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By James Terry Duce

The symposium on production for the year 1940 contains few papers on the foreign situation. It is probable that the foreign part of next year's symposium will be even shorter. This is due to rigid censorship in various countries, as the question of the volume of petroleum supplies has become one of great strategic importance. This is even more true than in the last war, owing to greater mechanization of armies. 'It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts from Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not de-terminable frod data available to the author, please inserty; in spaces where the proper entries are determinable by the author, make such entries. y implies a hope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In sucli cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved') and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when

Jan 1, 1941

By A. H. Larson, R. J. McClincy

ALTHOUGH arsenic has a very high vapor pressure and vacuum distillation appears to be a likely method for its removal from lead, the published literature contains virtually no information concerning the vacuum removal of arsenic from lead. Caldwell, Spendlove, and St. Claire1 mention arsenic in their investigation of the removal of volatile metals from lead by vacuum distillation. They do not, however, give any data for arsenic removal or refer to any actual experimental work involving arsenic dissolved in lead. Moriyama, Kozuka, and Miura2 have determined the activity of arsenic in dilute As-Pb alloys in the temperature range from 450" to 600°C using a closed galvanic cell. They found that the activities of both arsenic and lead showed a positive deviation from ideality at 600°C. In view of the lack of experimental data regarding the vaporization of arsenic from As-Pb alloys, a limited vapor pressure study was made on liquid alloys containing from 0.5 to 3.3 wt pct As in lead at 703°C. The pressure of As4(v) above the alloys studied was determined from weight-loss data collected by means of the inert-gas saturation method. The experimental apparatus and procedure used were similar to that discussed by Alcock and Hooper9 with modifications as described by the authors., The technique involved was one of passing a known volume of inert gas over the alloy to be studied in a known amount of time and determining the loss in weight of the sample. Because of the low vapor pressure of lead at 703"C, the observed weight loss could be attributed solely to the vaporization of arsenic as the tetratomic molecule AS43 Measurements of the apparent vapor pressure were repeated at different inert-gas flow rates until from three to five values were obtained which were independent of inert-gas flow rate. This value of the apparent vapor pressure was taken to be the equilibrium vapor pressure of the alloy under consideration. The vapor pressures measured in this investigation have been converted to the activities of arsenic in As-Pb alloys, Table I, by use of the data compiled by Elliott and Gleiser5 for the vapor pressure of pure arsenic. The standard state for arsenic was chosen as the pure, hypothetical, supercooled liquid. The activity of arsenic was calculated from the fourth root of the ratio PAs,/PAS,. The low magnitude of the vapor pressures given in Table I explains the difficulty en- countered by earlier workers in successfully vacuum distilling arsenic from very dilute As-Pb alloys. The data shown in Fig. 1 indicate that the As-Pb system behaves ideally. The apparent outlier represented by the alloy containing 1.43 mol pct As is a result of the fact that the pressure of As, above the alloy was barely detectable by the experimental procedure used in this investigation. Because of this, the apparent vapor pressure determined for this alloy could be in considerable error. Moriyama, Kozuka, and ~iura' have reported that arsenic shows a positive deviation from ideality in dilute solution in lead. However, details of their results have not been made available. This research was made possible by a grant from the National Science Foundation (GK-196) for which the authors are very appreciative.

Jan 1, 1970

By James Kemp

PostScript to a paper presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 129 to 154. The writer looked over the quarry with care in the search for fossils, having in mind shells or corals of fairly large size. In the brilliant summer sunshine, none were observed on the glaring white ledges. The impression was gained that none were present and the statement to this effect was made in the edition of this paper published in the Bulletin' of the Institute for February, 1915, p. 136. On closer examination in the laboratory it has been discovered that the limestone itself is made up of minute organisms, which are clearly revealed by microscopic examination of thin sections. The principal component of the rock is a small foraminifer, 0.1 to 0.3 in. (2.5 to 7 mm.), of the genus Orbitoides, presumably an Oligocenic form. Figs. 1 and 2. illustrate it. The accompanying description has been kindly summarized by Marjorie O'Connell, M. A., Curator in Paleontology in Columbia University, who first detected the evidences of organisms in the rock. Orbitoides kempi O'CONNELL N. SP.1 The foraminiferan which makes up the Seboruco limestone is an Orbitoides of a Species new to North America. The only Orbitoides heretofore described from this country is 0. mantelli from the lower Oligocenic of the Gulf States. This form from Cuba, then, so different in all of its characteristics from the 0. mantelli, is of great interest as perhaps forming a basis of correlation over wide areas. The most closely related Species is 0. dispansa Sowerby, which occurs in the Nummulite limestone of the Eocenic of the Bavarian . Alps, in the Priabona beds of the lower Oligocenic of Massano, and elsewhere in Italy, as described by Gümbel.2 The age of the limestone in Cuba would thus Seem to be of upper Eocenic or lower Oligocenic age, probably the latter. The fossil has the form of a sphere Surrounded by a wavy rim of horizontal extent, the whole resembling two flat-brimmed, round-crowned hats placed base to base. The total extent of the Shell ranges up to 7+ mm., while the thickness of the central sphere is 2.5 mm. in one of the largest individuals. Like all of the other Species of Orbitoides, this form begins with a Single layer of chambers which multiply in one plane and assume a circular outline; but it is in the subsequent growth that the distinguishing specific characters appear, for the chambers at the central portion of the shell increase more rapidly than do those near the periphery and in consequence a Swelling is produced which finally gives the Spherical form which is so characteristic. The rim, on the other hand, shows little chamber-increase and remains thin. This is clearly Shown in the sections figured, where the central row of larger chambers forms the equatorial zone. Radiating from this row, in section, there appear, a number of solid cones alternating with broad reticulated ones. The solid cones mark the more dense structure forming the walls surrounding the reticulated or chambered cones. These appear upon the Surface as distinct pits, whereas the solid part appears as raised walls.

