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By J. Moore Samuel

THE prospective change in ore receipts at the Copper Queen reduction works necessitated a careful study of conditions to determine the most economical method of smelting. The first step, calculating the known, probable, and possible results, showed the economy of a unimetallurgical flow sheet f which the three pyrometallurgical stages would be roasting, reverberatory smelting, and converting. The past and future ore receipts (not including converter flux) are as follows: AVERAGE MONTHLY FUTURE MONTHLY RECEIPTS, 1918 RECEIPTS TONS PER PER CENT. OF TONS PER PER CENT. OF MONTH TOTAL RECEIPTS MONTH TOTAL RECEIPTS Ore 84,553 82.3 43,000 44.0 Gravity concentrates 16,375 15.9 25,500 26.0 Flotation concentrates 1,883 1.8 29,400 30.0 Total 102,811 100.0 97,900 100.0 Of the 102,811 tons per month received in 1918, only 28,945, or 28 per cent., was treated in the roasters and an average f 14.1 roasters out of 20 were in operation; the remaining ore was treated in the blast furnaces. The change to "all reverb." practice, therefore, called for considerable additional roaster capacity, which could be obtained either by building additional units, or by remodelling the present units so as to give increased unit capacity. In view of the progress in roasting practice since the construction of the Copper Queen roaster plant and the heavy investment in that roaster plant, the second plan seemed to be the more desirable. The Copper Queen roaster plant consisted of twenty six-hearth, McDougall roasters, 18 ft. in diameter, equipped with cast-iron arms that originally were water cooled but now are air cooled. They have no top dry hearth and the feed is discharged through the top arch, near its periphery, by plunger feeders from two bins at opposite sides of the roaster.

Jan 7, 1921

By J. L. Gillson

Joseph H. Birman (Chairman, Dept. of Geolcgy, Occidental College, Los Angeles, Calif.) Many thanks to J. L. Gillson for so comprehensive a survey of the titanium sand deposits of the world. Over the past two years, the writer studied rather carefully some of the Cretaceous ilmenite deposits in New Mexico and Colorado, including the Sanostee deposit shown in Gillson' s map, Fig. 6. The deposits were geologically mapped and sampled, surveyed by magnetometer, and the Sanostee deposit was drilled. Moat of the genetic interpretations made by Gillson concerning the recent sedimentary ilmenites can be clearly read in the Cre-taceous deposits in New Mexico. The deposits are in marine regressive members of the Mesaverde group. The deposits trend within a few degrees of N 55° W and persistence of this trend through both distance and time (the deposits are in different members of the Mesaverde group) implies that the deposits are offshore bar accumulations. Heavy mineral content ranges from about 10 pct to more than 50 pet. Thicknesses are from 4 ft to as much as 20 ft, widths range from 150 to 600 ft, and lengths range from a few thousand feet to a few miles. All are locally or completely overlain by carbonaceous shale and thin coal. The deposits are strongly altered, and from X-ray diffraction the principal titanium alteration product appears to be anatase. Drilling of the Sanostee deposit shows that the alteration is not related to the present erosion surface but took place at the site of deposition and before burial by the overlying sediments. Iron oxide derived from the alteration cements the grains and is the chief coloring agent in the immediately overlying shales. In the Sanostee deposit, there is virtually no feldspar, the gangue mineral being almost exclusively quartz. Sorting is excellent, but the quartz grains are subangular to angular. Petrographic examination reveals that the angularity is not due to overgrowths. Therefore, short distance transport is implied. The mineralogical composition suggests a low relief granitic terrane as the source area. Feldspar may have been decomposed by weathering at the source, but an alternative preferred by the writer is that each of the deposits represents a long-term concentration site (for example a large sand bar) which was continually being deprived of light minerals by wave action and selective transport. Feldspar may have been mechanically reduced in size more quickly than the quartz, and thus its rate of removal may have exceeded that of quartz. Concentration of heavy minerals would thus occur until the marine regression removed the zone of maximum wave energy from the site. Chemical alteration would then become the most important process until burial by encroaching swamp deposits.

