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By Lee Hillard Meltzer, Ralph E. Davis

INTRODUCTION During the past few years emphasis has been placed upon methods of estimating the future expectancy of gas production from natural gas fields. Before technical methods were applied, the production expectancy over future years was based upon the knowledge of gas well behavior, learned through long experience and embedded in the "know-how" of men long in the gas producing business. It is doubtful that a technical study of future expectancy of a gas field or a group of fields was ever prepared for the preliminary planning of a natural gas pipe line system built prior to about five years ago. The decline in well production capacity was naturally recognized by all familiar with the business since its earliest beginnings more than 75 years ago. In 1953, the Bureau of Mines published Monograph Number 7, "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices," which gave to the industry the first technical analysis of the decline in production of individual gas wells. This method affords a means of estimating the future production in relation to decline in reservoir pressure. The demand for technical determination of expectancy of future gas productivity from fields or a group of fields led technical men to the application of the knowledge of well behavior to the problems. The decline in a well's ability to produce as pressures declined could be estimated by the use of the curve known as the "back-pressure potential curve" as developed by the Bureau of Mines. A field containing few, or even numerous, wells could be analyzed on the basis of the sum of potentials of all wells. In most studies of this nature, the problem is to estimate the rate of production that can be expected, not only from present wells but also, from wells that will in the future have to be drilled into the reservoir being studied. The "back-pressure potential" method requires that the following data be known or estimated: (1) Proved gas reserves. (2) Current shut-in pressures and rate at which shut-in pressures change with production. (3) Back pressure potential data on wells in the source of supply. (4) Ultimate number of wells which will supply gas, and their potential. (5) Limitations on productivity such as line pressures against which the wells will produce, friction drop in the producing string, and so forth. It is evident that the resulting estimate of gas available in each year for a future of say, 20 years, contains many uncertainties. While the method may have considerable merit for a field that is fully developed, it cannot be completely dependable in fields that are only partially developed. In such cases, some of the data upon which it is based can only be estimated or assumed. In the study of this problem during the past few years, a method has been developed which we believe has great merit, especially when applied to fields subject to substantial future drilling, and when applied to the study of fields which, on the average, appear to have characteristics similar, in general, to the average of the fields used in the development of the "yardstick" outlined herein. From an analysis of the production history of 49 reservoirs which are depleted, or nearly depleted, a curve has been constructed which shows the average performance of the reservoirs during the declining stages of production. When properly applied, this "average performance curve" can be used to determine the stage of depletion at which a reservoir or group of reservoirs will no longer be able to yield a given percentage of the original reserves. "AVAILABILITY" AND "AVAILABILITY STUDIES" The rate at which. a reservoir will yield its gas depends basically upon physical factors, such as the thickness and permeability of the sand, the effect of water drive, if any, and other conditions, and upon economic factors, such as the number of wells drilled. Within the ranges set by the physical conditions, a rate of delivery tends finally to become established. The rate (or range of rates) represents a balance between the interests of the operator, who desires the maximum return from his property and of the pipe line owner, who desires to maintain a firm supply for his market. This balance, which is influenced by the terms of the contract, determines the capacity which will be developed by the operator, and the time and rate at which the decline in production is permitted to occur. Thus the "availability" of gas

Jan 1, 1953

By J. E. Kirby, L. B. Schnitz, H. E. Stamm III

The production history of a gas-cap-drive reservoir was reproduced by calculations, and predictions were made for operations under primary depletion, pressure maintenance by gas injection, and pressure maintenance by water injection. Although the general equations used in this analysis have been available to the industry for a number of years, the procedure has not had extensive use because of the unusually large time requirements for developing numerical results. The use of digital computing equipment for processing the calculation work generally reduced the time usually required for an extensive analysis of this type. Calculation techniques were developed that were equally applicable for solving the gar-cap-drive problem, whether digital computing equipment or desk calculators are used. These techniques are outlined and the procedures are illustrated by the field problem. INTRODUCTION The analysis of a gas-cap-drive res-ervoir requires the simultaneous solution of the volumetric balance1 and displacement2 equations. Equations for the analysis of combination drive reservoirs were presented by Wooddy and Moscrip in a previous paper." These equations permit the evaluation of possible operating processes in order that the optimum method of pro- ducing the reservoir may be determined. Although these equations represent the basic technique known for the detailed analysis of gas-capdrive reservoirs, the calculation processes are quite complex and time consuming; hence, the procedure has not had extensive use. Recently, these equations were satisfactorily applied with the aid of a digital computer to investigate the completion history of a gas-cap-drive reservoir under the following operating methods: primary depletion, depletion under full pressure maintenance by gas injection, and depletion under full pressure maintenance by water injection. The use of digital computing equipment substantially reduced the time necessary for making the computations and permitted a more concise investigation of the reservoir's depletion history than was possible when the desk calculator was used. This more rigorous investigation also permitted a detailed analysis of the calculation procedures necessary in the solution of the gas-cap-drive problem. This paper outlines the procedure of analyzing a gas-cap-drive reservoir and illustrates the process with an actual field problem. CHARACTERISTICS OF THE RESERVOIR ANALYZED Production in the field under consideration is obtained from a Frio formation of Oligocene age at a depth of approximately 5,740 ft sub-sea. The accumulation, which is bounded on the flanks by strand lines, is semirectangular in shape with gentle narrowing toward the base of the structure as shown by the sand limits and completion map in Fig. 1. The reservoir development indicates an oil column of 319 ft that is defined by gas-oil and oil-water contacts. Basic data relative to the characteristics of the formation and the formation fluids are shown in Table 1. The formation exhibits considerable shaliaess and thinning near the oil-water contact indicating that little or no benefit will be received from natural water influx. This is substantiated by the fact that wells completed near the original oil-water contact have not produced water. A sizeable gas cap is present; however, considerable faulting is in evidence, and it is believed that only a limited portion of the gas cap will aid in oil displacement and pressure maintenance. Although the reservoir was in an initial stage of depletion, it was believed that as soon as the equilibrium gas saturation in the oil zone was exceeded and a number of upstructure wells were invaded by the expanding gas cap, the resulting high gas-oil ratio production would rapidly dissipate the natural drive and lead to limited oil recoveries and inefficient reservoir operation. This analysis evaluated the effectiveness of the primary displacement mechanism and

