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By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By E. P. Abrahamson II

The effect of transition elements which form binary solid solution upon the recrystallization temperature of zirconium has been investigated. All additions raised the recrystallization temperature. A correlation is obtained between the logarithm of the rate of change of recrystallization temperature with atomic percent solute and the free atom ground state electron configuration of the solute element. ThE work of Abrahamson, et al., on dilute binary solid-solution alloys indicated a correlation between the free-atom ground state electron configuration of the solute and either the brittle-ductile transition or recrystallization temperature. These studies were carried out on bcc base materials. The implication is that the outer s and d electrons of the solute are the prime determinant of the absolute rate of change of recrystallization or transition temperature. Furthermore, the limit of linearity has been shown to be a function of solute electron configuration for recrystallization in iron and vanadium. To date no Complete systematic recrystallization study of dilute binary zirconium base alloys has been made. It is the purpose of this study to note whether the change in solvent structure from bcc to hcp will influence the correlation. It was also desired to learn more of the role of the electron configuration of the solvent on recrystallization temperature. PROCEDURE All alloys were made using 99.87 pct Zr with 0.01 Cr, 0.04 Fe, 0.006 Hf, 0.003 Mg, 0.003 Mn, 0.003 N, and 0.080 0 (132 BHN). The solute elements were 99.9 pct pure. According to the published binary phase diagrams6 and metallographic examinations at X750, all alloys used were solid solutions. The alloys were arc melted and remelted six times in the form of cubic 200-g buttons under an argon atmosphere. They were then hot pressed at 950°C to 0.450 in., upset pressed to 0.350 in., and annealed at 800°C for 1 hr. The specimens were then Blanchard ground to 0.250 in., removing 0.050 in. from each side. The grain size of the material at this stage was found to be 8000 100 grains per sq mm. The specimens were then cold rolled to 0.130 in. and cold pressed to 0.125 in., yielding 50 1 pct cold work. All alloys were then chemically analyzed for the principal addition. The interstitial contents remained at the values of the starting material when checked on random alloy specimens. The rolled sheet was cut into 6.75 by 0.25-in. lengths and heat treated in a gradient furnace for 1 hr. The gradient was 250o to 900°C over the 6-in. length, recorded continuously by six thermocouples resting on each specimen. Control was 3oC, accomplished at the hot end. The recrystallization temperature was determined metallographically using polarized light. The criterion chosen was the point on the specimen showing the first recrystallized grain at a constant magnification, X200. Specimens were repeated, and the agreement was found to be 3°C. RESULTS Three different pure zirconium specimens were tested, and the recrystallization temperature was

Jan 1, 1962

At the meeting of the Board of Directors of the Institute on Jan. 26, 1917, the following actions were taken: Messrs. A. C. Clark, Lawrence Addicks and G. D. Van Arsdale were appointed Tellers to count ballots for Officers and Directors. Messrs. T. T. Read, V. S. Harper, and. E. J. Hall were appointed Tellers to count ballots on revised spelling. The Finance Committee's audit for the year 1916 was approved and ordered filed. The Report of the Finance Committee upon the method of raising this Institute's share of the deficit on the additions to the building was approved and accepted. Upon the recommendation of the Secretary, increases in the salaries of some of the employees were approved. The St. Louis Section received an appropriation of $200 for the year 1917. The Columbia Section received an appropriation of $150 for the year 1917. The Montana Section received an appropriation of $100 for the year 1917. The Colorado Section received an appropriation of $175 for the year 1917. The Utah Section received an appropriation of $125 for the year 1917. The Puget Sound Section received a set of Transactions in standard binding. The International Engineering Congress received a loan of $300 until the Congress can realize upon some of its assets.

