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By John R. Spencer

A capillary tube variable volume cell is described, which has operated satisfactorily over a range of 100°F and 3,500 psi to 550°F and 1,500 psi. The cell contents are entirely visible over the length of the capillary with the exception of a space at the top amounting to three per cent of the total volume. Observations on the critical behavior of simple systems have been greatly facilitated by the apparatus, it being possible to establish the critical conditions for a particular mixture in the course of a day's run. INTRODUCTION Many types of apparatus have been designed for obtaining data on the phase relationships of hydrocarbon systems. Such apparatus can in general be subdivided into two classifications; (l), indirect measurement of phase volume, and (2), direct visual observation of phase volume, each of which has outstanding advantages and disadvantages. Indirect measurement of phase volume requires the use of rather elaborate apparatus including internal probes in which are located the device for determining the locus of the interface between phases. Such equipment is by its very nature costly, and is complex from the standpoint of operating technique. Probing techniques can be used, however, over wide ranges of temperature and pressure with a high degree of reproducibility. Apparatus for visual observation of phase behavior obviously has the advantage of enabling the experimenter to see exactly what takes place, but because the material to be tested is contained in a cell constructed of both metal and glass, is limited severely as to the temperature range of operation. Furthermore. the maximum pressure usually is limited by the choice of material used for sealing the glass to the metal, and by the strength of the glass itself. In the interest of increased efficiency of observation, as much of the cell as possible should be visible to the eye. Glass capillary tubes have been used successfully but have always given difficulty at the metal-to-glass seal. An apparatus has been devised to overcome the problems of sealing and resistance to temperature effects that have heretofore been the limiting factor with glass apparatus in the observation of phase volumes at elevated temperature and pressure. APPARATUS The objective which dictated the general arrangement of the apparatus (Figs. 1 and 2) was simplicity of operation. The air bath, A, was constructed of an iron framework to which was attached approximately one inch of glass wool bats which were covered on the outside with "Masonite." A roughly octagonal center piece was installed to provide forced circulation of the air by the fan, B, past the heaters, D, cell, F, and thermoregulator, C, respectively. The entire top of the box is removable to facilitate charging of the cell and to permit easy maintenance. Two windows are provided before and behind the cell to allow the operator to observe the contents against the background fluorescent light, E. The heaters,

Jan 1, 1951

By T. P. Meloy

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,

Jan 1, 1963

By H. I. Meyer, D. F. Searcy

INTRODUCTION The analysls of our previous paper' on the behavior at two immiscible fluids separated by gravity into two dlstinct saturated zones in the porous medium was shown to be theoretically valid only if one of the two fluids was immobile. The practical problems associated with flow of both phases have so far been impossible of solution by these analytic methods. We, therefore, decided to resort to a simulator study to answer the following pertinent questions: 1. If the lighter fluid is produced from a point above the fluid-fluid interface, how long will it take for the heavier fluid to come up to the point where production of both fluids is taking place? 2. After steady-state two-phase production is established, what is the relative production rate of each phase, on what physical variables does this depend, and what are the boundary conditions at the outflow face? 3. A third question was at least partially answered in the course of this investigation: that of the shape of the interface under flow conditions. These questions are of fundamental importance in the fields of hydrology and the reservoir mechanics of oil and gas production. In order to simplify equipment used and still retain a fair physical representation of these phenomena, it was decided to use a Hele-Shaw type of analogy in which the flow took place between two vertically mounted pieces of plate glass. The advantage of this system is that it eliminates any surface effects between the matrix of the porous medium (e.g. packed sand) and also allows equilibrium conditions to be established more quickly. The principle disadvantage (apart from the obvious one of being one more step removed from the prototype) is that our equipment limited us to two dimensional flow studies. In spite of these limitations answers to the questions were obtained which seem adequate for our purposes. We would like to see more work of this nature done to verify and to improve our conclusions. DESCRIPTION OF EQUIPMENT AND PROCEDURE A drawing of the equipment used in this study is shown in Fig. 1. Fluid flow takes place between the two 36 in. x 12 in. pieces of plate glass held apart at the long edges by two spacers of cellulose acetate sheet (Kodapac IV) which is available in several thicknesses. This sandwich was clamped together by small c-clamps whose stress was distributed by long pieces of 3/8-in. keystock. Accurate spacing was obtained by tightening these clamps as indicated by micrometer measurements on the outside of the glass. At the upstream end of the plates a piece of 6-in. diameter pipe simulated an infinite reservoir, while at the downstream end a 2-in. Lucite cylinder with a small hole near the top of the flow region served to drain the fluid. Sealing was achieved by O-rings, the whole system being tightened by pressure on the Lucite tube provided by set screws (not shown in the drawing). The total head

