practice, one is not always able m fulfill these rigid requtirements. This report shows a methor1 by which varying-rate data can be converted to a constant-rate pressure response, called the unit response function. After obtaining the unit response function, one may analyze it, using techniques described in the literature. The method uses tile principle of superposition. Necessary data is a time history of pressure and production. If pressure changes and/or rate changes are very drastic, the unit response function becomes erratic and oscillates The erratic and oscillating results are obvious, and under those circumstances, no answer can he obtained. It appears, however, that a response function without oscilla-tion will not contain any appreciable errors —- one gets either good results or no results. This report includes a mumber of examples of converting constant-rate data to constant terminal-pressure data and vice versa. In addition, a number of field-test applications are given. This method should be useful in converting mathematical solutions from one boundary condition to another. It already has proven useful in converting varying-rate data to constant-rate conditions. INTRODUCTION Pressure drawdown tests are performed on production wells to determine various reservoir characteristics, including permeability, distances to discontinuities, reservoir continuity and wellbore conditions. An ideal drawdown test is performed at a constant production rate with pressure observation during the drawdown period. A typical drawdown curve for a constant rate of production is shown in Fig. 1. In practice, a constant production rate cannot always be maintained. Fig. 2 shows a pressure drawdown curve for a varying rate. Usual methods of analysis are not applicable to tests such as this. It is, therefore, necessary to convert the varying-rate data somehow, before usual analytical techniques can be applied. This report describes a method of obtaining a response function. A response function can be defined as the relationship between pressure and time for a well producing at a constant unit rate. Such a response function can be analyzed by the usual analytical techniques. Hutchinson and Sikora&apos; first approximated a resistance function (response function), and by applying the superposition principle, pressures were calculated using the varying rates. If no match was obtained, adjustments were made to the response function and the closer approximation was used again in an attempt to match calculated and observed pressure behavior. If a good match was obtained: the response function was then used to extrapolate the future aquifer behavior.

Jan 1, 1966

By C. H. Lee, R. Maddin

The diffusion rates of Ag110 in cylindrical single crystals of 99.99 pct pure silver, which were twisted to a total surface strain of 0.91 during the diffusion anneal at temperatures of 700°, 750°, and 800°C, were measured by sectioning and counting as a function of the strain rates. The ratio of the diffusivities while strain ing occurred (Ds) to those of the unstrained specimens varies linearly with the rate of twisting and attains values of near 100 for some of the rates used. The enhancement of diffusion by straining is inversely proportional to the temperature at which diffusion occurs. The activation energy for diffusion determined from the data plotted as a function of the rate of twisting decreases from 44,090 cal per mole for zero strain, to an asymptotic value of 21,000 cal per mole for the strain rates of 22 x it)"5 see-l. Qualitative explanation for the observations based on the generation of nonequilibrium number of defects by plastic deformation will be discussed. The initial research of Buffington and cohen1 on self-diffusion in a iron under compressive stresses contributed the first quantitative information concerning the effect of applied stresses on diffusion. These results were obtained from radioactive Fe55 plated on one of the horizontal surfaces and compressing the large-grained specimens while the diffusion-anneal was occurring. Enhancement of diffusion of a maximum of seventeen times was observed provided the strain was in the tertiary stage of creep and the rates of straining were at least as fast as rates used in the normal creep test. On the other hand, Darby, Tomizuka, and Balluffi,2 extending silver single crystals up to 30 pct elongation at rates of straining about equal to those used by Buffington and Cohen observed no effect. For the past two and a half years at the University of Pennsylvania, we have been investigating the effect or torsional strains on self-diffusion in silver single crystals. If enhancement is observed as has been reported1 a possible explanation may be based upon the generation of fairly large numbers of point defects and their role in the diffusion process. Hence, since torsion should produce an abundance3 of point defects, an increase in the diffusivity while the crystal is being twisted should easily be measured. EXPERIMENTAL PROCEDURE Our research uses single crystals of silver prepared from 99.99 Ag by the Bridgman method in a dynamic vacuum of less than 25 µ. As grown, they are about 25 cm long by 1.3 cm in diam. The crystals are cut into 7.5 cm lengths with a jeweler&apos;s saw and machined to the shape shown in Fig. 1. The test length of the crystal is machined to a 0.6 cm diam after which the ends are masked and the test section etched heavily in HNO3, and KCN:(NH4),S2Os , solution to remove the effects of machining. The specimen is then annealed in vacuum for 8 to 12 hr at 800°C to remove any residual stresses and also to recrystallize the end sections. The recrystallized ends are necessary since experiments showed that single-crystalline end sections are too soft to transmit the desired torque. Occasionally, recrystalliza-

Jan 1, 1960

By John F. Abel

The following quotation is from "Guidelines for evaluation of undergraduate curricula in geological engineering, mineral processing, and mining engineering" prepared by the Committee on Education of SME of AIME. "The objectives of the Engineers&apos; Council for Professional Development (ECPD), as delineated in its constitution, are: (a) To promote and advance all phases of engineering education with a view to the promotion of the public welfare through the development of the better educated engineer and engineering technician." (Italics added.) The problem is that no one has as yet seriously developed a method of supplying engineering technicians. There were great hopes that the expansion of junior colleges would help satisfy this need. Sadly, they have not; and it appears they are unwilling or unable to supply the need for mineral engineering technologists. Apparently, the junior colleges cannot afford staff for such courses, even when the colleges are located in mining districts.

