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CYRIL STANLEY SMITH, Chairman CARL E. SWARTZ, Past-Chairman ARTHUR PHILLIPS, Vice-Chairman E. E. SCHUMACHER, Vice-Chairman H. A. MALONEY, Treasurer FRANK. T. SISCO, Secretary 9 West 39th Street, New York, N. 1. Executive Committee 1944 1945 WILLIAM C. ELLIS C. S. BARRETT ALAN MORRIS T. A. WRIGHT KENT R. VAN HORN L. L. WYMAN

Jan 1, 1943

By Frank C. Greene

Missouri has had one of the best years in history in the development of gas, the 49 completed gas wells having an average of nearly 1,000,000 cu. ft. initial open flow. Altogether 101 wells were drilled in the western part of the state, from Andrew County on the north to Vernon County on the south. Of these 49 were gas wells (including four old wells drilled deeper) with an initial open flow of 48,850,295 cu. ft., eight were oil wells (including one old well drilled deeper) with an initial capacity of 125 bbl. per day and 44 were dry holes (including five old wells drilled deeper). All the oil wells were in previously discovered pools in Jackson and Cass Counties. The outstanding discovery was a "shoestring" of a sand that is termed the Bartlesville, trending northwest and southeast across townships 48 and 49 N., R. 32 W., in central Jackson County. The sand is believed to be a narrow channel or bar, probably not over 800 ft. wide, lying at a higher horizon than the Bluejacket or true Bartlesville sand. A total of 32 wells with 47,453,080 cu. ft. initial open flow has been completed along the 6 miles of the shoestring. The largest individual well had an open flow of 4,500,000 cu. ft. The depth of these wells ranges from 350 to 635 ft., depending on surface elevation. The rock pressure ranges from 145 to 169 pounds. The Missouri Valley Gas and Oil Co. and Panhandle Eastern Pipe Line Co. have laid pipe lines into the area and most of the wells are now connected. In other parts of Jackson County and in other counties of the state there was very little activity during 1937. Of the 101 completions, 88 were in Jackson County. Cass County had five oil wells and three dry holes, Bates County one dry hole and Vernon County two dry holes. In the northern counties, Andrew and Clinton were represented by one dry hole each. At the end of 1937 drilling and leasing operations were very active and wildcatting promises to feature the coming year.

Jan 1, 1938

By James R. Grage

The lead deposits of Missouri may be divided into three districts, the southwest, middle, and southeast. As too much time would be required to devote a detailed account to each district, only a description of the modes of occurrence of the lead ores in the southeast district will be given. The lead mining region proper of Southeast Missouri is embraced in an area of about twenty-five miles in width by about one hundred in length. The country embraced in this district is very broken, and traversed by ridges from one hundred to three hundred feet; in height, with an occasional knob rising higher. Porphyry forms almost the entire substructure of the region, with here and there outcrops of granite. The crystalline rocks were eroded into ridges and valleys before the deposition of the limestone took place. These porphyries are older than the Silurian limestones, and " belong (according to Pumpelly) to the Archaean (Azoic) formation, of which they may be the youngest member in Missouri. They are the near equivalents, in point of age, to the great iron-bearing rocks of Lake Superior, New Jersey, and Sweden."

