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By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By William A. Johnson

The mathematical analysis of diffusion curves in solid metals is carried out ordinarily by analogy with the flow of heat in a continuous medium and no account is taken of the fact that the materials involved are composed of discrete particles that move discrete distances at irregular intervals. It is possible to treat the problem on the basis of simple assumed atomic mechanisms, in which case, because of the small scale of the elementary process compared to the gross effects observed experimentally, the two procedures lead to the same expression for the variation of concentration with distance. Thus, for engineering purposes, the usual methods are quite satisfactory. If, on the other hand, our purpose is to go beyond the mere collection of data, however desirable this may be, it is necessary to recognize and understand the factors that are of fundamental importance. One factor that has not hitherto been considered when dealing with solid metals is the difference in atomic weights of the isotopes of a single metal. While all the atoms of a given element are alike chemically, their weights may vary by a small but significant amount, and atoms of different weights may have different diffusion rates. With gases this variation in isotopic weight produces a change in the rate of diffusion by a factor inversely proportional to the square root of mass. While, except for the lightest gases, this is not a large effect, it is, for example, sufficient to permit a considerable concentration of one isotope at the expense of others. If metals exhibit a similar phenomenon, some modification of the analysis of the diffusion process will be required, since the different isotopes of a given metal will have different probabilities of moving and the heat-flow analogy will contain a fundamental error. This situation cannot be rectified by using a diffusion coefficient based on the average probability of moving, and it can be shown that even when the diffusion coefficient is independent of composition, the diffusion curve will not agree with the simple theory except in the rare cases where only one isotope exists; e.g., gold. If, however, the mass effect in the solid state were no larger than in the gaseous, the errors arising therefrom in the analysis of ordinary diffusion curves would be quite negligible. Nevertheless, our desire to obtain all possible information concerning the details of the diffusion process, and the possibility of diffusion in the solid state as a means for separating isotopes are cogent reasons for undertaking an experimental study to determine whether isotopes of different masses diffuse at different rates. Experimental Procedure If isotopes of different masses diffuse at different rates, the ratio of the concentration of one relative to another will vary with the distance from the diffusion inter-

Jan 1, 1946

By J. J. Arps

This paper reviews the methods currently in use for estimating primary oil reserves and discusses the principles on which these methods are based. Particular emphasis is placed on how these methods change with the type of information available during the life cycle of an oil property. This paper contains various novel estimating methods and shortcuts heretofore unpublished. INTRODUCTION Estimating oil reserves is one of the most important phases of the work of a petroleum engineer since the solutions to the problems he deals with usually depend on a comparison of the estimated cost in terms of dollars, with the anticipated result in terms of barrels of oil. His recommendations to management regarding the best course of action are therefore normally based on the most favorable balance between these two. Specific engineering problems which require such a knowledge of recoverable oil reserves and a projection of future rates are: [a.] the exploitation and development of an oil reservoir; [b.] the construction of gasoline plants, pipelines and refineries; [c.] the division of ownership in unitized projects; [d.] the price to be paid in case of a sale or purchase of an oil property, and the magnitude of the loan which it will support; [e.] the proper depreciation rate for the investment in oil properties; and [f.] evaluation of the results of an exploration program. This discussion will be confined to the various methods and tools which are currently in use for estimating oil reserves to be obtained during the primary phase of an oil-producing reservoir and for a projection of the future production rates. Reserves which may be obtained by secondary recovery methods or fluid injection programs and gas and gas condensate reserves will not be discussed in this paper. Unfortunately, reliable oil reserve figures are most urgently needed during the early stages when only a minimum amount of information is available. Management's interest in the oil recovery from a property—aside from its use for accounting purposes—usually declines when the property approaches its economic limit, just at the time when the reliability of the estimates is at its best. To illustrate this general idea a chart is presented (Fig. 1) showing the three periods in the life of an imaginary oil property. Time is shown on the horizontal axis, while the cumulative production and estimated ultimate recovery are plotted vertically. No particular units are used and this schematical chart is not to scale. During the first period, before any wells are drilled on a property, any estimates will of necessity be of a very general nature, based on experience from similar pools or wells in the same area, and usually expressed in barrels per acre. This will

