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By S. W. Kessler, R. B. Pond

Metal specimens were solidified through a measured thermal gradient so a free surface and the liquid-solid interface could be examined. A line structure was observed on the surface and a hexagonal structure on the interface. A model to explain these forms is proposed. NUMEROUS observations of the dendrite form have been made both in nonmetallic and metallic systems. From these, extrapolations have been made as to the probable dendrite form in pure metals. Observations of the dendrite form in pure metals, nevertheless, have been scanty. In general, these observations have been made on the skeleton dendrite after the mother liquid has been drained from around it, and a mechanism of the formation of the dendrite has been postulated from this solid form. Recent investigations have been conducted in an endeavor to make a study of the formation of the dendrite in several pure metals and the effect of several variables on this mechanism and final form. For these investigations, an apparatus was designed and constructed as shown in Fig. 1. It consists of a talc block containing a half-cylindrical depression, the end of which terminates in the conical recess of a copper block having an external attachment for cooling. A heating coil extends the length of the mold just beneath the lower limits of the cavity. The entire cavity for holding metal is coated with a thin film of graphite. Six thermocouples are equally spaced in the cavity and under the graphite, and six microammeters indicate the temperatures at the particular thermocouple stations. Readings were taken of all meters at the same instant time measurements were taken by photographing the panel of microammeters and a stop watch which was started at the beginning of the run. It was possible with this apparatus to solidify metals through a measured thermal gradient and to observe the progression of the liquid-solid interface with time by following the formation of the dendrite markings in the surface of the solid material. These

Jan 1, 1952

By S. Floreen

Seven iron alloys ranging from 5 to 12 pct Ni and 5 to 14 pct Cr were studied. All alloys transformed to bcc massive martensites. Tempering increased the strengths , probably because of relief of residual stresses generated by the martensite transformation. The major strengthening mechanism appeared to be solid-solution hardening by nickel and chromium. Studies of the work-hardening behaviw, of the effects of prior austenite grain size, and of the effects of changing strain rate and test temperature gaue results very similar to iron or low-alloy steels. Increasing nickel contents markedly improved the toughness at subzero temperatures. Studies of the flow properties did not, however, indicate the reason for the beneficial effect of nickel on toughness. The marine atmosphere corrosion resistance of the alloys was improved primarily by chromium additions, but increasing nickel contents were also beneficial at low levels of chromium. J\ number of maraging and PH stainless steels are strengthened by precipitation hardening in a low-carbon Fe-Ni-Cr martensite matrix. To some extent the resultant properties of these steels must depend upon the properties of this matrix. The present study therefore was conducted to evaluate the transformation characteristics and mechanical properties of a series of Fe-Ni-Cr martensitic ternary alloys. A limited evaluation of the corrosion resistance of the alloys in marine atmosphere was also made. ALLOY PREPARATION Seven 100-lb air induction melts were prepared using electrolytic iron, nickel, and chromium metal additions. The initial Fe-Ni charge also contained 0.05 wt pct graphite to produce a carbon boil during melt down. After melting of the base charge, the heats were refined with 0.1 wt pct additions of manganese, silicon, aluminum and titanium and poured into cast-iron molds. The ingots were homogenized at 1250°C and uni-directionally hot-rolled to 2-in. plate. They were then homogenized another hour at 1250°C, and unidirection-ally hot-rolled to %-in. plate at a finishing temperature of approximately 1050°C. The compositions of the heats are given in Table I. Two additional heats were prepared as 40-lb vacuum-induction melts using electrolytic iron, nickel, and chromium metals, and commercially pure molybdenum chips. A carbon boil, and 0.1 wt pct additions of aluminum and titanium were again employed, but manganese and silicon were not added. The heats were converted to %-in. plate using the procedure described above. The compositions of these heats are included in Table I.