By M. Cohen, C. Wagner, J. E. Reynolds

If the total volume of a diffusion couple changes during the diffusion, the measurement of distance becomes ambiguous. Use of distance parameters as suggested by Hartley and Crank is discussed. For small concentration differences, the standard form of Fick's second law is retained with conventional length units and the in- terdiffusion coefficient D. It is shown how D can be calculated from experiments involving large concentration differences and analyzed in terms of distance parameters. 'The merits of incremental diffusion couples involving small concentration differences are emphasized. THE conventional form of Fick's second law for one-dimensional diffusion of component B in a binary solution of A and B is where c, is the concentration of component B; x, the distance; t, the time; and D, the interdiffusion coefficient which may depend on ca. Hartley and Crank' have pointed out that Eq. 1 applies only if the total volume of the diffusion couple does not change during the diffusion process; otherwise, the definition of x becomes ambiguous. No change in total volume takes place if the specific volume of the solution is a linear function of the weight fraction Wb, or if the molar volume is a linear function of the mol fraction N. In some alloys, however, these relationships do not hold, and then it is necessary to introduce a modified measure of distance, 4 in order to retain the general form of Eq. 1. The application of Hartley and Crank's suggestions to diffusion in alloys has been discussed by Wagner.' Relation Between Measure of Distance and Units of Concentration The definition of [ depends on the choice of units for the concentration c,, as follows: 1—If the concentration ca is measured as the weight fraction W, (or weight percent), [ = 5, has to be defined so that equal increments of contain equal increments of mass m of the solution, e.g., dm = pSdx = Sdw [2] where p is the local density of the solution, and S is the cross-sectional area in sq cm which is taken to be constant in this problem of one-dimensional diffusion." * da Silva and Mehla have demonstrated the constancy of the cross-sectional area in the usual type of diffusion couple. However, experiments involving diffusion into thin wires4, 5 may exhibit changes in cross-sectional area, and therefore are excluded from the present treatment. Thus and the unit of is gram per sq cm instead of cm. 2—If the concentration c, is the mol fraction N, must be defined so that equal increments of contain equal numbers of mols of solution, e.g., dn= (S/V)dx= Sd [41 where V is the local molar volume of the solution. Thus dt, = dx/V [51 and the unit of is mols per sq cm. 3—If, as may be advisable in the case of interstitial solutions, the concentration C is measured in terms of the molar ratio of components B and A (c,, = Y, = nH/nA, where n and nl are numbers of mols of B and A), = Y has to be defined so that equal increments of contain equal numbers of mols of A, e.g., dnA= (NAS/V)dx = Sdf [6]

Jan 1, 1954

EVERY mould, of whatever kind it may be, must have an entrance appropriate to the material if it is wished to fill its inner space with bronze or other metal. It is likewise necessary that it have vents, that is, air holes, for there is nothing that is not full of air even though it be called empty. Now, molten bronze is a material that has an immediate effect because of its heaviness, and because it is as hot as fire or even hotter,

Jan 1, 1942

By George W. Maynard

In the biographical notice of Thomas F. Witherbee, published in.Bulletin NO. 32, August, 1909 (p. xxv), it is said that "he is believed to have been the first manager in America to use the chemical laboratory for the purpose of controlling the regular running of the blast-furnace." Since the year is not given, I cannot decide as to Mr. Witherbee's priority; but the statement leads me to contribute a bit of history, showing an early departure from the " rule-of-thumb " blast-furnace work to the employment of a chemist. In the autumn of 1868 the department of mining and metallurgy was established at the Rensselaer Polytechnic Institute. In connection with the assay-department a laboratory was equipped for making general commercial analyses. In January, 1869, Alexander L. Holley, the manager and builder of the Bessemer plant at the Rensselaer Works of John A. Griswold & Co., the first plant erected in the United States under the Bessemer patents, began to send me samples

Jan 1, 1911

By Don K. Smith

The Reclamation Program for the Northern Zone of the Indus Plains in West Pakistan involves the construction of 30,000 irrigation wells to serve 20 million acres with an annual pumpage of nearly 40 million acre-ft. Detailed hydrologic studies indicated that mild steel would be satisfactory for casing; however, within two years after construction, about 10% of the wells began to fail due to encrustation and corrosion of the casing. A search to find a noncor-rosive substitute for the steel casing disclosed that only fiberglass-reinforced plastic pipe satisfied all requirements. The results of initial use of fiberglass have been highly satisfactory and have resulted in a lower over-all well cost. Advances in technology pomise further reduction in prices and improvement in performance. The northern zone of the Indus Basin comprises a vast area of essentially level land in West Pakistan which is irrigated by means of a complex system of canals that distribute more water to more land than any other irrigation system in the world. In spite of the development of this extensive irrigation system, production of food and fiber has not met the requirements of the country. The major reasons that crop production has not reached anticipated levels are the lack of adequate irrigation supplies and effective subsurface drainage. As a result, yields per acre are among the lowest in the world for areas where irrigation is practiced, and many thousands of acres of valuable crop land have been removed from production or seriously affected by salinity and waterlogging. To rectify the problems of irrigation supply and drainage the Government of Pakistan has undertaken a program of Salinity Control and Reclamation which is being administered by the Water and Power Development Authority. The Authority retained Tipton and Kalmbach, Inc., of Denver, Colo., as engineers for the program in the northern zone of the Indus Basin. This program consists of the construction of about 30,000 irrigation wells to provide drainage for waterlogged lands and full irrigation supplies, including leaching requirements, for all cultivated lands. The program will ultimately ensure the productivity of 20 million acres and involve an annual pumpage from groundwater storage of nearly 40 million acre-ft of