Jan 3, 1917

By L. W. Bahney

MANY methods for the determination of gold or silver, or both, in cyanide solutions have been published, which with care in manipulation, and modification in some cases, will give results that are satisfactory. It is possible to classify or group these methods as follows: 1. Evaporating the solution in a porcelain or agate-ware dish containing litharge,1 or in a "boat" made of lead foil. 2. Forming a lead sponge containing the precious metals by means of zinc shavings,2 zinc dust,3 or a piece of aluminum.4 3. Decomposing the cyanide solution with an acid and precipitating the precious metals by the use of one or a combination of some of the following: Copper sulphate,5 sodium sulphite,6 hydrogen sulphide,7 cement copper.8 4. Precipitating the silver by zinc dust held in a Hooch crucible and determination with a standard solution of sulphocyanate.9 5. Electrolysis.10 6. Colorimetry.11

Jan 2, 1915

By W. C. Phalen

The production of salt in the United States divides itself at the outset into two distinct classes…

Jan 1, 1915

This consolidated index covers all publications of the Institute for the years 1926 through 1935. The following list indicates subjects of volumes and gives numbers or abbreviations used to designate them. TRANSACTIONS VOLUME *G26. Petroleum Development and Technology in 1925 (Published in 1926). *G26. Petroleum Development and Technology in 1926. *E27. Institute of Metals Proceedings. 73. Nonferrous Metallurgy, Milling and Concentration, Nonmetallic Minerals, Institute of Metals and Iron and Steel. [ ]

Jan 1, 1936

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult's law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult's law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.' One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys' revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult's law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.' Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By L. E. Lynd

Ilmenite concentrates prepared from beach and dune sands of Florida, India, Australia, and other localities deviate to varying degrees from the theoretical composition of pure ilmenite, and generally contain more TiO2 than the formula FeTi03 would indicate, and some Fe2O3. This variation in composition is due to different amounts of altered ilmenite in the concentrates. (') The alteration has been shown to take place by oxidation and leaching of the iron in ilmenite, to yield residual products consisting of amaphous or very finely crystalline titanium dioxide and ferric oxide. Other studies(2) have stressed that ilmenite may alter first to an amorphous titanium-iron oxide, or to an amorphous mixture of titanium and iron oxides, with later alteration to crystalline titanium dioxide. There has been some speculation as to whether alteration of ilmenite is usually caused by weathering or by hydrothermal pr0cesses.(3,4,5 Three main methods of approach were used to study the mechanism and rate of ilmenite weathering. (1) Etch tests were used to learn the relationship between crystallographic orientation and the rate of chemical attack on ilmenite. (2) Altered ilmenites in New Jersey sands were compared with ilmenite in rocks of the area from which the sands were probably derived. (3) Experiments were carried out to determine at what rate, and by what agents, originally fresh ilmenite could be altered in the laboratory under simulated weathering conditions. ETCH FIGURES ON ILMENITE CRYSTAL PLANES A rather large ilmenite crystal from Sannidal, Norway, about 11/2 x 11/2 x 2 inches, bearing a few natural faces with imperfect surfaces, was prepared for etching by grinding and polishing crystal planes whose Bravais-Miller indices (referred to hexagonal axes) had been determined by X-ray methods to be 00.1, 10.0, and 10.2. Metallographic examination showed that the crystal was homogeneous, and uniform in orientation, except for the presence of twin lamellae which were oriented with their broadest surfaces parallel to the 00.1 planes of the large crystal. Since ilmenite is rather inert to standard etch reagents, strong solutions of hot sulfuric acid and cold hydrofluoric acid were used. Preliminary tests established that better etch figures were obtained using HF than with H2So4 solutions. The etch figures produced on 00.1 and 01.0 planes of ilmenite by etching 3 to 5 minutes in cold concentrated HF solution are shown in Figures 1, 2, and 3. The figures on 00.1 are "etch hillocks", rather than pits, and according to Honess(6), this phenomenon