Jan 1, 1967

By A. G. Weber, H. J. Welge

A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. INTRODUCTION The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature.1-3 When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well's limit of drainage. Calculations can be made for the producing history both before and after cone breakthrough. A typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). Vertically, the blocks are bounded by horizontal planes located at different depths through the

Jan 1, 1965

By S. W. Churchill

A digital computer was used to obtain an exact numerical solution for the transient behavior of the insulation and earth adjacent to an isothermal, submerged flat surface for a single set of parametric values. Comparison of the computed results with analytical solutions for limiting conditions revealed that a complete and general solution for all parametric values could be constructed from these limiting solutions. Complete and general solutions for insulated spheres and cylinders can also be constructed from limiting solutions. The procedure is illustrated in part for an insulated spherical tank. The heat flow was found to fall rapidly to a pseudo-steady state; after some time, it then decreased slowly to zero for a flat plate and cylinder, and to a low steady-state rate for a sphere. The accumulative heat flow during the initial falling-rate period may be a significant fraction of the heat flow during the entire first year. INTRODUCTION Underground storage of liquefied natural gas and liquefied petroleum gas has received considerable recent attention. The rate of heat flow from the earth to the storage cavity and the resulting temperature field in the earth are important factors in the technical and economic evaluation of such storage facilities. The objective of this paper is to indicate how complete solutions can be developed for the transient flux and temperature field for various geometrical configurations. The representative properties and dimensions, and the resulting parameters utilized in the illustrative results, are indicated in Table 1. The results presented herein are for dry earth. The effect of the latent heat of solidification of water in the soiI will be described in a subsequent paper. The temperature field in the insulation and earth is determined by energy balances, boundary conditions and initial conditions. The physical problem can be described mathematically with virtually no idealizations insofar as physical properties are known. It appears possible to solve the equations by numerical integration on a high-speed digital computer for any geometrical configuration and conditions. For complex situations, however, the computations are expensive and the results are highly specific. Analytical solutions have been developed for a few simple but important geometrical configurations and conditions, including one-dimensional heat transfer from (or to) earth at an initially uniform temperature to (or from) flat plates, spheres and circular cylinders. The solution for an insulated flat plate has also been derived but is in the form of a slowly converging series involving taklated functions. It was planned to use a computing machine to evaluate this series for a number of representative conditions. However, upon examination of the results of preliminary computations it was discovered that a complete, general and accurate solution could be developed by interpolation between several much simpler solutions for limiting conditions. This technique then was used to develop a a complete solution for an insulated sphere. The equations presented herein are derived in Carslaw and Jaegerl and other books on applied mathematics, or they are simple extensions of these previous results. Hence, all derivations are omitted. Emphasis is instead placed on the results and their

By John Birkinbine

The favor with which the members of the Institute received Mr. Fernow's paper upon the use of charbon roux in the manufacture of iron has encouraged me to present this paper, in the hope of having the discussion upon the manufacture and use of the oldest and undoubtedly the best fuel for producing pig iron continued. Owing to the advances made in employing anthracite coal, bituminous coal, or coke, or mixtures of them, we are apt to forget how much of our present development is due to the pioneers in iron manufacture and the fuel which they employed in the production of pig iron. In Mr. Swank's last compilation of the iron and steel works of the United States, the furnace capacity of the country is given as 5,868,000 tons, of which 1,000,000 tons can be made in the 264 charcoal furnaces. In other words, over one-third of the furnaces now in existence use charcoal for fuel, and produce more than onesixth of the iron made. If to this is added the 130,000 tons of blooms and billets turned out by the 122 forges and bloomaries, the importance of the charcoal industries will be appreciated.

