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By D. G. Russell

Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary eflects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estitnates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. On the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. INTRODUCTION The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottom-hole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + ?t)/ ?t (where At is shut-in time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "afterproduction" or "fill-up" portion of the pressure build-up. During the period that the well fill-up effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the afterproduction period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the afterproduction period is a paper by Gladfelter, Tracy and Wilsey.1 In the approach of these authors it is necessary to measure the rate of influx into the well during the afterproduction period. This is done through sonic measurements or through measurement of tubing-head and casing-head pressures simultaneously with

Jan 1, 1967

By RAYMOND M. LARSEN

The area covered by this paper is the same as that covered in 1944. Colorado, Montana, Utah, and Wyoming are included in the discussion and statistics, and brief mention is made of activities in the adjoining states, except Nebraska and New Mexico, which are considered separately (see pp. 187-189). The other adjoining states, North and South Dakota, Arizona, Nevada, and Idaho, have had virtually no oil or gas production, except in the gas field of Cedar Creek. Montana, which extends into North Dakota; the Pierre field in South Dakota, where gas is produced and separated in gas-water wells, and the abandoned Payette area in western Idaho. Seven gas wells were drilled in North Dakota, but no wildcatting was reported. Several unsuccessful wildcats were drilled in South Dakota, and some were continuing at the end of the year. Activity in Idaho and Nevada was negligible.

Jan 1, 1946

By J. Geertsma

The relationship between porosity and the speed of propagation of acoustic waves in fluid-saturated porous rocks as measured by the Sonic log and by ultrasonic tecbniques is analyzed. Biot's continuum theory 1 is used to explain the difference in acoustic wave propagation between a dry and a liquid-saturated porous material. The porosity is a variable in this theory. However, the acoustic wave propagation in the dry rock depends too on porosity, and this dependence is not predicted by the theory. Frequently in dry sandstones, a nearly linear relationship between reciprocal acoustic wave velocity and porosity is observed in the low-porosity range. The physics behind this behavior is outlined. An empirical relationship of the form, 1/v = A + F, applies accordingly for many porous dry rocks, provided the porosity is the only variable. The presence of a liquid in the pores changes the value of B, and this change is found to be in agreement with the Biot theory. The time-average relation introduced some years ago2 results in an equation of the same type — 1/V = F/Vf + (1 - F)/Vr — but is not based on a sound physical picture. Still, this relation sometimes predicts approximately correct A and B values. Carbonate rocks with their complicated pore structures sometimes show a different relationship between wave velocity and porosity, unfavorable for log interpretation. Examples are presented. The simultaneous presence of calcite, dolomite and anhydrite, with their different grain densities and matrix compressibilities, complicates acoustic-log interpretation in carbonate rocks still further. Other complicating effects of acoustic-log interpretation are discussed. They are related to the influence of shale streaks and natural fractures on the average wave velocity observed by the logging tool and to the effect of adsorption phenomena on wave propagation in unstressed rocks particularly in sandstones. INTRODUCTION The velocity of propagation of sound waves in porous sediments as a function of depth is a quantity frequently measured. Velocity loggers of various d-sign may be used, for which velocity is defined as the. distance between a wave generator and a wave detector (one-receiver system) or the distance between two wave detectors (two-receiver system), divided by the shortest time required for a vibrational pulse to cross this distance. Velocity loggers ale used to assist in seismic prospecting, to differentiate between the various types of sedimentary rock layers, and also to determine rock porosity and pore fluid content. This paper is especially concerned with the relation between velocity and porosity and the effect of the pore fluid. Most velocity-log interpretation in terms of porosity is based on a formula advocated by Wyllie, et al,2 suggested earlier by Hughes and Jones,3 and known as the "time-average relation". This formula app1ies for a model consisting of a layered system of parallel alternating slices of a solid and a liquid, crossed by the wave path perpendicular to the interfacrbs. This must be an unsuitable model for the derivation of wave propagation properties of liquid-saturated porous media. It suggests that only rock matrix and fluid properties influence the wave velocity. The surprising fact, nevertheless, is that applications of this formula to clean sandstones under specific conditions (sufficient effective stress) results in porosity predictions which are close to reality. Other authors, such as Gassmann,4 White and Sengbush,5 Brandt,6 and Hicks and Berry,7 make use of more realistic models to arrive at a wave velocity formula for porous sediments. Their models consist of various liquid-saturated packings of frictionless spherical grains and are, therefore, also highly idealized. A number of experimental results obtained in the laboratory can be better explained with these model theories than by the time-average relation. A study of a general character, not depending a priori on a special model of the porous structure, was still lacking.