Jan 1, 1957

By Bernard Greifer, Walter Rose

The purpose of this note is to call attention to a source of difficulty which can be responsible for inaccurate estimates of wetting liquid pressure gradients in mixture flow experiments of the Hassler1 type. It has been our experience occasionally to observe what were indicated to be negative pressure gradients, and these were regarded as anomalous in the sense that physically they seemed to contradict the requirement that the flux be in the direction of the potential field. At first it was thought that our scheme of assembling barriers and core sample led to such asymmetry in the distribution of isobars that the manometric leads at each end of the core were responding to internal pressures (within the core sample) which could be either positive or negative with respect to each other, and which in fact might tend to reflect on different effective core lengths in an unpredictable fashion as the wetting liquid saturation was changed. However, no compelling evidence of this possibility has been established. In addition, we were cognizant of the requirements to be satisfied in selecting manometric instrumentation to minimize the delay in response of the manometer to the differential pressures being measured, and were thus assured that our observations of anomalous pressure gradients could not be explained by faulty instrumentation. What we suggest is that if a leak sink occurs in the fluid lines connecting the core to either side of the differential manometer, errors exceeding 100 per cent may result in the estimation of wetting liquid pressure gradient, even though the leak is of such small magnitude that its existence would tend to be obscured by evaporation effects. This is because in a system with leaks at the specified places, the manometer rec- ords at steady state the pressure drop across the manometer barrier elements in addition to the pressure drop across the core sample. This possibility will be illustrated below analytically and by numerical example for the special case where the leak occurs on the high presure side of the core, since we are especially desirous to explain the significance of our observations of the so-called negative pressure gradients. It will be indicated, however, that leak sinks on the low pressure side of the core can account for observations of anomalously high values of pressure gradient, and that multiple leaks on both sides of the core can provide for some compensation so that the errors in pressure estimation are reduced. However, the major point to be emphasized is the fact that the impractical-ity of detecting the small leak sinks which give rise to the difficulties makes it a complicated task for the experimenter in a particular case to know with certainty that his estimation of pressure gradient lies within the limits of error which can be tolerated. Fig. 1 shows the electrical analog of the flow system we have employed in our studies. The inflow and outflow barriers. Rbl and Rb2, the manometer barriers, Rm1, and Rm2, and the core sample, Rc— for a particular fluid saturation and distribution— are all designated as resistance elements; the flowmeter is designated by an ammeter, A; the pressure source is designated by E; and the manometric device is designated by the voltmeter, V. Included in the circuit are the variable resistances, Rx and Ry, which may be regarded as the leak sinks, and which, in general, can vary in magnitude from zero (i.e., a large hole or shunt in the system) to infinity (i.e., no

