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By E. W. Hough, B. B. Wood, M. J. Rzasa

An apparatus for the determination of fluid-fluid interfacial tension by the pendant drop method has been constructed. The apparatus is refined beyond those previously described in that the samples are introduced into an evacuated windowed cell without contacting air or mercury. Interfacial tension data are reported for the water-methane system between 74 and 280°F and 15 and 15,000 psi. The variation of wettability of the stainless-steel dropper tip with pressure and temperature was observed incidentally to the measurements. INTRODUCTION The most refined previous apparatus --for the determination of fluid-fluid interfacial tension at reservoir conditions was built by Hauser and Michaels.' These authors used the pendant drop method, previously investigated by Andreas, Hauser, and Tucker.' Recently, Fordham3 has made the pendant drop method an absolute one by numerical integration of the differential equation of drop shape. It is necessary to know the difference in density of the two fluids and the acceleration due to gravity in order to evaluate the interfacial tension from measurements of drop dimensions. Contact angle is not involved in the measurements by this method. Some precise tests of the method have been made at atmospheric pressure and 77°F by Douglas," who found agreement with established values to within about 0.1 per cent for water and air, cyclohexane and air, benzene and air, and benzene and water. No values of interfacial tension from the recent pendant drop apparatusJ have been published by Hauser and Michaels. However, values for the water-benzene and water-decane systems are given in Michaels' thesis5 or Dressures from 15 .to 10,000 psi and temperatures from 73 to 268ºF. Some determinations on gas-oil and gas-water systems in the range of 15 to 4,000 psi and 78 to 178°F have been made by Hozott,' by the drop-volume method. The capillary rise method has been used to investigate the interfacial tension in gas-oil systems at 88°F to several thousand psi by Swartz.7 Other determinations in gas-oil systems at pressures under 1,000 psia have been made by Jones: and Beecher and Parkhurst.9 The scarcity of data for pressures above 5.000 psi is apparent. APPARATUS An assembly drawing of the working section of the interfacial tenqion apparatus is given in Fig. 2. 'The endanant drop (A) is housed in a pressure chamber having glass windows (B). An agitator (6) is provided. The metal parts of the apparatus coming into contact with the sample are made of AISI: Type 316 steel. Drain grooves are provided around the whdows so that the sample in contact with the O-rings is not returned to the working section when the pressure is reduced. A schematic arrangement of the apparatus is given in Fig. 3. The working section containing the pendant drop (A) is filled by samples from bombs (B) with the aid of the vacuum system (C). The O-ring sealed pistons (D) used to separate the sample from the hydraulic fluid are shown together with the pressure production and measurement system (E). A front view of the apparatus is shown in Fig. 1. Most of the hydraulic system is at the top of the panel. The pump and displacement piston are at the lower right. The Variacs for the air bath heaters. the camera. and the vacuum gauge are a1so visible on the panel. The working section together with a window closure and a drop-forming tip closure are shown in Fig. 9. The carbon arc light source with filter is visible in the upper part of the picture. Two sides of the air bath with the impeller and a part of the convection shield can also be seen. The assembled air bath is shown in Fig. 10.

Jan 1, 1951

By Eugene F. Broome, Hugh A. Walls

Self-diffusion coefficients were measured using the modified shear cell technique over a temperature range from 31" to 401°C. These data agree within experimental error with those of Petit and Nachtrieb, which were determined from 30°to 99°C. LIQUID self-diffusion behavior in gallium has been studied previously by Petit and Nachtrieb&apos; using their shear cell technique.&apos; Data were obtained in that investigation over temperatures ranging from 30.6 to 98.7"C, and these comprise the only published data for liquid gallium. In the work reported here, diffusion data were obtained from 30.8 to 400-9.Cusing a shear cell technique different from that of Petit and Nachtrieb. This modified shear cell method and the mathematical analysis for diffusion in a finite capillary geometry have been previously described.3 PROCEDURES AND ANALYSIS The segments of the modified shear cell were fabricated from types 304 and 316 stainless steel. No corrosion problems with gallium were encountered until attempts were made to obtain data at 500°C. The diffusion capillary diameter was 1.59 mm and capillary lengths for the four sets of cell segments used are given in Table I. Gallium with a purity of 99.999 wt pct was obtained from Var-Lac-Oid Chemical Co. The gallium-72 isotope used to measure the self-diffusion coefficients was produced from this inert gallium by irradiation in The University of Texas Reactor Facility, and was checked for radiochemical purity. Following a period of isothermal diffusion controlled to within 0.0l°C, the contents of each capillary section were emptied into a counting planchet, weighed to assure that gallium had not been lost during handling, and the radioactivity determined by windowless gas-flow proportional counting. Great care was taken to obtain a reproducible counting geometry for the samples. Diffusion coefficients were obtained from the solu-tion3 to the diffusion equation for the modified shear cell problem, viz.: in which B2= C2(t)Li + L2)- CSL1-COL2 P* (C0-Cs)(L1+ L2) and L, and L2 are the capillary segment lengths. The step-function initial concentration distribution was expressed as C(x,O) = C, for -L1 = x < 0 and C(x,O) = Co for 0 < x 5 L?. Also, C2(0 = ^- fcix,t)dx Computation of the diffusion coefficients was done numerically as described in our earlier paper.3 Because of the short half-life of gallium-72 (14.1 hr) and the relatively long counting times taken to give a precise value of the diffusion coefficient, it was necessary to account for the radioactive decay both during the actual count and between counts for different samples (before and after diffusion). Thus, the average count rate Cz(t) for a second sample counted from times t3 to t4 can be made consistent with the average rate Co determined for a first sample counted from times t1 to t2 by the relationship: N(e-»i-e-M») , , C2(f) " &-«,)(*-«.-«-»«) [21 in which N is the total number of counts taken and is the decay constant. RESULTS AND DISCUSSION The self-diffusion coefficients determined in this investigation are listed in Table 11. Values of the parameters used to calculate the coefficients are given in the table, as are values of the random counting error &apos; for the concentration ratio pz and the corresponding expected random variation AD in the diffusion coefficient. The quantity is calculable from: &apos;Cg — C2(t)} , „ ,2 .-„¦, M co-csl(ACs)J W in which AC is the error in the individual count rate. The mean values of the diffusion coefficients within each temperature group are also given in Table 11. Such temperature groupings of data are reasonable because of the small variations between the temperature~.~

