Search Documents

By R. A. Foos

During the radium boom in the early part of the twentieth century, the basic chemistry of uranium was fairly well defined. Uranium production has progressed from the status of a radium by-product to a very important industry. With the ever increasing need for more efficient and cheaper methods of processing uranium ores, new techniques are being developed. Since uranium and vanadium often occur together in nature, the latter element will also be considered. As production rates, costs, and certain aspects of uranium chemistry are still classified by the Atomic Energy Commission, these will not be discussed. Domestic uranium deposits, in general, are composed of the minerals carnotite, which contains hexavalent uranium, and to a lesser extent, pitchblende and uraninite, which contain tetravalent uranium. Carnotite also usually contains vanadium. The uranium and vanadium contents of these ores vary considerably. The ores currently processed on the Colorado Plateau assay from 0.2 to 0.4 pct U and from trace amounts to 5.0 pct V. On the other hand, the phosphate rock deposits of the southeastern U. S., from which uranium is also recovered, contain only about 0.01 to 0.02 pct; processing of the

Sep 1, 1956

BOSTON SECTION ALFRED C. LANE, Chairman, GEORGE A. PACKARD, Vice-chairman, E. E. BUGBEE, Sec'y-Treas., Mass. Inst. of Technology, Cambridge, Mass. R. L. AGASSIZ, FRED W. DENTON. Forty-sixth Meeting The forty-sixth meeting of the Boston section was held at the University Club on Monday evening, Jan. 28, 1918. Thirty-six members and guests were present, which is a record for this Section. After a good dinner, President Philip N. Moore, of the Institute, was introduced, and spoke of the many problems of the Institute. The topics covered were the progress and growth of the Institute during the administrative year, the efforts to stimulate the local sections and to bring them more in touch with the policies and problems of the parent body and, last but not least, of the constructive results and patriotic work of the Institute in the national service of the war. The other guest of the Section, Mr. Thomas Nelson Perkins, Counsel for the Priority Board, spoke most entertainingly of recent experiences in Russia, England and France. After considerable discussion during which Mr. Perkins most obligingly answered innumerable questions, the meeting adjourned at about 10 p. m.

Jan 7, 1918

By C. G. Black

THE purpose of this paper is to present data obtained from an investi-gation conducted on the grindability of coal by the American Society for Testing Materials Tentative Standard ball-mill method. This investiga-tion has been conducted over a period of a year, during which time several hundred tests were run on a wide selection of different coals coming from Pennsylvania, Ohio, West Virginia and Kentucky. The data herewith presented tend to show that the tentative standard ball-mill method might give results that are misleading and that a volume measure might be more indicative of the true grindability 'of materials of varying specific gravity. A means whereby the time element might be reduced has been studied and other phases of this work such as preparation of samples, mechanical screening, reporting results and duplicating tests have been investigated. It is hoped that all criticism offered in this paper will be taken as constructive, with the purpose in mind of perfecting the method now tentative to show the true conditions and of making optional the manner in which certain parts of the test might be conducted to meet diversified laboratory conditions.

Jan 1, 1936

By Alan Probert

IN his inaugural address in 1949, President Truman made a policy declaration which launched the foreign technical assistance program known to the world as Point Four. Congress passed Public Law 535 defining the scope of the program and holding activities to certain limitations. It also provided $34.5 million for the first fiscal year. The Technical Cooperation Administration was established within the Department of State to coordinate and direct a program to include "economic, engineering, medical, educational, agricultural, fishery, mineral and fiscal surveys, demonstration, training and similar projects." The mineral programs of Point Four have been staffed and managed by two agencies of the Department of Interior, the Geological Survey and the Bureau of Mines. The Geological Survey is concerned primarily with water-supply problems, the discovery of mineral deposits, and the determination of habit, shape, and grade of mineral deposits. The Bureau of Mines is concerned with determining the commercial potentialities of mineral deposits, mineral technology, and the production and distribution of mineral commodities. Mineral projects comprised only 1 pet of the first year's budget. In spite of the relatively insignificant expenditure compared to those for food, agriculture, and health, a commendable record has been achieved.

