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By A. E. Worthington, R. F. Meldau

An analog computer study was made of the reduction of the magnitude of the SP by formation geometry and resistivity effects. Practical field .situations were studied. The analog data were converted to the form of departure charts. These charts may he used to determine the reduction in the SP due to the above eflects pith good precision Quantitative interpretation of the SP log in terms of formation water resistivity is presently based on the premise that the observed SP is equal to the electrochemical potential developed across a shale between the mud filtrate and the formation water. This procedure inherently assumes that, first, no electro kinetic (streaming) potential is present, and, second, that the SP is not reduced by resistivity or geometry effects in the formation. When, however, such a reduction of the observed SP does occur, one may write, SP = b,E, b, E, (1) where SP is the observed self-potential opposite the center of the bed under consideration. In this case, E, is the electrochemical potential, E, is the electrokinetic potential, b, is the electrochemical reduction factor, and h, is the electrokinetic reduction factor. The first assumption above is equivalent to assuming E, = O in Eq. 1 and the second assumption is equivalent to h, = b, = 1. Examination of electric logs shows that for many formations of interest the observed SP is reduced below its maximum value. The object of this work is to aid quantitative SP interpretation in at least some of these situations by obtaining values for b, and b, in Eq. 1 as functions of realistic combinations of bed thickness, depth of invasion, and formation resistivity. The only previously published work in this field known to the authors is by H. G. Doll' in 1948. He evaluated b, under conditions permitting exact analytical solution. His work clearly established the importance and qualitative nature of formation geometry and resistivity effects upon the SP, but the necessity of obtaining analytical solutions restricted his study to situations of limited practical interest. In order to extend such studies to practical combinations of formation parameters which do not lend themselves to feasible analytical solutions, the results reported in this paper were obtained by use of a special analog computer. THE ANALOG MODEL The analog model used for this study was the Guyed Analog Computer which originally was designed and built for resistivity log departure curve studies. It consists of a two-dimensional mesh of resistors, with the vertical mesh corresponding linearly to vertical distance along the borehole, and the horizontal mesh corresponding to radial distance from the borehole axis. By proper choice of horizontal resistor values, a three-dimensional, axially symmetric, borehole-formation problem can be modeled with this two-dimensional array. These and other details of the model are contained in a paper by H. Guyod'. The geometry used for the SP studies with the analog is depicted in Fig. 1. This configuration has a horizontal plane of symmetry, and, hence, the model, and the following discussion, need only to be concerned with one quadrant such as shown in Fig. 2. A further simplification arises by considering that both the natural potential sources and those used in the model have fixed internal impedance. Therefore, the current flows produced by these sources can be separated and studied independently ( i.e., the superposition theorem can be applied). SP = SP, i SP, = h,E, + b,E, ,(7)

By C. R. Fast, George C. Howard

Laboratory and field testing of various squeeze cementing techniques and materials revealed that many improvements could be made in squeeze cementing operations. The use of a slow-pumping squeeze cementing procedure permitted the control of the quantity of cement displaced into a formation and aided in obtaining a high final squeeze pressure. Field testing indicated the desirability of obtaining high final squeeze pressures, the need for improved formation breakdown fluids, and the necessity of controlling the pressure differential during testing after a squeeze job. INTRODUCTION During the past few years, squeeze cementing operations have been investigated, both from the theoretical as well as the practical point of view, in an effort to arrive at some solution to the many and varied problems that arise with this type of operation. A review of well files indicated that in many instances, wells were being squeeze cemented four and five times before a satisfactory pressure buildup was obtained. There seemed to be considerable variation in opinion as to the proper method of squeeze cementing, as well as disagreement as to the proper breakdown agent, the quantity of cement that should be used, type retainer and length of WOC* time that was necessary. Consequently, it was deemed advisable to approach this problem theoretically, field testing each idea developed in hopes of eventually arriving at a squeeze cementing procedure that would give reasonable assurance of a successful job after one squeeze cementing operation. This investigation was. therefore, divided into two broad headings: (1) Preliminary studies, which include both theoretical and laboratory studies, and (2) Field investigations to determine the proper squeeze cementing methods. PRELIMINARY STUDIES Overburden Pressure Studies Squeeze cementing problems are so intimately related to the earth's overburden pressure that solutions to them are very difficult, if not impossible, without an understanding of the nature and magnitude of the overburden pressures encountered at the depths of producing wells. It was thus felt that the first approach to research on squeeze cementing should be made through a study of these pressures. Since there has been rather loose usage of a number of the terms related to overburden preasure by different writers, the terms to be subsequently used are defined here. Theoretical overburden pressure is the calculated pressure at any given depth exerted by the theoretical weight of overlying formations as calculated from the average rock density. Fluid displacement pressure is that pressure at which fluid can be injected into a formation after it has been broken down. It may be more or less than the theoretical overburden pressure. Formation breakdown pressure is that pressure at which a formation parts or breaks and is usually thought of as fluid displacement pressure plus rock strength. Breakdown agent is that fluid with which the formation is fractured. The first step in the study of the earth's overburden pressures involved a review of pertinent technical literature. The general opinion expressed was that the overburden pressure gradient of the earth's formations is roughly 1.0 psi per foot of depth, and that application of sufficient pressure to stratified formations. will cause them to part at or parallel to the bedding planes. The second step in the study of overburden pressures involved a study of available well data in an effort to obtain some definite information as to the actual values experienced in the field for the above mentioned terms. Data from 115 cement squeeze jobs in the Gulf Coast area and 46 cement squeeze jobs and acid jobs in the West Texas-New Mexico area were closely analyzed. The analysis of these data showed that the average formation breakdown