Jan 1, 1970

By L. L. McDaniel

During the past few years a nuinber of improvements in smelting and power equipment have been made at the Douglas smelter of the Phelps Dodge Corporation at Douglas, Ariz. In the summer of 1935 work was started on the first unit of a new reverberatory waste-heat boiler plant which ultimately was to furnish steam for a modern high-pressure power pIant. A second reverberatory waste-heat boiler unit

Jan 1, 1944

By Charles W. Perry

The options of enhanced oil recovery, coal syncrude, and shale syncrude are compared by approximately equivalent economics. The physical constraints for the major enhanced oil recovery processes are described, followed by new estimates of cost. The range for all three options in terms of light syncrude equivalent are $22 to $40 per barrel in 1980 dollars.

Jan 1, 1982

By Walter Crafts, D. C. Hilty

The liquidus diagram for the iron field of the Fe-S-O system has been derived experimentally. The solubility of oxygen in molten Fe-S alloys has been measured at several temperatures and found first to decrease slightly and then increase rapidly with increasing sulphur content. IT is well-known that the types, distribution, and amount of inclusions in any given steel are closely allied with the oxygen and sulphur contents of the metal, so that the term "deoxidation" as conventionally applied in steelmaking refers not only to the control of oxygen and oxide inclusions but to collateral modification of sulphide inclusions as well. Inclusions commonly occur in steel as mixtures of oxides and sulphides, sometimes closely associated and sometimes apparently completely divorced. Their effects on the properties of the metal may vary widely depending on their types and distribution as well as on their quantity. The mechanism by which inclusions form, however, and the means for controlling it are exceedingly complex and not well understood. Nevertheless, as described by Benedicts and Lofquist' and by Wentrup' all oxide and sulphide inclusions, excluding mechanically entrained matter, must result from specific modifications of the basic equilibria of the Fe-S-O system. In an investigation of the mechanism of deoxidation and inclusion formation being carried out at the Union Carbide and Carbon Research Laboratories, it became evident that quantitative data for the fundamental Fe-S-O system were essential to a better understanding of the problem. Consequently, the liquidus surface of the portion of the Fe-S-O diagram of interest in steelmaking has been determined, and the solubility of oxygen in liquid iron containing sulphur has been measured. Fe-S-O Diagram The portion of the Fe-S-O diagram of specific interest in steelmaking is the Fe-FeS-FeO corner. Of the contiguous binary diagrams for this partial system, only those for Fe-FeO and Fe-FeS are known with reasonable certainty.3 Several attempts to derive the FeO-FeS diagram have been made, chief among them being the work of Giani as reported by Oberhoffer,4 and, more recently, that of Vogel and Fulling." Although both Giani and Vogel and Fulling published diagrams for the FeO-FeS system, their observations indicated that the oxide component approximated Fe3O4 rather than FeO, so that there is doubt whether the system is truly binary. Benedicts and Lofquist and also Wentrup published qualitative sketches of the ternary diagram based on the assumption that it was of the type described by Marsh for a ternary system in which two of the contiguous binary systems are simple eutectic systems and the third exhibits a solubility gap in the liquid. Apparently, however, the only previous effort to establish the diagram experimentally was that of Vogel and Fülling whose results are reproduced in Fig. 1. Although defining approximately the limits of the miscibility gap and the location of the ternary eutectic, point E in Fig. I, Vogel and Fülling's diagram must be considered only semiquantitative. It was derived from a limited number of observations mainly along two quasi-binary sections, and the directions of the tie-lines and the location of the critical point, K in Fig. 1, were estimated by computation. Experimental Procedure The experimental technique employed for the present investigation involved melting mixtures of ferrous sulphide and ferric oxide in contact with iron. Since it was considered that in this part of the system the vapor pressures of sulphur and SO, are so low that they would not affect the results significantly, the melting was carried out in a current of argon to sweep out products of any initial re-

