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By M. Muskat, H. H. Evinger

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By R. L. Manegold

This paper outlines the reasons for and the application of suspended magnets above belt conveyors for the purpose of removing tramp iron to protect equipment. The design of a magnet strong enough to extract iron through a distance of 24 in. is described along with the proper method of application in the field. Advantages of the suspended magnet in contrast to the conventional magnetic pulley are also discussed. IN RECENT years there has been a decided trend toward bringing ores and coal out of open-pit and underground mines by long, sloping single-stage belt conveyors. Because the high investment cost of haulage conveyors dictates maximum speed and full loading for economy, conveyor belts are running faster than ever before, with a greater burden on the belts. In addition, larger blocks of ore are being mined and conveyed. Rougher use of large mining equipment generates more tramp iron; mechanical loading rejects nothing. Therefore the extraction of tramp iron and other deleterious materials for the protection of haulage conveyors at transfer points, chutes, and idlers is becoming an increasingly difficult job. In our experience, the best method of protecting long haulage conveyor belts is to extract the tramp iron, at least the large tramp iron, ahead of the main haulage conveyor or series of conveyors. It is most practical to collect the tramp iron at the earliest source possible, usually directly after the primary car unloading dump or after the primary crushers, which are ordinarily not affected by tramp iron, see Fig. 1. The coal or ore from its primary source is fed by chutes or feeders onto a buffer or shock belt conveyor, a short, ruggedly built conveyor system that can be considered somewhat expendable. Its primary function is to bring the ore up to speed for transmission to the haulage conveyor. There is no assured method of protecting this conveyor from tramp iron damage at its feed end. Likewise, there is a possibility, although remote if the magnet applied to this belt is installed correctly, that the tramp iron extraction process will damage the shock belt, which is, however, short and comparatively inexpensive. Magnetic head pulleys with their maximum effective range of about 8 or 10 in. cannot be considered for large installations, even though they are desirable because of the continuous and automatic tramp iron removal feature. Further, the most dangerous form of tramp iron with respect to potential damage to a haulage conveyor is the long rod, roof bolt, or rail segment, which is not extracted satisfactorily because of the limited tangential contact of such an iron shape with the magnet. Magnetic head pulleys are also undesirable because the dribble or fines from the head pulley discharge at the same point as the tramp iron. Screens must be used to separate the fines from the magnetics, resulting in additional expense and loss of head room. Magnetic detectors have been used with success, but they only indicate the presence of iron, and the conveyor belt must be stopped for its manual removal. The stoppage of any conveyor means that all preceding equipment must be stopped or a cascade of material on the idle conveyor will result. Occasionally combinations of detectors and magnetic head pulleys are used. The detector precedes the magnetic head pulley and detects only large pieces of tramp iron, while the magnetic pulley subsequently takes out the smaller ferrous metals. Suspended magnets overcome the disadvantages of magnetic head pulleys, detectors or a combination of both. There are several magnetic extraction problems involved in applying a suspended magnet at this

Jan 1, 1953

By Carlos G. Valenzuela

The value generally accepted for stacking-fault energy, of copper has been approximately 40 ergs per sq cm based on Fullman's2 value for the coherent twin-boundary energy and the assumption that is twice the twin boundary energy However, Thornton and coworkers8 determined that the lower limit of for copper is approximately 60 ergs per sq cm, based on measurements of dislocation-node radii. They suggested that the assumption of = 2t is invalid. It is the purpose of this note to present results which indicate that the values of obtained by measurement of twin-grain boundary intersections and the values obtained by measurement of dislocation-node radii are actually compatible. The most reliable values for of the a brasses, based on electron-microscope observation of dislocation nodes, are probably those values reported by Smallman and Green6 who applied the Siems correction (1961) to data obtained by Howie and Swann.3 These values shown in Fig. 1 give an extrapolated value of approximately 70 ergs per sq cm for pure copper. In the present work, Fullman's method for determining the stacking-fault energy of copper was extended to the a brasses. High-purity copper (99.999 pet) and high-purity zinc (99.999 pet) were mixed in proportioned amounts and melted in sealed and evacuated quartz tubes. The alloys were homogenized for a week at 750°C and chemically analyzed by means of X-ray fluorescence. These alloys, along with a specimen of pure copper, were rolled to 98 pet reduction and a thickness of 0.009 in., resealed, and annealed for 40 hr at 715°C. Values for the ratio of twin-boundary energy to the grain-boundary energy, it gb, were obtained from measurements of dihedral angles formed at the intersections of twin boundaries and grain boundaries by using Fullman's2 mechanical analogy of surface tensions acting at the intersection of an annealing twin and a grain boundary. The angles between the twin traces and the grain boundaries were measured for a large number of twin-grain boundary intersections at a magnification of X500 using a rotating mechanical stage on a Reichert metallograph. The rotary stage has a calibrated angle scale with vernier so that measurements can be made to 0.1 deg. The mean twin-grain boundary energy and standard deviation were calculated for copper and each of the brasses by the use of an IBM 7072 computer. It was found that the mean value of gb stabilized after approximately 100 twin-angle measurements. This was determined by plotting the mean against the number of angles measured. Since the measured angles deviate from true dihedral angles, a correction factor for grain orientation, discussed below, was applied. The stacking-fault energy was then calculated from these values and the values of grain-boundary energy derived by Taylor.7 The data obtained are tabulated in Table I. Values for stacking-fault energy are plotted in Fig. 1. The value of gb for the specimen of 1.03 pet Zn is close to the value obtained by Fullman2 for OFHC (99.98 pet) copper, 0.045. It is believed that the purity of the copper affects gb significantly. The 99.999 pet purity Cu used in this investigation yielded a value of yt/ygb, 0.76, which is much higher than that obtained by Fullman. Additional evidence suggesting that the purity of

