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By R. C. Padfield

Experience over a 3-year period in Bethlehem Steel Corporation's plants has demonstrated the reliability of open-hearth roofs of bonded sprung-arch constructzon with burned basic brick. The design principles lor constructing these roofs include a minimum hot-strength requirement for the basic brick, expansion allowances that extend the full roof thickness, structural members to control arch contour, and a specified minimum roof rise. The greater stability of bonded roofs is explained in terms of the basic stress patterns of ring constrution and bonded construction. PRIOR to the development of successful sprung-arch roofs of basic brick, the majority of open-hearth furnaces in the United States were operated with sprung-arch roofs built of silica brick. Although many silica roofs used on open-hearth furnaces were ring-arch construction, Bethlehem Steel Corp. used bonded-arch construction because of its greater stability. In ring construction, each ring of brick is separately keyed and comprises an independent arch with the straight joints between rings traverse to the longitudinal axis of the furnace. In bonded construction, the bricks are laid in rows starting from the skewbacks so that the straight joints run parallel to the longitudinal axis of the furnace. Each brick in a given row is laid so that it spans the joint between two bricks in the row beneath it. Thus, the transverse joints across the arch are broken and the arch rings are thereby interlocked or bonded. When basic roofs were first being developed, the basic brick that were available had low hot strength. Such brick could not be safely used in sprung-arch construction without some means of suspending them. With the development of higher firing techniques by brick manufacturers and the recently introduced direct bonded bricks with high hot strength, the use of burned basic brick in sprung-arch roofs became feasible. The availability of high hot strength basic brick coupled with the potentially lower cost and proven stability of bonded construction prompted Bethlehem's Research Department to study the possibility of using basic brick in bonded roofs. With the full cooperation of plant ceramic engineers and open-hearth superintendents, particularly in 3 years of fur-nace trials, we developed the design criteria for bonded roofs and the corresponding property requirements for the basic brick that are discussed in this paper. DESIGN PRINCIPLES OF SPRUNG-ARCH BRICK ROOFS Stresses in Fixed Arches. A sprung-arch open-hearth furnace roof is generally built on rigidly held skewbacks. The constraint of the fixed support at each end adds a bending moment to the horizontal and vertical reactions at the ends of the arch. Fig. 11 shows the positive direction of forces acting on an arch fixed at both ends. Fixed arches can be analyzed when the members are continuous and have elastic properties. However, brick are inelastic, and arches built with individual brick segments cannot carry tensile stresses. Therefore, for practical solution of brick arches, empirical formulas have been derived from elastic theory that place design restrictions on arch dimensions to avoid development of tensile stresses. McDowell2 cites three main conditions for stability in sprung brick arches: 1) the thrust line of the arch should be maintained in the middle third of the thickness to avoid tensile stresses and resulting open joints in inner and outer curves of the arch; 2) the angle between the line of thrust at any joint and a line perpendicular to the joint must not exceed the angle of repose between brick; and 3) the maximum pressure at any point must not exceed the strength of the arch materials at furnace operating temperatures. The first and third conditions are particularly important in designing sprung-arch basic roofs because of the comparatively low hot strength of basic brick. According to McDowell's equation, if the thrust line is maintained within the middle third of the arch thickness, the unit pressure is obtained as follows: where p = unit pressure in psi, F, = resultant thrust normal to skewback in pounds per foot, t = arch thickness in inches, and z = distance in inches of thrust line from arch axis. When the resultant thrust normal to the skewback acts along the arch axis, z equals zero and unit pressure is simply the thrust divided by the cross-sectional area. If the thrust line moves to the limits of the middle third of the arch thickness, beyond which tensile forces would develop, z then equals one-sixth of the arch thickness and the unit pressure is double that when the thrust line is acting