Jan 1, 1879

By R. S. Dean

The careful work of Gross and Zimmerleyl has established the fact that the energy actually used in grinding is proportional to the new surface produced. This confirmation of Rittinger's law was made by crushing quartz in a frictionless drop-weight machine and determining the surface of the quartz by its rate of solution in hydrofluoric acid. The details of this procedure have been described adequately elsewhere and need not be repeated here. The resultant data furnish the only available basis for comparing accurately the efficiency of grinding machines. This method is so cumbersome experimentally that it has been little used. As an alternative all sorts of approximations have been proposed. The best of these is complete size analysis by sieving and elutria-tion. Such procedure is very lengthy and difficult to carry out accurately. Furthermore, any sizing method becomes very inaccurate for determining surface with very fine sizes where the ratio of surface to volume becomes very large. To avoid the lengthy and difficult technique of elutriation it has been proposed to estimate the size distribution below 200 mesh from various probability formulas. Such a procedure is at best an engineering approximation; at worst it is a mere guess. Some time ago Dr. V. H. Gottschalk2 found that the coercive forces of magnetite powders were directly proportional to the surface area, regardless of size distribution. It was at once apparent that this furnished a method for determining grinding efficiency quickly and accurately. The only requirement was a single determination of the relation between the work input of the Gross-Zimmerley drop-weight machine and the coercive force of the resultant crushed magnetite. For this purpose Ural Mountain magnetite in definite octahedra was

Jan 1, 1939

By R. S. Dean

The careful work of Gross and Zimmerleyl has established the fact that the energy actually used in grinding is proportional to the new surface produced. This confirmation of Rittinger's law was made by crushing quartz in a frictionless drop-weight machine and determining the surface of the quartz by its rate of solution in hydrofluoric acid. The details of this procedure have been described adequately elsewhere and need not be repeated here. The resultant data furnish the only available basis for comparing accurately the efficiency of grinding machines. This method is so cumbersome experimentally that it has been little used. As an alternative all sorts of approximations have been proposed. The best of these is complete size analysis by sieving and elutria-tion. Such procedure is very lengthy and difficult to carry out accurately. Furthermore, any sizing method becomes very inaccurate for determining surface with very fine sizes where the ratio of surface to volume becomes very large. To avoid the lengthy and difficult technique of elutriation it has been proposed to estimate the size distribution below 200 mesh from various probability formulas. Such a procedure is at best an engineering approximation; at worst it is a mere guess. Some time ago Dr. V. H. Gottschalk2 found that the coercive forces of magnetite powders were directly proportional to the surface area, regardless of size distribution. It was at once apparent that this furnished a method for determining grinding efficiency quickly and accurately. The only requirement was a single determination of the relation between the work input of the Gross-Zimmerley drop-weight machine and the coercive force of the resultant crushed magnetite. For this purpose Ural Mountain magnetite in definite octahedra was

Jan 1, 1939

By Joseph E. Pogue

The outstanding features of 1926 in the petroleum industry included the following: 1. Stocks of all oils (crude and refined) were reduced, making the first annual decline since 1918. 2. Domestic crude oil production increased steadily during the last 11 months of the year, accelerating during the fourth quarter, and ending the year at the highest level ever attained. 3. Three new major oil fields were developed—Panhandle, Spindle-top and Seminole. 4. Important advances were registered in production technique, tending to retard the declines of old wells and to maintain the flush periods of new wells. 5. The problem of gaining greater economic control of production through unit operations and gas conservation received growing recognition by the industry and the Federal Oil Conservation Board. 6. The rate of drilling was sharply increased during the second quarter of the year and suffered only a very slight retardation during the closing months. 7. The runs of crude oil to stills were maintained above normal throughout the year and underwent acceleration during the fourth quarter. 8. The gasoline situation was marked by a continuous and substantial increase in the rate of production of cracked gasoline, and by an improvement in the statistical position of the commodity. 9. Prices of both crude petroleum and its principal derivatives were characterized by more profitable levels and greater stability than for a number of years past; and, while showing declines during the fourth quarter, prices did not recede sufficiently to slow down materially either drilling or refinery operations. Change in Stocks The keynote of 1926 was a reduction in stocks of all oils to the extent of approximately 24,000,000 bbl., or 4.4 per cent., of which roundly