Jan 1, 1965

By J. H. Scaff, H. C. Theuerer

Germanium may be reversibly converted from n to p type by heat treatment. Data for the conversion and the associated changes in resistreatment.tivity are given and the results are interpreted in terms of changes in the donor-acceptor balance. MEANS for controlling the electrical properties of germanium in a predictable manner are of interest because of the increasing utilization of this element as the semiconducting material in electrical devices. Since both the mechanism and the magnitude of the electrical conductivity depend upon the kind and quantity of impurities present, the conductivity usually is adjusted by first carefully purifying the germanium, and then, by standard alloying procedures, adding the elements desired. The elements usually added are from the third or fifth periodic groups depending upon whether p- or n-type germanium is desired. However, in the development of germanium rectifiers during the war, it was found that it was possible also to modify reversibly the conductivity of germanium and even to produce conversion from n to p type by heat treatment.1,5 Since then a detailed study of this effect has been made. The data are presented in this paper and an explanation is offered for the effects observed. Preparation and Experimental Procedure The method used in preparing the germanium ingots for this investigation has been previously described.' The method consists essentially of (1) reduction of GeO2* and (2) preparation of a 50-g ingot from the reduced material. Graphite containers are used in both steps. In the first step the GeO2 is reduced in hydrogen at 650 °C to form a sponge germanium which, to assure complete reduction and to obtain massive materials, is fused subsequently in the reduction furnace by gradually raising the temperature to 1000°C. The button of germanium thus obtained corresponds to a yield of 99.8 pct. The final ingot is prepared by fusion of the germanium button in a helium atmosphere. A cylindrical crucible in a vertical silica tube furnace is employed and the crucible is heated by an external induction coil. The ingot is solidified from the bottom upward by raising the induction coil at a constant rate with power to the coil kept at a fixed value. In such ingots, segregation is normal and most of the impurities are concentrated in the last region of the ingot to freeze. It follows then that the major portion of the ingot is purer than it would have been if freezing had occurred in a random fashion. Moreover the orderly advance of the freezing surface during solidification establishes in the ingot a succession of surfaces of constant composition, if it is assumed that the liquid is homogeneous and that diffusion in the solid is negligible. Therefore, some information on the distribution of impurities in the ingot may be acquired by determining the shape of the solid-liquid interface at different stages of solidification. This is of importance because the concentration of impurities will be seen to affect the response of germanium to heat treatment. Such information is difficult to acquire by direct means, for the impurities responsible for the electrical properties of germanium prepared in this way are present

Jan 1, 1952

By C. W. Allen, B. D. Cullity, H. S. Choi

The torsional deformation of aluminum and magnesium crystals is investigated, with particular reference to the dependence of proportional limit on crystal orientation. The proportional limit is found to be governed by the average value of the resolved shear stress on the most highly stressed slip systems, but the proportional limit does not strictly obey a critical-resolved-shear-stress law. The behavior of a cylindrical single crystal stressed in tension is well known: plastic flow begins when the resolved shear stress on the most highly stressed slip system reaches a critical value. There is much less understanding of the effect of torsion on such a crystal and on the way in which the critical-resolved-shear-stress law should be applied to torsional deformation. In the present paper particular attention is paid to the dependence of plastic yielding on crystal orientation and lesser attention to the mechanism of flow after yielding has occurred. New work on aluminum and magnesium crystals is presented, and previous results obtained in this laboratory on magnesium1 are re-examined. STRESS DISTRIBUTION The problems involved in torsional deformation of single crystals are due entirely to the complexity of the stress distribution. In tension, if loading conditions are perfect, the shear stress on any particular slip plane is completely uniform over the entire area of that plane. In torsion, on the other hand, the stress on any selected plane in a particular direction varies not only from center to edge of the specimen but also around its perimeter. It is convenient to express the stress at any point in terms of t0, which is the shear stress acting at the surface of a cylindrical specimen on a plane normal to the axis and in a direction tangential to the cylinder. At point P of Fig. 1 this stress acts in the direction of axis 2 and is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. This stress can be resolved on any chosen slip system, and details are given in the Appendix. Let P be the point on the specimen surface where the stress is to be evaluated; P is defined by its angular distance A from an arbitrary reference line through 0 normal to the axis. his line is usually taken as the direction of incidence of the X-ray beam used to determine the crystal orientation.) Then the shear stress t, acting at P in direction Dona plane whose normal is N is given by Ts/TO = sin ? 0, cos ?d sin (?0, - ?) + cos ?, sin ?d sin (?d - ?) [2] where 0, and Od are the angles between N and D, respectively, and the axis, ?0 and ?d are the angles between the projections of N and D, respectively, on the transverse plane and the reference line through 0. By means of Eq. [2], the stress 7, acting in any given slip direction can be computed. In the previous work on magnesium1 only gross slip tangential to the specimen surface was considered, and this