Jan 1, 1957

By J. B. Hess, C. S. Barrett

Single crystal rods of cadmium collapse under uniaxial compression into peculiar kinks if the (0001) glide plane is nearly parallel to the axis of compression. In his report first describing this behavior, Orowan1 proposed that these "kink bands" do not develop entirely by ordinary gliding and twinning but by a special mechanism in which glide lamellae of uniform thickness snap abruptly to a tilted position that permits lattice continuity across the glide planes. He concluded that a portion of each boundary of a kink band consists of a plane (non-crystallo-graphic) which bisects the angle between the glide planes on the two sides of it, and along which the bending and the dislocations are concentrated. The data presented by Orowan seemed to us to be insuffcient to conclude that a wholly new mechanism of deformation was responsible for the kinks. Therefore, we have investigated zinc, which is hexagonal close-packed and has an axial ratio near to cadmium, to see whether similar bands are produced, and whether the ordinary mechanisms of glide, bend-gliding, twinning, and the formation of deformation bands can account for its mode of deformation. We find that kinks form profusely in zinc as shown in Fig 1. The structure of these kinks, reported below, seems to require no new mechanism for their explanation, but indicates that kink bands are a special form of deformation bands and develop gradually, solely from basal glide. A theory covering the formation and structure of the bands is presented in detail because it is seldom possible to study deformation bands under such simple conditions, yet many principles applying to these kinks should also apply to deformation bands in general. Experimental Procedures Single crystal rods of 2-3 mm diam and 10-15 cm length were grown by the Brideman technique from swaged wire of Horsehead Special zinc in un-coated pyrex tubes. Orientations of the rods were determined with an optical goniometer after cleaving the rods at liquid air temperature. Crystals of desired orientations were then selected and used as "seeds" to grow additional crystals approximately 4 ft in length from which all specimens were cut. The wires were compressed in two ways: in a simple hydraulic handpress —a "soft" machine—and in a Riehle hydraulic testing machine modified to produce very "stiff" action by the simple expedient of inserting lengths of steel bars at the sides of the zinc crystals between the compression plates. For metallographic examination, the specimens were mounted in sealing wax. Hand polishing was employed, with no grits coarser than No. 1 paper; following the abrasives about 0.025 in. was removed by an etch-polishing reagent.* Final etching to reveal ori-

Jan 1, 1950

By Kenneth C. Vincent, A. M. Gaudin

IN a study1of the action of amyl xanthate on chalcocite in water suspension, it was found that if the xanthate is added in relatively large quantity the xanthate group can be accounted for in three forms: (1) as xanthate ion remaining in water, (2) as benzene-soluble cuprous xanthate on the chalcocite, (3) as a benzene-insoluble coating on the chalcocite. Reduction in the amount of xanthate added leads to disappearance of form 1 then of form 2. With minute quantities of added xanthate, substantially all the reagent is of the "unleachable" kind. Yet this unleachable xanthate can be dissolved by pyridine to form a soluble cuprous xanthate complex, and it is sufficient in effectiveness to make chalcocite flotable even if insufficient in quantity to form a complete monomolecular film on the mineral. In that study it was also found that chalcocite abstracts cuprous xanthate from benzene solution, in what may (or may not) be a case of molecular adsorption. It seemed desirable, therefore, to study further the "unleachable" xanthate on the chalcocite, and particularly to ascertain whether it is formed as a result of the benzene leach or is actually formed during the conditioning of chalcocite in aqueous xanthate solution. A splendid tool to make such studies has recently been perfected; that is, the use of radioactive spies or tracer atoms. With this tool, it was thought possible to answer the problem stated above, but, unfortunately, this did not prove to be true. Answer to the flotation question was clouded by the existence of rapid and selective diffusion of copper atoms in the solid mineral-a phenomenon that was totally unexpected yet remains interesting and perhaps important. METHOD OF RADIOACTIVE SPIES The method of radioactive spies is discussed in many places. Two convenient references are the article by Evans2 and the book by Pollard and Davidson.3 The method was first developed by Von Hevesy and Paneth in 1913, when only natural radioactive isotopes were available. These isotopes are few in number, and so the method remained limited in scope. Recently the synthesis of over 350 active isotopes of all the known stable chemical elements4 has opened widely expanded possibilities for the method. A fundamental tenet of the method is that a radioactive atom and a nonradioactive atom are exactly alike until disintegration of the radioactive atom. Then, by its sudden death, the spy reveals its location. The relative abundance of spies at various locations makes it possible to ascertain the relative abundance of the corresponding nonradioactive atoms at the same times and locations. A second fundamental tenet of the method of radioactive tracers is that the radioactivity lies in the nucleus of the atom: transfer of radioactivity from one

Jan 1, 1944

By R. E. Miner, J. K. Jackson, T. L. Wilson

THE nature of the decomposition reactions producing hardening in aluminum-rich A1-Ag alloys is now fairly well understood. The silver is not uniformly dispersed even at temperatures above the solvus line: rather, it is clustered into zones and associated with dislocations.' During quenching, nearly all of the silver segregates into zones' and some is attracted to dislocations, producing stacking faults. Growth of these faults produces the semicoherent y precipitate.1 During aging, the larger zones and the y precipitates grow at the expense of the smaller zones. The large zones persist up to about 350°C; where they redissolve in favor of the y' and y precipitates.' The equilibrium hcp y precipitate occurs both by a cellular reaction at the grain boundaries1 and by growth of the Y' plates to a critical size where incoherency results. Damask and Nowick 4 observed an internal friction peak in an A1-6 at. pct Ag alloy at about 140°C (0.25 cps). The peak was found to exhibit a systematic instability. After aging at successively higher temperatures between 155' and 23Z°C, the peak first migrated to higher temperatures while increasing in height, then returned to lower temperatures and decreased in height. After aging at temperatures above about 200°C, the peak position remained constant while the height decreased very slowly. In quenched specimens, elastic after-effect measurements inhcated a rapid initial transient in peak position from low temperatures up to 155°C. The authors concluded that a stress induced growth and resolution of the clusters and the 7' was the most reasonable mechanism to account for the behavior. It would seem, however, very unlikely that both the clusters and the y' precipitate would provide damping contributions whose relaxation time and activation energies were identical, which is required for them to produce the same internal friction peak. The present investigation was motivated by this apparent anomaly and the development of a very low thermal inertia torsion pendulum5 capable of monitoring transient behavior. Low frequency internal friction measurements were made on four binary A1-Ag alloys nominally containing 5, 10: 15, and 20 at. pct Ag. The results of measurements made on a 10 at. pct Ag alloy in the quenched condition are shown in Fig. 1. There are two peaks apparent in the spectrum, one centered at about 160°C, the second at about 210°C. The two peak spectrum was observed in each alloy, but it was best resolved in the 10 pct Ag specimens. Because of the instability in the internal friction, 4 it seemed possible that the second peak was not a peak at all, but simply a manifestation of a single, sharply transient, peak. This effect has been observed in Au-Ni alloys.6 The existence of the higher tempera-

