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By H. S. Greismer

Alabama washes a larger percentage of its total coal output than any state in the Union. For producing coking coal, three-compartment jigs are favored; mines providing, steam and commercial coal use single-compartment jigs exclusively. Chemists are as necessary to washing plants as recording gages are to power plants. Experiments in Alabama indicate that the sludge released by coal-washing plants can be deposited in streams and on agricultural lands without disastrous results. CAMPBELL, 1 in 1896 said: "The Birmingham district in Alabama has certain great advantages for there are few places in the world where fuel and ore are so near together, although, unfortunately, both are of inferior quality; the ore being low in iron and high in phosphorus and the coal giving a weak and impure coke." This statement could not have been, questioned in 1894, but by 1896 several Robinson-Ramsay washers had been put into operation and weak and impure coke was a thing of the past. The Warrior coal field of Alabama contains six seams that yield coking coal of excellent quality. In descending- order, they are Brookwood, Milldale, Pratt, America, Mary Lee, and Black Creek. In each of these, however, bands of rock and bone coal of varying thickness are stratified with the coal; and while some of these impurities can be separated from the coal by the miner, much of it must be loaded out with the coal: Consequently, unless the coal is washed before being coked, it will yield a coke of varying ash and sulfur content quite unsatisfactory, for blast-furnace use. At present, the Gulf States Steel Co. is producing run-of-mine coal at its Virginia mine, from the America seam, that is uniformly low enough in ash to permit of coking without washing, but this is the only exception to the above statement. Alabama was the first state to experiment seriously with coal washers, was the first to install washers on a large scale and, up to the present, has maintained the lead. The Alabama State Mine Inspector reports that during 1923 20,919,303 tons of bituminous coal were mined in Alabama; 12,858,499 tons of which were delivered to coal washers for treatment.

Jan 9, 1924

By G. H. Bruce, C. E. Williams

The trend toward deeper drilling, together with the attcndant increase in power requirements for circulation of the drilling fluid, has emphasized the need for a critical examination of the factors affecting the removal of bit cuttings from the hole by the drilling fluid. The ability of drilling fluids to lift cuttings is called their carrying capacity. A series of laboratory and field experiments has been conducted to determine the minimrim annular velocity necessary to remove cuttings, and to investigate the effects of properties of drilling fluids on their carrying capacities. Consideration of the results of these experiments led to the following conclusions: 1. Turbulent flow in the well annulus is most desirable from the standpoint of cutting removal. 2. Low viscosity and low gel are advantageous in removing cuttings. 3. Increase in mud weight is effective in increasing carrying capacity. 4. The carrying capacity is higher when the pipe is rotated than when it is not. 5. If turbulent flow can be maintained, an annular velocity slightly higher than the slip velocity of the largest cuttings to be transported should keep the bore hole clean. This implies velocities of 100 to 125 ft per minute rather than the presently used 175 to 225 ft per minute. INTRODUCTION Power Savings by Reduction of Annular Velocities A large portion of the power expended in drilling operations is consumed in circulating the drilling fluid. An important factor in establishing the rate of mud circulation is the minimum velocity in the annulus necessary to remove bit cuttings. Empirically, it has been found that average annular mud velocities of about 200 ft per minute will remove cuttings. It was not definitely known, however, whether annular velocities of about 200 ft per minute were just above the minimum necessary to remove cuttings, or whether such velocities could be materially reduced without sacrifice of the ability of the mud to remove cuttings. It is apparent that if annular velocities could be reduced without impairment of cutting removal, a considerable saving in power requirements would result. Need for Research on Carrying Capacity The ability of a drilling fluid to transport cuttings is called its carrying capacity. Although it has been recognized that the carrying capacity of a mud is affected by mud properties such as viscosity and density1,2,3,4 there have been various views in the industry as to the effects of these mud properties on carrying capacity. The economic importance of the problem of carrying capacity and the scarcity of information on the subject indicated that research on the problem was needed. THE FACTORS AFFECTING CARRYING CAPACITY Qualitative Determination of Factors The mechanism of cutting transport is closely related to that involved in the separation of material by settling processes. A considerable amount of research has been done on settling problems, and discussions of sedimentation theory can be found in standard texts.5,6 Consideration of the information available from these sources, together with consideration of the mechanism of cutting transport, leads to the conclusion that the factors affecting carrying capacity are the dimensions of the system, the physical properties of the cuttings. and the physical properties of the drilling fluid. system Dimensions and Their Effect The dimensions of the fluid circulating system of importance to carrying capacity are the bore hole size, drill pipe size, pump capacity, and pump speed. These dimensions determine the annular velocity of the drilling fluid. Physical Properties and Their Effects The physical properties involved in the interaction between mud and cuttings are the density and shape of the cuttings and the density, viscosity and gel strength of the drilling fluid. The effect of the density factor on carrying capacity is fairly obvious; high density difference between cuttings and fluid results in a low buoyant force and therefore decreases carrying capacity. The effect of cutting shape is less obvious. Although

Jan 1, 1951

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 J. S. Pascover, J. K. Abraham