Jan 1, 1963

By J. R. Hornaday, A. E. Morris, N. A. Parlee, D. C. Carmichael

Rates of absorption and effusion of hydrogen in solid iron were measurede by a Sieverts type of apparatus. With clean a iron these rates are diffusion controlled down to 420°C and are represented by the equation D = 6.70 x e-'100' crn2 sec-I Certain surface impurities can affect these rates at all temper-atuves. Thin oxide films lower, the apparent diffusivity of annealed iron markedly. Cold-worked iron (75 pct) annealed at 430°C has practically the same solubility and diffusivity as anealed iron. THE mechanism of absorption and evolution of hydrogen in solid iron alloys is not fully understood despite the large number of investigations on the subject. While there appear to be many instances of simple solid-state diffusion control of rate, there are many cases where investigators have either concluded that surface reactions are rate controlling or that some "nondiffusible" hydrogen resides in discontinuities. The purposes of this research were 1) to develop a sound method for studying this absorption and evolution behavior, 2) to examine it in pure annealed iron, and 3) to determine the effects of important variables, such as cold work, surface condition, and composition. This paper relates the progress toward these objectives. Much of the present knowledge of the movement of hydrogen through iron alloys comes from permeability studies which involve the measurement of the rate of passage (under steady state conditions) through membranes of the order of 1 mm in thickness. This method is open to question on various grounds. If surface reactions are involved, two different surfaces operating under two different conditions must be considered. The presence of defects in the membrane even of microscopic dimensions may lead to erroneous results. A few people have studied evolution of hydrogen into vacuum, under carefully controlled (unsteady state) conditions, and some of the best diffusivity data come from these sources. Most of these methods measure rates of evolution only and thus do not make a rigorous test for reversibility of behavior. It appeared that an "unsteady state" method that would permit the measurement of both rates of evolution and absorption under controlled temperature, pressure, and other conditions would offer several advantages. Accordingly the modified Sieverts apparatus described below was designed and built. APPARATUS This apparatus is shown in Fig. 1. The sample bulb is detailed in Fig. 2. Hydrogen of 99.5 pct purity and argon of 99.99 pct purity were used. The hydrogen was deoxidized and dried by means of a Deoxo unit followed by a "Dri-erite" tower. The argon was only dried. The gas burette was graduated in tenths of a cubic centimeter, and, with the aid of a travelling magnifier, readings could be estimated to the nearest 0.01 cc. The level of mercury in the burette was adjusted by means of a leveling bulb operated by a fine screw adjustment. An electrical system, consisting of two slightly separated platinum electrodes inserted in one leg of the manometer and a small light bulb was used to obtain rapid accurate adjustment of the pressure. The capillary tubing of the Vycor sample bulb was 3 mm bore as was all tubing back to the gas burette. The samples were discs made from vacuum-melted Ferrovac-E iron of greater than

Jan 1, 1961

By D. H. Gray, G. Bergamini, I. Fatt

A method developed by soil scientists for measuring permeability anisotropy of soils has been adapted for use in studies of sandstone permeability aniso-tmpy. Studies on Berea and Bandera sandstone show that permeability of these materials decreases upon application of simulated overburden pressure. Permeability reduction of Berea and Grubb sandstone cores subjected to simulated overburden pressure is shown to be a function of the ratio of radial to axial stress. INTRODUCTION The effects of mechanical stress on reservoir rock parameters are now generally accepted as being important in reservoir engineering calculations. In several oil fields the unique behavior of the reservoir has been attributed to the influence of overburden pressure or internal fluid pressure on rock permeability or fluid content. l Although the gross effects of overburden pressure on permeability, porosity, waterflood efficiency, electrical resistance and sonic velocity have now been established,3-9 there are some very interesting, and perhaps important, details of rock behavior under stress that have not heretofore been studied. In this paper we will show that permeability anistropy of several sandstones is a function of overburden pressure. We will also show that permeability reduction of cylindrical samples of two sandstones, when subjected to mechanical stress, is a function of the ratio of radial to axial stress. Most studies of overburden pressure effects made in the past have attempted to duplicate reservoir conditions by applying hydrostatic external pressure on all surfaces of the sample. Assuming perfect elasticity, that is, no viscoelastic flow during geological time, reservoir rock in situ cannot be under hydrostatic stress as is apparent from the value of 0.25 for Poisson's ratio for most rock. In the absence of tectonic forces the horizontal stress component If there are directional permeability effects, as has been reported from field and laboratory studies, l0,11 then one would expect hydrostatic stress as used in the laboratory to give a different permeability reduction from that occurring under reservoir stress conditions. The influence of stress on directional permeability was measured by a modification of the method first described by Maasland and Kirkham for use on soil samples.12 Their method permits calculation of the permeabilities along each of the three mutually perpendicular axes of a cubic sample. The modification reported in this paper extends the method to observing these permeabilities when the sample is under hydrostatic stress. The Hassler sleeve type of core holder is satisfactory for studying overburden pressure effects on permeability if a known force is applied to the end plugs. Wyble6 used a sleeve core holder but did not load the end plugs. In this paper we combine sleeve pressure and axial force to give permeability changes which we believe are close to those occurring in reservoirs when reservoir pressure changes. The combination of sleeve pressure and axial force assumes, however, that the sleeve pressure simulates both vertical stress and horizontal stress in one direction. METHOD PERMEABILITY ANISOTROPY The Maasland and Kirkhaml2 method of measuring permeability anisotropy uses a cube of porous material which is Open On three faces and has discs with a Center hole for an air inlet cemented to the other three mutually perpendicular faces (Fig. 1). The rate at which air pressure falls in a bottle of known volume, and pressure slightly above atmospheric, when the bottle discharges through each disc, is