Jan 1, 1958

By J. H. Henderson, J. Naar

The displacement of a wetting fluid from a porous medium by a non-wetting fluid (drainage) is now reasonably well understood. A complete explanation has yet to be found for the analogous case of a wetting fluid being spontaneously imbibed and the non-wetting phase displaced (imbibition). During the displacement of oil or gas by water in a water-wet sand, the porous medium ordinarily imbibes water. The amount of oil recovered, the cost of recovery and the production history seem then to be controlled mainly by pore geometry. The influence of pore geometry is reflected in drainage and imbibition capillary-pressure curves and relative permeability curves. Relative permeability curves for a particular consolidated sand show that at any given saturation the permeability to oil during imbibition is smaller than during drainage. ' Low imbibition permeabilities suggest that the non-wetting phase, oil or gas, is gradually trapped by the advancing water. This paper describes a mathematical image (model) of consolidated porous rock based on the concept of the trapping of the non-wetting phase during the imbibition process. The following items have been derived from the model. 1. A direct relation between the relative permeability characteristics during imbibition and those observed during drainage. 2. A theoretical limit for the fractional amount of oil or gas recoverable by imbibition. 3. An expression for the resistivity index which can be used in connection with the formula for wetting-phase relative permeability to check the consistency of the model. 4. The Iimits of flow performance for a given rock dictated by complete wetting by either oil or water. 5. The factors controlling oil recovery by imbibition in the presence of free gas. The complexity of a porous medium is such that drastic simplifications must be introduced to obtain a model amenable to mathematical treatment. Many parameters have been introduced by others in Iprogressing" from the parallel-capillary model to the randomly interconnected capillary models independently proposed by Wyllie and Gardner3 and Marshall4. To these a further complication must be added since an imbibition model must trap part of the non-wetting phase during imbibition of the wetting phase. Like so many of the previously introduced complications, this fluid-block was introduced to make the model performance fit the observed imbibition flow behavior. THE IMBIBITION MODEL ASSUMPTIONS The following assumptions are common to many two-phase models previously described. 1. The wetting characteristics of the medium are clearly defined. 2. When two fluids co-exist in the medium, the wetting phase will fill the smaller pores and the non-wetting fluid the bigger ones. 3. The pores have a circular cross section. 4. Apparent pore radii are related to the capillary pressure (drainage) by

By I. Fatt

Networks of resistors are used as analog computers to obtain relative permeability and resistivity index curves for networks of tubes. These curves have all of the characteristics of those obtained on porous media and, therefore demonstrate the validity of the network of tubes model. INTRODUCTION In paper I' of this series the network model was shown to give information on the structure of porous media that could not be obtained from the bundle of tubes model. The agreement between the capillary pressure characteristics of a network of tubes and those of typical porous media does not prove the validity of the network made. The bundle of tubes model, although it gives less information, also shows this agreement. In this paper the flow properties of a network of tubes are shown to be in agreement with flow properties of porous media. The flow properties of the bundle of tubes model are not in adequate agreement with those of porous media. The dynamic properties of porous media, such as fluid permeability and electrical conductivity, have been found experimentally to be more sensitive functions of structure and pore size distribution than are the static properties such as porosity and capillary pressure characteristics. The network model can, therefore, be best tested by comparing the dynamic properties of a network of tubes with the observed properties of porous media. All static and dynamic properties of a completely valid model must agree with the observed properties. The most commonly measured sensitive dynamic properties are the relative fluid permeability and the relative electrical resistivity. Experimental measurements of these dynamic properties on sandstone, sintered glass, sintered alumina, and soil are reported in the petroleum and soil science literature. These properties were chosen, therefore, for the test of the network model. In the network model, relative permeability is the permeability of the network when some of the tubes are not conducting fluid, relative to the permeability when all tubes are conducting fluid. Similarly, the relative resistivity is the electrical resistivity of the network of tubes when some of the tubes are filled with a nonconductor. relative to the resistivity when all tubes are filled with the electrical conducting fluid. Single Size Tube Network The simplest porous medium is one in which all pores are of the same size. Such media can be approached by packing beds or columns of uniform size particles of sand, glass, or metal. The model of such medium in this study is a network of single size tubes. The network form, the ß factor, is usually not known for real porous media. If the validity of the network model can be established, then the study of the flow properties