Jan 7, 1915

By G. S. Upadhyaya, A. D. McQuillan

HERE would appear to be a simple relationship between the group number in the periodic table of the early transition metals and the maximum amount of hydrogen which they can absorb.' Thus group IIIA metals (Sc, Y, and La) yield a trihydride in which the metal atoms are on a fcc lattice and the hydrogen atoms occupy both tetrahedral and octahedral interstices. Group IVA metals (Ti, Zr, Hf) form dihy-drides in which the metal atoms are on either a fct or cubic lattice, but in which only the tetrahedral interstices are occupied by hydrogen atoms. In group VA (V, Nb, Ta) the hydrogen-saturated metal attains a composition slightly below that of a monohydride under normal conditions. Finally the metals of group VIA (Cr, Mo, W) do not dissolve appreciable quantities of hydrogen. The manner in which hydrogen solubility disappears on alloying a group VA metal with one from group VIA has previously been investigated.2 It is necessary, in order to obtain a general picture of the reactions of alloys of the early transition metals with hydrogen, to examine a system containing metals from groups IVA and VA in which there must be a change from a fcc to a bee hydride phase. The system chosen for investigation was the pseudobinary system between titanium hydride and niobium hydride. Metallic alloys were prepared by melting iodide-prepared titanium with zone-refined niobium in an argon-atmosphere are-furnace. To ensure homogeneity each alloy was cold-swaged and then heated at 1250°C in a high-vacuum furnace until metallo-graphic examination confirmed its complete homogeneity. Small weighed specimens of the alloys were charged with hydrogen using gaseous hydrogen generated by heating titanium hydride. The apparatus has been described elsewhere.3 Throughout the charging process the hydrogen pressure was kept at about 1 atm while the specimen, initially at 800 °C, was slowly cooled to 150°C over a period of days. The total amount of hydrogen absorbed by each specimen and the room-temperature crystal structure of the hydride powders were determined. The X-ray investigation indicates that the fee hydride phase arises from alloys extending in composition from titanium to 67 at. pct Nb. After a two-phase field lying between 67 and 74 at. pct Nb in which the fee and bee hydrides coexist, all alloys richer in niobium yield a distorted bee hydride. Data derived from parameter measurements are presented in Fig. 1. The atomic volume per metal atom has been plotted against the composition of the initial metallic alloy in order to facilitate comparison of the effects of hydrogen addition in the two phases of different crystal structure. The amount of hydrogen absorbed by each alloy at saturation in terms of the hydrogen to metal ratio and alloy composition is given in Fig. 2. Over the whole range of the fee hydride phase the hydrogen content remains constant, while in the distorted body-centred hydride phase, the hydrogen content increases with increasing titanium content reaching a hydrogen/metal ratio of 1.4 at the boundary of the two-phase region. It seems likely, therefore, that the maximum hydrogen content of the fee hydrides is limited to a hydrogen/metal ratio of 2 because hydrogen atoms

Jan 1, 1962

By Alistair Frame

INTRODUCTION In April 1988 discussions were about to start with BP on the possibility of buying their- mineral interests, and it took a long time to arrange a deal. I will talk about RTZ without BP Minerals, look at the new RTZ with BP Minerals, discuss the outlook for metal prices, and review the problems in South Africa and develop the case against sanctions on that country. RTZAT THE END OF 1988 Late in 1987, after completing a worldwide review of our strategic thrust, we decided: 1. That the business focus would be to remain a major diversified natural resource group with interests in related industries. 2. To divest non-core and low growth businesses. 3. To develop a logical acquisition plan. 4. To emphasise organic growth and, most importantly, to enhance shareholders' wealth by capital increase and a progressive dividend policy. Subsequently, we concluded that we should sell our oil and gas business and dispose of several assets for which we saw little growth potential. The disposal programme raised some U.S.$ 1,600 million, representing a significant capital gain on our various investments. All transactions were carried out by our small Head Office staff in London, without the help of merchant banks and lawyers, and we were able to safeguard the employment of our staff in all these operations. The most interesting disposal was of our oil and gas interests. Before the 1987 strategic review, we had ambitions to develop our oil and gas interests and to become the leader in the second division of European oil companies. Our interests, which were purely in exploration and production of oil and gas, consisted of the 100% owned RTZ Oil and Gas company, and 29% of LASMO, a publicly quoted U.K. oil and gas company with extensive worldwide interests. LASMO, in turn, owned 25% of Enterprise Oil, one of the more successful of the North Sea oil exploration and production companies. Prior to the end of 1987, our intention was to acquire control of both LASMO and Enterprise. However, when we evaluated the net asset value of these two companies based on our oil price assumptions, which were pessimistic for the next five years or so, we concluded that they were both trading in the market at significant premiums. This, taken with the additional premium required for acquisition and the high cost of exploration, led us to conclude that, since funds could undoubtedly be used to better effect, we should sell our interests. Turning to the other major achievements in 1988, we commissioned, and built up to design levels in a very short period of time, the Morro do Ouro gold mine in Brazil. This mine reached its design output of 100,000 ounces of gold per year within three months of start-up, which was on time and under budget. We are now considering a possible expansion of this property. In South America, Utah International, Mitsubishi and RTZ arranged non-recourse finance, with post completion guarantees, for the giant Escondida Project in Northern Chile. Financing came from a group of banks in Japan, Germany and Finland -- the countries to which most of the concentrates will be sold -- and from the LEC. The average output of the mine for the