By J. P. Myers, A. H. Flagg, E. S. Mardock, J. L. P. Campbell, J. M. Terry

The development process for the use of radioactive tracers as a means of locating zones of permeability is discussed. The general techniques for the safe handling of radioactive materials is given as developed by the Lane-Wells Co. and Well Surveys, Inc. The prob1em and. successes with tracers in waterflood systetns, oil and gas injection profiles, fracture sand tracing, squeeze (ement tracing. lost circulution, and cement top localion are discussed and illustrated. INTRODUCTION The exact location of the permeable zones lying within the productive horizon has been a major problem faced by the petroleum engineer for decades, and it has been a problem which has seldom been solved with certainty. Reservoir engineers usually have to incorporate a question mark in their estimates of future reservoir performance because of blanks in the core data. Although the use of radioactivity or electrical logs for the estimation of porosity has been of great assistance in furnishing a record for the reservoir engineer, this application of logging data has not completely solved the problem. In short, the industry needs an in-situ well surveying method which can locate and estimate the permeability of the zones existing within a given pay section. The initial development work with radioactive tracers has been towards filling the need for permeability information. Progress to date permits the location of permeable zones with a qualitative estimate of their relative importance with respect to permeability. The calibration of the method is still incomplete. but present development work on tracer preparations, borehole effect correction factors, and instrument limitations give a promise of quantitative "permeability profiles" in the near future. The development work on the radioactive tracer method discussed here began several years ago in the laboratories of Well Surveys, Inc., in Tulsa. At the outset of this work, three approaches to the problem were visualized as follows: 1. A fluid carrying a soluble, chemically inert, gamma ray emitting isotope is pumped down the borehole and out into the permeable zones of the formation. The greater gamma activity of the permeable zones thus permits them to be differentiated from the impermeable zones which contain no active tracer. It was found difficult to obtain a tracer material which was chemically inert. Absorption to some degree was noted in all experiments. Also, it proved impossible to hold the tracer near the horehole where it could be logged. 2. A fluid carrying a soluble, gamma ray emitting isotope is pumped down the borehole into the permeable formations. In contrast with proposal 1, above. the tracer is chemically active with the fluids and materials in the pore spaces of the permeable zones. The permeable zones are thus indicated by their higher radioactivity level. The main difficulty in this proposal was finding a tracer material which would not be absorbed by shale as well as in the permeable porosity. Very little field work was done with this system. 3. Radioactive particles suspended within the injection fluid are pumped down the well. As the fluid enters the permeable formations, the radioactive particles are filtered out on borehole wall. The permeable zones are differentiated from the impermeable by the gamma ray activity deposited on the formation wall.

Jan 1, 1956

By J. J. Arps

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

Jan 1, 1957

By J. K. Kerver, J. S. Osoba, J. G. Richardson, J. A. Hafford

A detailed study of a number of methods of relative permea-abilitv measurement has been made in a search for the tech-niqrle most suited to routine analysis of cores taken from reservoir rock. It has been found from tests run on the same samples of core material by a number of techniques that the Penn State, Hassler, Hafford, and dispersed feed techniques all yield results which are felt to be reliable. Conditions under which the faster single core dynamic technique may be used are described. Further work on the calculation of relative permeabilities to oil from data obtained by the gas drive method is needed before this latter rapid method can be utilized. Correlations between theoretical studies and experimental results have been obtained in studies of the boundary effect. pressure distribution in two-phase flow, and gas expansion effects. Previous conclusions that the effects of the outflow boundary could be made negligibly small have been substantiated. Results of experimentally determined oil and gas pressure distributions along a core sample during flow are presented. Further studies of the effects of rate of flow in the measurement of relative permeability-saturation relations have shown that results are independent of the rate of flow as long as the flow rate is below the point where inertial effects commence. An analysis of the effects of a severalfold expansion of gas along the flow path indicates that while saturation gradients are induced in the test sample, the errors caused by this phenomenon in relative permeability measurements are small. INTRODUCTION Many pages of literature have been devoted to pointing out the need for relative permeability-saturation relations in reservoir engineering. One of the most attractive ways of obtaining this information is by the analysis of samples of core material taken from the formation in question, and again literature has described man); methods for obtaining these data. It is the purpose of this paper to present the work that has been done in the study of some of these published methods together with some other methods that have been recently developed in this laboratory. Also, a study of some of the factors that influence the laburatory determination of relative permeability-saturation relations is presented. FACTORS WHICH AFFECT LABORATORY STUDY OF FLUID FLOW THROUGH RESERVOIR ROCK To determine relative permeability-saturation relations of samples of reservoir rock in the laboratory, it is important to know what factors affect these measurements in order that the magnitude of these effects can be ascertained and steps then can be taken to eliminate or, in some cases, to minimize them. The factors that have been investigated are the boundary effect, the effect of gas expansion. and the rate effect. Boundary Effect In laboratory experiments in which two immiscible fluids are flowed through a porous medium, there exists a discontinuity of capillary properties at the outflow face. This discontinuity exists became the fluids pass from a region of finite capillary pressure in the sample to a region of zero capillary pressure in an open receiving vessel. The capillary forces existing in the core caupe the rock to tend to retain

Jan 1, 1952

By H. H. Spain, R. C. Rumble, H. E. Stamm

This paper presents a reservoir analyzer study of the performance of the Woodbine formation in the East Texas basin. The study was made possible by the compilation of available information on the configuration. thickness and the pressure drawdown of the formation. The investigation was made of the pressure variations in the basin incident to production from the several Woodbine reservoirs. In addition, the apparent compressibility of Woodbine water was evaluated so that the potential water yield of the formation could be determined. The distribution of permeability of the Woodbine sand and the interference between producing areas were also investigated. In conjunction with this basic study of the Woodbine sand, an acceptable match of the production-pressure relationship in the East Texas Field was established on the analyzer. INTRODUCTION When production is taken from a reservoir contiguous to an aquifer, the resultant pressure gradient causes a water influx into the reservoir. For some years it has been the practice to predict the performance of water drive reservoirs with mathematical equations that relate the water influx into reservoirs to their pressure behavior. A rigorous solution of these equations is quite complex: hence, the conventional method requires the simplifying assumptions that the formation have constant thickness, permeability and poiosity, and that it have a known and regular shape. It is necessary to use performance records of the reservoir in question to determine the equation constants that make the results of the mathematical calculations duplicate the reservoir history. The values of the constants determined in this manner sometimes differ so greatly from theoretical or measured values that the constants appear unreasonable. The equation constants comprise such factors as the thickness, porosity and permeability of the formation, and the viscosity and compressibility of water. Usually the thickness, porosity and viscosity are known within a reasonable degree of certainty. whereas the formation permeability and the water compressibility are known with considerably less certainty. Hence. permeability and compressibility values are arbitrarily selected that will make the mathematical equations duplicate the reservoir behavior. In many reservoir studies the value of the compressibility of water thus selected has exceeded the reported value by a factor of from severalfold to manyfold. Whether this excessive value results from the inadequacy of the mathematical approach to take into account the shape irregularities and the heterogeneities of the aquifer, or is due to some type of formation compaction and decrease of porosity has not been established. Because of the significance of the potential water yield of formations with reference not only to oil reservoirs but to water resources as well, it is very important that a representative value for the effective water compressibility be determined. One of the best known examples of a field for which it has been possible in the past to predict the future reservoir pressure is the East Texas Field. Until about 1943 it was possible by means of mathematical equations to duplicate past pressure behavior and to predict with a high degree of accuracy the reservoir pressure of the field. Since 1943, however, the calculated pressures have deviated progressively from the observed pressures to such a degree that in recent years, it has