Jan 1, 1952

By G. E. Agar, A. L. Mular

G. E. Agar (Manager, Minerals Processing Research, International Minerals & Chemical Corp., Skokie, III.) — The author notes a discrepancy between the parameters a and ß which are the slopes of the size distribution and energy-size modulus plots respectively. The reason for the discrepancy and the systematic decrease in the magnitude of a with grinding time is abundantly clear from the work of Fuerstenau8 on dry grinding. Fuerstenau shows very clearly in his Fig. 5 that at short retention times the parameter a is the same as that obtained by sizing over the complete size range. From this figure, it is obvious that sizing to only 400 mesh gave distribution curves similar to Mular's - that is, the slope apparently decreased systematically with increased grinding. As a consequence of the improper determination of a, the magnitude of ß given by Mular must be larger than the true value. In order to demonstrate this, the following Fig. 6 was taken from Mular's paper (his Fig. 1). Fuer-stenau's results show that we can approximate the correct value of K by drawing lines parallel to the short retention time curves through the 400-mesh

Jan 1, 1963

By K. C. Li

TITANIUM, because of its high strength, weight ratio, and high melting point, became the metal of the jet age. Zirconium, because of its low neutron cross section and high corrosion resistance to hot water, became an integral part of the nuclear era. Since both metals are very similar chemically, more or less the same process is used for their production. The sudden rise of this new industry of titanium and zirconium seems to have caused some uncertainty as to the future development of processes for making these metals. Although zirconium was discovered in 1789 and titanium in 1790, it was not until 1945, six years after W. J. Kroll patented his process, that F, S. Wartman of the U. S. Bureau of Mines perfected the technique of producing ductile titanium, and it was not until 1946 that Kroll perfected the technique of producing ductile zirconium in commercial quantities. Since then the Government and private industry have spent millions of dollars each year constantly searching for new methods, with the hope that some day titanium can be produced as economically as aluminum and magnesium or as cheaply as stainless steel.

Jan 11, 1957

By G. St. J. Perrott

During the past year, the Bureau of Mines has carried on an investigation of liquid-oxygen explosives (L.O.X.) to supplement the work described in previous publications.' The present paper gives results of the first part of this work, which was a laboratory investigation of the properties of typical combustibles used in L.O.X., and the relation of these properties to the absorption and retention of oxygen by the explosives and their explosive characteristics. No attempt will be made to describe the development of liquid-oxygen explosives, because this phase of the subject has been well covered.2 The L.O.X. cartridge consists of a paper wrapper filled with an absorbent combustible material that is saturated with liquid oxygen by soaking it therein. After saturation, the cartridge is removed from the liquid and fired with fuse and cap, or electric detonator, in a manner similar to other explosives. Certain types of cartridge may be detonated with fuse alone, requiring no cap to initiate the detonation. ' By suitable variation of the nature and density of the combustible, cartridges having a wide variety of explosive characteristics may be made.

Jan 1, 1925

By Turno De Michelis

The Porto Marghera plant was erected in 1936 for the production of 10,000 tons of electrolytic zinc annually. Since then it has been continuously enlarged until annual production of the metal reached 40,000 tons in 1969. At the same time the processing cycle was modified bringing it up to date with modern techniques, and was completed by installations for the recovery of by-products in the minerals treated and subsequent processing of the base metal. 90% of the zinc produced is of 99.993% purity . At present the plant comprises, first of all, the zinc blende desulphuration department which has a single modern fluid bed furnace capable of processing 220 - 250 tons of dry crude mineral daily; it is connected to the sulphuric acid plant with its three catalysis sections each capable of producing 60-70 tons of sul9huri.c acid monohydrate daily. The roasted blende is conveyed pneumatically to plants for leaching of the zinc and purification of the resulting solution. During recent years this department has been completely transformed from the discontinuous cycle, for which it was built, to the continuous cycle, paying great attention to

Jan 1, 1970

By Henry M. Bates, Roscoe Pound

Mr. Chairman and Gentlemen: I accepted your Chairman's invitation to speak to a group of experts in this field with the greatest hesitation, because I know little or nothing about it. Certainly I can make no detailed suggestions, or suggest planning along very definite lines. You cannot do that sort of thing in a vacuum, and as I have suggested, my knowledge of the whole oil problem is next to nothing. It is possible that as a student of our public law, constitutional law particularly, for a number of years, I have acquired a perspective that may enable me to offer, for what they are worth, some general thoughts on these problems. I think that nothing in the whole field of law requires more definitely and clearly the functional approach than does the problem of a sound legal solution of the difficulties of the oil and gas industry. The industry is dealing with substances that are peculiar, and one must know how those substances act and what has been the history of the industry, to undertake to make anything like specific suggestions. I certainly am not qualified.

