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By Fathi Habashi

Nickel, copper, and elemental sulfur can be recovered from a low-grade pyrrhotitepentlandite type concentrate by leaching with HNO3 in a pressure reactor at moderate temperature and pressure. The bulk of iron is converted to an oxide. Same results can be achieved by leaching in an open vessel under a reflex condenser for an extended period of time.

Jan 1, 1974

EUGENE McAULIFFE, * St. Louis, Mo.-The method employed by the Engineer's Committee in arriving at a proper selling price for coal and coke represents hard painstaking effort based on a thoroughly scientific foundation; and the United States Fuel Administration can well point with pride to the work of this committee. The results so obtained placed

Jan 12, 1918

By James R. Stuart

AS the available remaining properties of iron ore reserves on the Mesabi Range are opened up for mining, the various properties located under lake beds are brought nearer an active status. The actual physical problems involved in stripping these properties do not act as a deterrent so much as the legal and political problems that are encountered.

Jan 9, 1951

By James E. Lawver, Jose M. Pastrana

Some of toe magnetic properties of minnesotaite (general formula: Fe3(OH)2Si4O10) were examined. Toe paramagnetic susceptibility values at various temperatures were determined from toe slope of toe magnetizing curve. These values were then compared with toe theoretical values estimated using toe Bohr magneton numbers for toe paramagnetic ions contained in toe missesotaite.

Jan 1, 1975

By David M. Hopstock, Jose M. Pastrana

The magnetic susceptibilities of samples of natural and artificial hematite and natural goethite were measured by the Faraday method as functions of temperature, magnetizing field strength and particle size. All samples showed weak ferromagnetism, which accounted for large variations in susceptibility with field strength and particle size. Three probable sources of the weak ferromagnetism were identified.

Jan 1, 1978

By Timothy E. LaTour, Robert Kerrich

Microstructures and mineral chemistry of amphiboles and plagioclases from two spatially related mylonite zones at the Grenville front are significantly different, suggesting different physical conditions (including temperature) for the formation of the two zones. Oxygen isotopes indicate multiple episodes of fluid-rock interaction, consistent with previously determined mylonitization temperatures and postulated tectonic evolution of the area.

Jan 1, 1982

By Warren K. Kourt

Many important discoveries of mineral deposits have been made as a result of routine exploration for oil and gas. Through the presentation of three hypothetical case histories, including cost data, the author shows how mineral evaluation can be performed during routine petroleum drilling operations and how mining companies and oil companies or oil operators can cooperate in such endeavors.

Jan 1, 1972

By M. J. Swan, W. C. Foshee, R. R. Klimpel

The large volume of water used in coal preparation plants makes water recycling a necessity. Economical cleaning of dirty water usually requires flocculation with an efficient organic polyelectrolyte. This paper discusses identification of optimum flocculant systems. Supporting laboratory data with on-site tests and full-scale field trails supplies information necessary for matching the polymer to the plant.

Jan 1, 1983

By W. H. Lewis, J. C. Yingling, M. H. Leon

This paper describes the present state-of-the-art and status of longwall lighting in the U.S.A. Specific subtopics discussed are as follows: review of MSHA lighting regulations and requirements for longwalls; overview of available lighting hardware; installation procedures and costs; analysis of installations to date, including operator and management acceptance, complaints, benefits, and maintenance considerations.

Jan 1, 1981

By Frank Firmstone

(Ottawa Meeting, October, 1889. Substituted for the briefer note on the same subject. pre sented at the meeting and subsequently distributed in preliminary pamphlet edition.) Prof. H. Hoefer's theory of blasting was published in the Oesterr. Zeitschrift, xxviii., 1880, and xxix., 1881; and Part 111. in Nos. 15, 16 and 17, xxx., 1882, and subsequent numbers of that

Jan 1, 1890

By R. D. Pehlke

THE impending commercial importance of iron-aluminum alloys has served as a stimulus for re- search on the preparation and properties of these alloys. However, the activities of the components of the binary system remain undetermined. The experimental determination of the thermodynamic properties of binary solutions of iron and aluminum has been hindered by the high liquidus temperatures

Jan 1, 1959

By W. C. Krumbein

GEOLOGICAL problems are approached from a geometrical (space relations) viewpoint, a kinematical (time sequence) viewpoint, or a dynamical viewpoint. The first two require sound training in conventional geology and in field methods. The third approach requires a solid foundation of chemistry, physics, and mathematics. Modern training for geologists should include close integration of basic sciences with geological principles.