By AIME AIME

THE following paragraphs comprise such information as the Secretary has been able to obtain concerning the members and associates whose deaths have been reported. Further particulars or corrections of errors, and biographical data concerning deceased members or associates not already noticed in this way, are solicited. Pat Doyle was born in 1849. At the age of fifteen he entered the Civil Engineering College of Madras, India, and left it at seventeen, having achieved special distinction in mathematics, chemistry,. and geology. Before be was eighteen years old he was in charge of two of the most important Sub-Divisions in the Madras Presidency, where he had ample opportunities for acquiring a preliminary knowledge of his profession, which was his chief object in joining the Public Works Department. In 1867, his energetic measures saved the island of Seringham from disastrous inundation. At this period he began contributing to the press ; and after a varied practical experience he came into public notice again in 1876, with an article in the Colliery Guardian on Indian Mines and Mining. In 1877 he became a Fellow of the Statistical Society of London. He was a founder of the Straits Branch of the Royal Asiatic Society and a life member of the parent Society of Great- Britain and- Ireland, as well as a member of the Independent Asiatic Society of Bengal. In 1878-9 he was Chief Superintendent of the Public Works of Perak; was active in having the Associate Member Class added to the Institution of Civil Engineers; and became a member of the Society of Engineers of London and of the North of England Institute of Mining and Mechanical Engineers. In 1880 he went to the Southern Colonies and held several appointments in Australia, where he became a member of the Johnsonian Club, Brisbane, and the Queensland Philo-

Jan 5, 1908

By Joseph R. Hatch

When compared to average shale composition, average coal is enriched in sulfur and selenium, has similar amounts of arsenic, beryllium, lead, antimony and molybdenum, and is depleted in at least 26 other elements. Within a coalfield, or region, some coals are enriched (10X average shale) in silver, arsenic, cadmium, cobalt, germanium, molybdenum, nickel, lead, selenium, uranium, and zinc. Important factors controlling element distributions in coal include geochemical conditions (primarily pH) in the peat swamp, composition and depositional environment of coal roof rocks, thermal maturity (rank), nature and intensity of any epigenetic mineralization, composition of ground waters that come in contact with the coal, and degree of weathering.

