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By Morris J. Elsing

FOR MANY YEARS lead and zinc have had the so-called protection of a tariff and it is the purpose of the following brief discussion to show what' such protection actually accomplishes with a view to forecasting the possible results of the present copper tariff. In analyzing the subject, tabulations of the United States production, consumption, imports and exports, including ore and concentrates and all of the metallic products, of both lead and zinc have been made for each year since 1900. Of these data, the relationship of the imports and exports and the relative foreign and domestic prices are shown in Table 1. The conclusions drawn from these figures are listed below. 1. The United States is an exporter of zinc. 2. The United States is an importer of lead. 3. The average price of zinc at St. Louis for the last 32 years has been no higher than on the London market even though zinc and zinc ore have "enjoyed" a protective (?) tariff of varying amounts per pound for 22 years of this period. 4. The average price of lead on the New York market for 32 years has been 1.2c. per pound higher than on the London market, the tariff varying from 0.75 to 1.5c. per pound of lead in ore, and 1 to 2c. or more on manufactured lead.

Jan 1, 1932

By Archibald Macmartin

THE Königin-Marien-Hütte is the only works in Germany where the Bessemer process is carried on by the direct method. The Besserner plant there, is arranged after the true English type, and the only resemblance to the Swedish mode of procedure is the dispensing with the use of spiegeleisen at the end of the "blow." In a new department of the establishment, started within three years, each of the converters is turned by means of a very neat and compact reversible engine, the steel shaft of which is an endless screw, which turns against the oblique cogs of a large wheel attached to the shaft of the vessel. An advantage which this arrangement possesses over the ordinary English hydraulic arrangement, is the fact that the endless screw suffices to turn the vessel, in either direction, any number of complete revolutions; while even the latest American improvements, so clearly explained to us by Mr. Holley at the opening session of this meeting, do not secure even one complete revolution without changing the angle of inclination of the hydraulic piston. In the endless screw arrangement, there being no limit to the working of the motor in either direction (no return-stroke necessary), the vessel can always, unless outside reasons demand the contrary, be turned around to any desired position by the shortest cut, whether backwards or forwards. Also, the diameter of the cog-wheel attached to the vessel can be made sufficiently great to avoid all unevenness of motion. In the old department the motive-power still continues to be hydraulic. If reports be true, the new department produces spiegelized steel, for the manufacture of all-steel rails. But the old department is still,' as from the beginning, devoted to the production by the direct method of steel for steel-headed rails. The most remarkable fact connected with this direct steel is the ease with which it welds to the iron' of the rail-packets, although no borax or other fluxing agent is used to facilitate the welding. It is very rarely that an exception occurs, and an ingot or a charge is discarded by the rail-mill. The mixture of pig-iron used for the production of this steel is melted in cupolas of very interesting construction (not to be de

Jan 1, 1874

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers'-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded' that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-' and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By Frederick Burbridge

The Morning silver-lead-zinc mine of the Federal Mining & Smelting Co. is about 'two miles northwest of Mullan, Ida. The lode is a metasomatic fissure vein. The orebody is approximately 2000 ft. long within the bounds of the property and varies in width from knife edge stringers to 50 ft. It has been developed to a depth of 3600 ft. and stands nearly vertical in Revett quartzite, which .strikes north 65" west. The high-grade veins and lenses are generally mixed with waste (siderite, quartz, and quartzite). The average grade of ore to sorting plant in 1921 was 4 oz. silver per ton, 8.6 per cent. lead, and 4.1 per cent. zinc. Wall rock stands only a short time without timbering. The minimum angle of gravity flow is 45". The ratio of waste sorted out to ore is 6 per cent. No gases are generated underground and temperature has no influence on mining operations. Fresh air is forced down the air raise and up the main shaft. Drifting and Stoping Main drifts 12 ft. wide and 13 ft. high are driven every 200 ft. (vertically) and are connected by raises 125 ft. apart. These raises consist of three compartments (chute, tramway, and timber slide) and are for the purpose of ventilation, access, and hoisting supplies to stopes. Ground is stoped between raises. Chutes are placed every 25 ft. for drawing off ore broken in stopes. Waste for filling is obtained from waste raises off the stope in walls or waste is dumped from the level above down the chute compartment of raises, which is bulkheaded so that waste can be drawn off at any floor as required. Timbering Posts and caps for square sets (varying in diameter from 6 to 24 in.) are cut to length in a sawmill on the surface. No preseratives are used. Timber is taken on a flat car along drifts to a raise nearest the working place and hoisted as required. Practically no timber is salvaged for