Jan 1, 1941

By J. Lindbo, B. Vigeholm

IN transmission electron microscopy, specimen thicknesses quoted are frequently based upon either traditionally familiar values or a few evaluations representing the whole material. Taking aluminum in 100 kv TEM as an example, average and maximum values are widely accepted as being 2000 to 2500 and 6000 to 7OOOÅ, respectively. It is the purpose of this note to revise these figures and to point out the importance of evaluating individual specimens carefully. All evaluations have been based upon slip trace widths and lattice orientations as determined from diffraction patterns. In many cases where two or more slip systems have been operating the geometrical method described by Crocker and Bevis1 has been applied as a check. The foils were usually oriented to within 2 deg from the exact Bragg angle. Kikuchi patterns were used as indications of correct orientations but not applied in the evaluations. The tilt of the foil surface relative to the beam normal may with certain geometrical relations between the tilt axis and the operating slip plane lead to substantial errors.2'3 Where these geometries were inevitable the samples were omitted in the investigations. Various measures were taken in order to overcome ambiguities, e.g., comparison with neighboring grains, tilts, evaluations based upon two or three slip systems,' and comparison with extinction contour evaluations where s = 0 conditions were obtained. Errors caused by misinterpretation of the slip traces on a micrograph are easily avoided by considering the bright-dark sequence on opposite surfaces and by taking into account the tapering of the foil usually leading to a distinguishable divergence of the pair of traces. In the investigations described here the interpretation was further facilitated as the slip trace formation was observed on the microscope screen and sketches taken down. In a few observations slipping was so violent that the distinction of pairs was considered dubious and consequently given up. To assess average values, thickness evaluations carried out in two independent investigations were analyzed: I) 99.998 pct A1 extruded, cold-drawn, and recrys-tallized to grain sizes between 35 and 500 um were deformed in tension at room temperature. In order to determine the dislocation densities as a function of strain,4 specimens prepared by spark machining and electropolishing in a PTFE holder were analyzed in the electron microscope at 100 kv. Thicknesses were evaluated for 569 selected areas. Histogram I in Fig. 1 shows the results, the average thickness being 4900Å. II) Electropolished specimens prepared from 99.9999 pct A1 with magnesium contents from 0.005 to 0.5 pct rolled to foil and annealed were subjected to fission fragment irradiationa2 For volumetric dose and defect concentration determinations thickness evaluations were performed on 123 areas. Histogram II in Fig. 1 shows the thicknesses of these areas averaging 4250Å. Whereas in investigation I no selection related to thickness has been made, some thin as well as thick areas have been omitted from I1 for experimental reasons. This and the application of two different microscopes although of the same type may account for the difference in average thickness. Assuming a mean error of 10 pct for a single evaluation, the error of the average should be negligible. In order to investigate the maximum transmissible foil thickness in aluminum, specimens were prepared from single crystals with (111) and (110) orientations parallel to the beam, and from polycrystalline material. Maximum values of thickness that could be measured were given by the stopping of the dislocations. The visibility often extended far beyond the end of the slip trace, but with no means of knowing the