Jan 1, 1961

By . M. Muskat

A THEORETICAL consideration of the mechanics of various water-flooding systems with the viewpoint of comparing their relative merits involves the study of two fundamental properties of such systems. On the one hand, it is important to determine the efficiency of the flood as measured by the percentage of the total area that is swept out by the encroaching water before water actually reaches the output wells. This is really a measure of the regional tendency of the water to "bypass" the oil. On the other hand, the various systems must be compared from the viewpoint of their resistances which determine the rate of fluid production obtainable for given pressures maintained at the water input wells. The first of these questions has been studied and very definite answers have been obtained by means of simple electrolytic models.1 These models showed that, in an ideal system, the percentages of the areas flooded out before water reaches the output wells are about 57 per cent for the direct line-drive flood (the input and output wells being equally spaced and placed in alternate parallel lines), 74 per cent for the regular five-spot network, and 79 per cent for the seven-spot network. With respect to the efficiency of the usual flooding arrangements, they are, therefore, given quite accurately by the above numbers. With regard to the resistances of the flooding networks, electrical conduction models have also been used successfully2 and are well adapted to the problem of determining experimentally the pressure distribution and streamlines, or over-all resistances of specific flooding networks. However, such models do not permit readily a study of the effect of changing dimensions or configuration within a network, since a new model must be made up for each set of dimensions considered.

Jan 1, 1933

Jan 1, 1965

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By K. J. Gill, P. Chiotti

Thermal, metallographic, and vapor pressure data were obtained to establish the phase diagram for the thorium-zinc system. Four compounds corresponding to the stoichiometric formulas Th2Zn, ThZn2, ThZn4, and Th2Zn17 were observed. The melting points of these compounds under constrained vapor conditions were found to be 1055°, 1105°, 1095°, and 1015°C respectively. Four eutectics exist in this system with the following eutectic temperatures and thorium contents in wt pct: 1040°C, 89 Th; 945°C, 79 Th; 1045°C, 55 Th; and 995°C, 35 Th. The standard free energy, enthalpy, and entropy of formation for the compounds were determined from zinc vapor pressure data. ALTHOUGH the thorium-zinc system has been of technical importance in the commercial production of thorium and more recently of interest to some proposed pyrometallurgical separations processes for reactor fuels or blanket materials no detailed investigation of this system has been made in the past. Some previous work has been reviewed by Hanssen.1 The existence of four compounds, Th2Zn17, ThZn4, ThZn2, and Th2Zn has been established and their crystal structures have been studied by X-ray diffraction techniques.2-4 Smirnov et al.,5 determined the solubility of thorium in zinc and investigated the two-phase region between Th2Zn17 and zinc. They calculated some of the thermodynamic properties for these alloys from emf measurements on the cells Th/ThCl4(fused)/Cl2, C and Th2Zn17(s)+ Zn (l)/ThCl4(fused)/Cl2, C. The possibility of reaction between the anode materials and fused thorium tetrachloride to produce a lower valent thorium salt would have to be resolved in order to evaluate the results obtained. The purpose of the present investigation is to establish the phase diagram for the thorium-zinc system and to determine the standard free energy, enthalpy, and entropy of formation for the compounds formed. MATERIALS AND EXPERIMENTAL PROCEDURES The metals employed in the preparation of alloys were Bunker Hill slab zinc, 99.99 pct pure and Ames Lalboratory thorium. The major impurities in the thorium in parts per million were oxygen—1250, carbon—350, iron—100, nitrogen-75, and silicon—70. The metals in the form of several small massive pieces, total weight about 30 g, were cleaned with acid, washed with water and acetone, and dried just prior to their use for alloy preparation. Tantalum containers were found to be suitable for all the alloys studied and were used throughout this investigation. The metals were sealed inside of small 1-in.-diam tantalum crucibles by welding on preformed tantalum covers. A small thermocouple well made from 1/8-in.-diam tantalum tubing was welded in the bottom of each crucible. These crucibles were enclosed in