Jan 1, 1950

By Paul B. Crawford, Bobby L. Landrum

Electrical model studies have been made of the effect of drainhole drilling on production capacity. Drain holes are those lateral holes which are sometimes drilled to assist in increasing the oil drainage into the main wellbore. The studies indicate that if the drainhole length i.r near 0.2 of the drainage radius, the increase in production capacity may be approximately 1.8, 2.08, trnd 2.33 for the case of one, two and four drain holes, respectively. If multiple drain holes are drilled, shorter holes are required to achieve a specific increase in production capacity than if one or two holes are drilled. To achieve increases in production capacities by factors near three it is shown that the drainhole lengths divided by the drainage radii must be approximately 0.64, 0.48, cnd 0.37 for the case of one, two and four drain holes, respectively. IN T RO DUCTION Kecent developments in drilling techniques have permitted the drilling of lateral or horizontal holes to increase the rate of production. The number of these drain holes may vary from 1 to 10, and they have been drilled laterally as much as 100 ft. Drainhole drilling at substantial depths is of recent origin but has been used in the Spraberry field of West Texas, the La Pas field in Western Venezuela, and certain fields in California. The diameter of the drain holes has been approximately 6 in. In drilling drain holes it is desired to know how much increase in production capacity may be expected, what additional benefit may be gained by drilling more than one drain hole, and what increase in production capacity may be brought about by lengthening the existing drain holes. In realization of the importance of lateral drilling, electrical model studies were made to provide quantitative estimates on the effect of drain holes on production capacity. ANALYSIS An electrical model was used in studying this problem. A wooden circular reservoir approximately 30 in. in diameter and 2 in. deep was filled with a dilute salt solution to a depth of 1 in. A copper band formed the periphery of the tank, and a copper wire was inserted in the center of the tank to represent the well. The drainage radius divided by the well radius was equal to 500. A diagram of this type model is shown in the inset of Fig. 1. An electrical potential was applied to the wire well and copper band at the periphery to determine the flow of current. Following this measurement copper wires of various length were soldered to the vertical wire well in such a manner as to simulate lateral wells drilled into the reservoir. Multiple lateral holes of various lengths were studied by varying the number and length of copper wires soldered to the vertical wire well. All multiple lateral wells were located symmetrically about the vertical well. The effect on production capacity by drilling an infinite number of lateral holes was studied by replacing the lateral hole with a copper disk. For each condition the flow of current was measured and compared with the flow of the vertical well only. The model which is thus described provides the steady state increases in production capacity which may be expected in some cases. The data conform to those which would be observed for a uniform homogeneous reservoir. The data may have primary application to those reservoirs producing above the bubble point. It is realized that few lateral holes are drilled in reservoirs of this type, but the data may be of some value in guiding future work or aiding to explain observed phenomena.

Jan 1, 1956

By D. P. Koistinen, K. E. Beu

THE application of the integrated intensity X-ray diffraction method to the measurement of retained austenite concentrations in hardened steels has been fully described.'-' In developing this particular method, the assumption was made that the samples used would have flat surfaces which were free from voids and in which austenite was homogeneously distributed. The original calculation procedure' was modified to include the constant factor G which relates the intensity of a given diffraction line to the concentration of the component giving rise to that line. In order to include A (0) in the constant factor G, it was further assumed that the geometrical conditions relating the X-ray beam, camera cylinder, and sample surface were precisely met.V has been demonstrated that these geometrical conditions can be met experimentally without difficulty in many cases;' however, for those samples which have irregular surfaces or where it is impossible to locate the sample in the proper position with respect to the X-ray beam and film cylinder, it is desirable to evaluate experimentally what effect these nonideal conditions have on the reliability of the austenite determination. This note decribes the results of such experiments. SAE 1095 bar stock was used throughout and all samples were heat-treated as follows: 1600°F for 1 hr in a neutral atmosphere, brine quench, and 300°F temper for 30 min. To control heat-treatment conditions as closely as possible, all samples were plated with 0.002 in. copper to protect the immediate surface from the heat-treating atmosphere. After heat treating, the samples were deplated electroly-tically so that only the copper was removed. The heat-treated surfaces thus obtained were nearly as bright and polished as the original surfaces before copper plating although no mechanical work was done on the samples after heat treating.