Jan 1, 1970

By J. F. Butler

Boron nitride, BN, has been identified in boron low-carbon steels by means of light microscopy, electron microscopy and diffraction, and chemical analysis. This boron nitride is responsible for strain aging suppression in these steels through the removal of nitrogen from solution; however, small oxidizing potentials which result in deboronization In the austenitic temperature range also result in boron nitride decomposition and the subsequent occurrence of nitrogen strain aging. THE addition of boron to low-carbon steels is an effective means of eliminating the detrimental effects of strain aging;&apos;,&apos; however, the mechanism by which boron suppresses strain aging has not been established. In studying the effect of heat treatment on the strain aging of boron low-carbon steels, Butler3 found that no detectable nitrogen was present in the ferrite solid solution after various heat treatments even though the total nitrogen analyses of the steels were 0.003 pct N. Apparently the function of boron in suppressing strain aging is the removal of nitrogen from solution to form a relatively stable second phase. A clue to the identity of this phase was found by Speight4 who extracted from an aluminum-killed boron steel an acid insoluble residue which contained boron and nitrogen in proportions corresponding to the compound, BN. Shyne and Morgan5 found that the addition of nitrogen to a hardenable boron steel lowered its hardenability in a manner which suggest-d the presence of nucleating particles (presumably BN) even at high austenitizing temperatures. Although this indirect evidence for the presence of boron nitride in boron steels has been found, the compound was not identified metallographically as a separate phase in these steels. Because boron has an affinity for oxygen comparable to that of silicon,5 boron steels must be thoroughly killed with aluminum in order to prevent the reaction of boron with oxygen.7 The affinity of boron for oxygen also is demonstrated through the ease of deboronization of a boron steel in an oxidizing atmosphere. Digges, Irish, and Carwile8 found that a mixture of wet natural gas and air caused both deboronixation and decarburization of a boron steel at 1900°F. The boron content rose at the surface of the steel due to the formation of boron oxide. Shyne and Morgan9 encountered deboronization at much lower oxygen potentials; loss of boron occurred in steels treated at 1750o F under argon purified to 0.0014 pct 0, even though decarburization did not occur. Boron oxide, B2O3, is much more stable than the nitride, BN, as is indicated by the standard free energies of formation at 980oC: -235 kcal per mol of B2O3 (liquid) and -28 kcal per mol of BN (crystal). It is evident that the oxygen potential must be kept low in the presence of BN in order to prevent its decomposition and the subsequent formation of B2O3&apos; The purpose of the work described in this paper was to identify the nitride phase responsible for the removal of nitrogen from solution and to study its stability under oxidizing conditions. IDENTIFICATION OF BN In order to identify the phase containing boron and nitrogen, several alloys high in boron and nitrogen were made up in a small vacuum furnace. In alloys 3 and 4, Table I, electrolytic iron was used as a charge material. Boron additions were made in the form of 18 pct B ferro-boron after the iron was molten. In the case of alloy 3, the charge was solidified at this point; for alloy 4, nitrogen at 1 atm pressure was admitted over the melt before it was

Jan 1, 1962

By W. F. Kieschnick, C. C. Miller, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By G. H. Enzian

THE effects of phosphorus and nitrogen on the properties and behavior of low carbon steels are important considerations to both the manufacturer and the user of such material. For one thing, these two elements are the principal points of distinction between the chemical compositions of Bessemer and open-hearth grades. Further, open-hearth steels themselves may vary considerably in nitrogen content depending on the raw materials and ..practice used. In addition, appreciable amounts of rephosphorized open-hearth steels are being used at the present time in some low alloy, high strength grades and in certain other cases. For these and other reasons, it was felt desirable to obtain more complete knowledge of the effects of simultaneous small variations in phosphorus and nitrogen content on such properties of low carbon steel as tensile strength, impact toughness, sensitivity to cold work, and strain aging. A long range investigational program designed to furnish such information, was carried out, and the present paper summarizes some of the data currently obtained. General Discussion The strengthening effect of relatively small amounts of phosphorus in steel has been recognized, and to some extent utilized, for many years. A number of investigators have pointed out, from time to time, that under proper conditions of control, phosphorus can be a useful alloying element in low carbon steels.1-3 Nevertheless, in spite of the volume of data on the subject, the use of phosphorus for this purpose has always been handicapped by widespread feeling that its presence makes the steel brittle, difficult to cold work, and unreliable at low temperatures. This belief on the part of some steel users is not entirely justified in many cases, and often stems from early experience with acid Bessemer steels which have appreciably higher phosphorus (and nitrogen) contents than basic open-hearth grades. Nitrogen in steel, and its effect on properties, has also received considerable attention in the literature.4 In 1906, Braune5 ascribed the brittleness of Bessemer rails to the nitrogen content, and proposed a schedule of nitrogen limits for steels for various uses. This was one of the first papers to recommend directly the use of nitrogen content as a quality control measure, but it did not meet with much favor or support; as a matter of fact, the Jernkon-toret was rather sharply criticized for publishing the paper. In the intervening years a number of papers have been published on the subject of nitrogen in steel. As a result, it is now generally recognized that nitrogen can have an important effect on the properties and behavior of steel and that the presence of this element should be considered in any systematic study of factors affecting steel quality. In 1932, Graham6 introduced the concept that the quality of various steels could conveniently be evaluated and compared in terms of "sensitivity", which was defined as "the characteristic reaction rate of a piece of steel toward brittleness or hardness." This concept formed the basis for a broad research program into factors causing variations in the quality of commercial steels. At an early stage of this work, it became apparent that the observed effect of either phosphorus or nitrogen on the sensitivity of steel depended, in no small measure, on how much of the other of these two elements was also present. Indeed, the combined effect of phosphorus and nitrogen in steel may often be more important than the specific effect of either. With a few exceptions, it is not possible to predict accurately the effect on steel properties of a change in the amount of either phosphorus or nitrogen in the steel without also specifying the approximate amount of the other element. It seems desirable, at this point, to discuss briefly the distinction between strain-sensitivity and strain aging as used in this paper. In the early stages of its development, the work-brittleness test7 (which will be described in more detail later) was used

