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By I. R. Kramer

The effect of the specimen diameter, d, on the flow stress, cra of polycrystalline aluminunz (99.997) was studied. The increase in the flow stress could be accountedfor by the increase in the surface layer stress, with decreasing specimen diameter. Both , and a, were found to be proportional to For the smaller-dianzeter specimen (< 0.033 in.) at strains less than aboul 0.1, the work hardening of the surface layer was greater than that associated with the bulk of the specimen. At higher strains the work hardening due to the bulk appears to be independent of the specimen diameter. THE increase in the strength of metals with decreasing diameter is well-known; however, an adequate explanation for the cause of the size effect is still lacking. The earliest systematic investigation of size effect appears to be that of Onol who reported that for aluminum monocrystals the resistance to slip at low strains increased as the specimen diameter decreased. A change in the stress-strain curve beyond 0.001 strain was not found. However, Suzuki et a1 .&apos; reported for monocrystals of a brass and copper having diameters in the range of 2 to 0.12 mm that the entire stress-strain curve was raised as the specimen diameter was decreased. The effect of size was most apparent when the diameter of the specimen was less than 0.5 mm. In the discussion of this paper Honey-combe reported a size effect in copper crystals as large as % in. diam. These results are in agreement with those of paterson3 and Garstone et al.4 While the majority of the investigations on size effects was conducted in terms of the variation in the diameter of the specimen, several investigators studied the influence of the specimen geometry. For example, Wu and smoluchowski 5 reported that in aluminum monocrystals the slip system was a function of the specimen dimension in the slip direction. King-man and Green 6 studied the influence of size on the compressive stress-strain relationship of aluminum monocrystals when the ratio of length to diameter was constant. Their specimen diameters ranged from to & in. For specimens oriented for single slip the critical resolved shear stress for the smaller-size specimens increased with decreasing diameter. No effect was observed in the large-size specimens. Specimens having an orientation near the corners of the stereographic triangle did not exhibit a size effect. Apparently, the increase in strength with decrease in the diameter of the specimen is a general phenomenon and has been observed in a brass |T and cadmium as well as in aluminum and copper.&apos; In a series of investigations (for example Ref. lo), it was shown that during deformation a surface layer was formed which imposes a back stress, a,, on the moving dislocations. It is reasonable to predict that this surface layer stress, as, should be a function of the specimen diameter and could possibly account for the flow stress size effect. In fact, experimental evidence will be presented to show that this is the case; i.e., the increase in flow stress with decreasing size is equal to the increase in the surface layer stress, as, with size. In addition, data will be presented on the variation with size of and a* where is the back stress associated with the generation of dislocation obstacles in the bulk of the specimen and a* is the net effective stress acting on the mobile dislocations. A limited investigation was carried out on gold specimens to determine the influence of an oxide film. EXPERIMENTAL PROCEDURE The aluminum specimens were prepared from -in. bar stock (99.997 pct purity). The 0.350- and 0.150-in.-diam specimens were machined directly from the bars while the specimens having a diameter of 0.033, 0.020, and 0.015 in. were prepared by swaging and drawing to 0.04 in. and electropolishing almost to final size. The specimens were prepared with a 2-in. gage length. The specimens were annealed in vacuum (-10-4 Torr) at 350°C for 8 hr. The grain diameter of the specimens in the various specimen diameter groups was 0.08 ± 0.02 mm. Gold specimens of two diameters, 0.14 and 0.03 in., were prepared in a similar way and annealed at 650°C for 8 hr. The grain diameter of the gold specimens was 0.2 mm. After annealing the specimens were electrochemically polished to the final size and tested in an Instron tensile machine at a strain rate, E&apos;, of 10- 3 per min. While it was possible to determine the surface layer stress, a,, in the larger-size specimens by measuring the difference, Aa, between the stress before unloading the specimens and the initial flow stress after removal of the surface layer as outlined in detail in Ref. 10, this method is not applicable for small wires because of the difficulty in obtaining a sufficiently accurate measure of the diameter. The values at the various strains were therefore determined by measuring after the specimen had been annealed at 35°C for 4 hr. It has previously been shown" that the two methods give the same results for a provided that the annealing temperature is low enough to affect only the surface layer and not the dislocation barriers in the bulk of the specimen. For the gold specimens a treatment at 150°C for 16 hr was found to be satisfactory for the determination of by the low-temperature annealing method. EXPERIMENTAL RESULTS Determination of a,, and a,. The stress-strain curves for the various diameter aluminum specimens, plotted in terms of the logarithms of the true stress, and true strain, are given in Fig. 1. These curves represent the average data taken from at least ten specimens at each size. Over the range of strains investigated the curves follow the empirical equation

Jan 1, 1968

By L. W. Saperstein, Y. J. Wang

The development of computer programs to solve complex ventilation networks has reached a point of refinement where these programs become a necessary tool of the ventilating engineer. Such a program is presented. This program has an increased efficiency over its predecessors; it also includes the important facility of fixed quantity branches. This is in addition to the earlier capabilities of free-splitting, internal or external fans, and natural ventilation pressures. The program is written in Fortran IV with double-precision arithmetic and is listed here. Sample problems with input and output are also given. The recent, and presumably continuing, official interest in mine safety is bound to result in more stringent control requirements for ventilation. Anticipating this requirement, the Dept. of Mining, The Pennsylvania State University, has developed a computer program for the solution of complex mine ventilation networks. It is the opinion of this department that the program has sufficient merit to warrant its use in normal industrial operating conditions. Although the undergraduate mining engineering students of this department are routinely trained to use the program, it was felt that this training did not present a fast enough means of dissemination; consequently, this paper was written. The conception of the program is not new;1; however, the present version incorporates features that changes it from a scientific endeavor to a useful operating tool. These features include those of earlier programs, such as free-splitting, external or internal fans, and natural ventilation processes plus the important ability of handling fixed quantity branches, and of increased efficiency giving reduced cost. The facility for fixed quantities will be discussed in more detail. The solution of any network depends upon satisfying Kirchchoff&apos;s laws. These state that the sum of flow at any junction is zero, and that the sum of the pressure drop in branches totals the pressure drop in the mesh constituted by those branches, that is that the pressure drop around any mesh is zero. The terminology is derived from Synge," and is, in fact, that used by Topologists. A branch is any airway of uniform characteristics; a junction is where two or more airways meet (the minimum number of two airways is useful for describing the point where a low resistance airway changes into a high resistance one due to some physical constriction); a mesh is a path, along some branches, that returns on to itself, but does not need to traverse the same branch twice in order to do so; and a tree describes all those branches in a network which, while connected through all the junctions, do not form any meshes. Obviously the branches-in-tree are open-ended and can be shown to be one less than the number of junction (J-1). The branches-out-of-tree, also called basic branches, are equal to the number of basic meshes and are M = N — J + 1, where M is the number of meshes and N is the number of branches. The major difference between this network and an electrical one is that the law attributed to Atkinson for pressure drop is utilized rather than Ohm&apos;s law. Atkinson stated that the pressure drop (potential) is equal to a resistance factor multiplied by the quantity squared. This is written H = RlQlQ where H is the head loss. Q? is written in this factored fashion so that H will always have the same sign as Q. A negative sign is used to indicate that flow in a branch is opposite to that of its containing mesh. A mesh takes the direction of its basic branch. Utilizing Atkinson&apos;s law in Kirchchoff&apos;s second law and bearing in mind that the first law must remain satisfied, the program will determine all quantities, or head losses as they are related, for the branches of the network. The program uses a Geuss-Seidel form of in-teration, starting from an arbitrary Q and using a correction factor of the type first suggested by Professor Hardy Cross&apos; that will handle the nonlinear equation of Atkinson&apos;s law. A fuller description of the interative process is included in Wang and Hartman.&apos; Iteration continues until the correction factor is less than or equal to a preset error (E) or until a maximum number of iterations (MAXIT) have been reached. Utilizing an E of 50 cfm, sample problems have had rapid solutions. Rapidity of solution is also ensured by the method of selecting meshes and basic branches. This is done by the computer, which chooses the highest resistance branches, fixed quantity branches, and those containing fans, as basic branches. Natural ventilation pressures are handled as fans of constant pressure and may be assigned to any branch. The computer will generate a fan characteristic by polynominal fitting if a few operating points from the desired fan are input. A fan may be placed in any branch of the network, except those with fixed quantities. The strength of the present program over its earlier versions is its ability to handle fixed quantity branches. This means that certain branches can have their quantity determined, or preset, by the ventilating engineer. Operating under this constraint, the program will analyze the network and output the pressure change necessary to achieve this desired quantity. A call for positive head loss would require an auxiliary fan; negative head loss would require a regulator. This represents a powerful tool for the ventilating engineer who must insure that certain quantities of air pass across the operating faces or through working stopes. McPherson6 suggested that a ventilation program would be useful for determining in advance which branches were receiving inadequate air, and that subsequent calculations would then indicate the necessary corrections. The present program makes these corrections. Thus the mine manager can know immediately the consequences of changes to his system;

