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By J. A. M. van Liempt

SINCE the discovery of von Laue, that a crystal forms a natural grating for X-rays, our knowledge of the structure of solids has gone forward with rapid strides. This progress is not only of purely scientific interest, but has also yielded direct technological results. One of the most valuable results is the broadening of our knowledge of the structure of pure metals and alloys. To promote these studies it is often desirable to have at our disposal pieces of metal consisting of one single crystal. As is so often the case in the natural sciences, we obtain the best results by making our earliest experiments on pure, simple materials and avoiding unnecessary complications. The Cryogen Laboratory at Leyden followed this method with much success, because the work was done at such low temperatures that the heat movement of the atoms was almost absent. Similarly we can simplify the studies of metals by leaving out of consideration the influence of the grain boundaries and the mutual influence of the crystals by using unicrystalline instead of polycrystalline metal. Methods of making single crystals have been scientifically studied during the past few years. Some methods were already known in the arts, but these have been improved and new methods have been developed. The methods for making metallic single crystals may be divided into the following groups: A. From the liquid state B. From the gaseous state C. Electrolytically D. By recrystallization in the solid state METHOD A 1. Tammann's Method. 1-Tammann succeeded in making bismuth single crystals of a maximum length of 20 cm. by undercooling the molten metal 0.1 to 0.3° G. below its melting point in glass tubes of a maximum

Jan 1, 1928

By J. A. M. van Liempt

Since the discovery of von Laue, that a crystal forms a natural grating for X-rays, our knowledge of the structure of solids has gone forward with rapid strides. This progress is not only of purely scientific interest, but has also yielded direct technological results. One of the most valuable results is the broadening of our knowledge of the structure of pure metals and alloys. To promote these studies it is often desirable to have at our disposal pieces of metal consisting of one single crystal. As is so often the case in the natural sciences, we obtain the best results by making our earliest experiments on pure, simple materials and avoiding unnecessary complications. The Cryogen Laboratory at Leyden followed this method with much success, because the work was done at such low temperatures that the heat movement of the atoms was almost absent. Similarly we can simplify the studies of metals by leaving out of consideration the influence of the grain boundaries and the mutual influence of the crystals by using unicrystalline instead of polycrystal-line metal. Methods of making single crystals have been scientifically studied during the past few years. Some methods were already known in the arts, but these have been improved and new methods have been developed. The methods for making metallic single crystals may be divided into the following groups: A. From the liquid state B. From the gaseous state C. Electrolytically D. By recrystallization in the solid state Method A 1. Tamwmnn's Method1—Tammann succeeded in making bismuth single crystals of a maximum length of 20 cm. by undercooling the molten metal 0.1 to 0.3' G. below its melting point in glass tubes of a maximum

H. S. COE, St. Louis, MO. (written discussion *)-I feel much gratified that Mr. Mishler has confirmed those principles of slime settlement expressed by Mr. Clevenger and myself. I wish to state that, when we wrote the article referred to by. Mr. Mishler we had not seen his earlier article in which he gave a formula to be applied to the settling rate off feed pulp for determining thickener area required at El Tigre. It has been my experience that in cyanide work the settling area required is determined by the settling rate of the feed pulp for perhaps 20 per cent. of all of the ores to be encountered. For the other ores, the area required is greater than that indicated by the settling rate of the feed and corre-sponds to the settlement of a somewhat thicker free-settling pulp. Mr. Mishler, in his paper, has thoroughly outlined a set of tests for determining thickener capacity, which, if carefully carried out, should be entirely reliable, provided allowance is made for changes in the mill feed from time to time. Two features of his paper, I, believe; need comment. In speaking of the time required for slime to flocculate after being fed, Mr. Mishler quite properly states that the actual settling rate for the feed pulp can-not be that of completely flocculated pulp because of this time lost in flocculation. It seems to me, however, that this feature cannot be of very great importance, for the following reason: The upper zones of pulp in a thickener may be, and often are, as thin as the feed pulp. If, therefore, the feed be introduced at sufficient depth below the pulp surface to prevent agitation at the surface, there will be ample time for it to become flocculated before it becomes the surface layer, and it, will