Jan 1, 1935

THE 127th meeting of the Institute was held in New York, Feb. 19 to 22, 1923. In addition to the usual large volume of technical matters under consideration, the meeting was particularly noteworthy for the amount of attention given to its business session; the convention of local section representatives also was full of interest. The total registration was 1201. The annual business meeting on Feb. 20, President Dwight presiding, was attended by 125 members, who listened with marked attention to the reports and addresses of the several officers. The chairman departed from the stipulated order of business in order to allow more time for the presentation of remarks on the state of Institute affairs. The previously pub-lished reports of the officers were accepted, as printed. On the report of the tellers, the following officers were declared elected: E. P. Mathewson, Director and President-District 0 T. T. Brewster, Director and Vice-president-District 6 Frank M. Smith, Director and Vice-president-District 11 W. H. Aldridge, Director-District 0 G. H. Clevenger, Director-District 1 A. N. Diehl, Director-District 3 Reno H. Sales, Director-District 7 Seeley W. Mudd, Director-District 10

Jan 3, 1923

By Jack Parker

There are some simple theoretical approaches to pillar design but they leave much to be desired. There are also more complex theoretical approaches, but at this time the most realistic approach is to go into the mines and observe and measure how real pillars are performing under real conditions; to allow the information thus gathered to ferment in our minds - then to project the behaviour of those pillars into our new designs and mining techniques, probably with no formulas at all. Examples, from half-a-dozen different mines, show how a simple- minded approach, through observation and measurement, led to changes in pillar design which often contradicted the textbook but made very significant contributions to mining safety, efficiency and costs. The good news is that we know a lot more about pillar design than we realize. We have, between us, looked at millions of pillars of all kinds, under all conditions, but we have overlooked what they are trying to tell us. We can take problem situations and turn them into opportunities and, in that way, become better stewards of the resources which have been given to us.

Jan 1, 1983

By F. H. Rhines, A. H. Grobe

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By A. H. Grobe, F. H. Rhines

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By Hugh M. Roberts, R. D. Longyear

Introduction ............................ 27 GEnERal Geology........................... 29 The ORebodY in Western Falco~ridgI TownsRip........... 31 Quartzite-Graywacke Formation................... 33 Greenstone............................ 33 Norite ............................. 33 Metamorphism.......................... 35 The Orebody........................... 36 Mineralogy ........................... 37 Grade of Ore........................... 42 Genesis oF tEe Ores . :....................... 43 Summary of Various Hypotheses.................. 44 Magmatic Segregation by Crystallization of Sulphides........ 44 Gravitational Segregation of Molten Sulphides at the Base of the Magma 45 Intrusion of Molten Sulphides after the Consolidation of 'he Nurite.. 45 Deposition by Hydrothermal Solutions.............. 46 Magmatic Segregation by Extraction from Crystallizing Norite... SO The Relationship between the Exploration and Theories of Origin .... 50 Volume Relations of Norite and Sulphides............... 62 Intimate Association of Norite and Sulphides............. 53 Granitic Material........................ 54 Uniform Content........................ 54 Sulphides in Walls......................... 54 Absence of Typical Hydrothermal Minerals.............. 55 SUmmaRY................................ 56 Introduction During 1916 and 1917. the E. J. Longyear Co. of Minneapolis. Minn., carried out a campaign of exploration for nickel-copper ore in the Sudbury District of Ontario. The work was initiated by W. E. Smith. a resident of Sudbury. who called the attention of W. J. Mead. Chief Geologist

Jan 1, 1918

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By H. A. Meyerhoff, R. J. Colony

Deposits of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residual limonite at the west end of the island near Mayagüezl-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7"9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugües, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By K. K. Kershner, W. A. Calhoun, C. W. Funk