Jan 1, 1962

By M. Cohen, P. E. Beaubien, D. Caplan

Addition of 1 pct Mn to Fe-26 CY ca/(ses a12 increase in scaling rate at 870° and 1090°C. Whereas only the rhombohedral oxide, formrs on tire manganese-free alloy, with manganese present major amounts of the spinel .Mn0 . Pro-duced through which diffusion is more rapid. At 1090°C the scale formed OH Mn is highly, irregular due to blistering and sintering, This is a second cause of faster oxidation Since much of the blistered oxide does not participate as part of the protective layer. The oxide phases that form at different times depend on the degree to which the surface metal has become depleted, in manganese by preferential oxidation. PREVIOUS work has demonstrated that the oxide scales formed on chromium steels at high temperature consist of both spinel and rhombohedra1 phases and may contain considerably more manganese, especially in the spinel phase, than is present initially in the alloy.' It has further been observed that a binary Fe-26 Cr alloy scaled less rapidly than an equivalent commercial steel and formed no spinel.' However, it is not established if manganese in chromium alloys actually promotes formation of spinel nor if it affects oxidation resistance. It seemed expedient to try to evaluate the specific effect of manganese by oxidizing an Fe-26 Cr alloy containing a small manganese addition under the same experimental conditions as used for the manganese-free alloy.' EXPERIMENTAL Table I shows the composition in weight percent of the Fe-26 Cr-1 Mn alloy and of the Fe-26 Cr alloy used as reference. The alloy with manganese was prepared from the vacuum-melted Fe-26 Cr alloy by remelting in vacuum with the proper manganese addition. The ingot was rolled to strip and specimens 1.1 by 0.035 by 5 cm and 1.1 by 0.5 by 4 cm cut out or machined. As previously described2 the specimens were smoothed by abrading through 600-grit Sic paper, electropolished in acetic-perchloric acid (20 to 1) to remove 10 p of metal, annealed at 1100°C in 20 torr of purified argon, and electropolished to remove a further 10 p of metal. They were then either rinsed in water and methanol and blotted dry or immediately etched for 45 sec in deoxy-genated 4 N HC1 under cathodic polarization at 10 pa per sq cm. Oxidation runs were carried out in a vertical tube furnace in a flow of purified oxygen at 1 atm while the weight increase was recorded continuously on a* automatic balance.3 Alter 98 hr at 870.C or 20 hr at 1090"C the specimens were removed to flowing argon and observed microscopically for evidence of spalling as they cooled. Subsequently they were examined by X-ray diffraction, the oxides analyzed chemically, and metallographic cross settions prepared. RESULTS Figs. 1 and 2 show the oxidation curves of Fe-26 Cr-1 Mn at 870' and 1090C. The Fe-26 Cr reference runs are shown as dashed curves. Experimental details of the six runs are included in Table 11. The first 20 hr of run 1 is repeated in Fig. 2 to show the effect of temperature. At 8'70°C the weight gain for Fe-Cr-Mn is about twice that of Fe-Cr (curve 1 vs curve 2, Fig. 1). Both alloys show regular oxidation curves. On parabolic coordinates (right-hand scale of Fig. 1) the

Jan 1, 1965

By R. G. Bentsen, D. A. T. Donohue

The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today.1-4 Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming. To use dynamic programming, we must be able to predict not only the production rate-time curve resulting from a given stimulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism. We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process. Oil Production Response Model The advantage of using a mathematical model is its generality and ease of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results. With this in mind, we kept our model as simple as possible, yet generally representative of the actual physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated. In

