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By J. S. Aronofsky

The first step in a quantitative analysis ot the mechanism of oil displacement by water in a fractured reservoir is usually conceded to be the solution of the differential equation describing the saturation distribution of two immiscible fluids flowing in a porous medium, where the capillary pressure is taken into account. In such a system the production mechanism may consist of displacement of oil both by the flow of water due to natural or artificially imposed pressure gradients and by imbibition, which implies a flow of water not due to external pressure gradients. Owing to the presence of the two oil displacement mechanisms, the mathematical model given by the differential equation intended to describe the system may not properly represent the behavior of the physical system. In fact, in the reservoir the rate of water advance may be very slow, and in the case of a fractured reservoir with a great number of large fractures, the pressure difference determining the flow of water through the matrix may be much less than 1 lb/'psi over lengths of a few feet. In such a case, imbi-bition (the exchange between oil in the matrix and water in the fractures resulting from capillary forces) may become, with time. a significant element of the production mechanism. It occurred Lo the authors, however, that without going into a physical analysis of the process of production, it might be possible by means of simple abstract reasoning to throw some light on the variation of recovery with time under conditions occurring in a highly fractured oil reservoir with rising water table. The object of this paper is to present both the reasoning and its application to a reservoir of the highly fractured type. Specifically, the analysis given here was undertaken to try to explain the increase of recovery (as defined later) with time as observed in this reservoir, without having to assume unlikely variations in the reservoir parameters with depth. This attempt has been successful as will become clear upon comparison of the computed recoveries with the actual field data. ABSTRACT MODEL Let us consider a small volume. of porous matrix saturated with oil at time, t = 0. Let the process of oil displacement by water start at time, t = t,,. At some time, t, the process will have terminated. Then a volume of oil equal to or smaller than the original oil contained in the matrix will have been produced. The first basic assumption that describes the model and guides the forthcoming reasoning is that the oil production from the small volume. dv, is a continuous monotonic function of time and that it converges to a finite limit. Such an assumption is not inconsistent with the results of laboratory waterflood tests as well as with results of imbibition tests where this is, in fact, observed. The second basic assumption is that none of the properties which determine the rate of convergence change sufficiently during the process to affect this rate or the limit. Let it be assumed that the form of the function of time relative to production from the matrix volume. dv, is given by where V,(t) is the volume of oil produced up to that time t. R is the limit toward which the recovery converges, A is a constant giving the rate of convergence, and V,(t) is the volume of oil originally in place in the volume, dv. It should be noted that recovery at time I will be understood here to he It follows that r. tends to R as t tends to infinity. CONSTRUCTION OF RESERVOIR FROM ABSTRACT MODEL Let the reservoir consist of a series of identical blocks of porous matrix stacked vertically and separated by fractures. Let each of these blocks satisfy the conditions of our abstract model. These conditions are: (1) that recovery is a continuous mono-tonic function of time converging to finite limit, and (2) none of the properties that determine the rate of convergence change sufficiently to affect the rate or the limit. Let water be rising in fractures so that oil production from any part of the block starts when the water comes in conLact with it. TOTAL RECOVERY FROM THE RESERVOIR COMPARED TO RECOVERY FROM A SINGLE MODEL ELEMENT As stipulated in Eq. 1, in the case of the abstract model,

By H. T. Clark

NO previous determinations of the deformation or recrystallization textures of titanium or of titanium-base alloys have been reported in the literature. The room-temperature structure of titanium is hexagonal close-packed with a c/a ratio less than 1.633. It would be expected, therefore, to have a rolling texture similar to that of other hexagonal close-packed metals, namely (0001) [1010]. Burgers and Jacobs1 have shown that zirconium, a metal isomorphous with titanium in its structure and similar in many of its properties, has such a texture with a scatter of the basal plane toward the transverse direction. This scatter is in the opposite direction from that found in magnesium by Bakarian2 but similar to that reported by Smigelskas and Barrett3 or beryllium. The rolling and annealing textures reported here for high-purity iodide titanium are significantly different from the . textures of any other hexagonal close-packed metal. All titanium used during this investigation was prepared by the iodode process." The annealed hardness of this material varied from 73 (material used for sample No. 2) to 97 Vickers hardness number. An estimate of the chemical composition of this grade of titanium has been reported by Finlay and Snyder.5 With one exception, shown in table I, the as-deposited titanium was cast into 10 to 20 g ingots in an electric arc furnace in purified argon before being rolled to sheet. The cast ingots were forged and ground until their cross-section was approximately rectangular, annealed 1 hr at 700°C in vacuum and cold rolled. Rolling was carried out in a two-high, 4 in. diam mill, using reductions no greater than 10 pct per pass. The direction of rolling was reversed after each pass, and, in order to avoid temperature effects, the sheet was allowed to cool after each pass. Unless the rolled sheet was sufficiently thin for X-ray penetration (about 0.004 in.), it was reduced to this thickness by pickling. Because of the possibility of introducing twinning or other deformation during grinding, no attempt was made to maintain uniform thickness of the sample during pickling by intermediate grinding or sanding operations. Those samples to be used for determining the annealed texture were recrystallized by vacuum annealing the cold-rolled sheet for 1 hr at 500°C. These thin samples were held between thick titanium sheets during annealing to prevent distortion. Table I outlines the rolling and annealing schedule of those samples for which photograms or texture patterns are shown. X-ray Techniques The usual techniques for determining textures were employed during this work. Molybdenum radiation was used for the transmission exposures and copper radiation for the glancing angle ones. Since titanium fluoresces under these conditions, it is necessary to employ a filter between the sample and the film. The Kß radiation filters are very satisfactory for this purpose. Sufficient grains having favorable orientation were present in both the cold-worked and in the cold-worked—500°C annealed samples to provide satisfactory patterns with the samples stationary. Because of the difficulties of comparing intensities of transmission photograms with those obtained