Jan 1, 1970

By Christian F. Baiz

INTRODUCTION Industrial minerals can have similar financing requirements to those needs of metaliferrous and coal mining projects. One of the outstanding differences is the understanding of the many different markets that these industrial minerals represent. There are in excess of 30 principal industrial minerals ranging in terms of annual production from the largest quantity such as sand and gravel, to possibly the smallest quantity of production of a legitimate industrial mineral which may be defined as industrial and rough gem diamond. (See Tables 1 and 2) Project finance techniques, analytical methods, and information requirements are covered elsewhere in this Chapter and Chapter 10. Some comments on equity finance aspects follow. EQUITY AMOUNT The amount of equity in a financing transaction provides a cushion to the lender in case the project runs into trouble. Generally speaking, the greater the amount of risk in a project, the more equity a lender will require. The amount of cash equity in a project financing transaction is between 25 and 40 percent. The amount of leverage (debt/equity) is negotiable based on such factors as the strength and extent of the sponsor's undertakings, of the project's economics, and the term of a strong sales contract. Naturally, a borrower seeks to obtain d loan with as little equity required as can be negotiated. Zero percent equity is usually associated with a take-or-pay contract (a hell-or-high- water unconditional commitment under which the purchaser must pay for the commodity as though it were shipped regardless of whether it is actually mined or shipped) with a financially strong corporate entity i.e., the parent company or an end user. As a take-or-pay contract is tantamount to a guarantee of payment, the banker views the credit basis of the loan as being other than the borrower's mining operation and therefore will analyze the creditworthiness of the institution purchasing the commodity on the basis of its corporate balance sheet. Do not confuse a take-or-pay contract with a take-if- tendered or take-and-pay contract. Another means in the United States of obtaining zero percent equity is the carved out production payment financing, typical of coal mine financing. This involves the sale, or conveyance, by the owner of the mineral property of a production payment to a nominally capitalized company. The nominally capitalized company is formed solely to buy the production payment and usually borrows 100 percent of the purchase price from a lender. Equity amounts of 10 to 20 percent generally are found in transactions which employ techniques such as an advance sale or a subordinated lease/loan. These agreements are viewed as quasi equity by most banks for several reasons. First, the proceeds represent a cash infusion early in the project's life - usually prior to the bank lending any funds. Thus, the repayment schedule is "behind" that of the bank debt. In the case of an advance sale, repayment is in the form of a long-term supply contract with favorable terms, usually priced close to the mining operation's costs. There is also usually a requirement that all costs of the project be paid for by the loan or equity, often making the sponsors financially responsible for any cost overruns. Cost overruns are a major risk in any project, large or small, and are often due to unforeseen factors such as wildcat strikes, a piece of faulty equipment, or any event which delays completion, e.g., remote location, weather, etc.. . The question of how overruns are covered can be negotiated. For example, in addition to the original debt/equity ratio of the project, there can also be a cost overrun ratio that will

Jan 1, 1985

By J. H. Jackson, P. D. Frost, C. H. Lorig, L. W. Eastwood, A. C. Loonam

R. S. BUSK*—I wish first to congratulate the authors of this paper both for the work done and the presentation of that work. We have also been working on this type of alloy development, but any technical contribution I might have is better reserved for a separate paper which is planned in the near future. However, I would like to insert a word of caution. The alloys described in this paper are still very much in the laboratory stage. There still remains the quite vexing problem of property stability at slightly elevated temperatures which must be solved before the properties quoted can be effectively utilized. These alloys are extremely interesting and I am confident that the problems can be solved. However, the present existence of those problems must not be overlooked. I have one question with regard to the work-hardening test. If the work harden-ability of magnesium is compared to aluminum using a more standard test such as the Meyer Analysis the magnesium is found to work harden the more rapidly. Is the test developed for this work truly a work-hardening test or a measure of something else ? J. H. JACKSON (authors' reply)—I am sure we appreciate the comments of Mr. Busk and we are pleased that the Dow Chemical Co. has also undertaken work in this field. It is a big field. We, of course, are continuing our research for the Navy Bureau of Aeronautics, since, as clearly shown in the paper, the alloys are not completely developed. With regard to Mr. Busk's comments on the relative work-hardenability of aluminum and magnesium, the comparison we cited in the paper was intended merely to show that the results obtained by our method of testing were independent of the yield strength of the materials. We believe that this test method afforded a rough indication of the work-hardenability of the magnesium-lithium base alloys. It is not known whether this method affords greater or less accuracy than the Meyer Process, which is based upon a hardness-test impression. It is quite possible, since work-hardenability is a function of metal purity, that our results, obtained for commercial aluminum and magnesium, would be different if high-purity metals had been used. A. C. LOONAM—Lithium has some very interesting effects on magnesium. The paper showed that even small percentages increased ductility. These small amounts changed the axial ratio of the hexagonal magnesium from 1.624 in the pure metal to 1.606 in the saturated alpha solution, a value close to that of titanium, which has a ratio of 1.601. You will recall an article in the January, 1949, issue of the Journal of Metals where it was stated that titanium can be cold-rolled over 90 pct without any significant edge cracking. At 4.9 or 5 pct lithium, a change begins in crystal structure—from a hexagonal close packed to body centered cubic. There are two phases over a short range of lithium content, but at 10 pct the structure becomes completely cubic. The melting points of alloys in this range of lithium content are relatively high. Alloys even up to the six ratio have melting points above 500°C; this represents a relatively small reduction in melting point from pure magnesium itself. The magnesium-lithium system has a number of very interesting characteristics. This is only a very small part of the story. J. H. JACKSON—I would like to remind you that Mr. Loonam is one of the authors of this paper, and the fact is that this work is based on many of his ideas. I am sure we appreciate his additional comments in this discussion. R. LEITER*—I am interested in Fig 19 in which Mr. Jackson compares