Jan 1, 1990

By J. M. Campbell, T. S. Buxton

The most widely used methods of predicting the volumetric properties of gas are based on the principle of corresponding states, which asserts that the compressibility factor is a universal function of reduced temperature and pressure. Previous studies have shown that the acentric factor, as proposed by Pitzer, l is an important addition to reduced pressure and reduced temperature as factors affecting the compressibility factor. Results of this study indicate that, if the pseudocritical temperature and pressure used to determine the reduced conditions are adequately predicted, characterization of natural gas-carbon dioxide mixtures with the acentric factor will allow reliable determination of the compressibility factor. Comparisons of predicted and experimental compressibility factors have shown that the pseudo-critical constant rules of Stewart, Burkhardt and Voo 2 are satisfactory for hydrocarbon mixtures. However, these rules fail to predict the pseduo-critical constants for hydrocarbon-carbon dioxide mixtures. Based on graphically determined pseudocritical temperatures for binary hydrocarbon-carbon dioxide mixtures, a correlation which gives the required correction to the Stewart, Burkhardt and Voo rules was prepared and a compressibility factor prediction technique was proposed. To test the proposed technique, compressibility factors for live mixtures of methane, carbon dioxide and either ethne or propane were experimentally determined at 100, 130 and 160F and pressures up to 7,026 psia. The predicted and experimental compressibility factors for these live mixtures had an average absolute deviation of 0.55 percent. INTRODUCTION Two-parameter generalized correlations based on the principle of corresponding states (PCS) are presently available for reliably predicting the compressibility factor of lean natural gas, i.e., natural gas with low concentrations of hydrocarbons heavier than methane. When these same correlations are used for mixtures of natural gas and carbon dioxide, large deviations between actual and predicted compressibility factors are observed. This study was undertaken to provide a means for accurately predicting the compressibility factor for such mixtures. In the past, two avenues of approach have been employed to extend the applicability of the PCS. The first has been to introduce additional parameters. The second has been to develop combination rules for predicting pseudocritical constants which do not suffer from the limitations of the commonly used molal average constants. In this study, both of these approaches have been considered and employed to arrive at a method for predicting the compressibility factor of mixtures of hydrocarbons and carbon dioxide. SELECTION OF A THIRD PARAMETER Failure of the original PCS to predict the compressibility factor for all pure gases, regardless of their mass, shape or polar moment, has led to the introduction of additional parameters into the PCS. Parameters have been introduced to correct for quantum deviations,3-5 non-spherical or globular shapes6-9 and for polar moments.8-12 In addition to these parameters which are based on some microscopic property and intended to correct for some specific cause of deviation, more general parameters based on some bulk property have also been introduced.1913-16 To use additional parameters to correct for each of the possible causes of deviation among the individual constituents of a gas mixture would require a rather complex form of the PCS. To maintain the PCS in as simple a form as possible, it is more desirable to have a single third parameter which is based on some bulk property influenced by several of the factors causing deviations. The third parameter selected for use in this study is a factor originally proposed by Pitzer.9

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation's supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation's need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By A. M. Gaudin, C. S. Chang