Jan 1, 1957

By James K. Stanley

WHEN a plastically deformed metal is heated to a certain temperature, it undergoes a complete change in microstructure, the consequence of which is a marked alteration of mechanical properties such as hardness, strength and ductility. This change in microstructure occurs by recrystallization and is a process involving the formation and growth of strain-free nuclei in the deformed matrix. These nuclei continue to form with time and grow until a new grain structure replaces the cold-worked structure. The formation of the nuclei in the deformed sheet of 1 per cent silicon ferrite is illustrated in Fig. 1. If a recrystallization is conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time leads to an isothermal recrystallization curve, first established in 1942.1 Such recrystallization curves are shown in Fig. 4. These curves show that the recrystallization of a cold-worked metal is best considered as a rate process rather than a time independent process such as is suggested by the improperly named and misleading recrystallization diagrams involving deformation, temperature, and grain size. 2-5 Any study of the rate of recrystallization resolves itself into a study of the component rates of nucleation and growth. The previous paper' provided an account of the determination of the rates of nucleation; N, the number of nuclei formed per unit time per unit of unrecrystallized area, and growth, G, the radial growth in unit time, in the recrystallization of silicon ferrite (1 per cent Si). A method was developed to furnish experimental data for evaluating the effect of the recrystallization variables on N and G. The mathematical analysis for the derivation of the isothermal recrystallization curve was developed for a two-dimensional case (in thin sheets where the diameter of the recrystallized grain is greater than the sheet thickness). The present paper is a continuation of the study of recrystallization of 1 per cent silicon ferrite begun in 1942.1 In this work the effect of the factors deformation, temperature, grain size, composition, and recovery is studied with respect to the rates of nucleation and growth. At the same time it is shown how the cooperation of N and G affects the isothermal recrystallization curve. The study of these variables on N and G has a definite bearing on the mechanism of recrystallization and should lay a foundation for a rational theory on the subject. PROCEDURE The procedure used in these experiments was essentially the same as that described previously but in certain details some changes were made in the interests of speed. With few exceptions, the procedure is the same for the study of all the variables. Where the procedure is different from standard manipulations attention is called to this fact.

Jan 1, 1945

By H. W. Hitzrot

The new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addition of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis-charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure—the new fine-ore bin designed and built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work. The many ideas and opinions behind this achievement were all ably organized and executed by the Hollinger milling and engineering staffs, and not a few were directly initiated by them. Excellent cooperation was afforded by the Hollinger staff to the engineers helping to conduct

Jan 1, 1939

By H. W. Hitzrot

The new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addition of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis-charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure—the new fine-ore bin designed and built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work. The many ideas and opinions behind this achievement were all ably organized and executed by the Hollinger milling and engineering staffs, and not a few were directly initiated by them. Excellent cooperation was afforded by the Hollinger staff to the engineers helping to conduct

Jan 1, 1939

By Herty, C. H.

Iron oxide (FeO) plays an extremely important part in the manufacture of iron and steel. In the three major processes- blast-furnace, open-hearth, and Bessemer converter-iron oxide is the chemically predominant compound and controls to a large ex- tent the operation of the furnaces and the composition and quality of their respective products. In order to emphasize the importance of iron oxide in each process, they will be considered individually in some detail. THE OPEN-HEARTH FURNACE. Iron oxide is introduced into the open-hearth furnace in four ways : 1. The scrap charged into the open hearth is oxidized by the furnace gases, the amount of oxide formed depending primarily on the amount and type of scrap charged. It has been found' that with large scrap, 1.7 Ib. of FeO is formed per 100 Ib. of scrap charged, whereas with scrap of medium size about 5.3 Ib. of FeO is formed per 100 Ib. of scrap charged, when the period between the charging of the scrap and the addition of hot metal is 3 hours. 2. The decomposition of the limestone sets free CO, by the reaction

Jan 1, 1957

By G. W. Healy, D. C. Hilty

MAJOR considerations in the production of stainless steel are the utilization of stainless steel scrap and the recovery of chromium and other metallic values from the initial furnace charge. The decarburization of a bath of molten chromium steel with gaseous oxygen is usually accompanied by a considerable amount of metallic oxidation. Since recovery of this metal from the slag may require substantial expenditures of time and materials for slag reduction, holding metallic oxidation to the minimum consistent with good operating practice is generally desirable. The important role of temperature in minimizing metallic oxidation is illustrated by Fig. 1, taken from the results of Hilty, Healy, and Crafts,' who established the quantitative relations connecting the amounts of chromium, manganese, and iron oxidized during the oxidizing period of chromium steel heats with the composition of the initial charge and the temperature and composition of the molten bath after oxidation. Higher temperatures after the oxygen blow result in lower metallic oxidation. Although high temperatures are desirable for minimizing metallic oxidation, practical operating considerations limit the degree to which they can be employed. Excessively high temperatures or prolonged operation at moderately high temperatures may cause serious damage to the furnace refractories, so that a compromise must be effected. The problem, therefore, is one of controlling the oxidizing period of chromium steel heats to the shortest time at the highest practical temperature. The most effective tool the steel melter has for attaining high temperature while decarburizing a chromium steel heat is now commonly considered to be the oxygen lance with an adequate supply of gaseous oxygen. In order for the tool to be effective, however, the heat resulting from the oxidation of carbon, chromium, silicon, manganese, and iron in the bath must exceed the heat losses from the furnace. General recognition, of this principle has stimulated a trend toward faster injection of oxygen. For example, Pachaly2 proposed a high temperature at the start of the oxygen blow or a high rate of oxygen input as a means of obtaining the desired carbon level with high chromium recovery. On the other hand, limited understanding of the specific effects of oxygen input rate has hampered development of optimum practices. As part of a broad study of the metallurgy of chromium steel melting, therefore, the Linde Air Products Co. and the Electro Metallurgical Co. at their Metals Research Labo-ratories have evaluated the heat-balance during the oxidizing period in terms of oxygen input rate. The evaluation has then been related to factors such as temperature increase, metallic oxidation, oxygen Utilization, etc., and extrapolated to include a wide