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

Jan 1, 1970

By C. E. Williams, G. H. Bruce

The trend toward deeper drilling, together with the attcndant increase in power requirements for circulation of the drilling fluid, has emphasized the need for a critical examination of the factors affecting the removal of bit cuttings from the hole by the drilling fluid. The ability of drilling fluids to lift cuttings is called their carrying capacity. A series of laboratory and field experiments has been conducted to determine the minimrim annular velocity necessary to remove cuttings, and to investigate the effects of properties of drilling fluids on their carrying capacities. Consideration of the results of these experiments led to the following conclusions: 1. Turbulent flow in the well annulus is most desirable from the standpoint of cutting removal. 2. Low viscosity and low gel are advantageous in removing cuttings. 3. Increase in mud weight is effective in increasing carrying capacity. 4. The carrying capacity is higher when the pipe is rotated than when it is not. 5. If turbulent flow can be maintained, an annular velocity slightly higher than the slip velocity of the largest cuttings to be transported should keep the bore hole clean. This implies velocities of 100 to 125 ft per minute rather than the presently used 175 to 225 ft per minute. INTRODUCTION Power Savings by Reduction of Annular Velocities A large portion of the power expended in drilling operations is consumed in circulating the drilling fluid. An important factor in establishing the rate of mud circulation is the minimum velocity in the annulus necessary to remove bit cuttings. Empirically, it has been found that average annular mud velocities of about 200 ft per minute will remove cuttings. It was not definitely known, however, whether annular velocities of about 200 ft per minute were just above the minimum necessary to remove cuttings, or whether such velocities could be materially reduced without sacrifice of the ability of the mud to remove cuttings. It is apparent that if annular velocities could be reduced without impairment of cutting removal, a considerable saving in power requirements would result. Need for Research on Carrying Capacity The ability of a drilling fluid to transport cuttings is called its carrying capacity. Although it has been recognized that the carrying capacity of a mud is affected by mud properties such as viscosity and density1,2,3,4 there have been various views in the industry as to the effects of these mud properties on carrying capacity. The economic importance of the problem of carrying capacity and the scarcity of information on the subject indicated that research on the problem was needed. THE FACTORS AFFECTING CARRYING CAPACITY Qualitative Determination of Factors The mechanism of cutting transport is closely related to that involved in the separation of material by settling processes. A considerable amount of research has been done on settling problems, and discussions of sedimentation theory can be found in standard texts.5,6 Consideration of the information available from these sources, together with consideration of the mechanism of cutting transport, leads to the conclusion that the factors affecting carrying capacity are the dimensions of the system, the physical properties of the cuttings. and the physical properties of the drilling fluid. system Dimensions and Their Effect The dimensions of the fluid circulating system of importance to carrying capacity are the bore hole size, drill pipe size, pump capacity, and pump speed. These dimensions determine the annular velocity of the drilling fluid. Physical Properties and Their Effects The physical properties involved in the interaction between mud and cuttings are the density and shape of the cuttings and the density, viscosity and gel strength of the drilling fluid. The effect of the density factor on carrying capacity is fairly obvious; high density difference between cuttings and fluid results in a low buoyant force and therefore decreases carrying capacity. The effect of cutting shape is less obvious. Although

Jan 1, 1951

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, ' the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

By F. J. Plecity, W. C. Leslie, F. W. Aul

During isothermal recrystallization, the rate of grain growth in dilute Fe-hlo alloys decreased rapidly with increasing Mo content, up to -0.04 at pct, and less rapidly therea-fter. Rate of growth also decreased sharply with time at constant temperature. The observed rates of boundary migration did not cor,espond to predictions of the Lucke-Detert theory. It is proposed that the growth of recrystallized grains is inhibited by clustering of solute atoms at inzperfections in the unrecrystallized matrix. It is now firmly etablished" that the rate of re-crystallization of cold-worked metals, i.e., the rate of growth of recrystallized grains into the deformed matrix, is greatly inhibited by the presence of alloying elements in solid solution. The effect is greatest with the first very small quantity of alloying elements, and additional increments cause much less pronounced retardation of growth. The early papers on this subject were reviewed in Ref. 6. The mechanism of retardation of growth is not clear; only one theory, due to Lucke and Detert? has been advanced. This assumes an elastic interaction between grain boundaries and solute atoms which tends to increase the concentration of the latter in the grain boundaries. Except at very low solute concentrations or at high temperatures, the mobility of the boundary is assumed to be controlled by the rate of diffusion of the accompanying solute atoms. Abrahamson and Blakeney2 have noted a correlation between "recrystallization temperature of binary alloys of iron and the number of d-shell electrons in the solute atoms. There is need for considerably more experimental data on the effect of solute elements on the rate of migration of grain boundaries into the deformed matrix, to provide the basis for an understanding of the annealing process in metallic solid solutions. Only a start has been made in this direction. To avoid unnecessary complications, alloys in which precipitation does not occur should be used, but to produce the maximum effects it is desirable to select alloys with a large difference between the sizes of the atoms of the solvent and solute. For these reasons, alloys of iron and molybdenum sen for this study. MATERIALS AND PROCEDURES A 30-lb. ingot of iron and four similar ingots of Fe-Mo alloys were vacuum melted in magnesia crucibles and poured into cast-iron molds. The molybdenum contents were planned according to the results of Abrahamson and Blakeney2 sothattwoalloyswould fall in the region of rapid change of recrystallization kinetics with change in composition (0.006 to 0.015 and 0.030 to 0.045 at. pct Mo) and two alloys would fall in the region of gradual change (0.18 to 0.24 and