Adsorption was measured for barium ion and laurate radical, using radioactively marked agents, over wide range of concentrations. Laurate adsorbed in absence of barium fails to float. With barium, flotation-effective laurate coating needs not exceed 5 pct of monolayer. Barium adsorption then is several fold larger. No barium laurate coating is obtained. IN general, fatty acids or their alkali salts do not cause clean quartz to float. However, the presence of multivalent ions, such as the alkaline-earth metal ions and heavy-metal ions, can activate quartz and thus make it respond to soap flotation. The mechanism of activation and soap flotation of quartz has been studied.'-' The problem was attacked by making flotation tests rather than by careful adsorption measurements on suspensions of ground quartz in solutions containing the activator and the collector. Attempts have been made to determine the adsorption of barium ion and calcium ion on quartz. The results have only qualitative value as the analytical methods were not adequately precise. Artificial radioactivity and progress in radioactivity detection have introduced a new analytical tool, which can have a sensitivity several orders of magnitude greater than that of other methods."-" In the experimental work described in this paper the radioactive tracers, barium 140 and carbon 14, were employed. Lauric acid was synthesized, having a radioactive carbon atom and was used with Ba" to study the adsorption of barium and laurate ions from aqueous solution on ground quartz. Flotation tests, using the vacuum flotation technique,' were run in conjunction with the adsorption experiments. The object of this investigation was to understand better the reaction mechanism of barium activation and soap flotation of quartz. Methods and Materials Quartz Sample Preparation: Lumps of hand-picked quartz, washed free of stains, were reduced in size to —20 mesh in laboratory crushers. The product was boiled in concentrated hydrochloric acid to remove the abraded iron. The cleaned product then was ground dry in a laboratory porcelain mill, using siliceous pebbles, to pass through a 200 mesh screen. The ground product was deslimed by sedimentation at 37 microns. This —200 mesh +400 mesh material was subjected again to boiling with concentrated hydrochloric acid, followed by washing with distilled water and further desliming. The cycle was repeated until no trace of iron could be detected in the wash liquor. During the final washing, the pH of the wash water was checked to insure the complete removal of the acid from the mineral. The quartz then was rinsed with conductivity water. The resulting product was dried in a drying oven and stored in mason jars. The impurities (spectrographic) were as follows: Al, 0.01 to 0.001 pct; Li, Mg, Mn, Na, each less than 0.001 pct; Fe and Cu not detected. The specific surface of the quartz sample was determined by the krypton gas adsorption method.' The average of two measurements was 881 sq cm per g. The calculated specific surface for 37/74-micron quartz particles, using a surface factor of 1.96; is 900 sq cm per g. This is in good agreement with the measured value of 881 sq cm per g. Beta-Counting Method: The radioactive isotope of barium used in the experimental work was barium 140. It has a sufficiently long half-life, 12.8 days, emits high-energy beta particles (up to 1.0

Jan 1, 1953

By H. B. Heller, T. J. LaChapelle

Phosphorus nitride has been used as a diffusant for introducing phosphorus into silicon under various conditions. It has a temperature -dependent rate of decomposition beginning in the 500°C range, increasing very rapidly above 1000 C, producing gas -eous phosphorus and nitrogen. Best control was obtained with a two-temperature arrangement, with silicon at the proper higher diffusion temperature. It is an easier compound to use than the usual P2O5 because it is nonhygroscopic and yields temperature-controlled surface concentrations together with excellent final surfaces. Surface doping nearly as high as that produced by phosphorus pentoxide has been observed for sources at 850" to 900°C. Reproducible high sheet resistances were obtained by using slow flow rates (1 linear in. per min) and staggered-baffle gas mixing with the nitride at 550°C. Both inert gas (argon, nitrogen) and oxidizing ambients have been examined. Oxygen reacts to produce anhydrous P2O5, consuming the source at a rapid rate. Nitrogen, except for short diffusion times, suppressed the dissociation reaction and sometimes produced inferior surfaces. Argon appears to be a more useful ambient. PHOSPHORUS is a common impurity atom which may be introduced into a semiconductor lattice to create a p-n junction or an nn contact region. Various investigators1-4 have described techniques which can be used with either elemental phosphorus or certain of its compounds. This paper discusses a newly available compound of phosphorus, phos- some processes silicon wafers are precoated with a phosphate glass which acts as the doping source. Although a nonoxidizing form like elemental phosphorus or a phosphine can be used, most diffusion methods usually involve the use of phosphorus pentoxide. Because of the rapid volatility of this compound, a two-step process is often used, combining a gaseous deposition to introduce a predetermined quantity of phosphorus into the silicon with a later redistribution to obtain the desired distribution and surface concentration. Such a process usually involves predepositing phosphorus at surface concentrations greater than 1020 cm-'. At such doping levels the phosphorus-diffusion coefficient appears to be strongly concentration-dependent.596 Distribution profiles5'9 for these high concentrations of phosphorus do not follow Fick's laws, having extended subsurface regions which appear electrically to be nearly uniformly doped with ionized impurity atoms. Radioactive-tracer experiments also show near-surface anomalies in the distribution profile. Additionally, it has been shown1' that the introduction of very high surface concentrations of impurity atoms into silicon (a step necessitated by the subsequent lowering of concentration during the redistribution) creates dislocations, even in material having no dislocations originally. For device fabrication the use of oxide masking introduces certain difficulties and limitations.7'8 The standard practice of using phosphorus pentoxide as an impurity source adds other problems to these because of the speed and ease with which this compound reacts with moisture present in any gas in contact with it. In fact, P2O5 is one of the fastest and most effective drying agents for gases. Because it is such an excellent desiccant, completely anhydrous phosphorus pentoxide is difficult to obtain and is even more difficult to keep dry. Adequately dry gloved boxes must be used for storage and transfer of the chemical. The presence of even traces of moisture will cause formation of phosphoric acids which, during the high-temperature diffusion, results in polyphosphoric acids of variable composition. Such reaction by-products end up as gradually accumulating viscous fluids in the cooler parts of the diffusion furnace. The calculation of the final solute distribution for