Jan 1, 1958

By Pedro Bolsaitis, Paul M. Sullivan

The activities of zinc in liquid Zn-A1 alloys in the temperature range of 1000' to 1160°K were determined by means of the isopiestic technique. The results are in reasonable agreement with the previous values determined by the radioactive tracer dew point method. Slightly negative excess entropies of mixing were found. The measured activities suggest that the a function for these alloys is not a constant, as has frequently been assumed, but is better represented by two straight line segments of different slopes. THE thermodynamic data of Al-Z alloys have been the subject of investigation by many authors. However, in the recent compilation of such data by Hult-gren et al.,5 the conclusion is reached that none of the previous measurements are reliable or consistent with each other. Since then two new sets of measurements have been reported,2, 8 both laying claim to good accuracies, yet showing very significant disagreement in the measured activity coefficients of zinc in Zn-A1 alloys and in the magnitude and sign of the excess entropies of mixing. Information on the thermodynamics of the system is of particular interest for interpreting results of the Bureau of Mines research on refining of zinc by distillation of die cast scrap. The present study was undertaken as an independent check on the recent values obtained from dew point measurements 8 and electromotive force measurements.' The isopiestic method, first introduced by Herasy-menko,' was chosen because it is one of the few thermodynamic techniques which, in principle at least, is carried out under perfect equilibrium conditions. The disadvantage of the method is that data are obtained at various random compositions and temperatures, which makes the interpretation somewhat cumbersome. The random errors arising from temperature gradients and fluctuations appear to be comparable to those of other techniques, as evidenced by the magnitude of the estimated uncertainties in the calculated integral thermodynamic quantities. An advantage of the method is that each run provides a relatively large amount of data; thus, it is less time consuming than those methods where samples of each composition must be measured individually. EXPERIMENTAL PROCEDURE The activities of zinc in liquid Zn-A1 alloys were measured by the isopiestic method which uses the principle of the tendency toward equilibrium of a series of samples at various temperatures under an imposed vapor pressure of the more volatile component (i.e., zinc, in this case). The basic apparatus is shown in Fig. 1. The small graphite crucibles that contained the metal samples were 15 mm ID and 13 mm deep with approximately 3 mm wall thickness. Each crucible was notched at the top and bottom to allow easy passage of vapor from one to another. At the beginning of an experiment each crucible was weighed on an analytical balance. Zinc and aluminum of spectrographic purity (99.999 pct) were then weighed into the crucibles. The amounts of each metal added were such that initial compositions varied above and below equilibrium values. One crucible contained only pure zinc. After weighing, the crucibles were stacked with the pure zinc on the bottom (corresponding to the lowest temperature in the furnace) and richest aluminum alloys at the top. The entire stack of crucibles was then placed in the silica glass container "E" which was then sealed under vacuum. Sixteen to twenty calibrated Chromel-Alumel thermocouples were attached by wire along the length of the silica tube, one or more adjacent to each sample.

Jan 1, 1970

By B. M. Harra, F. G. McCutcheon, O&apos

Until about 1930, the universal practice of horizontal-retort zinc smelters in the United States, as far as the writers are aware, was to operate the retort furnaces on a 24-hr cycle; that is, the retorts were charged in the early morning of one day, and in the early morning of the following day the residues were cleaned out, the retorts recharged, and a new cycle started. During the business depression of the early thirties, zinc production fell off to the extent that zinc smelters had idle retort capacity. Rather than continue to run some of the retort furnaces on a 24-hr cycle and shut down the remainder, a few companies decided to try out a longer cycle. Although the output of zinc per retort per day is lower, the longer cycle permits a larger charge per retort and improved zinc recovery. Advantages of the longer cycle were soon evident, and the practice spread rapidly. Various lengths of cycle were used, typical examples being 28-hr, 32-hr, 36-hr, and 48-hr. The 48-hr cycle fits in best with the standard routine of smelter practice that was built up on the basis of the 24-hr cycle; that is, the retort furnace "maneuver" always comes at the same time of day, and can be performed in the cool hours of the early morning. Under some conditions, particularly in some of the older plants, where the retorts are smaller than in newer plants, a 48-hr cycle is longer than necessary, and some intermediate length of cycle may theoretically be most economical. Use of an intermediate cycle, however, means that the maneuver comes at different times on consecutive days, and that sometimes it comes during the hottest part of the day. The work on the retort furnaces is extremely hot and arduous at best, and it is much worse, of course, if it is done during the heat of a summer day. When labor was plentiful and tractable, many plants were able to operate on cycles of intermediate length, but the workmen did not like the working hours. Under present labor conditions, it is hardly practicable to operate with a cycle of intermediate length, so the choice has narrowed down to the alternatives of 24-hr or 48-hr cycles. In any discussion of economics, too comprehensive generalization is not warranted, because local conditions affecting economics vary greatly. The best economic practice at one plant at any given time may be uneconomical at another plant, or even at the same plant at another time. To determine the length of cycle that is the better practice at a given plant at a given time requires a weighing of the advantages and disadvantages of each cycle, taking into consideration all the local conditions. some of the factors that must be considered in making the comparison are discussed briefly in the following paragraphs.

