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By C. D. Hall, F. E. Dollarhide

Fluid Ioss agent.s for crude oil and for water have been studied in dynamic tests. A treatment using a spearhead with a fluid loss agent followed by plain fluid appears feas ible in crude oil, but not in water. An equation for spearhead depletion shows that spurt loss relative to fracture width must be low, if the portion of spearhead fluid in the treatment is to be small. The presence of colloidal matter in crude oils aids the fluid Ioss agent. Unlike in kerosene, where flow limited the agent deposition, in crude oils the filter cake continually formed and leak-off declined. The volume-time relation varied somewhat for different crudes, but was best described by a square root of time function. Spurt loss was inversely proportional to agent concentration. After the fluid loss agent initiated the filter cake, the crude oil colloids built on it effectively. A 2-minute or a 5-minute spearhead with double the normal agent concentration gave the same fluid Ioss curve as the same concentration did for a 30-minute test. The agents tested in water gave fluid Ioss plots on which, for the first few minutes, volume was proportional to the square root of time, but later became proportional to time. For fracture area calculation the customary square root of time function is a satisfactory approximation. Leak-off rates and spurt losses were higher in water systems than in oils. The spurt Ioss tended to be inversely proportional to concentration. In spearhead tests, the filter cakes were not eroded by water flow. However, the rather high spurt loss values make spearhead treatments impractical for water-based fluids. Introduction The effects of dynamic testing conditions on the performance of fluid loss agents in kerosene have been studied previously.' We have extended the work to include crude-oil- and water-based fracturing fluids. An understanding has been gained of the mechanisms of formation and functioning of the filter cakes of fluid loss agents. The practical aspects of evaluating performance of agents in relation to fracture area calculations also are considered. The feasibility of using the fluid loss agent in a spearhead stage of the treatment is examined further for both types of fluids. Experimental Procedure The dynamic fluid loss tests were performed in an apparatus similar to the high-pressure apparatus described in a previous publication.' A fracturing fluid was circulated over a rock surface located in a closed pressurized loop. The fluid flowed axially over the cylindrical surface of a core 2 in. in diameter X 3.5 in. long, mounted (with the flat ends sealed off) in a pipe, with 0.117 in. annular clearance. The filtrate was collected in a central hole in the core and led through valves to graduated cylinders. Provision was made for changing quickly the circulating fluid during the test (spearhead runs) without interrupting the filtration pressure. The only modifications were to add heating tapes and water jackets for the tests with crude oils, all conducted at ISOF, and to change all parts exposed to the test fluid to stainless steel for the tests with water-based fluids. The latter tests were made at room temperature, 80F. Three crude oils were tested. A mixed crude, obtained from a local refinery, contained a considerable amount of light ends. For safety reasons, it was stripped to 250F vapor temperature before use in the fluid loss tests. The other two oils were used as obtained from lease tanks. One was a greenish-brown, 37" API paraffinic crude, and the other was a black, 32" API asphaltic crude. The fluid loss agent for oil, here designated for brevity as Agent A, was Adomite@ Mark II*, a granular solid commercial agent, the same as previously tested in kerosene.' Three different compositions of fluid loss agents were tested in Tulsa tap water. Agent B was adomit& Aqua*, a solid commercial fluid loss agent, comprising clays and hydrophilic gums principally derived from starch. Agent C was a mixture of three parts of Agent B with two parts of silica flour. Agent D was Dowel1 J137, a mixture of guar gum and silica flour. The test cores were cut from contiguous blocks of Berea or Bandera sandstones. For the oil tests, the cores were oven dried, evacuated, saturated with kerosene, and the kerosene permeability was measured. The cores used with the water-based fluids were pretreated by saturating with 3 percent calcium &loride solution to minimize pemeability damage by the fresh water due to clay migration. The

Jan 1, 1969

By R. O. Williams

Measurements have been made of the internal energy of deformation in a Cu-A1 alloy and a Cu-Zn alloy as the deference between the work and the released heat. The method required the rapid compression of samples to reduce thermal interactions. The rate of energy storage is low initially but then becomes almost linear with strain. Both alloys stored about 60 cal per mole at a strain of 0.4 in the recrystallized condition. The fractional rate of storage increases at low strains reaching about 0.25 at a strain of 0.15 and then decreases slowly with increasing strains. As do pure metals, these alloys release appreciable energy immediately following deformation; in contrast with pure metals, however, the release continued for extended periods of time. This energy release is somewhat sensitive to the amount of deformation, the deformation temperature, and prior thermal & eatment. It is believed that this release is a composite of that observed in pure metals which has been attributed to dislocations and that due to the motion of vacancies which produces increased short-range order. IT is expected that changes brought about by deformation of a pure metal can be understood in terms of the three defects—dislocations, vacancies, and interstitials—along with the interactions possible between these defects. Frequently stacking faults are created and must also be considered. 1t is not immediately clear whether or not the stress fields which are created should be regarded as independent of dislocations. For alloys there is the important additional effect of atomic configuration, for example short-range order, which must also be considered and will, in general, interact with each of the above defects. While it is true that a complete understanding of pure metals is not yet possible, it would seem very valuable to establish the similarities and differences between pure metals and alloys. Such knowledge could contribute to the understanding of both. A study of the changes in internal energy resulting from deformation of two alloys is reported here. Although some information has been available for alloys almost as long as for pure metals, the volume of work has been substantially less. Sato' and Quinney and Taylor' were responsible for the earlier work, both using brass and annealing calorimetry. tizhnova' studied stored energy in Cu-Ni alloys by a method somewhat similar to the one reported here. Bever and his co-workers have made extensive studies of Au-Ag alloys4'5 and more recently CU-AU'U' using solution calorimetry. Clarebrough et a1.' have recently studied brass using annealing calorimetry. EXPERIMENTAL METHOD The present results were obtained by the rapid, adiabatic compression of a sample about 1/4 in, diam by 1/2 in. long between two tungsten carbide hammers. A vacuum provided thermal isolation and oil provided effective lubrication between the sample and hammers. The increase in internal energy is the difference between the mechanical energy and the heat liberated within the sample. The mechanical energy was determined from the velocity of the hammers (calculated from the height through which the hammers traveled) and was essentially constant for each deformation cycle. The heat was determined from the temperature increase of the sample which was measured by an embedded thermocouple. Specific heat data were calculated from Neumann's rule using tabulated data for pure metals.9 Since the fraction of the energy which is stored is large compared to that for pure metals, specific heat data of high accuracy are not required. Successive increments of deformation were carried out by repeating the procedure, the limit being determined mostly by the decreasing accuracy caused by the increasing corrections and the decreasing storage of energy. About five cycles were used to give a true strain of about 0.5 while the time interval between cycles was 1 to 2hr.