Jan 1, 1964

By C. Perez-Rosales

A simplified method for evaluating specific surface of porous media is described. The theory takes as its point of departure a previous statistical method. Due to its simplicity, it is considered that the proposed method has certain advantages over methods currently used. By making some simplifications, the procedure for estimating specific surface is reduced to superposing, on an enlarged reproduction of a section of the sample to be analyzed, an evenly spaced grid and counting the number of intersections of the grid lines with the perimeter of pores. An indirect test of the theory is presented and the advantages of the method are discussed. INTRODUCTION The specific surface of a porous medium, defined as the surface area of the pores per unit bulk volume, is an important parameter with regard to flow of fluids through porous materials. In particular, it has long been recognized that specific surface is closely related to permeability. Since the internal surface of any porous material is extremely complex, the measurement of specific surface can only be accomplished by indirect means. It is considered that the best method' in current use for determining specific surface is the statistical method of Chalkley, Cornfield and Parka who originally applied it for estimating volume-surface ratios of morphologic components, such as cells or nuclei. This method will be outlined later. A method which has been used extensively in determining specific surface is based on the adsorption of a vapor by the internal surface of porous media. However, this method does not yield the surface pertinent to fluid flow, since it includes the tiny molecular interstices which do not influence the permeability of the porous material.' This method has been employed by Brooks and Purcell measure internal surface area of sedimentary rocks. The Kozeny equation, which relates the specific surface to the permeability of a porous medium, has found wide use in determination of specific surface. However, the KOzeny equation is not strictly correct. Large discrepancies have been found between theory and experiments.' Consequently. the specific surface estimated by this method is subject to serious uncertainties. Finally, there are other methods for specific surface measurements which are based upon a variety of physical and chemical properties: the heat conduction by a gas, ionic adsorption phenomena and direct chemical reactions of the surface with other substances. This paper describes a simplified statistical method for determining specific surface of porous materials. It is considered that, due to its simplicity, it has certain advantages over the methods presently used. For its validity, it is required that the porous structure of the material under study be of a spatially random nature. This is not a serious limitation since the naturally occurring porous media have this characteristic. THEORY The method proposed in this paper takes as its point of departure the interesting result obtained by Chalkley et al The method shows that if a line of length r is dropped repeatedly at random over a section of a porous medium, and counts are made of the number of times the two end points fall within pore areas (denoted by h for "hits") and the number of times the line intersects the perimeter of pores (denoted by c for "cuts"), then in a very large number of throws where S is the internal surface of the sample (surface of pores) and V, the volume of the pores (Fig. 1). Since the specific surface S, and the porosity 4 are given, respectively, by S. = Sl V, and 4 = V,l V,, where V, is the total volume of the sample, it follows from Eq. 1

By P. E. Baker

Approximate solutions are presented for the heat-flow equations in a loss-free linear system with a moving source and with heat transfer by convection and conduction, representing in situ combustion in an oil reservoir. The rate of heat generation and the velocity vf of the source (flame front) are assumed constant. A cold front or convection front caused by the cooling effect of in-jected air develops behind the flame front and moves with velocity vc, which is determined by the thermal properties of the air and rock. Because of thermal conduction the fronts are not sharp; i.e., they do not represent temperature discontinuities. The following solutions apply after a sufficiently long time. where Q is heat generated per unit volume of formation, k is thermal conductivity, CF is volumetric heat capacity, a is thermal diffusivity, and subscripts 1 and 2 refer to values behind and ahead of the flame front, respectively. The parameter CF2 is contained in v . Te is initial reservoir temper- . C2 e ature and air-injection temperature. Other mathematically possible solutions are presented. The different solutions result from the use of different values for various physical parameters. The solution just presented is thought to be most commonly applicable. INTRODUCTION In this paper, approximate analytical expressions are derived for the temperature profile developed in the underground combustion method of oil recovery. A qualitative description of the process may be found in a paper by Tadema.1 The flame front is regarded as a moving source with a constant rate of heat generation. Heat transfer is by conduction and convection. Previous publications, of which a few are cited here, 2-5 have also attacked this problem and have presented solutions pertaining to different methods of approximating or idealizing the process studied. The present paper also treats an idealized case: linear flow is assumed for heat and fluids, and vaporization and condensation effects are neglected. The results obtained are similar to those derived by Bailey and Larkin,3 but are obtained by an entirely different procedure. The method used here should give considerably greater insight into the physics of the in situ combustion process. Four types of cases are considered, distinguished by thermal and fluid-flow properties of the system. A constant rate of heat generation and constant rate of flame-front advance are assumed. Flame-front temperature is determined for each case using a heat balance which involves the entire temperature profile. The applicability of the different solutions to real systems is discussed after they are all presented. Again, this is done for the purpose of understanding better the physics of the process. Consideration of the nonapplicable solutions and of the reasons for their not applying is significant. In a paper by Cooperman,4 the only case solved is one considered here as not applicable. Fluid flow, as such (pressures, saturations, oil recovery, etc.), is not treated. This subject has been covered in a paper by Wilson, et al.6 Also, we are not concerned with requirements for continuance of the process; we only attempt to determine the temperature history for cases where the process has continued for some time. PHYSICAL SYSTEM AND APPROACH TO PROBLEM A linear flow (heat and fluid) system is assumed and the x-axis is taken parallel to the flow direction. The combustion zone (flame front) is vertical,