Jan 1, 1961

Jan 1, 1963

By David B. Dill, Edgar R. Lea

The zinc deposits of the Balmat-Edwards Division of the St. Joseph Lead Company in northern New York State provide some 10 per cent of the domestic zinc produced annually within the United States. These complex ore deposits are contained within marbles of the Precambrian Grenville series, in a repetitive sequence of dolomites and silicated units. The Balmat ore bodies are localized at various intervals throughout some 1800 feet of the stratigraphic column on the northwest side of a band of gneiss that has continuity to the Edwards area, some 10 miles to the northeast. The Edwards ore bodies are located to the southeast of this gneiss. The marble formations are thought to have included repetitive intervals of marine sedimentation that provided mineralized source "beds" and were subsequently folded, flooded, and injected with melts at great depth and were sheared, recrystallized, and reconstituted. Detailed structural and stratigraphic studies throughout the northwestern Adirondacks, in the Balmat-Edwards district, and at each mine in particular indicate the close dependence of the ore deposits on the enveloping structure whether it be local, district-wide, or regional in scope. Primary folding has developed a northeast regional trend with northwest dips. Secondary folding has been developed by an almost horizontal northeast-southwest-oriented shear couple in the plane of the regional trend. The secondary folding has produced crossfolds that intersect the regional northeast trend and plunge north to northwest at various angles. The ore bodies are found within certain stratigraphic horizons where repeated alternation of competent and incompetent beds encouraged unusually complex folding. Analysis of individual mine structures indicates that the location of each deposit is controlled by structural crossing of primary and secondary folding. The ore bodies, which are tabular, lenticular, or pod-like in form, have features that suggest parallelism to true bedding or modified flow banding, developed by northeast-southwest shearing stresses related to the development of the crossfolds. The ore deposits in general follow both structural and recrystallization trends within the wall rocks. Mobilization of the pre-metamorphic ore minerals is believed to have involved a combination of plastic flow under stress and solution of the sphalerite, minor galena, and pyrite. The ore fluids are thought to have been guided by secondary shearing and microbrecciation into structurally prepared areas where reprecipitation took place. The presumed premetamorphic mineralization now exhibits epigenetic high-temperature features related to late-stage metamorphism.

Jan 1, 1968

The Institute has prepared a list of Societies' publications, magazines, . etc., which were duplicates and were discarded at the time of the consolidation of the libraries of the three Founder Societies. These books will be disposed of about March 1, 1916 by the Board of Directors of the Institute through the Library Committee. If, meanwhile, members who have incomplete sets of these books, or for any other reason desire to secure some of them, they are asked to communicate immediately with the Secretary, as this is in unusual opportunity to secure books at a very low price. American Gas Light Journal, viols. 31 to 39. American Institute of Electrical Engineers, Transactions, vols. 5 to 26. American Machinist, vols. 3 to 20, 22 to 29. American Society of Civil Engineers, Transactions, vols. 2 to 10, 21 to 24, 26 to 33, 39 to 49, 52, 55, 58, 74. Index, viols. 1 to 21. American Society of Mechanical Engineers, Transactions, vols. 1 to 28. Index, vols. 1 to 20, vols. 1 to 25.

Jan 1, 1916

Bailey, Lewis Newton, Master Engineer, Senior Grade, 4th Regiment, U. S. Engineers, Headquarters Company, died of pneumonia at Camp Merritt, N. J., on April 30, 1918. Baird, Louis, Lieut., Royal Field Artillery, British Army, died on the battlefield in 1915. Cobeldick, William Morley, Royal Engineers, died from gas poisoning on October 7, 1915. Dougall, Ralph, killed in action. Evans, Alfred Winter, Lieut.-Col., New Zealand Rifle Brigade, D. S. 0., D. C. M., killed in action on October 12, 1917. Gorman, Thomas C., Lieut., Canadian Engineers, killed in France, Mar. 18, 1918. Hague, William, 1st Lieut., Engineer Officers' Reserve Corps, died in active service. Hall, William T., Capt., Royal Flying Corps, killed in action. Heine, Bernhardt E., Lieut., Aviation Service, killed at Fort Sill, Okla., Aug. 10, 1918. Irving, John Duer, Capt., 11th Engineers, A. E. F., died while on active service in France on July 26, 1918.