Jan 1, 1983

By R. L. Orr, J. D. G. Masse, Ralph Hultgren

The relative partial molar enthalpies of gold and tin in liquid Au-Sn alloys have been measured from Xsn = 0.474 to 0.510 at 696°K, slightly above the melting point of solid AuSn. Within an average precision of 6 cal per g-atom, the data are represented by two smooth curves, which satisfy the Gibbs-Duhem relationship and which do not show any anomalous behavior in the range of composition studied. The results give no support to the hypothesis that atomic associations in the equiatomic liquid alloy resemble those in solid AuSu. LITTLE has been firmly established as to the nature of atomic distribution in liquid metallic phases. A favored hypothesis assumes the existence of atomic groupings in the liquid phase which are similar to those in solid phases occurring at lower temperatures. Beginning with this hypothesis, it is often possible to adjust the values of certain parameters (such as degree of association) so that approximate agreement is achieved with certain features of the X-ray diffraction pattern of the liquid, even though many other possible structures might satisfy the data equally well. Thus, in this manner, the structure of liquid tin has been described as a dispersion of fragments of gray tin in a matrix of metallic tin.1 Four X-ray diffraction studies2"5 have been made of the liquid alloy of composition AuSn at temperatures slightly above the melting point of the solid. Each investigator concluded, on somewhat different grounds, that the liquid consisted to a large extent of arrays of atoms similar to the solid, with admixture of more disordered arrays. Solid AuSn has the nickel arsenide crystal structure: each tin atom has six nearest neighbors, all gold atoms; and each gold atom has six tin and two gold atoms as nearest neighbors. It remains highly ordered to the melting point. The liquid alloy has a large exothermic (?H700° K = -2700 cal per g-atom6) enthalpy of formation, favoring ordering and making the hypothetical molecular association not unreasonable. The possible existence of such solidlike arrays, or of a high degree of order that occurs preferentially at a specific composition in a liquid alloy, might also be revealed by thermodynamic behavior somewhat analogous to that in highly ordered solid alloy phases. The latter often exist over wide composition ranges, within which the highest degree of order occurs at the ideal composition for which the atomic fractions are equal to the fractions of sites which are "right" for each kind of atom. On departing from the ideal composition, the excess atoms occupy "wrong" positions, raising the internal energy and making it progressively easier for additional atoms to occupy "wrong" positions. Thus, on either side of the ideal composition, there should be a pronounced rise in the entropy and enthalpy, which would be shown particularly by the change in the relative partial molar enthalpies, ?Hi, since they depend strongly on d?H/dx. In the one case where accurate measurements have been made, the solid AuCu ordered phase, the structure becomes much less ordered as the composition deviates from the ideal, and relative partial molar enthalpies change sharply as shown by the data6 given in Table I. This suggests the possibility of finding similar pronounced changes in the relative partial molar enthalpies of gold and tin in liquid alloys near the composition AuSn if the postulated solidlike ar-

Jan 1, 1967

By K. L. Sutherland, J. Rogers

The relationships between collector and mineral, activator and mineral, and activator, collector and mineral will be considered herein. We propose to criticize current theories of flotation but we will not repeat the many pertinent arguments presented by Wark and Cox28 in 1937 in which the "chemical" or more strictly the "solubility" theory proposed by Taggart and co-workers22 is shown to be untenable. Recently Taggart, Arbiter and Kellogg24 have studied the long-chain aliphatic amines as collectors and have attempted to resuscitate the solubility theory for these particular collectors. Dean and Ambrose3 have felt that "we stumble over words" when we distinguish different mechanisms of adsorption. Our view is that nothing is more stultifying to the development of a science than attempts to force widely different phenomena into one classification. This oversimplification leads immediately to difficulties in the interpretation of results. Experimental Procedure The response of minerals to activator and collector was determined by "captive-bubble" tests. The methods of preparation of specimens26 and of testingin have been previously described. Results from captive-bubble tests were confirmed by flotation tests in glass-stoppered cylinders.26 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±o.2 pH units and ±5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible by a cross and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, the experimental results being indicated on the figures by a square. The curves show the limits of composition of solution in which flotation in a cell would be possible. Many factors other than those considered in these tests determine recovery or grade of a given mineral in practice.