Jan 1, 1949

By P. Hazebroek, C. S. Mathews, E. E. Allen, H. C. Lefkovits

A rigorous study was made of the behavior of reservoirs composed of horizontal layers, unconnected except at the well and filled with a compressible fluid. The report is presented in two parts. Part I deals with the practical implications of the results obtained; Part 11 contains the mathematical derivation of the solution. The main portion of Part I is concerned with application of the results to reservoirs composed of two layers. Relative rates of depletion of the layers are studied, and it is shown that differential depletion between layers exists in the transient stage of the reservoir, which generally is of an order of magnitude longer than the transient stage in a single-layer reservoir. In the transient stage, the more permeable layer is depleted faster than the less permeable. However, the reservoir approaches a steady-state situation where both layers contribute equally to production. Theoretical build-up curves from such reservoirs are presented, and the influence of a skin effect and flow into casing and tubing are also evaluated. The build-up curves are predicted to have, first, the familiar logarithmic straight-line section and, subsequently, a rising and flattened section. The results found are compared with an extension of an approximate theory, and it is found that this simplified theory is applicable over most of the life of the reservoir. Extensions to reservoirs containing more than two layers are indicated, and examples of the performance and build-up curves for three-layered reservoirs are presented. The theoretical results on build-up curves were applied to field examples of such reservoirs, and satisfactory results were obtained. From the build-up curve, the pemeability-thickness product, the wellbore damage and the static pressure are obtained. However, it apparently is not possible to determine the properties of the individual layers from the combined build-up curve. A large number of reservoirs have been found where the producing formation is composed of two or more layers of differing physical characteristics, such as permeability and porosity, and where also the thicknesses of the layers differ. Since in general a differential depletion should exist between the layers of such reservoirs, it would be advantageous to know the amount of the differential depletion under a given production history. It also would be valuable to know the pressure behavior, because it could be undesirable to produce a reservoir in such a manner that the pressure in one of the layers would have fallen below the bubble point of the oil at a time when another layer might still be virtually undepleted. The determination of static pressures in shut-in wells with slow build-up is another feature of importance in layered reservoirs. If the behavior of the reservoir differs appreciably from the predicted behavior of a single-layer reservoir, the type of analysis for build-up curves suggested for single-layer reservoirs is not applicable. Several authors have treated the problem of finding the pressure and production characteristics of multilayer reservoirs. Horner treated the problem of n layers in an infinite field, the layers being connected only at the well. Tempelaar-Lietz2 has presented an approximate treatment of the characteristics of a bounded reservoir composed of two layers of different permeabilities and equal thicknesses. Homer gave no information on differential depletion between layers, and the treatment of Tempelaar-Lietz was not applicable for prediction of pressure build-up behavior. In addition, it was thought that a more rigorous treatment than the one by Tempelaar-Lietz would be valuable in determining the range of validity of this solution. The present study, therefore, was made of a bounded reservoir composed of two or more layers,

By A. Taylor

NICKEL-RICH alloys hardened with small additions of titanium and aluminum and centered around that region of face-centered-cubic primary solid solution, 7, where the atomic ratio of nickel chromium is about 3 to 1, form an important series of high temperature materials because of their resistance to oxidation, high temperature strength, and excellent creep characteristics at elevated temperatures.' With suitable heat treatment it is possible to precipitate a phase based on the ordered face-centered-cubic y' phase, Ni,,Al, from the randomly ordered nickel-rich y face-centered-cubic primary solid solution. By adjusting the ratio of aluminum to titanium the precipitation of needles of the hexagonal intermetallic compound n-NiaTi may be effected. In the present investigation, the main interest was focused on the interrelationships among the y, y, and 7 phases. By using alloying elements of high purity and a suitable melting technique the presence of carbides and nitrides could be completely obviated, although it is realized that their presence is probably essential in alloys of commercial importance. As a preliminary to the study of the Ni-Cr-Ti-A1 system, it was necessary to establish the constitutional diagrams of the three contiguous systems, Ni-Cr-Al, Ni-Ti-Al, and Ni-Cr-Ti, which together form the nickel-rich corner of the Ni-Cr-Ti-A1 quaternary tetrahedron. Accounts of this work on the ternary systems have already been published by the author. A preliminary disclosure of the author's investigations on the ternary and quaternary systems has been made by Hignett2 and has since stimulated work in the same field by Nordheim and Grant." Before the detailed account of the quaternary system, a brief description will be given of the three contiguous ternary diagrams on which it is ultimately founded. Ni-Cr-Ti System The 750° and 1000°C temperature isothermals of the Ni-Cr-Ti system as determined by Taylor and Floyd' are shown in Figs. 1 and 2. The single phase fields of greatest interest are occupied by the extensive face-centered-cubic y primary solid solution of chromium and titanium in nickel, and the close-packed-hexagonal Daltonide, n-Ni3Ti, from which tie-lines radiate across the very wide y+n two-phase field. The chromium-rich primary solid solution is represented by a. As may be seen from the diagrams, the extent of the y phase field increases quite appreciably as the temperature is raised from 750" to 1000°C. Isoparametric lines for the y phase are shown in Fig. 1. They are interesting in that they are almost parallel to the y/r+n boundary. Thus the determination of the tie-line directions is entirely dependent on the exact stoichiometry of composition of the 7 phase. Ni-Ti-Al System The 750°C isothermal section of the nickel-rich portion of the system Ni-Ti-A1 as determined by Taylor and Floyd is shown in Fig. 3.' The regions of greatest interest are the extensive y primary solid solution of titanium and aluminum in nickel, the y' Berthollide phase field based on the ordered face-centered-cubic structure of Ni3Al, and the hexagonal Daltonide phase, n-Ni3Ti. As may be seen from Figs. 3 and 4 the area occupied by the y phase is substantially the same at 750°C as at 1000°C, but the area of the 7 phase is considerably greater at the higher temperature. The tie-lines radiate from n-Ni3Ti across the y+v and y' + v two-phase fields and are evenly distributed