Jan 1, 1954

By P. W. Neurath, R. E. Waite

INFORMATION is available on the effect of stress on permeability, coercive force, and hysteresis for a variety of materials' but for the technically important grain-oriented 3 pct Si-Fe' the stress effects are not adequately covered in the literature; in addition, most of the stress data do not permit estimation of what would happen to the 60 cycle watt losses of the material under stress. Direct measurement of these effects therefore has been made and appears to be of considerable theoretical as well as practical interest. Losses were measured on the central 25 cm portion of 40~3~0.035 cm samples which could be stressed in a small tensile machine built for this purpose. Under tension the following effects, illustrated in the figures by a particular example, were observed: 1—"Unstrained" material of commercially acceptable loss level shows no change or a small increase in loss at low elastic stresses. For the sample shown in the figures, this is illustrated during the initial run, where a 7 pct increase is observed (Fig. 1). 2—There is no additional change in loss when the sample is further strained up to the elastic limit (Fig. 1). Within that limit the loss-stress curve is reversible. This is not illustrated in Fig. 1. 3—Even in the plastic range only small increases in loss are observed as long as the sample is kept under stress (Fig. 2, point N); often no increase can be observed (Fig. 1). 4—A large increase in watt losses is observed after removal of the stress subsequent to plastic deformation (Figs. 1 and 2). 5—All, or nearly all, of the foregoing increase in loss due to plastic deformation can be eliminated by a reapplication of tensile stress but returns upon removal of this stress. This is illustrated in the third run (Fig. 3). This run remains within the elastic limit and shows the reversibility of the stress-loss curve under this condition. These findings have been confirmed on large Samples (approximately 200~10~0.035 cm and larger) except that under 1 no initial increase in loss was ever observed on these. The accuracy of the watt loss measurements is of the order of 1 pct. Neither bending of the sample in the tensioning device nor a redistribution of flux along the width of the sample accounts for these results. They therefore must be explained on the basis of either a change in the domain configuration due to stress or a change in the domain wall mobility. Acknowledgment The assistance of Mr. Robert L. TenBroeck with the instrumentation is gratefully acknowledged.

Jan 1, 1956

By Daniel M. Bass, Paul B. Crawford

Laboratory investigations have been made to study the effect of variations in fluid characteristics, gas saturation, water saturation, and water injection rate on oil recovery by water flooding. Three synthetic gas-saturated crude oils having bubble points of 860, 1,540 and 1,885 psi were used as reservoir fluids. Repeated tests were made in which a and pack, saturated with water and synthetic oil, was produced by solution gas drive followed by water flooding at various pressure levels. Oil recovery by solution gas drive and subsequent water injection is shown to vary with the pressure and rate at which the water flood is conducted. The pressure at which optimum flooding conditions exist is shown to be a functiotl of the physical characteristics of the reservoir fluid. For the systems studied, increases in oil recoveries of near 10 per cent were obtained by flooding at the most desirable conditions. Va- riations in initial water saturations gave results similar to those in the literature. INTRODUCTION Most of the waterflooding studies investigating means of improving present exploitation processes have been conducted at low pressures with little effort to simulate reservoir conditions. Holmgren and Morse' performed a waterflooding study at 300 to 500 psi wherein the gas saturation was created by injecting gas, letting dissolved gas evolve from the oil, and then flushing the core with "live" oil until the desired gas saturation was obtained. Their results show increasing oil recoveries with increasing gas saturations. Data presented by Guerrero' and Kennedy, et al, indicate that in some instances water flooding at approximately 500 psi below the original bubble point results in a lower residual oil saturation than is obtained when water flooding above the bubble point. In their work gas saturations were created by primary depletion. By correcting low pressure flooding data for fluid shrinkage, Dyes found that a maximum oil recovery may be obtained by flooding with initial gas saturations of from 7 to 12 per cent. The purpose of this work was to determine the variations in oil recovery caused by initiating a waterflooding program at various stages of primary depletion of a core. This is a part of a more comprehensive study of obtaining criteria for determining when to initiate a pressure maintenance program and what fluids to in-ject. EQUIPMENT A schematic diagram of the apparatus is shown in Fig. 1. Fluid transfer was accomplished with metering pumps. Pressure control was ob-