Jan 1, 1971

By J. W. Cuthbertson, R. A. Cresswell

THE constitution of Cu-rich alloys with 1.5 to 13.5 pct Sn and 0.25 to 3.0 pct Be and the precipitation-hardening characteristics of alloys with 1.5 to 13.5 pct Sn and 0.25 to 1.0 pct Be have been examined. The hardness and tensile strength of the alloys examined increase markedly after solution treatment at 700°C followed by heat treatment at temperatures between 200" and 450°C. By a combination of cold work and heat treatment, hardness values similar to those exhibited by commercial Be-Cu alloys containing 2.25 pct Be can be obtained with ternary alloys containing 9 pct Sn and 0.75 pct Be and containing 10 pct Sn and 0.5 pct Be. Marked hardening effects occur with alloys containing even less beryllium. By heat treatment alone, a hardness value of 310 diamond pyramid hardness can be obtained from an alloy containing 10 pct Sn and 0.75 pct Be. Preliminary tensile tests have shown that an ultimate tensile strength of 110,000 psi with an elongation of 23 pct is obtainable by precipitation hardening an alloy with 8 pct Sn and 0.75 pct Be. The precipitation-hardening process has been followed microscopically for certain alloys and the inference is that, while the initial hardening effect is probably explained by the precipitation of the ß phase of the Cu-Be system, further hardening, proceeding at a much slower rate, also occurs, apparently as a result of precipitation of phases of the Cu-Sn system, particularly precipitation of the 6 phase at temperatures below 350". The presence of the e phase of the Cu-Sn system in certain alloys at temperatures below 350°C has been confirmed. Tin-bronzes are widely used in engineering applications where a combination of high strength and good resistance to corrosion is wanted. The maximum strength is induced in these alloys by cold working, and it would be an advantage for many purposes if high strength could be achieved alternatively by an age-hardening process. While Cu-Sn alloys have a good fatigue resistance they can be surpassed in this respect by Cu-Be, but the use of the latter alloy is limited by its high cost. If, by adding beryllium to tin-bronze, the properties of the respective binary alloys could to some extent be combined, a most attractive alloy should result. As pointed out by Raynor,¹ beryllium is on the borderline of the zone of favorable size factors for copper, and the solid solubility of beryllium in copper is consequently much more restricted than if the size factor were strongly favorable. The size factor is sufficiently favorable, however, to permit an increase in solid solubility with rise in temperature, and there is thus a composition range in which CU- Be alloys are susceptible to hardening by precipitation heat treatment. Although the a phase of the Cu-Sn system is similarly susceptible to precipitation treatment, the time necessary to establish equilibrium in commercial alloys of this type is usually so great that age hardening becomes impracticable. The addition of beryllium to Cu-Sn alloys would appear to offer a means of conferring on the latter useful age-hardening properties. Masing and Dahl² and others have, in fact, shown that the addition of beryllium to Cu-Sn a solid solutions renders these alloys susceptible to precipitation hardening and after such hardening confers on them an encouraging improvement in physical properties. If this improvement could be achieved by the addition of substantially smaller amounts of beryllium than are customarily found in binary Cu-Be alloys, the ternary alloys should possess economic advantages which might make them more attractive than the binary alloy for some applications. Binary Systems Copper-Tin: The constitution of these alloys is now reasonably well known and is summarized in the equilibrium diagram published by Raynor.³ The following observations, due to Raynor,¹ on the structure of those phases of the Cu-Sn system that are likely to be found in the ternary alloy system will facilitate the subsequent discussion on the examination of that system. The ß phase is an electron compound at the electron-atom ratio 3:2 and has a body-centered cubic crystal structure. This phase is stable only down to 586°C, at which temperature it decomposes eutectoidally into the a and y phases. The y phase has a structure that is also based on the cubic system. This phase is stable down to 520°C, at which temperature it decomposes eutectoidally into the a and d phases. The d phase is an electron compound (Cu³¹Sn8) which has a crystal structure analogous to that of 7 brass. This phase is stable from 590" to 350°C; on prolonged annealing at the latter temperature it breaks down into a mixture of the a and E phases. The e phase is an electron compound (Cu³Sn) having the electron-atom ratio 7:4. Its structure may be regarded as a superlattice based on the close-packed hexagonal system. This phase is stable from 676°C to room temperature. The primary solid solubility of tin in copper increases to a maximum of 15.8 pct as the temperature falls from that of the peritectic reaction to 586°C. The solid solubility remains constant from 586" to 520°C. At lower temperatures the solubility decreases progressively. Below 350°C the fall in solubility is pronounced and is associated with the precipitation of the e phase. This precipitation is very sluggish and does not normally occur under service conditions. Copper-Beryllium: The Cu-Be system has been investigated by Borchers&apos; and others. Raynor5 summarized the present state of information on it.

Jan 1, 1952

By N. S. Stoloff, J. N. Mushovic

Age hardening response of a Mg-Th-Zr alloy has been studied at temperatures in the range 60° to 450°C. Transmission microscopy revealed clustering of thorium atoms at low aging temperatures, supporting a previous report of GP zone formation. Peak strengthening, which is observed at 325°C, is due to the formation of a coherent, ordered, DO19 type superlattice structure, of Hobable composition Mg3Th, as plates parallel to the matrix prism planes. These plates later reveal a Laves phase structure of composition Mg2Th. The equilibrium Mg4Th phase begins to precipitate in two different forms at an early stage, competitively with the Mg2Th plates. RECENT work on the Mg-Th system indicated that, unlike most magnesium-base alloys, complex precipitation phenomena may be occurring. The partial phase diagram of the Mg-Th system indicates that an equilibrium phase, Mg5Th, is the sole intermediate phase.&apos; sturkey,&apos; however, has reported, using X-ray and electron diffraction techniques, that a metastable fcc Laves phase, Mg2Th, precedes the formation of the equilibrium compound, which he identified as closer in composition to Mg4Th. Murakami et al.3 reported that the equilibrium phase precipitates preferentially on grain boundaries and dislocations in a Mg-1.7 wt pct Th alloy; Kent and Kelly4 aged a more dilute alloy, Mg-0.5 wt pct Th, for 4 days at 220°C and found similar results. In addition, they reported that a platelike phase with a structure close to that of the magnesium matrix forms perpendicular to the basal plane and is probably ordered. Research on a Mg-4 wt pct Th alloy by electrical resistance measurements and transmission electron microscopy has suggested that GP zones may form at low aging temperatures.3 However, the electron micrographs purporting to show this phenomenon were not conclusive. In view of the fragmentary evidence concerning the nature of the precipitation processes in the various Mg-Th alloys, an aging study was undertaken to clarify the characteristics of the various precipitates which form and to correlate the mechanical properties of the system with the direct precipitate-dislocation interactions. The latter results are presented elsewhere.&apos; The purpose of this paper is, therefore, to discuss the precipitation sequence in this system. EXPERIMENTAL PROCEDURE Sheet stock (0.060 and 0.010 in. thick) of a commercial Mg-3.93 wt pct Th-0.42 wt pct Zr alloy (designated HK3lA) similar to that studied by sturkey2 was supplied through the courtesy of Dr. S. L. Couling of Dow Metal Products Co. Zirconium does not enter into any precipitation reactions,&apos; but is present primarily as a grain refiner. The alloy was chill cast, warm rolled to 0.090 in. thick stock, and then finally reduced by a combination of hot and cold rolling. The alloy chemistry is given in Table I. This material was solution treated at 580°C for 4 hr in a dry CO2 atmosphere, and then water quenched. Material in this condition was fairly clear of precipitate particles and was fully recrystallized. Aging at temperatures less than 200°C was accomplished by immersing the alloy in a silicone oil bath; for higher temperatures, aging was done in a salt pot. Age hardening treatments were conducted at 60°, 80°, 105°, 135°, 160°, 250°, 325°, 350°, and 450°C for times ranging from 5 min to 400 hr. Hardness tests were performed on chemically polished 0.060-in.-thick blanks of solution treated material which were aged at the various temperatures for increasing lengths of time. For aging temperatures above 150°C the Rockwell Superficial 30T scale was employed, while samples hardened at temperatures below 150°C were monitored with the 45T scale. Each data point consists of at least three separate readings. Yield stresses also were measured at room temperature on both 0.060 and 0.010 in. sheet specimens aged at 325°C. The aged foils were thinned by the window method in a solution of 80 pct absolute alcohol and 20 pct concentrated perchloric acid (70 pct) maintained at 0°C. A stainless steel cathode was used and the applied voltage was 10 to 15 v. Thinned samples were rinsed in distilled water and pure methanol. After the me-thanol rinse the thin foils were quickly dried between filter paper. Foils prepared by the above method were examined in a Hitachi HU11B electron microscope operating at 100 kv. RESULTS A) Hardness. The hardness data are depicted in Figs. 1 and 2. Peak strengthening occurs at 325°C after aging about 6 min, see Fig. 1. Significant strengthening is achieved also at 350°C, but aging at 450°C produces only softening. The stepped curve at 250°C indicates that a complicated precipitation process may be occurring at that temperature. Fig. 2 suggests that at least two hardening mechanisms exist since the lowest temperature hardness peaks are displaced to the left of the peaks obtained at 135° and 105°C. A great deal of scatter is observed at long times in all cases due to magnesium surface degradation caused by the silicone oil bath. B) Identification of the Strengthening Precipitates. The structure formed atlowagingtemperatures (c10O°C) was not clearly resolvable by transmission microscopy. The only bright-field evidence for a change in structure was a mottled appearance which could be observed at extinction contours, as shown in Fig. 3(a), and the disappearance of this effect when dislocations produced under the influence of the electron beam passed through the matrix, as noted in