Jan 1, 1957

By George Ross Green

[In discussion of the paper of Mr. J. C. Bayles, read at the New York meeting of September, 1890, Trans., xix., p. 18.1 It is often so difficult to locate the causes of failures of machinery and apparatus which can be examined and studied at leisure, that it is not surprising that the causes of explosions should escape detection. Usually the explosion is the first evidence that anything is amiss, and the time for observing the conditions is necessarily brief. An incident in a welding-works near Essen, Germany, might be cited as exemplifying what trifling causes may lead to disaster, and how difficult, under the most favorable conditions, it may be to discover them. A blowing-engine was arranged with two suction-pipes at each end of the blowing-cylinder—one leading to the air, and the other to the gas-holder. Each pipe was provided with a valve, and all were so adjusted that the cylinder drew in gas and air in the proportions found most advantageous. The gases from the cylinder were carried directly to the furnace through suitable pipes, and while the cylinder was provided with relief-valves, every effort was made to prevent explosions, principally by compressing the gases to a point where the rate of efflux of the mixture was greater than the velocity of combustion, if the expression is here allowable. It was found that the apparatus would work satisfactorily for some time, and then the relative proportions of the mixture would change, and an explosion might have been the result. Experiments consuming days were made to discover a method of averting this danger, but they were unsuccessful, until it was observed that the change in the composition of the mixture of gas and air took place when the gasometer began to rise or fall—the back-pressure due to friction when the holder was rising or its absence when falling being sufficient to change the conditions. As soon as this was discovered,

Jan 1, 1892

By S. Gilbert, G. R. Bailey

A further evaluation of the bomb-sampling method for determining the oxygen content of liquid steel is presented. The results of this study and their close agreement with the results of an earlier evaluation confirm the conclusion that the bomb-sampling method is valid for obtaining representative samples for the determination of the oxygen content of a liquid steel bath. WHAT constitutes the most desirable procedure for obtaining a sample suitable for determining the oxygen content of a liquid steel bath has been a controversial subject for several years. In 1952 Huff, Bailey, and Richards' described a modification of the bomb-sampling technique originated by McCutcheon and Rautio.' In both the modified and original techniques, a small cast-iron or steel mold containing aluminum wire and appropriately covered is inserted into the furnace, coated with slag, and then plunged into the metal bath. Upon entering the metal, the cover melts and a sample of the steel bath enters the mold. The data presented by Huff, Bailey, and Richards' indicated that reproducible samples could be obtained by their method. Furthermore, the oxygen analyses from samples obtained by their method agreed better with those from controlled laboratory experiments than did analyses from samples obtained by methods previously suggested for sampling large liquid-metal baths. Most techniques, other than bomb-sampling, require that a sample of liquid steel be removed from the furnace in a well slagged spoon and poured into an iron mold containing aluminum or into a massive copper mold for rapid chilling. Pouring in this manner requires that the sample pass through the air. The controversy, then, is somewhat as follows: Proponents of the spoon-sampling method and similar dip-and-pour methods feel that the introduction of a cold steel mold into a molten steel bath may result in a localized boiling condition that may deplete the steel of oxygen to a significant degree in the area where the bomb is introduced. Conceivably this boil could cause results that are, on the average, too low and nonrepresentative of the bath composition. On the other hand, samples that are spooned and then poured through the air may also be nonrepresentative because of oxidation by the atmosphere. The restrictions imposed in sampling with a spoon are much more stringent than those imposed when sampling with the bomb-type mold within the furnace. The spoon sample must be taken in a well slagged spoon, a requirement that depends on the condition of the slag in the furnace. Also, the samples must be poured as quickly as possible, without shaking the spoon and without allowing slag to enter the mold. The necessity of fulfill-