Jan 9, 1918

By K. G. Gorling, S. J. Wallden, N. B. Lindvall

It is the policy of The Metollurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers according to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editorial Director, Rixford A. Beals; Associate Editor, James J. Burke; Assistants, L. Capria and R. K. Larkin. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. W. Thornton, Choirmon; Dennis Carney, John Chipman, J. C. Fulton, J. H. Hollomon, H. tl. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and O. Swan. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extractive Metallurgy Division T. B. King. Cha~rmon; S. J. Dickenson, R. P. Hermsdorf, R. Schuhmann, Jr.. and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman. F. Lincoln Vogel, Jr., Vice-chairman, W. A. Backofen, R. W. Balluffi, J. H. Bechtold, M. B. Bever, R. S. Busk, C. G. Goetzel, Paul Gordon, C. D. Graham. Jr., Robert F. Hehe-mann, R. I. Jaffee, F. E. Jaumot, Jr., lrving R. Kramer, A. J. Leno, Horold Margolin, C. J. McHorgue, Russell A. Meussner, J. 6. Newkirk, H. W. Paxton, G. E. Pell~ssier, I. S. Servi, Alan U. Seybolt, A. J. Sholer, and Sack Wahsburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B King, F. C. Langenberg, W. O. Philbrook, and T. B. Winkler. Published bimonthly by the American Institute of Mining Metallurgical and Petroleum Engineers Inc., 29 West 39th Street, New York 18, N. Y. Telephonne pennsylvania 6-9220.Petroleum Subscription Engineers$20 per year for non-AIME members in United States and North South and Central 6-9220.SubscriptionAmerica $25 toreign; $5 for AIME members. Single copies, $4.00, iinalo copies Southfpr;ign,andCentral $5 00. The AIME 'is $25not responsible for any statement made or opinion expressed in its publications Copyright 1958 1958 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . Registered coble address, AIME New York . . . Indexed in Engineering Index, Industrial Arts Index, ...and Chemical Abstracts . . . Application for second class mail privileges IS pending at New Yark, N. Y. Volume 212, Number 2.

Jan 1, 1959

Jan 1, 1961

Joseph W. RichaRds, South Bethlehem, Pa. (communication to the Secretary*): The hold experiment of Mr. James Gayley in drying the blast used in the Isabella furnace has attracted the attention of the whole metallurgical world, and has given rise to a wide discussion of the reasons for its great success. Mr. Gayley and the capitalists who backed him in his work deserve congratulations on the success of the venture, not only because it succeeded, but because they have been rewarded far beyond the maximum that could be expected from theory or probability. To state the case in its simplest terms, all that could have been predicted was: (1) that the removal of the moisture from the blaet would result in the saving of the heat required for its decomposition, representing from 3 to 5 per cent. of the heat-value of the coke used; hence about that quantity of fuel might be saved; (2) that the furnace would be somewhat more independent of variations in the weather; (3) that the campaign would be a little hotter; and (4) that the speed of the blowing-eugines would be decreased, at least in amount proportionate to the reduction in temperature of the air led to them. I do not think anyone anticipated a much larger output per day. The results actually attained were: (1) the furnace made an increase of 24.86 per cent. in the output of pig-iron per day; (2) it consumed 19.6 per cent. less coke per ton of pig-iron made; (3) the blowing-engines were run 15.8 per cent. slower; and (4) the saving in power made up for the power required to run the refrigerating-plant. In addition, the blast was hotter; the waste-gases cooler, because of their smaller volume; and there was a greater proportion of carbon dioxide to carbon