Jan 1, 1968

By Oren C. Baptist, Carlon S. Land

Laboratory research has been conducted to evaluute the effect of clay hydration on the permeability to gas of water-sensitive reservoir sands. Samples of a .sandstone containing trace amounts of montmorillonite and a sample of montmorillonite were .studied in the laboratory to detertnine whether swelling or dispersion was the cause of permeability reduction in these samples. Heliuin, containing various amounts of water vapor, was used to hydrate the clay minerals and to determine the gas permeability at various stages of clay hydration. The amount of water adsorbed by the samples using this method is small. The nonwetting-phase permeability at higher water saturations war investigated by saturating the with water and measuring the permeability to humid helium while decreasing the water saturation, Relative-permeability curves obtained from results of these procedures were used to estimate the effect of the swelling of trace amounts of mont/tlorillonite on the permeability of the .samples. Most of the damage to the permeability when reservoir sands containing trace amounts of montmorillonite are exposed to fresh water is due to dispersion and movement of clays. Blockage of pores by the increased volume of expanded montmorillonite is believed to result in permeability damage that is small in comparison to the observed damage to the samples tested. INTRODUCTION Studies have shown that permeability is severely damaged when sands containing only small amounts of montmorillonite are contacted by fresh water.15 When samples of sands containing large amounts of montmorillonite are placed in fresh water in the laboratory, these samples may completely disintegrate, forming an unconsolidated mass of larger volume than that occupied by the dry sample." In this case, it is apparent that the swelling of montmoril-lonite has destroyed the pore structure of the sand. If only a trace of montmorillonite is present in a sand. samples may remain intact when saturated with water, although the permeability to water is a small fraction of the gas permeability of the dry sample. Many workers in the field of water sensitivity have attributed this reduction in permeability to the blocking of pores and reduction of pore size by the increased volume occupied by expanded mont- niorillonite. if the sand contains a detectable amount of montmorill'onite or mixed-layer clay containing rnontmorillonite. Logically3 the smaller amount of montmorillonite present in a sand, the smaller should he the effect of montnlorillonite swelling on permeability; however, the quantity of montmorillonite sufficient to cause severe damage by swelling is not known. Although hundreds of samples have been tested in our laboratory, no correlation has been established between the amount of montmorillonite in samples and the permeability reduction caused by fresh water. To many petroleum engineers, the phrase "clay swelling" is synonymous with "water sensitivity", or "permeability reduction" implying that any formation damage due to the hydration of clays is caused by swelling. Although all clays adsorb water on their surfaces, montmorillonite is the only clay mineral commonly found in reservoir rocks which adsorbs water between intercrystalline layers, resulting in expansion of the clay particle. As montmoril-lonite swells, the first few layers of water adsorbed between platelets are strongly held and well oriented, and the montmorillonite retains its crystalline structure, although expanded. As swelling of sodium montmorillonite continues, the platelets become farther apart and the forces orienting the platelets in the crystalline structure become weaker, resulting in a less orderly orientation of platelets. In an abundance of water, small groups of platelets may become detached from the original monl-rnorillonite particle and may be dispersed throughout the water phase. Because of its swelling properties, sodium montmorillonite is very easily dispersed in water. Particles of other clay minerals. such as illite and kaolinite may also be dispersed in water. causing water sensitivity of sands not containing montmorillonite. The presence of an immobile layer of water adsorbed on the surface of clays has been considered a possible cause of the low permeability to water of dirty sands. Grim states that the thickness of the layer of immobile water held by sodium montrnorillonite is three nlolecular layers or 7.5 A (angstroms), with some orientation of water extending to 100 A. Assuming a very thick, immobile water layer adsorbed on the surface of a pore represented by a capillary tube, the maximum effect of the water layer on permeability can be calculated. Using a pore radius of 10 ' cm and an immobile water layer of 50 A. the calculation shows the permeability to be reduced only 2 per cent. Similar calculations can be used to show that the effect of electro-osmotic counterflow is of the same order of magnitude as that of bound water. The reduction of the permeability to water by either an immobile water layer

Jan 1, 1966

By F. E. Pawlek, J. K. Gerlach

The chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. In the first part of the investigations the reaction rate of the chlorides of sodium or calcium with gas mixtures of SO,-0, or SO ,-O2 ,-SO , was measured. The rate for reactions with gas mixtures SO2-O2 is ThE chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. At present the process is mainly applied to produce nonferrous metals which occur in pyrite cinders in small concentrations. Thereby the nonferrous metals are converted into water-soluble, acid-soluble, or volatile compounds whereas all the iron remains as insoluble oxide. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. The reactions occurring during the roasting process can be divided into two groups: solid-solid reaction and gas-solid reaction. The reactions between solids proceed by means of solid-state diffusion and are therefore of low velocity. The heterogeneous reactions between solids and gases of the roasting atmosphere5 are high-velocity processes and determine the velocity of the chloridizing roasting. These gas-solid reactions shall be the subject of the paper presented. In order to investigate the still little-known processes which occur during the chloridizing roasting 6-' the complex reaction is split into several partial steps. First the reactions of NaCl and CaCl, with gas mixtures of SO2 and 0, have been investigated at temperatures between 500" and 600°C by measuring the weight increase of the samples. The gas mixtures used in this series of experiments had first variable compositions, then the amount of SO 2 had been increased. Furthermore the influence of Fe 2 O3 admixtures upon these reactions, the behavior of pure Fe 2 O3 with the gaseous reactants, and the chlorination of the sulfides of lead, copper, nickel, and zinc have been investigated. FORMATION OF GASEOUS CHLORINE Pyrite cinders are never completely roasted and therefore contain still a small amount of sulfide sulfur. When heated again in air, this sulfur is converted into SO,. Accordingly the formation of chlorine can first be described by the reactions: dependent on the composition of the gas phase. If more than 1 pct SO 3 is added to the roasting gas, the reaction rate is determined only by the concentrations of the SO,. In the second part the reactions between chlorine and metal sulfides are discussed. The rate of formation of gaseous chlorine is higher by me order of magnitude than is the reaction rate between ZnS and chlorine. The reaction rate of NiS and PbS lies considerably below that of ZnS. The conversion rate of both pure Fe 2 O 3 and Fe 2 O 3 containing NaCl or CaCl2 when reacting with SO2-O2, mixtures with and without SO3 portions was measured at temperatures of 500", 550°, and 600°C. The weight increase of pressings was determined by means of a spiral balanceg and the reaction rate calculated therefrom according to Eqs. [ll to [31 and [5] to [7]. The prepared samples were suspended on a platinum filament in a vertically mounted tube of mullite (ID 4 cm, length 110 cm) which could be heated by a resistance tube furnace. The platinum filament was tied to the lower end of the spiral balance. A supremax glass tube (length 70 cm) was mounted gas-tight on top of the reaction tube. The unit was sealed up at its top by a ground-in stopper which was holding the spiral balance with the sample. The spiral balance therefore hung outside the high-temperature region of the furnace. Fig. 2 shows the experimental arrangement schematically. While lowering the sample into the reaction tube pure nitrogen was flowing through the reaction zone providing a protective atmosphere. After the sample had reached the reaction temperature within approximately 1 min, the protective gas was replaced by the sulfur dioxide-oxygen reaction mixture. It took about 30 sec until the mixture filled the tube homogeneously. A Ni/NiCr thermocouple placed in the center of the furnace where the sample hung during the measure-