Jan 1, 1955

By R. Taggart, R. H. Ericksen, D. H. Polonis

Transmission electron microscopy techniques hare been used to study the spontaneous marfensite phase that forms during the thinning of Ti-Cr alloys. The structure of this phase has been found to differ. from the hcp martensite and has been identified as a clisforted fcc lattice. The spordaneous marlensile in this system is interpreted as a metastable isomorph of the equilibriunz TiCr, phase. WHEN thin-foil specimens for transmission electron microscopy were prepared from metastable alloys of the Ti-Cr system, a spontaneous transformation occurred' when the foils contained the untrans-formed 0 phase or two-phase mixtures of the 0 and w phases. The purpose of this paper is to examine the relationship that exists between the crystal structure of the spontaneous product and that of the matrix. The differences between the martensite transformation that occurs in the bulk material and the spontaneous reaction that occurs during the preparation of thin foils are compared with the observations that have been reported for similar phenomena in a commercial titanium alloy.' A spontaneous reaction that exhibits characteristics similar to a martensite transformation has been reported to occur in thin foils prepared from the retained metastable structures of several alloy systems.1'3"7 ~ull~ observed such a spontaneous reaction in 0 brass and attributed the apparent increase in the martensite transformation temperature to a decrease in the non-chemical free energy associated with bulk strain energy. He also showed that the spontaneous product did not have a specific habit plane, but that its orientation relationships to the parent matrix were dependen on the thickness of the transforming region. It has also been pointed out by Breedis6 that in thin films the absence of the constraints imposed by a bulk matrix can cause different requirements for the martensite plate interface and lattice distortion which is reflected bv a dependence of the transformation mechanism on the specimen geometry. In the case of the spontaneous reaction reported for Au-Zn alloys7 a definite habit plane was determined and shown to correspond with the habit plane calculated on the basis of the Bowles and Mackenzie crystallographic theory of the martensite transformation.'- lo EXPERIMENTAL PROCEDURE A series of titanium alloys containing 5.5, 5.9, 6.4: 7.6, 8.0, 11.3, and 18.7 at. pct Cr were prepared from high-purity (iochrome) chromium and iodide-grade titanium by levitation melting. The experimental procedure used for sectioning the alloys and for thin-foil preparation has been reported in an earlier paper.' X-ray diffraction patterns were obtained using a 114-mm Debye-Scherrer camera and Cu-Ka radiation. In order to minimize fluorescent radiation from the specimen, a strip of aluminum foil 0.002 in. thick was placed in contact with the X-ray film. After a specimen was removed from the camera: an additional X-ray experiment was performed, to insure that no spurious lines were obtained due to the presence of the aluminum foil. The interstitial impurity analysis for the alloys used in this study was as follows: oxygen, 100 ppm: hydrogen, 30 ppm: nitrogen, 28 ppm. EXPERIMENTAL RESULTS Electron diffraction patterns were obtained from several individual crystals of the spontaneous marten-

Jan 1, 1970

By I. N. Zavarine

THE present paper is a continuation of the work on the relationship between the magnetic and the phase transformations in carbon steels during quenching. An account was given by the author in a previous paper It of an investigation of this relationship during a continuous quench. The experimental difficulties then encountered prevented a conclusive proof of the existence or absence of such a relationship. The conclusions of the previous paper were derived indirectly. The present paper deals with the same problem, but the method of attack is modified. The technique developed by Davenport and Bain2 in their well-known study of austenite transformation at subcritical temperature was adopted in the present investigation. They have shown that the austenite to martensite transformation can be caused to proceed at a relatively slow rate by quenching steels into a hot metal bath. Slowing down of the rate of transformation, together with an observation by Lewis3 that a eutectoid steel can be preserved in the nonmagnetic state by such quench-ing, pointed out a possibility of a study of both transformations under more favorable conditions than previously described. The preliminary steps were connected with the technique of the hot bath quench. To study this phase of the present work a modification of the apparatus previously describe1 was used. The modification con-sisted in the use of a hot quenching bath instead of brine, and in fixing the secondary and the primary coils of the apparatus in a stationary position in and around the bath. Tubular specimens, as in the previous investiga-tion, were heated in a suitable furnace to a temperature in the austenitic.

Jan 1, 1935

By Charles Fettke

IN 1914, the officials of the Brundred Oil Corpn., faced with the problem of introducing new methods to increase production in the old and nearly depleted pools of Venango County, became interested in the Smith-Dunn (Marietta) process which was at that time being tried out in southeastern Ohio and which was already yielding very encouraging results. A license to use the process in Pennsylvania was secured from the owners of the patents. These patents were later declared invalid. The method was first used in Pennsylvania on a property consisting of about 434 acres, of which 300 are productive, at Hamilton Corners, 15 miles northeast of Oil City, in Cherry Tree and Oakland Townships, Venango County. The producing horizon is the First Sand of the Venango Group. A small oil pool was opened up in this vicinity in 1904. By July, 1916, when the compressed air was first introduced to restore pressure, the production had dropped to a point where it was no longer possible to continue profitable operation. From that time until March, 1927, over 100,000 bbl. of oil have been recovered from the tract. The property is being operated at present by the Brundred Oil Corpn. and Lux. The 1926 production, amounting to 10,650 bbl., was only 400 bbl. short of the maximum reached during any year of the 10-year period that the process has been in operation. Inasmuch as the Hamilton Corners pool is the first one in Pennsylvania in which the Marietta process was tried out, and the one in which it has been longest in continuous operation, considerable interest attaches to the results obtained. Through the courtesy of H. D. Brown and W. J: Brundred, officials of the Brundred Oil Corpn., all their data on this operation were made available to the writer in connection with an investigation of rejuvenation methods in the State for the Pennsylvania Geological Survey.