Jan 1, 1963

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

By Eugene S. Machlin

A classical theory of solid solutions involving neavest-nergkbor intevactions with both central and linked-central forces between atoms has been developed. It has been found that the theory, where it can be checked quantitatively, is in ageement with experiment. The theory encompasses a description of many diverse pkenomena, such as antiphase shift structures, size effect, relative stabilities of various solutions, lattice para,neters, and order-disorder transitions. In particulav. a quantitative prediction not involving adjustable pavameters is made concevning the deviation of the Au-Cu interatonlic distance in long-range ordered (Ll,) Cu-Au I fronl the average distance based on the distances in pure gold and copper. This prediction, which is in agreement with expel-intent, has not been encompassed by any preuious theory. The theory of order-disorder is fragmentary. That is, no one theory exists that can explain the variety of qualitative phenomena observed. Further, many theories are not in good quantitative agreement with experiment. This subject has been reviewed by Muto and Takagi, Tuttman, and Oriani.3 There exists no doubt that the quasi-chemical approximation is not a complete description and that the inclusion of strain energy using macroscopic elasticity theory concepts leads to results in disagreement with experimenL4 The observation of antiphase domains and ordering systems such as Cu-Pt has led to Brillouin zone treat-ment of the order-disorder transition as opposed to the classical Ising model. The objective of this paper is to demonstrate that it is possible to develop a pairwise approximation model that can explain many of the observed order-disorder phenomena that have puzzled investigators in the past. This theory is based upon an empirical model due to ergmman' for the elastic constants of metals. This model is generalized for multicomponent systems. As will be shown, the theory yields a short-range ordering energy for the disordered solution which differs from the ordering energy calculated from the differences in energy of disordered and long-range ordered solutions. It will be demonstrated that there is no necessary correlation between heats of formation and the tendency to order or between size effect and the tendency to order. Also, the existence of antiphase domains and iso-short-range-order systems that form superlattices (Cu-Pt) is predicted on the basis of the theory. Further, the relative stability of competing superlattices is calculable from the theory. If single-crystal elastic-moduli data are available for the pure components and one superlattice then there exists but one adjustable parameter in the calculation of lattice parameters for both the disordered and ordered solid solutions. In one special case, no adjustable parameters are required and a quantitative prediction is made. For the calculation of energies and partial order, there exists but one additional adjustable parameter, the pair-exchange energy V used in the quasi-chemical approximation (or the Ising model.) However, in these calculations, much more precise values are required for the single-crystal elastic moduli than available if the quantitative uncertainties in the predicted values of the energies are to be sufficiently small. THEORY ~er~man' has developed a model with which he was able to obtain fair agreement with experiment for the relations between the elastic constants for metals. This model which we shall call Bergman's model is a linear combination of his models I and 11. In effect, Bergman, in this model, considers that each interatomic distortion is composed of two components: a classical central force distortion with an associated central force constant and what we shall call a linked-central force distortion with an associated linked central-force constant. The linked-central force distortion component obeys the constraint that the sum of such distortions over all the bonds equals zero. No constraint is imposed on the classical central force distortion component. Bergman' derives the constraint on the linked-central force distortion on the basis of application of Pauling's relation between bond distortion and bond number to metals.ga This assumption is not logically necessary, however, and the Bergman model may be taken as a mathematical model for elastic constants, e.g., a purely empirical model without a physical basis. In the present work, the method of Bergman has been applied to two-component systems (solid solutions). In place of an external strain—which would allow a calculation of the elastic constants for the two-component system—it is considered that internal interatomic distortions exist as a consequence of having three potentially unequal distortion-free interatomic distances and but one "average" interatomic distance. It is assumed that the distortion-free interatomic distances between atoms of the same element are those found in the pure element having the same undistorted crystal structure as the solid solution. The distortion-free interatomic distance between unlike atoms is in general not measurable except in the probably nonexistent

Jan 1, 1967

By Richard H. Jahns

Terminology and Basic Specifications Minerals and closely allied natural substances that are used for personal adornment, as raw stock for the fashioning of ornamental objects, or for other decorative purposes can be referred to collectively as gem materials. Industrial gem materials are those employed directly in various areas of industry. Substances that are manufactured for gem or industrial uses are termed synthetic gem materials; most of these correspond in composition and crystal structure to certain minerals found in nature. Imitation materials are those whose use is based upon their resemblance to substances of different composition and greater value. Gem stone is a designation commonly restricted to those materials suitable for personal adornment, and the complementary term ornamental stone is applied to the remaining materials not used industrially. This distinction is arbitrary and somewhat inconstant, owing to numerous geographic differences and historical shifts in end uses. Further, there is a complete gradation between the category of ornamental stones and that of dimension stone. Although many building and monumental stones are undeniably ornamental in their uses, treatment of such material is beyond the scope of this chapter. Substances that lose their identity in use are excluded from the gem category. Thus a transparent crystal of beryl would not be classed as a gem stone if it were treated as a source of beryllium metal. The adjectives precious and semiprecious have been employed as a means of distinguishing different gem materials on the basis of their recognized value. Diamond, emerald, ruby, and sapphire consistently have been regarded as precious stones, and in cut form they commonly are referred to as the noble gems. Opal, pearl, turquois, and chrysoberyl also have been classed as precious at various times. In recent years, however, it has been increasingly recognized that no satisfactory distinction can be based upon assessed value or any group of intrinsic properties, and at the present time all gem stones normally are referred to as precious. Indeed, the tendency is to extend this term to include many of the so-called ornamental stones, and the designation semiprecious has been essentially discontinued. Unlike most mineral commodities of economic value, gem materials are little altered in processing for end uses. Some stones are used in essentially their natural form, and most are reshaped and polished without significant changes in their fundamental properties. Thus the preparation of gem and ornamental stones is intended chiefly to emphasize or enhance desirable characteristics that are present initially. The worth of most synthetic gem stones is founded upon the identity between their major properties and the natural characteristics of the corresponding minerals, just as the pleasing qualities of imitation stones depend upon how well certain of their properties simulate those of more valuable substances. The most important specifications of gem materials represent four basic factors: beauty, durability, rarity, and portability. Beauty, whether expressed as splendor, "purity," attractiveness, or in some other way, is mainly a function of personal response to optical properties such as color, transparency, indices of refraction, and dispersion. Freedom from visible imperfections is important for transparent stones. For some substances beauty depends also upon asterism, opalescence, textural and

