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By C. R. Kyle, R. L. Perrine

A transparent model of a reservoir has been used to study some characteristics of instability in miscible displacement. The linear model dimensions are 1/4 in. x 91/2 in. x 10 ft. The model is packed with spherical glass beads. Thee groups of experiments have been performed. The objectives were to measure, respectively, the rate of growth of the transition zone, flow velocity variations in the transition zone, and the effect of a graded viscosity zone on stability. All experiments were compared, where possible, with theory. The transition zone grew almost linearly with distance traveled, regardless of flow rate, where adverse viscosity ratios were used. At very adverse viscosity ratios and large distances traveled, some reduction below linear growth was noted. This could be attributed to the effects of mixing. General similarity in flow pattern was commonly shown in different tests, although exceptions occurred at the higher viscosity ratios. Injection of tracer spots permitted direct experimental measurement of velocity variations. Statistical methods were used to compare observed velocity variations with recently published theories. Surprisingly good agreement with some theoretical predictions was obtained. In the experiments using an initially graded viscosity zone, macroscopic stability was reached before predicted by theory. Under conditions theoretically considered to be slightly unstable, any fingering tendency was too slight to become observable within a 10-ft long system. The general correlation of all experiments with published theory was good, and suggests that theoretical predictions can be extended to reservoir problems. INTRODUCTION Early laboratory studies of miscible displacement demonstrated the high recovery efficiency possible with this method. Linear laboratory models showed that, under some circumstances, all in-place hydrocarbons could be recovered using as little solvent as 5 per cent of the pore volume. These results led to a series of pilot field projects. Under realistic conditions, however, other laboratory studies showed that a small solvent bank may not recover much more oil than a conventional gas drive. The cause of this lack of efficiency is unstable viscous fingering. The size of the solvent bank required to give optimum recovery is, therefore, a question of great economic significance. The object of the experiments described in this paper was the quantitative measurement of unstable flow parameters, the verification of present theories on the miscible displacement process, and correlation of these theories with ex peri mental observation. Of the theories which have been advanced, those by Dougherty, Koval and Perrine show promise of predicting reservoir performance with reasonable accuracy.l-7 The present experiments were correlated, where possible, with the theories of Koval and Perrine. Dougherty's theory was not used because of the additional computational difficulty it presented and the belief that no further information would result. EXPERIMENTAL EQUIPMENT A transparent reservoir model, consisting of a vertical reinforced plexiglass column, was used for the experiments. The column was packed with glass beads, which served as the porous medium. To induce a known velocity disturbance in the flow, a double cosine wave restriction in the transverse cross-section was placed at the top of the column. To mark the flow field and provide a means of measuring the local fluid velocity, a dye-spot injection system was provided. The column was 10 ft high by 1/2 in. wide by 1/4 in. deep. The cosine restriction was placed 16 in. from the top of the column. The glass beads were smooth and spherical and had a mean diameter of 0.0102 cm. Liquids entered the top of the column through a manifold allowing three points of entry (left, center, and right, or any combination of these). A positive-displacement pump with variable-speed drive was used to control liquid flow rates. The pump transferred viscous oil from a reservoir to an accumulator, which displaced the test liquid into

Jan 1, 1966

By G. R. Speich, D. J. Mack

The transformation of was studied by isothermal methods. At all temperatures, the ß transforms quickly to fine grained ß" which develops silver-rich striations. At higher temperatures the striations disappear, the final structure being Widmanstatten a in ß'. At lower temperatures, the striated ß" is consumed by pearlite nodules of a + ß' which in turn form the Widmanstatten a in ß'. The transformation is unlike any previously reported for a eutectoid. AS part of a general program of study on the eutectoid reaction, the Ag-Cd eutectoid seemed particularly attractive because the ß phase which undergoes the reaction is another of the typical "electron compounds," AgCd, having the disordered body-centered cubic structure. This work deals with the eutectoid which occurs at 50.5 wt pct Ag, and not with the eutectoid which has been reported at 42.9 pct Ag.' There has been no work reported specifically on the Ag-Cd eutectoid which was studied. The only information available on this eutectoid is that work done in the determination of the phase diagram. For the most part, the terminal portions of the diagram, Fig. 1, are well established; however, the region from 40 to 60 pct Cd is still somewhat in doubt. The X-ray evidence'..' in this region is in conflict with the results of thermal analysis. X-ray analysis3 does not show a polymorphic transformation at about 240°C as indicated by thermal analysis.1,5 Even the X-ray evidence, within itself, is confusing in this region of the diagram. One investigator2 reports the ß phase as hexagonal close-packed and has found three phases in the one-phase ß field. Other X-ray investigators"' ' report the ß phase as body-centered cubic. The authors believe that much of the confusion resulted from incomplete homogenization of the alloys. It was found that it takes almost a week to produce a completely homogeneous two-phase structure at 370°C. Another possible source of error is the volatilization of cadmium from the surface and cracks of the specimen during annealing with the possible formation of a cadmium-poor phase. The only metallographic data available on this eutectoid alloy are those of Durrant1 and Fraenkel and Wolff.5 his information is very limited. The phase diagram chosen as most nearly correct is that in the Metals Handbook," which is almost identical with the phase diagram suggested by Durrant.1 Materials and Procedure The alloy was prepared from high purity silver (999.5 plus fine) and high purity cadmium (0.02 Pb, 0.005 Cu, trace Fe). The metals were melted in carbon under a nitrogen atmosphere. Some cadmium was lost by volatilization but by remelting several times and adding cadmium a 200 g ingot of approximately eutectoid composition was obtained. Because the CdO fumes are quite toxic, the exit gas from the furnace was led through a water trap to condense the CdO. The ingot was homogenized at 650°C for 24 hr, no attempt was made to prevent decadmiumization. This resulted in a narrow decadmiumized rim on the ingot which was removed. Filings for analysis were obtained from cross sections of the ingot. Silver was determined by the Volhard thiocyanate method,? cadmium by difference. The ingot analyzed 50.8 pct Ag at the top of the ingot and 50.7 pct at the middle and at the bottom of the ingot. This alloy was only slightly hypo-eutectoid compared to the accepted value of 50.5 pct Ag and was used for the isothermal studies. It was felt that further attempts to adjust the composition might be futile because of the volatility of the cadmium. The ingot was sectioned to specimens approximately 3/4 x 3/4 x 1/8 in. These specimens were "austeni-tized" for 3 hr in air at 650°C to yield homogeneous ß and then quenched into a salt bath held at constant subeutectoid temperatures where the transformation