Jan 1, 1925

THE book covers principally the assaying of silver and gold and the determination of these values in ores, sweepings, and base metal. It seems to have been written more for the goldsmith and jeweler than for the primary producer of metals. There were approximately sixty different substances needed in the operations described and not over a dozen different types of raw material (ore, matte, crude or alloyed metal) are mentioned. The methods of separation used were essentially simple and reasonably reliable, though the processes were not sufficiently understood to permit the selection of the simplest effective ingredients, and there was a great tendency to employ complicated fluxes, with unnecessary repetition of long-continued heatings indicative of a leisurely pace of life. Practically all the processes described are based on a few chemical facts: the inability of gold to combine with sulphur, while silver and the base metals form easily fusible sulphides; the ready oxidation of base metals; and the ii- solubility of gold in nitric acid. Fluxes serve to make earthy impurities fusible, and to carry oxidizing or sulphurizing ingredients. Many of the processes of assaying had changed little up to the beginning of the present century. Even as late as 1924, when the writer took a University course in fire assaying, the crucibles, cupels, scorifiers, molds, and tongs were identical with those of the sixteenth century, though the wind furnace had a stack on it and the muffle for cupelling was gas-fired.* The fluxes were purer, but of the same essential composition. That this branch- or twig-of metallurgy had not advanced in any funda-

Jan 1, 1949

By John Fritz

MEMBERS of the American engineering societies who were in London and Paris during the last days of. June and early July were present at many interesting gatherings. The official delegates of the Founder societies were the specially honored guests of the foreign engineering societies, but other American engineers took part in the meetings. The members of the delegation were: Arthur S. Dwight, Charles F. Rand, William Kelly, representing A. I. M. E.; Ambrose Swasey (general chairman of deputation), Ira N. Hollis, Jesse M. Smith, representing A. S. M. E.; F. B. Jewett, A. E. Kennelly, G. O. Squier, representing A. I. E. E.; Charles T. Main, Robert A. Cummings, John R. Freeman, D. C. Henny, representing A. S. C. E.

Jan 1, 1921

By Robert Linton

AT its meeting on May 21, the Board of Directors approved the recommendations submitted by President Lovejoy and named a nominating committee for the year that is especially well distributed as to major technical interest and as to geography. As may be seen from the list published herewith, two come from the East, two from the Midwest, and three from the far West. Mr. Linton, the chairman, has been a valued member of the Institute for 36 years. A memorandum drawn up by Paul D. Merica, representing the A.I.M.E., and W. R. Barclay, representing The Institute of Metals of Great Britain, setting forth a reciprocal plan for special memberships in each Institute for members of the other, was discussed. Both societies already have formally approved the plan in principle and Dr. Merica was clothed with full authority to agree on a few small details that have not been settled, and conclude the arrangement in behalf of the Institute.

Jan 1, 1936

By Sherwin F. Kelly

THE joint meetings of the Mining Geology Committee and the Society of Economic Geologists proved to be deservedly popular, and the interesting papers drew an attendance which strained the capacity of one of the large meeting rooms.. As might be expected these days when even the Supreme Court can't keep away from the subject of gold, the discussions opened on Thursday morning with several papers devoted to questions of structural and mineralogical relationships of the deposits of this metal. The presentation of Ira B. Joralemon's paper, "Veins and Faults in the Bralorne Mine," by Reno Sales, elicited considerable discussion on the relation of mariposite to gold, and the situation of the gold deposits with respect -to the Coast Range batholith. H. V. Warren stated that lie had observed mariposite always to be associated with gold in this region, but that gold was not always associated with mariposite. He pointed out that there is a series of veins on the west side of the batholith with a different mineralogy that, because of their richness but small size could quite easily make good, small mines. John A. Dresser concurred in this, and said lie thought this region was one of great promise for the mining geologist. He also reported having found mariposite associated with gold values below commercial limits, in the Appalachian regions.