Jan 1, 1960

By A. Martens

When I was honored with an invitation from the American Institute of Mining Engineers to present a paper at the Chicago meeting on the microstructure of iron, I hesitated about accepting, as the short interval that would remain at my disposal, after other pressing matters had received attention, could not but seriously affect the work of preparing such a paper. Unfortunately my fears have been realized and my work is neither completed, nor yet as comprehensive as I should desire. Mindful of my promise, however, and recognizing that 1 have reached a point where the results of my researches may prove suggestive, I am led to present them now, trusting that this brief explanation map secure indulgence for whatever deficiencies the paper may disclose. So far as my knowledge of published memoirs and treatises extends, microscopy cannot yet be said to possess a really firm foundation. In few cases only has any systematic development of the methods of investigation been undertaken, and broad gaps remain to be filled. It is not yet possible, therefore, to give a complete survey of the field, or, indeed, to supply a text-book on microscopic metallography. As Mr. F. Osmond, of Paris, a distinguished member of our profession, has undertaken to prepare for the Chicago meeting a historic review of the work actually accomplished I need not touch on that branch of the subject; but before entering upon my special theme, it may not be out of place for me to introduce certain explanations, as furnishing reasons for the course 1 have hitherto pursued, and to offer some suggestions for the further development of the methods of microscopic investigation. In microscopic metallography, the examination has to be conducted principally with incident light. Objectives of low power, in which the distance between the front lens and the abject is considerable, are adapted for directly incident light, and in such cases the relatively great depth of the image renders it possible to examine

Jan 1, 1894

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-B alloys has been measured up to the solubility limit for the formation of boron nitride. The activity coefficient of nitrogen increases with increasing boron content in the range 0 to 7 wt pct B. From experimen -tal data, values have been calculated for the B-N interaction parameter e3 at temperatures in the range 1550" to 1750°C. A value of 0.038 has been estimated for the boron self-interaction parameter eg at 1550°C. The standard free energy of decomposition of boron nitride into the elements dissolved in liquid iron has been determined to be: ?F° = 45,900 -21.25T in the range from 1550° to 1750°C. The nitride is assumed to be of composition BN. BORON nitride has an unusual combination of properties which make it appear attractive in a wide range of engineering applications. Some of its more important and most recent applications are in the nuclear area, particularly in connection with the liquid-metal cooled reactor concept now receiving considerable emphasis. Boron nitride has a high degree of stability at elevated temperatures. It also has excellent ma-chinability and the ease with which its crystals deform suggests applications as a lubricant. These properties stem from a hexagonal layer-type structure similar to the structure of graphite. One of its primary uses to date has been for seals in liquid-metal pumping systems. It is also used in nuclear reactors as an insulating layer to separate two solid metals which are not themselves compatible under the conditions of temperature and atmosphere in which they are used. Its inertness to liquid metals has also suggested use as a mold-release agent in casting processes. In addition to its excellent machinability and reported inertness to liquid metals such as iron, silicon, aluminum, copper, and zinc, boron nitride has high thermal conductivity and excellent thermal shock resistance. This combination of properties would make it appear ideal as a refractory crucible material for refining of high-purity liquid metals, for example high-quality steels. However, since it is known that concentrations of boron as low as 50 ppm can have a marked effect on the physical properties of certain steels,' in particular on the creep and stress-rupture properties, an investigation was undertaken to define accurately the chemical equilibrium among boron, nitrogen, and liquid iron in the range of steelmaking temperatures. EXPERIMENTAL PROCEDURE Two experimental approaches to this problem were employed: a Sieverts' method and a quenching method. In the first method, the Sieverts' technique was used to measure the equilibrium nitrogen solubility in liquid Fe-B alloys of 0 to 7 pct B as a function of nitrogen gas pressure over the melt. The solubility limit of the boron nitride phase formed was determined by the point of departure of the nitrogen absorption from Sieverts' Law. This technique has been applied to liquid Fe-Ti alloys by Rao and parlee,' to liquid Fe-A1 alloys by Evans and Pehlke,3 and to solid Fe-V alloys by Fountain and Chipman.4 In the second method a melt of liquid iron was held in a crucible of boron nitride under a known partial pressure of nitrogen gas. After thermodynamic equilibrium was attained, the melt was quenched in a stream of helium and then analyzed by wet-chemical methods for boron and nitrogen. The Sieverts' apparatus used in the first method was essentially of the same design as the one described by Pehlke and Elliott.5 The charge materials were vacuum-melted high-purity iron (Ferro-vac E) supplied by the Crucible Steel Co. and -325 mesh boron powder supplied by Cooper Metallurgical Associates of Cleveland, Ohio. The boron contained less than 0.02 wt pct O, according to supplier's analysis. Recrystallized alumina crucibles were used to contain the melt. Examination of solidified melts showed these crucibles to be satisfactory with no evidence of any reaction or physical penetration of the crucible wall by the melt. The melt temperature was measured by a disappearing filament-type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diam sight hole in the crucible lid. The pyrometer was calibrated against the melting point of pure iron in the same apparatus, taking the emissivity of