Jan 1, 1954

By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-

By H. A. Lesser, H. L. Stone, G. H. Bruce

ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. A mathematical model that represents the conduction heating of a rock formation of limited permeability is formulated. Heat is introduced by the injection of a hot condensing gas into horizontal fractures through the formation. The fractures are assumed to be equally spaced; the flow of fluid is linear. The model consists of three coupled partial differential equations and two functional relationships. Temperature histories for both fractures and formation are obtained by numerical procedures. Application of the model in predicting in situ heating of oil shale is illustrated with four sample cases. Influences of shale thermal diffusivity, fluid pressure in the fracture and fracture spacing upon heating rate are demonstrated. In all cases considered, several years were required to heat all the formation to 700F with 1,000F steam. Less than 32 per cent of the injected heat was utilized for heating the shale. To facilitate extensive calculations of this type, a set of seven dimension-less quantities are derived. With this dimensionless system, the effect of controllable parameters on economics can be explored. INTRODUCTION Vast deposits of hydrocarbons are contained in oil shale formations in the western United States and in other countries. These hydrocarbons, known as kerogen, are difficult to recover because they are immobile solids and because the rock formations in which they are found have very limited permeability. The kerogen can be converted through pyrolysis to recoverable liquids and gases if the formation temperature is elevated to the range 600 to 800F. To accomplish this heating, the formation might be artificially fractured and a hot fluid injected into the fractures. If the injection and production wells are vertical and the fractures horizontal, interwell communication will be established and the hot fluid will flow from an injection well to a production well. In this process, some of the heat in the fluid will be given up and conducted into the formation. Products of pyrolysis will flow from the heated rock matrix into the fractures and be produced, commingled with the injected fluid. The practicality of such a process is strongly influenced by the rate at which heat can be transferred from the hot fluids to the formation. An analysis of this heat conduction problem is the subject of this paper. Linear flow of a condensing gas through a set of horizontal, equally spaced fractures is considered. Temperature histories for both fractures and formation are obtained from numerical procedures. The analysis also applies to formations containing streaks of natural permeability instead of fractures. Heat flow problems similar to the one treated here have been studied by other workers. Thomas1 has solved a radial problem in which he considers the injection of a noncondensing gas into a single, horizontal fracture and approximates the temperature profile in the fracture by a step function. The solutions to other problems, which are less similar to the present problem than the one treated by Thomas, have been reviewed by Spillette.2 In addition to these mathematical studies, a field test of an in situ shale oil recovery process using hot natural gas as the injected fluid has been reported.3 The first part of this paper is concerned with the mathematical development of the problem. The differential equations, boundary conditions and functional relationships which describe the physical model are formulated and the equations are cast into finite difference form. The method of solution of the difference equations is discussed (Appendix B). The second part of this paper presents results computed for a typical oil shale formation for which steam at 1,000F is the injected fluid. Fracture spacing, horizontal and vertical thermal diffusivities

Jan 1, 1967

By W. F. Domis, F. von Gemmingen, F. Garofalo

The effect of rain size on the creep behavior of an austenitic iron-base alloy has been studied at 1300° F under conditions of constant stress. The average grain diameter varied between 9 and 190 p (ASTM 10.7-2). The subgrain size and apparent activation energy for creep were not found to depend in any systematic manner on gain size. Grain hozmdary serrations were observed in all specimens tested. The variation of the secondary-creep rate, 2,, with the pain diameter, 1, is given by: es = K(213m + 1 )/l.]; 1, is the grain diameter zohere is reaches a minimum. Results in the literature shoujthat 1,increases as the temperature increases. At low creep temperatures is is therefore proportional to 12, at intermediate temperatures <, exhibits a minimum, and at high creep temperatures is is proportional to 1/1. The dependence ofis on the stress, u, is given by: t, = A" (sinh acrln, a and n show little variation with 1. The dependence of A" on 1 is given by: A" = KA[(21k + 13)/1]. For 1 » >>lmn = 4, and at constant values 01- isat lozu stress levels, the steady-state stress is given by the Hall-Petch relation. The variation of c, with grain size is believed to he associated particularly with grain boundary generation of dislocations which becomes more important with increasing temperatures. SEEMINGLY inconsistent experimental findings have led to a certain amount of confusion concerning the effect of grain size on creep behavior. The confusion is attributed to a lack of test results obtained over sufficiently wide ranges in grain size, stress, and temperature. Experimental results presented in this paper and results available in the literature1-5 show a consistent behavior and lead to a unified concept for the dependence of secondary-or steady-state creep rate on grain size. In accordance with this concept, which is substantiated experimentally, secondary-creep rate should increase with increasing grain diameter at low creep temperatures, leading to greater creep strengths for fine-grained materials. At intermediate temperatures the secondary-creep rate should decrease to a minimum and then increase as the grain size is increased. At high creep temperatures the secondary-creep rate should decrease with increasing grain size, leading to greater creep strengths for coarse-grained materials. Whether a temperature is high or low for creep in a metal or alloy depends primarily on its melting temperature. MATERIAL AND TEST PROCEDURES The material tested was an austenitic iron-base alloy of the following composition (wt pct): C, 0.005; N, 0.017; Mn, 1.26; Ni, 14.21; and Cr, 17.18. Two 15 -lb ingots were forged and hot-rolled to 5/8-in.-diam bars which were then cold-rolled and cold-swaged to a diameter of 0.49 in. These were sectioned into 3-in.-long blanks and heat-treated at various temperatures to obtain different grain sizes. The procedures employed and the results obtained are summarized in Table I. The secondary treatment at 1400° F followed the primary treatment without intermediate cooling to room temperature. This final treatment was employed to minimize various effects arising from heating to different temperatures during the primary treatment, particularly differences in intragranular dislocation structure, segregation of interstitial atoms at grain boundaries, and density of grain boundary ledges. The intragranular dislocation structure was examined by electron transmission metallography after each of the treatments described in Table I. Isolated dislocations and a few tangles were observed but no evidence of subgrains was found after any of the treatments. No grain-size effect was evident on the density and distribution of dislocations. Stabilization of grain boundary structure is particularly important because, as will be discussed later, grain boundaries influence high-temperature creep behavior. Magnetic-permeability measurements after each treatment and