Jan 1, 1970

By W. R. Hibbard

Evidence is presented which confirms previous findings that models of solution strengthening depending solely on lattice parameter changes are incomplete. Direct evidence for the Suzuki interaction of chemical effects was obtained from alloys with constant lattice parameter, for which solution strengthening was nearly independent of temperature from 300° to 20°K. SOLUTION hardening principles have been reviewed recently by Parker and Hazlett.' In addition, the interactions of dislocations and solute atoms were reviewed by Cottrell.' It is not proposed to review this information again here, but to refer only to those details which are pertinent to the developments which have occurred since these papers were published. Literature Survey To set the stage, it has been known for some time that solid solutions are stronger than the pure parent metals, and that the strength increases with increasing amounts of alloying element. One of the most extensive earlier investigations was that of Lacy and Gensamer,3 who reported that the solid solution strengthening of iron is a power function of the composition, that the relative strengthening is a function of the solubility limit, and that the rate of strain hardening is a function of the amount of solution hardening. Thus, the slope of the plastic portion of the stress-strain curve increases with increasing yield strength. An approach to the development of principles resulted from work by Gulyeav,4 who reported that the strengthening effect of solid solution alloys is periodic in character when plotted as a function of the atomic number of the solute. A more quantitative approach was to relate the amount of solution hardening to the lattice parameter of a solid solution. This was done quite early by Norbury,5 and later by Brick, Martin, and Angier,6 Frye and Hume-Rothery,7 and French and Hibbard. This relationship is only approximate in character. The next development was to relate the amount of solution hardening to lattice stress, as proposed by Frye and co-workers.9 They calculated what they called ionic overlap from the lattice parameter changes represented as a change in volume, using Bridgman's hydrostatic compression equation. The resulting correlation was somewhat improved as compared to the simple correlation with lattice parameter. The next step was carried out by Dorn, Pietrow-sky, and Tietz,10 who suggested an effect of valence differences in addition to the effect of lattice parameter. Their proposed parameter shows flow stress as a single valued function of the concentration and a relationship involving these two atomic variables. In addition, they contributed new data on the temperature dependence of solution hardening which indicated that it was a strong function of temperature for aluminum alloys. Allen, Schofield, and Tate11 carried the valency effect even further by reporting data indicating that with a given solvent element the stress-strain curve is a function of electron density, entirely neglecting the size factor, which varied by a factor of two. This evidence led to a quantum mechanical calculation by Cottrell, Hunter, and Nabarro,12 based on the formation of a dipole around an edge disloca-

Jan 1, 1959

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in

By W. H. Bassett, C. H. Davis

In the commercial annealing of cartridge brass there are four points regarding which definite data are essential. They have to do with the correct interpretation of grain count in its relation to annealing temperature and, incidentally, to Brinell hardness. These points are: 1. The comparison of the grain sizes of two cartridge-brass mixtures: 69 copper, 31 zinc, 0.376-in. (9.5-mm.) gage; and 68 copper, 32 zinc, 0.130-in. (3.3-mm.) gage 2. The comparison of the grain sizes of annealed metal that had previously been reduced by rolling varying amounts; for instance, 20.0, 36.6, 50.9, and 59.1 per cent. 3. The determination of standards for grain sizes on annealed brass of the composition 68 per cent. copper, 32 per cent. zinc and 69 copper, 31 zinc. 4. The comparison of grain size with Brinell hardness on identical samples of annealed metal. In their comprehensive and thorough investigation of the recrystal-lization of cold-worked alpha brass on annealing,l Mathewson and Phillips have discussed the relations between temperature of anneal, degree of deformation, and structural alteration in alpha brass. They have also shown certain comparisons between the ordinary physical properties and the grain size of annealed brass. The purpose of the present investigation is mainly concerned with the grain size of cartridge brass, its relation to Brinell hardness, and the publication of sufficient data to enable those engaged in the inspection of such material to have a correct foundation upon which to work. The first alloy was taken from regular mill stock that had been rolled from 0.580 in. to 0.376 in. (14.7 mm. to 9.5 mm.) gage, a reduction of 35.1 per cent. This bar (No. 1) had the following composition: Copper, 69.20 per cent.; zinc, 30.76 per cent.; lead, 0.02 per cent.; iron, 0.02 per cent. The second alloy was also taken from mill stock of 0.325 in. (8.25 mm.) gage and was rolled as shown in Table 1, in order to get four bars reduced two, four, six, and eight B. & 5. numbers respectively. This second alloy