Jan 1, 1951

By H. N. Mead

In a reservoir when gas comes out of solution and rises, additional pressure is created because of the change in position of this gar in the bounded volume. If this pressure effect is not taken into account as a pseudo-influx ill mate rial balance calculations on reservoirs in which there is evolving gas, an error is introduced that is directly proportional to the length of oil column and amount of gas evolved and inversely proportional to the reservoir pressure. In reservoirs with small oil column this pseudo-influx is of little importance. The larger the oil column the more important the effect becomes. The most important application, however, will be for reservoirs with declining pressure in which increasing water entry has been indicated by material balance calculations. It could be that this indication is the result of the cited pseudo-influx and not water entry at all. This paper attempts to explain this phenomenon in relation to material balance calculations and prevents an approximate method of determining tile pseudo-influx. INTRODUCTION Only recently has the pressure-volume relationship of gas rising in a liquid appeared in engineering literature, although its effect has been discussed for several years—especially among engineers engaged in drilling operations. The writer published a paper in 1957 in which this phenomenon was examined in relation to blowouts in drilling wells.&apos; Also, in 1957 Stegemeier and Matthews&apos; authored a paper in which the relationship was presented with respect to pressure build-up tests when shutting in producing wells. In this paper the effect will be called "pressure inversion" which is descriptive of the phenomenon. Fundamentally, the effect just mentioned is the result of changing the position of a quantity of energy contained within the gas itself (as a result of its compression) within the bounded volume in which the gas exists. If the gas were allowed to expand "beyond all bounds" there could be no pressure inversion effect. This is because all of the energy contained within the gas as a result of compression would have been re- PRESSURE INVERSION A phase that has not been discussed in the literature is the effect of pressure inversion upon material balance calculations in reservoirs in which the reservoir pressure drops with reservoir withdrawal and is below the bubble point. This action releases solution gas which, after the critical gas saturation has been reached, will tend to rise and collect at the top of the reservoir. The pseudo-influx caused by this effect could be great enough in reservoirs of large oil column and high permeability to render invalid any analyzer studies made on them — if pressure inversion has not been taken into account. Most suspect would be those reservoirs with large oil column in which increasing water entry has been predicted but the bottom wells have not yet produced water. Example 1 Simply stated, this phenomenon exists in oil reservoirs because of the difference in density and expansibility between gas and oil. For example, if a bubble of gas exists at the bottom of a 1,000-ft column of oil having a gradient of 0.30 psi/ft with the pressure at the top of the column zero, the bubble of gas will be compressed to a pressure of 300 psi. If temperature and the combined volume of the oil column and the gas bubble remain constant, as the gas bubble rises in the oil column it will have the same volume and consequently the same pressure at any point. Under these conditions when thc bubble reaches the top of the oil column, the pressure will be approximately 300 psi at the surface and approximately 600 psi at the bottom of the oil column. If it is assumed that the oil is incompressible the pressures will be exactly 300 and 600 psi, respectively.

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen&apos; with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,&apos; indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina&apos; has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,&apos; 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.&apos; Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison&apos; reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

By S. C. Sun, John A. L. Campbell

Objective of the ittvestigation was to determine the electrokinetic differences, if ally, of anthracite lithotypes and thus establish the feasibility of making a coqlstituent separation by froth flotation or other surface-dependent processes. The elec-trokinetic properties were determined by streaming potential methods. In addition, chemical and physical analyses of the lithotypes were made to establish nonsubjec-tive parameters for their diflerentiation. Electrokinetic results indicate a difference in the characteristics of the lithotypes. The isoelectric points of 4 anthracites and 12 lithotypes were obtained. It was suggested that the relative flotation rates of the lithotypes were pH dependent and that the maximum flotation rate of anthracite occurs in an acidic circuit. Although there has been an increased interest in the electrokinetic properties of coal,&apos; research on the subject is still in an early stage of development."&apos; To the authors&apos; knowledge, no electrokinetic studies have been made on coal lithotypes, particularly anthracite litho-types. This paper presents the results of an investigation of the double layer properties displayed at the anthracite/water interface (whole coal and lithotypes) as determined by streaming potential methods. It is hoped that this investigation and related future investigations will provide correlations from which the surface properties of any coal can be predicted and then related to surface-dependent processes such as froth flotation and flocculation. Another aspect of this research, undertaken to determine the physical and chemical parameters necessary for anthracite lithotype differentiation, was previously published.? The number of parameters involved, lithologic, organic and inorganic, and the wide divergence of these parameters within an individual coal limits the practical utilization of the results; however, the result? are of value and of interest in guiding theoretical developments. Keeping the limitations in mind, the results are analyzed in terms of their application to froth flotation processes and are used to indicate the feasibility of making a lithotype separation by flotation. Experimental Procedure Prior to discussing the experimental work per se, it would be of value to establish an understanding of anthracite lithology. Anthracite Lithology: Coal seams display two different modes of variation, rank and type. A coal&apos;s position in the continuous series ranging from peats through anthracites determines its rank. The rank of the material under consideration is anthracite. The different bands of coal which constitute a coal seam are distinctly contrasted in regard to physical properties and chemical composition. These megascopic bands are the coal types and are termed lithotypes., A megascopic examination of 11 anthracites revealed three distinct, homogeneous, lithotypes. The classic description of bituminous coal lithotypes as proposed by Stope" was found to be quite adequate for recognizing the three lithotypes in anthracite, namely vitrain, durain, and fusain. The term vitrain describes the brilliant constituent of coal; durain describes dull coal; and fusain is the term applied to fossil charcoal. The anthracites studied were generally found to contain 60-80% vitrain, 10-30% durain, and 1-10% fusain. A complete description of the physical characteristics and chemical composition of the studied lithotypes can be found in a previous publication.&apos; Sample Preparation: Nine of the anthracites used in the investigation were from Pennsylvania, one was from Russia, and one from Wales. Table 1 shows the various designations and sources of the employed anthracites. The letter V, D, or F added to the whole coal designation indicates respectively the vitrain, durain or fusain lithotype of that coal. The samples were carefully collected to avoid contamination. To insure against oxidation, the samples were obtained as fresh as possible and stored under nitrogen or water. Generally a representative sample of the seam and samples containing high concentrations of one or another of the petrographic constituents were secured for each coal. Pure lithotypes were prepared by manual separation and selection. The pure lithotypes and representative samples were ground to —35 mesh and screened to 35 x 48 mesh. The 35 x 48-mesh fraction was then passed over a magnet to remove iron contamination, washed with doubly