Jan 1, 1964

By Donald B. Evans, Robert D. Pehlke

The solubility of nilrogen in liquid binary alloys of iron with Litanium. zivconium, columbium, vanndiurn, and tantalum was measured for alloy composiLions up to the solalbility limils of lhe alloy nitrides. All five alloying agents were found to decrease markedly the activity coefficient of nitrogen in liquid ivon. The metal/nitvogen mole ralios in the alloy nitrides formed were generally .found to be slighlly greater than 1.0, but in no case greater than 1.5. From the experimental data, the standard free energies of fortmation of titanium and zir-conium nitrides have been calculated for the Lemperaluve range 1550° to 1750 C. The solublily Products for columbium, tantalum, and vanadium nitrides are also reported. A number of research investigations have examined the effect of refractory metals on the solubility of nitrogen in liquid iron. Although data on zirconium are not available, investigators are in agreement that titanium, vanadium, columbium, and tantalum markedly increase the solubility of nitrogen in liquid iron. This fact alone makes desirable the acquisition of thermodynamic data for these elements in liquid iron. Since refractory metals are known to be stable nitride formers, they have been suggested as steel denitrifying agents, and some of their nitrides have recently been considered as containment materials for liquid iron and iron alloys. Most available thermodynamic data for these metals relate to their dilute concentrations, but effective thermodynamic treatment of these applications requires data at concentrations near the solubility limit of the alloy nitride. Although some work has been done at relatively high alloy concentrations in liquid iron (particularly for vanadium 2,3 and titanium 2,4), the results have been somewhat contradictory. Disagreement may be partly attributed to the fact that the compositions of most refractory metal nitrides have been shown to be nonstoichiometric, and to vary 2,5-8 depending on the temperature and nitrogen gas pressure with which the solid nitride phase is in equilibrium. One purpose of this study consequently has been to determine the compositions of the refractory metal nitrides precipitated from a liquid iron solution. EXPERIMENTAL PROCEDURE Rao and Parlee2 and Evans and Pehlke 9 have discussed the technique for measuring the solubility product of an alloy nitride phase in liquid iron by finding the point of departure of the nitrogen solubility from Sieverts' law. The method consists of measuring the solubility of nitrogen in a melt of iron containing a known concentration of a second metal as a function of the nitrogen gas pressure over the melt. In this study the second metal was one of the refractory metals titanium, zirconium, columbium, vanadium, or tantalum. When the nitrogen pressure at which the refractory nitride forms is reached, a deviation of the measured solubility of nitrogen in the melt from Sieverts' law is observed in the form of a "pressure halt." The concentration of nitrogen in the melt associated with this breakpoint in the nitrogen-absorption curve is then used to calculate the nitride solubility. The Sieverts method was used to measure nitrogen solubility as a function of nitrogen pressure and temperature. The experimental equipment for this technique has been previously described in detail. 1,9 Charge materials used were vacuum-melted high-purity iron (Ferrovac-E) and the best commercial grades of the refractory metals obtainable (in all cases at least 99.8+ pct pure). Recrystallized alumina crucibles were used to hold all melts except those containing zirconium, for which zirconia crucibles were necessary. Temperatures were measured by a disappearing-filament type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diameter sight hole in the crucible lid. By means of a technique previously described, 9 in which the refractory-metal nitride was precipitated at one temperature then redis-solved by raising the temperature 50°C and precipitated again at a higher temperature, it was possible to obtain data over a temperature range of up to 200°C on a single melt. It was found that this technique could not be used with melts containing zir-

Jan 1, 1965

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By S. Sumski, M. B. Panish, R. T. Lynch

The liquidus isotherms in the gallium-rich corner of the Ga-Al-P phase diagram have been determined from 1000" to 1200°C and at I100°C the corresponding solidus isotherm was obtained. A simple thermody-namic treatment which permits calculation of the solidus and liquidus isotherms is discussed. A technique which was previously used for the growth of GaxAl1-xAs was used for the preparation of solution epitaxial layers of GaxAl1-xP and ALP. An approximate value of 2.49 i 0.05 ev for the band gap of Alp at 300°K was obtained and the ternary phase data were used to estimate a value of 36 kcal per mole for the heat of formation 0f Alp at that temperature. The Gap-A1P crystalline solid solution is one in which there exists the possibility of obtaining crystals with selected energy gaps, within the limits imposed by the energy gaps of Gap and Alp. Such crystals are of considerable interest because of their potential value for optoelectronic and other solid-state devices. Furthermore, it has been amply demonstrated for GaAs and GaP,'-7 that device, or bulk materials grown from gallium solution generally have more efficient radiative recombination than materials prepared in other ways. This presumably due to the lower gallium vacancy concentration in such material.= Small crystals of GaXAl1-xP and A1P have been grown from solution,8-10 and A1P has been grown from the vapor," but neither have previously been grown by liquid epitaxy. In this paper we present the ternary liquidus-solidus phase diagram of the Ga-A1-P system in the region of primary interest for solution epitaxy, and discuss the thermodynamic implications of that phase diagram with particular reference to the liquidus and solidus isotherms in the gallium-rich corner of the GaxAl1-xP primary phase field and to the A1-P system. Several measurements of the absorption edge of GaxAl1-xP crystals have been made and the width of the forbidden gap of A1P has been estimated from these measurements. EXPERIMENTAL The differential thermal analysis technique used to determine the liquidus isotherms and the optical measurements used in this work are similar to those described previously12 for the Ga-Al-As system, ex- thermocouples in the thermopile for added sensitivity. The materials used were semiconductor grade Ga, Gap, and Al+ The composition and temperature range at which DTA studies could be done was quite restricted. The upper temperature was limited by the chrome l-alumel thermopile to about 1200°C, and the highest aluminum concentration to about 5 at. pct by low sensitivity caused by the reduced solubility of Gap with increasing aluminum concentration in the liquid. DTA studies were not possible at 1000°C and below because of the low sensitivity caused by low solubility of Gap in the Ga-A1-P system. The cooling rate for these studies was about 1°C per min. No heating studies were done because of limited sensitivity. Supercooling probably does occur, but our experience with other 111-V systems indicates that it is no greater than about 10 to 15.c. Solid solubilities were determined by analyzing epitaxial layers of GaxAl1-xP grown from the liquid, with an electron beam microprobe. The layers were grown on Gap seeds by a tipping technique in which the layer is grown over a short-temperature range (20" to 50°C) on the seed from a solution of known composition. The tipping technique reported by Nelsson1 for GaAs could not be used, particularly for solutions containing appreciable amounts of aluminum, because of the formation of an A1203 scum on the liquid surface. A system was therefore designed, which would effectively remove the oxides mechanically, so that uniform wetting and crystal growth could occur. This tipping technique has already been described in detail." The best control over the composition of the re-grown layer was obtained when the tipping was done at a temperature which corresponded to the temperature of first formation of solid for the solution being used. Generally, therefore, a solution was prepared by adding the amounts of Ga, Gap, and A1 required to yield a solution which would be completely liquid above the tipping temperature with solid precipitating below that temperature. For most of the work reported here, the 1100°C isotherm of the ternary was used. It was generally necessary to heat the solution to 50" to l00. C above the tipping temperature to dissolve all of the Gap in a reasonable length of time. The epitaxially grown layers were used both for optical transmission measurements to aid in the estimation of the way in which the absorption edge changed with aluminum concentration, and for the electron beam microprobe analyses to provide data for the determination of the solid solubility isotherm. RESULTS AND DISCUSSION Liquidus Isotherms in the Ga-A1-P Ternary Phase Diagram: Thermodynamic properties of the system. The only thermal effect studied in this work was that