Jan 1, 1970

The Hadsel Mill. By R. G HALL (Trans, vol 112 4000 words) This mill is designed to effect the entire reduction of ores by combined crushing and grinding from mine run size to material sufficiently fine for the usual operation of flotation or cyaniding The work is begun and completed in the same machine. The machine is designed on the principal of the elevator wheel, and crushing and grinding are accomplished by dropping a mixture of ore and water upon specially placed "breaker plates" in such a manner that the resultant material passes back into the buckets of the wheel for further elevation One method of removal of the finished product is to permit an overflow of wet pulp on one side of the mill through coarse screens A recent improvement provides for the removal of a pulp by a launder part way up the path of the buckets In either case the pulp passes to a classifier, and the oversize back to the mill in the manner familiar in ball-mill practice Although hardly through the development stage, the machine has given a very good account of itself in simplification of plant, by elimination of coarse and fine crushers with consequent reduction of installation cost and power consumption As compared with the ball mill alone, there is a reduction of power consumption as well as a material reduction of grinding steel There is an increase in cost of maintenance other than grinding steel, but as the machine passes out of the development stage there is a show¬ing of reduction of costs on this item It seems probable that with further develop¬ment and strengthening of the weaker parts further improvement may be made Ball Milling. By A. M Gow, M GUGGENHEIM, A. B. CAMPBELL AND W. H COGHILL. (Tech Pub 517; also Trans, vol 112. 24,000 words) This paper outlines a new philosophy in ball milling by using power as an index of mill operation and ascertaining the effects of the set and induced variables By recognizing the amount of ore in the mill as an important induced variable and recognizing that the amount of ore in the mill depends principally on the size of the discharge trunnion, ball volume, rate of feed, and speed of mill, obstacles formerly met were surmounted When the amount of ore in the mill is dealt with intelligently and the applied work is proportional to the amount of feed, series testing, which would otherwise give a hotchpotch, gives concordant results The study of ball paths and trajectories was seen to be fruitless when it was shown that the old attrition theory for slow mill speed

Jan 1, 1935

By Daniel R. Hull

IN 1026 Genders' reviewed the existing theories of this subject and stated his views in support of the gas-pressure theory. Again, in 1937, the subject was thoroughly reviewed by N. B. Vaughan,3 and by Phillips and Brick,2 so that no resume is called for here. The purpose of this paper is to describe certain observations made in the course of mill work, and to point out that they mostly tend to confirm the gas theory of Genders. VAPOR SEGREGATION There is, however, one type of inverse segregation that can be accounted for by considering the volatility of one of the constituents of an alloy. The most familiar case is ordinary brass, which is subject to a zinc enrichment of a few tenths of a per cent at the surface of a chill casting. This has been noted in 70-30 brass by Genders, and a typical example of it is given in Table I, which represents a [ ] cylindrical billet 7 in. in diameter by 5; in. long. After lathe-turning 1/32 in. from the surface, the remaining distance to the center was sampled at six equally spaced intervals. The lead, which is essentially the same throughout, will be mentioned later. Consider a brass-mill mold, either round or rectangular in cross section, standing several feet high. It may require a minute or two for pouring. Before it is full, the metal in the lower end has partly solidified and contracted somewhat away from the mold. The initial shell of solidification follows not far behind the top of the column, even if the central portion is liquid for a long way down. There is, then, a space between metal and mold that is filled with zinc vapor. The vapor has no exit, because the liquid at the top of the rising column is not only in contact with the mold but keeps up a fresh supply of zinc vapor, which has, perhaps, already begun to condense in the lower portion. The cycle is short. Within a minute or two after the mold is full the bar has cooled enough to condense all the zinc. Some of it may condense on the mold; it might be expected that most of it would condense there, but the mold at that time is well coated with a velvety carbon residue from the oil dressing, overlain by fluffy zinc oxide that commenced covering the inside of the mold as soon as pouring began. The clean skin of the freshly cast brass offers a preferred surface for condensation. Reabsorption is quick and inevitable. A simple experiment indicates that a surprisingly large quantity of zinc vapor is trapped in the space between mold and