Jan 1, 1964

By J. G. Early, F. V. Lenel, G. S. Ansell

The isothermal shrinkage rates of copper-powder compacts were determined in the temperature range from 760o to 1060oC. The rates for compacts fabricated from a pure spherical copper powder were compared, on the one hand, with those fabricated from a spherical powder containing a dispersion of aluminum oxide in the copper matrix and, on the other hand, with those fabricated from a pure copper powder having irregularly shaped particles. The irregular copper-powder compacts shrank much faster than the spherical copper-powder compacts and these, in turn, shrank faster than dispersion -strengthened copper -powder compacts. The experiments were run under a small external load. By varying this load, the stress dependence of the isothermal shrinkage rate could be measured for compacts from spherical-copper powders. This stress dependence was found to be approximately proportional to the 4th (dispersion-strengthened alloys) or 4.5th (pure metals) power of the stress. It is concluded that the material-trans port mechanism is due to dislocation climb rather than to Herring-Naharro creep. In this investigation the isothermal shrinkage rates of compacts made of copper powder with an average particle size of 70 g in the temperature range from 780o to 1060°C were studied. The aim of the investigation was to determine the mechanism of material transport responsible for the shrinkage of these compacts. Since the phenomenon observed in this investigation was shrinkage of compacts at high temperatures, it will be necessary to consider all the material-transport mechanisms possible in sintering. It is unlikely that evaporation and condensation, surface diffusion, or even volume diffusion of vacancies, in which surfaces of small radius of curvature are vacancy sources and those of larger radius of curvature vacancy sinks, will materially contribute to a sintering process involving shrinkage, i.e., one in which the centers of adjacent particles move towards each other. The two principal mechanisms which were considered were the so-called Nabarro-Herring mechanism and a plastic deformation mechanism by dislocation movement. Both of these mechanisms were originally conceived to explain creep, i.e., the plastic deformation of metals at elevated temperatures under a constant applied stress. The shrinking of metal-powder compacts which was studied in this investigation can be readily treated as a creep process. This means that the shrinkage rates observed are considered as creep rates under the influence of an applied stress. It is true that the stresses in sintering experiments are generally not constant but decrease continually with time, but, by considering creep rates or shrinkage rates over a relatively short time interval, the small changes in stress during this time interval can generally be neglected. Nabarro-Herring microcreep is a high-temperature deformation mechanism which is caused by a diffusional flow of vacancies from boundaries under a tensile stress towards those under a compres-sive stress. Herring1 has shown that in this type of microcreep the strain rate e is proportional to the applied stress and follows an equation of the form ma, aexp(-Q/RT) [l| where <j is applied stress, Q is the activation energy for self-diffusion, R is the gas constant, and T is the absolute temperature This type of creep can explain the shrinkage of a porous compact. The surface of the pores are subjected to the tensile stress of surface tension, while the grain boundaries are under a compressive stress also due to surface tension. Vacancies diffuse from the pore surface through the lattice to the grain boundaries, where they are eliminated. In order to maintain vacancy equilibrium at the pore surface the vacancies leaving the region of the pore surface are replenished from the volume of the pore, which means that the pores shrink.

Jan 1, 1964

By H. I. Smith

CONTENTS [PAGE Problems of Mining and Processing Mineral Aggregates (TP 1649, by NATHAN C. ROCKWOOD, Min. Tech., Nov. 1943. Discussion by H. I. SMITH, IRVING WARNER and the author) t Mica in War (TP 1749, by RUSSELL G. WAYLAND, Min. Tech., July 1944. Discussion by H. S. SPENCE) 3 Three Roofing-granule Plants in Pennsylvania (TP 1787, by RICHARD M. FOOSE, Min. Tech., Jan. 1945. Discussion by H. I. SMITH)5 Methods of Prospecting and Mining Optical Calcite in Montana (TP 1896, by E. W. NEWMAN, Min. Tech., Nov. 1945. Discussion by W. C. STOLL and FRANK C. ARMSTRONG, and the Glass Sand and a Glass Industry in Puerto Rico (TP 1939, by HOWARD A. MEYERHOFF and J. EARL FRAZIER, Min. Tech., Nov. 1945. Discussion by A. M. SHORT, the author and PHILIP The "Bonanza" Mica Operation of Purdy Mica Mines, Limited, Mattawsn Township, Ontario (TP 2154, by HUGH S. SPENCE, Min. Tech., March 1947. Author&apos;s supplement and discussion by JOHN A. BAKER, E. J. LINTNER, and the author) 7 Process for Manufacture of Dead-burned Magnesite and Precipitated Calcium Carbonate from Dolomite (TP 2155, by ROBERT D. PIKE, Min. Tech., March 1947. Discussion by 0. C. RALSTON and the author) 9] Problems of Mining and Processing Mineral Aggregates H. I. SMITH*-Mr. Rockwood has presented a very interesting paper on problems of the mineral aggregate industry in meeting specification requirements, which apparently are ever decreasing in tolerance. May I call attention to a method of mineral separation that may be of value in separating the flat aggregate particles from the more angular ones and possibly the soft particles from the hard. The method is the old Pardee spiral coal separator, extensively used many years ago in the anthracite region for separating rock and bone from anthracite coal.1 The success of the process depends on the relative coefficient of friction of the aggregate particles to be separated rather than on their relative specific gravity. The flat and the soft particles normally will slide more slowly and stay on the inner spiral until they reach the delivery spout at the bottom whereas the round and the angular pieces will work to the outer edge and fall off into a spiral of larger diameter. The capacity of the separator is increased materially by having three inner spirals, with a separate feed for each, on which the particles travel more slowly, and one outer spiral from which the more rapidly traveling pieces slide to the bottom. IRVING WARNER*-I have long been convinced that much of the equipment and methods developed for mineral dressing might be advantageously employed in the mineral aggregates industry, and more particularly in the production of sand and gravel. The two industries are not well acquainted with each other or their problems. They have separate trade publications. The difficulty with the situation is that there are few large sand and gravel plants and few provided with technical services in their own organization or by retainer. This does not refer to engineering organizations but rather to improvement of plant technic in processing.