Jan 1, 1951

By H. A. Wahl

This paper presents methods of designing hydraulic fracture treatments in formations saturated with slightly compressible liquids. Howard and Fast describe the fluid-loss control resulting from the viscosity and compressibility effects of the reservoir fluid in terms of a fracturing fluid coefficient. However, for horizontal fractures, this coefficient is applicable to infinitely thick reservoirs. These methods of evaluating fluid loss from horizontal fractures during treatment differ from previous methods in that: (I) formation thickness is incorporated in the velocity function describing the rate of fluid loss to the formation; and (2) for a given thickness the relative position of the fracture to the horizontal boundaries of the reservoir or any interrnediate permeability barrier is incorporated in the design procedure. This theory is applied to several actual and hypothetical field cases. The results of these calculations demonstrate that the eflect of formation thickness on fluid loss from horizontal fractures may result in fractures several times larger than predicted by other methods. INTRODUCTION Hydraulic fracturing has been the dominating well-stimulation technique during the last decade. From the time it was commercially available, fracturing has had a very favorable success ratio compared to other stimulation methods. However, numerous wells that were successfully stimulated remained economic failures. Only in the last few years has the oil industry recognized the importance of designing treatments for each well which will yield the maximum profit. This implies that for a given set of treatment conditions the size and general physical characteristics of the fracture can be determined. One of the outstanding contributions in the field of fracture design was presented by Howard and Fast.' In their paper, three flow mechanisms that control fluid loss from the fracture to the formation are defined: (1) viscosity effects of the fracturing fluid, (2) viscosity and compressibility effects of the reservoir fluid, and (3) wall-building effects of a treated fracturing fluid. The rate of fluid loss to the formation adjacent to a fracture is shown to be a function of time. For each flow mechanism the velocity function v(t) is expressed as a constant or fracturing fluid coefficient divided by the square root of time. This form of v(t) can be used in the Carter equation, as developed in the Howard and Fasc paper, to estimate the areal extent of fractures. This equation may be written as In the following sections the effect of formation thickness on fluid loss from horizontal fractures is evaluated when the controlling flow mechanism is the viscosity and compressibility of the reservoir fluids. The major assumptions inherent in the Carter equation are brought out in subsequent mathematical developments. THE EFFECT OF RESERVOIR FLUIDS ON FRACTURE EXTENSION When a fracture treatment is performed using a fracturing fluid identical to the reservoir fluid, the only flow mechanism controlling fluid loss is the viscosity and compressibility effects of the reservoir fluids. In developing a fracturing fluid coefficient for this mechanism, Howard and Fast considered a segment of the formation bounded by a unit area on the fracture face and extending to infinity in the direction of leak-off as shown in Fig. 1(a). The direction of leak-off z is normal to the fracture face. The equation governing the linear isothermal flow of fluid into this segment is where a = Eq. 2 is a form of the diffusivity equation. It is derived from the equation of continuity, Darcy's law and Eq. 3

By H. M. Bouton, G. S. Phipps, E. E. Schumacher

The seriousness of the present tin scarcity has stimulated large consumers of this vital metal to develop drastic conservation measures in order to extend the available supplies to cover the emergency period. By devising new soldering methods and alloys the Bell System has contributed a substantial share in the tin conservation effort. Fortunately, the changes, as far as can be determined now, have not introduced weakness into the soldered joints. Some of the new procedurcs were already in the process of development at the onset of the emergency, while others were devised under its stress. In some instances, the newly developed solders were found to be more difficult to use than the alloys previously available, and would not have been introduced under normal conditions. One major change made that previously had been under consideration will result in large savings of tin. Unless service difficulties are encountered, this modification gives promise of remaining after the emergency has passed. The change involves a reduction in the amount of solder placed on a wiped joint between the cable sheath and the sleeve. Instead of the customary full sized wiped joint, a wipe of fillet proportions is formed. Through this change, a solder saving of more than 60 per cent per joint can be realized. Plumbers and cable splicers for many years have joined lead pipes and cable sheath by a soldering process called " wiping." The name is an apt description of the operation. For a wiped joint, the sections to be united are heated by molten solder poured over their surfaces, and the resulting semiliquid mass is manipulated by wiping with cloth pads to a well rounded symmetrical form like the one shown in Fig. I. The operation requires considerable skill on the part of the splicer and close control of the composition of the solder. At first consideration, the problem of tightness in such joints seems simple but experience shows that even under the best conditions the fissures frequently found in the solder occasionally link and form a path that allows leakage to occur. In telephone cables not maintained under gas pressure, such leaks permit the entrance of water, which wets the paper-covered conductors and thereby impairs the insulation value and causes service interruptions. Ry going to an extreme and wiping off all the solder in excess of a fillet, it has been found that many causes of porosity are eliminated. Figs. 2 and 3 show cross sections of joints wiped in the old and the new ways. The saving in solder, and consequently in strategic tin, is evident. The field splicing forces find that joints are easier to make by the new method and are less likely to be porous. The metallurgical considerations that are responsible for the success of the fillet wipe are of interest. Much has been written about the wiping process of soldering cable joints and the many requirements of a good wiping solder have frequently been listed. The success of the procedure described