Jan 1, 1935

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By Paul F. Kerr

QUARTZ of a certain kind, is one of our strategic minerals, and Brazil is probably the one important available source. Crystals of quartz of suitable size and perfection for piezoelectrical application are rare; their most outstanding use is in radio work. Clear quartz, or "crystal," free from twinning, cracks, foreign particles of other disturbing lines of growth, and gaseous or liquid inclusions, is cut into plates which provide excellent control of frequency in broadcasting. The squares or rectangles are less than a millimeter in thickness and ordinarily on the order of 1 in. along each side. They are cut at definite angles with respect to the axes of the crystal, and ground with opposite surfaces parallel. Each small slab must be a section of one crystal, uniform throughout in atomic alignment. The thickness of the chip controls the frequency of a broadcast and it is most important to have the plates oriented and ground with utmost precision. Opposite surfaces are parallel to within 0.001 mm. and expansion or contraction due to the temperature is limited to one part in a million.

Jan 1, 1942

By T. A. Rickard

The purposes of composition are various; one purpose, for instance, is to make a record for the writer's own use, as in a diary. That does not involve responsibility to others. There is also the writing meant to influence opinion-to be persuasive, and pleasing. With such writing we need not concern ourselves at this stage of our study. The prime purpose of technical writing is to be informative-to convey information; therefore it must" be clear beyond the chance of misunderstanding. Such clearness is impossible if meaningless or ill chosen, words are sprinkled through the text. Discard the trivial phrases that are constantly at your elbow. Brush aside a host of vapid superlatives. Metternich exclaimed:' "The superla¬tive is the mark of fools". It is a false emphasis, like the underlining in a school-girl's letter. For example, the little word `very' can be deleted nine times out of ten; it is an impediment to terse and perspicuous writing, as 'the multitudinous hand-baggage of the British tourist is to his travel. 'Very' supposes comparison. A mine with a 1000-ft. shaft is very deep to the scribe who writes from the Joplin district', in Missouri, but it seems a shallow hole to a man living at Calumet, Michigan. A vein that is 10 feet across may be considered very wide at Cripple Creek, Colorado, but it is only a `stringer' to the miner at the Homestake, in South Dakota. Ore assaying $20 in gold is very rich at Juneau, Alaska, where .10,000 tons of $1 ore is crushed daily, but it is relatively low-grade to the pocket-miner at Alleghany, in California. It is all a matter of comparison; unless the reader knows your standards of depth, width, or richness, your `very' has no significance. "Where erosion was very rapid or oxidation very shallow"

Jan 1, 1931

Map

Jan 1, 1957

By JOHN R. SUMAN

TONIGHT I want to speak of the current problems and the postwar difficulties facing American industry. American industry has done an outstanding job in adjusting its operations to wartime necessity. The national income for 1942 was nearly $120,000,090,000 and of this outlay approximately $55,000,000,000 went for war material. The enormity of the expenditures for war material is indicated by the fact that the expenditures for war purposes alone were greater than the annual gross national income in the period 1931-34. This tremendous production job in turning out a record output of war products was accomplished by industry in spite of a large number of restraining and hampering influences, and I want to mention several of the more important problems.

Jan 1, 1943

By C. Schlumberger, M. Schlumberger

The object of this paper is to clarify the idea, so important when exploring by potential methods, of the depth of investigation attainable by electrical measurements. After defining, with some precision, .the term "depth of investigation'' in geophysics, the authors show how it is possible to regulate this depth in potential methods and to obtain an 'electrical drilling" from surface observations. They consider also the difficulties encountered in deep measurements and indicate how it is possible to reach greater depths than those having an industrial interest. Depth of Investigation The term, depth of investigation, in its general sense, is easily understood. For instance, a driller who can pull cores from a depth of 2000 m. is capable of working, with accuracy, to that depth. By means of a properly placed drill, he may locate an orebody at a depth of 1999 m., however small this orebody may be. On the contrary, the term as used in geophysics requires precise elaboration. As a matter of fact, no geophysical method, irrespective of the physical property studied (density, magnetic permeability, conductivity), can discover a very small body at a great depth because, in practice, the physical parameter upon which such a geophysical method is based is never regular enough, throughout the ground, to distinguish the feeble anomaly caused by the small, deep-lying body from the numerous anomalies due to irregularities of the encasing terrains. Aside from this question of the ratio between the size of the body being hunted for and its depth of burial, a second factor plays its role in the possible depth of investigation; that is the difference, for the parameter under consideration, between the body and its surrounding material. The greater this difference, and the more homogeneous the encasing terrains, the greater is the possible depth of investigation. This being generally established for all geophysical methods, it is possible to distinguish two main classes of these methods, from this same point of view