Jan 1, 1950

By Adrian C. Dorenfeld, Theodore Balberyszski, Strathmore R. B. Cooke

This paper reports results of studies of sulfidiza-tion of base-metal oxides and silicates with gaseous sulfur, hydrogen sulfide gas and pyrite and of their subsequent flotation with xanthate collectors. It has been established that a 100% conversion of the oxides of lead, zinc, copper and manganese into their respective sulfides is possible and is a function of reaction time and temperature. Sulfidization of chrysocolla (with malachite and azurite inclusions) resulted in a product containing covellite, chalcocite and digenite in proportions depending on conditions of sulfidization. Reacting cassiterite with gaseous sulfur, H2S or pyrite at various reaction temperatures resulted in its partial conversion to a tin sulfide. Flotation of the products of sulfidization indicated that their behavior is similar to that of natural sulfide minerals, the recovery being a function of the con-version of the oxides to their respective sulfides. The gradual depletion of high-grade sulfide mineral deposits has turned the attention of the mineral industry to the recovery of metals from the oxides and silicates. Anionic (fatty acid) and cationic collectors have in some cases made flotation of nonsulfides possible, although, in general, flotation of oxide ores is not as yet an economic process. Consequently, many attempts have been made to sulfidize the surface of the relevant oxide mineral and thus make it amenable to to In recent years, Bautista and sollenberger4 have investigated the conversion of a number of oxides to sulfides by reacting them with molten sulfur. This paper presents the results of .investigations carried out at the School of Mineral and Metallurgical Engineering at the University of Minnesota to study the flotation characteristics of some sulfidized minerals. It is divided into two parts: The first describes the sulfidization of a number of oxides and a silicate, and the second presents the flotation behavior of the products of sulfidization. SULFIDIZATION OF METAL OXIDES AND SILICATES Experimental Procedure: SULFIDIZATION WITH HYDROGEN SULFIDE GAS — Sulfidization with H2S gas was carried out in a horizontal tube furnace (Fig. 1). The temperature of the furnace was regulated by means of a Variac and determined with a chromel-alumel thermocouple. The constant temperature zone in the furnace was about 6 in. in length, and it was within this zone that the experiments were carried out. The gases employed were supplied from standard compressed gas cylinders, and passed through a glass-wool filtering tower before entering the Pyrex reaction tube. Gaseous products were bubbled through a water tower (used as a flow indicator) and excess H2S was burned off at the end of the outlet tube. Samples of reagents or minerals were placed in a 3-in. Alundum boat and inserted within the constant temperature zone of the furnace. Nitrogen gas (6 ppm O2 content) was passed through the tubes at room temperature to remove air in the tube, and continued to pass while the furnace was heating up. When the required temperature was reached, H2S was allowed to enter the tube and the supply of nitrogen was shut off. At the end of the reaction period, the reverse procedure was carried out, the samples being cooled to room temperature in a nitrogen atmosphere. The flow rate of H2S gas was maintained fairly constant in all experiments, although the rate was not determined. SULFIDIZATION WITH SULFUR POWDER - To study the sulfidization of minerals with sulfur (liquid or gaseous), samples of the mineral, together with a measured quantity of sulfur powder, were placed in a stainless steel (SS316) reaction vessel (Fig. 2). The reaction vessel was heated in a vertical resistance coil furnace, the temperature being regulated through a Variac. At the end of the experiment the vessel was cooled to room temperature before the sample was removed. Cooled products were leached with CS2 to remove any free sulfur. SULFIDIZATION OF TIN CONCENTRATES - Fifty gram samples of sulfidized tin ore were prepared by mixing -48 mesh Bolivian tin concentrate with -48 mesh Ottawa sand in various proportions and sulfi-dizing these samples with H2S in the horizontal tube

Jan 1, 1969

By John C. Draper

The principal object of an underground coal mine transportation sys tem is to move coal from the face where it is produced to the outside of the mine where it is prepared for market. In addition to the movement of coal, a transportation system must also move supply materials to the inside; it must move men in and out of the mine ; and it must move rock and other debris out of the mine for disposal. Usually, mine haulage is divided into three categories named for the various areas of the mine served: 1) Face Haulage. This is used at face from the mining machine to the intermediate transport system. 2) Intermediate or Secondary Haulage. Generally this is used between face haulage and main haulage. Sometimes this is merely an extension of the main haulage. 3) Main Haulage. This extends from the secondary haulage to the outside and is usually either a track or conveyor system, sometimes a combination of both. Transportation modes of coal in the various areas pose different problems, but the whole system must be synchronized. For instance, at the face the coal should be removed quickly from the various places to facilitate the movement of machines, whereas the intermediate system just passes the same coal on to the main transportation system. Selection of the transportation system must be based on the seam height, mining methods used to extract the coal, capacity required, ease of coal handling, and haulage efficiency. When driving rooms, mine cars can be used. They often simplify supply haulage and rock handling because they can also handle these items. Conveyors could be used and would have a greater haulage capacity but they cannot handle supplies easily or segregate the rock. When using a different mining method, such as longwall, mine cars cannot be used because there is not sufficient space to move the cars at the face nor can the cars haul the coal without delays which would cause excessive losses in production. As for ease of handling

Jan 1, 1973

By C. Zener, J. H. Hollomon

IT Is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect o rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. EARLIER INVESTIGATIONS A clear analysis of the conditions necessary for plastic flow and for fracture was first given by Ludwik,1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis, both a flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracture is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence or now stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The. curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated' by the authors. According to this principle of equivalence, strain rate E and temperature T affect the flow stress only through a single parameter p of the form: p = EeQ/RT [I] In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. Combinations of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

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 Richard H. Hopkins, R. W. Kraft