Jan 1, 1927

By P. Bouéry

This account of a contrivance which has been found serviceable in practice may be of interest to engineers, and especially to those engaged in hydraulic mining. In that process, one feature which seems at first sight to possess little significance, is highly important in its effects—namely, the regular supply of water to the " giants." The chief condition of this regularity is an even flow in the pipe-line from the penstock to the nozzle.' This, of course, requires that the penstock be kept full. Any considerable surplus of water, overflowing at the penstock, is a simple waste, unless it be otherwise utilized in the sluices. At all events, it does not affect the delivery of the nozzles. But a deficiency at the penstock may admit air into the pipe; and this may produce hydraulic recoil, injuring the line by incessant vibrations, giving rise to leaks, and even to blow-outs, and (when a partial vacuum exists at the time of the fracture) the collapse of the pipe. An accident of this sort in our main pipe-line, occasioned partly by a settling of the ground and partly by the presence of air in the pipe, led to the employment of the device here described. The line referred to is made of 30-in. pipe, successively reduced to 18 and 15 in. in diameter, for the supply of two giants. By reason of the causes above mentioned, the 30-in. pipe burst more than 1,400 ft. from the penstock, and, despite the air-valve, the 30-in. pipe was collapsed to such a degree that one length of it, next to the penstock, was squeezed together and positively swallowed by the main pipe, through which it traveled for 750 ft., piercing through a short elbow on the way. This remarkable result was undoubtedly the effect of the vacuum suddenly produced when the pipe burst.

Jan 1, 1907

By Arthur F. Wendt

In the manufacture of charcoal-blooms, washing or cleansing of the ore from adhering gangue has been practiced for many years. A sluice-box is even to-day used for that purpose in the Southern Appalachian Mountains. For the Lake Champlain bloomaries hard magnetic ores are crushed with stamps and then sluiced or jigged in hand-jigs. The stamps used in the Lake Champlain region are of the most primitive kind. They consist of a trip-hammer, dropping on a perforated cast-iron plate, through which the crushed ore escapes. Only friable rock can thus be successfully treated. To render the raw ore friable, a calcining or burning in piles on a bed of cordwood is resorted to. An expense of 35 cents per ton of crude rock treated is thus incurred. The crushed ore is shovelled or otherwise fed into jigs without previous sizing, except such as is incidental to crushing through the perforated bottom of the stamping-machine. In jigging this ore, it is allowed to pass through the bedding into the "hutch." The tailings are scraped off and wasted. They contain a large percentage of fine ore. In many instances, this is regained by subsequent sluicing. Such was the condition of the industry, when the writer's attention was first called to it in 1882. No attempt had been made to introduce into thiS branch of ore-dressing the notable improvements adopted in concentrating the ores of other metals. The result of the writer's investigations was the building in 1882 of the "Crown Point Separator." At the Crown Point Mines, N. Y., lean ore unfit for the blastfurnace (containing less than 331/3 per cent. of iron), was concentrated and used in the bloomary connected with the mines. The ore was burned here as elsewhere, and treated as described. The plant designed by the writer for Crown Point, is nearly a counterpart of that since erected by Messrs. Copeland and Bacon, contractors, for the Theal mine, Putnam County, New York, which is illustrated by the accompanying plate. The only difference is in

Jan 1, 1885

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.l Part II gives an account of the practical elaboration of the instrument, together with some description of measurements performed. I. Principle of Using Astatized Pendulums1 In order to reduce the trouble and waste of time attending the use of ordinary pendulums in measuring the force of gravity, various instruments of another type have been suggested for relative determinations, as a rule arranged in such a way that the attraction of the earth on a certain body or mass of fluid is balanced by elastic force from a spring or a shut-in mass of gas. A change in the force of gravity is then made manifest as a change in the position of equilibrium of the body, in that the deformation of the spring (or compression of the gas) is changed. With such instruments there are, however, great difficulties in keeping the elastic force constant or its variation known with sufficient exactitude, because of elastic after-working, influence of temperature, and so on. The author suggests for relative determinations of gravity another type of instrument, in which two directional forces (control coefficients) rather than two forces are compared with one another. By "directional force" or "control coefficient" is meant that quantity in a rotatable system that, multiplied by the angle of deflection, indicates the moment counteracting the deflection. In this way it will be possible greatly to reduce the influence of the elastic after-working, which in instruments with spring devices acts so disturbingly. The instrument is made with a rotatable system arranged in such a way that the total control coefficient acting upon it, is composed