Jan 1, 1962

By J. P. Sheehan, W. R. Hibbard, M. Baeyertz

This paper deals with molybdenum modifications of 5140 steel that have the same hardenability but a better tolerance for phosphorus than the AISI-SAE 5140 grade. Lack of toughness in steels with higher than normal phosphorus contents is well known to metallurgists. This problem is troublesome even within normal phosphorus ranges, if the heat treatment or the design of the part or the service is critical. Under such unfavorable conditions and also in the case of phosphorus contents toward the upper side of the commercial range, the use of molybdenum to replace a part of the chromium in 5140 steel provides a factor of safety. The toughness of steel is variously exhibited in different mechanical tests; broadly the term is applied to the capacity of the steel to deform prior to fracture. Defined in this way, toughness is considered to be an inherent quality that depends upon the composition and structure of the steel, and also upon its temperature during deformation and fracture in the test. In the present state of our knowledge, the type of mechanical test needs to be included in any discussion of toughness, because the revelation of this quality in steel depends on the stress state and rate of stressing imposed by the test. In comparing the toughness of one steel with another by laboratory testing, it has long been customary to use notched tests that impose severe constmint to deformation, and then to test over a range of temperatures to obtain the so-called transition. At temperatures above the transition, the steel fails after considerable deformation and absorption of energy. Below the transition, less energy is absorbed as the steel fails largely by cleavage. The transition range itself is characterized by a more or less abrupt change in energy absorption and type of fracture. The conventional V-notch Charpy impact test has been used exclusively in the work covered by this report. For the steels under study, rather sharp transitions are obtained with this test, at testing temperatures that are easily obtained in the laboratory. The position of the transition on the testing temperature scale provides a rather sensitive index of the toughness of the steel, when the steels under study are similar in character as they are in this work. Turning to the metallurgical reasons for the greater toughness of one steel as compared to another, the authors propose to limit the discussion to the small field under study. Only one structural state is considered, tempered martensite of a hardness of about 28 Rockwell C or 269 Brinell. The study deals first with the loss of toughness in AISI-SAE 5140 steel caused by increasing the phosphorus content from about 0.020 to 0.040 pct. A second part of the work deals with counteracting this loss in toughness by replacing a part of the chromium by molybdenum. A series of molybdenum modifications was studied, in each of which the chromium was reduced sufficiently to duplicate the hardenability of 5140 steel. Phosphorus affects the toughness of steel in two ways. An inherent lack of toughness of phosphorus-bearing ferrite as compared to low phosphorus ferrite has often been noted. Jolivet and Vidall have shown that phosphorus has the same effect in tempered martensite in chromium steels. The other well known effect of phosphorus is to make steel susceptible to temper embrittlement. Temper brittleness is a loss in toughness brought about by tempering steel within a limited temperature interval somewhat below the A1 temperature. In most of the standard AISI-SAE alloy steels, this temperature interval is approximately 850-1100°F. Either of these types of loss in toughness is easily followed by the shift in the transition temperature obtained with the notched-bar impact test. The data to be presented show the beneficial effect of substituting molybdenum for a part of the chromium in 5140 steel with either moderate (0.020 pct) or high (0.040 pct) phosphorus contents. Both the inherent lack of toughness of phosphorus-bearing steel and temper brittleness are counteracted by this use of molybdenum. The work of Jolivet and Vidal mentioned above shows the detrimental effect of phosphorus on the toughness of tempered martensite in the absence of temper embrittlement, as well as the temper brittleness caused by phosphorus. They used two steels, essentially 0.25 pct C-1.4 pct Cr, with 0.044 and 0.013 pct P, respectively. The nonembrittled state was obtained by quenching in oil from 1610°F, then tempering for one hour at 1200°F and quenching in water. In this state the transition temperature range of the low phosphorus steel in the notched-bar impact test was below that of the steel with 0.044 pct P. An additional treatment of 24 hr at 975°F (that is, in the embrittling range) caused both steels to lose toughness, but the high phosphorus steel showed the greater embrittlement. Recently Hollomon2 has published a comprehensive survey and bibliography of the literature on temper brittleness, to which the reader is re-

Jan 1, 1950

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy's Law is valid. 4. The formation is saturated with a single homogeneous fluid.