Jan 1, 1971

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By M. R. Geer, H. F. Yancey

THE performance of coal-washing equipment, that is, the effectiveness with which coal and impurity are separated, is a subject of undisputed interest to all concerned with the preparation of coal. Through the years much has been written in both American and European literature on the performance of coal-washing equipment and its interpretation, but until recently no effort has been made to consolidate this wealth of information into a single, comprehensive treatment of the subject. A splendid effort in this direction was made at the First International Conference on Coal Preparation held in Paris in June 1950 in which representatives from virtually every coal-producing country participated. Although the scope of the conference covered the entire field of coal preparation, many of the sixty-odd papers and a great deal of the discussion dealt with the subject of evaluating washery performance. Prominence was given this subject by the Centre d&apos;Etudes et Re-cherches, des Charbonnages de France, which sponsored the conference. This research organization, generally referred to as Cerchar, was formed in 1948 following the nationalization of the French coal industry. Since that date it has conducted an intensive study of coal preparation. Perhaps because of a fresh viewpoint, Cerchar realized immediately that complete information on the performance of French washeries and a thorough understanding of the mechanism of gravity separation were the fundamental prerequisites in a program to improve preparation practice. For this reason Cerchar concentrated on obtaining performance data and on a comprehensive study of methods of evaluating such information. Some idea of the magnitude of this work will be appreciated from the fact that 175 performance tests were made in 44 plants. The work performed by Cerchar emphasized a condition that is recognized by many of those concerned with coal preparation, namely that the lack of uniformity in presenting data on washery performance, the diversity of methods used in evaluating such information, and the frequent confusion of the terms related to performance have been prime factors militating against the progress from art to science. Thus, Cerchar feels that standardization of the methods employed for evaluating washery performance, not only in France but in the entire world, is essential to progress, and the prime objective of the Paris conference was to seek international standardization of the evaluation methods advocated by Cerchar. At the conclusion of the conference the question of standardization was referred to the International Standards Organization. A careful study of the dozen papers on the subject of evaluating washery performance presented at the conference reveals that none of the methods is new; most of them date back over a decade. Nevertheless, the intensive scrutiny of these methods brought about by the conference unquestionably has resulted in a valuable exchange of ideas and a clarification of thought that could scarcely be achieved in any other way. The object of the present report is to make available to the American coal industry the ideas developed at the conference which seem most important from an American viewpoint and to provide a critical analysis of some of the evaluation methods advocated by Cerchar. The various methods of evaluating washery performance are illustrated partly with data that have been published in American literature, and some new data have been obtained as the result of experimental work undertaken since the conference to provide information on certain controversial points. An English translation of the proceedings of the conference, including the discussion as well as the papers, will be available,&apos; and previous to the conference Coal Age2 published a very brief description of some of the principal evaluation methods used by Cerchar. Americans will appreciate as well as do the French the desirability of standardizing both the termi-

Jan 1, 1952

By G. W. Neighbor, M. S. Abrahams

The actice slip plane in InSb is found to be of the {111} type by using the method of two-tmce anulysis. Measurements of the rotation of the tensile axis with increasing plastic shear strain indicate that the tnacroscopic slip direction is a <110>. Recrystal-lization is first observed at a sheav strain of about 70 pct for a crystal deformed at a temperatzcre of 473° C and at a shear strain rate of 2.90 times 10- %ecc-I; the dislocation density corresponding to this value of the strain is 1 x 108 em-&apos;. At a shear strain of about 170 pct, the recrystallization process is complete. This appears to be the fimt time re-crystallization has heen observed in a semiconductor. V HE operation of the {Hi} glide plane in Ge was first noted by Gallagher.&apos; This finding was confirmed by Treuting who also extended the result to Si. Using X-ray techniques, Treuting3 demonstrated that the macroscopic slip direction in Ge was of the <110> type. The choice of the (111) <110> slip system in Ge is exected since in the diamond-type structure the {Ill7 plane is the plane of highest density and the <110> direction is the direction of closest packing.4 There is little reason to expect that the glide elements of InSb are different from those of Ge, since the zinc-blende structure characteristic of InSb is quite similar to the structure of Ge. With regard to InSb, Allen5 has indicated that the glide plane is the {111} type. There appears to be no quantitative determination of the glide direction, however. The present work was undertaken to establish both the glide plane and glide direction in InSb and also to see if recrystallization occurs at large shear strains. EXPERIMENTAL PROCEDURE Mechanical Deformation. The single crystals of InSb used in this investigation were deformed in uni-axial tension. The tensile axis of the specimens was [145] and the periphery was bounded by (111) and (321) planes as shown in Fig. 1. The metallographi-cally polished specimens were deformed in a dynamic atmosphere of He, using an Instron machine. The tensile tests were performed at temperatures in the range of 300°C to the melting point (525OC) and at shear strain-rates varying between 1.94 X 104 sec-&apos; to 1.94 x 103 sec-&apos;. Additional details concerning the preparation and deformation of the specimens have been presented previously.&apos; Analysis of the Glide Elements. The traces of the active slip plane in both (111) and (321) planes were analyzed according to the usual method of two-trace analysis." The macroscopic slip direction was determined by measuring the rotation of the tensile axis as a function of plastic strain,8 These measurements were made from Laue back-reflection X-ray photographs. The X-ray beam was perpendicular to the (111) plane. A given crystal was used for only one measurement of the rotation of the tensile axis after it had been strained to a predetermined value. Therefore, care was taken at all times to insure that the X-ray beam was parallel to the [Ill ] direction of all the samples. RESULTS AND DISCUSSION Glide Plane. After 3.4 pct plastic shear-strain, at a temperature of 369°C and a shear strain-rate of 1.94 x 104 sec-&apos;, the slip traces on the (111) and (3.21) planes appear as in Figs. 2(a) and 2(b), respectively. The results of an analysis of these glide markings demonstrate that the slip plane is (111). The operation of this plane is expected on the basis of the orientation of the specimen, since glide on this plane and in the [I011 direction will result in