A new technique facilitating the rapid determination of the three-dimensional morphology of phases suspended in an opaque matrix is described. The vapidity of the technique is based upon continuous cinephotomicrographic recording of specimen microstructure as the specimen surface is removed under controlled conditions in an electrolytic cell. The advantages of the technique for determining spatial morphologies in opaque materials are illustrated by application of this method to the study of the configuration of faults in a specimen of directionally solidified CuAl2-Al eutectic alloy. A spatial model of the eutectic fault network deduced in this manner has substantiated the facts that faults in this alloy tend to lie parallel to one another in a direction close to that of the specimen growth axis and that the majority of faults tend to bridge lamellae rather than run parallel to them as growth proceeds. For the specimen studied fault density decreased as growth proceeded. ALTHOUGH metallographic observation is a powerful tool for investigating the correlation between structure and properties in metallic alloys, ordinary metallographic methods suffer the fundamental limitation that any conclusions concerning the three-dimensional structure of these opaque materials must rely upon inference from two-dimensional microsections. For this reason it is frequently impossible to make valid judgments regarding the true spatial distribution of the micro-constituents in specimens under investigation. Several techniques have been devised to circumvent the basic limitation of planar microsec-tioning and employed with varying success. These include construction of three-dimensional models of alloy microstructure from sequences of photomicrographs,1-3 quantitative deduction of spatial features based upon statistical studies of data from random and/or selected plane microsections,4-6 and selective dissolution of one phase in a two-phase alloy to reveal the topography of the phase remaining.' However these techniques also have certain obvious disadvantages. Construction of three-dimensional models is a very time-con- suming procedure due to the tedious polish-etch-photograph cycle needed to obtain the necessary photomicrographs to portray the spatial microstructure. Statistical methods by their very nature give only average values of the quantities being studied and cannot therefore give a detailed physical picture of the microstructure to be observed. Finally, the technique of selective dissolution is only applicable in systems where the phases are of vastly different chemical reactivity; it is of little use in the study of single-phase alloys. Since the determination of the three-dimensional structure of opaque materials is hindered by two facts—the materials are opaque to radiation in the visible spectrum and construction of spatial models of microstructure is quite laborious—two solutions to the problem suggest themselves: 1) use radiation of energy great enough to render the alloy transparent, i.e., some microradio-graphic method, or, 2) devise a rapid means to section and record alloy microstructure. Stereomicroradiography has indeed been used to study internal arrangements of phases in several materials8,9 but the method, in general, is limited to very thin specimens (due to X-ray absorption) and simple microstructures. It would seem then that development of a rapid, simple, and generally applicable technique for studying the details of alloy microstructures in three dimensions can best be undertaken by following the second approach above. Using this idea a new technique for rapid evaluation of spatial microstructures was developed based upon cinephotomicrographic recording of the micro-structure of a specimen undergoing controlled electrolytic dissolution. It was further felt that application of this technique to the careful study of the spatial configuration of faults in a CuAl2-Al eutectic alloy would yield information that could be correlated with the extensive data3,6,10-12 already compiled concerning the solidification and crystallography of this eutectic. The practicality and usefulness of similar methods for studying three-dimensional features in alloys has recently been illustrated by the study of dislocation loops in zinc13 and spheroidized structure in steel.14

Jan 1, 1965

By Harry V. Welch

This paper presents a brief discussion of numerous devices and processes which have been utilized for the recovery of values from gases in copper reduction works and describes in greater detail the development and application in recent years of electrical precipitation, more familiarly known as the Cottrell process, to the problems of dust losses with furnace gases in copper-smelting and refining plants. The field for collection of suspended particles in gases is widely extended in our modern complex, congested .and industrialized mode of living, and its satisfactory solution is required by our increasing appreciation of the extravagant waste, unhealthful effects and nuisance which such uncontrolled emission of solid suspensions represents. Much of the special dust-recovery equipment in use today has been developed in one industry and carried over to many others. The early work of Cottrell was with sulfuric acid mists, aimed at the purification problem in contact acid manufacture, but the present uses of Cottrell equipment cover a diversified field—carbon black, combustible gas, oil mists, iron blastfurnace fumes and dusts, cement-kiln gases, as well as the purification of gases in contact and chamber acid plants and its wide and extended use in the nonferrous metallurgical field of copper, zinc and lead, and their associated metals. Dust and fume collection from furnace gases became a problem only with the modern development of large and amply powered auxiliary furnace equipment, which in turn permitted large furnace units, fast driving and large outputs of finished product per unit of furnace capacity. The ancient metallurgist with his small clay pot and hand-operated bellows had too little gas velocity to cause a real dust loss. As furnaces grew in size, flues and stacks were added, and undoubtedly the first observable dust losses were indicated by the deposits in the flue and stack base. Large flues, it was noted, collected more than smaller ones, and the expansion of a portion of the flue into a chamber represented the first serious attempt at recovery of furnace dust losses. For a century or more the settling chamber represented the best of skilled metallurgical practice in recovery of furnace dust, and it may be said to have reached