By C. K. Eilerts

Finite difference equations were programmed and used to integrate the second-order, second-degree, partial differential equation with variable coefficients that represents the transient linear flow of gas-condensate fluids. Effect was given to the change with pressure of the compressibility factor, the viscosity, and the effective permeability and to change of the absolute permeability with distance. Integrations used as illustrations include recovery of fluid from a reservoir at a constant production rate followed by recovery at a declining rate calculated to maintain a constant pressure at the producing boundary. The time required to attain such a limiting pressure and the fraction of the reserve recovered in that time vary markedly with properties of the fluid represented by the coefficients. Fluid also is returned to the reservoir at a constant rate, until initial formation pressure is attained at the input boundary, and then at a calculated rate that will maintain but not exceed the limiting pressure. The computing programs were used to calculate the results that would be obtained in a series of back-pressure tests made at selected intervals of reservoir depletion. If effect is given to the variations in properties of the fluid that actually occur, then a series of back- pressure curves — one for each stage of reserve depletion — is required to indicate open-flow capacity and related flow characteristics dependably. The isochronal performnce method for determining flow characteristics of a well was simulated by computation. INTRODUCTION The back-pressure test procedurel is based on a derivation of the equation for steady-state radial flow of a gas, the properties of which are of necessity assumed to remain unchanged in applying the test results. The properties of most natural gases being recovered from reservoirs change as the reserve is depleted and pressures decline, and the results of an early back-pressure test may not be dependable for estimating the future delivery capacity of a well. The compressibility factor of a fluid under an initial pressure of 10,000 psia can change 45 per cent and the viscosity can change 70 per cent during the productive life of the reservoir. There are indications that the effective permeability to the flowing fluid can become 50 per cent of the original absolute permeability before enough liquid collects in the structure about a well as pressure declines to permit flow of liquid into the well. The advent of programmed electronic computing made practicable the integration of nonlinear, second-order, partial differentia1 equations2.3 pertaining to flow in reservoirs. Aronofsky and Porter4 represented the compressibility factor and the viscosity by a linear relationship, and integrated the equation for radial flow of gas for pressures up to 1,200 psi. Bruce, Peaceman, Rachford and Rice5 integrated the partial differential equations for both linear and radial unsteady-state flow of ideal gas in porous media. Their published results were a substantial guide in this study of integration of the partial differential equation of linear flow with coefficients of the equation variable. The computing program was developed to treat effective permeability as being both distance-dependent and pressure-dependent. In this study all examples of effective permeability are assumptions designed primarily to aid in developing programs for giving effect to this and other variable coefficients. The accumulation of data for expressing the pressure dependency of the effective permeability is the objective of a concurrent investigation. FUNDAMENTAL DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATION OF FLOW Linear transient fluid flow is represented by the partial differential equation,

Jan 1, 1965

By F. R. Archibald, C. M. Nicholson

THE present paper may be considered complementary to an earlier contribution on the same subject by F. R. Archibald and C. F. Jackson.1 It is particularly concerned with engineering and technological aspects of the operations at the Harleyville Alumina Plant during its period of operation from January 1945 to July 1946. The plant was built for and operated by Ancor Corporation, at Harleyville, South Carolina, as part of the government sponsored wartime program related to alumina production from domestic raw materials. The main purpose of the program was to secure technical and engineering data, based on actual plant experience, that might serve as a foundation for large scale production of alumina from raw materials other than bauxite. The Harleyville plant was directed specifically to treatment of clays found in very extensive deposits in the Carolinas and Georgia using the lime-sinter process developed by Ancor Corporation. It is considered that the purpose stated above has been served and this paper is to record and discuss some of the more important findings. The main factor in location of the plant at Harleyville was the presence in that locality of a rather remarkable deposit of high calcium limestone. The clay mining operation was centered near Aiken, S. C., and although a rail haul of ninety miles was involved there were, at the time, factors favorable to the Harleyville location offsetting, in part, the cost of transportation of clay. There are, no doubt, locations in the general area where clay and limestone deposits may be found in closer proximity but they had not been proven up when the project was undertaken. Availability of power from the Santee-Copper development whose high tension line skirted the property; ready access to rail and highway transportation; the promise, realized in actuality, of ample supply of soft water; and availability of labor supply were other factors of importance. Moreover, the general area has the decided advantage, for this type of operation, of a mild climate. Construction was begun in August 1943, and although stopped for a time pending review of the general situation that fall, it was resumed, albeit with less urgency, and substantially completed by the end of 1944. The total capital cost was approximately $3460,000. The first alumina was turned out in April 1945 and from then until the plant was closed down in July 1946, the operations followed a succession of periods of production alternating with periods in which minor alterations were made in conformity with experience. Steady improvement was made and at the time operations were discontinued it was considered that experience and the necessary engineering were in shape for removal of the remaining bottlenecks and a somewhat major revision in one section of the plant. Unfortunately this could not be carried out and it was necessary to discontinue the