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By J. R. Hornaday, A. E. Morris, N. A. Parlee, D. C. Carmichael

Rates of absorption and effusion of hydrogen in solid iron were measurede by a Sieverts type of apparatus. With clean a iron these rates are diffusion controlled down to 420°C and are represented by the equation D = 6.70 x e-'100' crn2 sec-I Certain surface impurities can affect these rates at all temper-atuves. Thin oxide films lower, the apparent diffusivity of annealed iron markedly. Cold-worked iron (75 pct) annealed at 430°C has practically the same solubility and diffusivity as anealed iron. THE mechanism of absorption and evolution of hydrogen in solid iron alloys is not fully understood despite the large number of investigations on the subject. While there appear to be many instances of simple solid-state diffusion control of rate, there are many cases where investigators have either concluded that surface reactions are rate controlling or that some "nondiffusible" hydrogen resides in discontinuities. The purposes of this research were 1) to develop a sound method for studying this absorption and evolution behavior, 2) to examine it in pure annealed iron, and 3) to determine the effects of important variables, such as cold work, surface condition, and composition. This paper relates the progress toward these objectives. Much of the present knowledge of the movement of hydrogen through iron alloys comes from permeability studies which involve the measurement of the rate of passage (under steady state conditions) through membranes of the order of 1 mm in thickness. This method is open to question on various grounds. If surface reactions are involved, two different surfaces operating under two different conditions must be considered. The presence of defects in the membrane even of microscopic dimensions may lead to erroneous results. A few people have studied evolution of hydrogen into vacuum, under carefully controlled (unsteady state) conditions, and some of the best diffusivity data come from these sources. Most of these methods measure rates of evolution only and thus do not make a rigorous test for reversibility of behavior. It appeared that an "unsteady state" method that would permit the measurement of both rates of evolution and absorption under controlled temperature, pressure, and other conditions would offer several advantages. Accordingly the modified Sieverts apparatus described below was designed and built. APPARATUS This apparatus is shown in Fig. 1. The sample bulb is detailed in Fig. 2. Hydrogen of 99.5 pct purity and argon of 99.99 pct purity were used. The hydrogen was deoxidized and dried by means of a Deoxo unit followed by a "Dri-erite" tower. The argon was only dried. The gas burette was graduated in tenths of a cubic centimeter, and, with the aid of a travelling magnifier, readings could be estimated to the nearest 0.01 cc. The level of mercury in the burette was adjusted by means of a leveling bulb operated by a fine screw adjustment. An electrical system, consisting of two slightly separated platinum electrodes inserted in one leg of the manometer and a small light bulb was used to obtain rapid accurate adjustment of the pressure. The capillary tubing of the Vycor sample bulb was 3 mm bore as was all tubing back to the gas burette. The samples were discs made from vacuum-melted Ferrovac-E iron of greater than

Jan 1, 1961

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and It is now thought1' that the "{0,1,13)" habit reported for the Fe-Ni-C alloys'' is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove. The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics and reduce to the unit tensors and j so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel's paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel's attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,', y uranium, and perhaps zirconim.' The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors' reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato's value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,'' and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener's predictions.28 We have no quarrel with Hagel's placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By O. E. Palasvirta