Jan 1, 1934

By Aloys H. Wohlrab

[THE conditions that govern the selection of a suitable type of detachable bit for the small isolated mine, for rock work and tunnel contracting and for the large mine are quite dissimilar, therefore intelligent recommendation of a particular make of detachable bit must involve consideration of many factors. Small, isolated mines may find advantageous a detachable bit that a larger mine cannot afford to use, because of more efficient conventional steel sharpening and steel-distribution practice, but a small mine may of be able to adopt the practice of larger mines because of necessary capital expendites for equipment for detachable-bit sharpening and shanking. The perfect detachable bit, suitable for all conditions, has n yet been developed. CONVENTIONAL DRILL BIT IN USE That drilling speed increases as the hit gauge decreases is well known, but since small-hole drilling is the exception rather than the rule the rate of such increase is probably not so generally recognized. Tests married out by Holman Brothers Limited1 with 7/8-in. show that when bit sizes are reduced from. 1 ½ in. 1 3/8 in., and 1 3/16 in., to 1 3/8 in., 1¼ in., and it' in., respectively, the volume of the hole is15 per cent less and the drilling speed 4q per cent higher. Recent tests by the United States Bureau of Mines2,3in hard, uniform basalt showed that a reduction in average gauge from 2.077 to 1.826 in., a difference of 0.251 in., gave an increased drilling speed of 65 per cent. The limits to which a drill hole may be extended depend upon the loss in gauge. Since the conventional bit with 5° and 14° clearances did not possess sufficient reaming edge to permit the smaller gauge changes that were required for small-hole drilling, experiments were made in bit construction with a view to correcting this deficiency. This resulted in the adoption of the full reaming cross bit (having full Carr characteristics) by some mines.4 In order to drill holes having a minimum taper from the collar to the bottom of the hole, full reaming center-hole cross bits with 90° cutting angles, 5° and I4° wing tapers, forged on 7/8-in. quarter-octagon drill rods, are used in the conventional drill-steel practice at Hollinger. In the steel shop close attention is given to the condition of the dies and dollies, which, combined with a rigid inspection of the finished bit, ensures as nearly a perfect bit as can be forged economically. Shop practices and costs have been discussed in earlier papers.5,6 The method by which the radii for the special dies used for forging bits of different gauge diameter are obtained so that the points and reaming edges cut circles of the same diameter has been discussed by Hibbert.7 REQUIREMENTS FOR DETACHABLE BIT FOR HOLLINGER Under these circumstances, it was apparent that it would be difficult to introduce a detachable bit that could successfully compete with the conventional bit already in]

Jan 1, 1942

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.' Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By A. H. Geisler, R. F. Mehl, C. S. Barrett

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1'2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y' are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y' and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y' is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1'2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y' are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y' and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y' is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By D. W. Philips

The problem of strata control has of necessity been prominent in mining, and accounts of individual experience and research abound in the literature of most mining countries. Organized rescarch began in Britain by the formation of a committee, upon the recommendation of the Safety in Mines Research Board in 1923, to investigate methods of reducing accidents from falls of roof in coal mines. This committee examined current practice in supporting underground workings in the principal coal fields, and its findings have been published in the Board's publications.' - Toward the end of these investigations it was suggested by the Chief Inspector of Mines that committees of the several mining institutes be formed to examine the problem in their respective districts. The formation of these committees marked a new phase in research on strata control. The work, though being done in the separate coal fields, followed a scheme outlined by the chief Mining Engineer of the Research Board, and was coordinated by his office. FACTORS INVOLVED The subject is being considered in Britain from two aspects: 1. To provide. by supports, means to prevent falls of fractured ground. 2. TO develop methods whereby the strata can be maintained in the least broken condition and thus make falls less likely. The first aspect is the one that will most likely lead to immediate results from the accident standpoint. It depends largely upon the assimilation of already acquired knowledge regarding the properties of supports and their correct application. The second aspect is perhaps more fundamental, and involves also the properties of the strata and their behavior under the influence of the forces induced by mining. The problem involves many natural factors that cannot be controlled, such as depth, inclination and thickness of seam and nature of the rocks. Other factors, which may be considered to a certain extent controllable, cannot be varied readily and with sufficient frequency to facilitate easy investigation; some of these are: rate of advance of the working face, length of face, direction of the face with regard to cleat and inclination, system and arrangements of rock packing behind longwall faces. In any given case the very many factors present have a mutual influence upon the effects produced in the mine. For example, a study of the effects of rate of advance cannot be done without considering the effects of other factors such as nature of strata, direction of face and quality and arrangement of supports. Conversely, the length and direction of a working face