Jan 1, 1951

By R. L. Perrine

This paper presents results obtained by consider ation of unstable miscible displacement within a porous medium as a quasi-turbulent displacement process, that is, a process characterized by fluctuations around a simpler, mean flow behavior. The instability usually results from the miscible displacing fluid having a viscosity lower than that of the displaced fluid. Such instability is evidenced in suitable experiments by the presence of viscous fingering. A unified theoretical relationship applicable to both stable and unstable displacement is derived. Parameters in the theory are obtained by empirical means. Although the theory describes an idealized conceptual model, agreement with experiment is quite reasonable up to moderately adverse viscosity ratios, such as 17:1. INTRODUCTION Many experimental studies of miscible displacement in porous media have been conducted with prediction of reservoir displacement efficiency as the ultimate objective. Most such studies have utilized lower displacing than displaced fluid viscosity, scaled to potential reservoir fluid pairs. Theoretical approaches have been largely limited to unit viscosity ratios, however, in spite of the necessity for an understanding of the mechanism of the unstable, adverse viscosity ratio displacement process. An obvious reason is the difficulty of describing in mathematical form the viscous fingering characteristic of these conditions. Observation of experiments conducted with dyed fluids in transparent systems suggests an analogy between unstable miscible displacement and turbulent flow in a pipe. In both cases there are fluctuations around a simpler, mean flow behavior. An important difference is that flow behavior of interest in the porous medium is entirely transient, contained within a transition zone between displacing and displaced fluids. Transient behavior complicates description in that coefficients in the equations become variables rather than constants. In the study reported here, the analogy with turbulent flow has been used in treating unstable miscible displacement as a quasi-turbulent displacement process. The purpose has been to derive, even if restricted to an idealized conceptual model, a unified theoretical relationship applicable to both stable and unstable displacement. A relationship meeting these specifications up to moderately adverse viscosity ratios, such as 17:1, is presented. One fluctuation parameter in the theory and dispersion coefficients are obtained by empirical means. The idealized theory is compared with experimental results. UNSTABLE MISCIBLE DISPLACEMENT AS QUASI-TURBULENT DARCY FLOW The miscible displacement of one fluid by another within a porous medium is considered in this study. Flow conditions are such that Darcy's law is applicable. It is further assumed that, by the stability criterion proposed by perrine,1 initial flow conditions lie well within the regime of instability. Thus substantial viscous fingering is assured. We wish to show how this flow regime can be represented as quasi-turbulent. That is, the Reynolds number for the established flow conditions is below that for inertial or turbulent flow within a porous medium, and lies within the regime for which Darcy's law is valid. Yet flow behavior can be described as the combination of some relatively simple average result, and characteristic fluctuations that are superimposed on the simpler behavior. Stated another way, flow behavior includes the movement of layers of fluids with different velocities past or over one another. Such descriptions are characteristic of turbulent pipe flow. The fluctuations in the present case are a direct consequence of the local viscous fingering which accompanies the unstable displacement process. Should displacement become stable, fluctuations would die out. It is of particular importance to note that fluctuations such as these can interact in a way that contributes to material transport by the basic flow. The basic transport equations required for engineering calculations must be modified to reflect this fact.

By Stewart Murray, Philip Klapwijk

INTRODUCTION Forecasting commodity markets is like predicting winners in a horse race: to get the answers right, one needs both luck and judgement. Commodity analysts bear some resemblance to racing tipsters as they try to convince interested parties that they have an inside track on which metal is going to win the great minerals race of the 1990s. Commodity analysts share some features with the gentlemen of the turf: • They influence other people in how to spend risk capital, • They don't put their own money at risk, and • If their tips consistently fail to deliver, then they end up looking elsewhere for employment. In order to find winners we need to know about the kind of race we are in and the strengths and weaknesses of all the runners. Miners are not interested in a five furlong sprint: their race is a long distance affair -- after all, the lead-times between discovery and start-up generally approach a decade for mines that will provide the staying power which leaders require in this industry. We need to look at the environment in which our commodities will be competing: in racing parlance, the going. Our equivalent is the economic background: just as some horses are at a relative advantage when the going is soft, so some commodities will do better than others if economic growth is sluggish. If we are going to pick the winners for the late 1990s, and as an industry, make the right investment decisions, nothing is more important than being able to forecast (with at least a semblance of accuracy) how and where the world's economy is going to develop in the next decade. In addressing the question of whether minerals are going to be leaders in the 1990s, this paper considers the idea that it will increasingly be the world outside the industrialised OECD that will provide the incremental growth in demand for mineral products. Economic growth in the Developing World is fundamentally different from that in the OECD, and the pattern of demand for materials in relation to economic output is much more favourable than in the OECD. If we are to forecast the future, we need to be able to understand the past, both in the boom times of the so called Golden Sixties and in the lean years that followed them. This should help us to decide whether the future is going to be like one or other of these extremes or, on the other hand, a return to normality. Having forecast the going, we can look at individual competitors. • Which are best placed to take advantage of the economic, social and industrial trends that we can now dimly foresee? • Which can resist the continued onslaught of the new materials and technologies? • Which of them will best weather the economic storms (assuming that recessions have not yet been abolished)? If we can provide answers to these questions, we will be well on our way to picking winners, i.e., the metals and minerals that will reward their owners with growing demand, steady (and high) prices leading to profits beyond the dreams of avarice.

Jan 1, 1990

By O. P. Quist, S. H. Carpenter

The internal friction of single-crystal LiF has been investigated as a function of crystal orientation, while simultaneously applying a static compressive load. Three different crystal orientations were used, these being samples with the (100), (110), and (111) directions along the sample length. Results show the internal friction measured to be similar in appearance but different in magnitude for the (100) and (110) samples. With both orientations, application of a static stress caused an increase in the amplitude-independent damping, which recovered with time. The amplitude-dependent damping was found to first decrease with load up to the yield stress and then increase rapidly. Samples of the (111) orientation were found to have no measurable internal friction even when loaded up to 3.0 kg per sq mm. These results are discussed in terms of current theories of internal friction in ionic crystals. This paper presents the results of an investigation of the dislocation mobility and dislocation motion in high-purity single-crystal LiF at applied stress levels up to the yield stress. Internal friction measurements of the dislocation damping while simultaneously applying a static compressive load was the experimental technique used. LiF crystals much prefer to slip on the (110) set of slip planes. However, with a suitable stress distribution they can be forced to slip on the {100} set of slip planes.' For both sets of slip planes the slip direction is the same, namely (110). The object of this investigation was to try and learn more about the dynamical properties of dislocations on the different slip systems in LiF crystals. EXPERIMENTAL PROCEDURE Dislocation damping was measured, in terms of the log decrement, using a five-component marx2 composite piezoelectric oscillator. The apparatus used allows one to measure the dislocation damping while simultaneously applying a static compressive load on the sample. A schematic of the apparatus used is shown in Fig. 1 and a complete discussion of its construction and operation is given elsewhere.3 All measurements were made at room temperature with a longitudinal resonant frequency of approximately 50 kc per sec. Damping measurements were made using longitudinal vibrations with strain amplitudes from up to 10. Static loads up to 3.0 kg per sq mm were applied to the sample while the damping was being measured. Samples used in this investigation were high-purity single crystals of LiF purchased from the Harshaw Chemical Co. All samples were approximately of an in. square and were hand-ground in length to one-half wavelength to match the resonant frequency of the driver and gage quartz crystals. Samples of three different crystallographic orientations were used, namely, crystals with the (loo), (110), and (111) direction parallel to their length. The magnitude of the damping is a direct measure of the area on the slip planes swept out by dislocations during a complete oscillatory cycle. With a sample of the (100) orientation the maximum applied shear stress, due to longitudinal vibrations, is on the (110) slip planes with zero shear stress on the (100) slip planes. Thus, damping measured from a (100) sample is due entirely to dislocation motion taking place on the (110) set of slip planes. Similarly, for a sample of the (111) orientation there is zero shear stress on the (110) set of slip planes and the damping measured from a sample of this orientation is due entirely to dislocation motion on the (100) set of slip planes. Samples of the (110) orientation will have a component of shear stress on both sets of slip planes and