Jan 1, 1918

By R. D. Carter

Methods are presented for calculating the performance of multiwell gas reservoirs. These methods account for two-dimensional, unsteady-state flow of a non-ideal gas through a heterogeneous formation. The performance can be obtained for gas reservoirs with known physical properties and configuration subjected to specified development and production schedules. These methods may prove helpful in optimizing the exploitation of gas reservoirs. The numerical solrrtion procedures given for this non-linear problem are extensions of known techniques for the linear diffusion equation. Two of these procedures are based on a new difference equation given by Saul'ev. Limitations and advantages of these procedures are discussed. An example solution is presented and is used to compare the calculation methods. INTRODUCTION Li planning the operation of a multiwell gas reservoir, it is desirable to predict its performance for each alternate development and producing schedule under consideration. This paper presents three numerical procedures that can be used to calculate such gas reservoir performance using a digital computer. These methods account for two-dimensional transient flow of a non-ideal gas within the reservoir. Extension of these methods to three-dimensional flow is possible. The paper is divided into three parts. The first describes the problem for which a solution is wanted and three numerical procedures that can be used to obtain solutions. The second discusses the information necessary to set up a problem. This part will be of greatest interest to the field engineer. The third gives data and results for an example problem. PROBLEM AND SOLUTION METHODS In the following development, a gas reservoir is regarded as a sealed, porous, permeable, heterogeneous body in which a single, non-ideal gas phase is flowing. Flow is permitted in the x- and y-horizontal directions, but is considered to be negligible in the vertical or z-direction. The reservoir can be tapped by one or more wells. Methods to be described provide a basis for calculating the complete performance of the reservoir, including rates and cumulative production from the wells, and pressure distribution and decline in the reservoir. If the isothermal flow of a non-ideal gas obeying Darcy's Law occurs in two dimensions in a region R, the governing equation in this region is:

Jan 1, 1967

By G. Y. Chin, W. F. Hosford

It has long been recognized that, for a crystal to undergo an arbitrary shape change by crystallographic shear, at least five independent shear systems must be activated. Taylor1 analyzed the deformation of fcc crystals by {111}<110> slip and showed that the principle of minimum work could be used to determine which combination of slip systems might act to produce a given shape change. Later Bishop and Hi112 attacked the same problem by first identifying the state of stress which could physically activate five or more {111)(110) systems simultaneously and then invoking the principle of maximum virtual work to determine which combination would act for a given shape change. Taylor&apos;s general approach has been used to calculate the active slip systems and the relative strengths during axisymmetric flow of cubic crystals with other deformation modes, including {112}<111> slip3 and {111}<112> twinning.&apos; It is the purpose of this note to identify the stress states capable of activating simultaneously five or more of these systems. {111}<112> Twinning. The {111}<112> systems are defined in Table I and illustrated in Fig. 1. The sense of the shears are those for twinning in fcc crystals. The shear stress on any system may be written in terms of the stress components expressed relative to the 1,2,3 cube axes. For example, the stress For five or more of the systems ij to be activated simultaneously, it is necessary that Tij/T be equal to unity in at least five of the expressions [3], while Tij < T for the remainder. (These restrictions assume that the same shear stress T is required to activate each system and that the shear stress on any system cannot exceed that for its activation.) The discrete values of the stress components A through H which can satisfy these restrictions are listed in Table II together with the values of Tij/T for all systems. It may be noted that Tij/ T is not necessarily zero on all nonactive systems as found by Bishop and Hill for <110> {111} slip. In fact, for the case of twinning Tij/T may reach negative values as large as -2 for shear stress in the reverse direction, Table 11. This means that, if those stress states are to be valid, the shear stress to activate reverse twinning must be greater than twice that for forward twinning. Such stress states are probably valid in view of the directionality of the twinning process. There has been no documentation of reverse twinning thus far. It may be noted that the stress states fall into four classes, which may simultaneously activate eight, six, six, and five twin systems respectively. These solutions may be applied to the {112}(111)

Jan 1, 1970

By J. de la Vergne, L. O. Cooper

The hydrostatic steel mine shaft liner (HSL) Provides a permanent wall lining for drilled shafts. It is watertight and suitable for bad ground conditions. After a shaft has been drilled to its full depth, the HSL is lowered into it and secured in place with cement grout. The liner consists of a cylindrical steel shell usually reinforced with exterior stiffening rings. The shell is basically designed for compressive strength and the rings are provided to give the shell added resistance to buckling. There are no published standards for the correct procedures to design an HSL. This paper gives a method that appears logical. A design solution can be complex with increased opportunity for error. This paper presents simple formulas to produce sufficient accuracy for construction design. Two new concepts are presented, referred to as transition pressure and critical pressure. An example demonstrates use of the formulas and concepts presented. To facilitate comprehension and use of the formulas, Greek letters are avoided and most of the English alphabet symbols used refer by association to their definitions. An appendix shows derivation of the formulas.