Jan 1, 1932

By J. Campbell

The hydrostatic tensions in pure metals and long freezing range alloys are evaluated theoretically considering the viscous flow of residual liquid and the general plastic collapse of the casting. The former mechanism operates until the radii of the remaining liquid channels are of the order of 10-3 cm radius, after which the second process limits the attainable negative pressures which range from —1500 to -4200 atm for nickel, aluminum, copper, and iron. In previous reports1'2 the maximum possible hydrostatic tensions developed during solidification have been evaluated employing spherical symmetry. This inevitably involves the concept of totally confined liquid regions, the reality of which has recently been brought into serious doubt3 following observations of the freezing of various transparent materials. Regions of interdendritic liquid which are apparently about to be isolated by the growth of dendrite arms are observed not to be cut off because the advance of the dendrite tips is arrested until the region has completely solidified. Although this may be the result of the very low melting point liquid available at this late stage in freezing, or the result of a higher rate of heat transfer to the dendrite tips because of the acceleration in liquid flow rate near the completion of solidification, this point need not concern us. In this paper an attempt is made to approximate more closely to real conditions; thus the assumption of confined liquid regions is abandoned and cylindrical symmetry adopted. It has also been necessary, therefore, to consider the viscous flow of residual liquid through the remaining channels in the pasty zone. Furthermore, the rather special conditions of spherically symmetric solidification led to extremely high solidification rates and hence unusually high tensile stresses as solidification neared completion; the cylindrical Symmetry appears to yield solidification rates and stresses which are more typical of real castings. The rate of solidification is first considered since this critically affects both the flow of the liquid and the creep of the solid.

Jan 1, 1969

By Karl V. Lindell

THE Jeffrey mine of the Canadian Johns-Manville Co., Asbestos, Que. has operated for a number of years, supplying the parent company, Johns-Manville, raw material for asbestos products. The mine is situated in the 70-mile-long serpentine belt running from Asbestos, Que. on the west to East Broughton on the east. This district is the most important producing area in the world of quality spinning-fiber asbestos, with 11 operating mines supplying 70 pct of the world's needs. The Jeffrey mine, located 90 miles from Montreal and approximately 35 miles southwest of Thetford, accounts for 50 pct of the Canadian asbestos output. Production from the Canadian serpentine belt is the chrysotile asbestos, which is considered the best available for spinning. Consumers in the United States prefer the clean, fine fibers of the Canadian chrysotile of the type produced by the Jeffrey mine. Mining In 1881, when the mine was first opened, all work, including drilling, was done by hand. The deposit, located on a hillside, was first worked as a sidehill cut by hand drilling 15-ft holes and blasting with black powder. The fiber was chiselled from the broken rock. Hand derricks, later powered by horses, were used to raise the rock as the pit deepened. Eventually, the pit became so deep that derricks were, by necessity, replaced by aerial tramways. In the late 1930's, further deepening of the open pit, with the resulting constriction of the pit bottom brought about the need for altering the mining system then in use. The high ratio of overburden to be handled to mill ore mined and the value of surface structures, not company property, that would be destroyed in expanding the area of the pit, definitely indicated vertical rather than horizontal expansion would have to be used. One exception to this was that a small area on company property to north and east of the pit could be opened up. The mining problem then resolved itself into two phases; make the small lateral expansion and as rapidly as possible choose a mining method that would expand the mine vertically. Several methods for vertical expansion were studied and rejected. Methods considered included shrinkage stoping, block caving, glory holing, and various modifications of open workings. Block caving was finally accepted as the most suitable method of underground development. Cost factors and production were important factors in the decision, also, the asbestos mines in the Thetford area were already having success with this method. Original plans provided for the lateral expansion of the open mine where possible and beginning the underground operation. This program was based on the open pit being worked out in 1954, with the underground development and production gradually increasing until the open mine was depleted. In 1949, the plan was changed to allow underground development to progress at maximum so that underground output would be 550 tons per hr by 1951. Any deficit in ore would be mined from the open pit. This change permitted extending the life of the open pit through 1964 and in this time would make available a large quantity of readily attained ore. Block Caving at The Jeffrey Mine Plans for the underground operation were formulated on a 12,000-ton-per-day basis, and the adaptability of block caving methods to high production presented a desirable situation. As shown in the main-haulage plan, a continuous loop was laid out for smooth operation of the underground railroad from the loading points to the underground crusher. A feature encountered at the Jeffrey mine, as well as other asbestos mines using caving methods, is the large size of caved material, requiring that ore be crushed before hoisting.