Jan 1, 1969

By C. D. Cochran, F. H. Deily, M. M. White, Victor Horner

A laboratory study of the effects of physical and easily measured rheological properties upon dynamic filtration was carried out. The purpose was to determine the factors affecting dynamic filtration and thus learn how to control this important property. The recommended procedure for determining the amount of fluid loss prescribed by API Code RP 29 "Field Procedure for Testing Drilling Fluids,"' is very useful for mud conditioning purposes, but inadequate for comparing filtration properties of different muds under dynamic conditions. Where dynamic filtration control becomes important for purposes such as logging and coring, other means of evaluating filtration properties are needed. A special device and testing technique were developed to provide reliable data on filtration characteristics of different fluids under dynamic conditions. Liquid saturated rock samples were drilled with a microbit, and the amount of connate liquid displaced by the fluid being investigated was measured. The empirical testing procedure was considered reliable. A large number of laboratory-prepared and field-mixed dritling fluids with a wide range of physical properties were studied. These properties included: (I) shape of consistency curves, (2) apparent viscosity, (3) plastic viscosity, (4) yield value, (5) density, and (6) API filter loss. Test results indicate that very little, if any, trend could be established between changes in these fluid properties and dynamic filtration. INTRODUCTION During the process of drilling, excessive loss of liquid from the mud to the formation is undesirable for many reasons. Filtration can reduce production-zone permeability, cause sloughing of formations, affect electric log curves, and render the fluid data obtained from cores unreliable. Thus, it is very important that we gain a knowledge of the factors that control filtration. It is generally agreed that in any type of filtration (static, dynamic, or combinations thereof), the mechanics of filtering depend in great part upon the composition of the fluid. Moreover, it is also true that the physical and rheological properties are influenced by the composition of the fluid. Indirectly, then, it was hypothesized that a relationship existed between dynamic filtration and physical-rheological properties, two effects of a common cause—fluid composition. This paper discusses an attempt to relate filtration-while-drilling to physical and easily measured rheological properties. It is believed that the results of this study may prove useful to others in the industry who are working on the problem of understanding filtration. The industry accepted practice for determining fluid loss from drilling mud is described in API Code RP 29. The practice is to measure the amount of filtrate that passes during a given interval of time from a quiescent drilling fluid under applied pressure through a piece of filter paper. This is primarily a test of static filtration properties. Other investigators have studied filtration under dynamic conditions. Williams5 and Pro-kop5 studied radial filtration and filter-cake buildup by circulating fluid through a porous cylinder under conditions similar to actual mud flow. Nowak,4 Krueger,3,4 and Vogel3 studied the effect of filtration upon permeability by flowing mud past the face of rock Samples. In their tests, the bit action was simulated by mechanical scrapers that kept the filter cake from building up. Ferguson and Klotz2 studied three types of filtration: static, dynamic, and beneath-the-bit. They investigated each type separately, using a model well in which bottom-hole hydraulics and mechanics were closely approximated.

Jan 1, 1958

By F. J. Haller

IN 1943, we found, in the new Mather operation, a very unusual and disappointing condition in the footwall rock where all of our main haulageways were to be located. With the exception of a few hundred feet out of the thousands then planned and since driven, all of the openings require support. In general, the ground is not particularly heavy, at least by our standards, but it must be supported and the back carefully covered. Also, our operations require rather wide plat openings (16 to 18 ft) and rather flat curves at the turn-outs, all of which adds to the problem. When this completely unforeseen condition was discovered, ordinary timbering was the only answer, because of the impossibility of obtaining adequate steel supplies in time due to war shortages. Then by the time steel supplies were obtained and a practice developed, we found ourselves with between four and five miles of main haulage drifts and plat openings of a permanent nature, all of which were supported by hardwood timber, some of which had already rotted to an unsafe degree. Also, our drifting program was adding some two miles per year to the above figure. F. J. HALLER, Member AIME, is Superintendent, Mather Mine, Cleveland-Cliffs Iron Co., Ishpeming, Mich. AIME Columbus Meeting, September 1949. TP 2840 A. Discussion (2 copies) may be sent to Transactions AIME before May 31, 1950. Manuscript received Aug. 22, 1949. Revision received Jan. 17, 1950. To give all of the details of our experiments, studies, and experiences would fill a large book, but we were satisfied that our organization had done an excellent job, starting from scratch. You can appreciate our surprise when we discovered that we had added very little to an existing record. Attention was called to a footnote in a copy of "Carnegie Pocket Companion" year 1923. The note read: "Full information as to uses of H-Beams is given in pamphlet entitled 'Steel Mine Timbers.' " A search of our Engineering Library brought to light a pamphlet printed in 1911 showing extensive use of steel for this purpose. Except for welding in place of riveting, we have added very little to the designs in that book. We have, however, developed an experience which proves, at least to our own satisfaction, that steel mine supports pay off under the proper conditions. We are now convinced, in spite of the relatively high initial cost of materials, that steel sets, because of comparatively low installation cost, are actually cheaper than either treated or untreated wood sets, if they are properly designed and adapted. Several Sections in Use: Convenience guided our first experiments in steel sets, since for a number of years, we had used the 4-in. WF, 10 lb per ft section in 10-ft lengths as safety forepoles along with wood forepoles. This section replaced the 40-lb rail which had formerly been used for the purpose. Having the 4-in. WF sections on hand, it was natural that our first experiments in steel sets involved their use. Later, the rolling of the 10-lb section was discontinued in favor of the much stronger 13-lb section, which is now standard for both legs and caps in areas of no particular weight, but which, none the less, require permanent support. Our experiments involved the use of the 10- and 13-lb sections as legs and 6- and 8-in. I beams, 16 and 23 lb per ft, respectively, as caps. Experience soon indicated that, if the ground were heavy enough, and the opening wide enough to require a cap stronger than 13-lb, the 8-in, 23-lb should be used, eliminating the 6-in. I beam. We now know that the 8-in. WF section of the same weight, which we propose to use in the future, is considerably stronger for the amount of money involved. Comparative Strengths: Tables I to IV giving strengths of several species of timbers as compared with the structural sections that we now use have been prepared in accordance with accepted practice. Experience indicates that failure due to compression perpendicular to the grain of the wood does not destroy the effectiveness of a wood set frequently enough to be a practical factor. Therefore, no table of these values is included.