Jan 1, 1947

By J. Rogers, K. L. Sutherland

The relationships between collector and mineral, activator and mineral, and activator, collector and mineral will be considered herein. We propose to criticize current theories of flotation but we will not repeat the many pertinent arguments presented by Wark and Cox28 in 1937 in which the "chemical" or more strictly the "solubility" theory proposed by Taggart and co-workers22 is shown to be untenable. Recently Taggart, Arbiter and Kellogg24 have studied the long-chain aliphatic amines as collectors and have attempted to resuscitate the solubility theory for these particular collectors. Dean and Ambrose3 have felt that "we stumble over words" when we distinguish different mechanisms of adsorption. Our view is that nothing is more stultifying to the development of a science than attempts to force widely different phenomena into one classification. This oversimplification leads immediately to difficulties in the interpretation of results. Experimental Procedure The response of minerals to activator and collector was determined by "captive-bubble" tests. The methods of preparation of specimens26 and of testingin have been previously described. Results from captive-bubble tests were confirmed by flotation tests in glass-stoppered cylinders.26 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±o.2 pH units and ±5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible by a cross and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, the experimental results being indicated on the figures by a square. The curves show the limits of composition of solution in which flotation in a cell would be possible. Many factors other than those considered in these tests determine recovery or grade of a given mineral in practice.

Jan 1, 1947

New York State Museum, Albany, N. Y. D H. Newland, State Geologist. A complete list of publications or the latest lists of available publications will be sent upon application. A series of Bulletins on The Mining and Quarry Industry of New York are available as follows: Bulletin 51 (1910), 15 cents; 161 (1911), 20 cents; 166 (1912), 20 cents, 174 (1913), 20 cents; 190 (1915), 15 cents; 277 (1925-26), 50 cents; 295 (1927-1929), 40 cents. Another series discusses the Geology of the State by Quad¬rangles, available as follows: Bulletin 153, Broadalbin Quad (1911), 25 cents; 154, Sche¬nectady Quad. (1911), 20 cents, 170, North Creek Quad . (1914)

Jan 1, 1933

By B. J. Guarnera

There have been major changes in the makeup and nature of the uranium exploration industry in recent years. Significant price increases precipitated an increase in exploration activity-according to the Department of Energy, exploratory drilling in 1977, by 140 companies, was almost 8 million m (26 million ft). This represents a 37% increase over the prior year's drilling. Projections for 1978 indicate at least 9 million m (30 million ft) of exploratory holes will be drilled in the US. Exploration expenditures in 1979, including land acquisition, drilling, and other costs, were estimated by DOE at over $236 million. Domestic expenditures for 1978 are estimated at over $250 million.