Jan 1, 1947

Time as a Factor in the Making and Treating of Steel. By John Johnston. (Howe Lecture) (T.P. 1478) Influence of Chromium and Molybdenum on Structure, Hardness and Decarburization of 0.35 Per Cent Carbon Steel. By R. F. Miller and R. F. Campbell. (T.P. 1345) Mechanical Properties of Iron-manganese Alloys. By F, M. Walters, Jr., I. R. Kramer and B. M. Loring. (T.P. 1369) The Instability of Low-expansion Iron-nickel-cobalt Alloys. By I. R. Kramer and F. M. Walters, Jr. (T.P. 1370) The S-curve of a Chromium-nickel Steel. By B. M. Loring. (T.P. 1383) A Magnetic Determination of the A3 Transformation Point in Iron. By B. A. Rogers and K. 0. Stamm. (T.P. 1388) Rapid Tension Tests Using Two-load Method. By A. V. de Forest, C. W. MacGregor and A. R. Anderson. (T.P. 1393) Effects of Scrap in the Blast-furnace Burden. By C. L. T. Edwards. (T.P. 1270) Temperature Gradients through Composite Carbon Columns and their Application to Blastfurnace Linings. By F. J. Vosburgh and M. R. HatFIeld. (T.P. 1363) Correlations of Some Coke Properties with Blast-furnace Operation. By H. W. Johnson. (T.P. 1402) The Technical Cohesive Strength and Yield Strength of Metals. By D. J. McAdam, Jr. (T.P. 1414) Effects of Eight Complex Deoxidizers on Some 0.40 Per Cent Carbon Forging Steels. By George F. Comstock. (T.P. 1417) Significance of the Bessemer End Point. By H. T. Bowman. (T.P. 1428) Structural Diagrams of Nickel Irons and Steels. By J. T. EasE and N. B. Pilling. (T.P. 1432) Carbides in Low-chromium Steel. By Walter Crafts and C. M. OFFenhauer. (T.P. 1436) Hardenability Calculated from Chemical Composition. By M. A. Grossmann. (T.P. 1437) Recrystallization of Silicon Ferrite in Terms of Rate of Nucleation and Rate of Growth. By J. K. Stanley and R. F. Mehl. (T.P. 1438) The Solubility of Carbon as Graphite in Gamma Iron. By R. W. Gurry. (T.P. 1440) An Evaluation of the Factors Affecting Iron Oxide in the Open-hearth Bath. By J. E. Gould and H. J. Hand. (T.P. 1442) Precision in Creep Testing. By J. A. Fellows, Earnshaw Cook and Howard S. Avery. (T.P. 1443) Lattice Relationships in the Decomposition of Austenite to Pearlite, Bainite and Martensite. By G. V. Smith and R. F. Mehl. (T.P. 1459) Rate of Nucleation and Rate of Growth of Pearlite. By F. C. Hull, R. A. Colton and R. F. Mehl. (T.P. 1460) Weight Change as a Criterion of Extent of Decarburization or Carburization. By R. W. Gurry. (T.P. 1470) Observations in the Making and Use of Sulphite-treated Steels. By E. L, Ramsey and L. G. Graper. (T.P. 1476) Diffusion in Metal Accompanied by Phase Change. By L. S. Darken. (T.P. 1479) Engineering Properties of Heat-resistant Alloys. By Howard S. Avery, Earnshaw Cook and J. A. Fellows. (T.P. 1480) Distribution of Manganese and of Sulphur between Slag and Metal in the Open-hearth Furnace. By L. S. Darken and B. M. Larsen. (T.P. 1481)

Jan 1, 1942

By G. R. Love

i\ program has been written which allows fully automatic conversion of data for X-ray intensity, as a function of time, to finished conventional pole figures. The program accepts input data in the serial order in which they are taken and is therefore immediately compatible with automatic data-acquisition devices. From these data taped instructions are prepared for the Calcomp plotter to construct ink-on-paper drawings. Because both Siemens and Norelco pole figure goniometers are used in this laboratory, the program was written for pole figure data obtained from one or more interpenetrating spiral scans during which both the polar angle, @, and the equatorial angle, a, are varied simultaneously and continuously. The reference direction for a scan, that is the point @ = 0 deg, may be chosen coincident with either the normal direction (N.D. figures) or the rolling direction (R.D. figures). In either case the plotted figures are drawn with the transverse direction (a = 0 deg) at the right and the rolling direction at the top. The full, circular, pole figure is drawn as two semicircular figures labeled "front side" and "back side". As presently constituted, the program will also accept data from circular scans taken at constant values of @. In every case the angular coordinates of each intensity entry are generated in the computer from a relatively small number of auxiliary data. The X-ray intensity data are corrected for background scattering by direct subtraction of the intensity measured with 28 set appropriately "off" the Bragg angle. It is possible to enter this correction as an additional spiral scan through the a, @ space; because the background correction does not normally vary rapidly enough to warrant this detailed a determination, the background corrections are entered as one or more auxiliary data. All data are normalized to a multiple of random intensity. The data taken in this laboratory for N.D. figures are normally taken in a reflection geometry from from sheet samples and do not extend beyond <p = 75 deg; for these data random intensity must be determined from separate experiments and entered as auxiliary information. When the auxiliary information is not available, a number is chosen to give intensity values normalized to a scale of 1 to 10. In this laboratory, R.D. figures are based upon hemispherical samples for which data are taken out to @ = 90 deg; for these data random intensity is calculated by direct numerical integration of . sin @ d@ using the trapezoidal rule and the background-corrected values of the input data. Points necessary to the construction of the pole figure are identified by simple linear interpolation between adjacent data points to determine the loci of contour lines. Points lying on a given contour are connected to one another with straight-line segments and the search-calculation-drawing sequence is patterned to assure that different contour lines do not cross, that a single line does not branch, and that lines do not end in space. However, so that there be no ambiguity in the data presentation, all contour lines end at the limits of the input data. Since the curves are constructed of straight-line segments, they are not continuous in their derivatives. However,