Future resources of aluminum may require the utilization of low grade ores to provide a more permanent protection for the nation. Aluminum minerals such as cloy, shale, and high iron laterites may become important sources. An evaluation of reserves is given. New laboratory results are reported on the Vereinigte desilication process. THIS report on future resources of aluminum metal emphasizes the necessity for investigating utilization of low grade potential ores to provide more permanent protection for the nation. Partial or complete interruption of the importation of high grade aluminum ores must be given consideration. Ultimately, aluminum minerals such as clay, shale, and high iron laterites may become the principal sources of aluminum. The development of extractive processes for treating these low grade materials is a step in long-range national preparedness that should receive more attention. In formulating such processes, the application of beneficiation methods for the purpose of classifying the several types of minerals before subjecting each type to the more expensive extractive procedures should be considered, and a careful survey of the basic factors of power sources, transportation facilities, and sources of raw material should be made. Domestic Bauxite Resources Of the domestic supply of current, treatable-grade bauxite, 95 pct comes from Arkansas. The present reserve of Arkansas bauxite suitable for metal production, including abrasive-grade, Bayer-grade, and modified Bayer-grade ores, is 34,000,000 tons. The total reserve of bauxite of all grades is approximately 75,000,000 tons. Reserves are estimated on a mined and dried basis. Data available to the Bureau of Mines in 1948 to 1949 were used in preparing Table I, which shows a breakdown by grades of bauxite for about a half of the reserves of the state. The modified Bayer ore, 10,555,500 long dry tons, is based on a cutoff of 8 to 15 pct silica. The sub- marginal 10,074,700 long dry tons is assumed to contain more than 40 pct gibbsite, more than 15 pct silica, and less than 32 pct available alumina. A considerable amount of this low grade material was consumed in 1949 and 1950. Additional tonnages of bauxitic and kaolinitic clays are indicated by the Bureau of Mines drilling project.' Applying a 50 pct factor to arrive at long tons mined and dried, the results of this project are approximately 31,500,000 tons kaolinitic clay at +35 pct Al²O3 and 11,800,000 tons kaolinitic clay at 20 to 35 pct A1,0,. Total reserves of kaolinitic clays are probably quite extensive—several times the reserves shown in the Bureau's work. Total reserves of bauxitic and high iron clays from the drilling program and previously established figures are 63,980,000 tons. The mineral dressing methods,' the lime-sinter process, he lime-sinter modification of the Pederson process," the lime-soda sinter process,"-' and the Alcoa combination processa. have been described in the literature and will not be elaborated upon here. The less familiar Vereinigte Aluminium-Werke process used by the Germans during World War 11 may require some amplification. It was used to bene-ficiate boehmite ores containing 12 to 18 pct silica for a feed to the European Bayer process. Ore was

Jan 1, 1952

By C. F. Cockrell, H. E. Shafer, J. W. Leonard

A significant technological development is discussed for the processing of certain power plant flyashes that are a problem because they contain a high water-soluble mineral content and yield inferior flyash-based brick. This development is based on the addition of hydrochloric acid to the flyash-bottom ash-sodium silicate blends used for the production of flyash-based structures. Favorable changes are evi-dent in sodium silicate consumption, where about half the amount used for making brick from normal flyash is required, processing costs, and strength and appearance of the resulting freshly formed green and fired structural products. In some high cost in-stances (above the $30 or less per thousand brick estimated for normal flyash), hydrochloric acid additions can replace or reduce other costly additives normally required for problem flyashes. This results in savings of as much as $9 per thousand brick. These developments offer promising possibilities for utilizing problem flyashes as well as flyashes which may come into contact with water soluble sulfur as a result of the eventual application of certain experimental air pollution control processes. Much of the research datal-6 accrued through work by the Coal Research Bureau of West Virginia University for the Department of Interior's Office of Coal Research on converting waste power coal ash to valuable brick and other structural products, can be categorized as follows: (1) general ash-to-brick tech- nology; (2) specific ash-to-brick optimization; (3) pilot plant progress; (4) production cost estimates. A summary of the progress on bench-scale experiments indicates that coal ash can yield two types of brick. An acceptable brick is obtained by mixing 73.6% fly-ash, 23.5% bottom ash and 2.9% sodium silicate solution (dry basis). Depending on the flyash and bottom ash used, optimum brick can be manufactured by mixing 72-77% flyash, 20-25% bottom ash and 2.3-3.0% sodium silicate (dry basis) with Na2O : SiO2 ratio varied according to the composition of the flyash used. These blends are thoroughly mixed and mechanically formed into green brick shapes at pressures ranging from 1000 to the more usual 3000 lb per sq in. The green shapes then are dried and fired at temperatures ranging from 1975-2150°F using clay brick cycles that are shorter than standard. Other findings reported to date indicate that when making optimum brick, it is necessary to carefully control the top size of the moisture-releasing bottom ash so that it falls between 8 and 30 mesh, depending on the flyash used. Moreover, the chemical composition of bottom ash and flyash have been found to be of little significance with the exception of a few problem flyashes which are the subject of this paper. Finally, the pilot plant, which was previously reported under construction, is now in operation. This will indicate, among other things, the cost of brick production, which was earlier estimated for non-problem flyashes at $30 or less per thousand brick. The foregoing bench-scale technology is applicable to all the initially tested ashes as well as to the majority of ashes examined during the course of research. However, a few of the ashes yield green and fired products that may be structurally inferior or unacceptable, necessitating excessive and diverse reagent addition, and/or may be coated with unsightly surface deposits. These problem ashes generally originate in certain areas of Illinois, western Ken-