Jan 10, 1978

By T. L. Joseph, G. Bitsianes

The gaseous reduction of dense iron ore is a topochemical process in which reduction takes place at distinct interfaces between solid phases or layers. Under normal conditions, these interfaces remain parallel to the exterior surface of the ore body as they move inward. Certain conditions, such as cracking, high porosity, impurities, entrapped residual oxides, may cause departures from normal topochemical behavior. THE gaseous reduction of dense iron ore proceeds at interfaces between several solid phases or layers.',' Under normal conditions, these interfaces progress inward and remain parallel to the exterior surface of the ore body. This topochemical behavior is clearly illustrated in Fig. 1 which shows partially reduced specimens of natural and synthetic hematite. Using a coordinated sequence of macro, micro, and X-ray examinations, the authors1-'2 found that the number of interfaces and participating phases was in agreement with the Fe-0 system. Above 570°C, reduction of the ore involved a maximum of three common boundaries between four solid phases: iron, wiistite (Fe,O), magnetite (Fe,O,), and hematite (Fe,O,). Below 570°C, reduction proceeded through two interfaces between three phases: iron, magnetite (Fe,O,), and hematite (Fe,O,). The decrease in the number of phases below 570°C was due to the instability of wiistite below this temperature. The sequence of phases was also consistent with the equilibrium requirements. For example, the layers of iron oxides that were formed in topochemical fashion were always orientated in the order of increasing oxygen content. Thus, in Fig. 1 an outer layer of metallic iron is followed in turn by a thick intermediate band of black wiistite, by a thin layer of light magnetite, and finally by a relatively large core of hematite. This arrangement of the oxide layers was due to restrictions in reducing conditions which were imposed by the physical structure of the solid. The highly reducing gas on the outside of the particle gradually lost its reducing power as it penetrated into the specimen. On a macro scale, the layers of the various oxides appeared to be sharply defined and uniform in composition. Microexamination of the sections, however, revealed that the interfaces did possess measurable widths which varied with the porosity and chemical activity of the oxide phase undergoing reduction. For example, Fig. 2 shows three interfaces in a dense hematitic ore which was partially reduced at 850°C. At the iron-wiistite interface where the greatest porosity developed, the reaction proceeded over a zone 25 to 30 microns in width. Toward the interior, the interfaces became progressively narrower until at the magnetite-hematite boundary the reaction zone was about 1 micron wide. In this region the structure was exceedingly dense; the hematite possessing a porosity on the order of 3 pct. A careful micro study across polished layers of the various oxides revealed generally homogenous and single-phase structures. As reported in a previous paper,' the wiistite layer was characterized by an increase in oxygen content with depth of penetration. The topochemical behavior of reduction was studied in six types of ore of different origin, composition, and physical structure. In most cases, reduction proceeded at the boundaries of well defined layers or phases, and this behavior may be regarded as normal for most dense fine grained ores. Deviations from Ideal Topochemical Behavior A number of deviations from the normal topochemical behavior were noted. In these cases, the continuity of the reduction interfaces was disrupted in one of four ways: 1—Cracking of the specimen interrupted the geometric configuration, and the interfacial advance was no longer parallel to the exterior surface. 2—As a result of high porosity, the interfaces were spread over an appreciable distance and all but obliterated. 3—Impurities in the ore promoted a variety of deviations, including cracking. 4—A residual oxide phase was entrapped in the reaction product and left behind the advancing macro interface. Results from Cracking: A crack leading into the interior of an ore specimen presents a path of least resistance for the counter-flow of reducing gases and gaseous reduction products. Higher reducing conditions can be maintained along such cracks and reduction accordingly will propagate well ahead of the normally advancing reduction interfaces. Cracking was caused by a number of factors, one of which was the thermal spalling of impurities in the massive form. A more general type of cracking was due to reduction and was found in all dense varieties of natural and synthetic hematite, particularly in the temperature range of 500" to 700°C. The effect is shown clearly in Fig. 3. In this case, a dense sphere of pure hematite was partially reduced at 650°C for 100 min. The macrosection shows that one large reduction crack had penetrated the specimen and disrupted the normal topochemical advance of the interfaces. The outer layer of iron was only slightly affected but the thin dark layer of wiistite, adjacent to the ferrite, had widened perceptibly as it progressed along the crack. Farther inward, the magnetite layer was greatly disrupted and had penetrated irregularly to form islands of unaltered white hematite. A great deal of internal cracking is evident in the magnetite phase. From a practical point of view, the cracking of dense ores in the blast furnace could lead to desirable as well as undesirable effects. The general result

Jan 1, 1956

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,' there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By H. K. Shearer

Drilling for oil and gas in Arkansas in 1934 showed more activity than in any year since 1929; with a total of 96 completions, including 36 oil wells, 1 gas well and 59 dry holes. Of the producers, the lone gas well and 35 oil wells were in old fields, and one wildcat producer opened a new pool. Of the dry holes, 16 were in or near fields and 43 were wildcats. The total reported initial daily production of the oil wells was 9013 bbl., averaging 252 bbl. per well. Active drilling operations numbered 65 at the close of the year, compared with 26 at the beginning.

Jan 1, 1935

Organization Place Date 1919 American Society of Mechanical Engineers... New York, N. Y. Dec. 2-5 American Institute of Chemical Engineers.... Savannah, Ga. Dec. 3-6 Geological Society of America..: Boston, Mass. Dec. 29-31 American Society of Heating and Ventilating 1920 Engineers New York, N. Y. Jan. Mining and Metallurgical Society of America.. New York, N. Y. Jan. 13 American Institute of Min. and Met. Engineers New York, N. Y. Feb. 16-19 American Ceramic Society Philadelphia, Pa. Feb. 23-26 American Electrochemical Society Boston, Mass. Apr. 8-10* *On Apr. 9, a joint meeting will he held with the A. I. E. E.