Jan 1, 1928

By C. H. Cheng, C. E. Birchenall

The fundamental problem in the thermodynamics of solid solutions is the determinatiorl or calculation of the activities of the components as a function of temperature and composition. Since the theory of metals is not suficiently developed to allow a priori calculation of these quantities, they must be obtained from experiment. C. Wagner1 has reviewed the literature of this subject for the period before 1940. Although several important and extensive studies have been made in the meantime, the number of systems to which any sort of quantitative information can be assigned is vanish-ingly small. These data have become of great potential importance in studies of the structure of solid solutions2 and intermetallic compounds, the nature of the diffusion process,3,4 and perhaps even the mechanism of mechanical deformation.5 For these reasons, it. seems very worthwhile to extend the experimental data in this field. Although there is little use in duplicating Wagner's review, attention should be directed to the most recently reported investigations. A brief enumeration of the methods of measurement previously employed also should be valuable. The most direct method is the determination of the partial pressure of the components in the vapor phase in equilibrium with the solution. Both equilibrium and kinetic methods have been tried in metal systems, but almost exclusively on liquid phases. Only in the ease of carbon in iron alloys and in the copper-zinc system have extensive measure- ments been made which include solid phases. When one of the components is an element, such as nitrogen or carbon, which forms compounds which are very volatile and stable at normal temperatures and pressures (CH4, Co2, CO NH3), it is frequently possible to equilibrate mixtures containing these (such as CH4-H2, CO2-CO, NH3-H2) independently with the elernents (C, X) and with the metal (Fe, Ni, etc.). Such measurernents have been made for carbon in iron, iron-silicon, and iron-manganese alloys by Smith6 and in iron and iron-nickel alloys by Toensing.7 Differences between carbon activity values at the same temperature and carbon content when carboil is introduced from CH4-H2 rnixtures or CO-CO. mixtures indicate that the effects of hydrogen and oxygen in the system are not negligible, and one can only hope that the true value lies somewhere between these sets of results, probably nearer the CH4-H2 data since hydrogen is less soluble in iron than oxygen. This is essentially an equilibrium method, although flowing gas is employed. A kirletic method has been employed which consists of sweeping an inert gas (generally hydrogen) over the alloy at a series of rates, condensing the metal vapor out,, and analyzing it. The metal content can be extrapolated to zero flow rate (equilibrium). Wejnarth's8 work on Cd-Mg and Zn-Mg is a good example of this frequently used method. A variant of this consists of equilibrating a known volume of inert gas with the alloy, sweeping it out quickly, and analyzing for metal. In common with the above method, it has the disadvantage that the "inert" gas is generally somewhat soluble in the alloy. Moreover, the former continuously displaces the system from equilihrium and may give low values if solid diffusion is involved. The dew point method applied by Hargreaves9 to the alpha and beta brasses and by Schneider and Stolll0 to A1-Zn avoids the introduction of another component to the system, but is useful only in systems in which one component is much more volatile than the other. The alloy sealed in one end of an evacuated silica tube is heated to the desired temperature. The temperature of the other end is lowered until droplets of the volatile component condense. When the temperature is raised slightly, the droplets will evaporate. By careful adjustment of temperature, the range between evaporation and condensation can be narrowed appreciably. An independent determination of the vapor pressure of the . pure volatile component is necessary to give the partial pressure over the alloy. This is the method employed here to determine the vapor pressures of zinc and cadmium over their silver alloys up to 34 pct in cadmium and 76 pct in zinc. The former involves only the a solid solution, but the latter covers the a, ß, y, and e fields. In recent determinations, Herbenar, Siebert, and Duffenbarkl1 used the

Jan 1, 1950

By T. G. Chapman

The writer has carried on experimental work for several years with respect to the simultaneous dissolution of gold by cyanide and the adsorption of the dissolved gold on activated charcoal in ore pulps, followed by the recovery of the charcoal by flotation. The results of this experimental work have been sufficiently encouraging to suggest a new process based on the principle of simultaneous dissolution and adsorption of gold, applicable to certain ores and tailings that cannot be treated to advantage by countercurrent decantation or filtration. Applications for patents have been filed and The Dorr Company, Inc. has the exclusive right to license the use of the process. The purpose of this paper is to describe such a process, state its possible advantages and immediate field, and give some results obtained on a laboratory scale. Early Experimental Work In the early stages of the experimental work attempts were made to precipitate soluble gold from cyanide solutions with zinc and aluminum in ore pulps followed by flotation of the precipitated gold, but since the results were not promising enough to continue with these precipitants attention was directed to carbon. The first experiments with carbon comprised the addition of cyanide and alkali to the ore pulp, the addition of carbon at or near the end of the dissolving period, and the recovery of the carbon by flotation. With this method of procedure the assumption was made that carbon functioned as a precipitant of gold from cyanide solutions and as such should be added as are other precipitants, including zinc and aluminum; namely, at the end of the dissolution period. The assumption was then made that carbon functioned as an adsorbent, and that if such assumption proved to be correct, it could be added with success to the ore pulp at the time of adding the cyanide. The first experiment along this line was successful in that the feasibility of the dissolution of gold by cyanide and the simultaneous extraction of the dissolved gold by carbon in ore pulps was demonstrated, at least with respect to such treatment on a laboratory scale.

Jan 1, 1939