Jan 1, 1969

By R. T. Torgerson, W. A. Baginski

Alloying studies were conducted on modifications of Cb-10W-1OHf (C-129) alloy as part of a cooperative alloy development effort between The Boeing Co. and the Wah Chang Corp. The purpose of these studies was to develop a fabricable, high- strength columbium alloy with superior melding properties. The initial investigations of alloy modifications were conducted using laboratory-melted button ingots. An alloy with the composition exhibited excellent veld ductility, elevated-ternpevature strength, and fabricability. The yttrium-modified alloy was desigrzated C-129Y and was selected for further developrnetzt. Three prodziction heats of C-129Y weve processed into sheet. Welding, forming, and tensile proper-lies are presented for this material. Tungsten-are welds of. C-129Y exhibited a minimum bend radius of 1/2T in the as-welded conditioti compared to 8T for C-129 alloy. An investigation was conducted on Disil coating of C-129Y and test data are presented on oxidation resistance and effects of re-entry environments. The excellent combination of strength, fabricability, weldability, and low transition temperature of C-129Y alloy offers potential design advantages for use of this alloy in structures of aerospace vehicles. It is atiticipated that C-129Y will rapidly supplant C-129 and similar alloys clue to the versatility provided by its impvoved welditzg properties. COLUMBIUM alloys with improved properties are required to achieve better performance and efficiency of radiation-cooled structures for re-entry vehicles and recoverable launch systems. Cooperative work by The Boeing Co. and the Wah Chang Corp. resulted in the development several years ago of C-129 alloy, a high-strength Cb-W-Hf alloy.' This alloy has received favorable consideration for many advanced designs of high-temperature structures due to its excellent combination of properties. However, this alloy exhibits low weld ductility unless given a high-temperature stress-relief treatment. For this reason the development effort was directed towards modification of the C-129 alloy composition (Cb-1OW-1OHf) to eliminate the need for post-weld heat treatment. This paper describes the successful development of an alloy meeting this requirement. This new alloy was designated C-129Y and has a nominal composition of EXPERIMENTAL PROCEDURES Alloying Studies. Various Cb-W-Hf compositions were investigated using are-melted button ingots. These buttons were hot-forged using a protective glass coating and rolled into sheet specimens. Metal-lographic examination: tensile testing, and welding studies were conducted to evaluate properties of the experimental alloys. Sheet Fabrication. Three pilot production heats of C-129Y were fabricated into sheet to establish processing techniques and to determine sheet properties. The three heats consisted of 6-in.-diam ingots weighing from 140 to 250 lb. The ingots were prepared by electron-be am melting followed by vacuum-arc melting. The hafnium and yttrium additions were made during the are-melting operation by tack welding alloy strip additions to the Cb-W master-alloy electrode. The final ingots were machined into billets with samples of the machine turnings collected for chemical analysis. Ingot breakdown methods for the three heats are as follows: Ingot Ingot Heat Size Weiaht___Breakdown Method A 6 in. 250 lb Hot extrusion B 6 in. 140 lb Hot forging C 6 in. 250 lb Hot extrusion Sheet bars from the extrusion and forging operations were conditioned, recrystallized, and rolled into sheet. Initial rolling was conducted at elevated temperatures and final rolling was conducted at room temperature.

Jan 1, 1967

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957