Jan 1, 1947

By L. F. Mondolfo, W. T. Collins

A study of the relationship between undercooling for nucleation and structure in Sn-Cu alloys with 0.1 to 5 pct Cu has shown that in hypereutectic allojls the halo of tin that surrounds the primary crystals of Cu3Sn5 is larger, the larger the undercooling for nucleation o,f the tin. This increase of halo size results in a decrease of coupled eutectic, and, in alloys far from the eulectic composition, may produce its complete disappeavance, with the formation of a divorced eutectic structure. This was confirnred by the excrrnination of other alloys in which divorced eutectic slructuves are formed, and leads to the conclusion that they ave only an extrenle case of halo forrtzalion , which results when the two phases freeze one at a time and solidification of the first is completed Defove the second starts. It was also found that under proper conditions of nucleation all types of eutectic structures can be formed in the sartte system , and therefore divorced eutectics, like normal and anomalous, are not characteristic of the syslett~, but are mainly controlled by nucleatiorz. Dizlovced eutectics are formed when the phase that tutcleates the eulectic vequires a large undevcooling for ils nucleation and when the cotnpositiorz of the alloy is far from the eutectic., on the side of the primary phase that does not nucleate the other phase. It is recommended that the tevm "divorced" be used in preference to degenerate because it is more desct-iptice of the morphology and mode of forinalion of the structures. ThE variety of structures found in eutectic alloys has been extensively investigated and classified. The most accepted classification is the one by ~cheil,' in which three different types of eutectic were distinguished: 1) normal, 2) anomalous, 3) degenerate (divorced). ATornlal eutectics are typified by the simultaneous growth of the two phases ("coupling") by which the two phases appear as interpenetrating crystals. The presence of a crystallization front, in which the two phases grow side by side, creates the eutectic grains, with the boundaries where the fronts meet. The presence of eutectic grains is the .distinguishing feature of a normal eutectic, according to Scheil. Straumanis and Brakss2 examined the Cd-Zn system and showed that there was a crystallographic relationship between the phases. Later, others4 also investigated additional systems and found definite crystallographic relationships in the coupled eutectics. The anornalous eutectic shows much less coupling than the normal; the two phases are intimately mixed but 'grow without a uniform crystallization front—a consistent crystallographic relationship— and the eutectic grain is conspicuously absent. As in the normal eutectics faster rates of growth result in a finer structure, but there is not the typical uniform spacing of normal eutectics. The degenerate eutectic shows no coupling; in fact the two phases attempt to minimize their area of contact and to form separate crystals. It has been suggested5" that slow cooling may favor this type of structure. Scheil believes that normal eutectics are formed when the two solid phases are present in more or less equal proportions, whereas both anomalous and degenerate eutectics form when one of the phases is present only in small amounts. spengler7 extended much farther this qualitative relationship between the eutectic type and the ratio of the two phases, and added a relationship to the melting point of the constituents. On this basis he proposed two equations for determining into which of Scheil's classifications an alloy belongs. The first equation is: where TI is the melting temperature of the lower-melting component, Tp of the higher-melting component, and Te the eutectic temperature. The second equations is: where is the volume percent of the lower-melting phase and $2 of the higher-melting phase at the eutectic composition. If 0 and/or 4 are in the range 0.1 to 1, a normal eutectic is formed; if in the range 0.01 to 0.1, anomalous; if less than 0.01, degenerate. Although the examples given by Spengler show a good agreement with the formulas, chadwick found that the Zn-Sn eutectic is normal to all growth rates, even though the volume ratio is 12/1, and Davies9 reports that the A1-AlgCo2 eutectic is normal, with a volume ratio of more than 30/1. Many more discrepancies of this type can also be found. Neither Scheil nor most of the other investigators have considered nucleation as a factor in the formation of divorced eutectics. Daviesg states that divorced eutectics form when neither phase acts as

Jan 1, 1965

By P. H. Turnock, R. D. Pehlke

The effects of mutual interactions between elements on the solubility of nitrogen in liquid iron alloys containing chrormium, columbium, molybdenurn, nickel, or silicon have been determined. The equilibrium nitrogen solubilities in the liquid iron alloys were measured by the Sieverts method. The second-order effects caused by the presence of chrormium, columbium , or silicon in the melt were found to be significant. The solubility of nitrogen in liquid iron alloys containing several alloying elements has also been measured as a function of melt temperature and nitrogen pressure. The heat of solution of nitrogen in microcomponent iron alloys has been found to be a function of the logarithnz of the activity coefficient of nitrogen, irrvespectilje of the composition of the melt. The heat of solution of nitrogen in pure liquid iron was determined to be 1265 ± 450 cal per g-atom of N over the temperatxue range 1600° to 1800°. Sieverts ' law was obeyed for all melt compositions studied in the pressure interval 0.4 to 1.0 atm. The solubility of nitrogen in liquid pure iron and in many dilute binary liquid-iron alloys has been the subject of many investigations. Pehlke and Elliott' made a comprehensive investigation on this subject in which they summarized and compared previous researches. However, the practical application of these solubility studies requires prediction of the nitrogen solubility in the multicomponent alloys encountered in operating practice. The interaction parameter as defined by wagner2 has been used to predict the behavior of a solute in a complex alloy, and a modification of this approach has met with reasonable success in several instances.'1"5 The necessity for extending the nitrogen solubility data on binary alloys is caused by the lack of direct measurements of the solubility of nitrogen in molten alloy steels. A direct comparison between measured solubilities and those predicted for multicomponent alloys based on data in binary systems has been made in only a few instances, and most of these were reviewed by Langenberg,6 who developed a graphical technique for predicting nitrogen solubilities in multicomponent iron alloys. The solubility of nitrogen has also been studied over the entire Fe-Cr-Ni ternary system by Humbert and Elliott.? Both studies compared the solubilities computed from binary iron alloy data with those measured in ternary alloys in the liquid state at 1600°C. Most of the nitrogen solubility measurements referred to above were for iron alloys at 1600°C; thus, the ability to predict nitrogen solubilities in molten iron alloys has been restricted primarily to alloys at 1600°C. Recently, Nelsson8 devised an approximate method for calculating the change in nitrogen solubility in molten iron alloys as a function of temperature, but an assumption of regular solution behavior limits the applicability of the method. Chipman and Corrigan9,10 have developed an empirical correlation. based on the activity coefficient of nitrogen in the iron alloy at 1600°C, which facilitates the estimation of nitrogen solubilities at higher temperatures. This method also has limitations, due to the necessity of calculating the activity coefficient for nitrogen in a multicomponent iron alloy at 1600°C from the nitrogen solubility data for binary iron alloys. The shortcoming of such a straightforward approach to the problem of predicting nitrogen solubilities is the disregard of mutual interactions between elements in a complex iron melt. This investigation was conducted in an attempt to provide a more reliable method of predicting nitrogen solubilities in multicomponent iron alloys. The effects of the mutual interactions between chromium, nickel, silicon, molybdenum, or columbium in iron were studied, using the Sieverts' technique1,7 to measure the effects of alloy composition, temperature, and pressure on the solubility of nitrogen in ternary liquid iron alloys.