Jan 12, 1919

By Samuel S. Wyer

THE following description of methods for conducting gas-producer tests is probably the first attempt to give the subject an analytical, thorough and comprehensive treatment. In some cases where tests have been made, the methods have been so unsystematic and ambiguous that it has been impossible to secure comparable results. To eliminate this difficulty, the following provisional code of gas-producer tests-which has some resemblance to the code of boiler-trials of the American Society of Mechanical Engineers-has been developed. The primary object in testing a gas-producer is to determine whether the producer is working satisfactorily or, what is the same. thing, to see if the efficiency is as high as it should be with the type of producer in question, and also to find out if the composition of the resulting gas is adapted to the work it has to do. In order that the test shall be of any value, it must be thorough and comprehensive, and must be conducted with skill and care. When so conducted, the test will reveal the economy of the producer; and, by making suitable changes, the efficiency will often be increased very much. As a result of the tests made by Jenkins, 1 the efficiency was raised from 56.2 to 71.2 per cent. This shows the large saving that may frequently be made in the fuel-consumption by studying the results of a careful test.. The log of the test, given in Fig. 1, shows that, just as soon as the temperature became regular, the percentage of CO, decreased and that of CO increased.

Mar 1, 1905

By G. L. Fisher, R. Maddin

The rate of self-diffusion in silver single crystals during torsional strain was measured over a wide range of tenperatures and strain rates. The torsional strain was applied in a cyclic manner by reversing the divection of twist aftev a certain fraction of the total strain was reached. Surface roughening was substantially reduced in cyclically strained specimens compared with those strained entirely in one direction. Diffusion coefficients were determined using a special sectioning technique whereby slices could be removed parallel to the surface of a strained torsion specimen. The accuracy of the technique was first determined using roughened specinzens statically diffused to various penetration depths. Simultaneous strain-diffusion experiments were then performed over the temperature range 550' to 800 using strain rates of lo-' to 2.2 x 10' sec-'. The increase in silver self-diffusivity during torsional plastic strain was small. In only one case was the enhancement greater than twice the static value of the diffusion coefficzent. The enhancements increased slightly with decreasing tenzperature and increased with increasing strain rate. A dislocation pipe mechanism of enhancement was found to explain the present results satisfactorily. The magnitude of the enhancements and the tenzperatures at which they were observed suggests that a steady-state dislocation density of 10' to 109 dislocations cm-2 existed during the high-tempevature deformation. The diffusion coefficient in an fcc metal can be increased by 1) an excess concentration of point defects and 2) the rapid movement of diffusing atoms along grain boundaries and dislocations. Plastic deformation may be responsible for enhancements by both of these mechanisms. The results of simultaneous strain-diffusion experiments have caused a controversy over the magnitude of the effect of strain upon diffusion. Experiments reporting large enhancements have been criticized for the manner in which the diffusion coefficient was measured. Several of these experiments have been contradicted by other results obtained in a similar manner. No enhancement was reported by two investigators''' who performed their experiments at high temperatures where strain is expected to have little effect upon diffusion. A recent theoretical analysis3 indicates that strain enhancement by a vacancy mechanism will be small and exist only at low temperatures and rapid strain rates. It is doubtful whether any experiment has yet proven that strain enhancements can occur by an excess vacancy mechanism. In the present research, experiments were performed at extremes of temperature and strain rate in an attempt to measure enhancement of diffusion by strain. Self-diffusion of silver during torsional deformation was chosen since two separate investigations4j5 indicate that at least a small enhancement exists under these conditions. An accurate method of determining the diffusion coefficient, mechanical sectioning, was employed after a technique was devised to apply it to the roughened surface of a strained torsion specimen. First, the accuracy of the technique was determined for different penetrations (2fi). Then diffusion experiments were performed at temperatures between 550" and 800°C at strain rates of 10"" to 10"" per sec. I) EXPERIMENTAL PROCEDURE Preparation of Specimens. The experimental procedure detailing the growth of crystals, their treatment, and the annealing techniques during straining are contained in earlier publications.496 The dimensions and orientations of the torsion specimens are shown in Figs. 1 and 2. licatiin of Torsional Strain. The torsion procedure was changed from that used previously. The specimens were strained in cycles to reduce the gross distortion and surface roughening inherent in twisting to high strains in one direction. For all strains above 0.30, the total surface strain was obtained as follows: the specimen was twisted to 0.10 strain in a clockwise direction; the direction was reversed; the backlash in the torsion apparatus was taken up; and the specimen was twisted in a counterclockwise direction through the initial starting point to 0.20 surface shear strain in the opposite direction. The strain reversal took no more than 1 min to accomplish. The total accumulated surface shear strain was arbitrarily taken as the sum of the 0.10 strain in the clockwise direction plus 0.20 in the counterclockwise direction. Although cyclic torsional strain was beneficial, surface roughening and specimen distortion were not entirely eliminated. The variation in the diameter at various points on the specimen was often much greater than the depth of the diffusion zone. Since serious errors might result if specimens were sectioned in the usual manner, a technique of lathe sectioning was devised to allow sections to be taken parallel to planes of equal concentration.