Jan 1, 1970

By Karl F. Peterson, H. K. Najarian, Robert E. Lund

PRIMARY products of the Josephtown smelter are zinc metal of various grades, lead-free zinc oxide pigments, cadmium metal, and sulphuric acid. Zinc concentrates of domestic and foreign origin are blended and desulphurized at the roaster plant. The equipment includes five, 12-hearth Herreshoff roasters and two modified Trail-type suspension roasters. The sulphur dioxide containing gases from the roasting operation are diverted to a four-unit contact acid plant for the manufacture of sulphuric acid. The roasted calcines are agglomerated by sintering on Dwight-Lloyd-type sintering machines; the sinter is crushed and sized within required limits; and the sized sinter is smelted in vertical shaft-type electro-thermic furnaces. Of the 13 electrothermic furnaces of various sizes now in operation, four are designed to produce American process zinc oxidc of various specifications; and the remaining nine furnaces are equipped with vacuum-type condensers and produce zinc metal. Papers describing the general smelting practice at Josephtown have been published by AIME. Since both High Grade zinc metal and lead-free zinc oxide pigments are produced direct from the electrothermic furnaces without need for subsequent refining, the elimination of impurities such as lead and cadmium has to be accomplished during roasting and sintering operations. To effect the producing of both High Grade and Prime Western zinc products, the roasting and sintering operations are on two separate circuits. A High Grade circuit produces finished sized sinter low in lead, cadmium, etc., for the High Grade furnaces; and the Prime Western circuit produces finished sinter destined for the furnaces producing Prime Western metal. Sintering at the Josephtown smelter differs in many important respects from the sintering practice in smelters operating horizontal retort zinc furnaces. Requirements of the electrothermic smelting furnaces define the physical characteristics of the sinter, while the chemical composition of the sinter is controlled according to the grade of metal and oxide to be made as final products. Three principal objectives in the sintering process at Josephtown smelter are: 1. To transform the zinc calcine from the roasting operations into a hard, yet porous agglomerate that will not crumble in the smelting furnace. 2. Crushing and sizing of the sinter to obtain a proper screen analysis which is normally —% in. down to +1/4 in. particle size. 3. To eliminate, particularly in the High Grade circuit, as much of the impurities such as sulphur, lead, and cadmium as possible. The sintering plant as originally built in 1930 was equipped with three standard 42 in. x 44 ft Dwight-Lloyd sintering machines. Each machine was equipped with a 15x60 in. sintering corporation fan driven by 150 hp, 900 rpm synchronous motor through a magnetic clutch and capable of delivering 30,000 cfm of air at 15 in. of water and 150°F. Each sintering machine was driven by 7½ hp dc motor with controllers for varying the speed of the machine from 8 to 32 in. per min. The pallets were cast iron and the grates of the herringbone type. The charge was mixed in a 4 ft diam x 8 ft Stehli pugmill and transported by belt conveyor, elevator and tripper conveyor to a small bin over each machine. Shortly after the start of operations the following changes were found necessary: 1. The herringbone grates which plugged very quickly and were difficult to keep clean were replaced by straight, narrow cast-iron grate bars running at right angles to the travel of the pallets. These grate bars are held in place by a center bar extending across the pallet on the 24 in. dimension and by removable retaining plates which form the sides of the pallets. 2. Mechanical grate knockers were developed in conjunction with new grate bars for continuously and automatically cleaning the grates. 3. As the cast-iron pallets cracked, they were replaced with cast-steel pallets. In 1938, the capacity of the sinter plant was increased with the installation of two 42 in. x 22 ft machines which were brought from the company&apos;s Herculaneum lead smelter. With a circulating load of some 250 to 300 pct, production of finished sinter on the 42 in. x 44 ft machines at this time amounted to about three tons of sized sinter per machine hour. In 1945, one of the 42 in. x 22 ft machines was replaced by a 60 in. x 44 ft machine of our own design. In 1948, as part of the plant-wide expansion program, the sinter plant not only was expanded but also divided into two separate plants; namely, Prime Western and High Grade circuits. The sinter destined for furnaces producing Prime Western zinc metal is made in a new plant comprising two 60 in. x 44 ft Dwight-Lloyd-type sintering machines, each having a 45,000 cfm Sturtevant fan at 18 in. water static pressure and served by an 8 ft diam x 12 ft long rotary charge pclletizer and auxiliary crushing and sizing equipment. The sinter destined for furnaces producing High Grade zinc metal and zinc oxide pigments is produced in the old sinter plant which was expanded to accommodate four of the 60 in. x 44 ft sintering machines, replacing the old sintering units. In the High Grade sinter circuit, two units of the 60 in. x 44 ft machines are used as preliminary soft sinter machines; and the remaining two units of the 60 in. x 44 ft machines are used to make finished hard sinter. Purification Theory Partial elimination of lead and cadmium in the sintering of zinc ores is common knowledge. However, by some manipulation and by taking advantage of the double circuit, it is possible to make zinc sinter which is nearly free of contaminators. Lead