Jan 1, 1968

By J. L. Lehman, J. D. Sudbury, J. E. Landers, W. D. Greathouse

A full scale field experiment on cathodic protection of casing answers questions concerning (1) the proper criteria for determining current requirments, (2) the amount of protection provided by different currents, and (3) the transfer of current at the base of the surface pipe. Three dry holes in the Trico pool in Rooks County, Kans., were selected for cathodic protection tests. The three holes were in an area where casing failures opposite the Dakota water sand often accur in less than a year. Examination of the electric togs showed the wells to be similar to other wells in the field where casing in four of seven producing wells has failed. The three holes were cleaned out and cased with 75 joints of new 51/2-in. 14-tb J-55. Each joint was visually inspected and marked before it as run. The casing was bull plugged and floated in the hole 50 that the inside might remain dry and free of excessive attack. Also, if a leak occurred, a pressure increase could be observed on gawge at the surface. Extensive testing was done, including potential profiles, log current-potentid curves and electrode measurements from both surface and downhole connections. Based on these data, a current of 12 amps was applied to one well and 4 amps to mother. The third well was left to corrode. During the two-year period when the casing was in the ground, [he applied current was checked weekly, and reference electrode measurements were made about every two months. Three sets of casing potential profi1e.c were run. When the three strings were pulled, each joint was examined for type of scale formed, presence of sulfate-reducing bacteria, extent of corrosion nttnck and pit depth. Since the pipe was new when run, quantitative determination of the protection provided by current was possible. This is the first concrete field evidence to help resolve the many arguments about the proper method for selecting adequate current for cathodic protection of oilwell (-using. INTRODUCTION A casing string is run when a well is drilled. This pipe is supposed to protect this valuable "hole in the ground" for the life of the well. Often the casing does not last the life of the well; it is with these casing failures that this work is concerned. The cost of repairing a casing failure varies from field to field—from as much as a $30,000 per leak average in California to $5,000 per leak in Kansas. Additional costs other than actual repairs are also important. These include formation damage, lost production, etc. Casing damage caused by internal corrosion is important in some areas. Treatment normally consists of flushing inhibitor down the annulus, but further research is being done on control measures. The test described in this paper is concerned only with external corrosion. The problem of casing failure from external attack has appeared in several areas including western Kansas, California, Montana, Wyoming, Texas, Arkansas and Mississippi. Cathodic protection is currently being used in an attempt to control external corrosion. From reports in the NACE there are thousands of wells currently under cathodic protection. The quantity of current being applied ranges from 27 amps on some deep California wells to a few tenths of an amp being supplied from magnesium anodes on wells in Texas and Kansas. Considerable field and laboratory effort1,9,5,6 was exented on the problem of cathodic prctection of casing, and it became fairly obvious that this method could be used to protect wells. Early workers showed that current applied to a well distributed itself over the length of the casing and was not concentrated on the upper few hundred feet. Basic cathodic protection theory had shown that corrosion attack could be stopped by applying sufficient current. The problem resolved itself, then, into one of trying to decide just how much current was necessary. Various criteria were utilized in installing the many existing cathodic protection installations. These methods included the following. 1. Applying sufficient current to remove the anodic slope as shown by the potential profile." 7. Applying enough current to maintain all areas of the casing at a pipe-to-soil potential of .85 v.' 3. Applying the current indicated by a log current-potential (or E log I) curve." 4. Supplying the current necessary to shift the pipe to-soil potential .3 v." 5. Applying 2 or 3 milliamps of current per sq ft of casing."

By K. E. Brown, A. R. Hagedorn

A 1,500-ft experimental well was used to study the pressure gradients occurring during continuous, vertical, two-phase flow through 1-in., 1 1/4-in. and 1 1/3-in. nominal size tubing. The test well was equipped with two gas-lijt valves and four Mathak electronic pressure transmitters as well as with instruments to measure the liquid production rate, air injection rate, temperatures and surface pressures. Tests were conducted for widely varying liquid flow, rates, gas-liquid ratios and liquid viscosities. From these data, an accucrate pressure-depth traverse was construcred for each test in each of the three tubing sizes. From the results of these tests, correlations have beer] developed which allow the accurate prediction of flowing pressure gradients for a wide variety of tubing sizes, flow conditions, and liquid properties. Also. the correlations and equations which are developed satisfy the necessary condition that they reduce to the relationships approprate to single-phase flow when the flow rate of either the gas or the liqutid phase becomes zero. All the correlations involve only dimensionless groups. which is a condition usually Sought for in similarity analysis but not always achieved. The correlations developed in this study have been used to calculate pressure gradients for pipes of larger diameter than those upon which the correlations are based. Comparisons of these calcuclaed gradients with experimetally determined gradients for the same flow conditions obtained from the literature indicate that extrapolation to these larger pipe sizes is possible with a degree of accuracy sufficient for engineering calculations. The extent of this extrapolation can only he determined with additional data from larger pipe diameters. INTRODUCTION The accurate prediction of the pressure drop expected to occur during the multiphase flow of fluids in the flow string of a well is a wideiy recognized problem in the petroleum industry. The problem has been brought even more into prominence with the advent of tubingless or slim-hole completions which use small-diameter tubing. Many of the correlations which give reasonably accurale results in the lager tubing sizes are greatly in error when applied to small-diameter conduits. Small-diameter conduits are defined as 1 1/2-in. nominal size tubing or smaller. The study of the pressure gradients which occur during multiphase flow of fluids in pipes is exceedingly complex because of the large number of variables involved. Further difficulties relate to the possibility of numerous flow regimes of widely varying geometry and mechanism and the instabilities of the fluid interfaces involved. Consequently, a solution to the problem by the approach normally used in classical fluid dynamics based on the formulation and solution of the Navier-Stokes equation has not been forthcoming. This is primarily the result of the nonlincarities involved and the difficulty of adequately describing the boundary conditions. As a result of the foregoing, most investigators have chosen semi-empirical or purely empirical approaches in an efford to obtain a practical solution to the problem. Much of the previous work in this area was done in short-tube models in the laboratory. A number of problems arise, however, when attempts are made to extrapolate these laboratory results to oilfield conditions where a much longer tube is encountered. In those few studies where data taken in long tubes were utilized, the data covered only a limited range of the variables, and as a result inaccuracies are introduced when the correlations are extended outside the range of the original data. Also, as a consequence of the limited amount of data available for these studies, the effects of several important variables were overlooked. The problem of predicting the pressure drop which occurs in multiphase flow differs from that of single-phase flow in that another source of pressure loss is introduced, namely, those pressure losses arising from slippage between the phases. This slippage is a result of the difference between the integrated average linear velocities of the two phases, which in turn is due to the physical properties of the fluids involved. In contrast to single-phase flow. the pressure losses in multiphase flow do not always increase with a decrease in the size of the conduit or an increase in production rate. This is attributed to the presence of the gas phase which tends to slip by the liquid phase without actually contributing to its lift. Many investigators have attempted to correlate both the slippage losses and the friction losses by means of a single energy-loss factor analogous to the one used in the single-phase flow problem. In an approach of this type, hourever, many of the important variables, such as