Jan 1, 1941

By William A. Johnson

THE mathematical analysis of diffusion curves in solid metals is Carried out ordinarily by analogy with the flow of heat in a continuous medium and no account is taken of the fact that the materials involved are composed of discrete particles that move discrete distances at irregular intervals. It is possible to treat the problem on the basis of simple assumed atomic mechanisms, in which case, because of the small scale of the elementary process compared to the gross effects observed experimentally, the two procedures lead to the same expression for the variation of concentration with distance. Thus, for engineering purposes, the usual methods are quite satisfactory. If, on the other hand, our purpose is to go beyond the mere collection of data, however desirable this may be, it is necessary to recognize and understand the factors that are of fundamental importance. One factor that has not hitherto been considered when dealing with solid metals is the difference in atomic weights of the isotopes of a single metal. While all the atoms of a given element are alike chemically, their weights may vary by a small but significant amount, and atoms of different weights may have different diffusion rates. With gases this variation in isotopic weight produces a change in the rate of diffusion by a factor inversely proportional to the square root of mass. While, except for the lightest gases, this is not a large effect, it is, for example, sufficient to permit a considerable concentration of one isotope at the expense of others. If metals exhibit a similar phenomenon, some modification of the analysis of the diffusion process will be required, since the different isotopes of a given metal will have different probabilities of moving and the heat-flow analogy will contain a fundamental error. This situation cannot be rectified by using a diffusion coefficient based on the average probability of moving, and it can be shown that even when the diffusion coefficient is independent of composition, the diffusion curve will not agree with the simple theory except in the rare cases where only one isotope exists; e.g., gold. If, however, the mass effect in the solid state were no larger than in the gaseous, the errors arising therefrom in the analysis of ordinary diffusion curves would be quite negligible. Nevertheless, our desire to obtain all possible information concerning the details of the diffusion process, and the possibility of diffusion in the solid state as a means for separating isotopes are cogent reasons for undertaking an experimental study to determine whether isotopes of different masses diffuse at different rates. EXPERIMENTAL PROCEDURE If isotopes of different masses diffuse at different rates, the ratio of the concentration of one relative to another will vary with the distance from the diffusion inter-

Jan 1, 1946

By E. J. Duggan

The mine and mill of the Climax Molybdenum Co. are at Climax, Colorado. Climax is on Fremont pass directly on the Continental Divide, at an elevation of 11,400 feet. Description of Ore The Climax ore-bearing rock is essentially an altered and highly silicified granite, fully half of the gangue being quartz. Molybdenite is the only mineral of economic consequence and most of it is intimately associated with quartz in the form of fine veinlets and stringers. Other minerals are molybdite, pyrite, and chal-copyrite. While the molybdite may be readily extracted by hydrometallurgical methods, its content is too low to make such operations profitable. The pyrite content ranges from 2 to 5 per cent and that of the chalcopyrite from 0.03 to 0.05 per cent. There is not enough copper to make its recovery attractive and one of the metallurgical problems is the elimination of it and the pyrite from the product. On account of the close association of the molybdenite with the quartz and the necessity of eliminating the pyrite and chalcopyrite from the final product, fine grinding followed by flotation is the only feasible method of concentration. History Construction of the first milling unit was started in 1917 and it was operated during parts of 1918 and 1919. In the postwar years, there was almost no demand for the product and production was at a standstill until 1924. The Company's research campaign to develop the use of the metal began to show results in that year. From r926 to 1932 production ranged from 500 to 1200 tons per day. In 1931 an additional mill section was built and production was gradually increased until in 1934 and 1935 about 3000 to 4000 tons was milled per day. This tonnage overtaxed the milling facilities, and as the demand for inolybdenum was growing constantly, additional milling equipment was needed. In 1936 and 1937 another crushing plant, six additional mill sections and the necessary auxiliary plants were constructed and brought into operation. This plant was designed to mill I0,000 tons per day, but it was not long before 12.500 tons was being treated during periods of peak demands. During the summer of 1941, to meet defense needs, the mill has been required to treat 15,500 tons per day. This has been accomplished with little plant expansion and at no loss in recovery, as will be described later. TO increase capacity still further, one more primary section is now being built. This will bring capacity to 18,000 tons per day, which can be stretched to 20,000 tons at a small sacrifice in recovery. Crushing There are two crushing plants: No. I, of 5000 tons capacity (flowsheet in Fig. I) and No. 2, of 15,000 tons capacity (Fig. a).