Jan 1, 1952

By E. B. Mayo

David LeCount Evans (Consulting Petroleum and Mining Geologist, Wichita, Kans.)-—Not only E. B. Mayo but also W. C. Lacy, who apparently urged the preparation of this analysis, is to be commended. Regional thinking of this type is needed to assure future success in the never-ending search for new mineralized and petroliferous districts. As is usually the case, here is a regional study that will be read by the mining geologist alone. It is ironic that several of the trends established in this study have suggested themselves in northern mid-continent, detailed, and regional studies. These, where established, have offered new keys to petroleum exploration and have provided a possible basis for unraveling a number of broad generalities. The oil geologists, active in Colorado, Kansas, and Oklahoma, would find much food for thought in Mr. Mayo&apos;s projections. To be more specific: 1) The parallelism between E. B. Mayo&apos;s Texas Lineament and the Amarillo Uplift, the Wichita Complex and the Arbuckle Complex of the Texas Panhandle and Southern Oklahoma is viewed with interest and appears especially significant when compared with the similar northwest trend of the Central Kansas Uplift, a major trend of production. 2) Considering the various northeast zones of Fig. 2, and with particular reference to Mayo&apos;s C-C, the Jemez Zone is on direct line with one of several northeast-southwest controls which the present writer has been using with some success in Kansas subsurface correlations. Considering zones of shearing, with no apparent vertical displacement, but suggesting strike-slip movement, because of the staggered effect on other features which cross such trends, Mayo&apos;s philosophy presents regional possibilities for lines of weakness, considered to this time of only local significance. 3) And, finally, in an area as distant from the Southwest as central Kansas, the north-south trends of the Fiarport-Ruggles anticline, the Voshel-Hol-low Nikkel-Burrton structures, the Dayton to Stut-gart trend, the north, slightly east trend of the Ne-maha structural complex, and others all seem to approach the north-south alignments, a through f, of Mayo&apos;s Fig. 3. Mayo&apos;s employment of structural intersections to pinpoint crustal weakness, to localize igneous activity and its accompanying mineralization is not, perhaps, a new concept, but it is a 1958 model, produced by tools improved from the ever-increasing accumulation of geological observations. The use of intersecting trends in petroleum geology is not a new idea, since much production in earlier days was encountered via the straight line projections of established trends to centers of intersection. A tragedy in this age of specialization is that iron curtains have been raised between groups, all seeking raw materials, all acolytes at the altar of structural geology, but all smugly content in and protected by the ivory towers of petroleum geology, engineering geology, mining geology, and geophysics. Mayo presents basic ideas which can stimulate mid-continent structural thinking and, in the case of cen- tral Kansas. he provides a key to replace the broad and overworked simple monoclinal, sinkhole-dotted, Karst topography credo, which is not finding its share of new oil in a state where the declining discovery ratio is disconcerting. The American Association of Petroleum Geologists would do well to add E. B. Mayo to its list of Distinguished Lecturers. Evans B. Mayo (author&apos;s reply)—In reply to David LeCount Evans&apos; comments, it is pleasing to learn that some of the elements discussed in my paper may interest petroleum geologists as well as mining geologists. This should not be surprising, however, because the lineaments make up the framework of the continent, and the oil-bearing sediments must reflect to varying degrees adjustments of basement blocks along their boundaries. A further possibility that petroleum geologists must have considered is that the slow escape of heat from buried lineaments and their intersections has aided the separation of oil from the sediments and started the migration into traps. Regarding the specific points listed by Evans, the following are suggested: 1) The branch of Texas Lineament marked 1&apos; (Fig. 3) is thought to extend eastward through the Capitan Mts., New Mexico, through the long Tertiary dikes east of Roswell, and beyond via the Matador and Electra ranges of the Red River Uplift, Texas. Its further continuation might be the eastern flank of the Ouachita Fold Belt. The Amarillo-Wichita-Arbuckle zone of uplifts appears to continue east-southeastward the Spanish Peaks belt (3-5, Fig. 3). The northwest-trending Central Kansas Uplift would not belong to the above set, except insofar as the Central Kansas Uplift is traversed by west-northwest folds, possible continuations of the Uinta belt (5-5, Fig. 3). 2) The possible continuations into Kansas of the Jemez zone are new to me and are most welcome suggestions. 3) Most of the nearly north-south Kansan structures mentioned by Evans are unfamiliar to me, but the Nemaha Uplift itself appears to be part of a very pronounced structure traceable from the Cerralvo Fault Zone, south of the Rio Grande, through the Bend Arch, Texas, and the Nemaha Uplift, into the Pre-Cambrian of Minnesota (?). This nearly meridional zone is crossed and broken by the Rio Grande Embayment and by the Red River-Wichita Syntaxis. Petroleum geologists realize the economic importance of these features. Perhaps it is inevitable that some papers of general interest be buried in the journals of specialized groups. Moreover, papers dealing with regional, or lineament, tectonics and its applications to exploration for economic mineral deposits are as yet few in the American literature. The opportunity to advance this field is open to all those who are not ultra-conservative and who have a lively curiosity, plenty of patience, and not too many business restrictions. In conclusion, much appreciation is extended to D. L. Evans for his comments.

Jan 1, 1960

HIGH-GRADE manganese ore, from which manganese is obtained commercially, is not found in large quantities in any major steel-producing nation in the free world. The U. S. is a "have not" nation with respect to deposits of directly mineable high-grade manganese ore. Known resources of 48 pct Mn or better grade ore amount to less than 200,000 tons. In 1950 the U. S. steel industry consumed 1.8 million short tons of metallurgical grade manganese ore that contained about 800,000 tons of manganese. About 16 pct of the manganese content was lost in processing, so that about 650,000 tons, or 13 pounds per ton of steel actually entered into steel production. Under present practices use expands directly with steel output, and by 1975 the demand in both the U. S. and the rest of the free world is expected to be roughly 60 pet greater than in 1950. In peacetime about 80 pet of manganese consumption goes into steel production; high-manganese steel, dry cells, and chemicals account for the remainder. The manganese supply problem centers around high-grade ore for ferromanganese production. Use of ores containing less than 35 pet Mn sharply increase the costs of making ferromanganese. Use of ferro-manganese of grade below 70 pet in turn requires changes in steelmaking that increase steel cost. Under normal conditions the present small domestic production cannot be expected to increase. Major resources in the U. S. consist of 12 low-grade deposits. The cost of mining and treating these ores to extract a product as good as that yielded by imported ores is at least twice and in some cases more than four times the 1951 price of foreign ores delivered to the U. S. However, as long as trade relations and overseas shipping are not interrupted, deposits in India, Africa, and Brazil can meet steadily increasing demand at approximately present costs. Cost considerations indicate that the U. S. should continue to rely upon overseas sources for its peace-time supply, and that this situation is satisfactory. But, this does not take into account the question of how the U. S. will be able to meet its needs in war. Position of the Rest of the Free World In 1950, free world steel producers outside the United States, with a steel output of 70 million ingot tons, consumed about 1.3 million tons of metallurgical-grade ore. Their manganese ore demand, expected to increase directly with steel production, will by 1975 be about 2.3 million tons. Russia possesses over half the known manganese ore reserves of the world and is producing twice the tonnage of any other country. It supplied more than a third of the U. S. manganese requirements up to 1938 and again in 1948, but by 1950 Soviet manganese exports to the free world had virtually ceased. The free world&apos;s supply of manganese now comes mainly from India and Africa. Somewhat over 10 pet of U. S. imports came from Brazil and Cuba. Security Considerations In the event of war the U. S. might be substantially cut off from 90 pet of present sources. Reduction in manganese specifications might cut consumption by over 10 pet without seriously affecting steel quality. By elimination of losses in the production of ferromanganese savings as high as 10 pet might be possible. But, wartime manganese requirements cannot be met through conservation alone. To meet possible future emergencies the U. S. should continue its comprehensive security program for manganese, including stockpiling and research on the economic use of low-grade ore, domestic ores, the recovery of manganese from slag and the reduction of manganese requirements in steel production. If this work, including additional pilot plant operation is pursued vigorously, it should be possible in an emergency to get an adequate supply of manganese from domestic sources. The national stockpile then can be looked upon as a source of supply during the period of at least 2 years required to reach full-scale production from low-grade resources. Ferromanganese Smelting In comparison with smelting of pig iron, ferro-manganese smelting is a very wasteful process. Under present ferromanganese blast-furnace smelting practice, about 8 pet of the manganese in the furnace charge is lost to the slag, and roughly the same amount is lost to the stack gases; the total loss approaches 15 pct. Present practice is a compromise between excessive slag loss and excessive stack loss. In fact, it may be seriously questioned whether conventional blast furnace design is suitable for manganese smelting. U. S. Resources The known manganese deposits of the U. S. contain a total of 3500 million long tons of raw material and 75 million long tons of metallic manganese. More than 98 pct of this contained metal is in 12 large low-grade deposits of which the most important are those at Chamberlain, S. Dak; Cuyuna, Minn.; Aroostook County, Maine; and Artillery Peak, Ariz. Reserves of high-grade ore (48 pct Mn) amount to less than 200,000 tons. About 20 million tons of ore average over 15 pct Mn, and when grade is decreased to 10 pct Mn reserves amount to about 100 million long tons. If cut-off grade is decreased to 5 pet Mn, resources amount to 800 million long tons. Many of these low-grade ores may be beneficiated by flotation or other concentration methods. Pyrometallurgical Methods For smelting ferromanganese, it is essential to have an ore containing at least 50 pct manganese, with an Mn:Fe ratio of about 8:1. Direct smelting of 20 pct Mn concentrates is not promising. The only method that offers any promise involves two-step smelting.