Jan 1, 1948

By Harry M. Bendler, W. A. Wood

Electron metallography has been applied to the study of the torsional fatigue of polycrystalline OFHC* copper. The development of slip bands, fis- sures, and microcracks has been followed as a function of strain amplitude and number of cycles. Those factors that have been found to be relevant to a geometrical theory of the fatigue process are described. From the point of view of this theory it is important to distinguish between the effects of cycling at large amplitudes and at small amplitudes (true fatigue deformation). EARLY investigations showed metal fatigue cracking is caused by continued reversal of a small plastic strain. Fundamental study of fatigue, therefore, has been largely concerned with the cumulative effects of these plastic reversals on the metal structure. In particular, recent work has shown that the plastic reversals produce slip movements that are finer than the slip movements produced by unidirectional increments of plastic strain; individual slip movements in fatigue, for instance, are too fine to see by optical microscopy.2 It has also been shown that the fine slip movements of fatigue tend to concentrate in bands and that in this way they can build up, after enough cycles, a progressive surface disturbance. It is this disturbance which, in effect, makes the slip movement visible. It is also in this disturbance that the first cracks appear to form. From this point of view, therefore, the problem of fatigue becomes one of finding why the fine slip movements should concentrate in bands and why the. bands should finally open into cracks. Thus far, study of the slip bands has been limited to the changes they produce at the surface only. These studies have given interesting results. Ewing and Humfrey3 many years ago showed that the bands in iron could extrude debris. Forsyth found that bands in aluminum alloys could extrude thin tongues of material. Thompson showed that, after lightly dissolving away the surface of copper specimens, some bands persisted as superficial cracks might, and that the life of a specimen under fatigue deformation might be prolonged by dissolving away the surface at intervals. Thus these and related results have suggested that the metal structure in fatigue bands may disintegrate and that this may happen long before obvious cracking. These surface studies, however, have not shown definitely how cracking may begin, for they do not show sufficiently what is happening in depth. However, some advance in this direction has been made recently by a new approach, summarized later, which reveals slip bands and their surface disturbances in section. In the work done thus far, the sections have been studied by optical microscopy only. In the present work they have also been studied by electron microscopy with extended results. This paper also describes some observations on the surface disturbances prior to sectioning. These observations are relevant to a suggested theory of fatigue cracking. REVERSED SLIP MOVEMENTS Slip movements in fatigue deformation must reverse direction in each cycle. The question arises: DO the "backward" and "forward" movements take

Jan 1, 1962

By Hugh Rose

The properties of the company lie within the Pachuca district, State of Hidalgo, Mexico, connected by three railway lines with Mexico City, 55 miles southwest, and by two lines with Vera Cruz, 250 miles southeast. The ores were formerly divided by sorting into two classes, smelting and milling, the former averaging about 2 oz. gold and 335 oz. silver, the latter 0.12 oz. gold and 23 oz. silver. The smelting ores were sold to custom plants, principally the American Smelting & Refining Co. at Aguascalientes. The milling ores were treated by the patio process at the Guadalupe Hacienda, at Pachuca. This patio was probably the largest in existence at the time and continued in active operation up to March, 1910. In January, 1910, the mines and patio were sold to English interests, represented by Camp Bird Limited. Two new companies were formed, the Compania de Santa Gertrudis, S. A., to operate the mines, and the Compania Beneficiadora de Pachuca, S. A., to build and operate a custom cyanide milling plant. (Pig. 1.) Geology The historical geology of the Pachuca district is described by Fred J. Pope as follows: 1. The most recent sedimentary rooks in the district belong to the Cretaceous period. 2. The Cretaceous rocks were penetrated by large intrusions of ande-site (referred to hereafter as primary andesite) which occur as elliptical dome-shaped masses, striking northwest-southeast. These andesite bodies are from 8 to 15 miles long and from 6 to 10 miles wide. 3. A period of erosion during which the contour of the andesite domes was changed. 4. Andesite flows (secondary andesite) which rest unconformably on the primary andesites.

Jan 1, 1917

By Raymond D. Sloan

During 1944, substantial gains were recorded in practically every phase of the petroleum industry in Oklahoma. With the spotlight of activity focused on other states during the more recent years, the production momentum that was achieved in Oklahoma through the discovery and development of such outstanding pools as Oklahoma City, Fitts. and major pools in the Seminole area during the late 1920's and early 1930's was practically spent by the end of 1943. However, with much of the industry's exploratory efforts greatly reduced in Illinois, Indiana and Kentucky, the strong demand for Mid-Continent crude and the optimism created by some discoveries in the state toward the end of 1943, Oklahoma has again become the recipient of much activity and interest, with its 1944 drilling activity, production and refinery runs to stills registering substantial gains over the preceding year. Development and Exploration Since the discovery of the West Edmond pool in April of 1943, with the substquent drilling and development boom, the scene of exploratory activity has shifted from the central. south and east portions of the state to the general trend of the . Granite Ridge, where leasillg and wild-catting were greatly activated within a wide radius of this high subsurface feature. Leasing activity, however, jumped the confines of the Granite Ridge trend and extended into all of the northwestern counties in the state. Seismograph activity at once began following and keeping pace with this shift in the leasing and exploration locale, by the concentration of a large number of seismograph crews in the area. At one time during the year,35 crews were concentrated in Oklahoma, the majority being west of the Granite Ridge and extending into the northwestern counties. To illustrate the increase in geophysical work done in the state during the year, records indicate that 377 crew months were worked in 1944, which is a 21 per cent increase over the 311.5 crew months activated in 1943. With the discovery in 1943 of several encouraging prospects and the finding of West Edmond as an incentive, drilling operations increased some 54.3 per cent, for a total of 1986 completions during the year. This is compared with a figure of 1287 for wells drilled in 1943, an increase of 699 wells. The industry, with a total of 1064 oil producers, enjoyed a success percentage of 53.6 per cent. Gas wells completed were 223, while 699 dry holes were drilled. In 1943, completions included 587 oil wells, 127 gas wells, and 573 dry holes. The number of oil producers completed during the Year was almost double the numher of wells in 1943. Of the total drilling wells completed in the state, 350, or 17.6 per cent, were wildcat operations—an increase of 5.1 per cent over the 194.3 total of 333. The wildcat success percentage was 13.4 per cent, 47 successful wells being completed for an average initial potential of 160 bbl. In the state, 23 gas wells were completed with an average initial production of