Jan 1, 1906

By V. J. Parks, Leonard Obert, A. J. Durelli

The state of stress in the region where core discing initiates has been investigated through the use of three-dimensional photoelastic models and the results of this study have been compared with those of a previous investigation of rock models. This comparison showed that discing initiates at a point of maximum shear stress, but that the magnitude of the shear stress, as determined photoelastically, is much larger than the shear strength of the rock as deter-mined from conventional triaxial testing. Moreover the shear stress required to produce discing is not constant, but depends on the applied stress field. Possible explanations for these effects are included in this article. In both exploration core drilling and overcore drilling to determine the stress in rock, occasional sections of the core obtained are broken into a series of discs.I* This discing phenomenon has been investigated in the laboratory to ascertain the state of stress required to produce it. The objective of the study was to obtain information that would make it possible to approximate the state of stress in subsurface rock from which disced cores are obtained. Referred to as the discing test, this laboratory study was conducted to determine the applied axial and radial loads required to produce discing in cylinders of rock from several sources. The dimensions of these cylinders are given in Fig. 1. Discing was produced by first applying an axial load to the cylinder and then diamond drilling the core along its axis. The radial load was then incrementally increased until discing initiated. The discs fractured or ruptured* on surfaces approximately normal to the axis of the core (planes A, B, C, D, E, Fig. 2). In many instances, the bottommost disc fractured before the drill had advanced past the points F and F', cre- ating a mush room-shaped fracture surface FEF'. Alternatively, it was also found that the same shaped fracture surface could be created by first drilling in an unloaded core to some point, say F and F', and then triaxially loading the core until fracture occurred on the plane FEF'. Jaeger and cook4 produced similar fracture surfaces in specimens subjected only to a radial biaxial load. From these laboratory studies and observations made in the field, it can be inferred that fracture or rupture initiates in the proximity of the lowest point in the kerf area, (at F and F', Fig. 2) and that the fracture or rupture surface progresses inward from this point. The experiments described above, however, do not provide any information as to the state of stress at the point at which fracture or rupture initiates. In the investigation discussed in the following sections, a three-dimensional photoelastic analysis was conducted to determine the stress distribution in the proximity of the kerf area of a triaxially loaded plastic (epoxy) cylinder containing a short section of core.

Jan 1, 1969

DURING September, the Coal Commission pre- pared for issue a series of 18 reports on varied aspects of- the bituminous coal industry; the final report, dated Sept. 22, sums up the facts and offers recommendations addressed to Congress, to the industry, and to the public. The few following paragraphs are selected: Bituminous coal is the real foundation of that great industrial and transportation structure which enables more than a hundred million people to live in America and be so well supplied with things necessary for their health, comfort; and convenience; it also furnishes domestic fuel for two-thirds of the homes of the land. The distribution of the output of the bituminous mines tells the story: 28 per cent. goes to the railroads, 25 per cent. to the boiler houses of factories and mills of all kinds, 15 per cent. to the coke ovens and gas plants, 10 per cent, to the homes, 7 per cent. to steel plants and the same percentage to power plants and street railways, 4 per cent. is exported, 2 per cent is used for power at the coal mines, and the remaining 2 per cent. goes to the seaboard for steamship fuel. Bituminous coal enters into interstate commerce on a scale approached by no other commodity; less than a fourth of the coal mined in the United States fails to enter interstate com-merce. All but one of the 45 coal producing districts in the United States ship coal outside the State in which it is mined. Three hundred miles of cars loaded with coal is the daily output of the bituminous mines of the United States. The public-welfare element in coal is seen in the dependence of public health and safety on an unfailing supply of fuel, in the close connection between the prosperity of most industries and the uninterrupted operation of the coal mines, and in the obvious fact that without coal the great network of railroads which binds together this great country would be idle. The railroads and the public utilities, themselves so clearly obligated to render what-ever public service is demanded of them that the constitutionality of their public regulation is unquestioned, are of all industries most dependent upon coal. Thus, coal makes up over 35 per cent. of the operating cost at the gas plant and over 25 per cent. at the electric power station, and in the operating expenses of. a railroad the cost of coal is the largest single item, next to labor. The practical logic that half a century ago clothed with a public interest the steam locomotive and in later years the electric-power station must recognize a large element of public service in the coal mine that furnishes the necessary energy to both locomotive and power-plant.