Jan 1, 1919

By W. J. Verner, J. R. Lucas

Billions of tons of bulk solid materials are processed through our industrial plants each year, and the tonnage is steadily rising. It has been estimated that for every dollar spent in industry as a whole, approxinlately 30 cents is consumed in the handling of bulk solid materials. It is in this category that tremendous savings are possible through the use of improved techniques. Since World War 11, the mining, steel, chemical, and grain industries, among others have made use of increased materials-handling automation in order to gain some of these savings. However, in a chain of automatic operations, every link must be completely reliable, for if there is a single failure, the whole system immediately becomes ineffective. Only too often the weak link in the chain proves to be the flow of bulk solids from bins. To contribute to the fundamental knowledge in this area, a research study has been continuing at The Ohio State University. The principal objective of the investigation has been to study the internal stresses existing in confined bulk solids. LITERATURE SURVEY Literature studies have revealed that many outstanding people have made contributions to the field of bulk solids. For instance, C. F. Jenkin,1 suggested: a. The pressure on a bin wall is not directly proportional to the depth beneath the surface of material in the bin. b. The vertical pressure distribution on the base of a bin is not actually uniform but is a variable. c. Arches form in bins as a result of very small deformations of the material in the bin. This deformation causes a series of gaps to appear, and consequently causes the disappearance of diagonal forces that cannot act across these gaps. The removal of the diagonal forces causes horizontal forces to be introduced which seem to be the chief cause of arching. 11. A. Janssen,4 in 1895 in connection with his experiments on bins, derived a differential equation to describe both the lateral and vertical pressure in bins with vertical sides. This represents a significant contribution to bulk solid theory, and thus its solution is reproduced as follows: L = KV = RW/U' [l-e -U'KY/R] I where L is the lateral pressure of the bulk solid in psf., V is the vertical pressure of the bulk solid in psf., K is the ratio of the lateral pressure to the vertical pressure at any point, R is the hydraulic radius of the bin in feet, W is the density of the bulk solid in lbs. per cubic feet, U' is the coefficient of friction between the stored material and the bin wall, and Y is the head of material above the point in question in feet. In 1903, Jamieson,6 in an elaborate series of experiments on full sized bins measured vertical and lateral pressures by hydraulic diaphragms. He determined many values for mediums of corn, wheat, peas, and flaxseed. In 1951, Caughey, Tooles, and scheer3 measured both lateral and vertical pressure in deep bins by using strain guages on steel bands. Values were calculated for cement, gravel, sand, soy beans, shelled corn