Jan 1, 1984

By A. J. Miller, G. R. Brophy

THE Grossmann principle1 for the calculation of hardenability of steel from composition is attractive because of its simplicity. It postulates that the hardenability of a steel for any particular grain size may be expressed in terms of an ideal critical diameter, which is the product of an ideal critical diameter for a "pure" iron-carbon base multiplied by a succession of factors for each element of composition contained, including the incidentals. It infers that the multiplying factor for a given quantity of an element is constant for all combinations of composition. Grossmann has stated that in the great majority of cases the experimental values of hardenability are found to be well within 10 per cent of the calculated values. The validity of the scheme has been confirmed in principle by Crafts and Lamont2,3 and by Kramer et al .4 Their results differ from the original in the magnitude of the effect of some elements but, since they accepted the product concept and followed its direction, it is to be expected that similar results would be obtained. Crafts and Lamont, in their second paper, recognized that the factor relations for manganese and nickel were not continuously linear, but beyond certain critical amounts increase sharply. Austin, Van Note and Prater5 demonstrated nonlinear relations between hardenability and alloy contents. Their curves for chromium, silicon, manganese and nickel were all convex upward to show decreasing incremental effects. They concluded that Grossmann&apos;s factors underevaluate the hardening effect of low percentage additions of these elements, and overevaluate the larger additions. [ ] More recently W. Steven6 has found that the factor method fails when applied to complex steels containing two or three principal alloying elements other than carbon. Multiplying factors derived from his results bear a complex relation to composition and are not constant for a given amount of an element as the base composition varies. C. A. Liedholm7 found that, using either the Grossmann or the Crafts-Lamont multiplying factor values, not only were

Jan 1, 1945

For the third year in a row total value of the Nation&apos;s mineral production broke all previous records. A new peak of $20.4 billion was reached in 1964. So says the U. S. Bureau of Mines. The Bureau&apos;s preliminary estimate for 1964 is $800 million higher than the value reported for 1963, and $1.6 billion greater than the 1962 figure. The unprecedented demand for minerals, has stimulated development of new mines and expansion of processing capacity in many parts of the country.

Jan 2, 1965

By G. R. Smithson, John E. Hanway

This paper, the first of two papers covering the development of a metallurgical process for the treatment of a complex ore, describes the bench-scale experimental Program undertaken as a basis for initial process design. The results of using various potentially applicable process steps are detailed and the basis for selecting certain of these steps for Pilot-plant development is outlined. A process consisting of the steps of sulfate roasting, leaching, copper recovery, solution purification, zinc electrolysis, and brine leaching for lead recovery was recommended for further study. THIS paper describes the bench-scale development of a sulfate roasting process designed to recover copper, lead, and zinc from a complex ore. The extrapolation of the bench-scale results to pilot-plant design and the results of pilot-plant operation will be described by Lund, et al.&apos; in a subsequent paper. Several years ago, the research divisions of the St. Joseph Lead Co. became responsible for the development of a metallurgical procedure to treat a complex sulfide ore containing copper, zinc, and lead sulfides. The primary objective was to devise a procedure which would permit economic recovery of the nonferrous values. As could logically be expected, the study of conventional flotation procedures was undertaken; in addition, however, because the physical nature of the mineral association in the complex ore indicated that physical methods of ore beneficiation might not prove to be entirely satisfactory, a program also was established to investigate alternative methods of direct metallurgical treatment for recovery of the metal values. Exploratory test work by the St. Joseph Lead staff led to the conclusion that a sulfate roasting technique represented the most attractive approach for a direct metallurgical process. Sulfate roasting would provide for the selective conversion of the nonferrous values to forms soluble in conventiona1.1 leaching agents and would permit their efficient separation from the insoluble iron and other gangue materials. It should allow efficient utilization of the thermal energy available from oxidation of the sulfide raw material, and might provide an opportunity for recovering byproducts such as iron and sulfur. The decision to evaluate a selective sulfation procedure as a basic processing step also was influenced by the excellent results obtained by the St. Joseph Lead Co. in using this procedure for the recovery of cadmium from zinc sulfide concentrates. The choice of selective sulfation as a major processing step served as a basis for an extended experimental investigation of the process with bench- and pilot-scale equipment to prove its feasibility. St Joseph Lead Co., aware that Battelle Memorial 1nstitute had participated in the development of several fluidized-bed sulfate roasting procedures, asked Battelle to undertake the bench-scale development of a suitable sulfation process. This paper describes the procedure used and the results obtained at Battelle in the treatment of the complex sulfide ore. EXPERIMENTAL WORK Nature of the Raw Material. The sulfide ore deposits of interest are essentially a massive sulfide, with the indivudual ore minerals being extremely fine grained and intimately intergrown with each other and with the associated gangue. The zinc in the ore is present mainly as sphalerite (ZnS), the lead as galena (PbS), and the iron either as pyrite (Fes2) or as pyrrhotite (FeS). Table I shows the chemical analysis of various individual samples of the ore. These analyses illustrate the variability of the ore body and impose a rather severe requirement on any type of metallurgical process—that of being able to tolerate probable wide variations in the assay of the head ore. The tentative flowsheet designed to serve as a guide for the initial experimental investigation of