Jan 1, 1952

By G. A. Stamboltzis, N. Arbiter, C. C. Harris

Fracture under low-velocity free-fall and double impact and under slow compression have been investigated. The pattern of breakage and the size distribution of resulting fragments of sand-cement and glass spheres have been determined. Photoelasticity methods were used to simulate the stress distributions in free-fall impact in order to explain the observed patterns of breakage. Oblique fracture planes, occurring only in free-fall impact, develop along lines which coincide with the trajectories of maximum compression as determined by mathematical analysis. Breakage efficiencies for different modes of fracture were compared for both types of spheres. For the same specimen and loading system, static loading and low-velocity dynamic loading induce geometrically similar stress fields resulting in reasonably similar fracture patterns and shapes of fragments. This work had its origin in a desire to understand three fundamental processes involved in autogenous comminution: namely; free-fall impact, double impact, and slow compression. To simplify the investigation, it is preferable to reduce the entire multi-stage fracture process to its most elementary form; that is, to study products resulting from a single-stage operation, such as the breakage of a specimen under single fracture conditions. The goal of this research is to study the energy utilization in the single fracture of brittle specimens and to relate the pattern of breakage and the resultant fragment size distribution with the nature of the material, the specimen size, the manner of load application, and the rate of loading. Published works on single fracture have mainly been concerned with tests on large (> 1-in.) irregular mineral pieces, especially coal and coke. These were mainly friability tests employing a single blow on closely sized pieces. More recently, small mineral specimens in the sieve range and glass spheres have been investigated.5-7 Kick8 has reported free-fall and double impact tests with large large cast-iron, cement, and clay spheres. The establishment of a minimum breaking height independent of size in the free-fall impact tests, and the direct proportionality between the minimum work required for fracture and the volume of the specimen in double impact tests were used by Kick as an experimental proof of his classical law of "Proportional Resistances." In the present work, spherical shapes were chosen because of their simple body geometry and consequent impact and stress field symmetry. Because the study involves several physical principles in connection with brittle-fracture, it may be of interest in fields where the strength of materials is of importance. APPARATUS The equipment for the free-fall impact testing is illustrated in Figs. 1 and 2. This consisted of a massive (17 x 17 x 3-in.) hard steel plate onto which specimens were dropped and a specimen release mechanism which could be set at any desired height up to 10 ft above the plate so that the impact velocity could be varied up to about 25 ft per sec. Double impact breakage is characterized by two points of loading situated at opposite poles. For this mode of breakage the apparatus was modified (Figs. 3, 4 and 5) so that a falling mass provided an impact of predetermined magnitude on a specimen resting on the plate. A spring-loaded device operated immediately after fracture to arrest the falling mass and to record its residual kinetic energy. Precautions were taken to avoid secondary breakage. Slow compression tests were performed on a conventional hydraulic testing machine, the specimen being held between two hardened parallel bearing blocks. In the case of glass spheres, carbide bits were used. Photoelasticity studies were performed on two-dimensional models held in a loading frame equipped with a force gauge (Fig. 6). The models were viewed in a polariscope and isochromatic fringe patterns were recorded photographically. SPECIMENS Sand-Cement Spheres: A series of sand-cement spheres were prepared by molding in spherical glass flasks.

Jan 1, 1970

By R. P. Alger, C. A. Doh, M. P. Tixier

The principle, the equipment and field operation of sonic logging are described. The tfio-receiver system produces logs independent of hole size and mud. Field experience is given and forms the basis for the interpretation of the log. The derivaiion of porosity values from measured velocities is discussed, according to the type of formations (hard formations, compacted sands, and unconsolidated formations). The time-average equation proposed by M. R. J. Wyllie, A. R. Gregory and L. W. Gardner is uscd as a basis for the computation of porosity in limestones, cemented sandstones and compacted sands. Variations in the lithologic character of limestones do not seem to change the porosity calibration markedly. The compaction of sands is related to the compaction of shale adjacent to them; and, thus, the shale velocity is used for the establishtnent of empirical relations for the computation of porosity in un-consolidated formations. Various forrnu.las are tentatively presented to account for shale and fluid content. Field experience demonstrates that considerable attenuation of sonic energy takes place in unconsolidated formations, particularly when gas bearing, and in fractrured formations. Unusually large attenuation produces skipped cycles, a feature easily recognized. The application of sonic logging to structura1 studies is featured, showing its possible integration with the dipmeter. Correlation and its application to the irrterpretation of seisrmic surveys are reviewed. The paper is illustrated with field examples. Sonic logging is the recording of the time required for a sound wave to traverse a definite length of formation. Sonic travel-times are inversely proportional to the speed of sound in the various formations. The speed of sound in subsurface formations depends upon the elastic properties of the rock matrix, the porosity of the formations and their fluid content and pressure. Below the "weathered" or low-velocity layer extending from 50 to 100 ft or so below the surface, sound velocities may range from about 6,000 ft/sec in shallow shales to as much as 34,000 ft/sec in dolomites. In hard formations (well cemented and/or compacted), the sonic log reflects the amount of fluid in the formations; hence, it correlates well with their porosity. In unconsolidated formations, which are usually of fairly high porosity, the sonic log gives an approach to porosity determination, when its readings are corrected for lack of compaction, shaliness, and fluid content. In such formations the sonic log may also indicate the presence of gas and may distinguish between oil- and water-bearing beds. Field experience with the sonic log in soft formations is more limited than that in hard formations. As a result, interpretation in soft formations is not as well developed at the present time. In all types of formations the sonic log is of considerable value for correlation and for the more detailed and accurate interpretation of seismic data. EQUIPMENT AND PRINCIPLE FIELD OPERATION The basic features of the sonic log" are a two-receiver system and two available short spacings. The log is recorded on film using a standard field unit. An SP curve is run along with the sonic curve to give a more interpretable log and to establish absclute depth control for comparison with other logs run in the same well. If desired, a gamma-ray curve may be recorded simultaneously with the sonic curve. Fig. 1 shows the sonic-gamma ray combination sonde. The sonic portion consists of a sound transmitter and three receivers mounted 3, 4 and 6 ft from the transmitter. When the first and second receivers are used, a sonic log of I -ft spacing (distance between receivers) is obtainea. Use of the first and third receivers provides a 3-ft spacing. The transmitter emits pulses at the rate of l0/sec. After the transmission of a pulse the first arrival of sound energy at each receiver triggers its response system. The differ-

By J. C. Melrose

The contact angle is one of the boundary conditions for the differential equation specilying the configuration of fluid-fluid interfaces. Hence, applying knowledge concerning the wettability of a solid surface to problems of fluid distribution in porous solids, it is important to consider the complexity of the geometrical shapes of the individual, interconnected pores. As an approach to this problem, the ideal soil model introduced by soil physicists is discussed in detail. This model predicts that the pore structure of typical porous solids will lead to hysteresis effects in capillary pressure, even if a zero value of the contact angle is maintained. The model is generalized to situations in which the contact angle takes on values between zero and 40 degrees. For the imbibition branch of the capillary- pressure function, the model predicts a considerable departme ftom the usually assumed cos 0 relationship. In fact, according to the model, it is possible that a displaced wetting phase will not be able to reimbibe, even when the contact angle does not exhibit hysteresis. INTRODUCTION The subject of capillarity in porous media has long been of interest in many branches of engineering and applied science. The earlier investigators were those concerned with the physics of soils. 1-5 More recently, petroleum engineers and others dealing with the problems of petroleum production from reservoir rock have given much attention to the subject.6-10 Also, important additions to the literature of capillarity have been contributed from the field of chemical engineering.11-12 These attest to the wide range of industrial applications in which capillary phenomena play a role. The present paper is concerned with the role which wettability plays in capillary action in porous media. As is well known, capillary-rise (or capillary pressure) phenomena have frequently been interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This approach has enjoyed a certain degree of success in correlating experimental results.13 The generalization of this model, however, to situations which involve varying wettability, has not been established and, in fact, is likely to be unsuccessful. In this paper another approach to this problem will be discussed. A considerable literature relating to this approach exists in the field of soil science, where it is referred to as the ideal soil model. Certain features of this model have also been discussed by Purcel114 in relation to variable wettability. The application of this model, however, to studying the role of wettability in capillary phenomena has not previously been attempted in detail. In the present paper, additional features of the model are introduced. These features are critical in determining the quantitative behavior of the model. GENERAL FEATURES OF CAPILLARY HYDROSTATICS BASIC PRINCIPLES When the interstices of a typical porous solid are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. Hence, fluid-fluid interfaces are found within a certain fraction of the pore openings. The fundamental equation of capillarity specifies the configuration of these fluid-fluid interfaces. This is known as the Laplace equation, when derived from mechanics, and as the Gibbs-Kelvin equation when derived thermodynamically.15 Given two fluid phases, a and ß, in hydrostatic equilibrium, the Laplace equation states that the respective fluid pressures in regions close to the interface are related by Here oaß is the surface or interfacial tension and rl and r2 are the principal radii of curvature of the surface or interface. The pressure difference, Pa-Pß, is the capillary pressure, PC. As Buff15 has shown, Eq. 1 states the condition for hydrostatic equilibrium within the two-phase confluent region, which is referred to as the interface. It thus can