Jan 1, 1951

By F. J. Haller

IN 1943, we found, in the new Mather operation, a very unusual and disappointing condition in the footwall rock where all of our main haulageways were to be located. With the exception of a few hundred feet out of the thousands then planned and since driven, all of the openings require support. In general, the ground is not particularly heavy, at least by our standards, but it must be supported and the back carefully covered. Also, our operations require rather wide plat openings (16 to 18 ft) and rather flat curves at the turn-outs, all of which adds to the problem. When this completely unforeseen condition was discovered, ordinary timbering was the only answer, because of the impossibility of obtaining adequate steel supplies in time due to war shortages. Then by the time steel supplies were obtained and a practice developed, we found ourselves with between four and five miles of main haulage drifts and plat openings of a permanent nature, all of which were supported by hardwood timber, some of which had already rotted to an unsafe degree. Also, our drifting program was adding some two miles per year to the above figure. F. J. HALLER, Member AIME, is Superintendent, Mather Mine, Cleveland-Cliffs Iron Co., Ishpeming, Mich. AIME Columbus Meeting, September 1949. TP 2840 A. Discussion (2 copies) may be sent to Transactions AIME before May 31, 1950. Manuscript received Aug. 22, 1949. Revision received Jan. 17, 1950. To give all of the details of our experiments, studies, and experiences would fill a large book, but we were satisfied that our organization had done an excellent job, starting from scratch. You can appreciate our surprise when we discovered that we had added very little to an existing record. Attention was called to a footnote in a copy of "Carnegie Pocket Companion" year 1923. The note read: "Full information as to uses of H-Beams is given in pamphlet entitled 'Steel Mine Timbers.' " A search of our Engineering Library brought to light a pamphlet printed in 1911 showing extensive use of steel for this purpose. Except for welding in place of riveting, we have added very little to the designs in that book. We have, however, developed an experience which proves, at least to our own satisfaction, that steel mine supports pay off under the proper conditions. We are now convinced, in spite of the relatively high initial cost of materials, that steel sets, because of comparatively low installation cost, are actually cheaper than either treated or untreated wood sets, if they are properly designed and adapted. Several Sections in Use: Convenience guided our first experiments in steel sets, since for a number of years, we had used the 4-in. WF, 10 lb per ft section in 10-ft lengths as safety forepoles along with wood forepoles. This section replaced the 40-lb rail which had formerly been used for the purpose. Having the 4-in. WF sections on hand, it was natural that our first experiments in steel sets involved their use. Later, the rolling of the 10-lb section was discontinued in favor of the much stronger 13-lb section, which is now standard for both legs and caps in areas of no particular weight, but which, none the less, require permanent support. Our experiments involved the use of the 10- and 13-lb sections as legs and 6- and 8-in. I beams, 16 and 23 lb per ft, respectively, as caps. Experience soon indicated that, if the ground were heavy enough, and the opening wide enough to require a cap stronger than 13-lb, the 8-in, 23-lb should be used, eliminating the 6-in. I beam. We now know that the 8-in. WF section of the same weight, which we propose to use in the future, is considerably stronger for the amount of money involved. Comparative Strengths: Tables I to IV giving strengths of several species of timbers as compared with the structural sections that we now use have been prepared in accordance with accepted practice. Experience indicates that failure due to compression perpendicular to the grain of the wood does not destroy the effectiveness of a wood set frequently enough to be a practical factor. Therefore, no table of these values is included.

Jan 1, 1951

By M. P. Tixier, K. S. Kunz

A method for the interpretation of temperature curves recorded in gas producing wells is described. One essen-tial feature of the method is a simple graphical construction which conveniently reflects the amount of gas flowing from a given producing formation. This method, applied in conjunction with the Induction Log and radioactivity logs, is valuable to determine the points of entry of gas and to estimate the over-all thickness of the producing zones and their respective contributions to the total production. The method in particular is helpful in evaluating the effect of fracturing operations. An outstanding result of the application of the method is to bring to the light the relative importance of sand-shale interfaces in the production of gas. The paper is illustrated with field examp1es. INTRODUCTION The electrical logging tools involving conventional systems are not applied in wells which do not contain water base mud (empty holes, or wells filled with oil base mud), because of the absence of electrical connection between the electrodes and the surrounding formations. It is, therefore, common practice in this case to use other methods which do not require the presence of a conductive fluid in the borehole: resistivity log with scratcher electrodes, Induction Log, radioactivity logs, temperature log. . . . Such conditions are encountered in some regions, as the San Juan Basin, N. Mex., where a technique of drilling gas wells, using gas as a drilling fluid, has been introduced in the last two years. By the middle of 1953, an appropriate method for the logging of these wells was devised on the basis of field tests and of theoretical studies. It is the purpose of the present paper to give a description of this method. In these wells the logging operations are performed during the process of gas production, so that the temperatures in the boreholes are strongly affected by the cooling due to the expansion of the gas. On the other hand, a special thermometer, with a high sensivity and a short time constant, has been recently made available, which has enabled much more detailed and accurate recordings of the borehole temperatures than with the conventional instruments. As a result of these two circumstances, the temperature log constitutes the essential element of the method, in making possible the detection of the gas producing zones, the definition of their boundaries, and the estimation of the respective contributions of each separate zone to the total production. The method also involves the radioactivity and Induction Logs, as auxiliary documents. These logs in the present instance are helpful in the determination of the reservoirs. However, the information they give in this respect is limited. This comes from the fact that, due to the absence of the MicroLog and/or MicroLaterolog and of the SP log, the estimation of formation factors and connate water salinities is somewhat conjectural. Furthermore, little help is obtained from the Neutron log for the evaluation of porosity and of formation factor because the variations of gas saturation affect the Neutron log in a way similar to the variations of porosity. It should be said also that even an exact knowledge of the gas saturation of the reservoir beds would not

Jan 1, 1956

By E. Eichen, G. S. Ansell. L. R. Sefton

A Technique for the Preparation of Thin Films of Two-Phase Alloys Suitable for Use in Transmission Electron Microscopy In order to obtain foil sufficiently thin to permit transmission electron microscopy of two-phase alloys, particularly alloys in which the second phase is present as a very finely dispersed second phase, a technique has been developed to permit the thinning of these materials without either the large degree of pitting present in the electrochemical or chemical thinning process or the slicing of the second phase particles accompanying the mi-crotoming process. The metal or alloy to be thinned is first ground to initial sheet thickness of approximately 0.002 in. by hand grinding on 4/0 emery paper. This starting sheet of material is then reduced in cross section by an air-abrasion technique using an S. S. White dental abrasive unit. This unit consists of a supply of compressed CO, which provides a stream of high velocity gas impinging on the metal surface. Incorporated in the machine is a hopper-type of device in which fine abrasive particles of alumina are introduced into this high velocity gas stream. The abrasive particles are irregular in shape, approximately 30 across. If any particles are introduced into the sample during thinning, they should be readily observable. Impingement of this gas abrasive mixture on the metal surface causes rapid removal of the metal in a rather uniform manner. The rates of metal removal may be adjusted by both regulating the gas pressure and amount of abrasive material introduced into the gas stream. By moving the gas stream abrasive mixture slowly about the specimen or sheet surface, a large area of the sheet may be uniformly reduced to a thickness which is then suitable for use in transmission electron microscopy. Attendant with this metal removal is a result in cold working of the metal surface due to the impingement of the abrasive particles. The resultant foils, therefore, if made from materials which are desirable to view in the annealed condition, have to be subsequently heat treated. If the alloy from which these foils have been made has been initially heavily worked or deformed during manufacture, then no subsequent heat treatment is, necessary as in the case of the SAP-type alloys. Following this initial abrasive thinning technique, the material is then given a final electropolish which is just sufficient to remove any oxide which has formed on the metal surface during the abrasion technique. Care has to be exercised in this technique to make sure that none of the attendant problems associated with the chemical or electrochemical removal process are encountered. An electrolyte solution which has been found suitable for aluminum-aluminum oxide SAP materials is one containing 78 ml of perchloric acid, 120 ml of distilled water, 700 ml of ethanol, and 100 ml of butylcellosolve. The current density used is 1 amp per sq cm and a polishing time of 3 sec on each side of the foil is used. Extreme care must be used in choosing the current density and time to ensure that just the oxide film on the specimen is removed. Times or current density which are greater than this will lead to perforation of the film due to the removal of the A1,0, particles or a complete loss of the film due to complete solution of the matrix. Once the oxide film is removed the specimens must be kept in alcohol until placed in the microscope to prevent any further oxidation. Fig. 1 shows -an electron micrograph at X28,000 of a thin foil of an aluminum-aluminum oxide SAP-type alloy prepared using this technique. The alloy consists of a matrix of commercial purity aluminum containing a very finely dispersed second phase of aluminum oxide flakes. In the electron micrograph, the dark patches are the aluminum oxide particles. The lighter portions of the micrograph are the aluminum matrix. Within the aluminum matrix, the dislocation structure of the alloy is clearly visible. This structure consists of intersecting twin boundaries and single dislocations. No abrasive particles were observed in the samples. In addition, thin films of commercial purity aluminum were prepared using this method and observed in the electron microscope. Here also, there was no evidence of abrasive particles introduced in the samples. The technique presented provides a satisfactory method for the production of thin films of aluminum-aluminum oxide SAP-type alloys for use in transmission electron microscopy where none of the usual thinning techniques appears to be satisfactory.