Jan 1, 1967

By J. C. Griffiths, D. W. Bennion

A mathematical model, which does not assume a priori that stratification exists, but was designed to test for the stratification was developed. The model segmented the reservoir horizontally into areas of common variance, then divided it vertically into strata (if strata were present). Next, trend surface techniques were used to determine the lateral extent and variation of each stratum. The model was tested on two reservoirs (sandstone and limestone) using porosity as the reservoir rock property. The sandstone reservoir contained approximately 60,000 samples from 2,000 cored wells, while the limestone reservoir had approximately 24,000 samples from 430 cored wells. Within the areas of common variance tested, the model was able to distinguish four separate lithological units or zones in the sandstone reservoir, four in the Marly section and seven in the Vuggy section of the limestone reservoir. INTRODUCTION To accurately predict the movement and production of fluids from a reservoir rock, it is necessary that the reservoir engineer have a knowledge of the rock properties and their distribution throughout the reservoir. For this study, a reservoir rock is defined as a solid containing interconnecting holes or voids which occur relatively frequently and are dispersed within the rock in a regular or random manner. The fraction of bulk volume that these interconnecting voids occupy is called porosity. The rock must also possess sufficient permeability to allow fluids to move through it and it may be composed of one or more strata or lithological units. A stratum or lithological unit as defined in this study is a body or volume of reservoir rock whose properties are so distributed that its lateral and vertical extent can be traced throughout or through a portion of the reservoir. Operationally, the existence of strata are question- able unless the variance within strata is less than among strata. Within the past few years computers have been widely used as a tool for calculating movement and production of fluids from reservoirs. Most prediction models require some type of a mathematical description of certain reservoir rock properties. In the past, most of these models have been relatively simple. Some have assumed vertical variation but no lateral variation, while others have assumed lateral variation but no vertical variation. In general, most of these models have not used functional relationships to predict reservoir rock properties as functions of position. The object of this study was to develop a model which would predict lateral and vertical variations of reservoir rock properties. Since samples are usually available from only a small portion of the total reservoir rock, it seemed logical that if measurements from these samples were to be used to infer the properties of the actual reservoir, the data should be treated statistically as a sample from the total population (reservoir). Therefore, the model developed in this study to predict reservoir rock properties was a stochastic model. The model was tested using porosity (a macroscopic reservoir rock property) measurements from two reservoirs — the first, a sandstone reservoir from which 60,000 samples were obtained; and the second, a limestone reservoir with 24,000 samples. Several investigators have proposed methods to determine the vertical and areal variation of a reservoir rock property. Stiles: Dykstra and Parsons 2 and Suder and Calhoun3 have all developed waterflooding prediction techniques which assume vertical variation but no lateral variation. Stiles developed a method to segment a reservoir arbitrarily using frequency distribution. Law4 suggested that porosity has a normal frequency distribution and that permeability has a log-normal frequency distribution. Elkins and Skov 5 proposed that when a reservoir is segmented vertically, the

Jan 1, 1967

By P. G. Shewmon

Radioactive MgZA has been used to study the rate of self-diffusion in oriented single crystals of magnesium in the temperature range 468O to 635OC. The diffusion coefficients parallel and perpendicular to the c-axis are: Dl, = 1.0 exp (—32,200IRT) cm2 per sec and Dl = 1.5 exp (—32,500IR T) cm Qer sec. The ratio Dl/Dll was found to vary from 1.13 at 468 to 1.24 at 575 C. Assuming a vacancy mechanism, an explanation of this aniso-tropy of diffusion follows from a consideration of the difference in the saddle points for diffusion in and out of the basal plane. RECENT discovery of radioactive Mg2"'-' has made possible the study of self-diffusion in magnesium. The experimental procedure and the results of a study of diffusion in polycrystalline magnesium have been described in an earlier paper.V he present work is an application of the same techniques to the study of self-diffusion in oriented single crystals of magnesium. In the general diffusion problem the diffusion coefficient is a second order tensor relating the two vectors, the diffusion flux, and the concentration gradient. In a hexagonal lattice, such as magnesium, the complete determination of the diffusion coefficient D as a function of direction in the lattice requires a knowledge of D,, and D,, i.e., the diffusion coefficients parallel and perpendicular to the c-axis, respectively. It can be proven quite generally that in a hexagonal lattice D is independent of direction in the basal plane, and that out of the basal plane it varies with 0, the angle between the c-axis and the direction of diffusion, according to the equation D(B) = D,,cos2B + D,sin2B. [I] The proof of Eq. 1 depends only upon the symmetry elements of the hexagonal lattice and upon the transformation properties of a second order tensor." Therefore, Eq. 1 holds for any mechanism of diffusion and any c/a ratio. Experimental Procedure The experimental procedure used with polycrystalline specimens can be briefly outlined as follows. Radioactive Mg" was produced by bombarding a NaCl crystal with 350 mev protons and was chemically separated from the target as MgO. The Mg" was then vapor deposited on a specially cleaned magnesium specimen by heating the MgO on a tantalum ribbon in a vacuum. During the diffusion treatment, oxidation and vapor loss of the radioactive material were minimized by annealing the samples in pairs with the active faces in contact, each pair being inside a magnesium container, which was in turn surrounded by an argon atmosphere in a sealed Pyrex tube. The distance-activity profiles were obtained by measuring the activity of thin sections cut parallel to the original interface with a lathe. The only technique which was peculiar to this work was the preparation and orientation of the single crystal specimens. The single crystals used in this work were grown by E. C. Burke of the Dow Chemical Co., using a modified Bridgman method, in which the furnace and specimen were stationary while the temperature gradient moved.' In growing these crystals the starting material was distilled magnesium, the crucibles were machined from Acheson electrode graphite, and the furnace atmosphere was tank argon. The crystals were grown from sublimed magnesium with the following analysis: 0.0002 pct Al, 0.0017 pct Fe, 0.0009 pct Mn, 0.0001 pct Ni, 0.0006 pct Pb, and less than 0.01 pct Ca, 0.0001 pct Cu, 0.001 pct Si, 0.001 pct Sn, and 0.02 pct Zn. The two crystals used were roughly lh in. diam and eight in. long. The c-axis made angles of about 7" and 78", respectively, with the specimen axes. If the values of D obtained by the use of these two crystals are taken equal to D,, and D,, respectively, the error introduced by this assumption is less than 1 pct. This can be shown by combining Eq. 1, the identity sin% + cos'8 = 1, and the experimental fact that DJDn in magnesium was always less than 1.25.