Jan 1, 1943

By Morris Muskat

A general theory has been developed for the effect of permeability stratification on the efficiency of the gas-injection phase of cycling operations. It has been applied to three special types of permeability variation; namely, exponential, probability, and linear. In the case of the exponential permeability distribution the effect of areal pattern sweep efficiency was also taken into account. The exponential permeability distribution can be characterized by the ratio of the maximum to minimum permeability, which has been termed the stratification constant. Curves were calculated for the variation in total wet gas recovery and total gas throughflow, to give that recovery to various abandonment limits of the wet gas content in the produced gas, as a function of the stratification constant. The cumulative wet gas recovery decreases monotonically as the stratification constant increases and is generally higher at the lower values of the wet gas content abandonment limits. The total gas throughflow first rises to a maximum as the stratification increases, and then ultimately declines. The effect of the areal sweep pattern efficiency is relatively minor as compared to that of the stratification constant, except in the region of low values of the latter where the formation is substantially uniform. The probability distribution can be characterized by a "variation" parameter varying from o to I as the formation changes from strict uniformity to extreme variability. The curves of total wet gas recovery and total gas throughflow to different abandonment limits of wet gas content versus the variation parameter have the same general characteristics as for the exponential permeability distribution. In the linear permeability distribution the ratio of maximum to minimum permeability also serves as a stratification constant index defining the distribution. The curves of total wet gas recovery and gas throughflow to fixed abandonment limits versus the stratification constant are similar to those for the exponential permeability distribution. However, for the higher values of the stratification constant the recoveries and throughflows do not asymptotically fall to o as in the latter, but approach constant values determined by the abandonment limit of wet gas content in the produced gas. Introduction It is becoming generally recognized that one of the most important factors determining the economic feasibility of cycling operations is the areal continuity and permeability distribution of the producing formation. While the effects of areal variations in permeability, porosity, thickness, and well pattern on the sweep efficiency can be evaluated by electrical model studies,' those due to permeability stratification require separate treatment. Several studies have been reported2,3 on the' influence of permeability variations on the wet gas recovery by cycling. In these, however, discontinuous permeability variations either have been assumed explicitly, or the analysis has been carried through as if they were discontinuous. While, in fact, the actual permeability profiles will undoubtedly be discontinuous, recent develop-

Jan 1, 1949

By Basil B. Zavoico

Production of crude oil in the U.S.S.R. during 1940 is estimated at 222,600,000 bbl., as compared with the revised figure for the preceding year of 220,866,000 bbl., an increase of 0.79 per cent, and at least 20 per cent under the planned output. Baku district (Transcaucasus) remained the outstanding producing area, accounting for 72.33 per cent of the country's production, and this relative importance of the Apsheron Peninsula oil fields will probably continue lor many years to come. In the North Caucasus the Grozny-Dagestan area further extended its decline and the current production in this district amounts to only 6.06 Per cent Of the total U.S.S.R. output, as compared with 35.76 Per cent in 1931 The production of the Kuban-Maikop district remained virtually ullchanged from the preceding year, amounting to 7.64 per cent of the country's total. The Caucasian Province, therefore, in I940 produced 86.03 Per cent of the total production of the U.S.S.R. The promising new Permian Basin district, called Ural-Volga, and referred to sometimes as the "Second Baku," increased its production appreciably during 1940 and the output of that area amounted to 8.31 per cent of the country's total, as compared with 6.35 per cent during 1939. Production in the secondary districts of Russia continued unchanged though some new discoveries in the Emba salt-dome basin suggest that the output of that district may show some increase during the coming years. The drilling operations in Russia during 1940 reached a stage of virtual breakdown and the original footage plans were fulfilled only to the extent of around 50 per cent, while exploration drilling schedules were fulfilled only to the extent of about 25 to 35 per cent. This condition was due to the obvious lack of modern drilling rigs, of good drill pipe and of strong casing. Extended breakdowns occurred with deeper drilling, particularly because with few good drilling rigs available speed was being attempted with rotation rates that the inferior drill pipe and bits could not stand. Twistoffs and endless fishing jobs resulted. The difficulties became so serious a handicap to the Soviet oil industry that it was found imperative to order American drilling equipment and pipe in quantity, a policy that was never favored in the U.S.S.R because it requires expenditure of gold or exchange in major volume, and such exchange usually is reserved only to less bulky key items or to orders directly connected with armaments; also, oil-field machinery is very bulky and the prevailing lack of bottoms makes the transport of the indicated equipment a major problem. But little progress was similarly made in other branches of the Soviet oil industry. NO new major pipe-line construction work was undertaken, consequently the railroads continued to be overburdened with traffic that could be much more effectively handled by pipe lines. No new refinery construction of any magnitude was initiated, though several plants that had been in course of construction for several years were completed during 1940 and operation 554