Jan 1, 1969

By M. M. Slotnick

IT was once aptly said that a sign of approaching senility is ceasing work on a subject and beginning to talk about it. Perhaps that explains why, after many years in which part of my duties has been the training of college men in various branches of petroleum exploration geophysics, I have now begun to talk about it. In making an outline of what I believe ought to be discussed under the general heading of the title, I found it almost impossible to subdivide the ideas into an ordered set of discrete subjects. Rather, the pertinent remarks seemed to interlock almost everywhere. The consequence is that it will be necessary to start with the conclusions and then try to justify them by jumping back and forth. However, based on the types of men with whom I have had to deal, the subject naturally divides itself into two parts. In the first part, I should like to deal with the case of those undergraduates whose natural bent is toward the physical sciences and who may decide to enter the geophysical fold as a career. The other part will deal with those many men, geologists and engineers for the most part, who have drifted into exploration geophysics by one means or another, and whom it is necessary to train for geophysical work while they are occupied in their routine jobs. Here it may be in point to remark that most men in exploration geophysics at present have been developed from precisely the latter group, and that the problem of training here is of great importance even though, in this paper, it will perforce occupy the secondary place. TRAINING OF A GEOPHYSICIST The outstanding reason for the perplexing problem on the training of a geophysicist is that ideas differ on the answer to the question: "What is a geophysicist?" In any of the scientific "specialties," like physics, for example, it is relatively simple to pigeonhole a man as being qualified to call himself a physicist. That appellation applied to an individual does not mean that he has mastered only the branches of intellectual endeavor usually associated under the broad name of "physics." We expect him also to have a more than mere acquaintance with mathematics and chemistry and some understanding of most of the other sciences. But note this important point-we expect our physicist, whom we have chosen as an example, to be intelligently trained so that, if necessary, he can and will know how and where he can get the proper information on a subject in which he is not a specialist; he will know how to absorb that information and turn it to his uses. It seems to me that this is the outstanding characteristic of a man who can truly call himself a scientist: that he is a specialist in one of the broad branches of science and that he has enough training and discipline in the scientific approach so that, when called upon to do so, he can intelligently absorb knowledge from another bordering science (and all sciences not only border upon one another to some extent, but more often, overlap one another), and

Jan 1, 1941

• Pellets of concentrated iron ore have been smelted in the blast furnace by Armco and the results proved satisfactory. Various percentages of pellet burdens were tried and it has been found that charges up to 70 pct pellets are workable. •In the reorganization of the Department of the Interior, two new assistant secretaries were appointed and the work divided between the four assistant secretaries. C. Girard Davidson will head a division of mineral resources including the Bureau of Mines, Geological Survey, Division of Oil and Gas and Division of Geography. •Germanium, one of the rarest of metals and a wartime strategic material, has been discovered almost in the shadow of the Capitol. The only catch is that the scattered nature of the deposits makes profitable recovery extremely doubtful. Nevertheless, experts have tabbed the concentration in the District of Columbia area the world&apos;s second richest known concentration of the element. • Cakes of mica, weighing up to 500 lb, have been formed at the Colorado School of Mines by a new "cool hearth" method. The process avoids use of crucibles and contains the molten mica in a basin of unmelted raw mixture from which the melt was derived. Crystallization takes place in this melting basin which forms a center pool surrounded by a solid cool mass of the unmelted raw mixture. • William 1. Baxter, of the International Economic Research Bureau, predicts a period of deflation because of war-essential restrictions on consumer credit and materials use. He stated; "the recent prosperity was based mainly on the sales boom in autos, homes, and household accessories." •Two subsidiaries of United States Steel have decided to build four new ships immediately to augment iron ore and limestone carrying capacity on the Great Lakes to meet demands created by the national defense emergency. •The Norfolk and Western Railway is making a complete change over to coal to drive its locomotives. •A national roster of scientific personnel similar to the one used in the last war will be established by the Office of Education, by agreement with the National Security Resources Board. The new unit, the National Scientific Register Project, will make studies of the Nation&apos;s scientific manpower supply and recommend steps to increase the numbers of skilled personnel where needed. •National Lead Co. will start construction immediately of new facilities at St. Louis, Mo., for production of titanium pigments for paints. Producers of titanium pigments have been under considerable pressure to meet all demands from paint manufacturers, particularly for titanium dioxide. •The basic criteria for deferment of reservists in civilian occupations are (1) the Department of Labor List of Critical Occupations, and (2) the Department of Commerce List of Essential Activities, both of which were announced Aug. 3. Fundamentally, the reservist deferred must be engaged in a critical occupation which is necessary to a highly essential activity, and he will be deferred only until he can be satisfactorily replaced in that occupation. A delay in call to active duty, it was emphasized, may not be considered as an indefinite exemption from military service.

Jan 9, 1950

By J. Murray Riddell

The method of treating hazards wherein value is decreased, is cited by R. D. Parks. Quite properly, the theory of probabilities is made use of when multiple hazards are under consideration. E. F. Fitzhugh, Jr. $ deals with the enhancement phase graphically and uses percentage of expectancy as derived by a study of conditions and the selection of a chance factor. It is believed that both of the authors referred to fully recognize the part which human judgment plays, and as coupled with experience, training, and the application of the theory of probabilities; in that respect the composer of this paper is in accord. Within the past year, the task of arriving at a mathematical method for handling the enhancement phase, and, additionally, coupling the negative and positive phases, was explored. In citing the hazard, or negative phase, reference is made to the text by Parks. Types of Items far Consideration On the hazard, or negative, side some of the common items to be considered are: 1. Subsidence and resulting damage. 2. Flo wage of water above that anticipated. 3. Geological. (a) Decline in quality of probable ore, and/or (b) Decline in quantity of probable ore. 4. Depressed economic conditions. 5. Litigation. Similarly, on the enhancement, or positive, side common items to be considered are: 1. Flo wage of water below that estimated. 2. Geological. (a) Increase in quality of probable ore, and/or (b) Increase in quantity of probable ore. 3. Elevated economic conditions. 4. Litigation. 5. Technological advance in the art. Tn all of the above items no consideration is given to placing a value on, or giving consideration to, possibilities. For example, referring to Table 1, the estimated normal present value (Vp) of a property, exclusive of risk consideration, is taken as $100,000. If subsidence affects the usefulness of the shaft, the present value of the property will decrease to $60,000, and it is judged that there is a 1 in 4 chance that the shaft will be impaired;, consequent.ly, if subsidence took place, the present value would be reduced ($100,000-$60,000) $40,000, but since the chance is 1 in 4, the allowable reduction would be only one-fourth of $40,000, or $10,000, or a discount of 10 pct (hazard factor) of the original value; the related safety factor is taken as unity minus 0.10, or 0.90. Thus, the original Vp, $100,000, multiplied by the safety factor ($100,000 X 0.90) gives $90,000, which is the adjusted present value of the property in this single instance. Additionally, there is a water hazard, which, if encountered, will reduce the present value to $85,000. The chance is 1 in 3. Following through with the same reasoning as shown above, the derived safety factor will be 0.95. To arrive at a single multiplying factor which will express the combined risks, the two safety factors are multiplied together, 0.90 X 0.95 = 0.855. That factor when multiplied by the origirial Vp will give the adjusted, and