Jan 1, 1962

By M. S. Seltzer

High temperature steady-state creep rates have been determined jor lead sulfide single crystals whose defect concentrations were fixed by equilibration under controlled sulfur pressure. The activation energy of creep, Qc , for undoped lead sulfide, is a function 01 composilion, decreasing from 2.9 to 2.2 ev as the carrier concentration increases from 9 x 1016 to 8 1018 electrons cm-3 for lead excess crystals, and increasing from 1.7 to 2.3 ev as the concentration of holes increases from 4 x 1017 to 1 x 1018 cm-3 in sulfur excess material. For five different composilions, Qc for undoped and bismuth-doped crystals has been found to be equal to Qpb + Qs, the self-diffusion activation energies for lead and sulfur in PbS. It is well-established1 that high-temperature steady-state creep of pure metals is a diffusion-controlled process, where the activation energy of creep is equal, within experimental error, to the activation energy of self-diffusion. The relationship between the activation energy for steady-state creep and those for self-diffusion in binary compounds is more complicated, however, because two different diffusing species must be considered, and becayse the activation energies may be influenced by compositional variations and by foreign atom additions.2-4 In some cases experimentally determined creep activation energies are correlated with those for self-diffusion of the slower-moving species, but such agreement is by no means universal. Interpretation of experimental results is difficult because few investigations include measurements of creep rates and self-diffusion coefficients of both diffusing species on single crystals of similar composition and foreign atom concentration. The objective of this investigation, therefore, is to determine the influence of stoichiometric defects and foreign atoms on steady-state creep and self-diffusion for a well-characterized binary compound. Lead sulfide, a compound semiconductor which crystallizes in the NaC1-type structure, and whose homogeneity range includes compositions on either side of the 1:l atom ratio, was chosen for study in this investigation. The pressure-temperature-composition relations for PbS are available,5,3 and deviations from stoichiometry may be monitored by electrical measurements.7 Single-crystal specimens are available to allow observation of effects due to bulk phenomena without interference from grain-boundary effects. These crystals have been employed to determine steady-state creep rates under compressive stress for "pure" and bismuth-doped PbS as a function of sulfur pressure and temperature as well as crystal orientation and applied stress in order to establish the relationships between defect concentrations and creep rates. EXPERIMENTAL PROCEDURES Crystal Growth. Lead sulfide crystals, prepared by the Bridgman method, are grown in evacuated quartz crucibles, filled with almost equal atomic proportions of high-purity (99.999 pct) lead and sulfur, and heated to a temperature above the melting point of PbS (about 1127°C) so that the lead and sulfur react to form molten PbS. The crucible and melt are dropped through the hot zone of the crystal-growing furnace at the rate of 1 cm per hr. The maximum melting point of PbS is slightly on the lead-rich side of the 50:50 composition; hence crystals grown from a near stoichiometric melt are usually n-type semiconductors containing excess lead atoms. Typically the lead excess concentration in solid solution with the PbS is 3 x 1018 atoms cm-3. Crystals containing either 1/20 or 1/2 mole pct Bi2S3 were prepared by addition of the foreign atoms prior to crystal synthesis. Preparation of Specimens of Controlled Stoichiom-etry. Since it is difficult to grow crystals of desired composition, the process of crystal growth and control of stoichiometry are separated into two distinct operations. Equilibration of as-grown PbS to a desired composition is most easily accomplished by first annealing the n-type crystals under high sulfur pressure (about 1 atm) at temperatures above 700°C. This process serves to put excess lead precipitates into solution, yielding 0 -type crystals upon quenching to room temperature. Inter diffusion occurs readily in crystals so treated, and the methods described by Bloem may then be employed to obtain crystals of controlled stoi-chiometry. For the creep measurements made in this study, this involves heating crystals in mixtures of H2 and H2S The equilibrium constant for H2S is given by: Thus the sulfur partial pressure is obtained from knowledge of the H2/H2S ratio and Kh2S for the temperature in question. Fig. 1 shows the p-T-x diagram for PbS. It can be seen that, within the stability limits for single-phase lead sulfide, desired compositions may be obtained by equilibrating under a specified sulfur pressure and temperature. Characterization of Crystals. The principal methods for evaluating PbS crystals include measurement of electrical properties and mass-spectrographic analysis. The measured electrical parameters include Hall coefficient, conductivity type, and electrical resistivity Bloem7 has shown that there is a 1:l relation between the defect concentration and carrier concentration obtained. Hence, if the contribution to the carrier con-