Jan 1, 1961

By Mehmet Guney

At the Armatcuk mine in Turkey, various modifications of sublevel methods have been tried during the last decade in an effort to eliminate gob fires, dangers from roof falls, and surface subsidence, and also to increase extraction efficiency. From the experience thus gained, it was decided that the most likely system to give maximum benefits, considering the existing geological conditions and coa1-seam characteristics, was hydraulic stowing. This paper examines trends in the working techniques of hydraulic stowing and discusses the favorable results and technical problems that the method produced at Armutcuk. The Armutcuk mine, a subsidiary of Eregli Coal Mines (EKI), produces 1300 tons of run-of-mine coal daily from thick (about 10-90 ft) and highly dipping (about 50-90°) coal seams. The coal is highly volatile with good coking properties that make it highly suitable for industrial use. Most of this coal is used in the iron and steel industry at Eregli on the Black Sea coast. Complete recovery of the coal is of vital importance to industrial development and progress. Initial coal extraction was carried out by means of a sublevel mining system modified to accommodate local geological conditions and coal seam characteristics. This method is similar to that employed in metalliferous mines. Several problems arose from the application of the method, one of them being the prevalence of gob fires which caused periodic shutdowns in some sections. To achieve maximum coal extraction with minimum dilution, to eliminate gob fires and surface subsidence, and to reduce fatal accident rates, a decision was taken to change from this method to a hydraulic stowing system. The pres- ence of large deposits of conglomerate and sandstone on the surface contributed to the decision to employ this new method. Although hydraulic stowing practices have been carried out in America and Germany, Upper Silesia may, so far as coal is concerned, be considered the birthplace of the method. Here the process was adapted to thick coal seams on a large scale to reduce dangers from gob fires and damage from surface subsidence. Today, the mining system is not only widely used in the coal mines of France, the Saar, India and Poland, but has also been successfully applied to the iron ore and potassium salt mines in Russia and Germany. LOCATION AND HISTORY The Kandilli-Armutcuk coal field, the most western outcrop of the North Anatolian coal basin, extends for five miles along the Black Sea coast (Fig. 1). The Armutcuk Mine is situated on the southern boundary of the coal field about 40 miles from Zonguldak and about 12 miles from Eregli. The history of coal mining in the North Anatolian coal basin goes back more than a century. Mining commenced on a small scale in the Kandilli-Armutcuk coal field in the late 1880's, and from this time until nationalization in 1940 the mines were operated by private Turkish and foreign interests. In 1940, Eregli Coal Mines was established to takeover the management of these enterprises. The Armutcuk Mine was developed for the first time in the mid-1940's. Since then it has been in continuous production and it now produces an annual 440,000-ton run-of-mine output from which 320.000 tons of salable coal is obtained. MINE GEOLOGY The carboniferous inlier of the Kandilli-Armutcuk coal field crops out over an area about three miles long and one mile wide. The major part of the inlier consists of the Namurian formation with only a relatively small area of Westfalian-A visible on the surface (Fig. 2). The Namurian formation, which has no exploitable coal seams in the Armutcuk Mine, consists mostly of arkose sandstones and black shales often having

Jan 1, 1969

By R. N. Edmondson, L. Mair, M. Tenenbaum

It is the policy of The Metallurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers according to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editor, Dr. Gerhord Derge; Editorial Assistant, M. A. Redmyrski; Staff Coordinator, James J. Burke. THE METALLURGICAL SOCIETY: W. R. Hibbard, Jr., President; J. C. Kinnear, Jr., Past-President; John Chipmon, Vice President; T. D. Jones, Treosurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. w. Thornton, Chairman; Dennis Carney, John Chipman, J. C. Fulton I. H. Hollomon H. H. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and D. Swan. Review and selection of manuscripts is under the supenision of the following Publications Committees: Extractive Metallurgy Division: T. 0. King Chairman; S. J. Dickenson, R. P. Hermsdorf R. Schuhmann. Jr.. and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman F. Lincoln Vogel Jr., Vice-chairman, W. A. Baikofen, R. W. Boliuffi J. H. Bechtold M. B. Beyer. R S. Busk, C. G. Gaetzel, Paul Gordon C. D. Groham, Jr., Robert F. Hehe-mann,' R. I. Joffee, F. c. Joumot Jr lrving R. Kramer A. J. Lena Harold Morglin, C. J. McHargue, Russell A: Meussner, J. B. Newkirk H. W. Paxton, G. E. Pellissier, I. S, Servi, Alon U. Seybolt, A. J. Shaler, and Jack Washburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B King, F. C. Langenberg, W. 0.. Philbrook, and T. 0. Winkler. Published bimonthly by the American Institute of Mining Metallurgical and Petroleum Engineers Inc., 29 West 39th Street, New York 18, N. Y. Telephon: pEnnsvlvanio 6-9220. Subscription 522 Per year for non-AIME members in United States and North South and Central America; $25 foreign;, $5 for AIME members. Single copies, 54.00, single copies foreign, $5.00. The AIME is not responsible for any statement made or opinion expressed In its publications . . . Copyright 1958 by the American lnstltute of Mining Metallurgical and Petroleum Engineers Inc. . . . Registered cable address AIME New York , . . lndexed in Engineering Index Industrial Arts Index and Chemical Abstrats . . . Application for second class mail privileges ii pending at New York, N. Y. Volume 212, Number 4.

Jan 1, 1959