Close examination of most so-called n.eu processes in mineral dressing reveals that they were conceived and developed a long time ago. High-intensity magnetic separation is no exception. Although its application in iron ore beneficiation seems new, in Germany the process has been commercially successful for almost two decades. High-intensity separators have long been standard equipment in the glass sand industry; they have also been used in concentrating some of the more unusual para-magnetic minerals. The basic features of an induced-rotor, high-intensity magnetic separator were described by Desire Korda in Paris in 1905,' and many patents have since been issued for improvements on the original design. Fig. 1 shows the basic design of an induced-rotor separator. Several U. S. manufacturers have been supplying induced-rotor separators for many years, but these are all devices of relatively low capacity, not suitable for treating such low-cost commodities as iron ore. On the other hand, two German manufacturers are offering induced-rotor separators of high capacity, both proven in the field. The present investigation was prompted by the apparent success of the German installations and by the discovery of iron ores on this continent which may be amenable to high-intensity separation. The objective was to gain better insight into the underlying principles of separation in a high-intensity field and to use this knowledge in selecting or designing an optimum separator. THEORETICAL CONSIDERATIONS he well known low-intensity magnetic separators are. without exception, of the the magnet type with more or less similar field shapes. It is therefore permissible to speak of their comparative strengths in terms of field intensity alone. However, proper understanding of the high-intensity magnetic separation process requires somewhat deeper analysis of the relationship between the magnetic field and the attractive force. Contrary to a widely held belief, a magnetic field of parallel lines of flux exerts no attractive force on a magnetically susceptible particle, but merely aligns its poles parallel to the lines of flux. On the other hand, a non-uniform field attracts a magnetically susceptible particle in the direction of the converging lines of flux. Thus the force of magnetic attraction varies as the product of the field intensity and the field gradient: dH ds As the induced-rotor magnetic separator is primarily intended for separating feebly magnetic materials, it is important that maximum attraction be attained. For the designer, then, the relationship between the magnetic field and the attractive force has the following implications: 1) Insofar as possible, the separation gap must be saturated with flux. 2) The rotor surface must be shaped to insure maximum convergence of lines of flux toward the rotor. 3) The primary pole face (opposite the rotor, on the other side of the separation gap) must be shaped so that the lines of flux do not diverge from it at any location in the effective separation zone. The actual attractive force of the rotor, and its critical speed, can be calculated as shown by Runo-linna, provided that the true flux density, the field gradient, and the magnetic susceptibility of the mineral can be measured with sufficient accuracy. The irregular shape of the rotor surface makes flux measurements difficult, but it can be done if a suitable gaussmeter is available (see Fig. 2). Calculations by the author, and comparisons with the centrifugal force exerted by the rotor, indicate that the force pinning a hematite particle to the rotor is of the same order of magnitude as the force holding a

Jan 1, 1960

By Stanley L. Lopata, Eric B. Kula

The problem of preferred orientation has been considered in quantitative phase analysis by X-ray diffraction techniques. The average intensity of a diffraction peak can be obtained by integration over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. For rod or wire, where the pole figure shows rotational symmetry, the intensity is measured along a radius of the pole figure. Where no symmetry is present, rotational symmetry is imparted by rapid rotation of the sheet around its surface normal during measurement. These methods are applied to the determination of aus-tenite in an Fe-31 pct Ni rod and Fe-28 pct Ni sheet. X-RAY diffraction techniques are frequently used for quantitatively determining the relative amounts of two or more phases present in a structure.1,2 Briefly, the method requires a measurement of the intensity of a Bragg reflection for each phase. The method is based on the principle that the intensity of a Bragg reflection, IA, is directly proportional to the volume fraction of the given phase present, CA: T KRACA/2µ [1] where K is a constant independent of the diffracting phase, RA can be calculated and depends on the Bragg angle ? and the particular reflection measured, and µ is the linear absorption coefficient of the mixture.' For a mixture of two phases A and B, IA = RAcA [2] IA/IB=RAcA/Rbcb and CA+ CB = 1 [3] This allows the volume fraction of a phase to be calculated directly from the measured integrated intensities of the two phases present. This method is frequently used for quantitatively determining retained austenite in steels, but can be used for the quantitative determination of in titanium alloys, as well as phases in other alloy systems. The intensities are generally measured by diffracting only from planes whose normals are perpendicular to the specimen surface, with the implicit assumption being made that this intensity is typical of reflections from planes whose normals lie at other angles to the surface. If the specimen contains a texture or preferred orientation of the crys- tallographic planes by virtue of previous mechanical working, however, this measured intensity is correct only if the intensity level fortuitously is one times random. Examination of pole figures for actual rolled sheet shows that the intensity level at the center of the figure is seldom at the random level, and can very easily differ by a factor of five or more, leading to a commensurate error in the calculated amount of the phases. Textures have been commonly found in materials which are cold-rolled or recrystallized after cold rolling. This problem is becoming of greater importance since structural materials in use today, such as the high-strength stainless steels, frequently are further strengthened by cold rolling, and hence contain textures. Although high-strength carbon-containing alloy steels generally do not contain textures, some of the newer thermomechani-cal treatments will impart a texture even in these cases. In the case of hexagonal metals, such as titanium, probably every wrought sample will show some anisotropy. Since the standard X-ray techniques are inapplicable in all these cases, there is a clear need for some method of taking this anisotropy into account. The specific problem is to obtain the integrated intensity of a Bragg reflection for each phase, averaged over all orientations of the sample with respect to the X-ray beam. This can be done either by purely mechanical means or by a mathematical averaging. Mechanically, a small spherical speci-