Jan 1, 1940

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.l Part II gives an account of the practical elaboration of the instrument, together with some description of measurements performed. I. Principle of Using Astatized Pendulums1 In order to reduce the trouble and waste of time attending the use of ordinary pendulums in measuring the force of gravity, various instruments of another type have been suggested for relative determinations, as a rule arranged in such a way that the attraction of the earth on a certain body or mass of fluid is balanced by elastic force from a spring or a shut-in mass of gas. A change in the force of gravity is then made manifest as a change in the position of equilibrium of the body, in that the deformation of the spring (or compression of the gas) is changed. With such instruments there are, however, great difficulties in keeping the elastic force constant or its variation known with sufficient exactitude, because of elastic after-working, influence of temperature, and so on. The author suggests for relative determinations of gravity another type of instrument, in which two directional forces (control coefficients) rather than two forces are compared with one another. By "directional force" or "control coefficient" is meant that quantity in a rotatable system that, multiplied by the angle of deflection, indicates the moment counteracting the deflection. In this way it will be possible greatly to reduce the influence of the elastic after-working, which in instruments with spring devices acts so disturbingly. The instrument is made with a rotatable system arranged in such a way that the total control coefficient acting upon it, is composed

Jan 1, 1940

By Cyril Smith

THE method of thermal analysis, so important in the development of metallographic science, has of recent years been falling into disuse owing to the development of other physical methods which give results easier of interpretation and which can be used for the study of either equilibrium or transitional conditions because they do not require a continuously changing temperature. Nevertheless thermal analysis remains useful in the study of reactions that take place rapidly, and the simplicity of the experimental technique and the general availability of the apparatus involved are points in its favor. Theoretically, thermal analysis is capable of giving specific and latent heat measurements and therefore should permit the study of reactions on a more fundamental basis than any other method. It is, however, difficult or impossible to obtain quantitative heat measurements from cooling curves obtained in the usual way. Even if the furnace containing the sample is cooled or heated at a linear rate, or if a gradient furnace is employed to maintain a constant rate over a large range of tempera-ture, the heat flow from or to the specimen depends on its previous his-tory, for the difference of temperature between the specimen and its surroundings varies. The emissivity of the specimen surface, moreover, is unlikely to be constant. The able mathematical analysis by Russell,1 although it prevents misinterpretation of data, has an effect rather the reverse of that intended, and leaves the reader doubtful of the possibility of ever obtaining quantitative results from thermal curves. Nothing can be done to apply thermal analysis to the study of equilib-rium conditions of reactions that are not completed at rates of tempera-ture change below about 1° C. per minute, and this unfortunately excludes most solid transformations in alloys. ? For the determination of liquidus