Jan 1, 1962

By Lo-Ching Chang, J. Chipman

The perennial and increasing interest in the chemical behavior of steelmaking slags has led to numerous attempts to formulate the thermodynamic properties of these solutions. The classical view is that of a solution of the component oxides in which certain acidic oxides are more or less completely held in combination with basic or metallic oxides, the nature of the interoxide compounds being derivable from the chemical behavior of the slag or from the mineralogy of a solidified specimen. The known electrical conductivity of slags has pointed to the existence of ions in the solution and a number of attempts have been made to account for the observed facts of slag behavior on the basis of a theory of complete ionization of the solution. It is the purpose of this paper to examine, in the light of ionic theory, a number of recently published series of data on slag-metal and slag-gas equilibria, with the purpose of obtaining a more complete or more satisfactory generalization than has been possible on either of the single bases of simple compound formation or complete ionization. The attempt to formulate the ionic constitution of a complex solution is fraught with many uncertainties. An ion is not something that can be plucked from the solution and examined in detail, nor can its true formula be determined with certainty by any single experimental method. In attempting to express the composition of a slag by various ionic formulas it can be expected that alternative hypotheses of essentially equal merit will present themselves. In the present state of early development of the ionic theory of slags, it may be necessary to make some rather arbitrary choices of ionic formulas in the absence of su- cient information to yield complete certainty. Acids and Bases The classification of slag-forming oxides as acidic or basic apparently dates back into the days of Berzelius. It is difficult to see how the concept could have originated in the early twentieth century when it was fashionable to define an acid or a base as an aqueous solution containing hydrogen or hy-droxyl ions. It is, however, entirely consistent with the modern and more general theory of acids and bases. In this theory, as originally formulated by G. N. Lewis,' a basic molecule is one that has an electron pair which may enter the valence shell of another atom thus binding the two together by the electron-pair bond. An acid molecule is one which is capable of receiving such an electron pair into the shell of one of its atoms. The acid, the base, and the product of neutralization may be either ions or neutral molecules. The product of such a reaction may itself be a base or an acid if it is further capable of giving or accepting an electron pair. Thus a base is a donor of electrons, an acid, an acceptor. In oxide slags the typical and ever-present base is oxide ion, 0-—. In behavior and in importance it is analogous to hydroxyl ion, OH-, which is the typical base of aqueous solutions. There is nothing in the chemistry of slags which is quite analogous to the acid H30+ in aqueous solutions. This is not surprising for in slag systems there is nothing which can be designated as a solvent and no ubiquitous positive ion. The chemistry of slags is in fact more complex than the chemistry of aqueous solutions and the concepts which must be evoked in its study are correspondingly broader. In seeking a basis for a classification of slag-forming oxides as basic or acidic it must be remembered that these terms are not absolute but relative. A substance which acts as a base toward a second substance may act as an acid toward a third. This is less likely to happen among strong bases or acids than among the weak ones; there are numerous examples of weak acids which under the influence of a stronger acid behave as weak bases. Such substances are called amphoteric. A classification of the glass-forming oxides has been proposed by Sun and Silverman² and further developed by Sun3 in which the oxides are arranged in order of decreasing acidity or increasing basicity, each substance being potentially capable of acting as an acid toward substances below it in the list and as a base toward those above it. It is based upon the relative strengths of the metal-to-oxygen bond as determined by the energy required to dissociate the oxide into its component atoms.' Data are available for computation of this energy, at least approximately, for the oxides of slags and glasses. In general those oxides from which it is most difficult to remove the positive atom are the strong acids while those in which it is most loosely held are the strong bases. It is in the latter, of course, that formation of oxide ion occurs most readily as, for example, in CaO which in solution ionizes to form the weak acid Ca++ and the strong base O—. The order of arrangement found by Sun is shown in the first column of Table 1, to which have been added the data for

Jan 1, 1950

By A. F. van Everdingen

The pressure drop in a well per unit rate of flow is conrolled by the resistance of the formation, the viscosity of the fluid. and the additional resistance concentrated around the well bore resulting from the drilling and completion technique employed and, perhaps, from the production practices used. The pressure drop caused by this additional resistance is defined in this paper as the skin effect. denoted by the symbol S. This skin effect considerably detracts from a well's capacity to produce. Methods are given to determine quantitatively (a) the value of S, (b) the final build-up pressure, and (c) the product of average permeability times the thickness of the producing formation. INTRODUCTION Equations which relate the pressure in a well producing from a homogeneous formation with pressures existing at various distances around the well are generally used within the industry. The relation ii quite simple when the fluid flowing is assumed to be incompressible. It becomes somewhat more complicated when the flowing fluid is considered compressible so that the duration of the flow can he considered. In each case the major portion of the pressure drop occurs close to the well bore. However analyses of pressure build-up curves indicate that the pressure drop in the vicinity of the well bore is greater than that computed from these equations using the known, physical characteristics of the formation and the fluids. In order to explain there excessive drops it is necessary to assume that permeability of the formation at and near the well bore is substantially reduced as a result of drilling. completion and, perhaps. production practice. This possibility has been recognized in the literature. A method to compute the pressure drop due to a reduction of the permeability of the formation near the well bore. which is designated as the skin effect. S, is given in the following paragraphs. To start, equations normally used to describe flow in the vicinity of a well are given without considering this effect. These equations then are modified to include the effect of a skin on the pressure behavior. Finally a method is given to estimate the effect of the skin on the pressure and production behavior of a well. PRESSURE EQUATIONS Incompressible Fluid Flow If p is defined as the flowing pressure in a well of radius the pressure at distance r from the well has been shown to be:" The total pressure drop between the drainage boundary, and the well bore is given by These equations are valid only if the flow towards the well occurs in a horizontal homogeneous medium and the fluids are incompressible. The assumptions imply that all fluid taken from the well enters the system at r a condition rarely encountered in practice. Compressible Fluid Flow, Steady State A more realistic equation is obtained if it is assumed that the compressibility, c, of the flowing fluids is small and has a constant value over the pressure range encountered. After the well has been producing for some time so that its rate has become constant and steady state is reached, the pressures throughout the drainage area are falling by the same amount per unit of time, and the pressure differences between a point in the drainage area and the well are constant. When these conditions are met. the rate of production, q, from a well is equal to where dp/dt is the pressure drop per unit time. The fluid flowing at a distance from the center of the well is equal to From the last equation and from Darcy's law it can be shown that The equation holds for a depletion-type reservoir of radius drained by a well located in its center, provided the compressibility of the fluid per unit pressure drop is small and constant, and no fluid moves across the boundary Compressible Fluid Flow — Nonsteady State Table 111 of reference (5) shows the relationship between the pressure at the well bore and the reduced time, The pressure-drop function, p represents the drop below the original reservoir pressure, p caused by unit rate of production for several values of R, the ratio of drainage boundary radius to well radius, r In most reservoirs the values of approach infinity. and under these conditions the values of p shown in Table I of reference (5) can be used where p then signifies the difference between the pressure in the well and the prevailing reservoir pressure per unit rate of flow. The total pressure drop below prevailing reservoir pressure amounts to where the factor converts the cumulative pressure drop per unit rate of production to cumulative pressure drop for actual rate. q. For values of T > 100 the P function may be written (equation VI-15 of reference 5) as Using the time conversion the difference in pressure between reservoir and well becomes If values for the physical constants of the formation and the fluids are inserted, it is found that T exceeds 100 after a few seconds of production (or closed-in time), so that the approximation becomes valid almost at once. A simple relation between the pressure in the well and in the reservoir can also be derived by considering the well as a point source"" '" instead of a unit circle source, that is, by using Lord Kelvin's solution instead of the unit circle source