Jan 1, 1966

By H. I. Kaplan, C. Laird

Pulsating contpresslon experiments have been carried out on coppev single crystals in order to test the adequacy of mechanisms which have been suggested for stage I cvack grouth when tension-compression loading is the mode of- applying stress. Although dejorrrzation continues slowly for many millions 01 cycles under Pulsating compression stresses both within slip bands formed in the first cycle and by the creation of new bands, the morphology of these bands is not typical of fatigue slip bands in general and neither initiation of cracks nor propagation of artificially induced cracks was observed. It is therefore concluded that 1) initiation and growth of cvacks in fatigue is a consequence of repeatedly reviersed, microplastic deformation rather than intermittent, unidirectional deforma-tion, 2) gvowth of- cracks in polycrystalline specimens FAILURE of a plain specimen subjected to cyclic tension-compression stresses is known to take place by two stages of cracking.1,2 The first stage is characterized by propagation along slip planes roughly at 45 deg to the stress axis, in the outermost layers of the specimen, and at a rate of the order of angstroms per cycle. The average macro orientation of a stage I crack is normally at right angles to the stress axis,3 however, except in a few cases, e.g., single crystals in suitable orientation, when both the micro and macro directions of propagation are at 45 deg to the axis. After a stage I crack has penetrated to such a depth that the stress on the remaining section of metal is significantly increased, stage II crack propagation succeeds stage I, at right angles to the stress axis both micro and macroscopically. Direct evidence of the processes occurring during a subjected to pulsating compression stresses is caused by the setting-up of local tensile stresses due to interactions between grains, and 3) both unslipping mechanisms and operation of the "plastic blunting process " within a single slip band are adequate descriptions 01- stage I growth, being fundamentally similar. The slip mode of a material, however, is considered to control whether unslipping or the plastic blunting process takes place. Thus materials of planar slip mode fauor unslipping while those hacing a wavy mode, and capable of cross slip, can fail in stage I by the plastic blunting process. Similarly, and perhaps more importantly, reversed torsion and tension-compression modes of applying stress may be expected to cause the unslipping mechanism and the plastic blunting process, respectively. single stress cycle4,5 shows that stage II crack propagation takes place by a repetitive plastic rounding and closing of the crack tip. This mechanism has come to be called the "plastic blunting process".6 On the other hand, the extreme smallness of the phenomena occurring in stage I growth prevents elucidation of its mechanism by direct observation. Many suggestions have been proposed for this mechanism,&apos;"-" most of them involving some kind of random or systematic unslipping process. It is possible, however, that the mechanism of stage I growth is essentially the same as that of stage 11, but occurring on a much smaller scale.6 In this situation, it has been observed that cracks propagate along slip bands comprising dislocation cell structures and bounded on either side by regions of different dislocation density and distribution." Since there is evidence that such bands are softer than their matrix, * it may be expected that the plastic blunting process occurs within a single slip band during stage I growth, rather than on two gross bands as in stage 11, when the acting stress is greater.= The blunting of the crack tip allowed by coordinated

Jan 1, 1968

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967

By N. H. Harrison, J. K. Rodgers, S. Regier

This paper presents comparisons of data obtained from a laboratory reservoir study and from a calculated behavior prediction with the actual production history of a condensate reservoir. A small non-commercial discovery was depleted under closely controlled conditions and the well fluids were sampled at frequent intervals. Data on the reservoir and production variables were accumulated on a fixed schedule. A laboratory reservoir study war made using the initial well fluid samples as charging stock. The production procedures and operating conditions were held constant throughout the study wherever possible and in general paralleled the field work. The well fluid compositions and the cumulative recoveries ar a function of the reservoir pressure were also calculated using conventional flash vaporization procedures and equilibrium constants. Comparisons based on the composition of the well fluid show good agreement, the laboratory study agreeing within experimental accuracy with the field work and the calculated data comparing equally well. The gas-oil ratios are also in good agreement, but with somewhat greater deviations at the higher pressures. In the overall picture, it is believed that a model st,~tiy can predict within experimental accuracy the production history of a condensate reservoir. Better equilibrium constants for the heavier hydrocarbons are needed in order to attain improved composition accuracy by calculation. INTRODUCTION In Aug., 1955, a gas condensate well was completed in San Juan County, Utah, that was initially thought capable of good commercial production. These conclusions were derived principally from core data and electric logs, which indicated good permeability, porosity and gas content. However, after the usual series of potential tests it was found that the reservoir pressure had declined some 22 per cent, and it was obvious that the zone tapped was but a small pocket or trap. It became apparent that, with a controlled depletion of a small reservoir, a unique opportunity was available to compare laboratory and calculated studies with an actual field depletion and to further the present knowledge of condensate reservoirs. FIELD WORK The Coalbed Canyon Well No. 1 was conventionally completed in the Paradox limestone formation to a total depth of 5,912 ft. The producing zone from 5,762 to 5,806 ft was perforated with four jet shots per ft. The wellhead and field equipment were also conventional, the major items consisting of a two-pass indirect fired line heater, a high- and a low-pressure separator with the necessary controls and accessories, gas meters, back-pressure regulators, flare stacks and condensate stock tanks. The initial testing of this well con-sisted of a series of flow potential and pressure build-up tests during which some 30 MMcf of gas was produced. The reservoir pressure declined from an estimated 2,300 to 1,782 psig during this period, from which it was concluded that the reservoir was very small. In order to approach steady-state conditions in the reservoir and so provide optimum conditions for making comparisons, the field depletion was programmed to approach, if possible, constant production conditions. Bi-hourly readings were taken of the tubing pressure, the pressure and temperature of the separators, oil and gas rates, and other pertinent operating data. The gas rate, as indicated by the orifice meter, was held constant by the adjustment of the choke in the line heater. The temperature of the first stage separator was held constant by adjustment of the line heater jacket temperature. Practical considerations of production made the maintenance oi a constant gas rate impossible. The test started with a gas rate of 4 MMcf/D and a separator pressure of 250 psig. This rate was maintained until the choke was fully opened. The gas rate then declined with the falling tubing pressure and production was continued until the rate was about 2

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi&apos;s solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith&apos; have applied Raimondi&apos;s solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,&apos; Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By L. F. Mondolfo, B. E. Sundquist

The crystallographic orientation relationships resulting when lead is nucleated from the liquid by Ni, Cu, Ag, and Ge were determined. For each nucleating agent several definite orientatioz relationships were found. These relationships seemed to be controlled by good symmetry relations and low crystallographic disregistry between mating planes. For any given nucleating agent the under colling for nucleation was found fairly constant and independent of the orientation relationship and consequent disregistry. It was also found that, upon re melting and refreezing the Pb, the orientation relationship was changed. These findings prove that crystallographic disregistry is not the controlling factor in heterogeneous nucleation from the liquid. The results of this investigation tend to confirm the theory presented in a preceding paper that heterogeneous nucleation starts with the formation of an adsorbed layer of nucleated metal on the nucleat-ing impurity. Evidence is given that cavities in the nucleating agent act as centers of nucleation. IT has long been known&apos; that solid extraneous particles are active in catalyzing phase transformations that occur in a system, particularly condensation and crystallization. It is well established that these heterogeneities act as catalysts by providing surfaces upon which nuclei of the precipitating phase can form with activation energies smaller than those required for homogeneous nucleation. Numerous investigations have shown that in this process of heterogeneous nucleation: a) the nucleus forms with one, or several, definite crystallographic orientation relationships with the nucleating phase2-4 and b) that there is a small range of undercoolings or super saturations characteristic of the nucleation of a given solid on a given Substrate.5-10 Turnbull and vonnegut11 have developed a theory based on theories developed by Volmer12 and Turn-bull and Fisher1= for heterogeneous nucleation from gases and liquids, that relates the super saturation or undercooling required for nucleation to the dis-registry between the lattices of the nucleus and the nucleating agent. This theory predicts that nucleation should occur with the orientation relationship between the nucleus and nucleating agent that minimizes the disregistry. Further, it predicts that the undercooling or super saturation necessary for nucleation should be a function of the disregistry. Numerous investigations have dealt with the orientation relationships resulting from the condensation of vapors onto crystalline solid substrates2,3 and a few with the nucleation of one phase by a second phase in solidification4,14. Others have dealt with the supersaturation8-10 and undercooling5-7 associated with nucleation in condensation and solidification respectively. However, there is virtually no report that gives both of these factors for the same system. In this investigation a study was made of the undercoolings and orientation relationships resulting when Pb is nucleated from the liquid by Ni, Cu, Ag, and Ge. It was the purpose of this investigation to check the Turnbull-Vonnegut theory, i.e., the importance of crystallographic disregistry between nucleating catalyst and nucleated metal. The results indicate that disregistry is not an important factor in nucleation and that the nucleation process is probably somewhat more complex than current theories suggest. EXPERMENTAL PROCEDURE Small single crystals of nickel, copper, silver, and germanium were prepared from materials of four to five nines purity, and the Pb used was also 99.999+ pet pure. Cu and Ag single crystals were prepared by sealing small chips of Cu or Ag in an evacuated quartz capsule and heating the capsule at 2000°F for 1 hr before cooling. Nickel crystals of 200 diam were also prepared in evacuated quartz capsules, but melting was done by heating the capsules in an oxy-acetylene flame for a few minutes. These spheres were invariably polycrystalline so