Jan 10, 1923

By R. C. Neavel

One of the most important requirements to be met by any coal producer is delivery of size consists tailored to specific applications. Generally these specifications include a minimum as well as a maximum size limit. The customers of a major Indiana coal producer noticed that some shipments of sized coal contained a large proportion of undersize pieces. Also, in these shipments, the pieces which remained within the specified limits were cracked and, when handled, crumbled readily. The producer, certain that these shipments had been properly sized at the tipple, suspected that degradation had occurred in transit. The Indiana Geological Survey was requested to examine the coal from one of these shipments to attempt to determine the cause of breakage. Two basic facts about coal and coal seams led to the employment of petrographic techniques in this investigation. First, all coal seams consist of accumulations of diverse organic and inorganic constituents; and second, most coal breakage, either desirable or undesirable, can be attributed to the inherent weakness of some of these constituents or to poor adhesion between certain constituents. Analyses of degraded coal Sampling: Samples were secured from 2 stock piles of 2-by 4-inch coal in a dealer's yard. The coal in both piles had received the same treatment from mining to storage, although it had been mined and shipped on two different days. The size consist of one pile, however, appeared smaller than that of the other. The sample from the degraded pile is referred to as the slack sample, and the other is called the unslack sample. Size analyses: In order to determine the actual size consist, the samples were screened, with a minimum of rough handling, on square 2-inch, 1-inch, 1/2-inch, and 12-mesh screens. It is assumed that 100 percent of the 2-by 4-inch coal is retained on a 2-inch round screen at the tipple. Analyses of several loads at the tipple indicate that approximately 26 percent of the 2- by 4-inch coal, 100 percent of which was assumed held on a 2-inch round screen, passed through a 2-inch square screen. Twenty-six percent may be taken as the normal difference between round and square screens. Results of the analyses of stockpile coal are shown in Table 1. Cumulative percent versus size are plotted on a Rosin-Rammler chart as Figure 1. Both samples approximately follow normal size distribution; this indicates that breakage is not size preferential and also that the samples are representative of the stockpiles. Although both samples exhibit the same general size distribution, the median size of the slack sample is considerably smaller than that of the unslack sample. Fifty-five percent of the unslack sample was undersize (29 percent greater than the normal 26 percent difference), and 83 percent of the slack sample was undersize (57 percent greater than the normal 26 percent difference). Both piles contained a greater percentage than normal of undersize coal; this indicates that they were both affected by degradation, but to a different degree. Bedding-plane analyses: Coal, because of its laminated nature, will break preferentially along bedding planes, especially where adjacent constituents are poorly cemented to each other. Subsequent breakage perpendicular to the

Jan 1, 1961

By L. H. Simons, H. H. Spain

I NT RODUCTION Theory indicates that linear water-floods should exhibit scaling and stabilization properties in both oil-wet and water-wet porous media'. Experimental verification of these proper-ties in oil-wet media was obtained some time ago', and more recently, Perkins', employing a high permeability unconsoli dated sand and a low oil-to-water viscosity ratio, has obtained flooding data in a water-wet medium which follow the pattern of scaling and stabilization. Also, Root and Calhoun3 have found similar trends in the displacement of gas by liquids from unconsolidated sands. In general, however, the experimen-tal evidence appears still somewhat conflicting since scaling and stabilization of water floods in water-wet media has not been observed in most of the studies to date'.".'. The purpose of this paper is to provide a more comprehensive picture of waterflood behavior in water-wet media and to corroborate the validity of the scaling and stabiliza-tion concepts. The need for differentiating between the intrinsic nature of water-oil displacements inside a porous medium and perturbating secondary end effects is discussed, pertinent experimental procedures are outlined and the results of flooding tests conducted at low and at high oil-to-water viscosity ratios on con- solidated, water-wet Alundum cores are analyzed. END EFFECTS IN WATER-WET MEDIA Outlet End Effects The peculiar feature of the outlet end effect in water-wet cores is that it not only results in an excessive wetting phase saturation at the outflow face,'.' but that it also retards the moment of water breakthrough: i.e., causes an undue delay in the appearance of water in the produced effluent. Conditions existing in a water-wet core when water first arrives at the outflow face are schematically shown in Fig. 1. At this flooding stage the saturation distribution, Fig. la, has not yet been distorted by the outlet end effect. A water-invaded pore at the outlet core face, opening into the oil-filled void space between the end of the core and the end plate of the flooding cell, is illustrated in Fig. lb. The curvature of the water-oil interface is concave toward the outlet, and the pressure on the water side of the interface is lower than on the oil side by an amount equal to a certain capillary pressure (Fig. lc). Before the water (of this particular pore) can be produced from the core, it is apparent that the pressure in the water phase must exceed that in the oil outside the core. Accordingly. when water first reaches the outlet face, it will not leave the core but will accumulate inside, and only oil will be produced. Eventually, as the water injection is continued. sufficient pressure is built up in the water to reverse the curvature of the interfaces in the outlet pores, and only then will water be produced from the core. This stage, illustrated in Fig. 2. corresponds to the conventional "water breakthrough" observed in flooding experiments. For purposes of discussion, it is convenient to distinguish between the flooding stage at which water first arrives at the outlet face of a core (Fig. 1) and the stage at which water is first produced from the core ( Fig. 2). The former will be referred to as "water arrival" and the latter water breakthrough. In oil-wet media