Jan 1, 1941

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By John M. Kelly

New Mexico produced 38,882,342 bbl. of oil in 1943, and regained seventh place among the oil-producing states. This production was an increase of 6,968,526 bbl., or 21.8 per cent, over the figure for 1942. The maximum per-well allowable on Jan. I, 1943, was 38 bbl. daily and at the end of the year this figure had been increased to 48 bbl. Allocations as set by the New Mexico Oil Conservation Commission closely followed recommendations by the Petroleum Administrator for War and the average daily pipe-line runs were 106,476 bbl., being within 2.2 per cent of these allocations. Production for Lea County was 33,043,925 bbl.; Eddy County, 5,405,-967 bbl.; northwestern New Mexico, 432,070 bbl., and Chaves County, 380 barrels. Drilling activity for New Mexico in 1943 was only 75 per cent of that in 1942, with 255 completions. Of these completions 180 were oil wells, 10 gas wells and 65 dry holes. The ratio of dry holes to producers, more than I to 3, was the greatest in recent years. Of these dry holes, 46 were drilled within the boundaries of proven . areas while 19 were wildcats. Wildcat drilling during 1943 was responsible for the discovery of four new oil fields and one new gas field, as well as three extensions to existing proration areas. At the close of the year the New Mexico Oil Conservation Commission had designated 64 areas as proven for oil and/or gas. The Monument area was again New Mexico's largest producing oil field, with an annual production of 7,228,855 bbl. Next was Eunice, with 6,461,044 bbl., followed by Vacuum with 4,946,110 bbl. IIobbs, ranking fourth, with 3,799,114 bbl., was the leader in total recovery with an accumulated production of 104,180,53I bbl., or more than 10,000 bbl. per acre to date. Drilling activity in Lea County accounted for completion of 67 oil wells, 2 gas wells and 24 dry holes. One of these oil wells was the discovery well of a new area and three extended proven areas. The most active drilling campaign in the county was again in the Maljamar area, where 18 oil wells were completed. The Maljamar Cooperative Repressuring Agreement affected 141 producing wells, and operations were a decided success, more than 85 per cent of the gas produced being returned to formation. The new oil field for Lea County was designated as the San Simon area although boundaries have not been established to date. Discovery well for this area was the Skelly Oil Company's State U. No. I, in theNE. NE. K of sec. 5, T.22 S.,R.ssE. This well was drilled to a total depth of 4183 ft. and plugged back to 4138 ft. after encountering bottom-hole water. Initial production was 124 bbl. per day on the pump. This oil is 37.4' gravity and has a sulphur content of I per cent. Productian is from Yates sand of Permian age. The Lynn area of southern Lea cbunty was extended 145 miles to the northwest

Jan 1, 1944

By Howard I. Epstein, John R. Buzek

Thickeners are simply large tanks, usually circular in shape, which are designed to allow settling of solids and to operate with continuous overflow of clear water and underflow of thick pulp. The dimensions of the thickener are usually such that dewatering of very fine pulps may be accomplished while still overflowing clear water. Some thickeners such as the Center, Hardinge and Hydrotator types combine thickening with filtering2 while others such as the Dorr type are pure thickeners. l .2 , 3 A schematic diagram of the traction type Dorr thickener is shown in [Fig 1]. This type is appropriate for tanks over 15 m (50 ft) in diameter. This tank employs a rotating raking mechanism which moves the settled material toward the central discharge. For this and other thickeners, it is common to have a shallow conical tank bottom in order to conform to the geometry of the raking mechanism, and it is often desirable to elevate the tank for ease of access to the product. When the tank does not rest on the ground, the forces resisted by the cone are large, and thick plates must be employed. The fabrication of these tanks requires temporary supports in order to erect the cone. A flat-bottomed tank could also be used because the settled material would soon form a hardened conical surface. However, because of the presence of large bending forces, even larger plate thicknesses are required than for the conical bottom. Significant cost savings often can be realized by the use of a scalloped-bottomed tank such as the one partially shown in [Fig. 2]. The particular scalloped bottom discussed in this paper employs radial beams forming the outline of the cone-shaped bottom. These beams are supported directly by columns. Cone segments are hung between adjacent beams. The exact geometry of these segments depends upon the cone angle and radius, the number of radial beams, and their inclination. The geometry is chosen to satisfy certain clearance restraints and to utilize the material as efficiently as possible. The resulting thickness of these segments is significantly less than that of the equivalent plate for the tank with a conical bottom. This result, along with the simpler fabrication procedures required, accounts for the cost savings associated with this design. The raking mechanism employed may be the same as for the conventional conical bottom since the settled material soon forms a conical surface. Determination of the internal force mechanism for the scalloped bottom leads to designs that utilized material efficiently and thus maximize the cost savings. The complicated geometry of these bottoms along with the difficulty in analyzing the structure are factors which may have limited the use of scalloped-bottomed tanks to date. When such tanks have been built, the uncertainties associated with the internal forces have led to designs that are somewhat inefficient. In this paper, equations relating the geometric parameters are presented along with simplified closed-form solutions for the internal forces in the cone segments, from which the loads applied to the beams and the loads carried to the cylindrical tank shell can be deduced. An example is presented to show the magnitude of the savings which may be realized with this configuration.