Jan 1, 1970

By L. A. Rapoport, W. J. Leas, C. W. Carpenter

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By Peter Greenfield, Paul A. Beck

Thirty binary systems of vanadium and chromium group transition elements with second and third long period transition elements were explored in regard to the intermediate phases formed. It was found that the phases predominating in these systems are s, AB type with ordered a-tungsten or C8 structure, close-packed-hexagonal with small unit cell dimensions and, finally, phases isomorphous with 1-manganese. IN recent years, considerable information has become available concerning the intermediate phases in binary systems of the transition elements. Thus, the s phase has been found to occur in most of the binary systems of vanadium, chromium, and molybdenum with the group of elements manganese, iron, cobalt, and nickel.' It was observed that, while the rr phases formed by chromium with manganese, iron, or cobalt possess a considerable temperature range of stability, particularly in the Cr-Co system, the corresponding s phases with molybdenum are limited to a temperature range of less than 400" above about 1200°C. Goldschmidt' reported v phases of tungsten with iron and cobalt, and these are apparently stable only at (and above?) 1400°C." Exploratory work in this laboratory with Fe-W and Co-W alloys of approximately 60 atomic pct W annealed at 1300°C did not produce X-ray patterns suggesting the presence of a phase. It appears then that the phases of iron and cobalt with the chromium group elements decrease in stability as the two components are chosen from long periods further removed from each other. From the available information, it might be concluded that the controlling factor is the increasing difference in atomic radii between the components. In contrast to the a phase, the phases formed by iron and cobalt with chromium group elements' are stable only when the latter have large atomic radii (molybdenum and tungsten); the corresponding phases with chromium do not occur. When the difference in atomic size becomes still larger (r,/r,, approaching the ideal value of 1.225), the u and p phases are replaced by Laves phases (AB,), as in the alloys of iron and cobalt with columbium," tantalum." and titanium."-" However, atomic size certainly cannot be the sole determining factor, since, for instance, in contrast to the very stable (Mo, Co)p phase, no such phase occurs in the Mo-Ni system even though the atomic diameters of cobalt and nickel are nearly the same. Similarly, chromium and cobalt form a a phase in a wide temperature range," but the corresponding s phase in the Cr-Ni system is missing. It has been shown that the composition of the u phase in various binary and ternary systems of transition elements in the first long period may be correlated in a fairly quantitative manner with the number of electron vacancies. The influence of electronic structure is probably present also in binary and ternary phases' and to some extent, apparently, even in Laves phases." " Although the absence of phases in the Cr-Ni and Mo-Ni systems has not as yet been explained on the basis of electronic structure, it appears reasonable to suspect a connection. One of the great difficulties in arriving at well founded rules in regard to the alloying behavior of transition elements lies in the lack of reliable information concerning the details of their electronic structure in the metallic and alloy form. The theoretical penetration of this field appears to be beset by very considerable difficulties, even when the complications due to alloy formation are disregarded. Another great source of uncertainty is the scarcity of phase diagram information even for binary systems of the transition elements so that only a very limited basis is provided for generalizations as to the occurrence of intermediate phases. For instance, very few binary phase diagrams of second and third long period transition element systems have so far been published. The present work was undertaken in order to survey the various types of intermediate phases occurring in 30 binary systems of elements of the group vanadium, columbium, tantalum, chromium, molybdenum, and tungsten with the elements rhenium, ruthenium, rhodium, palladium, and platinum. For most of these binary systems phase diagrams are very incompletely or not at all known, as will be further reviewed.*

Jan 1, 1957

By Robert A. Rapp, Jan E. Verfurth

From the measurement of internal-oxidation band widths in Ag-In and Cu-A1 alloys, products for the solubility No and the diffusivity Do of oxygen in silver and apparent NODo products in copper have been obtained over a range of temperature. The NODO products for silver are in agreement with the product of the individually determined No and Do values of Eichenauer and Müller. Although interstitial diffusion of oxygen in silver is expected, the temperature-independent factor Do of the diffusion coefficient does not agree well with the theory of Wert and Zener. For Cu-A1 alloys internal oxidation does not follow the expression derived for ideal kinetics, since the apparent NODo product calculated from internal-oxidation measurements is a function of the alloy content in the specimen. Thus, unequivocal values for No or DO or even the product NODO in copper are not available from the literature. RELIABLE values for the saturation solubility NO and diffusivity DO of oxygen in fcc metals are lacking and difficult to determine, partially because internal-friction measurements are not applicable. Permeability experiments and Sieverts7-type adsorption -desorption methods3 have met with difficulty; however, Eichenauer and Müller4 have recently reported on the solubility and diffusivity of oxygen in silver as determined by the latter technique . Rhines, Johnson, and Anderson,5 and independently Meijering and Druyvesteyn,' introduced the possibility of deriving values for the product NODO in a metal from measurements of the widths of internal-oxidation zones (subscales) formed during the internal oxidation of alloys. In addition to these authors, several other investigators7-9 have made such measurements in various silver and copper alloys at various temperatures, mostly using me- chanically polished specimen surfaces. The purpose of this investigation was to determine over a range of temperature the calculated products NODO in silver and copper from systematic measurements of the widths of internally oxidized zones in Ag-In and Cu-A1 alloys, using specimens with electro-etched surfaces. Consider the internal oxidation of a dilute solid-solution alloy in which the base metal is not oxidized. If diffusion of oxygen is the rate-controlling step, then the depth 5 of the internal-oxidation zone is given by where y is a dimensionless parameter and t the oxidation time. Based on the solution of the diffusion equation, wagnerl0 has shown that under certain conditions several mathematical simplifications may be used in the evaluation of y, so that Eq. [I] may be expressed for the case that y « 1, and y(Do/DB) 1, where N(so)the is the equilibrium solubility (mole fraction) of oxygen in the solvent metal for the given oxidizing atmosphere, is the mole fraction of the solute metal in the bulk alloy, 4 is the diffusivity of the solute in the base metal, and v is the ratio of oxygen atoms to solute atoms in the precipitated oxide BO,. Rearranging Eq. [2] Maak' has derived an expression analogous to Eq. [3] for the case that an external-oxide scale, in addition to an internal-oxidation zone, is formed. For this combined external and internal oxidation for the case that 5/2 where 5 is the distance of the internal-oxidation front from the original external s.urface, and X is the distance of the external oxide/metal interface from the original external interface. The function F is defined by the expression