Jan 1, 1966

By J. Lewis, J. Harper, M. F. Ashby

A grain boundary in a metal interacts with second-phase particles, which exert a pinning force (first estimated by Zener) on the boundary opposing its motion. We have computed the shape of boundaries which interact with more or less spherical second-phase particles and have constructed a soap-film model to reproduce the shape of the boundary surface. An important result is that measurement of this shape allows the pressure, or driving force, on the boundary to be measured. We hare applied this technique to grain boundaries in two alloys and hate measured the pinning force exerted by single second-phase jwrticles on the boundaries. It is in good agreement with Zener's estimate. J\. boundary between two grains, or two bulk phases, interacts with small inclusions or particles of a second phase, whether they are gas or solid. This interaction means that the boundary, forced to migrate by a difference in free energy between the material of the two grains or phases which it separates, exerts a force on a particle which it touches, tending to drag it forward. (The movement of inclusions through metals under the influence of this force, has, in fact, been observed. 1-3) Equally, the particle can be thought of as exerting a pinning force on the boundary, tending to hold it back. Zener (in a celebrated private communication4) first realized that this interaction, and the resulting pinning force, existed. His calculation of its magnitude was crude but adequate: a spherical inclusion of radius r blanks off an area nr2 of the boundary on which it sits; since the boundary has an energy of rMM x per unit area, the blanlung-olf decreases the energy of the system by MM: this energy is returned to the system if the boundary is pulled free from the inclusion— a forward movement of the boundary by a distance r will do this—so that the maximum pinning force is Trrym.M- A similar argument can be made for inter-phase boundaries. The nature of the particle itself did not enter this, or two subsequent treatments.5,6 When it is considered, tic leifthe energyoftheb a) The boundary may enter and pass through the particle if the energy of the boundary is lower within the particle than in the matrix. Fig. l(r/). Certain coherent precipitate particles behave like this. h) More usually, the boundary will bend round the particle, enveloping and bypassing it. Fig. l(b). In doing so, it changes the structure and energy of the interface between the particle and its matrix. This means that the boundary does not touch the particle surface at right angles, as early treatments assumed,5'9 but at some angle a which depends on this change in surface energy of the particle, and can be calculated from the equilibrium of surface tensions. Most precipitate particles and inclusions behave like this. Gas bubbles or liquid drops can be regarded as belonging to either group. The progress of bypassing is conveniently measured by the angle shown in Fig. 1. When the nature of the particle is ignored, its maximum pinning force is exerted when - 45 deg. When it is considered, this critical value of is found to depend on a and thus on the nature of the particle. The maximum pinning force lies between nryMM and 2jtjMM (Appendix 1). not very different from Zener's result. In reality, a boundary between crystals has a specific energy and tension which varies with the orientation of the boundary. Furthermore, recent experiments7 indicate that such a boundary is not atom-ically smooth, but has steps on it: migration of the boundary corresponds to the sweeping of these steps across the boundary surface, like the Frank model of crystal growth from the vapor. This means that the interaction of a boundary with particles should really be considered in terms of the way in which particles hinder the movement of these steps. To suppose a grain boundary or interphase boundary to be smooth, and to ignore the variation of its energy with orientation, is to liken it to a soap film. The advantage of this soap film approximation, which we have used throughout this paper, is that interaction energies and boundary shapes can be calculated easily. We have done this by numerical computation and by using a soap film model, and have compared the results with grain boundaries in an aluminum-based and a copper-based alloy. It turns out that the shape of the boundary which bulges between particles allows the pressure an it to be calculated; that is, the local driving force an the boundary can be measured. This has allowed us to check the Zener relationship experimentally.