Jan 1, 1950

By D. W. Fuerstenau

MEASUREMENT of zeta potentials is a useful tool to study the surface chemistry of minerals under flotation conditions.1,2 Because there is continued interest in this approach, the apparatus for obtaining zeta potentials of nonconducting solids by the streaming potential method is outlined here. Fig. 1 illustrates the streaming potential apparatus." The streaming potential cell or plug consists of two 24/40 standard ground joints (4) joined with a piece of pyrex tubing 60 mm long and 12 mm in diam (5). The electrodes are made of bright platinum disks 19 mm in diam and 1 mm thick through which 0.5-mm holes have been drilled (6). To the surface of each is welded a piece of 80-mesh platinum gauze. Each electrode is permanently mounted on the ends of the inner parts of the two standard joints by means of a platinum wire (7) which connects it to the tungsten seal at the end of the cell (8). For ease in cleaning and handling the apparatus, the streaming cell is fastened to the 500-ml reservoir flasks (1) by means of two 18/9 ball and socket joints (2). This particular arrangement permits passage of the solution in either direction through the plug of particles. Flow of solution can be stopped by a stopcock (3). One of the reservoir flasks has a large opening to permit insertion of either a thermometer or a pair of electrodes for measuring pH of solutions within the system. In making the experiments, the plug is filled with 48 to 65-mesh particles, but a layer of 28 to 35-mesh particles is placed at each electrode to prevent any of the finer particles from passing through holes in the electrodes. The assembled apparatus is shown schematically in Fig. 2. To eliminate CO2 from the solutions, all experiments are conducted in a nitrogen atmosphere. Nitrogen, used to drive solutions through the plug, is passed through a bottle of concentrated KOH solution to remove CO2 (9). A 9-liter ballast reservoir (10) is used to maintain a more nearly uniform pressure. A series of stopcocks controls the direction of flow nitrogen to the flasks (11). Tubes of as-carite prevent backflow of CO2 into the system (12). Driving pressure, which can be set at any desired value, is measured with either a water manometer (13) or a mercury manometer (14). Reservoir flasks have side arms for making pressure corrections for the difference in water levels in the flasks. Streaming potentials are measured by the circuit illustrated in Fig. 2. The electrodes from the plug are connected through mercury wells (15) to a reversing switch (16), which reverses the polarity of the electrodes depending on the direction of flow of solution through the plug. The streaming potential is measured with a Leeds and Northrup type K2 potentiometer (17). Proper choice of null instrument is important because Eq. 1 assumes that the current which escapes through the measuring instruments is negligible. An ordinary galvanometer cannot be used to determine the null point because

Jan 1, 1957

Time as a Factor in the Making and Treating of Steel. By John Johnston. (Howe Lecture) (T.P. 1478) Influence of Chromium and Molybdenum on Structure, Hardness and Decarburization of 0.35 Per Cent Carbon Steel. By R. F. Miller and R. F. Campbell. (T.P. 1345) Mechanical Properties of Iron-manganese Alloys. By F, M. Walters, Jr., I. R. Kramer and B. M. Loring. (T.P. 1369) The Instability of Low-expansion Iron-nickel-cobalt Alloys. By I. R. Kramer and F. M. Walters, Jr. (T.P. 1370) The S-curve of a Chromium-nickel Steel. By B. M. Loring. (T.P. 1383) A Magnetic Determination of the A3 Transformation Point in Iron. By B. A. Rogers and K. 0. Stamm. (T.P. 1388) Rapid Tension Tests Using Two-load Method. By A. V. de Forest, C. W. MacGregor and A. R. Anderson. (T.P. 1393) Effects of Scrap in the Blast-furnace Burden. By C. L. T. Edwards. (T.P. 1270) Temperature Gradients through Composite Carbon Columns and their Application to Blastfurnace Linings. By F. J. Vosburgh and M. R. HatFIeld. (T.P. 1363) Correlations of Some Coke Properties with Blast-furnace Operation. By H. W. Johnson. (T.P. 1402) The Technical Cohesive Strength and Yield Strength of Metals. By D. J. McAdam, Jr. (T.P. 1414) Effects of Eight Complex Deoxidizers on Some 0.40 Per Cent Carbon Forging Steels. By George F. Comstock. (T.P. 1417) Significance of the Bessemer End Point. By H. T. Bowman. (T.P. 1428) Structural Diagrams of Nickel Irons and Steels. By J. T. EasE and N. B. Pilling. (T.P. 1432) Carbides in Low-chromium Steel. By Walter Crafts and C. M. OFFenhauer. (T.P. 1436) Hardenability Calculated from Chemical Composition. By M. A. Grossmann. (T.P. 1437) Recrystallization of Silicon Ferrite in Terms of Rate of Nucleation and Rate of Growth. By J. K. Stanley and R. F. Mehl. (T.P. 1438) The Solubility of Carbon as Graphite in Gamma Iron. By R. W. Gurry. (T.P. 1440) An Evaluation of the Factors Affecting Iron Oxide in the Open-hearth Bath. By J. E. Gould and H. J. Hand. (T.P. 1442) Precision in Creep Testing. By J. A. Fellows, Earnshaw Cook and Howard S. Avery. (T.P. 1443) Lattice Relationships in the Decomposition of Austenite to Pearlite, Bainite and Martensite. By G. V. Smith and R. F. Mehl. (T.P. 1459) Rate of Nucleation and Rate of Growth of Pearlite. By F. C. Hull, R. A. Colton and R. F. Mehl. (T.P. 1460) Weight Change as a Criterion of Extent of Decarburization or Carburization. By R. W. Gurry. (T.P. 1470) Observations in the Making and Use of Sulphite-treated Steels. By E. L, Ramsey and L. G. Graper. (T.P. 1476) Diffusion in Metal Accompanied by Phase Change. By L. S. Darken. (T.P. 1479) Engineering Properties of Heat-resistant Alloys. By Howard S. Avery, Earnshaw Cook and J. A. Fellows. (T.P. 1480) Distribution of Manganese and of Sulphur between Slag and Metal in the Open-hearth Furnace. By L. S. Darken and B. M. Larsen. (T.P. 1481)