Jan 1, 1964

By R. M. N. Pelloux

This study of aluminum-copper alloys had two aims: 1) To determine the effect of the amount and distribution of a second phase, CuAl2, on the creep-rupture strength, ductility, and fracture characteristics of the alloys. The work of Gemmell and grant' on single-phase aluminum-copper alloys provided a basis for the present study. 2) To attempt to provide a relation between the microstructure and strength of two-phase alloys deformed at comparatively high temperatures (greater than 0.45 T,). The creep behavior of the two-phase magnesium alloys Mg;Ce and Mg-A1, has been treated by Roberts. 9 In work reported by Sully and Hardy4 and by Underwood, Marsh, and Manning~ on A1-Cu two-phase alloys, and also in a portion of the work of Gemmell and grant,' aging took place during the creep tests. 'In the present work, overaged aluminum-copper alloys were subjected to creep deformation at two temperatures, 500 and 700OF. The overaging treatments to produce the precipitate dispersions were performed prior to the test, at temperatures which were the same as the ultimate respective test temperatures. Hence, the present study is concerned with the creep behavior of stable (in contrast to "underaged") two-phase A1-Cu alloys, i.e., alloys in which no depletion of the solid-solution matrix occurred during: creep. MATERIALS AND PROCEDURE A 2 and a 3 pct Cu alloy, supplied by Alcoa, were studied; Table I shows the compositions. The grain size of the specimens, 0.9 to 1.0 mm, was achieved by annealing the machined test bars for 2 hr at 1000°F, followed by furnace-cooling to 900°F, and homogenizing for 4 hr. Both compositions are in the single-phase condition at 900°F. Two types of overaged dispersions, termed "over-aged I" and "overaged 11" were prepared after the grain size and the homogenization anneals. The overaged I alloys were prepared by quenching to room temperature after homogenization, aging at either 500' or 700°F for 72 hr, and air-cooling to room temperature. The overaged I1 alloys were prepared by furnace-cooling after homogenization, to either 500' or 700°F, and holding at the necessary temperature for 72 hr. The times for furnace-cooling from 900°F to 700° and 500°F were, respectively, about 2 and 3.5 hr. The structures of the A1-2 pct Cu alloys are shown in Fig. 1 (overaged I) and in Fig. 2 (overaged 11). A comparison of Figs. 1 and 2 shows that in the overaged I alloys the precipitate particles along the grain boundaries are much more closely spaced and the grain boundaries are straighter than they are in the overaged I1 alloys. Further, the particle size and spacing in the grains are smaller than in the overaged I1 alloys. Microstructures of the A1-3 pct Cu alloys have not been shown; the structures of these alloys differed from those of the A1-2 pct Cu alloys only in that the distribution density of the particles was greater. The creep specimens had a gage section 1 in. long with a diameter of 0.155 to 0.195 in. Before testing, specimens were electropolished in a solution of 100 cc glacial acetic acid, and 30 cc of 60 pct perchloric acid, at 40' to 50°F, at 24 v. The specimens were kept refrigerated prior to testing to avoid precipitation at room temperature. Constant stress creep tests were conducted; the load was applied 75 min after heating of the specimens to test temperature had begun. EXPERIMENTAL RESULTS Creep-Rupture—Fig. 3 shows the log stress-log rupture life plotfor the overaged alloys studied, and also for the underaged A1-2 pct Cu alloy.' At 700°F, the stress-rupture life relationship is nearly independent of both the amount of precipitate (i.e., composition) and of the type of overaging treatment (i.e., precipitate dispersion). At 500°F it is apparent that the increase in rupture life that was ex-