Jan 1, 1953

By H. E. Strauss

The time-to-fracture test has been applied to pure platinum and to two alloys of platinum under the special conditions of small cross-sectional area of the specimens and of a test temperature above the annealing temperature. While the results are similar in character to those secured with large specimens of steel at temperatures below the annealing temperatures, two differences are noted: (I) an upward inflection in the curves for log stress vs. log time for the alloys, and (2) a sharp break in the curve for log stress vs. log time for pure platinum when single crystals filled the wire. The experiments showed that: (I) platinum and 10 per cent rhodium-platinum maintained their strengths at IIOO°C. better than did to per cent iridium-platinum, and (2) the rhodium-platinum after a time exceeded the iridium-platinum in strength at IIOO°C. Platinum alloys in their service at high temperatures encounter conditions somewhat similar to those that exist in the usual form of the "time-to-fracture"l test with steel. This paper is intended primarily to present results obtained by a "time-to-fracture" test under conditions approximating actual service for platinum (at the temperature IIOO°C. under oxidizing conditions) with three materials, pure platinum (99.99 per cent), a platinum alloy with 10 per cent iridium, and a platinum alloy with 10 per cent rhodium. The experimental procedure differed from that previously used in this type of measurement in that the samples were of small diameter (0.010 in.), were fully annealed, and were tested at a temperature definitely above their annealing points (600°C., IOOO°C. and 1050°C., respectively, for 60 per cent cold reduction and 15 min. heating time2,3). The experimental arrangement was similar to that previously described,' using as heating unit a small, horizontal, platinum-wound furnace, ½ by 12 in., maintained at constant temperature by an automatic controller. The samples were 0.010-in. wires, which had been annealed at 1200°C. by drawing them slowly through the furnace. The time-to-fracture was measured electrically. Elongation was not determined because of the difficulties inherent in the experimental arrangement. Life—that is, the time-to-fracture—was considered the important property in these first tests. No attempt was made to measure the reduction in area, but the types of fracture were noted qualitatively; in the text they are referred to as (I) the normal, plastic, or necked fracture, (2) the knife-edge fracture, and (3) the brittle or intercrystalline fratture with small reduction of area. Results for different constant applied stresses are plotted in Fig. I. In all cases at least two trials were made for each stress, although they cannot always be indicated separately on the curves. The breaking Stresses drop very rapidly to a small frat-286