Jan 1, 1942

By M. M. Slotnick

It was once aptly said that a sign of approaching senility is ceasing work on a subject and beginning to talk about it. Perhaps that explains why, after many Years in which Part of my duties has been the training of college men in various branches of petroleum exploration geophysics, I have now begun to talk about it. In making an outline of what I believe ought to be discussed under the general heading of the title, I found it almost impossible to subdivide the ideas into an ordered set of discrete subjects. Rather, the pertinent remarks seemed to interlock almost everywhere. The consequence is that it will be necessary to start with the conclusions and then try to justify them by jumping back and forth. However, based on the types of men with whom I have had to deal, the subject naturally divides itself into two parts. In the first part, I should like to deal with the case of those undergraduates whose natural bent is toward the physical sciences and who may decide to enter the geophysical fold as a career. The other part will deal with those many men, geologists and engineers for the most part, who have drifted into exploration geophysics by one means or another, and whom it is necessary to train for geophysical work while they are occupied in their routine jobs. Here it may be in point to remark that most men in exploration geophysics at Present have been developed from precisely the latter group, and that the problem of training here is of great importance even though, in this paper, it will perforce occupy the secondary place. Training oF a Geophysicist The outstanding reason for the perplexing problem on the training of a geophysi-cist is that ideas differ on the answer to the question: "what is a geophysicistp" ln any of the scientific "specialties," like physics, for example, it is relatively simple to pigeonhole a man as being qualified to call himself a physicist. That appellation applied to an individual does not mean that he has mastered only the branches of intellectual endeavor usually associated under the broad name of "physics." we expect him also to have a more than mere acquaintance with mathematics and chemist~ and some understanding of most of the other sciences. But note this important point—we expect our physicist, whom we have chosen as an example, to be intelligently trained so that, if necessary, he can and will know how and where he can get the proper information on a subject in which he is not a specialist; he will know how to absorb that information and turn it to his uses. It seems to me that this is the outstanding characteristic of a man who can truly call himself a scientist: that he is a specialist in one of the broad branches of science in that he has enough training and discipline in the scientific approach so that, when called upon to do so, he can inteugently absorb knowledge from another bordering science (and all sciences not only border upon one another to some extent, but more often, overlap One another), and

Jan 1, 1946

By Anal J. Mehta, Theodore D. Tiemann

Growing demand for steel and increasing dependence upon foreign ore makes the need for developing the technology for treatment of low-grade iron ores greater than ever before• Representative of these added interests were the studies carried on at the University of Wisconsin• These studies included among others: anionic and cationic flotation, magnetic separation, roasting followed by magnetic separation, electrostatic separation, a hydrogen reduction process,6,7 and caustic digestion• The idea of removing silica by caustic extraction is not new•-1; The principle of concentrating siliceous iron ores by this method is based on the fact that silica is soluble in sodium hydroxide solution while iron oxides are essentially insoluble• For this process to be economically feasible, it is believed that some method of recovering silica from solution as a marketable by-product, with recycling of spent liquor is necessary. Precipitation of silica with carbon dioxide will allow subsequent causticizing of the spent liquor with lime• Caustic thus produced can be recycled for digestion• A flowsheet of the envisioned process is given in [Fig• 1] The purpose of this paper is to describe results obtained from the investigation of carbon dioxide precipitation of silica from sodium silicate solutions, which could be later applied to the caustic extraction process to treat low grade siliceous iron ores, particularly taconites.15 Theoretical Considerations The soluble silicates of sodium include sodium orthosilicate (2Na2O•SiO2), sodium metasilicate (Na20•SiO2), sodium disilicate (Na1O•2SiO2), and more highly siliceous products approaching Na2O•4SiO2• These materials have been described in detail by Vail•16 Stones has reported that the extraction of silica is not significantly affected by the amount of silica in solution until the Si02/Na20 ratio exceeds that of orthosilicate (Ratio = 1/2)• However, as the Si02/Na2O ratio exceeds that of metasilicate (Ratio = 1), silica extraction is significantly impaired• The present experimental work was confined to orthosilicate and metasilicate solutions, as to be successful the envisioned commercial process for the extraction of silica from siliceous iron ores would operate in this region. The mechanism of extraction of silica from aqueous sodium silicate solutions is complex in nature. For the carbon dioxide process-18 of core and mold making in which silica is also precipitated from sodium silicate solutions by gassing with carbon dioxide, the reaction of aqueous silicates with gaseous carbon dioxide has been represented by the equations: [ ] However, these equations are very much oversimplified• It has been shown that the reaction between aqueous sodium silicates and carbon dioxide gas is ionic in nature 18 Considering this fact and the mechanism for digestion of silica in aqueous sodium hydroxide, the overall conversion of aqueous sodium silicates to solid silica may be represented in ionic form by the following equations: [ ] Silicon in the silicate ion is shown here with a coordination number of 6• This may be in doubt, but it is known that ion (SiF°)-2 exists; it seems logical that the Si (OH) e 2 ion should be equally capable of existence•