Jan 1, 1962

By H. A. Wriedt

Zinc-vapor pressures in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C were measured by an isopiestic method. Thermody-na?nic properties of zinc in these solutions were derived directly and those of iron with a Gibbs-Duhem integration. Zirzc and iron exhibit large, positive, and moderately temperature-sensitive deviations from ideality. Excess enthalpies and Gibbs energies are positive in the ranges studied. It has been establzshed in relating published phase equilibria to the Gibbs energies of forming solid solutions that positive departures from ideality also exist in the fcc solutions. Tlze stability, as defined by Darken, of the bcc solutions is small but positive at 703.5"C. Its decrease with decreasing temperature indicates that a miscibility gap may exist in the stable or metastable bcc solutions at lower temperatures. The changes of thertnodynanlic properties relatable to changes in magnetic state are minor compared to other changes due to alloying. The accuracy with which the relation between lattice parameter and composition of the bcc solutions is known has been improved. Zinc increases the lattice parameter of a iron by O.ZOZA per unit atom action zinc to at least NZn = 0.25. TO our knowledge, only Ciganl has previously investigated thermodynamic properties of the bcc solutions of the Fe-Zn system. He measured zinc-vapor pressures in the temperature range from about 320" to 360°C by an effusion technique. We have measured the vapor pressures of zinc in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C by an isopiestic technique. This investigation and the pursuant thermodynamic computations are part of a program for studying several properties of these solid solutions. In the appendix we report a remeasurement of the relation at room temperature between the lattice parameter and zinc content. Related work not reported herein embraces measuring the diffusivity2 of zinc in ferrite at 700" to 900°C and the Curie point temperature3 as functions of composition. EXPERIMENTAL METHOD AND APPARATUS Purified iron at a series of constant temperatures was saturated with zinc at a series of constant zinc-vapor pressures, the range of conditions being so limited that the equilibrated solid solutions were ferri-tic. The equilibration was conducted in long capsules, Fig. 1, that had been evacuated, gettered with titanium, and sealed. The purified iron, part of a vacuum-melted ingot of electrolytic-iron stock (Glidden Co. 1044-grade), had the impurity contents listed in Table I. It was used in the form of millings about 0.001 in. thick. A zinc of 99.999 pct purity (United Mineral and Chemical Corp.) and later one of 99.9999 pct purity (Cominco Products, Inc.) were used, with no observed difference in results. Sufficient zinc was placed in the capsule (separate from the iron and kept at a different temperature) to supply the vapor phase and the iron alloy, while leaving a pool of pure liquid zinc throughout the run. The imposed temperature of the residual zinc pool fixed the vapor pressure of zinc throughout the capsule; condensation was avoided at other locations by making this the lowest temperature in the capsule. Two common complications of nonisothermal systems were, we believe, effectively absent from ours: first, molecular species other than monatomic have no appreciable concentration in zinc vapor at 700" to 900~~: second, the development of zinc-pressure differentials in the capsules was suppressed by use of relatively large-diameter tubing and the absence of diluents in the zinc vapor other than desorbed impurities. The specimens and zinc pool were located at two isothermal zones (each ranging within 1°C over several inches) of a wire-wound, 37-in.-long vertical-tube furnace. The required temperature distribution was achieved by external adjustment of the currents in three electrically isolated windings. The temperatures of the isothermal zones were controlled independently by ther-

Jan 1, 1968

By T. D. Mueller

Many investigators have used the response of the "dimensionless aquifer" to a unit pressure drop or a unit fluid-withdrawal volume to calculate the performance of an aquifer in supplying water influx to an oil reservoir. In the past, these response functions have been calculated with the aid of the Laplace transform. With the advent of ultra highspeed digital computers, it becomes practical to solve for the response functions with finite-difference techniques. The computer method also permits extension of the dimensionless-aquifer concept to include the nonhomogeneous aquifer wherein the permeability and other properties vary as a function of the space co-ordinates. This paper gives results of calculating the response functions for a series of nonhomogeneous aquifers. Response functions are presented for both linear and radial aquifers whose thickness, permeability-viscosity ratio and porosity-compressibility vary. These functions are new and should prove useful to the petroleum engineer in analyzing the behavior of nonbomogeneous aquifers. Results are presented in the form of charts that can be easily used by the field engineer. INTRODUCTION Aquifers which surround many oil and gas reservoirs have the ability to supply water influx to such reservoirs as oil and gas are withdrawn. This water influx, called natural water drive, provides one of the most effective driving mechanisms for the production of oil and gas. In producing a reservoir, therefore, it behooves one to make the maximum use of natural water drive. To achieve the maximum use, the reservoir engineer must be able to predict the performance of an aquifer under a variety of production schemes that may be proposed for the reservoir. Unfortunately, the physical properties which dictate aquifer behavior often are known only within limits. Seldom do wells penetrate the porous strata of the aquifer. Even when they do, quantitative information regarding porosity, permeability and water compressibility is seldom available. It is known, however, that the water efflux from most aquifer systems is governed by a single, relatively simple, linear, partial differential equation. Also, the general physical location of the aquifer boundaries often are known. A technique originall proposed by Hurst1 and van Everdingen and Hurst2 has been found useful in analyzing reservoirs in this situation. The idea was later expanded by van Everdingen, Timmerman and McMahan3 to include the mathematical technique of least-squares fitting. This latter method will be referred to as the VTM method. The basic assumptions of the VTM method include the following. 1. The location of the physical boundaries of the aquifer are known. 2. The flow conditions at these physical bound-daries are also known. 3. The aquifer is homogeneous; e.g., thickness, permeability, water compressibility and porosity are constant throughout. In the VTM method, a material balance is made on the fluids entering and leaving the reservoir. In the balance equations, the water-influx term is represented as the product of the water influx from an arbitrarily-selected, dimensionless aquifer system times an unknown conversion number. This balance can be formed as many times as there are data points in the history of the reservoir. Each time, the conversion number can be evaluated. If the reservoir engineer has picked the correct dimensionless aquifer to represent the real aquifer, the conversion number remains constant for all balances that have been made over the history period. If such a situation occurs, the reservoir engineer can then predict the performance of the reservoir for any type of production scheme by using the function associated with that particular dimensionless system and the derived conversion number. These functions will be referred to as the response function of the aquifer. If the aquifer is nonhomogeneous (e.g., if the porosity, permeability, thickness, porosity, or