Jan 1, 1943

By W. G. Pfann

In zone-melting, a small molten zone or zones traverse a long charge of alloy or impure metal. Consequences of this manner of freezing are examined with impurerespect to solute distribution in the ingot, with particular reference to purification and to prevention of segregation. Results are expressed in terms of the number, size, and direction of travel of the zones, the initial intermsofsolute distribution, and the distribution coefficient. IF a charge of binary solid-solution alloy is melted and then frozen slowly from one end, as for example in the Bridgman method of making single crystals,' coring usually occurs, with a resulting end-to-end variation in concentration. Such coring, or normal segregation, is undesirable where uniformity is an object. On the other hand, for certain systems, it can be utilized to refine a material by concentrating impurities at one end of the ingot.'. ' In the present paper a different manner of freezing will be examined with respect to the distribution of solute in the ingot. A number of procedures will be indicated which have in common the traversal of a relatively long charge of solid alloy by a small molten zone. Such methods will be denoted by the general term zone-,melting, while the process described in the preceding paragraph will be called normal freezing. It will be shown that, in contrast to normal freezing, zone-melting affords wide latitude in possible distributions of solute. Segregation can either be almost entirely eliminated or it can be enhanced so as to provide a high degree of sttparation of solute and solvent. A number of simplifying assumptions will be invoked which, while not entirely realizable in practice, nevertheless provide a suitable point of departure for more refined treatments. Moreover, our own experience with zone-melting has shown that, for certain systems at least, the analysis holds quite well. The present paper will be confined to a discussion of principles and a general description of procedures. Comparison with experiment is planned for later publication. Normal Freezing Before considering zone-melting, segregation during normal freezing will be reviewed briefly. If a cylinder of molten binary alloy is made to freeze from one end as in Fig. 1, there usually will be a segregating action which will concentrate the solute in one or the other end of the ingot. If the constitutional diagram for the system is like that of Fig. 2, then the distribution coefficient k, defined as the ratio of the concentration in the solid to that in the liquid at equilibrium, will be less than one and the solute will be concentrated in the last regions to freeze. If the solute raises the freezing point, then k will be greater than one and the solute will be concentrated in the first regions to freeze. The concentration in the solid as a function of g, the fraction which has solidified, can be expressed by the relation: C = kC0 (1-g)k-1 [I] where C, is the initial solute concentration in the melt. Eq 1 is based on the following assumptions: 1—Diffusion in the solid is negligible. 2—Diffusion in the liquid is complete (i.e., concentration in the liquid is uniform). 3—k is constant. Concentration curves representing eq 1 for k's from 0.01 to 5.0 are plotted in Fig. 3. This equation, in one form or another, has been treated by Gulliver,³ Scheuer,4 Hayes and Chipman5 for alloys and by McFee2 for NaCl crystals. It is derived in Appendix I. It should be pointed out that the k which is calculated from the phase diagram will be valid only in the ideal case for which the stated assumptions are correct. In all actual cases, the effective k will be larger than this value for solutes which lower the melting point, smaller for solutes which raise the melting point, and will probably vary during the beginning of the freezing process. For simplification it will be assumed that the ideal k is valid. Zone-Leveling Processes The processes of this part are designed to produce a uniform, or level, distribution of solute in the ingot. Single Pass: Consider a rod or charge of alloy whose cross-section is constant and whose composition, C2, is constant, although permissibly varying on a microscopic scale." Such a charge might be a rapidly frozen casting or a mixture of crushed or powdered constituents. Cause a molten zone of

Jan 1, 1953

IF you wish to make the acid that is vulgarly called common aqua fortis,* for parting gold from silver, you must first provide as many cucurbits and alembics, receivers, and materials as you wish, and then make a furnace that is long and conveniently wide for holding three or four pairs of cucurbits or as many as you wish. If you have to make this by art in order to work a large quantity, you could make several small furnaces for it seems that not more than three or four pairs are suitable for one. Prepare the places where the cucurbits are to stand with bottoms or covers made of potter's clay or tiles that are half round like the bottoms of the cucurbits and have a little rim around the top so that they can be built in. Proceed to build these in in pairs, one by the other with convenient spaces between, placing an iron support across to make this place stronger and more secure. In every corner and also in the middle a hole must be made as a vent for the smoke, as is done in all furnaces. You will see the form of this somewhat roughly drawn here. [Figure 25] Near this prepare a number of cucurbits which are made of glass, as clear and uniform as possible and very well formed. There must be no bubbles or other indentations in these, for they would be dangerous and uncertain for your work. Lute these with lutum sapientiae up to within three dita or less from where the neck narrows. This lute must be spread out well all over to the thickness of two threads or a little more. Then cover and make them strong with this well-made plaster, and finally dry it, taking care that there are no clefts or cracks such as clays are often prone to make even though they be well prepared. For greater security choose among these [64v] a clay that is lean and then mix it with at least a fourth part or more of wool-clloth clippings and about an eighth part of wash