Jan 1, 1970

By James Terry Duce

The symposium on production for the year 1940 contains few papers on the foreign situation. It is probable that the foreign part of next year's symposium will be even shorter. This is due to rigid censorship in various countries, as the question of the volume of petroleum supplies has become one of great strategic importance. This is even more true than in the last war, owing to greater mechanization of armies. 'It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts from Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not de-terminable frod data available to the author, please inserty; in spaces where the proper entries are determinable by the author, make such entries. y implies a hope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In sucli cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved') and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when

Jan 1, 1941

By James Terry Duce

The symposium on production for the year 1941 contains few papers on the foreign situation. Rigid censorship prevails in various countries, as the question of the volume of petroleum supplies has become one of great strategic importance. This is even truer than in the last war, owing to greater mechanization of armies. It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts from Circular to AutHORs In order to facilitate interpretation of the data in this chapter, we print the fol-lowing excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not de-terminable from data available to the author, please insert y; in spaces where the proper entries are determinable by the author, make such entries. y implies a hope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In such cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved") and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir.. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when

Jan 1, 1942

By Basil B. Zavoico

The symposium on production for the year 1942 contains no papers on the foreign situation except those on Argentina and Mexico. It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts From Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not determinable from data available to the author, please insert y; in spaces where the proper entries are determinable by the author, make such entries. y implies a Rope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and it is an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In such cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved") and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when subtracted, should give the approximate thickness of the productive zone. For fields where this is not true because of unusually high dip or for some other reasons, it is suggested that the authors indicate in their text the approximate average thickness of the productive zone.

Jan 1, 1943

By R. C. Gifkins

R. C. Gifkins (CSIRO)—In this paper evidence is put forward to support the idea of grain boundary shearing in aluminum at 4.2°K and the phenomenon is explained in terms of a low-temperature "equicohesive temperature". It is stated that these findings show that grain boundary shear cannot be ruled out in any situation by temperature arguments alone. We believe, from our own recent study of "apparent grain boundary sliding'' at temperatures below 0.45 Tm, that it can be ruled out on temperature arguments alone.45 Our experiments were made principally with magnesium and a Ms-A1 alloy ("Magnox A12"). Careful examination of offsets of marker lines or steps at grain boundaries produced by deformation at room temperature (-0.3 Tm) showed many of these to result from curvature over narrow zones along the grain boundaries. A significant residuum did, however, appear as a sharp offset or step. It was found that the mean value of this step rose to a small value during the first 0.5 to 1 pct strain and then remained at this level with further strain. Moreover, exactly the same values were obtained (at the same stress) at 75°C instead of 21°C. That is, in this range of temperature the "apparent sliding" was not temperature-sensitive. At 125°C and above there was sliding which increased with strain and which was temperature-dependent. When this temperature-dependent sliding was used to calculate the sliding to be expected at room temperature, this underestimated the "apparent sliding" by a factor of 104. The conclusion drawn is that the "apparent sliding" consists of shear localized in a zone of a width measured perhaps in microns, whereas it seems that true sliding occurs on the boundary surface.46 A model for such localized shear has been developed in general terms, following a similar model of Urie and Wain.47 Other strong evidence for low-temper- ature sliding has been based on the offsets of marker lines consisting of a substructure seen using the electron microscope to resolve these.48 We have repeated this work and found that the effects can be accounted for in terms of cracks in an oxide film which is produced when the substructure is etched up; these cracks form over zones of shear rather than at actual interfaces. However, in aluminum at room temperature (-0.3 Tm) there is no "apparent sliding" which is optically detectable. We suggest that, when the temperature is much lower (and possibly the rate of strain higher, too), as in the experiments of Chin et al., then aluminum behaves like magnesium at room temperature, and a narrow zone of shear develops to accommodate differences in strain across the grain boundary. Such a zone could well give rise to triple-point cracks. It is hoped to investigate these suggestions further. B. Y. Chin, W. F. Hosford, Jr., and W. A. Backofen (authors' reply)—It is interesting to have Dr. Gif-kin's comments, although it is somewhat difficult to reply in detail without the reference containing the work that he describes. Apparently though, he does find a low-temperature temperature-independent sliding that would seem to be related to the observations reported here. Perhaps some of the difficulty has semantic origins, growing out of the distinction between ('true sliding" and "apparent sliding".

Jan 1, 1965

By Joseph J. Becker

RECENTLY the "oriented growth" hypothesis of recrystallization textures has been receiving considerable attention. According to this view, "whenever a new generation of grains is growing in a highly oriented matrix . . . one may assume . . . that from among available nuclei of a great variety of orientations those with suitable orientation relationship with respect to the matrix have by far the highest rate of growth (oriented growth) and will, therefore, predominate."' This statement includes primary recrystallization of single crystals and of polycrystalline materials showing strong deformation textures as particular cases. While the phenomenon of oriented growth undoubtedly does operate, and may be of importance in coarsening or secondary recrystallization, the writer feels that its extension to primary recrystallization is a different matter. Several aspects of this phenomenon may be pointed out which are difficult to rationalize on the basis of oriented growth. In recrystallizing deformed single crystals of alpha brass, Maddin, Mathewson, and Hibbard2 found that the twin composition planes of the recrystallized grains were parallel to the three operative slip planes they observed, and not to the fourth octahedral plane. The writer's current work seems to indicate further that when only one or two slip systems can be seen to operate, the recrystallized grains are aligned only with those slip planes actually observed. This behavior could hardly be accounted for by oriented growth, because on the latter basis the recrystallized texture of a deformed single crystal should certainly have the same symmetry as the crystal itself. Growth rates could not be expected to distinguish between crystallogra- phically equivalent directions, unless the presence of a visible slip system vastly increases the growth rate in the appropriate direction. This seems unlikely. These relationships were observed by the writer only when considerable care had been exercised before annealing to etch away the effects of cutting out the centers of tensile specimens with a jeweler's saw and to etch off the ends of compression specimens. When these.precautions were not taken, nu-cleation inevitably appeared to occur at the saw cuts or at the ends, and the resulting orientations never showed a [111] rotation but appeared quite random. The provision of many nuclei of many orientations did not enhance the correlation, but destroyed it. Recrystallization textures are sometimes strongly dependent on annealing temperature, which would imply that the anisotropy of growth rates is a suddenly varying function of temperature. This might be regarded as unlikely. Recrystallization textures can be strongly dependent on the degree of deformation. If textures are to be explained by selective growth from among nuclei of all orientations, it is difficult to see how the recrystallization process could have any dependence whatever on the manner or degree of deformation. It is felt that the above points should be considered before the oriented growth hypothesis is applied to primary recrystallization, with the necessary complete divorce of the mechanism of recrystallization from the details of the deformation process. References 1P. A. Beck and H. Hu: Reply to discussion of their paper on Recrystallization Texture and Coarsening Texture in High Purity Aluminum. Trans. AIME, 188, 1057; Journal oF Metals (Aug. 1950) TP 29083. 'R. Maddin, C. H. Mathewson, and W. R. Hibbard, Jr.: The Origin of Annealing Twins in Brass. Trans. AIME, 185, 655; Journal of Metals (Sept. 1949) TP 26763.