Jan 1, 1957

By W. D. Bennett

AN interesting effect has been observed in the vacuum etching of titanium in the high temperature ß phase. Using a high vacuum annealing furnace, operating at less than 2x10-6 mm with a tubular titanium liner, it has been found possible to etch polished metallographic specimens at different temperatures between room temperature and 1000°C without contamination or increase in hardness.' Heat etching of titanium has been reported by other workers,' but the following example is of interest as an experiment under high vacuum in the absence of any contamination. Two polished specimens of iodide-processed titanium are placed at different positions along the axis of the furnace corresponding to temperatures of 900" and 800°C above and below the a-ß transus. The specimens are then raised to these temperatures and annealed simultaneously for 3 hr under the same high vacuum conditions. After cooling and withdrawing the specimens, their surfaces are photographed without further treatment. Figs. 1 and 2 show the results for the 800" and 900°C specimens, respectively. Fig. 1, corresponding to a vacuum etch in the a region, shows a typical equiaxed structure with what appears to be a slight shift of grain boundaries. Fig. 2, corresponding to a vacuum etch in the ß region, shows an equiaxed type of structure with the growth of striations in certain grains. The striations are only superficial, as a light polish and chemical etch restores the clean equiaxed structure. The vacuum etch, occurring as it does above the a-ß transus, records the state of the metal in the ß phase by means of the surface relief produced by the selective evaporation of metal from different grains; the metal itself reverts to the equiaxed a on cooling. The nature of the ß etch" (Fig. 2) suggests that, in transforming from the close-packed-hexagonal a to the body-centered-cubic ß lenticular-shaped laminae are formed parallel to common planes of the two structures. This would explain why some grains appear to be unaffected by the etch. The technique has interesting possibilities in the investigation of the mechanics of high temperature transformation. Acknowledgment This note is published by permission of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By Emma Smith, R. W. Guard

INVESTIGATION of the nickel-rich end of the Ni-Zr system has been prompted by an interest in the effect of small amounts of zirconium in high temperature alloys. Hansenl presents a hypothetical diagram based on the work of Allibone and Sykes,2 who investigated the system up to 44 atomic pct (55 wt pct) Zr by metallographic means. Since the alloys they used were melted in Alundum crucibles they were probably contaminated with appreciable amounts of aluminum. They found two compounds which they called Ni3Zr and Ni4Zr. Hayes, Roberson, and Paasche3 identified a compound NiZr (50 atomic pct Zr) with a melting point of 1470°C. Such a high melting compound is not compatible with the observation of Allibone and Sykes2 hat a eutectic is formed near 50 atomic pct. The alloys containing up to 60 atomic pct Zr were melted in an inert atmosphere in a noncon-sumable electrode arc furnace. Analysis of most of the alloys indicated negligible loss of zirconium. The alloys were examined in the as-cast condition and also after annealing for 6 hr at 1175°C (or 1000°C for the alloys between 25 atomic pct and 45 atomic pct). Metallographic specimens were etched using mixtures of HF-HNO3-H2O or acetic acid- HN0,-H,O. The specimens for the solidus determinations were wrapped in molybdenum foil and sealed in evacuated quartz tubes. Specimens to be heated above 1300°C were enclosed in zirconia tubes inside the quartz to prevent reaction with molybdenum. The solidus determinations were carried out by heating the specimens at various temperatures for a few minutes and then examining the interior structure metallographically to determine at what temperature melting began. The 150 mesh powders for X-ray analysis were annealed in an evacuated quartz tube for 2 hr at 540 °C to remove cold work. Alloys with 22.5 atomic pct Zr and 44.4 atomic pct Zr required annealing at 700 °C for complete recovery. The grains of both of these alloys were soft and rather ductile. Both Debye-Scherrer film patterns and spectrometer traces were made for each alloy using filtered copper radiation. Results and Discussion The presence of a substantial amount of second phase in an alloy with 1.1 atomic pct Zr indicated that the solid solubility of zirconium in nickel is somewhat less than 1 atomic pct. The a0 value for the face-centered-cubic matrix in the same alloy was equal to that of pure nickel, so that the solubility must be very small. This observation is as expected from the large atom size difference. Annealed specimens of alloys with 15.0, 16.7, 22.5, 28.6, 44.4, and 59.4 atomic pct Zr showed. micro-structures that were essentially single phase. When