Jan 1, 1953

By James J. Bean

HE task of measuring the specific gravity of the -*- operating medium in a heavy-media separation system has never presented a particularly difficult problem because the medium is fairly stable and the overflow of the separatory vessel, as well as its underflow, can be sampled easily and accurately and the specific gravity of the suspension determined easily by weighing a known volume. However, while this method is simple and accurate it does require the operator to take the sample by hand and to weigh it and there is considerable temptation to avoid the periodic sampling if everything seems to be going well, or if something is occupying the attention of the operator. Furthermore all operators do not sample in exactly the same manner and considerable practice is required for two operators to be able to "check" each other to the last few hundredths, particularly if the sample is cut underneath the drainage screen where location of the point of sampling and load on the screens tends to influence the determination. While none of the above presents much of a problem, we have all recognized that some mechanical method of continuous measurement and recording would be advantageous since the operator would merely have to glance at the meter to check the gravity and to have an indication of the trend of any changes. Also if the instrument were of the recording type, a permanent record would be available for the guidance of the superintendent. The Eagle-Picher Mining and Smelting Co. was the first heavy-media user to actually install such a recording meter. In 1946 they installed in their Central Mill at Cardin, Okla., a specific gravity recorder manufactured by the Bristol Co. of Water-bury, Conn. R. A. Barnes, of the Bristol Co., working with E. H. Crabtree, Jr. and Elmer Isern, of Eagle-Picher, made the application and worked out the problems of sampling and measuring. Their attempts to measure the specific gravity of the medium in the cone itself were not entirely successful and they resorted to an outside sample tube for actually making the determination. Because of the particular flowsheet used, it was possible to tap off from the medium return pipeline a stream of medium and divert it into the sampling tube, which was provided with a constant level overflow and a spigot underflow, and into which the bubbler tubes dipped. The Eagle-Picher installation was successful and its possibilities were recognized by the Mineral Dressing Laboratory of the American Cyanamid Co. It was decided to install a similar unit in the heavy-media pilot plant to investigate further its possibilities. Chief among these was the continuous record which it was felt would be proof of the steadiness of the gravity in a heavy-media cone, something which is not always appreciated by POtential users. Because the heavy-media pilot plant is required to operate at a wide range of specific gravities, it was realized that the unit would have to record all gravities from 1.25 to 3.50, and do it to the nearest 0.01. It would not be necessary to record all of this wide range on a single chart and the method selected was to have 4 bands, each band range overlapping the other a small amount and calibrated so that with standard charts one division would represent 0.01 sp gr. A shift from one band to another could be arranged without alteration of the instrument itself, being accomplished by a simple change in the bubble-tube lengths, as described later. Accordingly, a recording type instrument was purchased and installed. Because there were some advantages in doing so, the first installation attempted to measure the gravity of the cone proper by placing the bubble tubes in the cone. This was not at all satisfactory and the second scheme utilized a fixed vertical screen at the surface of the cone, and an external sample-tube arrangement. We were particularly anxious to make this work as we felt it would be advantageous to measure the top level of medium where the separation was actually being made, but we were doomed to disappointment because it was impossible to keep the screen clean of float. Since the top gravity of the cone is the most convenient place to sample for control, a launder about 2 in. wide was installed longitudinally beneath the

Jan 1, 1951

By James J. Bean

HE task of measuring the specific gravity of the -*- operating medium in a heavy-media separation system has never presented a particularly difficult problem because the medium is fairly stable and the overflow of the separatory vessel, as well as its underflow, can be sampled easily and accurately and the specific gravity of the suspension determined easily by weighing a known volume. However, while this method is simple and accurate it does require the operator to take the sample by hand and to weigh it and there is considerable temptation to avoid the periodic sampling if everything seems to be going well, or if something is occupying the attention of the operator. Furthermore all operators do not sample in exactly the same manner and considerable practice is required for two operators to be able to "check" each other to the last few hundredths, particularly if the sample is cut underneath the drainage screen where location of the point of sampling and load on the screens tends to influence the determination. While none of the above presents much of a problem, we have all recognized that some mechanical method of continuous measurement and recording would be advantageous since the operator would merely have to glance at the meter to check the gravity and to have an indication of the trend of any changes. Also if the instrument were of the recording type, a permanent record would be available for the guidance of the superintendent. The Eagle-Picher Mining and Smelting Co. was the first heavy-media user to actually install such a recording meter. In 1946 they installed in their Central Mill at Cardin, Okla., a specific gravity recorder manufactured by the Bristol Co. of Water-bury, Conn. R. A. Barnes, of the Bristol Co., working with E. H. Crabtree, Jr. and Elmer Isern, of Eagle-Picher, made the application and worked out the problems of sampling and measuring. Their attempts to measure the specific gravity of the medium in the cone itself were not entirely successful and they resorted to an outside sample tube for actually making the determination. Because of the particular flowsheet used, it was possible to tap off from the medium return pipeline a stream of medium and divert it into the sampling tube, which was provided with a constant level overflow and a spigot underflow, and into which the bubbler tubes dipped. The Eagle-Picher installation was successful and its possibilities were recognized by the Mineral Dressing Laboratory of the American Cyanamid Co. It was decided to install a similar unit in the heavy-media pilot plant to investigate further its possibilities. Chief among these was the continuous record which it was felt would be proof of the steadiness of the gravity in a heavy-media cone, something which is not always appreciated by POtential users. Because the heavy-media pilot plant is required to operate at a wide range of specific gravities, it was realized that the unit would have to record all gravities from 1.25 to 3.50, and do it to the nearest 0.01. It would not be necessary to record all of this wide range on a single chart and the method selected was to have 4 bands, each band range overlapping the other a small amount and calibrated so that with standard charts one division would represent 0.01 sp gr. A shift from one band to another could be arranged without alteration of the instrument itself, being accomplished by a simple change in the bubble-tube lengths, as described later. Accordingly, a recording type instrument was purchased and installed. Because there were some advantages in doing so, the first installation attempted to measure the gravity of the cone proper by placing the bubble tubes in the cone. This was not at all satisfactory and the second scheme utilized a fixed vertical screen at the surface of the cone, and an external sample-tube arrangement. We were particularly anxious to make this work as we felt it would be advantageous to measure the top level of medium where the separation was actually being made, but we were doomed to disappointment because it was impossible to keep the screen clean of float. Since the top gravity of the cone is the most convenient place to sample for control, a launder about 2 in. wide was installed longitudinally beneath the