Jan 1, 1962

By B. A. Wilcox, A. H. Clauer

The tensile and creep deformation characteristics of fiber reinforced composites have been studied, primarily at room temperature. The matrix was an alloy of Mg-14 wt pct Li-1 wt pct Al (LA141A alloy) and the reinforcing fiber consisted of continuous wires of a high strength precipitation hardening stainless steel (AFC-77 alloy). The ultimate tensile strength and strength-to-density ratio of composites were much improved over that of the mmix, both at room ternperatwe and up to 200°C. Creep studies at room temperature revealed logarithmic weep behavior for wires and composites and steady state creep for the nonreinforced matrix. It was concluded that creep of the fibers controlled composite creep. The instantaneous logarithmic weep rate of the composite, 6, was related to the average tensile stress on the fibers, where n = 3.4. Mg-Li alloys are the lightest structural metals commercially available, e.g., the alloy LA141A (Mg-14 wt pct Li-1 wt pct Al) is 27 pct less dense than beryllium Although Mg-Li alloys have moderate tensile strengths at normal strain rates and ambient temperature, their creep strength is relatively poor, even at room temperature. Reinforcement by fibers offers a means of increasing the tensile strength as well as overcoming the limitations of low creep strength. With a proper choice of reinforcing filament, composites could be designed with higher strength-to-density and modulus-to-density ratios than the matrix alloy. This communication reports a study on the tensile and creep characteristics of alloy LA141A reinforced with continuous wires of a high-strength precipitation hardening stainless steel (AFC-77 alloy). The matrix has a bcc structure, with possible precipitates of AlLi and MgLi2A1,3 and is ductile at room temperature Stainless steel wire was chosen as the -reinforcing filament since previous work at Battelle4 showed that a good bond between wire and matrix could be produced in this system. For all volume fractions of reinforcing wire, the theoretical composite strength-to-density ratio is greater than that of the matrix and the modulus-to-density ratio is somewhat lower than that of the matrix. EXPERIMENTAL PROCEDURES The 0.004-in. diam AFC-77 wire was obtained from two suppliers: National-Standard Co.* and Crucible 0.13 Si, 0.18 V, 0.011 P, 0.012 S, balance Fe. In the as-received condition, wires from both sources had room-temperature ultimate tensile strengths of 585,000 to 590,000 psi with approximately 2 pct total elongation and 40 pct reduction in area. Composite preparation was accomplished by the vacuum infiltration technique. This involved placing the continuous wires in a mild steel tube (1/8-in. ID), capping one end of the tube with a sheet of the matrix alloy, and evacuating the other end of the tube. When the capped end was placed in a crucible of the molten matrix alloy and held for 31/2 min at 70O°C, the liquid metal was drawn up the tube approximately 7 to 8 in. A cross-sectional view of a typical composite is shown in Fig. 1. This preparation technique promoted excellent bonding between the matrix and wires, and porosity was rarely observed. Test specimens for both creep and tension studies were prepared by machining off the steel tube. Tensile tests on the wires and composite specimens were made in an Instron using a cross-head speed of 0.01 in. per min. The composite specimens had no reduced section and were held in self-tightening grooved serrated grips. Most of the specimens broke in the effective 1-in. gage section. Even though several tests fractured in the grip section, their ultimate strengths were essentially the same as those of specimens which fractured in the gage section. Creep specimens of the composite were gripped in a similar manner, and

Jan 1, 1970

By Paul A. Farrar, Harold Margolin

The system Ti-Cr has been re investigated From 40 to 100 pct Cr. The high-temperature modification of TiCr, was found to exist in the temperature range from 1365 where it terminates in the eutectoid reaction TiCr,(TI)* — HE chromium-rich region of the Ti-Cr system was investigated by Vogel and Wenderott,&apos; Mc Quillan,&apos; Van Thyne et dl.,&apos; and Cuff Duwez and Taylor determined the crystal structure of the low-temeperature modification of TiCr, to be fcc a = 6.943A and Levinger&apos; discovered the existence of a second (high-temperature) modification of TiCr, and determited its crystal structure to be hexagonal a = 4.932A, c/a = 1.617i. No information was obtained as to the temperature range over which each modification of TiCr? existed; therefore the present investigation was initiated. I) Experimental Techniques Alloys employed for the delination of this system were prepared from iodide titanium and high-purity chromium. The purity of these materials is as follows: Iodide titanium: purity 99.99 pct; major impurities—carbon 0.0001 pct; oxygen 0 to 0.002 pct; nitrogen 0 to 0.002 pct; silicon 0 to 0.005 pct; manganese 0.001 pct; copper 0.001 pct (Foote Mineral Co., Lot 609-29). Chromium #1: metallic purity 99.997 min.; interstitial content—oxygen 0.27 to 0.46 pct; hydrogen 0.028 to 0.038 pct; nitrogen 0.0002 pct (Ave-quipo Inc.). Chromium #2: purity 99.9 pct; major impurities—carbon 0.01 pct; oxygen 0.013 pct; nitrogen 0.02 pct; silicon 0.01 pct; sulfur 0.03 pct; iron 0.01 pct (Fulmer Research Institute Ltd.). A total of sixteen alloys of thirteen different compositions was prepared in the range from 40 to 95&apos; *All percentages are given in weight percent. pct Cr. The compositions of the alloys prepared were as follows: Ti-40, 45, 50, 60, 62, 64, 66, 68, 70, 80, 85, 90, and 95 pct Cr. Two buttons were prepared of the 66, 90, and 95 pct Cr alloys. The 40 pct Cr and one of the 66 pct Cr alloys were prepared from the chromium # 2. All the other alloys were prepared from chromium #1. The alloys were arc-melted as 25-g buttons in a copper-hearth glass-walled furnace7 under an inert atmosphere of high-purity helium. The alloys were sintered at 250 amp and melted twice at 350 amp for 30 sec with the buttons being turned over between melts. Weight losses during melting were determined and in the range 45 to 68 pct Cr they were found, in all cases, to be less than 1.25 pct of the total alloy weight. A number of the high-chromium alloys shattered during cooling from either the first or second melt, which made the weight loss considerably larger than usual. The 70 and 80 pct alloys lost approximately 5.7 pct of their total weight, the 85 pct alloys 1.5 pct, the 90 pct alloy 2 pct, and the 95 pct alloy 3 pct. However, it is felt that the actual composition of the alloys in this region is probably within approximately 1 pct of the intended composition, as a large portion of the material lost was that due to shattering after melting. Nominal compositions were therefore used in plotting data and referring to the alloys. The alloys were cut into specimens, wrapped in molybdenum sheet, and encapsuled in argon-filled quartz or Vycor tubes for heat treatment. The heat-treatment times and temperatures are given in Table I. The specimens were quenched in iced brine (I.B.Q.) following heat treatment. The standard techniques of grinding, polishing., and etching were used in preparing the specimens for metallo-graphic examination. For alloys below 68 pct Cr