Jan 1, 1971

By Kenneth A. Moon

Kenneth A. Moon (U.S. Army Materials Research Agency)—The authors are to be congratulated for a very interesting and valuable paper. Their discussion of the structural implications of the results shown in their Fig. 5, however, requires a small correction. The model of Speiser and Spretnak with 0 = 1 and z&apos; = 2 is perfectly reasonable for the Ti-O a phase, but Eq. [3] is valid only for solutions sufficiently dilute that the number of empty sites excluded by more than one filled site is negligible. The composition at which intrinsic saturation occurs therefore cannot be deduced from Eq. [3], but but must be decided by consideration of the structural details of the phase in question. In this case, intrinsic saturation is expected not at the composition Ti3O but at Ti2O, because Ti2O has the anti-Cd structurel4 for which each filled octahedral site has two nearby empty sites, one in the hexagonal plane immediately above it, and one in the similar plane below it. The other two models, with ?=1/3 and 1/2, imply a distinction between octahedral sites in pure titanium which is not easy to justify. The problem of extending Speiser&apos;s and Spretnak&apos;s treatment in a general way to more concentrated solutions will be the subject of a forthcoming publication by the writer. M. T. Hepworth and R. Schuhmann, Jr. (authors&apos; reply)—The authors wish to thank Dr. Moon for calling to their attention the paper by Holmberg which presents the results of X-ray studies of Ti-O solutions ranging from 0 to 33 at. pct 0 and quenched from various annealing temperatures between 400" and 1800°C. Within these ranges, Holmberg found three types of phases: 1) At high oxygen contents (above 25 at. pct) and low annealing temperatures, he found the anti-Cd(OH)2 structure referred to by Dr. Moon. In this structure each titanium atom is in contact with 3 oxygens and each oxygen is in contact with 6 titaniums, the "available" oxygen sites corresponding to every other layer of octahedral sites in the titanium matrix. The limiting composition is Ti2O. However, this anti-Cd(OH)2 structure was not observed for samples containing 25 at. pct 0 or less. 2) For the specimen containing 25 at. pct 0 annealed at 400°C an ordered Ti3O structure was observed. This structure is related to the anti-Cd(OH)2 structure but differs from it by providing only two oxygens adjacent to each titanium atom and thus is consistent with the model represented by Eq. [5] in our paper, with 6 = 1/3, z&apos; = 0. 3) For dilute solutions and for more concentrated solutions annealed at higher temperatures, the structure corresponds to that of the metal with random distribution of oxygens among all the octahedral sites. Thus, it is interesting to observe that the thermo-dynamic indications of ordering in the vicinity of Ti3O can now be supported qualitatively at least by Holmberg&apos;s X-ray evidence of the existence of an ordered phase of the composition Ti3O. That is, for solutions with oxygen contents close to that of Ti3O, both the thermodynamic data and the X-ray data are more consistent with models based on the ordered structure of Ti3O than they are with the model which Dr. Moon suggests corresponding to "intrinsic saturation" at Ti2O.

Jan 1, 1963

By J. W. Downey, J. B. Darby, L. J. Norton

THE only previous investigation of the phase equilibria in the Ta-Pd system was reported by Greenfield and Beck.1 Their work (actually a portion of a much broader survey) was limited to the composition range 50 to 75 at. pct Ta and to a single temperature, 1000°C. The results indicated that no intermediate phases were present at this temperature. They pointed out that this was an unexpected result in view of the fact that niobium, which belongs to the same group in the periodic table as tantalum and has essentially the same atomic size, forms a o phase with palladium.&apos; Also, tantalum in combination with rhodium,&apos; iridium,&apos; or platinum&apos; stabilizes the s phase. By analogy, the Ta-Pd system would also be expected to contain a s phase. The present investigation was therefore undertaken to explore more fully the phase relationships in this system. Alloys were prepared by arc melting on a water-cooled copper hearth in an argon-helium atmosphere. The purity of the starting materials was greater than 99.9 pct. The weight losses on melting were less than 1 pct and therefore the alloys were not analyzed chemically. Specimens were wrapped in molybdenum foil, encapsulated in quartz capsules under a vacuum of at least 1 x 10-5 mm of Hg, annealed as indicated in Table I, and water quenched. Optical and X-ray metallography were used for identifying the phases present in the annealed and quenched alloys. The alloys were resistant to attack by several acids; however, a sodium cyanide electroetch and an immersion etch containing 1 part HF, 1 part HNO3, 2 parts H2SO4, and 5 parts H2O by volume were found satisfactory. The X-ray diffraction patterns were taken with a Straumanis-type Debye-Scherrer camera and filtered copper or chromium radiation. A summary of the phases found in this investigation is presented in Table I. No attempt was made to determine the composition limits of the various phases. The present results indicate that this system consists of two terminal solid solutions separated by at least four intermediate phases at the approximate compositions Ta3Pd, -TaPd, TaPd,, and TaPd3. The Ta-rich solid solution, containing less than 10 at. pct Pd at 1150°C, is in equilibrium with a o phase which is stable in the vicinity of 25 at. pct Pd. The latter phase is also in equilibrium with a bct phase at the equiatomic composition. At high temperatures it appears that the Pd-rich solid solution extends to at least 66.6 at. pct Pd and is in equilibrium with the bct phase. When annealed at 900°C, a sample containing 66.6 at. pct Pd transformed to an unidentified phase designated as X. An X-ray diffraction pattern of this phase contained sharp low-angle lines while the high-angle lines were characteristically diffuse. The observed d-spacings and relative intensities for lines in the low-angle region are presented in Table 11. In the vicinity of 70 at. pct Pd an intermediate phase having the TiA13-type structure is formed. It is stable to at least 1100°C, and presumably dissolves congruently into the ter-

Jan 1, 1963