Jan 1, 1960

By O. P. Arora, M. Metzger, G. R. Ramagopal

Single-phase aluminum containing 0.0001 to 0.06 pct Cu was studied in strong acid, mainly through observations of hydrogen evolution. The strong influence of copper was exerted almost entirely through the imposition after a certain delay time of an auto-catalytic localized-corrosiott reaction. Additions of cupric ion to the acid produced lower accelerations. The significance of the quantity and distribution of copper was discussed, and the implications for intergranular corrosion and neutral chloride pitting were indicated. AN investigation of intergranular corrosion in single-phase high purity aluminum exposed to hydrochloric acid indicated the copper content of the metal to have an influence on corrosion at lower levels than previously suspected.&apos; The work reported here was a closer examination of the action of copper but dealt with general corrosion to gain the advantage of having a continuous measure of corrosion through the volume of hydrogen evolved, the reduction of hydrogen ion to hydrogen gas being the principal or only cathode reaction in strong hydrochloric acid. Previous work on the hydrochloric acid corrosion of aluminum was sometimes insufficiently structure-conscious and the need for care in evaluating it arises from the low solubility of the iron impurity,&apos; and of some alloying elements, and the known or possible presence in many of the compositions studied of second phases leading to greatly increased corrosion rates.3 These increases are attributed to the presence of low hydrogen-overvoltage cathodes provided by the second phase.3&apos;4 For the present single-phase work, a few studies which used high-purity base material and small copper additions5-&apos; provide the essential information most unambiguously. The corrosion rate was shown to be increased markedly by the introduction into the acid of small quantities of the ions of copper (and of certain other metals) which cement on the aluminum and provide cathodes of low overvoltage.5 When there was sufficient copper in the aluminum, the same result was produced during the course of corrosion leading to a rate which increased with time as the reaction was stimulated by one of its products (autocatalytic reaction). In 2N (7pct) HC1, an accelerating rate was observed at 0.1 pct Cu but not at 0.01 pct.5,7 The present work dealt with corrosion rate and morphology and their correlation with the quantity and distribution of copper catalyst for copper contents from 0.0001 to 0.06 pct. PROCEDURE A lot of high-purity aluminum containing 0.0021 pct Cu, 0.001 pct Fe and 0.003 pct Si (Alloy A) was alloyed with copper to yield aluminum containing 0.014 pct Cu (B) and 0.06 pct Cu (C). Later it was found necessary to include the lower copper Alloy K which contained 0.0001 pct Cu, 0.0004 pct Fe and 0.0004 pct Si. The upper limit for any other element can be confidently estimated as 0.0005 pct. No element other than copper appears to be present in quantities sufficient to have an effect on general corrosion as great as the observed effect of the copper in A, B, and C. The only other heavy metal detected by spectrographic examination was silver (< 0.0001 pct). The acid was made up from a selected lot of 37 1/2 pct CP hydrochloric acid containing 0.1 ppm heavy metals (mainly Pb), 0.05 ppm Fe, and < 0.008 ppm As and from water distilled from 1 megohm-cm demineralized water and believed to have contained negligible quantities of heavy metals influencing corrosion. Acid strength was adjusted to within 0.05 pct HCl of the stated value by using precision specific gravity measurements. Test blanks 10 by 41 mm were sheared from 1.65-mm cold-rolled sheet. Edges were finished by filing. The blanks were annealed in air at 645°C for 24 hr in alundum boats and rapidly water quenched. The anneal is thought to have produced a substantially homogeneous solid solution—for iron, copper, or silicon, for example, the annealing temperature was 200°C or more above the solvus-and the quench is considered to have preserved the high-temperature structure except for the condensation of lattice vacancies into dislocation loops.&apos; The 0.06 pct Cu alloy did not appear unstable in respect to slow precipitation reactions at room temperature since two pairs of tests failed to show significant differences between specimens heat treated 3 1/2 years earlier and specimens heat treated 1 or 2 days before.

Jan 1, 1962

By B. G. Agnew

In evaluating fracture treatments, the need to answer such questions as "What zone or zones were actually treated?" and "What was the vertical extent of the treatment" is necessary, since determining effectiveness of the fracture treatwrent depends on knowledge of the reservoir portions stimulated and the vertical extent of the fracture system or systems. Injection of hot or cold fluids during fracturing operations will transfer heat to the surrounding formations and fracture faces mainly by heat conduction. Once injection ceases, temperature anomalies will develop opposite the zone fractured because the rate of temperature decay is less than that opposite zones heated or cooled by flow inside the wellbore or along the cement sheath. Thus, temperature surveys can he used to determine where fractures were generated outside the wellbore and to reasonahly estimate the vertical extent of the fractrires. This technique has been used successfully to evaluate over 344 fracture treatments at depths ranging from 1,500 to 15,700 ft. Examples of actual temperature surveys are presented to show how this method of fracture treatment evaluation can be used effectively and beneficially. INTRODUCTION Stimulation of producing or injection wells by fracturing is commonplace in the industry today. In evaluating these treatments, two basic questions which arise are "What zone or zones were actually stimulated?" and "What was the vertical extent of the treatment?". Knowledge of the reservoir portions stimulated and vertical extent of the fracture system or systems is vital to effect efficient and economical well completions and to assure maximum recovery from reservoirs. Not all fracture treatments are successful and many times the desired or anticipated results are not achieved. When this occurs, it is in most cases the engineer&apos;s job to determine why. The answer to this problem forms the primary basis for deciding whether to spend more money for development drilling and/or completion attempts or to forego additional expenditures to improve the particular zone. Also, knowledge of the reservoir portion actually stimulated is invaluable in planning future workovers. This is especially true in wells producing from reservoirs containing multiple porosity stringers or zones. For various reasons, all zones within a reservoir may not be perforated on initial completion with the thought of developing remaining zones through future workover operations. Because particular zones are perforated and fracturing fluid pumped down the wellbore, it cannot be assumed that all perforated zones are stimulated, and in turn drained. Occasionally, unperforated zones which are planned for future development are actually stimulated on initial completion. eliminating the need for future recompletion attempts or all zones perforated initially are not stimulated, thus requiring additional completion work to insure that these zones are adequately drained. In most cases, it is costly. if not impossible, to determine with assurance why a fracture treatment is unsuccessful after the job has been completed and the results tested. Further, unpredictable upper and lower fracture barriers. as well as possible borehole communications (cement channels), do not permit it to be taken for granted that the formation opposite the perforations is the only zone receiving the fracture treatment. Thus. evaluation of fracture treatments is necessary for efficient and prudent well completion practices and should be done simultaneously with the fracture job. Several methods have been used to locate fractured zones, all of which are based on detection of radioactive tracer materials added to either the fracturing fluid or the propping agent. These methods have been helpful in increasing knowledge of fracturing operations; however, they are seriously limited because of cost and inability to detect accurately radioactive tracer material more than a few inches away from the borehole. To develop a better diagnostic tool to pinpoint which zone or zones had actually been fractured, temperature surveys were run after fracturing with heated and cooled fluids. Significant temperature anomalies were found to exist opposite zones suspected of receiving the fracture treatment. From the analysis and examples to be shown, it can be seen that temperature surveys run in a stabilized wellbore several hours after a fracture treatment using hot or cold fluid will yield temperature anomalies which show the actual reservoir portion stimulated, the vertical extent of the fracture system or systems and a qualitative indication of the portion of fracture-fluid volume entering a given depth interval. The experience and illustrations used in this paper are based on evaluation of over 344 fracture treatments during the past three years using this diagnostic tool at depths ranging from 1.500 to 15,700 ft and fracture volumes ranging from 2.000 to 110.000 gal. Based on analyses of these temperature surveys, analyses of fracture gradients and evaluation of several open-hole packer impressions in the West Texas area,&apos; vertical fracturing is the predominant mechanism and horizontal fractures occurred frequently, if at all.