Jan 1, 1943

By M. Yokoi, K. Yoshida, T. Ishihara

The solubility of aluminum in cryolite melts has been determined by measuring the weight loss of aluminum submerged in melts contained in closed silicon nitride crucibles. The solubility in pure cryolite has also been checked with radioactive isotopes. The solubility decreases with increasing A1203 concentration, decreasing temperature, and decreasing cryolite ratio. The change of aluminum solubility in pure cryolite with the activity controlled by using Al-Ag and A2-Cu alloys supported the assumption that aluminum would dissolve in the form of monovalent ions according to the reaction 2AI + A1' —3 A1'. DURING the electrolytic production of aluminum, the electrodeposited metal redissolves in the bath in some form and is subsequently oxidized back to the former ionic state. This dissolution is believed to cause a decrease in current efficiency. Reported data on the solubility of aluminum in cryolite melts are scattered. The mechanism of the dissolution has not yet been determined, although certain tentative interpretations have been proposed. Many previous studies were performed under different test conditions. Studies were performed in open Systems and closed systems,'o and some were apparently not given sufficient time to Saturate." The solubility can be determined either analytically or gravimetrically. The analytical determination involves measurement of hydrogen gas evolved when frozen cryolite bath saturated with aluminum is treated with sodium hydroxide or hydrochloric acid. The gravimetric determination, adopted by many investigators,'-37'3>14 involves measurement of weight loss of the metal after equilibration with a known amount of salt. It appears that the former technique yields much smaller values of solubility than the latter technique. This large difference in results strongly suggests that the dissolved metal in the cryolite melt is no longer in the metallic state. In the present study, the solubility was determined by the gravimetric technique at various activities of aluminum using A1-Ag and Al-Cu alloys. An attempt was also made to determine the ionic (or atomic) state of the dissolved metal from the solubility data. 1) EXPERIMENTAL Apparatus. Preliminary tests demonstrated that silicon nitride was suitable as a container material since it is compatible to both the fluoride melts and molten aluminum. Crucibles were made from silicon powder nitrided with Nz gas at 1600°C. The good compatibility between crucible and melts is due to the near perfect nitrogenation of silicon. Only small amounts of silicon were found in the aluminum metal after the experiments. The crucible dimensions were 90 mm inside height, 38 mm ID, 105 mm outside height, and 50 mm OD. Close-fitting lids made of silicon nitride were also prepared. The crucible was placed in a close-fitting graphite crucible heated by a vertical Kanthal furnace, Fig. l. The lid and crucible are fastened tightly together by the condensation of vaporized bath in the narrow gap between them. The temperature was measured in the wall of the graphite crucible and controlled within * 5°C. The temperature difference between the measuring point and the interior of the melts was initially determined. Materials. The materials used were: Greenland cryolite (impurities CaF,, 0.5 pct; AlzO3, 0.2 pct; high-purity aluminum metal (purity 99.99 pct); A1203 and AlF, (provided by Nippon Light Metal Co., Ltd); reagent-grade NaF and CaF2; and 99.9+ pct Ag and Cu. Powdered reagents were carefully dried before use. A1-Ag and A1-Cu alloys were prepared before the experiments; their composition was checked by analysis

Jan 1, 1969

By A. E. Bellis

There is a wide difference of opinion among rifle experts in the matter of barrel steel, and the relative importance to the life of the barrel of the steel's composition, heat treatment, structure, and physical properties. In order to promote discussion, which it is hoped may' lead to the discovery of the source of some of the traditional beliefs on the subject, the results of some tests are presented here, with data on heat treating, physical tests, and erosion. The detailed metallographic study of this steel is given in another paper.l The conclusions from these tests should be capable of wider application than their direct bearing on the barrel-steel problem. The Government specifications for barrel steel for model 1903 rifle (Springfield) call for carbon 0.50 to 0.60 per cent., manganese 1.00 to 1.29 per cent., silicon under 0.25 per cent., sulfur under 0.06 per cent., phosphorus under 0.08 per cent. The minimum physical requirements are: Tensile strength, 110,000 lb. per sq. in. (7733 kg. per sq. cm.); yield point, 75,000 lb. per sq. in (5472 kg. per sq. cm.); elongation, 20 per cent.; reduction of area, 45 per cent. Material fulfilling these requirements gives practically no failures when proof-fired, with charge of 70,000 lb. per sq. in. pressure, which is 40 per cent. in excess of the service charge. The turning and drilling operations show up any seams or laps such as accidentally occur even in the best heats of open-hearth steel, so that faulty stock is practically all eliminated before proof-firing. These physical requirements are met either by rolling billets at a proper temperature down to the form of tapered barrel blanks or by heat treating bars that have been upset to cnlarge the breech section. The transformation temperature of this steel, on heating, is around 1350" F. (732' C.), varying somewhat with the composition and the rate of heating. The actual treatment of the barrel blanks, as carried out by different manufacturers, gives four kinds of barrels, which will be called A, B, C, and D, for convenience. A barrels result from heat treating upset blanks by quenching at