Jan 1, 1968

By W. David Leyshon

This paper compares the general characteristics of Florida phosphate rock for the manufacture of fertilizers and phosphoric acid. The subjects covered are relative reactivity for superphosphate manufacture and various properties of the rock for use in phosphoric acid production, including gypsum filterability, sulfuric acid consumption, foaming, relative cor-rosiveness, chemical composition, and others. Comprison will include rocks of North Africa, the western U.S., and other locations. This paper reviews some of the important properties of phosphate rock, giving particular attention to a comparison of Florida phosphate with some of the major phosphates produced in the world. It also discusses some of the techniques available for evaluatine Phosphate. rock for phosphoric. acid and fertilizer use. The use of Florida rock outside the U.S. has been increasing steadily, evidence in itself of certain desirable properties of this rock. Table I is a list of the major producers and exporters of phosphate rock as of 1965. Florida, meaning in this case Central Florida, was the largest producer of phosphate rock and the largest exporter of rock. Of a total world production estimated at 60 million tons, about 50 million tons were produced during 1965 by the areas listed in Table I. One major producing area omitted from Table I and from subsequent evaluations in this paper comprises Nauru, Ocean, and Christmas Islands, whose output totaled about three million tons in 1965. This phosphate is marketed entirely by the British Phosphate Commissioners, primarily in Australia and New Zealand, and does not get into the world market elsewhere to a significant degree at the present time. South Africa, Egypt, Israel, and North Vietnam also produce lesser quantities of rock for the international market, and these materials are also excluded from this review. The phosphate industry is now seeing the introduction of several new areas that will be significant factors in the rock market in the future. The North Carolina and North Florida areas each have capacity at present or in the near future for producing about three million tons per year. The Djebel Onk mine in Algeria has a potential of about 800,000 tons per year. In addition, announcements have been made of significant development of deposits in Peru and in the Spanish Sahara, and sizable expansions are planned in several of the existing areas that are now of minor importance. Competition for the rock market appears to be increasing so that more attention will probably be paid to evaluating phosphates available from different areas. It is not possible here to go into all the properties of even a few of the materials listed in Table I. However, it is practical to discuss some comparative properties important for making phosphoric acid and fertilizers, and to touch on the techniques used for the evaluation of various phosphate rocks. Table II gives typical analyses of the major phosphate rocks available in the world as of 1965. There is, of course, an inherent danger in labeling any analysis as typical, but it appears that variations between two samples of rock within one given area are generally less than between two samples from different areas. The analyses listed were compiled from several years of data so they may not be representative of the present output of any particular area. The range of grades represented by these analyses goes from 66 BPL for Gafsa rock to 85 BPL for Kola