Jan 1, 1952

By W. L. Worrell

R. C. Gifkins (CSIRO)—In this paper evidence is put forward to support the idea of grain boundary shearing in aluminum at 4.2°K and the phenomenon is explained in terms of a low-temperature "equicohesive temperature". It is stated that these findings show that grain boundary shear cannot be ruled out in any situation by temperature arguments alone. We believe, from our own recent study of "apparent grain boundary sliding'' at temperatures below 0.45 Tm, that it can be ruled out on temperature arguments alone.45 Our experiments were made principally with magnesium and a Ms-A1 alloy ("Magnox A12"). Careful examination of offsets of marker lines or steps at grain boundaries produced by deformation at room temperature (-0.3 Tm) showed many of these to result from curvature over narrow zones along the grain boundaries. A significant residuum did, however, appear as a sharp offset or step. It was found that the mean value of this step rose to a small value during the first 0.5 to 1 pct strain and then remained at this level with further strain. Moreover, exactly the same values were obtained (at the same stress) at 75°C instead of 21°C. That is, in this range of temperature the "apparent sliding" was not temperature-sensitive. At 125°C and above there was sliding which increased with strain and which was temperature-dependent. When this temperature-dependent sliding was used to calculate the sliding to be expected at room temperature, this underestimated the "apparent sliding" by a factor of 104. The conclusion drawn is that the "apparent sliding" consists of shear localized in a zone of a width measured perhaps in microns, whereas it seems that true sliding occurs on the boundary surface.46 A model for such localized shear has been developed in general terms, following a similar model of Urie and Wain.47 Other strong evidence for low-temper- ature sliding has been based on the offsets of marker lines consisting of a substructure seen using the electron microscope to resolve these.48 We have repeated this work and found that the effects can be accounted for in terms of cracks in an oxide film which is produced when the substructure is etched up; these cracks form over zones of shear rather than at actual interfaces. However, in aluminum at room temperature (-0.3 Tm) there is no "apparent sliding" which is optically detectable. We suggest that, when the temperature is much lower (and possibly the rate of strain higher, too), as in the experiments of Chin et al., then aluminum behaves like magnesium at room temperature, and a narrow zone of shear develops to accommodate differences in strain across the grain boundary. Such a zone could well give rise to triple-point cracks. It is hoped to investigate these suggestions further. B. Y. Chin, W. F. Hosford, Jr., and W. A. Backofen (authors' reply)—It is interesting to have Dr. Gif-kin's comments, although it is somewhat difficult to reply in detail without the reference containing the work that he describes. Apparently though, he does find a low-temperature temperature-independent sliding that would seem to be related to the observations reported here. Perhaps some of the difficulty has semantic origins, growing out of the distinction between ('true sliding" and "apparent sliding".

Jan 1, 1965

By James Terry Duce

The symposium on production for the year 1941 contains few papers on the foreign situation. Rigid censorship prevails in various countries, as the question of the volume of petroleum supplies has become one of great strategic importance. This is even truer than in the last war, owing to greater mechanization of armies. It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts from Circular to AutHORs In order to facilitate interpretation of the data in this chapter, we print the fol-lowing excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not de-terminable from data available to the author, please insert y; in spaces where the proper entries are determinable by the author, make such entries. y implies a hope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In such cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved") and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir.. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when

Jan 1, 1942

By Basil B. Zavoico

The symposium on production for the year 1942 contains no papers on the foreign situation except those on Argentina and Mexico. It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts From Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not determinable from data available to the author, please insert y; in spaces where the proper entries are determinable by the author, make such entries. y implies a Rope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and it is an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In such cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved") and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when subtracted, should give the approximate thickness of the productive zone. For fields where this is not true because of unusually high dip or for some other reasons, it is suggested that the authors indicate in their text the approximate average thickness of the productive zone.