Jan 1, 1957

By N. Mungan

Formation damage, i.e.. reduclion in permeability, has been generally attribuled to clay minerals which expand or disperse upon contact with water that is less saline than the connate water. Luboratory, studies show that penneahility reduction can also occur in formalions containing only nonexpandable clays such as illite or kaolinite, and can be caused also by changes in pH. Furthermore, pH changes can damage even formations that are essentially free of clays. It is suggested that permeability reduction is due to the small passages being blocked by particles, which may be dispersed clays, cemenlion material or other fine parricles. These particles are dislodged by dispersion of clays due to changes in salinity or by dissolution of calcareous cement by acids, or of silicaceous cement by alkaline solutions. In working with reservoir cores, it was found that extracted cores damaged more easily and extensively than nonextracted cores. The extent of damage depended also on tenlperatltre. INTRODUCTION Permeability is an important property of porous media and has been the subject of many studies by engineers and geologists. Many of these studies are conccrned with formation damage, i.e., reduction in permeability, resulting from exposure of oil-producing formations to water substantially less saline than the connate water. This effect causes understandable concern since during drilling, completion and production phases formations are often exposed to fresh water. The damage resulting from contact with relatively fresh water has been attributed to expansion and dispersion oF clay minerals. During laboratory investigation of the use of NaOH as a wettability reversal agent to increase oil recovery from oil-wet reservoirs, several cores used in the displacement studies suffered loss in permeability. Despite the traditional usage of NaOH for conditioning aqueous mud systems, the role of the caustic filtrate in wellbore damage seems to have been overlooked. Browning2 as recently reported on the effects of NaOH in dispersing clay minerals but he was concerned only with complications that may arise in drilling massive shale beds. The following study was made to examine the role of pH and salinity changes in core damage. Where cores from reservoirs were used, tests were performed with extracted and nonextracted cores both at room and reser- voir temperatures, since it was felt that the test environment and core condition may affect the results. Because of its limited coverage and exploratory nature, this study is not intended to provide answers to field formation damage problems. It is hoped that it will encourage research into new aspects of the permeability reduction problems, particularly those allied to new recovery and production processes. PROCEDURE In all permeability tests, fluids were pumped through the cores at a constant volumetric rate. Only deaerated fluids and reagent grade chemicals were used. The fluids were passed through two ultrafine filters before injection to remove any entrained particles. The cores, with the exception of the unconsolidated cores, were mounted in Hassler holders. Water was used to transmit pressure to the sleeve. The inlet endpiece had two entry ports which permitted scavenging one fluid with another to avoid any mixing in the small holdup volume. The cores were flushed with CO2 gas, evacuated for 5 to 6 hours and saturated with the first liquid at a pressure of 1,000 psi for 24 hours to eliminate any free gas from the cores. Pressure differences up to 20 psi were measured by transducers, calibrated in inches of water and continuously recorded. For greater pressure drops, gauges were used. All reservoir cores were cleaned with a light refined mineral oil, then with heptane, and finally dried with CO2. Compatibility tests showed that no precipitates formed when mineral oil and the crudes were mixed. Some cores were extracted in Dean-Stark-type solvent extractors using xylene and trichloroethane and dried in a vacuum oven at 450F. Each test consisted of a sequence of water, test solution, and again water flow. RESULTS AND DISCUSSION STUDIES IN BEREA CORES Salinity Contrast Berea cores 2-in. in diameter and 12-in. long were cut from sandstone quarried in Cleveland, Ohio. The clay minerals were identified by X-ray diffraction to be chlorite, kaolinite, illite and incerlayered illite. Flow of fresh water or 30,000 ppm brinc does not cause any permeability reduction (Fig. 1). However, after injection of brine the core is readily damaged by fresh water. Damage starts almost instantly as the fresh water injection is begun, and at a cumulative injection of 1.2 PV fresh water, the permeability has dropped from 190 to 0.9 md. Upon continued injection, the effluent contains clay minerals dislodged from the core. The final core per-