Jan 1, 1963

By H. E. Lee, P. C. Feddersen

Greenockite is the only known cadmium mineral of importance. It occurs rather universally, in minor concentrations, as a secondary mineral in sphalerite deposits. The world&apos;s cadmium output is obtained through the processing of metallurgical by-products, largely from the treatment of residues from electrolytic zinc, retort zinc and lithopone plants. These sources are supplemented by the processing of fumes from lead and copper smelting operations. The development of modern selective flotation practice in the decade 1920-1930, which permitted the economical mining of complex lead-zinc ores, resulted in significant increases in the quantities of cadmium entering lead smelting systems. Being closely related to zinc as to occurrence, properties and production, most detailed description of cadmium recovery methods are to be found recorded in connection with zinc metallurgy. Other than occasional articles pertaining to particular operational procedures, literature offers but little in the nature of a balanced survey of lead smelter cadmium recovery practices. While many of the basic operations described for the recovery of cadmium from zinc by-products are applicable to the treatment of lead plant products, the inherent problems involved differ widely. In general the cadmium content of related by-products from routine lead smelting operations is present in lower concentrations, exists in a less soluble state and is associated with both a greater quantity and a greater variety of detrimental impurities. To cope with these problems, lead smelter practices are found to follow the general outline: Preparatory Processing 1. Concentration operations 2. Sulphation operations Cadmium Plant Processing 1. Leaching operations 2. Purification operations 3. Sponge precipitation operations 4. Metal recovery operations 5. Refining and casting operations As in the case of related zinc plant operations, cadmium recovery practices at lead smelters are not standardized. They not only vary as to type, but also extent. Depending upon prevailing conditions, lead smelter cadmium operations range from simple concentration campaigns, for the purpose of sufficiently "up-grading" products for shipment elsewhere, to complete processing steps for the production of refined metal. Preparatory Processing The cadmium content of lead smelter receipts is low and, as a rule, proportionate to the zinc content; the usual range of cadmium contained being of the order of 0.01-0.05 pct. Were it not for the low boiling point of cadmium, such small concentrations would, no doubt, be lost in the large tonnages of slag, metal and other smelter end products. However, the ready volatility of cadmium and its compounds at prevailing lead smelting temperatures results in its concentration in fractional portions of fume collected. This collected fume comprises a circulating load within the smelter system. Thus, the cadmium content of blast furnace fume* increases with each successive circulation until an equilibrium value is reached when the sum of the cadmium losses, due to handling and in slag, waste gases and other end products, becomes equal to the intake as ore. With ore receipts averaging, say 0.03 pct cadmium, the concentration value obtainable, through fume circulation in a routine manner, approaches 10-12 pct. In such operations, cadmium concentrations in blast furnace fume of from 3-5 pct are readily .attainable. However, the concentration gain beyond this range, with each additional circulation, is progressively decreased as a result of mounting losses occurring through handling and in end products. Therefore, to avoid excessive cadmium loss and to enhance the ultimate concentration anttainable, it is customary practice to isolate blast furnace fume at some intermediate cadmium content for special concentration procedure. The most common type cadmium concentration "campaign" involves special smelting operations wherein a relatively high portion of blast furnace fume at 3—6 pct cadmium is incorporated into the sinter charge. This type practice is roughly illustrated by the diagram on p. 111. Cadmium fume collected from lead blast furnace operations is not amen-

Jan 1, 1950

By C. C. Miller, W. F. Kieschnick, E. R. Brownscombe

The possibility has been mentioned that large pressure gradients in a solution gas driven field caused by high production rates might lead to a reduction in the ultimate recovery obtainable compared to that which would be obtained by a very slow rate of production. In the present study the reservoir conditions accompanying a high rate of production and the corresponding ultimate recovery were compared with those obtained if the reservoir were produced at some marginal rate throughout its entire life. The method of calculation involved the application of fluid flow - material balance analysis to a series of successive steady state conditions in the reservoir. In the case studied very little difference in recovery was obtained at the abandonment pressure. An analysis of the basic factors involved indicates that the sane results would hold for considerable variation in properties of reservoir fluids, permeability of the formation or well spacing. Even if the reservoir has a water drive it appears that no harm will be done by- open flow production if the rate is cut back before any appreciable free gas is produced. However, any condition which leads to disproportionate withdrawal rates and which causes large pressure differences over large areas might result in substantial loss in ultimate recovery. INTRODUCTION When the pressure declines in a reservoir, gas is evolved from solution causing a shrinkage in the reservoir oil so that a stock tank barrel of oil with its residual dissolved gas occupies a smaller volume than originally. For a given reservoir oil saturation, therefore. stock tank oil content will be higher at the lower pressure. At the same time the evolved gas which remains in the reservoir reduces the reservoir oil saturation, and this would be expected perhaps to cause a reduction in stock tank oil content. However, around the well the shrinkage occurs so rapidly that stock tank oil may actually accumulate in this region in spite of the simultaneous reduction in reservoir oil saturation. If this accumulation should continue, spreading into a larger zone, the loss might be appreciable and because larger pressure gradients accompany higher rates the accumulation might possibly be large if wells are produced at too high a rate. It is the purpose of this paper to determine the effect of rate of flow on ultimate recovery by solution gas drive. The problem under consideration involves the unsteady state flow of oil in a closed radial system from which oil is produced by the evolution of gas as a finite drawdown is estalllished and the reservoir pressure declines. A somewhat similar unsteady state production problem dealing, however, with a linear system has been considered by Muskat and Meres, but these authors do not discuss the effects which rate may have on recovery. Other methods have been reported for estimaling recovery as a function of pressure decline when producing at an infinitesimal rate, and Muskat and Taylor&apos; have shown the effect of fluid and reservoir characteristics on recovery under these conditions. Assuming steady state to exist, Babson has given a procedure for computing the decline in well productivity as the field is depleted, and Moyer has combined these methods to estimate abandonment conditions and the resulting ultimate recovery. These latter approaches to the problem either do not consider the effect of rate or assume steady state can be established. In detail this paper presents the behavior of the reservoir producing under unsteady state conditions and considers the effect of production rate during this unsteady state flow on the recovery attained. The analysis also shows that there will exist at abandonment a type of steady state, and on this basis a method has been clevelopetl for rapid calculation of abandonment conditions.