Jan 1, 1979

By K. H. Coats

In tnany oil and gas fields, significant investments are required in piping networks for collection, injection and disposal of various fluids. This paper treats the problem of optimally locating the trunkline(s) for a given systet to nlinimize both the total length of piping connecting the individual wells or lease batteries to the trunkline and the length of the latter. Single and multiple trunklines, varying line sizes, and grouping of wells are considered. Some attention is paid to the case of a curved trunkline. A field case is treated and conclusions are that the problem of locating a single trunkline is relatively straightforward while the location of multiple trunklines requires further research. INTRODUCTION la many oil and gas fields, significant investments are required in piping networks for collection, injection and disposal of various fluids. A single field may concurrently require piping systems for gathering of oil, gathering of gas, injection of water or gas and disposal of salt water. Two problems arise in the consideration of any one of these networks. The first involves the sizing of the various segments of the network to minimize piping and compression costs. The second problem, treated herein, is that of optimally locating the trunkline(s) for a given piping system to minimize the total length of pipe connecting the individual wells or lease batteries to the trunkline. This minimization problem may arise in field automation if it involves replacement of individual lease batteries by a central field battery which will require trunklines and connecting pipelines to individual wells. The problem also arises in connecting a gas pipeline through a subsidiary trunkline to wells in a gas storage field. The first analysis given below treats the case of a single trunkline and of separate connecting lines for all field units.* The analysis is then extended to consider multiple trunklines and common connecting lines for groups of field units. Varying sizes, and therefore costs, of the connecting lines are taken into account. A simplified development is given to illustrate the manner in which line sizing calculations may be integrated with the line placement problem. This study is primarily directed toward the placement of straight trunklines, although for certain field shapes or well distributions curved trunk-lines might be preferable. Some mathematical consideration is therefore given to the placement of a curved trunk-line in a field. The determination of optimal locations for two or more trunklines involves some difficulties which are discussed below. The need for further research in this area is emphasized. The problem of a single trunkline is solved in relation to an actual oil field. The problem of optimally locating two trunklines in the same field is also treated and the results are compared to the single-trunkline case. All calculations reported were performed on an IBM 7072 digital compker. The importance of right-of-way, roads and terrain in locating trunklines and connecting lines is realized. The present analysis is advanced on the premise that in planning piping networks one should start with the optimal conditions whenever possible and proceed therefrom.

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By B. D. Cullity, O. P. Puri

The magnetostrictia of nickel after increasing amounts of plastic elongation was measured at field strengths up to 1500 oe. In addition, the residual stress was measured by means of X-ray line shifts. The observed decrease in magnetostriction following plastic strain is shown to be associated with residual compressive stress. If a metal bar, whose longitudinal axis is taken as the x direction, is plastically elongated in the x direction and then unloaded, X-ray diffraction measurements will indicate the presence of a residual compressive macrostress 0%. However, stress measurement by means of mechanical relaxation does not reveal any macrostress. In a previous paper1 the fictitious macrostress indicated by X-rays was ascribed to a particular distribution of micro-stress, namely, one in which the bulk of the material was stressed more or less uniformly in compression and a very small portion in tension. It was shown that this distribution would account for Neurath's measurements2 of magnetic losses in silicon steel, because of the effect of residual stress on magnetostriction. The present paper is concerned directly with magnetostriction, in nickel, and with the effect on magnetostriction of the residual stress created by plastic elongation. The residual stress was determined by measurements of X-ray line shifts. MATERIAL AND METHODS Commercially pure "A" nickel was investigated. Its nominal composition, in weight percent, is 99.4 Ni + Co, 0.2 Mn, 0.15 Fe, 0.1 Cu, 0.1 C, 0.05 Si, and 0.005 S. Magnetostriction was measured by means of SR-4 electrical-resistance strain gages mounted on specimens 1/4 in. sq and 8 in. long. Magnetic fields up to about 1500 ce were provided by a multilayer, non-cooled solenoid. A considerable amount of heat was developed at the higher field strengths, and, to avoid errors due to changes in the specimen temperature, the following procedure was adopted. Each measurement of the magnetostriction X at a particular field strength H was preceded by demagnetization and an adjustment of the strain indicator to zero; the field H was then quickly switched on and the strain read immediately. Curves of ? vs H were flat for field strengths above about 750 oe for all specimens, and this constant value of X was accordingly taken as the saturation magnetostriction ?s The X-ray measurements of residual stress were made with a Norelco diffractometer on specimens cut from flat bars 1 1/4 in. wide, 1/8 in. thick, and 12 in. long. These measurements were confined to lattice planes parallel to the surface of the specimen. Two reflections were studied: the 311 CrKß line at 28 = 157 deg, and the 420 CuKal line at 28 = 155 deg. The line centers were determined by fitting a parabola to the peak of the line, as suggested by Ogilvie3 and as modified by Koistinen and Marburger.4 The CuKa doublet from the plastically elongated specimens was first resolved by the Rachinger method5. All X-ray measurements were made by counting at fixed angular positions. RESULTS The results of the magnetostriction measurements are shown in Fig. 1 and Table 1. The magnitude of