Jan 1, 1967

President-Mrs Andrew E Beer, Richardson Ave, Sea Cliff, L I, N Y First Vice-President-Mrs Lyman H Hart, 6-F Essex House, Garth Woods Apts, Scarsdale, N Y Second Vice-President-Mrs John R C Mann, 90 Edgemont Road, Scarsdale, N Y Third Vice-President-Mrs Edward P Chapman, Jr, 2632 Vista Larga Dr N E, Albuquerque, N M Fourth Vice-President-Mrs R A Cattell, 7717 14th St, N W Washington 12, D C

Jan 1, 1959

By R. C. Earlougher, F. G. Miller, T. D. Mueller, H. J. Ramey

There are many studies of flow in radial systems that can be used to interpret unsteady rerervoir flow problems. Although solutions for systems of infinite extent can be used to generate solutions fur finite ow systems by superposition, application is tedious. In this paper a step is made toward simplifying calcu1ations of such solutions for finite flow systems. Superposition is used to produce a tabulu-lion of the dimension1e.s.s pressure drop function at several locations within a bounded square that has a well at its center. The square system provides a useful building block that may be used to generate flow behavior for any rectangular shape whose sides are in integral ratios. Values of the tabulated dimensionless pressure drop function are simply added to obtain the dimensionless pressure drop function for the desired rectangulm system. The rectangular system may contain any number of wells producing at any rates. Furthermore, the outer boundaries of the rectangular system may be closed (no-flow) or they may he at constant pressure. Mixed conditions also may be conyidered. Tables of the dimensionless pressure drop function for the square system are presented and various applications of the technique are illustrated. Introduction In 1945, van Everdingen and Hurst' published solutions for the problem of water influx into a cylindrical reservoir. Since this problem is mathematically identical with the depletion of a cylindrical reservoir with a well at the origin, the van Everdingen-Hurst solution may be used to study the depletion problem. In their analysis, they assumed that the fluid had a small, constant compressibility such that flow was governed by the diffusivity equation For a constant production rate q starting at time zero, van Everdingen and Hurst showed that the unsteady pressurc distribution for both finite and infinite systems could be expressed in terms of a dimensionless pressure 'Sabulations of the dimensionless pressure drop for a unit value of r, were provided by van Everdingen and Hurst,' and later by Chatas.' Others also presented values in graphical or tabular form." If the radius of the well becomes vanishingly small, r,+ O, the line source solution may be used for Eq. 2 when infinite systems are considered. Eqs. 5 and 6 are excellent approximations for Eq. 2 under certain conditions: In 1954, Matthews, Brons and HazebroekV emonstrated that solutions such as Eq. 5 can be superposed to generate the behavior of bounded geometric shapes; i.e., the behavior of a bounded single-well system can be calculated by adding together the pressure disturbances caused by the appropriate array of an infinite number of wells producing from an infinite system. These wells are referred to as image wells. Matthews, Brons and Hazebroek considered systems containing a single well producing at a constant rate. This superposition can be represented analytically as