Jan 1, 1945

By T. B. Massalski, Horace Pops

The occurrence and the temperature dependence of the athermal martensitic transformation in bcc Cu-Zn ß-phase alloys have been studied by cold-state microscopy, differential thermal analysis, and electrical -resistivity measurements. CinenzatograpJzic studies have shown that in the majority of alloys the transformation occurs in two stages. A thermoelastic phase, having a 'needlelike" uppearance, forms initially at the MS temperature and grows relatively slowly, chiefly in the edge (lengthwise) direction. With further cooling, an additional martensitic phase forms in rapid bursts at a lower temperature, MB, Both martensitic phases appear to have the same cry stallographic habit hut their modes of formation and growth are different. For the composition range studied, between 38.55 and 41.49 wt pct Zn, the habit planes determined are close to the (2.17 ,12) plane of the matrix, in general agreement with the prediction of the phenomenological theory of martensite formation. Thermal cycling through the MB temperature produces permanent plastic deformation in the 0 matrix and gradutally eliminates the typical burst phenomena. Thermal cycling only through the MS temperature produces no noticeable deformation effects. THE bcc Cu-Zn ß-phase alloys tend to become unstable at low temperatures and undergo a martensitic transformation,'-3 but the details of the transformation have not been completely determined. Following earlier metal log raphic and X-ray work1 Tichener and ever' determined by means of electrical-resistivity measurements the temperature range of the martensite transformation during continuous cooling. The transformation temperature was found to decrease with increasing zinc content, becoming about -130°C for an alloy containing 40.04 wt pct Zn. Hull and Garwood3 made a metallo-graphic study of Cu-Zn 0 brasses at temperatures down to -160°C, and determined the habit plane of the transformation product for an alloy containing 38.88 wt pct Zn. No metallographic studies below liquid-nitrogen temperatures have been reported. The martensitic transformation in ß-brass alloys can also be induced by deformation.1,4 The MD temperature corresponding to the appearance of the strain-induced martensite is some 300°C higher than that observed without strain, and hence the transformation can be strain-induced in alloys containing a higher percentage of zinc. Massalski and Barrett4 found that alloys containing as much as 51.89 wt pct Zn could be transformed into a faulted hcp structure by cold working at liquid-helium temperature. Because the details of the MS temperature and morphology reported in the literature are somewhat incomplete, a further study has been made of some of the above features. A design of a cryogenic stage for optical metallography5 has permitted the examination of specimens at temperatures down to 4.2oK, and the use of a cinecamera has permitted a study of the morphology on cooling and heating. The particular aim of the present work was to examine the transformation temperatures, the habit planes, and the growth morphology over a wide composition range in the ß-phase field. The effect of thermal cycling upon the subsequent transformation was also examined.

Jan 1, 1964

By Joseph Jensen

THE history of the normal oil field is supposed to show an oil graph stalting high in flush production, descending more or less steeply into the curve of settled production and dropping gradually to the vanishing point of economical operation. Together with this at somewhere in the early history of the field, there appears from a vanishing point a graph showing the production of water. During the period of settled production this graph rises higher and, toward the close, unless extensive work is done in the line of correction, rises far above the oil graph to where the cost of operation terminates profitable pumping. Fields that start out with a high relative content of water are generally very short lived. Fields that never develop a water problem are exceedingly rare.