Jan 1, 1943

By K. L. Young

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection case. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. INTRODUCTION When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressures. The two methods are Cullender and Smith1-" (numerical integration), and average temperature and com-pressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correcton. The average temperature and compressibility method, in addition to neglecting kinetic energy change, asumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. l or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. where 111.1 qeC2/d p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation,

By James Terry Duce

The symposium on production for the year 1940 contains few papers on the foreign situation. It is probable that the foreign part of next year's symposium will be even shorter. This is due to rigid censorship in various countries, as the question of the volume of petroleum supplies has become one of great strategic importance. This is even more true than in the last war, owing to greater mechanization of armies. 'It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts from Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not de-terminable frod data available to the author, please inserty; in spaces where the proper entries are determinable by the author, make such entries. y implies a hope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In sucli cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved') and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when

Jan 1, 1941

By J. H. Jackson, P. D. Frost, C. H. Lorig, A. C. Loonam

THIS paper describes (1) the effect of sodium on the tensile ductility of magnesium-lithium base alloys, and (2) the precautions necessary to avoid sodium contamination. Effect of Sodium on Properties The harmful effect of sodium in magnesium-lithium base alloys has been recognized by other investigators.1,2 However, quantitative data on its effect have not hitherto been published. The effect of sodium on the ductility of an 87 pct Mg-9 pct Li-4 pct Zn alloy is shown in fig. 1. The sodium was introduced by adding sodium chloride to the flux, which consisted of 50 pct LiC1-50 pct KC1. Moderately high ductility was obtained at an indicated sodium content of about 0.05 pct. Actually, the value probably was less than 0.05 pct, be-cause analyses of the lithium, which were more accurate than those of the alloy, indicated that the highest ductility was obtained when its sodium content was 0.02 pct or less. In fact, in alloys having somewhat greater strength than this particular composition, the sodium content of the lithium must be under 0.01 pct to avoid embrittlement. The effect of sodium on the ductility of several alloys having fairly low strength levels is shown in fig. 2. These alloys were melted with a flux containing 75 pct LiC1-25 pct LiF, to which various quantities of sodium chloride had been added. Sodium had no significant effect in pure magnesium but markedly decreased the ductility of the magnesium-lithium-zinc alloy, even though the alloy contained only 3 pct Li. As the lithium content of the binary alloys was increased, the ductility of the sodium-free alloys also increased. However, the effect of sodium on ductility became progressively more pronounced. Sodium raised the minimum hot-rolling temperatures, particularly those of the high-strength alloys, but its effect, in this respect, was less critical than its effect on tensile ductility. For optimum cold roll-ability, a low-sodium content was required. No deleterious effect of sodium on the stability of properties at slightly elevated temperatures was found. Control of Sodium in the Alloys Optimum ductility is obtained in the magnesium-lithium base alloys when sodium-free materials are used. Commercial lithium was formerly the chief source of contamination. Now purified lithium is usually available. When lithium of ordinary purity is used, the effects of sodium can be minimized by using a flux consisting of 75 pct LiC1-25 pct LiF. Bubbling nitrogen through the melt also helps remove sodium. The damaging influence of sodium on the ductility of the magnesium-lithium base alloys was observed very early in the alloy development program. The discovery came about as a result of chemical analyses made on the lithium used in the alloys. Ductile alloys had been made from lithium containing about 0.2 pct Na, whereas the lithium used in the brittle alloys contained about 0.9 pct Na. The first magnesium-lithium alloys were melted under commercial fluxes ordinarily used in melting magnesium alloys. These fluxes were unsuited for scavenging the contaminating sodium, and the resulting alloys were not ductile. Next, a flux containing 50 pct KC1-50 pct LiCl was tried. This was somewhat more effective but still was not satisfactory. After a number of different experimental fluxes had been investigated, one containing 75 pct LiC1-25 pct LiF was adopted. This flux made it possible to obtain good ductility in the alloys. The

Jan 1, 1951

By Herbert Hoover

IT is always a pleasure for me to join in the Ameri-can Mining Congress, for not only has my own professional life been closely linked with the industry, but the Secretary of Commerce is specifically enjoined in the organic act creating the office to promote and foster the interests of the mining industry. And it is a vital part of our national life. It is one of those indus-tries without which. the nation could not go on for a week. It ranks second only to the agricultural industry in its contribution to our raw materials. Its production amounts to nearly 6 ½ billions annually, providing direct support to probably ten millions of our people through employment to about two million workers. But the in-dustry has a greater importance than even these figures indicate, for with agriculture, forestry, and water power it furnishes the raw materials upon which the whole work of our civilization rests. When the raw ma-terials of our mines emerge. from manufacture with the added expenditure of labor and capital upon them, they have a wholesale value of over fifteen billions of dollars. And in this, the second stage of their application, they give employment to another two million workers and support to about ten million more of our people. A large portion of these manufactured commodities must filter through the retail trade; their total value when delivered to the consumer exceeds twenty billions of dollars. And from this distribution arises the support of many more millions of our people. It is estimated that the products of agriculture when they reach . the consumer, with transportation, manu-facturing, and distribution costs added, have about the same value as the mineral industries-each of them thus contributing about one-quarter of our total na-tional income. No other continent has demonstrated its possession of such a magnitude of minerals as has ours, and such a bountiful distribution over our whole land. But our mineral resources differ in one essential from our other natural resources-they are not renewable. Agricul-ture, forests, and water power replenish their supplies from season to season. Some people conclude from the non-renewable character of the mineral supply that they must shortly be exhausted. The practical question is ,one of time, and time in these matters needs to be measured in generations, and apprehension of exhaus-tion needs to be tempered with many probabilities in-cluding the advance in technical methods of extraction. In some of our minerals, such as coal, iron, and building materials we can, through a knowledge of their geologi-cal structure and occurrence, make fairly good estimates of our reserves. We. know that they will outlast many generations of Americans. In non-ferrous metals and oil, geology affords us no great basis for an estimate of future supply. We only know of the occurrence of minerals of this type by actual exposure of them, and we can thus make no estimates except upon reserves which have been proved by actual development by the process of mining. To develop them ahead merely for national satisfaction of assured future supply would imply an unbearable waste of capital. The consequence is that in these groups there is never a demonstrable assurance of more than a few years' supply ahead of us. Yet we have never failed from year to year to find new deposits and extension of old deposits.