Jan 1, 1952

By Zárate G. E.

Practical and statistical considerations concerned with the sampling, sample preparation and chemical analysis of precious metal ores are reviewed. The principal requirements related with the characteristics of sample cutter, sample preparation, equipment and methods are discussed. The main errors introduced in the different stages of the sampling systems are defined. The application of statistical techniques to evaluate these errors to determine the ore grade variation and to design the number of increments needed to get an accurate assay are presented. Finally, results obtained with the application of this method to gold and silver ores are analyzed and some recommendations are given.

Jan 1, 1984

By H. M. Roberts

H. M. ROBERTS, Minneapolis, Minn. (communication to the Secretary*). -The rifling of drill cores is a frequent source of interest to men engaged in diamond drilling. Previous to the appearance of Dr. Crane's paper, there has been little record of connected observation or rigid speculation as applied to the cause of rifling. Replying to one of Dr. Crane's letters of inquiry, I ventured my opinion that the cause of rifling was a complex problem in physics, which I had not attempted to solve up to that time, except to ascribe it to the general cause of rotation and vibration of the rods. The question is worth attention not only as a matter of curious scientific interest but also for the reason that it stimulates thought on

Jan 10, 1916

By W. B. Mather

THE object of this paper is to record and interpret data collected during the examination of over 250 barite deposits in the Central Mineral District of Missouri. [ ] In the course of this study, the origin of the deposits, which the author believes to be hydrothermal, has been given particular attention. Economic barite deposits occur in two main areas in Missouri: (I) in the Washington County District of Southeast Missouri, from which over go pct of the state's production is derived; and (2) in the Central Mineral District, which includes portions of 15 counties in Central Missouri (Fig I). Barite in the smaller Washington County District is mined from widespread low grade, relatively shallow residual deposits, whereas in the Central District, it is mined

Jan 1, 1947

By T. S. Hutchinson, C. E. Kemp

The bottom water drive analysis presented by Muskat has been extended to include fields with wider well spacings. Curves are presented from which volumetric sweepout, water-oil ratio, and rate relations may be calculated. The effects of non-unity ratios on sweepout eficiency and productivity decline have been studied by an approximate method. Also, the effect of gravity on volumetric sweepout has been approximated for a particurlar geometry. INTRODUCTION The purpose of this paper is to report work done in applying the analysis of bottom water drive reservoirs given by Muskat1 to a larger class of reservoirs, to extend this analysis to include the effects of gravity and non-unity mobility ratios in an approximate manner, and to investigate the rate of decline of productive capacity. The bottom water drive type reservoir is one where the oil is underlain by a water zone of sufficient thickness that water movement is essentially vertical. This system is defined in more detail in the appendix and a one well element is shown diagrammatically in Fig. 1. Muskat obtained solutions to the equations describing the volumetric displacement efficiency of idealized bottom water drive systems by assuming that gravity effects due to differences in density betwecn oil and water were negligible and that the mobilities of oil and water were the same. If either of these assumptions is not made, the complexity of the system makes an analytical solution well nigh impossible at the present stage of mathematical development. Coles and Stade' developed an approximation to consider these factors. The authors have refined approximations, starting with the same basic assumption, which should give a somewhat quantitative picture of bottom water drive performance when mobilities are not equal and the effects of gravity are not negligible. The results of these approximate calculations can then be used to obtain the decline in well productivity as the field is depleted.

Jan 1, 1957