Jan 1, 1920

By J. E. Hilliard

Isobaric sections of the eutectoid region of the iron-carbon phase diagram have been exgerimentally determined at 35, 50, and 65 kb. The phase boundaries were located by metallographic analysis of specimens quenched after equilibriatwn at known temperatures and pressures. With increasing pres -sure a pronounced decrease in the solubility of FesC in austenite was observed together with a depression of the eutectoid temperature. These two effects resulted in a shift of the eutectoid composition toward a lower carbon content; at 65 kb the eutectoid was at less than 0.2 wt pct C. These results are in qualitative agreement with thermodynamic calculations. It has also been shown by calculations that Fe3C in contact with saturated austenite will be stable with respect to both graphite and diamond formation at all pressures above -3.5 kb. 1 HE investigation described in this article was part of a more general study of the effect of high pressure on transformations in Fe-C alloys. Thermodynamic calculations and exploratory runs made in 1959 at the start of the program indicated an appreciable change with pressure in the phase equilibria of Fe-C alloys. However, the calculations were not considered reliable enought to provide the quantitative information required for the interpretation of the effect of pressure on the kinetics of transformations. An experimental investigation was therefore made to determine a series of isobaric sections of the eutectoid region of the phase diagram at pressures up to 65 kb. EXPERIMENTAL PROCEDURE Materials. Seven alloys with analyzed carbon contents of 0.10, 0.20, 0.38, 0.60, 0.77, 0.93, and 1.20 wt pct C were prepared from Ferrovac" iron and high-purity graphite induction melted in magnesia crucibles under argon. The ingots were hot worked and swaged down to 0.19-in.-diam rod which was then centerless ground to a final diameter of 0.125 in. Samples for chemical and spectrographic analyses were taken from each end of the rods. The prin- cipal impurities were found to be Ni, Al, Co, and Si which were present in amounts up to 0.03, 0.02, 0.01, and 0.01 wt pct, respectively. Specimens were prepared by slicing the ground rods into pills 0.06-in. thick which were silver plated to reduce decarburization during the equilibration. Silver was chosen for this purpose because of its very low solubility for carbon and its mutual immisicibility with iron. High-Pressure Apparatus. The high-pressure runs were carried out in the "Belt" apparatus.' As shown in Fig. 1, this consisted of a cylindrical cell compressed between two Carboloy punches loaded by a uniaxle press. Radial support to the cell was given by the "belt" which was a Carboloy die heavily prestressed by a series of steel binding rings. Laminated gaskets of lava and metal separated the punches from the inner surface of the "belt". A cross-section of the high-pressure cell is shown in Fig. 2. Two specimen pills were located inside a resistance heater of 0.20-in.-diam Nichrome tubing. The ends of the tube were sealed with alumina and lava pills tamped in place after the

Jan 1, 1963

By E. C. Houston

The presence in the Tennessee Valley of extensive deposits of olivine, a silicate of magnesium and iron that contains approximately 28 per cent magnesium, has been recognized since 1896 when Lewis8 published a survey of basic magnesium rocks of western North Carolina. A recent field survey by T.V.A.7 showed that more than two hundred million tons of high-grade olivine occurs above local drainage levels in western North Carolina and northern Georgia. Except for sporadic attempts to work the olivine for its nickel and chromium contents,10 the ore received little attention industrially until 1926 when Goldschmidt3 suggested its use in the manufacture of refractories. Only one instance is recorded of an attempt to utilize the ore commercially for its magnesium content;" in this case a process was used in which olivine was treated with sulphuric acid, the resultant mixture was leached with water, and the leach solution was purified and evaporated to form epsom salts, which was the end product. As a part of its program of contributing to the development of the natural resources of the region, the Tennessee Valley Authority became interested in the olivine deposits as a source of metallic magnesium because of their high magnesium content and proximity to hydroelectric power. Studies were undertaken to determine the feasibility of producing magnesium chloride by extraction of olivine. The experimental work was carried out successively at the T.V.A. Minerals Testing Laboratory, Norris, Tenn., at the Georgia State Engineering Station,* Atlanta, Ga., and at the T.V.A. laboratory at Wilson Dam, Ala. The present paper describes a process. developed through the pilot-plant stage, whereby magnesium chloride suitable for reduction to metallic magnesium can be prepared from olivine by extraction with hydrochloric acid and subsequent purification. Research on the magnesium-from-olivine process, originally intended for peacetime use, was given impetus by the shortage of magnesium that existed at the beginning of the current world war. By the time the process was sufficiently developed to justify a proposal for its inclusion in the war program, the shortage had been met by expansion and development of other processes. However, it is believed that the magnesium-from-olivine process may have advantages that will warrant consideration of its use after the war, when the economics of the various processes rather than production on a wartime scale will be the criterion for commercial production of magnesium. Description OF Process Metallic magnesium is produced electro-lytically by the Dow and the Elektron