Jan 1, 1939

By R. P. Carreker, R. W. Guard

True stress-true strain data are given for nominally pure molybdenum (99.95 pct) over the temperature range -196° to 1540°C (0.027 to 0.63 T/T). Strain rate sensitivity was determined by rate change tests and stress relaxation tests. Inhomogeneous yielding and strain aging effects were observed. The yield stress and tensile strength depend markedly on temperature below 400°C and are insensitive to temperature in the range 400' to 800°C. The ductile to brittle transition range is +25O to -25OC. Strain rate sensitivity and stress relaxation effects are very large near room temperature. THIS report presents data which were obtained as a part of a continuing program designed to document the deformation behavior of nominally pure metals over a wide temperature range.'" This research program is rooted in the conviction that sufficient tensile and creep data of appropriate quality and detail does not exist to provide precise phe-nomenological descriptions of the deformation behavior of pure metals as a function of temperature, strain rate, and grain size. Such knowledge is needed to provide a firm base for alloy design and an experimental framework to which theories of deformation must conform. These data also complement a parallel exploratory program investigating the properties of refractory metals, including molybdenum, and their alloys. Several important reviews and research reports dealing with the tensile properties of molybdenum as a function of temperature have appeared."-lo To a great extent the work to be reported in the present paper parallels that of Bechtold and of Pugh. The authors' results are in general agreement with those of Bechtold and Pugh. The principle differences be- tween the present experiments and those published previously are as follows: 1—Wire specimens prepared from arc cast molybdenum were used in the present experiments, bar specimens were used by others. Pugh used arc cast material while Bechtold's most extensive results" were obtained on powder metallurgy specimens. 2—Several different grain sizes were tested in the present experiments. 3—The testing range was extended to cover from -196°C to 1570°C (0.027 to 0.63 T/Tm). 4—The combination of wire specimens, high speed autographic recording, and a stiff testing machine permitted more detailed study of initial yielding. The principle contribution of the present paper is the demonstration of the relatively consistent mechanical properties of nominally pure arc cast molybdenum specimens of differing metallurgical history. Bechtold and Scotts have shown that arc cast and powder metallurgy molybdenum samples have comparable tensile properties in the range —75" to 200°C when processed to have the same re-crystallized grain size. Material The molybdenum used in this investigation was supplied by the Climax Molybdenum CO. Its metallurgical history is outlined in Table I; the final products were 0,030 in, diam wire specimens annealed at 1100' and 1375°C and 0.060 in. diam wire

Jan 1, 1957

By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By Morris Muskat

Analytical calculations have been carried out on the effect of casing perforations on the productivity of wells, and formulas have been derived for general types of perforation patterns. The numerical calculations, however, show that the resultant well productivity is essentially independent of the perforation pattern, but is determined mainly by the total perforation density. Thus, for example, for a density of three perforations per foot of casing, the well productivity will be cut to one third of that of the uncased well for a perforation radius of 1/8 in., and to approximately one half for a perforation radius of 1/4 in., regardless of the detailed manner in which the perforations are distributed over the casing surface. The analytical theory is also extended to include wells completed with slotted liners. It is shown that the reduction in productivity due to such liners will be relatively small as compared with that due to perforated casings. The increasingly important role being played by productivity factors of wells in determining well potentials and in the general evaluation of producing formations lends interest to the analysis of all the various factors that may infuence the productivity of a well. In recent papers1 the results have been given of theoretical studies made to determine the effect on the productivity factor of a well of the gas-oil ratio of the production and the connate water within the sand. These have served to show that both of these factors may, under suitable conditions, materially reduce the effective productivity factors below those that would be anticipated on the assumption that the wells produce homogeneous fluids. In this paper will be presented the results of the analysis of an entirely different factor influencing the productivity of a well. This refers to that resulting from the increased use of the method of completing wells by setting casing opposite all of the productive strata and then gun-perforating the particular zones of immediate interest. The practical success of this method of completion would appear to be an answer to the question as to whether it seriously reduces the well productivity or materially cuts down the ultimate oil recovery that may be derived from the producing section. Nevertheless, it is of interest to examine just how great the effect of the restricted flow channels, represented by the gun perforations, may be in increasing the over-all effective sand resistance. Of course, to the extent that the well potentials are severely restricted by proration regulations, minor reductions in well productivities are even less serious than if the wells were to be allowed to produce wide open. On the other hand, even under these circumstances there may be at least the academic interest in such calculations in being able to correct and evaluate the effect of the perforations in order to carry