Jan 1, 1968

By C. D. Hall

This paper may be divided into two main parts: (1) analysis and data to show that Eq. 6 adequately correlates the authors&apos; experimental data, and (2) the assertion that Eq. 20 "should permit scale-up with data taken from one pipe diameter for Newtonian, inelastic non-Newtonian, and viscoelastic fluids, such as dilute polymer fracturing fluids, which produce considerable pressure reductions." The authors might well recommend that this broad grouping of fluid types could be correlated by using Eq. 6 (requiring data from at least two pipe diameters). On the other hand, Eq. 20 is only shown to be adequate for conditions within the range of the present data set. Specifically, predictions by Eq. 20 for diameter scale-up to casing sizes would give larger deviations than implied in Table 2, and scale-up for some other fluids that give large drag reduction could be grossly in error. The description of a class of fluids "which produce a diameter family of straight parallel lines on a log (d?p/4L) vs log (8 v/d) plot. . ." defines a necessary condition for using Eq. 6; i.e., that s shall be constant for each fluid. The proposal that Eq. 20 is applicable to turbulent flow of such fluids is equivalent to saying that the spacing of these parallel lines, with A being constant, will be found to correspond to m = -1.20 for all such fluids. Table 1 shows the values of m derived from data on 16 non-Newtonian fluids. The key statement of this paper is that the diameter exponents "do not vary significantly from . . . -1.20." In statistical terms, this says that the m value for each fluid, which was obtained from all the measurements made on that fluid. has not been shown to be different from the arithmetic mean of the m values for the 16 fluids tested. This implies that the group mean, -1.20, is a more reliable value to use for an individual fluid than is the m value derived from the data on that fluid alone. No statistical test is described to support the key statement that the diameter exponents do not vary significantly from -1.20. Such a test would have to take into account that each individual m value is shown to correlate the pressure gradients for its fluid, with only about 3 percent standard deviation over the diameter range covered. That is, the m value is not the result of a single independent measurement. Thus, it would not be sufficient, or valid, to compare the deviation of one of the m values with the variance of the 16 values of m about their mean. An alternative interpretation of the key statement is that the diameter exponents do not vary appreciably from -1.20; i.e., that using -1.20 does not cause serious inaccuracy. Table 2 seems to be offered in support of such an assertion. However, such a statistical treatment (1) is unnecessary and (2) cannot lead to any valid scale-up generalization. The amount of error introduced by using a 1"wrong" value of diameter exponent — i.e., -1.20 instead of m — is determined by Eq. 6. The ratio of the pressures predicted by Eqs. 6 and 20 for scale-up from ds in small pipe to d, in casing is The pressure for 30-percent calcium carbonate slurry (m = -1.112) in 10-in. ID pipe would be predicted 30 percent higher by Eq. 6 than by Eq. 20, if based on tests in 0.5-in. ID pipe. The data set tested in Table 2 represents only a limited sample of pipe diameters (ratio of about 4:l) out of the population of diameters that would

Jan 1, 1970

By H. Dykstra

Calculated wellbore pressures were obtained for parameters of radilcs ratio and permeability. In all cases bur two, after-production was allowed to occur for one day. The calculated pressure build-up data were compared with actual pressure build-up data from a condensate well. The paper discusses the comparison, gives reasons for, inability to match calculated (2nd actual data, and presents conc1usions derived from the comparison. INTRODUCTION Considerable information has been published on the decline in wellbore pressure for oil and gas fields resulting from production of fluids. Considerable information also has been published on pressure build-up for oil fields, but relatively little has been published for gas and condensate fields. Perrine&apos; summarized the equations derived for pressure build-up in oil wells and showed how the different methods could be applied. On the other hand, very little theoretical information has been published on pressure build-up in gas or gas-condensate wells.2-4 Tracy,&apos; by pointing out the similarity between the equation describing oil wellbore pressure decline and the equation describing gas wellbore pressure decline, showed how methods of pressure build-up analysis could be applied to a gas well. In analyzing pressure build-up data for gas or gas-condensate wells, it would be very desirable to compare actual pressure build-up data with calculated pressure build-up data. Such a comparison would lead to a better feeling for the quantitative picture of gas-well build-up curves and would help to establish a degree of confidence in a given build-up curve. This paper discusses the comparison and presents conclusions made from it. Calculated wellbore pressures are given for parameters of radius ratio and permeability. In all cases but two, after-production was allowed to occur for one day. The work was done in an attempt to evaluate the reserves of a gas-condensate field. As will be discussed later, it was not possible to make an evaluation. METHOD OF CALCULATION The method used for solving the depletion and pressure build-up behavior for a gas-condensate well was that developed by West, Garvin and Sheldon.5 or the IBM 704 computer program used, it was assumed that liquid condensing out of solution would have only a minor effect on the flow behavior. Therefore, the field was treated as having single-phase flow, with the gas saturation S, remaining constant at unity minus the connate-water saturation Sw. As will be discussed later, this may not have been a good assumption. It also was assumed that oil production could be considered as equivalent gas production by using a conversion factor based on an analysis of the liquid produced. An outer boundary condition of no-flow was assumed. BASIC DATA The data required for the study were reservoir properties, fluid properties and production data. Reservoir properties included the following: thickness h, 179 ft; porosity, 0.194; connate-water saturation, 0.43; gas saturation, 0.57; permeabilities k, 1.0, 0.5, 0.25 and 0.15 md; radius ratios re/rw, 800, 1,000 and 2,000; wellbore radius rw, 5 in.; initial reservoir pressure P, 6,529 psia; and reservoir temperature, 272°F. The selection of permeabilities was based on core-analysis data showing an average air permeability of about 2 md. With a relatively high connate-water saturation, the average effective gas permeability would be about one-half, or less, of the air permeability. The selection of radius ratios was based partly on the observed rapid decline in wellbore pressure during production and partly on the fact that the well was believed to be located in a relatively small fault block. Reservoir fluid properties were obtained from a reservoir fluid study on a recombined sample of gas and condensate. Gas formation-volume factors were calculated from pressure-volume measurements made at reservoir temperature. Gas viscosities were calculated by the method of Carr, et al,G from an analysis of the re-combined sample. These data are shown as a function of pressure in Table 1. The production schedule from the gas-condensate