Jan 1, 1949

By R. H. Fillnow, D. J. Mac

IT has been demonstrated that alloys in systems structurally analogous to steel undergo reactions during heat treatment similar to those of steel, and yet very little work has been done on such systems, particularly from the standpoint of isothermal transformation. The literature shows that most of the isothermal work has been done on copper-alu-minum alloys.'-3 One paper has been reported on a eutectoid copper-silicon alloy,' and one on iron-nitrogen alloys.' There are no published reports of previous investigations on the isothermal transformation of a eutectoid beryllium bronze. At least two papers have been reported on isothermal age-hardening phenomena in beryllium-copper alloys of lower beryllium content.5,6 No information on eutectoid transformations in this alloy is given in Rimbach's book, "Beryllium." ' This paper reports the results of an investigation on the isothermal transformation characteristics of a eutectoid beryllium bronze. Materials Used and Procedure The eutectoid beryllium bronze used in this investigation was centrifugally cast at the Ampco Metal Co., Inc.. Milwaukee. Wis. A master beryl-lium-copier alloy, purchased from the Brush Beryllium Co., was used to make the beryllium addition to the copper. The alloy was melted under a protective carbon cover and Centrifugally cast into a graphite mold preheated to 920°F. Some trouble with segregation of beryllium in the melt was encountered but was eliminated by violent stirring during melting and pouring. Since very thin .specimens were used for the various heat treatments, only one casting of the four prepared was necessary for the complete isothermal study, thus eliminating any discrepancies caused by a change in composition. The analysis of this casting was 94.035 pct copper and 5.965 pct beryllium. A slight trace of iron was found. The castings were sawed into specimens approximately 3/32 in. in thickness. The specimens were first given an "austenitizing" heat treatment at 788°C, well within the single phase beta region, in a vertical tube furnace. The specimens were then quenched individually into an adjacent molten salt bath and held there for a definite time, after which they were quenched into water at room temperature. Temperature was held to ± 2°C in the salt bath. No homogenizing treatment was given the specimens other than the soak at 788°C. Despite the fact that this was a cast alloy, no evidence of segregation or coring was found in the microstructure of any specimen, either as cast or as heat-treated. Upon completion of the heat treatment, the speci-mens were subjected to metallographic examination

Jan 1, 1951

By Henry J. Welge

Laboortory apparatus has been devised which permits study of the displacement of oil from cores by water and by gas. The cores used contained interstitial brine as well as oil. Experiments were run to determine the comparative effect of varying the properties of the fluids used. No great effect was noted on the maximum displacement achieved. This observation made it unnecessary in initial work to use fluids in their exact reservoir conditions. Consequently, the displacements were run at near-atmospheric pressure in Pyrex glass equipment, using stripped crude oils. Introduction and Theory The chief object of this work has been to determine the efficiency of gas and water as primary agents for displacing oil from reservoir rock under laboratory conditions in which capillary phenomena were predominant. To this end the maximum displacement of oil from cores has been ascertained. This maximum displacement may not be equal to the maximum displacement from a reservoir; but it will be a close approxirnation to it sometimes, and other times the laboratory information will be useful in reservoir engineering predictions. It is] believed that the laboratory experimental maximum represents the upper limit for the reservoir recovery. The experiments were carried out by obtaining cores of interest from the reservoir, and filling the pores with interstitial brine and oil with the restored state tech- nique.1 Then the oil was displaced from the core as described later, either by brine from below, or by gas from above. The former type of displacement suggests analogy to production by water drive, but not to water flooding, for reasons discussed below. The latter type of displacement is believed to simulate production by gas cap displacement. The displacements were performed by what may be termed the capillary-pressure method. The cores are placed in capillary contact with an oil-wetted membrane which has very small pores (about I micron in diameter). Pores of this size will transmit oil but Prevent the Passage of gas or water, unless the Pressures used are higher than the capillary Pressures employed in this work. Accordingly, use of the membrane makes it possible to apply a capillary pressure differential between the displacing phase and the oil in the core. AS in the displacement of brine toward that condition of oil and water distribution existing originally in the reservoir,' it may not always be desirable to reduce the oil saturation in this experiment to an absolute minimum. With reservoirs having small productive closure, it is preferable to evaluate and use a displacing pressure no higher than the capillary pressure, Ap, which will ultimately become available for displacement in the reservoir. This pressure may be calculated from a knowledge of the density of the oil-in-place, do, the density of the displacing phase, dl, and Ah, the vertical distance between the section of the

Jan 1, 1949

By J. M. Bugbee

The engineer and the conservationist agree that effective water drive is the desirable reservoir production mechanism. Water drive may result either from the expansion of edge water, the reservoir water bordering an oil pool, or from the artesian flow of edge water from the outcrop. Thus, the extent of the reservoir has an important bearing upon both the rate and the ultimate quantity of water influx to an oil pool. Lens-type reservoirs are generally recognizable, but the complete structure of the more important domal types, having possible limitations from crestal and synclinal faulting, is not well understood. The delineation from cores, electrical logs and exploitation phenomena of the crestal portions of reservoirs is increasingly exact. This paper suggests that inference from these factual pictures, combined with the scattered well and geophysical data of the synclines and with consideration of the dynamics of structural formation, may be applied to solving the complete geologic structure. Since faulting on the domes and in the synclines may effectively seal and thus limit the size of a reservoir and bar additional water influx, consideration of geologic structure and its possible effects is essential to complete analysis and prediction of reservoir performance. Introduction Implicit in reservoir studies is the fact that the oil must be displaced from the reservoir rock by some other fluid, either gas or water, and this understanding yields the terms descriptive of the major reservoir production mechanisms, gas expansion and water drive' Three recent papers1-2-3 make clear the economic and conservation preeminence of Water drive as a production mechanism; in fact, the title of the latest of these is " Production under Effective Water Drive as a Standard for Conservation Practice." There appears to be an assumption at times among analysts that the effectiveness of a water drive is solely dependent on the rate of oil production; that is, if water drive appears to be insufficient or lacking, a lower oil-recovery rate would increase or reveal it. This assumption might result from the fact that the analysis has been wholly developed during the period of production curtailment; that is, since 1929. The writer takes it that the recurrent phrase in De Golyer's paper,3 "some degree of water drive," is related to this assumption. In California, an extraordinary phrase, "inactive water drive," is rather common and the connotation of uncertainty regarding our knowledge of reservoir performance is evident. Wyckoff2 speaks of the type of reservoir and performance as follows: "In general, reservoirs may be any one or a combination of domal, faulted, lenticular, or stratigraphic traps. Insofar as the dynamic performance of such reservoirs is concerned, the particular type merely determines whether regional flow is symmetrical as in a uniformly developed domal or lenticular type, or one-sided as in many stratigraphic or faulted traps." But whether the flow is

Jan 1, 1943