Jan 1, 1958

By L. J. Klinkenberg

It is pointed out that the current concept of pore size distribution is not unequivocally defined and that different methods aiming at a determination of such a distribution therefore do not lead to the same results. A pore size distribution should not be based on the idea that a core should, under all circumstances, behave as a bundle of straight non-interconnected capillaries of the same pore size distribution. This is illustrated by calculations and experiments on the displacement of miscible liquids. INTRODUCTION The introduction of the concept of pore size distribution has been an attempt to characterize the intricate geometry of the flow channels in porous media. As pores in a porous medium are interconnected it is impossible to describe exactly what is meant by a "pore" and, therefore, the term pore size distribution requires further amplification. In the visual method for the determination of pore size distribution "the pore" is considered to be the hole between the grains as observed on thin sections or on a polished surface of the rock under a microscope. In all other presently known methods,1,2 a displacement process is studied and it is ascertained what as- semblaae of straight cylindrical capillaries would show the same behavior. The distribution of the capillary diameters of this assemblage is said to represent the size distribution of the pores of the actual porous medium. From the foregoing it is already apparent that it is useless to try to decide which process or which method of investigation leads to a "correct" pore size distribution. To illustrate this further a displacement process in which a fluid is displaced by another miscible with it will be discussed and the results will be interpreted in terms of a pore size distribution. DISPLACEMENT EXPERIMENTS WITH MISCIBLE LIQUIDS OF NEARLY IDENTICAL VISCOSITY AND DENSITY Interpretation in the Form of a Pore Size Distribution If distilled water is displaced from a homogeneous unconsolidated sand pack by, for instance, a dilute solution of NaCI, the breakthrough recovery i.e., the amount of distilled water produced at the moment the first trace of NaCl can be detected in the effluent water, is between 95 and 100 per cent of the pore volume of the pack. This result can be understood by following in imagination the course of one particle of the liquid. Imagine a length, ?l, at the end of which a liquid particle has an independent chance of a renewed choice of pores of different diameters. In other words, the particle has a choice of traveling time, at, for any length ?l; instead

Jan 1, 1958

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By W. R. Aufricht, E. H. Koepf

The theory, measurement, and application of capillary forces in reservoir rock have been treated ex-tensively in the various petroleum publications.1,2,3,4 These forces are of prime importance in oil production, and data on capillary properties are among the most important tools used in the study of reservoir mechanics. The principal application of measured capillary pressure data by the production and reservoir engineer is in the determination of the initial distribution and mobility of fluids in the reservoir. The distribution refers to the magnitude of the oil and interstitial water saturations under capillary equilibrium conditions and to their variation throughout the reservoir as a result of changes in rock properties and nearness to free water. The magnitude of the water (or oil) saturation, as well as the porosity, is required in volumetric calculations of oil in place. In low permeability reservoirs, where long transition zones are common, the magnitude of the oil content, even below the depth interval where commercial rates of flow of oil can be obtained, must be evaluated since this oil contains energy available to the production of the remainder of the reservoir. The mobility of the water phase is of particular importance in water-flood calculations since mobile water may condemn what would otherwise be a successful water flood. In reservoirs with predominantly small pores, high immobile water contents are possible. Conversely, reservoirs with predominantly large pores may contain mobile water even though the interstitial water contents are relatively low. This presentation reviews the distribution and mobility of interstitial water contents as determined from capillary pressure data and shows typical data for various types of carbonate reservoirs. A discussion of the variations found in different types of carbonate reservoirs is given. DISCUSSION Interpretation of Laboratory Data Fig. 1 is a typical laboratory capillary Pressure curve where water saturation as Per cent of Pore space is plotted vs capillary Pressure (psig) for an air-water system. This par- ticular curve was obtained by measurement on a sample of San Andres dolomite with intergranular-type porosity. The sample studied had a permeability of 10.0 md and a porosity of 18.8 per cent. The capillary pressure-saturation relationship illustrated is an inherent property of the rock (a function of the size and distribution of the pores) and represents the ability of this water-wet rock to retain water against the pressure differential exerted by a non-wetting fluid (oil or gas) to remove it. In the laboratory a known pressure differential is exerted from a pressure source; in the reservoir the pressure differential is controlled by the density difference between the hvdrocarbons and the water. The laboratory capillary pressure values may be converted into terms of equivalent height of water column using known values of reservoir oil and water density and measured or average values of interfacial tension