Jan 1, 1963

By T. W. Healy, P. Somasundaran, D. W. Fuerstenau

The flotation behavior of quartz in the presence of alkyl ammonium acetates as a function of alkyl chain length has been interpreted in terms of hemi-micelle formation at the solid-liquid interface. The van der Waals cohesive free energy that is responsible for hemi-micelle formation has been found from these results to be 1.0 kT per CH2 group. This is in excellent agreement with literature values obtained from research on the properties of micelles in bulk systems. Collectors of the type CH3(CH2)n-2CH2-P, where P is a polar group and n is the number of carbon atoms in the straight alkyl chain, will induce flotation of an appropriate mineral at lower concentrations as n increases. This reduction in collector concentration with increasing n has been reported for such systems as xanthates on sulfides1,2 and amines on quartz.' The effect of chain length of alkyl surfactants on such solution properties as conductivity,' surface tension,' and solubility6 and such interfacial properties of solids as contact angle7 and electrokinetic potential8 have received considerable attention, but only limited quantitative descriptions of the effects have been given. The electrokinetic studies of alkyl amine salts on quartz indicated that the solution concentration of collector at which the marked change in electrokinetic potential of quartz occurs decreases systematically as the length of the alkyl chain increases. The aim of the present work was to obtain a quantitative description in terms of current theories of flotation of the effect of the hydrocarbon chain of alkyl ammonium acetates on the flotation behavior of quartz. BASIC PRINCIPLES The marked changes in electrokinetic potentials of quartz in dodecylammonium acetate (DAA) solutions were postulated to result from the association of adsorbed collector ions into two-dimensional aggregates, called hemi-micelles.9 Subsequently, the rapid increase in flotation rate of quartz was shown to coincide with hemi-micelle formation." We would like to discuss briefly the concept of hemi-micelles in terms of recent interpretations of micelles in bulk solution. Micelle hypothesis: In dilute solutions, alkyl ammonium and related salts behave as ordinary strong electrolytes, but at a certain concentration there is a marked change in physical properties of the solutions, e.g., in equivalent conductance, transport number, freezing point lowering and viscosity. To account for these phenomena, McBainl1 introduced the concept of micelles, which are aggregates of long-chain ions. It is believed that the ionic heads of the constituent ions of the micelle are in contact with water, whereas the nonpolar groups turn away from it and are in contact with each other. Work must be done to bring these charged polar groups together, but energy is gained (i.e., so called van der Waals cohesive energy) when hydrocarbon chains are expelled from the water and allowed to associate. For a given polar group, the tendency to form micelles will therefore strongly depend on the hydrocarbon chain length. Theoretical treatments of micelle formation by Shinoda12 and Phillips13 and others lead to the following expression for the concentration at which micelles form (the critical micelle concentration or cmc) in aqueous solutions of long- chain electrolytes

Jan 1, 1964

By John M. Kelly

New Mexico produced 38,882,342 bbl. of oil in 1943, and regained seventh place among the oil-producing states. This production was an increase of 6,968,526 bbl., or 21.8 per cent, over the figure for 1942. The maximum per-well allowable on Jan. I, 1943, was 38 bbl. daily and at the end of the year this figure had been increased to 48 bbl. Allocations as set by the New Mexico Oil Conservation Commission closely followed recommendations by the Petroleum Administrator for War and the average daily pipe-line runs were 106,476 bbl., being within 2.2 per cent of these allocations. Production for Lea County was 33,043,925 bbl.; Eddy County, 5,405,-967 bbl.; northwestern New Mexico, 432,070 bbl., and Chaves County, 380 barrels. Drilling activity for New Mexico in 1943 was only 75 per cent of that in 1942, with 255 completions. Of these completions 180 were oil wells, 10 gas wells and 65 dry holes. The ratio of dry holes to producers, more than I to 3, was the greatest in recent years. Of these dry holes, 46 were drilled within the boundaries of proven . areas while 19 were wildcats. Wildcat drilling during 1943 was responsible for the discovery of four new oil fields and one new gas field, as well as three extensions to existing proration areas. At the close of the year the New Mexico Oil Conservation Commission had designated 64 areas as proven for oil and/or gas. The Monument area was again New Mexico's largest producing oil field, with an annual production of 7,228,855 bbl. Next was Eunice, with 6,461,044 bbl., followed by Vacuum with 4,946,110 bbl. IIobbs, ranking fourth, with 3,799,114 bbl., was the leader in total recovery with an accumulated production of 104,180,53I bbl., or more than 10,000 bbl. per acre to date. Drilling activity in Lea County accounted for completion of 67 oil wells, 2 gas wells and 24 dry holes. One of these oil wells was the discovery well of a new area and three extended proven areas. The most active drilling campaign in the county was again in the Maljamar area, where 18 oil wells were completed. The Maljamar Cooperative Repressuring Agreement affected 141 producing wells, and operations were a decided success, more than 85 per cent of the gas produced being returned to formation. The new oil field for Lea County was designated as the San Simon area although boundaries have not been established to date. Discovery well for this area was the Skelly Oil Company's State U. No. I, in theNE. NE. K of sec. 5, T.22 S.,R.ssE. This well was drilled to a total depth of 4183 ft. and plugged back to 4138 ft. after encountering bottom-hole water. Initial production was 124 bbl. per day on the pump. This oil is 37.4' gravity and has a sulphur content of I per cent. Productian is from Yates sand of Permian age. The Lynn area of southern Lea cbunty was extended 145 miles to the northwest

Jan 1, 1944