Jan 1, 1977

By M. M. Slotnick

It was once aptly said that a sign of approaching senility is ceasing work on a subject and beginning to talk about it. Perhaps that explains why, after many Years in which Part of my duties has been the training of college men in various branches of petroleum exploration geophysics, I have now begun to talk about it. In making an outline of what I believe ought to be discussed under the general heading of the title, I found it almost impossible to subdivide the ideas into an ordered set of discrete subjects. Rather, the pertinent remarks seemed to interlock almost everywhere. The consequence is that it will be necessary to start with the conclusions and then try to justify them by jumping back and forth. However, based on the types of men with whom I have had to deal, the subject naturally divides itself into two parts. In the first part, I should like to deal with the case of those undergraduates whose natural bent is toward the physical sciences and who may decide to enter the geophysical fold as a career. The other part will deal with those many men, geologists and engineers for the most part, who have drifted into exploration geophysics by one means or another, and whom it is necessary to train for geophysical work while they are occupied in their routine jobs. Here it may be in point to remark that most men in exploration geophysics at Present have been developed from precisely the latter group, and that the problem of training here is of great importance even though, in this paper, it will perforce occupy the secondary place. Training oF a Geophysicist The outstanding reason for the perplexing problem on the training of a geophysi-cist is that ideas differ on the answer to the question: "what is a geophysicistp" ln any of the scientific "specialties," like physics, for example, it is relatively simple to pigeonhole a man as being qualified to call himself a physicist. That appellation applied to an individual does not mean that he has mastered only the branches of intellectual endeavor usually associated under the broad name of "physics." we expect him also to have a more than mere acquaintance with mathematics and chemist~ and some understanding of most of the other sciences. But note this important point—we expect our physicist, whom we have chosen as an example, to be intelligently trained so that, if necessary, he can and will know how and where he can get the proper information on a subject in which he is not a specialist; he will know how to absorb that information and turn it to his uses. It seems to me that this is the outstanding characteristic of a man who can truly call himself a scientist: that he is a specialist in one of the broad branches of science in that he has enough training and discipline in the scientific approach so that, when called upon to do so, he can inteugently absorb knowledge from another bordering science (and all sciences not only border upon one another to some extent, but more often, overlap One another), and

Jan 1, 1946

By J. C. Williams

The operations described in this paper are those of the flotation plant of the Valley Forge Cement Co. at Conshohocken, Pa., and concern the use of a particular cationic reagent—namely, DP-243. The role of this reagent in this plant may be better understood by first considering the purpose of beneficiating cement rock in general and the specific problems at the Valley Forge plant. The ultimate purpose of beneficiating cement rock is to obtain a kiln feed of the desired chemical composition in a form suitable for the most efficient kiln operation. The chemical composition is governed by the type of cement to be made. Before government restrictions (the purpose of which is to simplify operations during wartime) limited the types of portland cement a manufacturer is permitted to produce, five principal types of cement were generally recognized by the industry. They are based upon chemical and physical specifications proposed by the American Society for Testing Materials, federal and other governmental agencies, state highway departments, water boards and other users of large quantities of cement. The physical as well as chemical specifications for any particular type of cement necessitate proper proportioning of the major components—that is, the silica, alumina, iron and lime—and it is necessary to establish and maintain definite limits for each in the raw mix. The manufacturer must then prepare a kiln feed of a composition that will yield a final product that will fulfill the desired specification. This step is further complicated for kilns using coal as fuel, by the amount and analysis of the ash introduced. The amount and nature of the dust lost during burning will also affect the composition of the kiln feed. The problem of preparing a kiln feed of the desired chemical composition is not a simple one, and it is the final product that governs the methods used to obtain such a feed. For example, in starting with a material deficient in lime for the mix sought, it may not be sufficient to raise it to the required lime content. The other constituents must also be present in the proper proportions. In some cases, it may be necessary to raise the lime content to a point greatly exceeding that of the final mix, then, by addition of one or more other materials lower in lime, obtain the mix. The rock used at the Valley Forge plant is a metamorphosed argillaceous limestone of the Jacksonburg formation, the same formation as that of the Lehigh Valley cement rock (which occurs approximately 50 miles north), and its oxide composition is similar to that of the latter. The only practical differences between the two are that, as a result of metamorphosis, crystallization of the Valley Forge rock is considerably coarser and it contains less carbon than the Lehigh Valley rock as well as slightly more magnesia in the form of magnesian mica. The calcium carbonate content of the various strata in the Valley Forge quarry ranges from about 65 per cent to over 85 per cent, the average for the entire quarry being somewhat under the requirement for manufacture of cement, which usually is from 75 to 76 per

Jan 1, 1947

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957

By B. Post, D. Moskowitz, F. W. Glaser

Lattice parameters of various hafnium compounds, two borides, a carbide and a nitride were determined. Some physical properties were measured and comparisons with the properties of the corre-sponing zirconium compounds were drawn. A LTHOUGH borides of transition metals have A been extensively investigated in recent years, there are few references in the literature to borides of hafnium. This is not surprising, in view of the extreme scarcity and great cost of the purified metal. Becker&apos; reported the existence of a boride, carbide, and nitride of hafnium; he listed the formulas as HfB, HfC, and HfN. However, in his work no mention was made of chemical analyses of the reaction products. In this paper results of a study of various hafnium compounds, including borides, carbides, and nitrides, are reported. It was expected, of course, that these compounds would closely resemble their zirconium analogues, which have previously been extensively investigated. Three borides of zirconium are known: ZrB,² ZrB,² and ZrB212.4 In addition, one carbide, ZrC,5 and one nitride, ZrN,5 have been reported. It should be noted that ZrB and ZrB12 are stable phases only in relatively high-temperature regions, unlike ZrB2, which is stable from room temperature to its melting point." It was felt that hafnium would yield corresponding borides, carbides, and nitrides with similar stability ranges. Experimental Procedures and Results A quantity of hafnium metal that was better than 97 pct pure, with zirconium as its major impurity, was furnished by the Argonne National Laboratories. The boron powder used was approximately 96.5 pct pure. In general, the procedure involved mixing the metal and boron powders in the desired proportions, and subsequently hot pressing them. The resulting specimens were analyzed chemically and phases present were identified by X-ray diffraction methods. A Philips Norelco Geiger counter spectrometer was used for identification of components and for measurement of lattice constants. Filtered copper radiation was used for all X-ray work. Electrical resistivity and density measurements were carried out at room temperature. The stable diboride, HfB2, will be described first. Stoichiometric quantities of boron and metal were heated to approximately 2000°C during hot pressing. The reaction product was shown by X-ray diffraction methods to be isomorphous with ZrB2 (space group Dlgh; P6/mm). Values of lattice constants of HfB2 compared with those of ZrB2 are shown in Table I. The calculated density of HfB2 is 11.2 g per cc, compared with a measured (pycnometric) value of 10.5 g per cc. HfB2 specimens prepared under a wide variety of conditions (including variations in initial Hf-B ratios) showed only insignificant variations in lattice constants, indicating a very narrow range of homogeneity. Like ZrB2,7 HfB2 is an excellent electrical conductor. The resistivity at room temperature of hot-pressed samples, approximately 85 pct dense, is 12 microhm-cm. This compares favorably with the electrical resistivity of 10 mi-

Jan 1, 1954