Jan 1, 1969

By R. W. Kewish

The preparation of massive uranium metal containing very low concentrations of a number of light elements by bomb reduction of UF4, with calcium is described. Details of procedures are given for preparing high-purity ingredients for the bomb reduction. The as-reduced uranium metal contained, on the average, less than the following amounts of light element impurities, in ppm: Li, 0.1; Be, 0.1; B, 0.1; C, 25; 0, 70; Na, 1; Mg, 3; Al, 2; and Si, 7. Other impurities for which the metal was examined averaged, in ppm: Ca, < 10; V, < 10; Cr, 2; Mn, 6; Fe, 50; Co, < 5; Ni, 8; and Cu, 1. THE preparation of very high-purity uranium metal in massive form for research purposes is of great importance. Recently the kilogram-scale preparation of uranium metal containing less than 70 ppm of detected impurities was accomplished by Blumen-thal and coworkers by vacuum remelting of high-purity crystals of uranium obtained by fused salt electrolysis.1"3 Albert and coworkers4 have reported successful experiments in lowering the concentrations of certain impurity elements in uranium, notably iron, to a few ppm by the zone-melting method. The present paper describes the preparation of high-purity massive uranium metal by the bomb reduction of UF4, with calcium. Early in 1951 a program was undertaken at the Los Alamos Scientific Laboratory to prepare uranium metal of very high purity with respect to a number of the light elements. The methods considered for this purpose were 1) bomb reduction of a uranium halide with calcium, 2) electrolysis of fused salts, and 3) hot wire decomposition of UI4, The first of these processes had been used extensively at Los Alamos since 1943 (and still is used) for the production of uranium metal.5 In considering the three processes it was evident that either of the last two would require an extensive development program with no certainty of success. On the other hand, a study of available data showed that uranium metal of very high purity with respect to some light elements had occasionally been made in routine processing by the first method. It was therefore decided that an intensive study of the bomb-reduction process would be made to see if it could be improved to yield uranium metal with very low concentrations of light elements. DEVELOPMENT OF PROCEDURES The bomb-reduction process used at Los Alamos consists of reducing UF4 with calcium, using iodine as a booster. The reaction is carried out in a magnesium-oxide crucible enclosed in a steel bomb. Argon is used in the bomb to avoid objectionable side reactions which would occur in the presence of air. All ingredients for this bomb-reduction process were examined as possible sources of light elements. It was known that high-purity UF4 was required. The calcium used in the reductions was a source of carbon and magnesium. The magnesium-oxide crucibles were sources of boron, silicon, and magnesium. The iodine did not appear to be a source of any impurities. Pure UF4- The UF4 for bomb reduction is prepared from U3O3 , by successive reduction to UO2, with hydrogen and hydrofluorination of the UO2, with anhydrous HF. Since it was known that no impurities were normally introduced during the gas-solid reactions, effort was directed toward the preparation of high-purity U3O3. Of the many possible procedures for the purification of uranium solutions the following were investigated: 1) Precipitation of uranium peroxide. (Two procedures were tried. The first consisted of simultaneously adding hydrogen-peroxide and ammonium-hydroxide solutions to a uranyl-nitrate solution, containing citric and malonic acids, at such relative rates that precipitation was carried out at a constant pH of 1.5 The second consisted of simultaneously adding uranyl-nitrate, ammonium-hydroxide, and hydrogen-peroxide solutions to an aqueous solution

Jan 1, 1960

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K&apos;K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K&apos;, and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943