Jan 1, 1928

By R. M. Douthwaite, G. Birkbeck

The effect of grain size and specimen dimensions on the occurrence and magnitude of a yield point drop in pure iron has been examined. The tests were done at room temperature. The results indicate that gain size is the critical factor determining whether a yield drop occurs. The specimen diameter:gain size ratio does not influence the magnitude of the yield drop for the range of gain size and specimen diameters investigated. HUTCHINSON,' petchY2 and worthington3 have investigated the grain size dependence of the upper yield stress (uUYP) and the yield point drop, ouyp - aLYP, in Armco iron, mild steel, and Si-Fe, respectively. These authors used center-annealed wires to avoid stress concentration from specimen shoulders and to ensure uniformity of the applied stress. Coarsegrained specimens show no yield point drop; the yield point drop then increases as d-'I2 increases (where d is the grain diameter). These results can be understood in terms of Petch's analysis2 in which the magnitude of amp depends on the strain rate in the (limited) number of grains deforming plastically at the upper yield point. If N grains per unit volume are undergoing plastic deformation, the strain rate in the deforming grains is l/Nd3 times higher at the upper yield stress than when the whole specimen deforms homogeneously. If N is constant and independent of grain size at uUyp, then all the grains are deforming when ~d~ = 1, so there is no yield point drop. At finer grain sizes, the yield point drop is given by: where AU, is the friction stress increase corresponding to a tenfold strain rate increase. Christ, Smith, and Burton studied the upper yield point in 0.050-in.-diam wire specimens prepared from zone-refined iron. Each end of the 2; -in. specimens was soldered to a & -in. diam steel ball and the load applied through the two balls. There was a yield point drop in specimens with grain diameters less than 0.1 mm; no drop was observed in specimens of grain diameter greater than 0.1 mm that were free from veining substructure, but specimens of grain diameter 0.129 mm, annealed in the y range, showed an upper yield point. and this was associated with the presence of a veining substructure in these specimens. Christ et al. suggested the upper yield point occurs when more than a specific number of grains fill the specimen cross section so a multiplicity of slip is required to initiate plastic deformation. Table I summarizes the published data on the grain size at which the yield drop disappears. On the basis of this data the ratio of specimen diameter:grain diameter = 5 to 27 appears to be the critical value for the occurrence of a yield point drop. Thus, petch2 interprets the appearance and magnitude of the yield point drop in terms of the limited number of grains deforming plastically at uuyp, whereas Christ et a1. consider that the occurrence of the yield drop depends on the ratio specimen diame-ter:grain diameter. The published data cover a wide variety of materials so some variation between the results is to be expected, but the size range covered in the data of Table I is rather limited. In an attempt to discover whether the specimen diameter:grain size ratio or the grain diameter is critical in determining

Jan 1, 1969

By L. D. Wooddy, W D. Moore

Water drives may be natural or artificial. For the case of a natural water-drive reservoir, the volume of water influx corresponding to reservoir pressuve-production history may be calculated by means of the material bal-ance-unsteady state equation. For the artificial water drive or pattern injection water flood, the material balance equation is sufficient to determine the reservoir pressure-production, injection history. However, for both cases to reliably predict reservoir performance, it is necessary to calculate the saturation distribution of the reservoir fluids at different stages of depletion. This paper consolidates the various equations used to determine the performance of water-drive reservoirs into one approach that is applicable to any reservoir that has a natural water drive or is to be produced by water injection. The numerical procedure has been simplified considerably, and the solution is adaptable to either hand calculations or digital computer operation. INTRODUCTION A water-drive reservoir is one in which the predominant source of energy for production of oil results from the encroachment of water into the oil zone. The water drive may be either natural or artificial. Water invasion takes place by expansion of water in the aquifer as a result of the pressure decline transmitted from the oil reservoir. Because water is practically incompressible, a natural water drive requires an extensive aquifer containing a volume of water many times the volume of oil in the reservoir. Provided the permeability of the formation is reasonably high, a moderate decline of reservoir pressure usually causes adequate water influx. If the reservoir pressure decline becomes excessive because of low permeability or a high rate of production, part of the oil production may result from the liberation of dissolved gas which may cause excessive quantities of free gas to be produced along with the oil. In extreme cases, reservoir pressure may decline so rapidly as to cause the oil to be produced predominantly by dissolved gas drive, leading to abandonment of the reservoir before the advancing water has had a chance to flush the entire reservoir. In reservoirs that are not connected to extensive aquifers, an artificial water drive may be created by injecting water into or around the lower edges of a reservoir. Sometimes water is injected within the reservoir through wells interspersed among the producing wells. When injection is carried out in such fashion, the reservoir is in effect subdivided into a number of separate producing segments, in each of which the displacement of oil is simultaneously taking place, and the shapes of which are fixed by the well patterns employed. Because of the natural tendency of oil and water to segregate according to their relative densities, water will tend to migrate downdip regardless of where injected. Accordingly, the injected fluids can be retained within the intended reservoir segments only when conditions are unfavorable to their migration under the force of gravity. Pattern injections are usually confined, therefore, to reservoirs having low structural relief, or low permeability, or when production and injection rates are such that fluid movements in the reservoir are dominated by the pressure gradients rather than by the force of gravity. In the case of natural water-drive reservoirs and artificial water-drive reservoirs in which the water is in-

Jan 1, 1958