Jan 1, 1951

By J. Lohrenz, R. J. Francis, G. C. Clark

Compositional material balance methods have been extended to solution gas-gas cap-water drive reservoirs. Partial or complete pressure maintenance as well as reservoir repressuring by gas and/or water injection may be considered. Increrments of reservoir withdrawals and injections equivalent to a given time increment are used as the basic iterative step to allow the extension. An example field study shows how the reservoir volumes. extent of the water drive, and relative permeability ratio function may be estimated. Knowing these, the methods can be used to predict reservoir behavior. INTRODUCTION The compositional material balance is similar to conventional material balances in many aspects. The assumption of a pressure-homogenous reservoir with no transients is common to all conventional material balances1-1 although numerical methods are different. The compositional material balance also contains this assumption. Inclusion of phase equilibria directly in reservoir calculations is the key difference and improvement in the compositional material balance. A continuous account of the compositions of the reservoir fluids and effluents is determined. Calculations of fluid phases and properties can be based on these compositions. Excepting fluid phases and properties determined in this manner, the compositional material balance uses procedures exactly analogous to conventional methods. Brinkman and Weinaug5 and Jacoby and Berry6 have given compositional material balances for simple solution gas drive reservoirs; subsequently Jacoby and Berry' extended their procedure to include pressure maintenance by gas injection at constant reservoir pressure. This paper extends compositional material balance techniques to a more general combination drive reservoir with various types of pressure maintenance operations. The procedure for this extended compositional material balance and an example of its field application are presented. PROCEDURE The numerical calculations of this compositional mate- rial balance are performed on a high-speed digital computer. The most comprehensive case the present compositional material balance program can handle is a solution gas-gas cap-water drive reservoir with (1) water production, (2) water influx, (3) separate or commingled production from the oil and gas zones, (4) any surface processing arrangement including LPG and gasoline production, and (5) gas injection into the gas and/or oil zones." This description of the procedure applies to this most comprehensive case. Appropriate deletions in the procedure can be made for more simple mechanisms. ASSUMPTIONS In common with conventional material balances, the compositional material balance makes the following assumptions: (1) the total reservoir is at a uniform pressure at a given time; (2) the volumetric ratio of gas to liquid withdrawal at reservoir conditions is directly proportional to their mobilities; and (3) instead of assuming a pressure-dependent total gas-oil equilibrium, the cornpbsitional material balance makes a sianificantly different and more rigorous assumption as follows. Thermodynamic equilibrium exists for each component in the liquid-gas mixtures in the reservoir and in surface processing. These three assumptions are fundamental in the compositional material balance procedure. Other assumptions involve arbitrary simplifications of the reservoir mechanisms. This compositional material balance uses the following simplifying assumptions: (1) no bulk mixing occurs between the gas and oil zone; (2) total mixing occurs between any injected gas and the contents of the injection zone; (3) no in situ hydrocarbon liquid is produced from the gas zone; (4) no reservoir gas is retained behind any net bottom-water influx; (5) the residual saturation of hydrocarbon liquid at reservoir conditions behind any net bottom-water influx is constant; and (6) fluids retained behind any net bottom-water influx exert no further influence on the reservoir. These six assumptions are not fundamental. Modifications of the present procedure can be made for different assumptions of the reservoir mechanisms. THE TIME INCREMENT Previous compositional material balances have used a pressure increment for simple solution gas drive reservoirs"" and an increment of injected gas for pressure maintenance.' These increments are suitable for these simple cases. They are, however, inadequate for reservoirs with time dependent drive mechanisms including water drive. A time increment removes this inadequacy and is

By M. G. Benz

The superconducting performmce of diffusion-processed Nb3Sn is influenced by its micro structure. High isotropic transverse current density may be achieved in this material by a process which forms a precipitate of ZrO, within the Nb3Sn. FOR an ideal type-I1 superconductor, little or no transport current can be carried in the mixed state; i.e., little or no transport current can be carried above the lower critical field H,,, where the field penetrates abruptly in the form of current vortices or fluxoids, even though full transition to the normal state does not occur until the upper critical field H,,.' Fortunately, nonideal type-I1 superconductors can be readily obtained and these carry large transport currents up to the upper critical field H. Both theoretical and experimental investigations have attributed this current-carrying capability for nonideal type-I1 superconductors to pinning of the fluxoid lattice by heterogeneities in the microstructure of the superconducting material. These heterogeneities may take the form of dislocations or dislocation clusters,2"5 grain boundaries: structural imperfections introduced by phase transformations; radiation damage,8"10 or precipitates.11"15 Nb3Sn formed by diffusion processing is a type-I1 superconductor. Heterogeneities are needed for high superconducting critical currents above H,,. This paper will cover: a) what the microstructure of diffusion-processed NbSn looks like; b) what changes in the microstructure take place when the system is doped with precipitates, and c) how these changes in microstructure influence the superconducting critical currents. EXPERIMENTAL Preparation of Samples. Diffusion processing was used to form the Nb3Sn. The procedure used was as follows: a) coat the surface of a niobium tape with tin; b) heat-treat this tape at a temperature above 930°C to form a layer of Nb3Sn at the Sn-Nb interface. Such a layer of NbsSn is shown in Fig. 1 The thickness of the NbsSn layer formed was controlled by the time and temperature of the heat treatment. The same general procedure was used for preparation of both undoped samples and samples doped with a precipitate. An additional step was included in the preparation of the doped samples which consisted of internal oxidation of zirconium to form ZrOn. The details of the doping process will be reported in a later paper. Sample Testing. The Nb3Sn tape samples were soldered to a copper or brass shunt. Current and voltage leads were then attached to the sample in the usual four-probe resistance measurement configuration. The sample was cooled to 42°K. In some cases it was cooled in the presence of a high magnetic field and in other cases with the field turned off. The results were the same for both cases. The samples were oriented in a configuration with field transverse to current but could be rotated such that the angle between the field vector and the wide side of the tape sample could be changed. Measurements up to 100 kG were done in a superconducting solenoid and measurements above 100 kG in a water-cooled copper magnet at the MIT National Magnet Laboratory. Once the test field was reached, the current in the sample was increased until voltage was detected across the sample. The critical current was taken as the current at which voltage was first detected in excess of background noise. In most cases this was 1 to 2 x 10~6 v for a— in.-wide sample carrying several hundred amperes with a in. separation between voltage leads and with a 10 "-ohm shunt resistance. RESULTS AND DISCUSSION Microstructure. Examination of the microstructure of the undoped Nb3Sn shows rather large-diameter (1 to 2 columnar grains growing outward from the niobium surface toward the tin surface. As the layer is made thicker by longer diffusion times, these grains grow longer. Few new grains are started. Transmission electron microscopy shows little or no second-phase material within the bulk of the Nb3Sn layer. The microstructure of a diffusion-processed NbsSn layer changes quite drastically when the system is doped so as to form a precipitate within the NbsSn layer. Instead of large-diameter columnar grains of NbaSn forming, smaller-diameter (0.5 to 1 ) equiaxed grains of Nb3Sn decorated with the precipitate form. Fig. 2 shows a transmission electron micrograph of a Nb3Sn layer doped with zirconium oxide. This layer has been etched so that one may look between the grains