Jan 1, 1949

By G. L. F. Powell, L. M. Hogan

Large degrees of undercooling have been produced in bulk samples, 400 g, of copper and Cu-O alloys by melting in a slag of commercial soda-lime glass. The maximum degrees of undercooling obtained for copper, hypoeutectic and hypereutectic Cu-O alloy samples were 208°, 218°, and 97°C, respectively. No grain refinement as a function of undercooling was observed for the pure copper samples although in Cu-O alloys there was a marked decrease in grain size at degrees of undercooling greater than 150°C. The grain size change is the result of recrystallization during or immediately following the freezing process. THE first report of a large degree of undercooling in a bulk sample of metal was that by Bardenheuer and Bleckmann1 who produced 258°C undercooling in a 150-g sample of iron by melting in a glass slag. Garbeck2 extended this technique to nickel, cobalt, and copper and reported maximum undercoolings of 220°, 230°, and 60°C, respectively, while Fehling and schei13 undercooled a large number of metals as 2 to 20-g samples slagged in glass. Subsequently, one of the authors4 applied the glass slag technique to bulk samples, -500 g, of silver and obtained a maximum undercooling of 250°C. It was concluded that impurities which normally catalyze nucleation at small degrees of undercooling could be removed by oxidation and solution in a glass slag. Large undercooling of bulk samples of iron, nickel, cobalt, and their alloys has also been reported by other authors.8&apos;10&apos;11 Of the five metals mentioned above, copper was the only one which had not been undercooled by at least 200°C in the form of a large bulk sample. Since copper exhibits high liquid solubility for oxygen, as do iron, nickel, cobalt, and silver, it was considered that a much larger degree of undercooling than that observed by Garbeck for copper should be possible. This was obtained by modification of the technique applied previously to silver and the results of undercooling experiments with 400-g samples of copper form part of this paper. The undercooling behavior of Cu-O alloys was also studied, and the influence of a small oxygen content on the grain structure of undercooled copper was observed metallographically. 1) EXPERIMENTAL The copper was obtained as oxygen-free high-conductivity copper, the major impurities of which were Fe 0.01 pct, Zn 0.015 pct, and Si 0.02 pct. Melting was carried out in an open-ended vertical cylindrical fur- nace wound with Kanthal wire. A schematic diagram of the experimental setup is shown in Fig. 1. The undercooling technique previously used for silver4 involved preoxidation of the samples by melting the silver in contact with the atmosphere. The oxygen content was subsequently reduced by freezing the samples under a glass slag, whereby the oxygen was evolved as gas and the continuous glass cover over the surface prevented re-solution of oxygen when the sample was remelted. Since oxygen is not released as gas when a Cu-O alloy is frozen. the technique had to be modified for use with copper. Also, copper is oxidized during fire refining so that an in situ preoxidation treatment of the samples was not considered to be a prerequisite to large undercooling. Experimentation proved that this supposition was correct. Instead, it was found that care was necessary during melting of the copper under glass to minimize oxygen pickup. Samples of copper weighing 400 g were prepared by adding 50-g pieces of copper to a vitreous silica crucible partly filled with soda lime glass at a temperature of approximately 1000°C. Each piece was quickly immersed in the glass slag and held at this temperature until the oxide coating on the surface decomposed. This change was easily observed and coincided with the formation of gas bubbles in the glass

Jan 1, 1969

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

By R. F. Mehl, G. T. Horne

Diffusion coefficients and mobilities were determined as functions of concentration in the a phase of the Cu-Zn system. Use was mode of incremental diffusion couples to determine the Kirkendall effect at various concentrations. Darken&apos;s analysis was used to calculate the individual diffusion coefficients and mobilities from these data. The general diffusion coefficient is a single-valued function of the concentration in this system to within the limits of accuracy of the experimental methods used. The form of the various functions (diffusion coefficients and mobilities) of concentration is the same in every case: it is essentially the same as the usual D vs c curve. AS Darken&apos; has pointed out, the knowledge that the movements of different atoms diffusing in the same lattice need not proceed at the same rate is old. Ionic lattices are the classical examples; application of the generalization to lattices with metallic bonding was much more slowly accepted. It remained for Kirkendall&apos;&apos; to show clearly that metallic diffusion need not be symmetrical with respect to both species. Several investigators" have confirmed the initial observation of a "Kirkendall effect:" marker movement accompanying diffusion. They have extended it to other systems and conditions. The theoretical interpretations have been many; ne of the first and simplest of these is that of Darken"&apos; which is essentially mechanism independent. Darken has shown that the Kirkendall experiment permlts a calculation of the individual diffusion coefficients and, coupled with activity data, offers a means of measuring the mobilities of the separateatoms in a binary diffusion process. There is no published information on the effects of concentration and temperature on the individual diffusion coefficients or on the mobility values in binary solid solution; this paper provides such information for zinc and copper in a brass. For purposes of clarity, the overall D value obtained, for example, from the Boltzmann-Matano solution to Fick&apos;s law, will be designated as the "general diffusion coefficient;" and the diffusion co- efficients for the separate diffusing species will be designated as the "individual diffusion coefficients." Experimental Procedure The authors have accepted Darken&apos;s analysis and have measured mobilities on this basis. The findings of da Silva and Mehl are accepted: that the Matano interface, defined as the origin of coordinates for the Boltzmann-Matano solution to Fick&apos;s law, coincides with the original weld interface; that the "shift" of a marker is the distance between the Matano interface and the marker; that the observed porosity is too small sensibly to affect this result; and that the shift is a linear function of the Matano area, the area defined as the absolute magnitude of the area on either side of the Matano interface. Alloys: The a-phase of the Cu-Zn system was chosen for investigation. The measurements were made on incremental couples for two separate reasons: l—it has been questioned whether D, the general diffusion coefficient, is a single-valued function of concentration (a comparison of the D-values for couples with small concentration range, e.g., 10 vs 20 pct Zn, against those from a wide concentration range, e.g., 0 vs 30 pct Zn, will answer that question); and 2—on the Darken analysis, the mobility can be determined only at the concentration at which the marker is observed to lie (this is but one concentration in a single couple) but choosing a series of incremental couples in the range between 0 and 30 pct Zn provides mobility values at several concentrations, thus giving mobility as a function of concentration. Four alloys were chosen; nominally, pure copper, copper with 10 pct Zn, copper with 20 pct Zn, and copper with 30 pct Zn. This allowed six different types of diffusion couples to be prepared, promising mobility determinations at six different concentrations, but having a minimum range of 10 pct Zn. The copper was an especially prepared pure copper supplied through the courtesy of the Ameri-