Jan 1, 1930

By A. J. Griest, P. D. Frost, H. A. Robinson

The flow characteristics and uniform elongation of alpha-beta titanium alloys in the solution-treated condition were shown to be markedly affected by the solution temperature. Two classes of alpha-beta alloys were distinguished, based on the effect of solution temperature on the uniform elongation. Martensitic alpha-beta alloys, which are relatively weakly beta-stabilized, showed decreasing values of uniform elongation as the solution temperature was initially increased. However, after solution-treatment at still higher temperatures in the alpha-beta field, the uniform elongation of these alloys was again high, and often attained its maximum value. Nonmartensitic alpha-beta alloys, which are more heavily beta-stabilized, showed a continuous decrease of uniform elongation with increasing solution temperature. The behavior was rationalized in terms of the alpha-beta ratio and the alloy content of the beta existing at the solution temperature. The data indicate that in commercial practice close temperature control may be required to get maximum uniform elongotion, and hence, maximum potential formability, in solution-treated sheet. Bend-test data also were obtained for the solution-treated conditions. A MOST important objective of current titanium research is the development of age-hardenable alloys with superior formability in the solution -treated condition. Alpha-beta titanium alloys have been shown to be amenable to high-strength aging treatments after solution-treatment in the alpha-beta field.' However, heat-treatment data on the properties of solution-treated sheet, such as uniform elongation, minimum bend radius, and flow properties, which have a bearing on the potential formability, have not been widely available. This paper presents only the most significant results of a research program conducted at Battelle for the Air Force in an effort to develop sheet alloys that can be formed readily as solution-treated and subsequently aged to very high strengths. Data for 10 compositions representative of the more than 25 alloys studied in this program are presented. A primary objective of the paper is to demonstrate the pronounced dependence of the flow characteristics and uniform elongation on solution-treatment temperature. This effect is believed to be vitally important in the commercial heat-treatment of age-hardenable titanium sheet alloys. Experimental Procedures Melting and Fabrication—The nominal and actual compositions, beta transi temperatures, and rolling temperatures of 10 of the 30 alloys studied are presented in Table I. Stock :€or two of the alloys, E (Ti- 8Mn) and J (Ti-6A1-4V) was obtained from commercial heats. The remaining heats, except D and I, were double melted as 10-lb heats in a consumable-electrode furnace. Melting stock was 120 Brine11 hardness sponge. The oxygen and hydrogen analyses spotted throughout the heats indicate the range of interstitial levels resulting from the melting practice used. Heats D and I were melted as 20-lb ingots with the same grade of sponge. These ingots were cut in half and one portion used in the present evaluation. The ingots, which were about 4 in. diam and 4 in. in height, were upset forged and drawn at 1750°F to sheet bar 5/8 in. thick by 2 1/2 in. wide in such a manner that the top of the ingot corresponded to the top of the sheet bar. Slabs of the sheet bar, 5 1/2 in. in length were scalped to 1/2 in. thickness and rolled at the temperatures indicated in Table I to approximately 0.055 in. sheet. Elongation during rolling took place at 90" to the original forged length. The fabrication procedure used is described in some detail since the experimental heats showed considerable directionality in mechanical properties. The rolling procedures for the commercial heats were unknown, but were such as to produce essentially isotropic properties. All heats, as rolled, showed microstructures typical of alpha-beta alloys worked in the alpha-beta field; that is, the structures consisted of equiaxed alpha particles in a beta matrix. Heat Treatment— The effects of solution and aging heat-treatments on the properties of the alloys were evaluated uSing longitudinal and transverse tensile and bend coupons sheared from the sheet. Two or three solution-treated conditions were evaluated for each alloy. In addition, the alloys were also tested after annealing at 1200°F for 4 hr and furnace cooling. The solution-treated and annealed conditions were those in which the alloys might be expected to

Jan 1, 1959

By C. E. Taylor, L. V. Fegan

With on-stream electrical-resistance measurement as a basis, Bethlehem Steel developed a system for the completely automatic control of moisture in the feed to pelletizing. This system was later successfully adapted to the sintering process, with automatic control of moisture serving to maintain the air permeability required for effective burnthrough. Control of moisture content is an important factor in the agglomeration processes by which iron ores are converted into either pellets or sinter for use in blast furnace burdens. In both pelletizing and sintering the iron ore feed must be mixed with the proper amount of water so that capillary attraction and surface tension forces can be utilized to cause the ore particles to coalesce and form larger agglomerates. The success or failure of the entire pelletizing or sintering process depends on maintaining the proper moisture. Therefore, continuous automatic control of moisture is one of the conditions for the automation and optimum use of both pelletizing and sintering processes. In pelletizing, variation in moisture can cause ball size to change and is a common cause of cycling which results in a fluctuating feed to induration. Excessive moisture can cause lumps to form at the cutter bar and contributes to the formation of buildup on the green pellet screens. Green pellets with excess moisture deform and reduce bed permeability. In sintering, accurate control of moisture is also important because moisture must be within the limits that give the bed the required permeability for good burnthrough. In response to these problems, a moisture meter, based on the principle of electrical resistance measurement, was developed. This moisture meter has been a key factor in the development of systems for providing uniform feed of concentrates in most of Bethlehem's pelletizing and sintering plants. The automatic moisture control system for pelletizing was successfully plant-tested and resulted in the following: (1) Control of moisture in the green pellets to +0.2%. (2) Up to 50% reduction of bentonite consumption. (3) Control of unscreened green pellets so that 85% of the furnace product at Cornwall was within the size range of -5/8 +3/8 in. (4) Improved quality of product with a tumble test of 94 and a "Q" index of 90 as the result of feeding a consistently uniform feed to a shaft furnace. In sintering, where sinter-mix temperature change and variable feed could cause errors in moisture measurement, the system was designed to maintain the correct moisture under virtually all plant operating conditions. It was successfully plant-tested and is now in use in most of Bethlehem's sintering plants. The system achieves: (1) Control of moisture within the desired limits for optimum production. (2) Continuous measurement and control of moisture even with intermittent feeding of mix, so that attention by the operator is seldom required. The two automatic control systems provide smoother startup, minimize upsets and contribute to the consistent control of process variables in pelletizing and sintering. MOISTURE-CONTROL SYSTEM FOR PELLETIZING Fig. 1 shows the general arrangement of the system for automatic control of moisture in pelletizing.1 In this system a bin level controller, using a single probe which regulates filter speed, maintains a uniform low concentrate level in the bin.' The moisture meter, comprised of an analyzer and control components, continuously measures the moisture in the bed and adds water to adjust to the desired level. The meter is placed in an open-loop (feed-forward) control, i.e., water addition occurs downstream from the probes. Filter vacuum must be set so as to produce a filtercake moisture which is below the optimum for pelletizing. Bentonite is added after the