By E. V. Murphree

CREATION of atomic energy, aside from its influence on war or peace, has posed these basic questions for the world: How soon can energy from atoms be harnessed to do man&apos;s daily work? How much of this power will there be, to what degree will it supplant present fuels, and what does it imply for the future of civilization? Answers to these questions may be found in part in analysis of just what atomic energy is and how far its development has come. The answers are encouraging. One of the first questions encountered in considering the application of atomic reactions is whether such reactions can be controlled. Fortunately, this has been adequately demonstrated by the operation of the Government plutonium plants at Hanford, Wash. Here nuclear reactions are carried out on a large scale involving liberation of about a billion B.t.u. per hour. This hourly heat liberation is equivalent to that obtained from about 7100 gallons of fuel oil. It has been possible to operate these plants day in and day out with the reaction controlled at the intensity desired. There should therefore be no question that, under proper conditions, reactions involving nuclear fission can be controlled.

Jan 1, 1946

By Francis P. Sinn

IN the zinc smelting industry the year 1947 seems to have been one of putting one&apos;s house in order rather than one of any material technical development or radical change in operating conditions. Labor generally has been in better supply but several plants report a scarcity of skilled workmen. Some plants continue to operate on the basis of a six-day week and will probably continue to do so until labor is more plentiful. Only one plant is known to have operated on a curtailed basis because of labor shortage, but here the difficulty was lack of proper housing facilities. Necessary materials and equipment for much-needed maintenance and modernization have been in short supply so these programs have often been delayed. Laborsaving devices of the "Payloader" type have been more generally used for handling materials. Slab zinc production was discontinued during the last months of the year at Danville, 111. and at Langeloth, Pa. Both of these plants used the Hegeler type of furnaces fired with producer gas. It is understood that the rolling mill and possibly the acid plant at Danville will continue to operate. At Langeloth acid will be produced from

Jan 1, 1948

By AIME AIME

OUR own Institute of Metals and Iron and Steel divisions cooperated with the Iron and Steel Division of the American Society of Mechanical Engineers, the American Welding Society, and the American Society for Steel Treating in a busy week at Cleveland. The morning sessions were held at the Hotel Cleveland and the afternoon ones at the Auditorium, where the metallurgical exhibition under the auspices of the American Society for Steel Treating not only occupied the arena of the Auditorium but completely filled the huge adjacent Annex. In the intervals of sessions the members thronged the exhibits but in the evenings the local attendance was so great that if the crowds had been any larger it would have been difficult to see the exhibits. With so many firms, both producers of metals and of equipment accessory to their production and use, it would be impossible to mention them -all and unfair to single out a few, since no two individuals&apos; judgment would coincide as to relative interest and importance. In any case an exhibit is a thing to be seen rather than described, and these were well worth seeing.

Jan 1, 1929

By A. W. Schlechten

The proposition is advanced that edutcation specifically for exlractive metallurgy is desirable not because the course content is cmique but rather as a means of indoctrinating the student with a backgrocmd that will give him an interest and pride in the profession. Factors that have caused the decline in enrollment in metallurgical engineering courses emphasizing extractive processes are being overcome. There is a need to distinguish between the sciences of metallurgy and the engineering applications to avoid confusion both in and out of the profession. AS a first step in preparing the 1967 EMD Lecture I searched the literature to determine what my predecessors had done hoping thereby to gain some clues for my own performance. The Transactions of the Metallurgical Society show that the first EMD Lec- turer in 1959 was Dr. W. J. Kroll, known chiefly today for his pioneering work on the production of titanium and zirconium, but equally respected by an earlier generation for his contributions to lead refining. He has been followed by a series of well-known and competent metallurgists all possessing specialized knowledge that has served as a basis for their lectures. The EMD Lectures have in general been a review of the development of a certain aspect of the extractive metallurgical industry or a preview of a particular area of science or technology that has applications in extractive metallurgy. The usual format is to describe developments of the past, summarize the present state of knowledge, and make predictions for the future. There has been great variation in the relative amount of time devoted to these three subdivisions, the past, the present, and the future. For example, Professor Gaudin, the 1961 EMD Lecturer, in speaking of Separation Engineering on the Moon, did not have too many examples of past practice and so had to emphasize the future. It is cheering to observe that all of these authorities were optimistic in their predictions. Despite the fact that four of the previous EMD Lecturers have been educators, Professors Gaudin, Pidgeon, Schuhmann, and Kellogg, none of them discussed the subject of education for extractive metallurgists. I might say parenthetically that lecturers in other divisions, such as B. M. Larsen, J. B. Austin, F. D. Richardson, John Chipman, and R. F. Mehl, have commented with concern on the present state of training for extractive metallurgy. What can you say that is new about extractive metallurgy education? Certainly nothing new can be said about the educational process itself. Professional educators do have new approaches to teaching and learn-