Jan 1, 1956

By E. V. Kleber, V. F. Novy, R. C. Vickery

The constitutional diagram has been determined for the system gadolinium-nickel. Nine intermetallic compounds have been found at compositions corresponding to the following gadolinium-nickel ratios: 3:1, 3:2, 1:1, 1:2, 1:3, 2:7, 1:4, 1:5, 2:17. The GdNi and GdNi5 compounds have congruent melting points of 1300&apos; and 1500°C, respectively while the remaining compounds melt in-congruently. Eutectics exist at 15 wt pct Ni, 31 1/2 wt pct Ni and 87 wt pct Ni with melting points of 6703 8803 and 1220°C, respectively. IN a continuing investigation of the properties of rare earth alloys, a study has been made of the gadolinium-nickel system. Previous work encompassed the iron containing alloys and a subsequent paper will deal with the constitution of the gadolinium-cobalt system. Vogel,1 examined alloys of nickel with lanthanum and cerium. R3Ni, RNi, RNi2, RNi3, RNi4, and RNi5 compounds were found. Endter and Klemm,2 Fulling et al.3 Heumann,4 and Nowotny5 found the 1:2 compositions of this series to exist in a C-15 (face-centered cubic) structure, and the 1:5 compositions in a hexagonal system. Jepson and Duwez6 more recently examined these 1:2 and 1:5 compositions and generally confirmed earlier data while Wernick and Geller7 most recently have given additional data on the GdNi5 compound. Comparisons with our results will be made in the appropriate section of this report. EXPERIMENTAL Methods of alloy preparation, annealing procedures, and experimental techniques have been given in our earlier paper.8 Chemical analyses of the alloy samples were made by dissolving the specimen in nitric acid, precipitating the gadolinium as hydroxide and the nickel with dimethylglyoxime. Both precipitates were ignited to oxide and weighed. RESULTS Microstructure— Metallography of alloy specimens in this series has been conducted on both arc-melted and annealed materials. Etchants used have been 5 pct nital with approximately 10 pct distilled water added, for high gadolinium samples; Carapella&apos;s ferric chloride solution for intermediate compositions; and Marble&apos;s (copper sulfate) reagent for high nickel content alloys. Because of difficulties encountered in the grinding and polishing of specimens containing 40 to 75 wt pct Ni, no photomicrographs were made of such specimens. The microstructure of an arc-melted 5.3 wt pct Ni alloy is shown in Fig. 1. Light etching primary grains of gadolinium are embedded in an eutectic matrix. The microstructure of an alloy of 9.55 wt pct Ni alloy, Fig. 2, annealed 50 hr at 700°C, consists almost entirely of the intermetallic compound Gd3Ni. The structure of an arc metal alloy of approximately 19 pct Ni, Fig. 3, consists of grains of the compound GdNi embedded in the Gd3Ni2-Gd3Ni eutectic. The arc-cast structure of the 38.7 wt pct Ni alloy is shown in Fig. 4. Large primary grains of a compound rest in a matrix structure of coarse GdNi-GdNiz eutectic. Because of the occurrence of several peritectic compounds in the central region of the diagram, identification of the primary structure in this alloy is not certain. As has been indicated above, microstructures of alloy specimens containing between ca 40 and 75 wt pct Ni have not been photographed. These specimens were highly brittle, and macro- and micro-cracking were impossible to control in the grinding and polishing procedures. Prolonged annealing did not alleviate this condition. Visual observations in small specimens did, however, provide evidence for a multiplicity of phases and peritectic dissociations of compounds although rationalization of structures was not possible.

Jan 1, 1962

By J. Nutting, D. H. Kirkwood

The oxidation of lead sulfide in air between 200° and 350°C has been investigated by electron diffraction from thick sulfide films and from galena surfnces. It has been demonstrated that sulfate is the stable reaction product up to 570°C. Sulfate is HAGIHARA has investigated&apos; single crystals of galena roasted in air by the reflection electron-diffraction technique, which owing to the very limited penetration of the beam into the crystal gives information of the nature of the surface only. He has shown that up to 280°C the first oxidation product is lead sulfate, followed by lead mono-oxysulfate (PbO . PbS04). At longer times and higher temperatures more complex patterns appeared which could not be analyzed. All of these patterns were of streaks or spots arising from crystals oriented on the galena surface, and it is probable that these crystals are lead compounds whose structures have not been determined, such as the other oxysulfates (2Pb0 • PbS04 and 4Pb0 . PbS04) or a number of oxides. Certain lead sulfide films, formed chemically, give ring patterns in transmission electron diffraction2 because they are polycrystalline, and should also give ring patterns of the products after oxidation. It was thought that a diffraction study would reveal the sequence of phases produced in the reactions at different temperatures, since X-ray powder patterns are available for many lead compounds. PREPARATION OF FILMS The films were prepared by passing H2S over a saturated solution of lead nitrate in water. Once a silvery film had formed on the solution surface, no further thickening was apparent. The films were transferred by a gauze to a bath of distilled water for washing and pieces of film were caught on small discs on which they were dried. The discs were formed initially on galena up to temperatures of 300°C, followed by oxide and oxysulfates in turn at longer times. The appearance of- these phases is believed to result from an inadequate rate of supply of sulfur to the top surface 01. the crystal. standard Siemens mounts, made of platinum alloy, and had seven 20-p apertures drilled through them. The parts of the film which had dried onto the disc surface were light blue in color, which is the interference color of a film about 600A in thickness. A strong pattern of lead sulfide was obtained in transmission electron diffraction through the apertures but slight broadening indicated a crystallite size of around 200A. Tilting a sulfide film in the beam produced arcing of the rings, increasing the intensities of the (Ill), (3111, and (222) rings and reducing (200) and (220). This arises from preferred orientation in the film, a [loo] direction of the crystallites being normal to the plane of the film. These specimens were oxidized in an oven maintained at the required temperature. The reported times include that taken to heat the film to the reaction temperature. STABLE PHASES FORMED IN OXIDATION The conditions in which various oxidation products of lead sulfide are stable have been considered by the authors in a previous paper.3 It was shown that in a normal atmosphere, taken as containing lo-&apos; atm of SOs, lead sulfate would be stable up lo about 570°C. This was confirmed by oxidizing thin films of sulfide for several days, and the analysis of the transmission-diffraction pattern is given in Table 1. The fit with the patt$rn from X-rays is good, except for the missing 3.62A ring. Some disagreement in intensities of reflections given by X-rays and electrons is to be expected. Up to 570°C a spotty pattern of sulfate was still obtained, indicating grain growth, but above this temperature the film disintegrated. Probably this is associated with the decomposition to PbO . PbS04. It needs to be emphasized that the atmosphere

Jan 1, 1965