Jan 1, 1950

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By G. A. Deitz, J. Halpren

The kinetics of dissolution of silver in cyanide solutions under oxygen pressure have been investigated over a wide range of conditions with a view to establishing the reactions involved and the factors which influence the rate. The results indicate that the rate is determined principally by the transport of reactants in solution to the silver surface. The thermodynamic features of the reaction with particular reference to the influence of pH and CN- are also discussed and summarized in the form of potential-pH diagrams. METALLIC silver is readily attacked and dissolved by cyanide solutions in the presence of oxygen. This reaction has long been recognized and extensively applied1 in the well-known cyanide process for the extraction of silver from its ores. While this process has been subjected in the past to a number of investigations2,3 both of a practical and fundamental nature, some features relating to the chemistry of the reactions involved, the role of oxygen, the nature of the rate-controlling step, and the effects of pH and certain reagents such as lime, are still not fully understood. It was felt that this situation justified a further investigation of the reaction, made with a view to obtaining a better understanding of its kinetics and mechanism. In the present investigation rate curves for the dissolution of silver were determined over an extensive range of carefully controlled reaction conditions. By carrying out the reactions in a pressure vessel, the partial pressure of oxygen, and hence its concentration, could be varied widely. The influence on the reaction of other variables including temperature, pH, and the concentrations of cyanide, peroxide, and other salts was also examined. The results of these kinetic studies are presented and discussed in this paper, together with a summary of available thermodynamic information relating to the possible reactions which can accompany the attack on silver by aqueous solutions of cyanide and oxygen. Chemistry and Thermodynamics of the Reaction The chemistry of the reactions of gold and silver with aqueous cyanide solutions has been the subject of several recent reviews.'." It has been proposed' that the following reaction occurs when silver dissolves in cyanide solutions in the presence of oxygen: 4Ag + 8CN- + 0, + 2H.0 -t 4Ag(CN); + 40H- [la] An equation of this form, for the corresponding dissolution of gold, was first suggested by Elsner." Bodlaender5 proposed a similar overall reaction, but suggested that it took place in two steps, 2Ag + 4CN- + O2 + 2H2O ? 2Ag(CN),- + 2OH- + H2O2 [2a] followed by 2Ag + 4CN- + H2O2? 2Ag(CN); + 20H- [3a] On the other hand, Janin- suggested that the dissolution of gold can occur with the liberation of hydrogen, rather than by reduction of oxygen. The corresponding equation for the dissolution of silver is 2Ag + 4CN- + 2H20 -t 2Ag(CN); + 20H + H2 [4a] All these reactions represent oxidation-reduction processes and may be resolved into the corresponding separate oxidation and reduction components. The oxidation step involves the formation of the argentocyanide ion and is the same for all the reactions, i.e., Ag + 2CN? Ag(CN)2 + e [51 However, reactions la, 2a, 3a, and 4a differ in the nature of the reduction steps which are, respectively, O2 + 2H2O + 4e ? 4OH- [lb] O2 + 2H2O + 2e ? H2O2 + 2OH- [2b] H2O2 + 2e ? 2OH- [3b] 2H2O + 2e? 20H- + H2 [4b]

Jan 1, 1954

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By H. Margolin, A. Coucoulas

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKcll radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuAl2, and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band.1,4 Europium in EuAl2 appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref. 1. One of the other phases was identified as Co5Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acia Cryst., 1959, vol. 12, p. '162. A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently hiher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1 week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by