Jan 1, 1969

By V. J. Kniazeff, S. A. Naville

The problem of unsteady-state condensate-gas flow through porous media leads to a set of second-order non-linear partial differential equations. Such a set of equations is numerically solved in the case of radial two-phase flow around a well, taking into consideration both the thermodynamical properties of the fluid and the mechanical properties of the reservoir. The fluid properties, reflecting the PVT relationship of the gaseous and liquid phases, are expressed by using the partial specific masses of the two main separator products in these phases. The flow properties of the reservoir rock are expressed by the generalized Darcy's law for the liquid phase and by a quadratic relationship between the rate of flow and the pressure gradient for the gaseous phase. The numerical solution of the equations for pressure and saturation US radius and time is worked out through programs written for a computer. The evolution of bottom-hole pressures, well productivities or- deliverabilities and effluent compositions with the depletion of the reservoir is easily derived. The application to the Saharian gas-condensate field Hassi R'Mel led to a better understanding of the drainage mechanism. A zone of fairly high liquid saturation develops around the wells, reducing the effective permeability, and represents a loss of condensible products in addition to the PVT-like retrograde condensation. lnside this zone, near the well, the deviation from Darcy's law for the flow of the gaseous phase governs the well deliver-ability. A back-pressure test has been computed and correlates with the field results. INTRODUCTION Two-phase flow of volatile hydrocarbons, like condensate gas or light crude oil, may be treated as the flow of a binary mixture by an arbitrary division of the chemical components into two groups. This is translated into two equations of mass continuity, which constitute a set of relation- ships for the pressure and the saturations vs the space coordinates and the time. The equations contain the laws governing the composition and the motion of the phases. The problem so defined is solved with the assumption that the compositions of the phases at any pressure are respectively the same as those observed in a PVT measuring cell under differential liberation. In a first series of computations, it was assumed that the flow obeys the generalized Darcy's law. A satisfactory representation of the retrograde condensation around the well was thus obtained. In addition, the trend toward decreasing effective permeabilities was obtained, and the computed composition of the effluent checked the laboratory values. However, it has not been possible within this basic assumption to represent the non-linear relationship between the production rate and the bottom-hole pressure drawdown as observed for gas wells in the field. Following the advice of A. Houpeurt it was decided to consider the relative permeability to gas as a function of the velocity of the gas Phase.1 The necessary physical determinations were made by E. COstaséque using a method devised by A. Houpeurt and R. Iffly. As numerical processing of the equations progressed, several difficulties were encountered which were overcome through collaboration with the computer manufacturer. This mathematical model of two-phase flow in porous media had been primarily intended for and extensively applied to the case of the Hassi R'Mel gas-condensate field, operated by SN Repal for SEHR, a joint subsidiary of SN Repal and CFP (A). The programs have also found their applications to forecast the behavior of several fields in the Sahara area containing light and volatile hydrocarbons. BASIC EQUATIONS We will consider a zone in the porous reservoir where the flow properties and the in situ composition of the fluids can be assumed to be uniform. A part of the equations of transient flow can be written with the specific gravity of the fluids being taken equal to the sum of the contributions due to the

Jan 1, 1966

By James H. Hance

Several years ago the writer was connected with the Mint and Assay Service of the Federal Government as Assistant Assayer at the Salt Lake Assay Office. At that time cyanide bars formed approximately half of the bullion purchased by that office. Disagreement in valuat,ion between the producer and the office was not infrequent and to a lesser extent between the Assay Office and the Mint, this latter issue being soon obviated, however, by adopting uniform methods of sampling the bars. A nice problem seemed to offer itself for research and the writer began a series of experiments which were soon terminated, however, by his going into other work, and which he regrets have not since been completed. The results attained may suggest lines of approach to this problem and are, therefore, offered in this article. Frederic P. Dewey, Assayer of the Mint Scrvice, U. 5. Treasury, has had abundant opportunity to study this phase of metallurgy, and has published several articles relative thereto.1 In the last article cited Dewey quotes analyses of cyanide bullion similar in content to that with which the writer worked, and which show some of the variations met with. In the discussion of these papers,2 comparison has been made in terms of copper bullion, but to the writer this seems of questionable value. Copper bullion may resemble silver bullion, but its similarity to gold bullion with little or no silver content is another thing. The freezing-point diagram of Roozeboom, reproduced on page 881 of the discussion cited, is for the gold-silver series as stated. The original problem under discussion, however, is not this alloy but gold with base metals other than copper. As for the statement that the corners are the worst places or

Jan 1, 1916