Jan 1, 1966

By J. S. Pascover, J. K. Abraham

The influence of the early stages of precipitation on the kinetics and structure of martensite formation in Fe-27Ni and Fe-29.5Ni alloys containing from 0 to 10 pct Ti was examined with X-ray and electron microscopy techniques. The formation of a coherent, ordered preprecipitate had a profound stabilizing effect on the austenite. The Ms was decreased by increased titanium content and aging time up to a critical time. When the critical aging time was exceeded, the Ms was observed to increase markedly. The formation of the clusters was insuppressible and the volume fraction of clusters formed during the quench was a function of the titanium content. Martensite resulting from transformation of the clustered austenite is tetragonal with the c/a ratio increasing with titanium content. A model for the tetragonality is suggested. The morphology and substructure of the m artensite is inter-preted in terms of the above information and the cur-rent models of twinned martensite. ThE ramifications of precipitation in austenite to the properties of austenite have been the subject of numerous investigations. The current research is concerned with the influence of precipitation in austenite on the kinetics and structure of subsequent marten-site formation. In a previous investigation, Abraham et al.1 followed the aging reaction in an Fe-29.5Ni-4.2Ti* (at. pct) alloy using an X-ray diffraction technique. This technique, employing a Guinier camera, provided kinetic measurements through observation of the side band position as a function of aging time. The salient results of this work were: 1) The initiation of precipitation was not suppressed by quenching, i.e., there was a finite cluster zone size at zero aging time; and 2) The hardness of the aged austenite correlated extremely well with the zone size. During the previous work it was noted that the mar-tensite formed after aging was tetragonal, substanti-ating an earlier observation.2 Systematic investiga-tion revealed that the martensite was tetragonal in both the solution-treated then quenched, and the solu-tion-treated, aged, and quenched condition, and, furthermore, that a marked stabilization of the austenite occurred as a function of aging time. The present work is concerned with documenting the tetragonality and the stabilization phenomena as well as the ob- served microstruction with a suggested rationale for the behavior noted. EXPERIMENTAL PROCEDURE The compositions of the alloys are listed in Table I. The analyses were performed after the solution treatment of the strip material. Nickel was determined using the standard dimethy1-glyoxime procedure whereas titanium was determined colorimetrically with hydrogen peroxide and volumetrically by titrating with ferric iron. The materials were melted in a 5-lb vacuum induction furnace, cast into 2-in.-diam ingots, and forged in a temperature range of 950. to 1200°C to 1/2-in. slabs. The three higher titanium containing materials cracked during forging; therefore, to get the alloys into strip form, slices 1/8 in. thick were cut from the slab, homogenized 4 hr at 1150°C, then cold-rolled to a 0.04-in. thickness. The remaining slabs were hot-rolled, homogenized 4 hr at 1065"C, then cold-rolled to a final thickness of 0.03 in. All of the heat treatments were performed under a protective atmosphere of argon. The Ms temperature for most of the alloys is below room temperature; therefore, it was possible to solution treat, quench to room temperature, polish, and then observe the transformation optically on a cold-stage microscope. To determine the effect of aus-tenitizing temperature on Ms, eight of the alloys were treated at two temperatures, 1025" and 1120°C. No measurable variations in Ms were noticed. The remaining alloys were treated at 1025°C. The specimens, : by 5/16 by 0.03 in., were austeni-tized in a vertical tube furnace under a dynamic argon atmosphere. The bottom of the tube was submerged in water for quenching purposes. The question of stabilization that may be operating at room temperature was investigated and found to be negligible. Many of the specimens were held at room

Jan 1, 1970

By R. W. Parsons, P. R. Chaney

Oil recovery by the imbibition mechanism can be important in fractured carbonate reservoirs with a bottom water drive. Laboratory experiments were performed on water-wet carbonate rocks to model this process. The results are interpreted in light of the applicable scaling laws. The imbibition production behavior of a pillar of rock subjected to a slowly rising water table can be synthesized from data on total immersion experiments on small rock samples. If the rate of water table rise is slow enough and if the physical properties are such that the imbibition zone is of a small vertical extent, then only the final oil recovery on the small samples need be known. Applying laboratory imbibition data to a real reservoir should be done with caution because of possible wettability problems and the unknown behavior of two-phase flow in fractures. INTRODUCTION The spontaneous taking up of a preferential wetting fluid into a porous medium with the simultaneous expulsion of the contained fluid is termed imbibition. One of the many physical imbibition processes is the production of oil by the taking up of water into a water-wet reservoir rock. In certain types of heterogeneous reservoirs, e.g., fractured, it is realized that imbibition alone may be the dominant mechanism. Theoretical studies of imbibition oil recovery have followed several lines of attack. The behavior of certain mathematically tractable and conceptually simple models have been analyzed. Birks1 considered a bundle of vertical capillaries model, while Perotti et al.2 and Kelemen3 used a model of a series of vertically oriented fractures. If the oil production behavior from a block of reservoir rock is known, then the cumulative behavior of a vertical stack of these blocks subjected to a rising water table can be determined by a method outlined by Aronofsky et al. 4 Knowing the capillary pressure and relative permeability functions should uniquely set the imbibition behavior for a given sample. Solutions of the partial differential equations describing the process, however, present some formidable problems. Digital computer techniques have been applied to displacement processes in which the capillary pressure has been included.5"8 More recently, similar techniques have been used by Blair 9 to calculate countercurrent imbibition behavior. The fact that imbibition behavior is described by the usual fluid flow equations (Darcy's Law and continuity equation) implies that the derived scaling laws should apply equally to this situation. Use of model experiments to study imbibition has been employed by Graham and Richardson 10 and Mattax and Kyte,11 who actually tested the scaling law applicability. This study is concerned with scaled model imbibition experiments on water-wet carbonate rocks. Of particular interest is the slowly rising water table experiment. This simulates a highly fractured reservoir with the water table rising uniformly through the vertical fracture system. Experiments were performed on different sized samples and with different rates of rise of the water-oil interface surrounding the rock pillar. Total immersion imbibition experiments on smaller rock samples were performed to test the basic linear scaling laws and to see if these simpler tests could be used to synthesize the rising water table experimental results. THEORY IMBIBITION SCALING LAWS Scaling laws for the flow of two incompressible immiscible fluids in a porous medium have been presented by Rapoport.12 These are derived directly from Darcy's Law for the individual phases and the continuity equation. Results from a laboratory model experiment will duplicate those from some reservoir prototype if a constant proportion is maintained among the three forces acting on the fluids — the capillary pressure gradient, the gravitational gradient and the flowing pressure gradient. Operation of the model (i.e., fluid injection or withdrawal) must be conducted in accordance with specific equations. If the

Jan 1, 1967