Jan 1, 1969

By G. R. Pickett

Examples are presented which show that the velocity~ amplitude, attenuation and apparent frequency of several acoustic waves can be recorded in the borehole. Examination of such recordings, termed "character" logs, indicates that the wave types observed include a refracted compressional wave and a wave which travels with formation shear velocity. Laboratory data are used to show that compressional and shear wave velocities are dependent on porosity, effective stress and lithology; but that the change in reciprocal velocity per unit change in porosity is larger for shear waves than for compressional waves. We, therefore, conclude that. the accuracy of porosity determinations can sometimes be improved by use of shear wave velocities, provided that the shear wave amplitudes are large enough to delineate the shear arrival from the preceding compressional arrival on the character log. Borehole data are presented which show that the difference between shear wave and compressional wave reciprocal velocities can be used to predict porosities. This is a refinement which may allow the prediction of porosities from single-receiver acoustic logs without introduction of errors from borehole fluid traveltimes. Laboratory and field data are presented to show that the relationship between compressional and shear wave velocities can be used to indicate lithology. An example is presented to show that fractures usually cause a greater reduction in borehole shear wave amplitudes than in compressional wave amplitudes, an effect which may offer a more reliable means of detecting fractures. The complexity of the borehole acoustic wave train can rake presently available cement bond logs highly sensitive to the gate and bias settings used. The character log offers a means to circumvent possible misinterpretations by recording all amplitudes, from which the interpreter can select the appropriate data for evaluating the cement bond. Character logs may also be used as a quality control for open-hole transit-time logs when existence of small compressional wave amplitudes interferes with the proper functioning of bias-controlled timing devices. Evaluation of the potential uses of character log data is not complete; but a character log presented in a form convenient for routine use would be a desirable addition to currently available logs. To summarize, possible applications for such a log in formation evaluation include the following (1) quality control of transit-time logs, (2) refinement of porosity predictions, (3) determination of lithology, (4) improvement of fracture detection and (5) improvement of cement bond evaluation. Suggestions are made regarding the requirements for a suficient but practical character log for routine use. INTRODUCTION Acoustic logs have become a widely used porosity tool in formation evaluation. In addition, there is a growing application of acoustic logs in cement bond evaluation and fracture detection. These applications have mainly involved the use of logs of first-arrival transit times and amplitudes and have not included detailed studies of the complete signal. The purpose of this paper is to show that significant benefits in formation evaluation can be gained by a more complete use of the acoustic wave train generated in the borehole by an acoustic logging tool. We hope that this discussion will also stimulate further development of logs suitable for routine use so that these benefits may be realized. Examples of acoustic wave train logs, termed "character" logs, are presented to show that several identifiable acoustic waves are present in the borehole. The measurable characteristics of these acoustic waves and some of their relations to formation properties of interest are also discussed. The more obvious potential uses of character logs are listed, and some suggestions are made regarding the requirements for a sufficient but practical character log for routine use. CHARACTER LOGS Some 10 years ago, Vogel' and Summers and Broding' noted that the signals received uphole from an acoustic logging tool located in a borehole had a number of interesting characteristics. The logging tool consisted of two or more pressure transducers spaced on an acoustically insulated body (Fig. la). One of the pressure transducers was used as a transmitter to generate pressure waves in the borehole fluid. The other transducer served as a receiver to detect any pressure waves reaching it in the borehole. The receiver then converted these pressure waves to electrical signals which were transmitted to the surface and displayed on an oscilloscope as a record of time vs receiver-signal amplitude. Fig. lb is a schematic representation of a typical record. The interesting characteristics seen in the earlier' and subsequent experiments were (1)

By C. L. Meyers, A. V. Levy, G. Y. Onoda, R. J. Kotfila

This paper presents the hypothesis that solid-solution hardening of regions in the order of tens of angstroms thick along grain boundaries is the most important mechanism controlling the ductile -brittle transition behavior of poly crystalline bcc refractory metals. Further, a physical model is developed and a general equation is derived to describe the dependence of the solute concentration at grain boundaries on temperature, nominal impurity concentration, thermal treatments, vain size, and prior plastic deformation. Analytical curves of the solute concentration at grain boundaries us temperature, calculated by means of the derived equation, are found to have the same general form as curves of ductility us temperature plotted from experimental data. Senziquantitative relationships between the transition temperature and metallurgical variables can he determined by using the physical model. The room-temperature brittleness of the poly-crystalline refractory metals (tungsten, molybdenum, and chromium) is a result of their high ductile-brittle transition temperatures. Recently studies on single crystals have revealed that, when sufficiently pure, these crystals have much lower transition temperatures than polycrystalline specimens of similar purity.'-3 For example, the transition temperature (measured by reduction in area in tensile tests) for very high-purity tungsten crystals has been reported to be as low as -50°F whereas polycrystalline specimens of similar purity had a transition temperature near 400" ~.' These results suggest that the ductile-brittle transition behavior of these polycrystalline metals can be attributed principally to the influence of grain boundaries on plastic flow and fracture. This paper contains a discussion of the manner in which grain boundaries influence the ductility of the poly-.crystalline bcc refractory metals and proposes that the segregation of impurities to grain boundaries is the most important mechanism for controlling the ductile-brittle transition behavior of these metals. Further, this paper contains an analysis of the effect of the compositional and structural variables on the grain boundary-ductility relationship, and introduces a semiquantitative model that can provide a foundation for more theoretical treatment to describe the influence of these variables on ductile-brittle transition behavior. PHYSICAL MODEL FOR PREDICTING DUCTILE-BRITTLE TRANSITION BEHAVIOR Grain Boundary Segregation of Impurities. Based on their own observations and on theoretical grounds, numerous investigators have suggested that impurities segregate to the grain boundaries. Such segregation would be expected because regions exist where both large and small foreign atoms fit with less strain than within the undistorted crystal structure. Therefore, the concentration of impurities should be higher at boundaries than within the grain body. TO estimate the degree (i.e., the ratio of grain boundary to nominal bulk concentration) to which an interstitial solute tends to segregate at boundaries within a solvent metal, the solubility rather than the size misfit could be used as a guide because solubility expresses the joint effect of both elastic and electronic factors.5 The solubilities of interstitial elements such as carbon, hydrogen, nitrogen, and oxygen are low in the group V-A metals and very low in the group VI-A metals.6 These low solubilities suggest that segregation to grain boundaries should occur for each of these solutes in both refractory metal groups. The difference between the ductility of single-crystal and polycrystalline bcc refractory metals can be described in terms of two distinct effects.4 The first of these is the general observation that grain boundaries hinder slip within grains and slip transfer between grains, and the second is that deformation is more complex in each grain of a polycrystalline specimen than it is in a single crystal. Mc Lean has pointed out, furthermore, that strong slip-hindrance effects at grain boundaries should occur in metals having strong segregation of impurities to grain boundaries. Therefore, the effect of grain boundaries on the hindrance of slip is expected to be the dominating influence on the ductile-brittle transition behavior of these polycrystalline refractory metals. cahn5 has suggested that temperature and solute mobility should influence solute equilibrium segregation at grain boundaries, and Fig. 1 illustrates

Jan 1, 1965

Jan 1, 1914

Jan 1, 1895