Jan 1, 1967

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman&apos;s arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman&apos;s paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman&apos;s work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"&apos;. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963

By David W. James, Howard Jones, George M. Leak

Conditions are described for producing, by primary recrystallization, a matrix suitable for the growth of large grains near (110)[001] orientation in silicon iron strip by secondary recrystallizaliun in a steep temperature gradient. The orientation distribution of these large grains is expressed in terms of rotational deviations about the cross-rolling direction, the rolling direction, and the normal to the sheet, the deviational spread increasing in that order. With the aid of cowplenientary published data on the orientation dependence of growth rate, it is shown that this observation is consistent with the oriented-growth theory of recrystallization lextures. It is conclutled that growth-rate and orientation-distribution data obtained in a steep thermal gradient should be used with caution to account for isothermally Produced recrystallization textures. SEVERAL authors have reported methods of growing large grains by re crystallization of a small-grained matrix in silicon iron 1- B and pure a cr The present study was a preliminary in the growth of single crystals and bicrystals for surface relaxation," grain boundary mobility, and grain boundary diffusion studies. The method was to control the growth of a seed crystal into a suitable primary re crystallized matrix by feeding through a steep temperature gradient. The driving energy for growth derived from the grain boundary energy released as the seed crystals grew into the matrix. Thus, stability of the matrix against normal grain growth was considered to be essential for success. It was known that the manganese sulfide dispersion present in commercial silicon iron performs this function during secondary recrystallization to the (110)[001.] texture.12 Hence commercial, rather than high-purity, material was used throughout. The paper describes the growth conditions for grains large enough to be used as seed crystals for further growth into single crystals. The orientation distribution of the seed crystals is analyzed and its significance for the theory of recrystallization textures is discussed. EXPERIMENTAL PROCEDURE Strip material was supplied by the Steel Co. of Wales, Ltd. The chemical analysis in weight percent was Si, 2.90; C, 0.015; Mn, 0.059; P, 0.011; S, 0.027; Ni, 0.032; 0, 0.009; Fe, balance. A gradient furnace of similar design to one described previously4 was loaned from B.I.S.R.A. It consisted essentially of a vertical water-cooled copper slot projecting downwards into the hot zone of a molybdenum furnace. Hydrogen was passed through the furnace to protect both heating element and specimen from oxidation. Strip specimens up to 8 cm wide and 0.2 cm thick were sealed into the furnace at the mouth of the copper slot. A coating of light oil on the strip surface maintained the seal during translation of a specimen. The maximum temperature gradient in the region just below the copper slot was 500°C per cm over 1 cm, with the hottest point controlled at 1175°C. Several large grains would usually grow by secondary recrystallization from the primary matrix when a specimen was immersed in the hot zone for about 30 min. A back-reflection X-ray camera was constructed to facilitate rapid and accurate orientation determinations of the large grains produced. It was possible to reproduce a standard geometry, with regard to strip and camera, without the tedium of careful alignment on each occasion. Specimens, typically 4 cm wide and 75 cm long, were cut with the longitudinal axis parallel to the rolling direction of the original strip. The surfaces were cleaned by immersion alternately in a hot aqueous solution containing 2 pct hydrofluoric acid plus 10 pct sulfuric acid and in cold 10 pct nitric acid. The nitric acid etch was just sufficient to reveal the grain structure. Rolling and annealing treatments to prepare the matrix (discussed below) were followed by growth of seed crystals in the gradient furnace. The matrix was transformed to a single crystal by growth of a selected seed crystal connected to the matrix by a thin neck. 4,5 Growth was promoted by controlled feeding into the gradient furnace. Several single crystals of controlled orientation were grown successfully from seed crystals by twisting the interconnecting neck in a reorien-tation jig.4 EXPERIMENTAL RESULTS AND DISCUSSION Growth Conditions. A suitable matrix for growth of large grains was prepared starting from primary re-crystallized strip 1.9 mm thick. This was cold-rolled in two stages each being followed by a recrystallization anneal at 800°C for a few minutes. Such treatment gave the required growth matrix only if the two cold-reduction stages were each performed in several passes and in the following ranges: the first, 30 to 70 pct; the second, 10 to 50 pct. Immersion in the temperature gradient otherwise resulted in an equiaxed

Jan 1, 1967

By S. J. Hruska, G. M. Pound

The critical supersaturations for appreciable nucleation rate of cadmium crystals on copper and glass substrates at 186°Kwere measured as a junction of thermal-beam energy over a range of source temperatures between 616" and 839OK. There was no effect of source temperature on critical super saturation. This implies that the adsmbate prior to nucleation is in thermal equilibrium with the substrate. THE deposition of metallic vapors on solid substrates has been found to exhibit a critical behavior in that the rate of formation of deposit increases markedly when the intensity of the vapor source is increased slightly.* Evidence of the ability of sub- where Je is the flux which would arrive if the substrate were equilibrated with bulk condensate at the adsorbate temperature. The following work was undertaken to test this hypothesis. A) Energy Exchange Between Metallic Vapor and Substrates. When a freely translating atom collides with a stationary solid body its energy and momentum undergo changes which determine whether the atom is reflected or adsorbed. An atom is considered to be reflected if it returns to a freely translating state after remaining under the influence of the body for only a time comparable to the period of oscillation of atoms on the surface. An atom which remains for a longer time is said to be in an adsorbed state. The parameter which describes the energy transfer occurring at the interface is the thermal-accommodation coefficient which may be defined in terms of energy as Ei = average energy of impingent atoms, Eeq = average energy of an emergent atom which has equilibrated with the substrate, and Eem = average energy of an emergent atom. If a temperature is assigned to each of these energies, we have at as defined by Knudsen.2 Since this allows no distinction between reflected and evaporated atoms, a more specific definition is introduced for the present purposes, namely 71 = probability that an impingent atom is transferred to an adsorbed state, aj = thermal-accommodation coefficient for reflected atoms, and aTc = thermal-accommodation coefficient for adsorbed atoms. During a time t,, the mean stay time, prior to evaporation the adsorbed atom (adatom) will interact with the substrate and this will have the net effect of transferring the adatom towards a state of

Jan 1, 1964

By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967