Beyer Barometric Condenser The Ingersoll-Rand Co. is now offering to the trade complete steam­condensing plants for all service conditions. This equipment includes the Beyer barometric condenser, for' which the company has secured the patent rights, Imperial duplex and Ingersoll-Rogler straight-line reciprocating dry vacuum pumps and, where required, Cameron simplex and centrifugal pumps. The Beyer barometric condenser is of the counter-current type, in which air and cooling water flow in opposite directions. The steam inlet is at the bottom of the condensing v el, the water inlet above and the air-removal opening at the top. The sheets of cooling water over owing the pool at the inlet point meet the entering steam. The two are brought into intimate contact by conical baffle plates which assist the water to absorb to its full capacity the latent heat of the steam. The non-condensable air liberated in the condensing action rises through the falling water to the removal point at the top, being cooled to practically the temperature of the incoming water. It is also to be noted that ample opportunity is given for the removal of the air content of the water before

Jan 8, 1916

By Alfred E. Hunt

By the death of Joseph Dame Weeks, past-President of this Institute, which occurred December 26, 1896, the world has lost an earnest and unwearied philanthropist; the Christian church, a zealous, active and consistent representative; the United States and the State of Penusylvania, a patriotic, pub-

Jan 1, 1898

INSTITUTE OF METALS DIVISION Ferrous and Nonferrous Physical Metallurgy (By-laws in Transactions, Vol 156, 1944) Established as a Division April 26, 1918 Walter A Dean, Chairman R. M. Brick, Past-Chairman Morris Cohen, Senior Vice-Chairman J H Scaff, Vice-Chairman Ernest Kirkendall, Secretary-Treasurer

Jan 1, 1952

Established as a Society February 26, 1957 John S Bell, President Wayne E Glenn, President-elect Basil P Kantzer, Past President R E Howard, Vice, President M B Penn, Vice-President Everett G Trostel, Treasurer Joe B Alford, Executive Secretary 800 Fidelity Union Bldg Dallas 1, Texas

Jan 1, 1959

Ferrous and Nonferrous Physical Metallurgy Established as a Division April 26, 1918 T A Read, Chairman O T Marzke, Past Chairman J H Jackson, Senior Vice-Chairman David Swan, Vice-Chairman D C Johnston, Secretary-Treasurer AIME, 29 West 39th Street New York 18, New York

Jan 1, 1960

By Earle E. Schumacher, Alexander G. Souden

IN the field of physical metallurgy it is becoming increasingly difficult to keep abreast of the recent develop¬ments since the diversity of investigations is so great and the literature so voluminous. The purpose of this review is to present the more important advances in the nonferrous field during the past few years, the topics discussed being classified broadly as fundamental and practical. The former includes those studies that have done most toward developing the basic science of metals and alloys, and the latter includes technical developments and applications. With the rapid growth of the metal

Jan 1, 1938

By M. ROWE, H. E. Gilliland, L. BARNES

The authors of this paper are to be commended for a clear exposition of a timely subject. However, some important conclusions, in addition to those presented in the paper, can be drawn from the results of their elaborate and rather complete numerical computations. First of all, the major part of the calculations presented in the paper are for semi-infinite slabs of oil shale (the authors designate this as Model I) and a question must be posed — Are these elaborate computations needed to arrive at realistic estimates of the shale oil displaced. Consider the model of Lauwerier* that corresponds to the authors Model I if thermal conduction parallel to the fracture be neglected. If one also neglects the finite (but relatively small) heat capacity of the material in the fracture, it is easily shown from Lauwerier's solution that the cumulative oil production would be:

Jan 1, 1969