Jan 1, 1958

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

By W. H. Holman, J. B. Wagstaff

IN spite of considerable interest among blast furnace operators on the question of the penetration of air into the furnace, there is still uncertainty as to how far the blast does, in fact, penetrate. Moreover, it is not always clear just what is meant by the word penetration in this sense. In 1952, Elliott et al.1 showed that at the end of each tuyere of a blast furnace there is more or less of a void. In this region, coke particles are blown around by the force of the air. This explained the well-known observation reported by Sweetser2 hat if a bar is pushed into a furnace through a tuyere it will go easily into the furnace a distance of some

Jan 1, 1958

By E. S. Davenport

IT is indeed an honor and a responsibility to have been selected to present the thirty-fourth in this series of Henry Marion Howe lectures, established to perpetuate the memory of a great teacher and one of America&apos;s outstanding scientists. Previous Howe lecturers have established high standards for this annual AIME event. It has been my good fortune to have enjoyed close association with five of these former lecturers; namely, Bain, Grossmann, Johnston, Sosman, and Vilella, all of whom have been prominently identified with the research activities of the organization with which I am connected. Some years ago I had an opportunity to examine a letter written by Professor Howe in 1904. This document was particularly interesting to me since I never had the privilege of personal acquaintance with Professor Howe and do not recall even having seen him during his long and active career. In view of the fact that the letter dealt, to some extent, with matters related to the subject of today&apos;s lecture, I would like to quote briefly from it. The letter is datelined, "Bad Kissingen, June 11, 1904." The salutation reads, "Dear Bradley," which suggests that it was probably addressed to Bradley Stoughton, who, I believe, was working with Howe at Columbia University at that time. The letter reads, in part, as follows: "Austenite and Martensite. I have not examined what Osmond says in his new book. His former remarks about austenite I found very confusing, indeed unintelligible. I think we can reconcile matters well enough for the present by assuming that martensite is a transition step between austenite at one end and ferrite and cementite at the other. Above critical range for steel of 0 to 1.80 carbon, austenite is normal state; below Ar1, ferrite and cementite are normal." The letter then continues with a discussion of Osmond&apos;s ideas on metallographic nomenclature, particularly his use of the terms martensite, troostite, and sorbite, including the following pointed comment: "For common purposes it seems to me unwise to drag them in, and much simpler to confine ourselves to the end stages Austenite Ferrite plus Cementite Osmond does not really know his own mind— or does not clarify his ideas to others—as to nomenclature." Thus we see that, as far back as 1904, the transformation of austenite, and the products of that

Jan 1, 1958

By L. C. IlsLey

Briefly, a permissible schedule of the Bureau of Mines establishes certain minimum standards for safety; it gives details of test methods adopted to determine whether these standards have been met, and a list of charges for such tests. Any manufacturer has the privilege of submitting his product for test in accordance with the conditions outlined in the schedules. His action is wholly voluntary, for the Federal Government has no jurisdiction as to what equipment shall be used in mines, this authority being left to the various States. When the product of a manufacturer has met the schedule requirements, he is permit¬ted to advertise this fact and to attach an approval plate with the bureau&apos;s seal to each machine he makes that is identical in every way with the equipment tested, inspected, and approved by the bureau. This work of approval has grown by the addition of new schedules until at present a great many mines are using one or more classes of permissible equipment, and there is still a demand for other approved apparatus in the ever-widening field of electrically operated machinery. The safety of electrical equipment of this type depends on four fundamentals, namely, (1) correct principles of design; (2) proper assembly of parts at the factory; (3) proper assembly and installation of equipment at the mine; (4) and proper operation and maintenance after installation. The first two factors are within the province of the manufacturer. The bureau either inspects and tests several models of one product, such as electric cap lamps, or one model, such as an electric motor. If this series of tests proves satisfactory, the manufacturer is given the privilege of making other appliances, and assembling them in the same way; the approval plate he attaches is his guaranty that the equipment is identical with the one tested and inspected by the bureau. The third and fourth factors concern those who use such permissible equipment, and it is to them that this paper is mainly addressed, in an effort