By H. J. Morel-Seytoux

Methods of predicting the influence of pattern geometry and mobility ratio on water flooding recovery predictions are discussed. Two methods of calculation are used separately or concurrently. The analytical method yields exact solutions in a convenient form for a unit mobility ratio piston-like displacement. A few typical pressure distributions, sweep efficiencies and oil recoveries are presented for various patterns. For non-unit mobility ratio, one may resort to a numerical method, such as that of Sheldon and Douherty. 1,2 Because the domains of applicability of the analytical and numerical techniques overlap, the exact solutions provide estimates of the errors in the numerical procedures. The advantages of the analytical and numerical methods can be combined. To develop a numerical technique as independent of geometry as possible, the physical space is transformed into a standard rectangle. The entire effect of geometry is rendered through one term, the "scale-factor", derived from mapping relations. The scale factor can be calcu-lated from the exact unit-mobility ratio solution for the particular pattern of interest. By this means recovery performances for arbitrary mobility ratio con be obtained for many patterns. A sample of tesults obtained in this manner is presented. INTRODUCTION Pattern geometry and mobility ratio are two major factors in making a waterflood recovery prediction. Because assisted recovery has become increasingly important to the oil industry, pattern configuration and mobility ratio also assume a greater significance in the assessment of the economic value of recovery projects. The influence of pattern geometry and mobility ratio in shaping a recovery curve and on the other quantities of interest to the reservoir engineer is the main subject of this paper. Much effort has already been spent on estimating quantitatively the influence of either pattern or mobility ratio or both on oil recovery. The literature reports many investigations of this nature. 3-9 However, many results or methods of recovery prediction presented in the literature cannot be considered fully satisfactory. Even for unit mobility ratio and piston-like displacement, where analytical solutions are available, the literature shows discrepancies. For non-unit mobility ratio, the divergence in the results is extreme. For infinite mobility ratio in a repeated five-spot, depending on the investigator, the sweep efficiency ranges from 0 per cent to 60 per cent. With respect to the influence of pattern on recovery, only the repeated five-spot has received much attention. Other confined patterns and pilot configurations have received very little attention. Two calculation methods are presented in this paper, either separately or concurrently: the analytical method of potential theory and the numerical method of finite-difference approximation. The analytical method is more restricted in scope than the finite-difference method, but it has the definite advantage of providing exact solutions within its range of applicability. If a unit-mobility ratio piston-like displacement is assumed, the analytical approach is possible. A few typical results are reported in this paper; the detailed description of the general method and of a great variety of results will be the subject of other articles. Fornon-unity mobility ratio, we must resort to a numerical scheme. The numerical technique is that which was described by Sheldon and Dougherty.l,2 It is not limited to piston-like displacement. However, mainly single interface results will be presented here. Because the respective domains of applicability of the analytical and the numerical method overlap, useful comparisons of exact and numerical solutions can be made for a variety of patterns. The advantages of the analytical and numerical approaches can be combined. The reason for the success of this analytical-numerical approach can be summarized in the following two points: 1. The numerical solution for arbitrary mobility ratio can be programmed most efficiently when the physical space in which the displacement actually takes place is transformed into a standard shape; and 2. This can be done with remarkable simplicity whenever an analytical expression for the pressure

Jan 1, 1966

By C. Cronquist

Since April, 1962, Shell Oil Co. has operated a peripheral line-drive waterflood of the 10.750-ft lower Tuscaloosa (Cretaceous) Denkman sand in the Little Creek field. Located in southwestern Mississippi in the lower Tuscaloosa trend, the field was discovered by Shell in Jan., 1958. Among the largest in the trend, the accumulation is controlled stratigraphically and occurs in an extensive series of alluvial-point bar deposits across a nose that dips gently to the south. The crude oil is 39" API gravity and was highly undersaturated at initial conditions. Early production behavior indicated a depletion drive with slight water influx; primary recovery wm estimated to be 25 million bbl, or 24.5 percent of stock-tank oil originally in place. A.s a result of a favorable mobility ratio and remarkably uniform rock properties, the volumetric sweep eficiency in the waterflood has exceeded 90 percent. Despite the high connate water saturation (56 percent), the displacement efficiency by water injection has been quite efficient, contrary to traditional concepts. Based on observed field flood-out performance, ultimate recovery is calculated to be 46 million bbl. As anticipated, the production rate began declining during 1964 due to a continu ing reducrion in the number of producing wells as flood fronts advanced across the field. Cumulative recovery as of Jan., 1968, was 44.8 million bbl; waterflood operations ~hould be complete by 1970. Introduction Most waterfloods described in reservoir engineering literature involve pattern operations, the most common of which is the five-spot pattern. Only occasiona&apos;lly are linear drives described, even though there probably are increasing numbers being put into operation. Increasing use of linear floods may reflect the accelerating trend towards early application of fluid-injection programs when linear drives are more efficient, as was the case at Little Creek. However. the Little Creek operation is unusual in several respects. It is one of a few successful waterfloods conducted in sands with connate water saturations approaching 60 percent, and it is among the deepest successful water-floods being operated anywhere. Development The Little Creek field was discovered in Jan., 1958, in the lower Tuscaloosa trend in southwestern Mississippi (Fig. 1). The discovery well, Shell-Lemann No. 1, was drilled on a seismic closure about 2 miles southeast of lower Tuscaloosa production at Sweetwater. The well was completed in the Denkman sand at 10,752 ft, and on initial potential it flowed 588 BOPD of 39" API crude on a %+-in. choke; psi was 730 and GOR was 442:l. Development proceeded rapidly on 40-acre spacing, and by the end of 1958 the field was producing approximately 9,100 B/D from 56 wells. Almost all this production came from the northern half of the field. The southern part was discovered in Nov., 1958, at a location almost 2 miles from previously established production. Subsequent drilling established an apparent conneotion about half a mile wide between the twd areas. Development of the field was practically complete by 1961 with the drilling of 155 producers and 35 dry holes. Some early wells were completed open hole but moslt are completed with casing cemented through the productive interval and perforated for production. Geology The lower Tuscaloosa structure in this area is a north-south nose with maximum dips of about 2" on the flanks. There is no discernible faulting at the producing horizon. Productive limits of the field are shown in Fig. 2, which is contoured on a marker just above the main productive zone. A common water level at 10,415 ft subsea was logged at both the northwest and southeast ends of the field. There is a gross oil column of nearly 100 ft (Fig. 2). Since there is less than 40 ft of closure, it is apparent that bhe accumubtion is controlled stratigraphically, being limited by a sand pinch-out across the creslt of the nose. The total produc-

Jan 1, 1969

By E. J. Harris

Mathematical solutions to complex mine ventilation problems are possible, but often the airway network is so complex that the mathematical solution becomes tedious and impractical. A fluid network analyzer, designed and built for analyzing mine ventilation problems has been in service at the Bureau of Mines&apos; Pittsburgh station for approximately nine years. Using this analogue as a model, the mine ventilation network is simulated electrically by a combination of series and parallel circruits laid out to conform with actual mine airways. A tungsten filament lamp, referred to as a Fluistor, is used to simulate mine airway resistance. With the analogue ventilation model established, voltages of the proper amplitude to represent ventilating pressures are impressed across the circuit at points where mine fans and airshafts are located. Comparison of mathematical solutions of complex systems against analogue results showed a maximum variance of 3% for pressures and 2% for quantities. An electrical fluid network analyzer, designed and built especially for analyzing mine ventilation distribution problems, has been in service at the Bureau of Mines, Pittsburgh, for approximately nine years. It is a nonlinear, low voltage, fluid network analyzer of the type developed by the late Malcolm S. McIlroy, Professor of Electrical Engineering, Cornell University, who cooperated with G. E. McElroy, of the Bureau of Mines, in adapting the instrument to mine ventilation systems. Several modifications have been made since the original installation, but a considerable part of this paper is drawn from G. E. McElroy&apos;s original description of the analogue.&apos; The analysis of water or gas distribution systems2,3 led to the development of this type of network analyzer. Several similar units are now employed by utility companies for this purpose; however, the Bureau of Mines unit is the only one designed specifically for mine airflow problems. Other airflow analogues employing a similar principle have been used at the Central Research Station of the Netherlands State Mines,4 in England,5 and in South Africa.6 Information on these devices indicated they were somewhat inflexible because commercial lamps with a sufficient range of resistance are difficult to obtain. Computers for mine ventilation analysis have been developed in Germany which instead of lamps use a variable resistance to adjust for turbulent flow laws. These units are expensive, but excellent results have been reported in their application. THE ANALYZER Theory of Application: As airflow generally follows the law of turbulent fluid flow, resistance to flow is nonlinear; consequently, the problem has been to find a nonlinear resistance element of suitable range that can be used for electrically simulated airflow. Tungsten filament lamps operated on alternating or direct current approximate the square-law resistance characteristics of mine airflow over a large range below maximum or rated voltage; that is, the voltage drop varies approximately as the square of the current. Consequently, the heart of the network analyzer is a nonlinear resistor known as a Fluistor, which is simply a custom-made low voltage, tungsten filament lamp that is available in a progressive series of relative resistance values ranging from 0.05 to 500 in nominal 5% steps. However, variations in manufacturing large groups result in differences of 1 to 3%, but series arrangements required for high-loss branches can be matched within about 1%. Utilizing a combination of Fluistors and load circuits, the mine ventilation system is duplicated electrically. Intake load circuits are connected from power intake to primary points of the circuit network; segments of unregulated flow along intakes and returns are represented by Fluistors, regulated splits and leakage paths are represented by load circuits and Fluistors of proper capacity; and mine exhausts are connected to ground from the last point of the network to complete the circuit. For the special purpose of representing booster fans or natural draft conditions, boosters or separate source circuits are provided that can be inserted between any two points of a network to increase voltage to the required value. Physical Layout: The analyzer consists of three 42

Jan 1, 1963