Jan 1, 1968

By C. R. Kuzell

The Editor desires to call attention to the charts in the paper of the above title which were published in the August Bulletin on pages 2190 and 2191. It was impracticable to include in the Bulletin. charts of sufficient size to be used as working diagrams for the direct determination of operating values, but the Institute is prepared to furnish copies of these charts on a large-size scale, at a moderate cost, to those who desire to have them for this purpose. CORRECTIONS Page 2185, line 3. For "is accessory apparatus" read "in accessory. apparatus." Page 2188. Substitute for lines 11 and 12: Nitrogen, oxygen, carbon monoxide, Cp = 6.50 + 0.0010T Hydrogen, Cp = 6.50 + 0.0009T

Jan 9, 1914

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well&apos;s production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. &apos;The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm&apos; A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By R. R. Angel

Drilling rate is a parameter that should be considered in determining the volume requirements for air and gas drilling. The use of past methods which ignore the effects of the solids content upon the pressure and velocity of the annulus flow stream can result in undercalculation of the required volurne by as much as 50 per cent. A vertical-flow equation is presented for determining volume requirements. This equation includes the effect of the solids that are transported up the annulus in the flow stream by incorporating the drilling rate as one of the parameters. The effect of down-hole temperature on required circulation rates is also ana-lvzed. A simple approximate method of determining volume requirements is presented. This method is more accurate than the methods used in the past. Hole cleaning difficulties are analyzed for a recent air drilling job where past methods indicated that - excess air was being used. Sample curves of calculated boitom-hole pressures are presented for air and gas drilling in several hole sizes. INTRODUCTION In certain areas the use of air or natural gas as a circulating medium for drilling oil and gas wells is becoming a common practice. Large increases in penetration rate and bit life are achieved through the use of these media in preference to mud or water. Drilling rates as high as 90 ft/hr have been obtained in shales. The importance of maintaining adequate circulation rate is generally recognized; however, much disagreement exists among drilling operators as to what constitutes "adequate" circulation rate. In quarry drilling, where annular velocities can be accurately determined, an annular velocity of 3,000 ft/min of standard air is required for best results in rocks having approximately the same density as those commonly penetrated in drilling oil or gas wells&apos;. Although this standard air velocity has proven satisfactory for quarry drilling, some oil and gas well drilling operators believe that an equivalent annular velocity of more than 4,000 ft/min is required; others believe that as little as 2,000 ft/min . is sufficient. Much of this disagreement results from determining the required circulation rates with methods which fail to incorporate the drilled solids in an equation which is applicable to vertical flow. Hughes Tool Co. Bulletins No. 23&apos; and 23-A3 present data for determining circulation rates based on the Weymouth formula. These data do not include the drilling rate as a parameter and, therefore, neglect the effect of the solids being transported up the annulus. In spite of this apparent defect and the fact that the Weymouth formula is not applicable to vertical flow, the Hughes data have well served the drilling industry in many areas and are important and timely contributions to the science of air and gas drilling. The Hughes data purposely omit a correction for increasing down-hole temperature. At slow drilling rates this effectively compensates for the use of a formula which is not valid for vertical flow; however, volumes determined by the Hughes method are not sufficient to support rapid drilling rates at moderate and great depths. For example, Phillips Petroleum Co.&apos;s Cauthorn "D" No. l in the Vinegarone field for Val Verde County, Tex., was air drilled from 1,500 to 9,300 ft using a compressor delivering 1,400 cu ft/min. The 8 3/4-in hole was drilled with 5-in. drill pipe, and drilling rates as high as 90 ft/hr were obtained between 7,000 and 9,300 ft. No water or caving hole was encountered. At 7,728 ft it was necessary to wash-out 60 ft of cuttings to reach bottom after a trip to change bits. At 8,130 ft a twist-off occurred and the drill col-lars were stuck in drill cuttings. These difficulties indicate that the 1,400 cu ft/min of air was not sufficient to keep the hole clean. Hughes data indicates that 1,180 cu ft/min is sufficient to produce an annular ve-

Jan 1, 1958