Jan 1, 1942

By Earl S. Greiner, Eric R. Jette

The constitution of the iron-silicon alloys containing from 14 to 33.4 weight per cent silicon has been studied by a number of investigators, whose results have been reviewed in a monograph published by the Engineering Foundation1. In these previous researches, the solubility of silicon in iron was determined by thermal, microscopic or magnetic methods and the compound Fe3Si2 was reported to be stable at temperatures from 0 to approximately 1030' C. This paper describes the results of an X-ray investigation of the solubility of silicon in iron and gives data which prove that the Fe3Si2 phase is unstable below 825" C. In order to obtain the present results on the solubility of silicon in iron, the authors have utilized the lattice constants of the alpha-phase iron-silicon alloys given in a previous publication2, and also some additional data which will subsequently be described. Materials and Methods The alloys used in this investigation are listed in Table 1. They were prepared in 30 or 50-gram ingots by melting specially purified silicon and electrolytic or carbonyl iron in alundum crucibles under a pressure of less than 1 mm. of mercury. The purity of the silicon, electrolytic and carbonyl irons has been given by the authors in previous publications2, 5. The ingots were homogenized in vacuo at approximately 1000" C. for at least 96 hr. and then slowly cooled. The homogenized specimens were ground to powder in a hardened steel mortar. This powder was passed through a 150 or 200-mesh screen and sealed in evacuated quartz, Jena or Pyrex glass tubes and heat-treated as noted in the various tables. Specimens 23A, 24B, 33 and 35 and the specimens heated for one month at 700" C. were quenched by quickly removing the tubes from a horizontal tubular furnace and dropping them into water. The other specimens were quenched by means of a drop-quenching device, which has been described previously3.

Jan 1, 1937

By F. N. Rhines

STUDIES upon the sintering of metal powders, in the solid state, have led to the proposal that the surface energy of the powder particles provides the driving force that causes points of contact between pairs of particles to grow into broad welds which isolate the residual vacant space into pores that tend to spheroidize and gradually to diminish in total volume.' Investigators differ with regard to the mechanism of the movement of the metal, under the influence of surface energy, to accomplish these changes. One school asserts that there is a mass movement of the metal, referred to as a "viscous flow," while the other school prefers to view the movement as a self diffusion process, wherein individual atoms are, transferred without disturbance of the basic pattern of the crystal lattice. Extensive experimental studies upon the sintering of copper, conducted recently by A. J. Shaler,2 have been in- terpreted by their author as support for the viscous flow mechanism of transport, the theory of which was developed originally by J. Frenkel.3 Duplicating a portion of this work with minor changes, G. C. Kuczynski4 is led to the alternate view, namely, that the initial stages of sintering, at least, proceed as a self-diffusion process. Both of these investigations were designed to deal with an isolated unit of sintering, i.e., with the shrinkage of a single pore, or with the growth of a single point weld. It remains to ascertain the behavior of a typical metal powder compact composed of a large number of particles of varying size and sintering to a body with a multiplicity of pores. The observation of density changes alone during sintering is not sufficient in such a case; it is essential to know how the internal geometry of the compact changes. This has been the object of the present investigation, the results of which are used to support the self-diffusion mechanism of sintering. The present studies consist in the measurement of the number of pores as a function of size and time at temperature during the sintering of a copper compact made from a commercial copper powder lightly pressed and sintered in several different atmospheres. A brief survey was made also of the change in shape of the pores, under the influence of the same variables. All of this was done by direct observation with the microscope. Densities were measured on the same sample. It is found that, while the compact is exhibiting an overall shrink-