Jan 1, 1922

By R. S. James, E. J. Gleim

Not long after electrically driven equipment was introduced into coal mines it became apparent that the spark-producing parts, such as controllers and motors, required safeguards to prevent the ignition of mine gas that might come into their vicinity. Many of the early designs attempted to provide protective enclosures having ventila¬tion and relief for pressures if ignition should occur within. The principal feature of the Davy safety lamp, namely, the wire gauze, was employed widely for this purpose. Other devices were developed to reduce the temperature of products of combustion escaping through the protected openings to a value below that which would cause ignition of surrounding explosive atmospheres. Although many such devices performed their intended function satisfactorily under laboratory conditions they were not so satisfac¬tory when subjected to the rigorous conditions encountered under¬ground. Corrosion, mishandling, and accumulations of grease and dirt reduced or destroyed their protective qualities after a period of service in the mines. In the United States this has led to abandon¬ment of special devices in favor of what is called " total enclosure " which means that no regular provision is made for ventilation and release of pressure but rather that the housings or enclosures are built strong enough to withstand the explosion pressures without rupture. As a further protection the joints usually are made of broad, closely fitting surfaces. It is impractical to make such joints absolutely gastight in ordinary machine practice when provision must be made for partial or complete disassembly to facilitate ad¬justments and repairs. Therefore, when an explosion occurs within such enclosures flames may escape through the joints. If the latter are broad enough and not separated too widely, however, the flames will be cooled by contact with the metal surfaces (flanges) of the joints, by rapid expansion, or by both cooling and expansion, with the result that an explosive atmosphere surrounding the enclosure will not be ignited. This is termed " flange protection." In testing parts of cutting machines and other equipment for coal mines, with the ultimate object of approving the equipment for use

Jan 1, 1935

By A. L. Martikainen

Booster fans increase air pressure to overcome resistance, the objective being to force adequate amounts of air through distant workings. They are used in areas that are difficult or uneconomic to ventilate with main fans alone. Booster fans are currently permitted in underground coal mines in some countries; the United Kingdom, South Africa, Australia and Canada have been defined as major users. Booster fans are not allowed in the US bituminous and lignite coal mining operations at the present time due to safety concerns. This paper presents the history of booster fan use in coal mines of the United States during the last 90 years. Changes in regulations, as well as advantages and disadvantages of booster fan use, are discussed. Research and petitions for booster fan use are highlighted in order to bring the debate into focus.

Jan 1, 2010

By J. Organiscak

A majority of continuous mining machines employ a water spray system and a machine-mounted flooded-bed scrubber to suppress and capture dust during coal mining. These machine-mounted dust control systems must be designed to function within the localized face ventilation system at the mining section to control both dust and methane. Spray systems can impede or improve the scrubber effectiveness in controlling dust or methane at the mining face. Laboratory experiments were conducted to examine the effect of spray type, spray pressure, machine body blocking sprays and scrubber airflow on dust and gas levels, while using a 12.2-m (40-ft) exhaust ventilation curtain setback from the face. These experiments were conducted with the mining machine positioned at the end of a simulated 6.1-m (20-ft) sump and slab cut. Results indicate that the hollow cone nozzles with blocking sprays best complement the flooded-bed scrubber performance in an exhaust ventilation system. This external spray system notably reduced dust and gas levels on the off-curtain side of the mining machine for both the sump and slab cut compared to the flat spray nozzles. Higher scrubber airflows reduced dust and gas levels on the curtain side and in the return of the continuous mining machine. The remote operator position, located on the off-curtain side and parallel to the inlet end of the exhaust curtain, sustained the most stable and lowest dust levels around the mining machine.

Jan 1, 2010