Jan 1, 1943

By Morris Muskat

Analytical calculations have been carried out on the effect of casing perforations on the productivity of wells, and formulas have been derived for general types of perforation patterns. The numerical calculations, however, show that the resultant well productivity is essentially independent of the perforation pattern, but is determined mainly by the total perforation density. Thus, for example, for a density of three perforations per foot of casing, the well productivity will be cut to one third of that of the uncased well for a perforation radius of 1/8 in., and to approximately one half for a perforation radius of 1/4 in., regardless of the detailed manner in which the perforations are distributed over the casing surface. The analytical theory is also extended to include wells completed with slotted liners. It is shown that the reduction in productivity due to such liners will be relatively small as compared with that due to perforated casings. The increasingly important role being played by productivity factors of wells in determining well potentials and in the general evaluation of producing formations lends interest to the analysis of all the various factors that may infuence the productivity of a well. In recent papers1 the results have been given of theoretical studies made to determine the effect on the productivity factor of a well of the gas-oil ratio of the production and the connate water within the sand. These have served to show that both of these factors may, under suitable conditions, materially reduce the effective productivity factors below those that would be anticipated on the assumption that the wells produce homogeneous fluids. In this paper will be presented the results of the analysis of an entirely different factor influencing the productivity of a well. This refers to that resulting from the increased use of the method of completing wells by setting casing opposite all of the productive strata and then gun-perforating the particular zones of immediate interest. The practical success of this method of completion would appear to be an answer to the question as to whether it seriously reduces the well productivity or materially cuts down the ultimate oil recovery that may be derived from the producing section. Nevertheless, it is of interest to examine just how great the effect of the restricted flow channels, represented by the gun perforations, may be in increasing the over-all effective sand resistance. Of course, to the extent that the well potentials are severely restricted by proration regulations, minor reductions in well productivities are even less serious than if the wells were to be allowed to produce wide open. On the other hand, even under these circumstances there may be at least the academic interest in such calculations in being able to correct and evaluate the effect of the perforations in order to carry

Jan 1, 1943

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By W. H. Blauvelt

W. H. BLAUVELT, Syracuse, N. Y. (communication to the Secretary*).-I have read Mr. Howland's paper on Calculations with Reference to the Use of Carbon in Modern American Blast Furnaces with much interest, and believe that his method of analysis of the subject will be of material assistance in our study of the action of coke in the blast furnace. Mr. Howland quotes Professor Richards' statement that from the standpoint of the generation of the maximum quantity of heat in the furnace, Grüner was right in saying that all the carbon burned in the furnace should be first oxidized at the tuyères to CO and all reduction of oxides above the tuyères should be caused by CO, which thus becomes CO2. It is clear that the maximum quantity of heat is generated in the furnace when the greatest amount of carbon is burned to CO2 irrespective of whether it is burned at the tuyères or further up the furnace. So it would appear that Grüner's theory is sound regarding the maximum production of heat only because if all the carbon is burned to CO at the tuyères the reduction of the ores will have to be effected by the further oxidation to CO2. Whereas, if the reduction of the ores is effected in part by solid carbon, part of this carbon might be oxidized only to CO, resulting in a higher percentage of CO in the escaping gases than from Grüner's "ideal conditions.? But in studying the combustion of coke in the furnace, it is clear that the production of the maximum quantity of heat is not of the first importance in blast-furnace operation, or in the utilization of the fuel charged into the furnace. To my mind the production of a high thermal head at the tuyères is of the first importance, and the best coke is that which reaches the tuyères in proper condition to produce the highest temperature at the tuyères, and in just sufficient quantity to do the amount of work required there under the conditions produced by this maximum temperature. The combustion of a much larger amount of fuel at the tuyères, under conditions that will fall short of producing the highest possible temperature, cannot produce as good results, either in fuel economy or output. If this statement is correct, does it not correspond with Mr. Howland's statement that too much wind is inimical to low coke consumption? Nothing is more fatal to obtaining the highest temperatures than an excess of air for combustion. In the blast furnace an excess of air dilutes and cools the products of combus-

Jan 10, 1916