Jan 1, 1951

By T. Sterry Hunt

BUT little was known of the coals of Southeastern Ohio until the present survey of the State under Dr. Newberry began its work. The results of the geological investigations of Prof. E. B. Andrews in this region, and of the chemical investigations of Prof. T. G. Wormley, both of which appear in the reports of the survey for 1869 and 1874, and more recent special reports by the former, together with some data for which I am indebted to the kindness of Dr. Newberry, and my own limited observations, have served me for the preparation of the following notice of the coals lying on the western border of the great Appalachian coal-basin in the region drained by the Hocking River and its tributaries, and belonging to the Lower Coal-Measures. Some uncertainty exists as to the place in the succession of the lower coals to be assigned to the seams known and mined in the Hocking Valley. It is the opinion of Prof. Andrews that the inequalities of the original surface were such that we cannot identify in that region the lowest coals known in Northwestern Pennsylvania and the contiguous parts of Ohio, but that we must rather count from above downwards. These conclusions Dr. Newberry is not prepared to accept, and further researches will be necessary before certainty can be attained in this matter. Meanwhile it seems, from a study of its relations to the Pomeroy or Pittsburgh seam, that what is known as the great vein of the Hocking Valley, occupies the horizon of the Upper Freeport coal, E of the Pennsylvania survey, or No. 6 in Dr. Newberry's enumeration, counting from the base. This seam, in the region in question. assumes certain characteristics which, taken in connection with its geographical position, give it a great importance among the coals of the State. The area to be noticed includes the whole or parts of several townships in Perry, Hocking, Vinton, and Athens Counties, lying near the margin of the basin over which the vein in question assumes the character of a dry-burning or splint coal, and has a thickness varying from six to ten and even twelve feet. Its precise limit southward cannot at present be clearly defined, but it has been found as far south as the line of the Marietta and Cincinnati Railroad, with a thickness of six feet, and is mined at various points along the valley of the Hocking River, near Nelsonville, where it attains six or seven feet. To the northward, along the tributaries of this river, Sunday and Monday

Jan 1, 1874

By Michel David

One of the most important questions that arises in ore estimation can be stated as follows: What is the error when one extends the grade of a sample to a certain volume? The theory of regionalized variables, with the concept of extension variance, provides a response to that crucial question for any kind of sample extended to any volume. For the usual "extensions" encountered in current mining practice, some simple results can be derived from that theory which was initiated by Dr. G. Matheron. These results have been applied to a stratiform lead-zinc deposit for which several estimations of grade, tonnage and related precision have been made for a series of grid sizes such as might be used in a progressive exploration program.

Jan 1, 1969

By H. M. Woodrooffe

Three of the world's largest phosphate deposits are located in the USSR. These have an estimated reserve of 2,600 million short tons of elemental phosphorus. The best known lies in the Khibiny Massif, an alkalaic rock formation some 600 square miles in area with mountain peaks rising to an altitude of 3300 ft above the surrounding terrain. The Khibiny Massif is north of the Arctic Circle in the Kola Peninsula at a latitude of 67° 30' north and a longitude of 35° 30' east. It is connected by rail to Murmansk, 100 miles northwest, and Leningrad, 900 rail miles south.

Jan 12, 1972

By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,'.' who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy's law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy's law, as extended to two-phase flow including the effect of capillary pressure,' is as follows:

By M. Albertson

At Cobalt, Ontario, Canada, a lake was drained to facilitate mining, by the Mining Corpn. of Canada, during the spring and early summer of 1915. Previous to pumping out the water, great quantities of sands and slimes from concentrating plants had been discharged into the lake and during and after the lake's drainage, its basin was a receptacle for tailing products. As the writer was at work along the shore line as the lake was being drained, he had a good opportunity to observe the changes that took place as the water was withdrawn. Some adjustments between the incoming sands and the mud in the lake had taken place before pumping was commenced. One of the most interesting results was the appearance of a small dome in a path the writer traversed twice a day for several months; he remembers distinctly the difficulty of crossing this. Cobalt Lake owed its existence to the gouging out of a rock basin by glaciation. The long axis of the basin closely follows the strike of a thrust fault of about 500 ft. (160 m.) vertical displacement. The lake was originally shaped somewhat as shown. The length was about 3000 ft. (914.4 m.), the width at the lower lobe was about 1000 ft., and the width at the narrows probably 400 to 500 ft. The original depth of water varied from 20 to 30 ft. (6.1 to 9.1 m.), near where the island later was formed, to 60 to 70 ft. (23.6 to 27.6 m.) in the widest part of the lower lobe. At the narrows, the depth was 30 to 40 ft. Above the bed rock was sand, with boulders near the bottom, and mud. During the building of the railroad in 1903, considerable filling was done along the right of way. With the commencement of mining operations, about 1905, waste rock and mill tailings were dumped into the lake. One of the mining companies operated a hydraulic giant to remove the glacial debris from several hundred acres of rock surface; much of the sand and clay from this operation was deposited in the lake. About 1,500,000 tons of mill tailings, composed of sands and slimes, were discharged into the lake's waters previous to 1915. Most of this material

Jan 1, 1921