Jan 1, 1965

By W. A. Tiller, D. H. Lane

A simple zone melting technique for investigating the effect of ultrasonic irradiation upon ingot solidification is described. The effect of i) ultrasonic power level, ii) freezing velocity, iii) constant or variable frequency, iv) direction of irradiation, and v) transducer-cozlpling bar joint upon the grain size of type 316 stainless steel have been investigated. The results of this study support the postulate that the ultrasonic vibrations increase the nucleation probability in the layer of liquid adjacent to the freezing interface. In the first paper of this series,l the possible mechanisms whereby ingot structure may be altered by irradiating a solidifying melt with ultrasonic vibrations have been discussed. A new technique for efficiently introducing the ultrasonic energy into the solid-liquid interface region was presented and applied to ingot preparation by the consumable-electrode arc-melting technique. The experimental results support the postulate that the ultrasonic vibrations may refine the ingot structure by increasing the nucleation probability in the zone of liquid adjacent to the solid-liquid interface. The present paper describes the application of the same technique to a relatively simple laboratory-scale zone-melting apparatus. This apparatus is found to be well suited to the detailed study of ultrasonic technology in this area and allows one to determine, in particular, the minimum ultrasonic power level needed to produce a certain grain size in a particular material. The results of this study support the nucleation mechanism for grain refinement, but do not provide any deeper insight into the specific nucleation mechanism responsible for the effect. EXPERIMENT The apparatus used in these experiments is shown in Fig. 1 and illustrated schematically in Fig. 2. The material to be studied, type 316 stainless steel, was in the form of a 3/4-in. sq bar 30 in. long. This bar was placed in a square open-topped mold with open ends made from high-purity graphite coated with a flame-sprayed Al2O3, skin. Surrounding the crucible was a molybdenum susceptor with 3/8-in. diam holes spaced at 1-in. intervals along its length to serve as sight ports. A tapered transducer horn was brazed to one end of the specimen. The entire assemblage was enclosed in a quartz tube, the transducer itself projecting out one end and resting in a cooling tank. A vacuum seal between the coupling bar and the end plate enclosed one end. A similar plate and seal enclosed the other end. The system is gas tight and can be operated under vacuum or an inert atmosphere. For these experiments, flowing argon at 15 in. of Hg pressure was used. The heat source for melting the stainless steel specimen was a 2-in. long 3-kc induction coil placed around the quartz tube; this source heated the susceptor, inductively melting about a 3-in. zone of the sample by radiation. To move the molten zone at a specified rate, the induction coil was moved down the tube at this rate with the aid of a simple pulling device. Thus, the sample could be irradiated at varying ultrasonic frequencies and power levels and could be solidified at varying rates. The power input to the transducer was measured using a "John Fluke Model 120 VAW-Meter." 1 The power delivered to the interface region is probably only about 50 pct of that measured on the VAW-meter. In a typical run, when the ultrasonic power was turned on, the interface of the molten zone closest

Jan 1, 1961

By Granville S. Borden

MANY complaints have been filed by mine prospectors, explorers and producers about inequities in mining taxation. They have insisted upon improvement, and in the past 35 years there has been some progress. Many of the best taxation provisions made to date are those contained in the Revenue Act of 1951. Mining economics presents special problems, a fact even recognized by many textbooks. Certain provisions have been made to take care of mining taxation rights, but these have been made by Congressional act and do not represent basic, constitutional, guarantees. Despite special provision, in the form of depletion allowances, there remain injustices. The industry faces the problem of gaining adequate income tax allowances for exploration and development expenditures, operating losses, and bonus and subsidy payments. Problems in mine taxation arose soon after the adoption of the 16th Amendment. This amendment gave Congress the power to impose income taxes. Supreme Court decisions against a number of mining companies held that Congress, under its power to tax income, could tax net operating revenue before depletion allowance was deducted. The court also ruled that the right to deduct depletion is a matter of Congressional permission. There is no statute provision permitting mining stockholders to recover their investment out of dividends while the mine is being operated. The Supreme Court did not recognize that part of mining proceeds are actually amortization of the cost of mineral rights. Both these omissions stem from failure to recognize that by its very nature mining consumes its mineral rights and therefore that a part of gross proceeds are not income but recovery of capital. Suppose a Congress unfriendly to mining interests repeals the provisions that allow deductions for depletion. Under such a situation assume that a corporation buys a mineral deposit for $300,000. They mine the deposit and earn an operating profit of $500,000. At the current rates they would pay a Federal Income tax of in excess of $250,000. This venture results in a loss of $50,000 as shown in the table below. For the example given the absence of depletion provisions in income tax law would turn ore into waste rock, because the word "ore" connotes commercially mineable rock. [ ] In retrospect the conclusion is clear: If the Supreme Court had recognized that a part of mining proceeds represent in reality sales proceeds of mineral rights, then profits derived from such sales would have been taxed at the favorable long-term capital rates, instead of being taxed at the high normal, surtax and excess profits rates. It is a question whether percentage depletion allowances offset this tax situation. History The history of depletion allowances has been one of general improvement. The original act did not include depletion, but an allowance at the rate of 5 pct of gross proceeds was provided in 1913. The Acts of 1916 and 1917 allowed depletion upon cost of property, and in 1918 the law was further changed to permit depletion upon cost, or market value as of date of discovery. In 1932 metal, coal and sulphur properties were permitted to elect depletion in percentages of gross income, limited to 50 pct of net income, in lieu of cost depletion. Shortly thereafter the rule was changed and percentage depletion is now allowable in any case where it is higher than cost depletion. Since 1942 percentage depletion allowances have been extended to cover many nonmetals, and in 1951 the rate for coal mines was increased from 5 to 10 pct of gross income. It is interesting to note that these allowances have been retained, and even

Jan 1, 1952

The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-