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By C. H. Lieb

ONE astounding fact in the production of petroleum is the comparatively recent realization by producers that flowing production is the cheapest crude produced. About 1910 or even later, operators actually endeavored to get a producing well to pumping as quickly as possible after completion. A well was not really considered to be completed until it was operating on the pump. Remarkable progress has been made since then. It was not until about 1920 that producers began to take a serious interest in pressures and to think a little about proper methods of handling oil wells. Pressure gauges were installed, and records of pressures maintained, which was quite an innovation. Desultory experiments were made with tubing of different sizes, as well as experiments with placing the bottom of the tubing string at different levels in the well. Probably the first important departure from customary procedure was about 1926, during the Seminole development, when gas lift

Jan 1, 1936

By S. H. Penn

One of the more challenging aspects of the unfolding age of space travel centers about the opportunity for man to use the natural resources of other worlds. The first of the extraterrestrial worlds to be exploited will be the moon. After only a scant few thousand years of scratching the earth's crust, man will embark upon a venture that for centuries has excited the imagination of many (while staggering that of most) and may become a reality within the next decade. There has never been a time when so much money and effort will have been expended to exploit an area about which so little is known. Paradoxically, this effort combines much of the detached objectivity so typical of our analytical time with the proverbial optimism of the indefatigable prospector. As the earliest manned lunar missions will be brief and exploratory in nature, astronauts will not be expected to attempt to exploit any of the possible lunar natural resources. In later missions, with a more extended period of time available for the astronauts to stay on the moon, it may be desirable or even necessary to "live off the land". The resulting exploitation of lunar resources will be intended primarily to reduce the dependence of manned missions upon terrestrial logistic support and to reduce the cost of maintaining lunar bases.

Jan 3, 1966

By E. J. Duggan

CLIMAX ore is an altered and highly silicified granite, about half of the gangue being quartz. Molybdenite is the only mineral recovered and most of it is intimately associated with the quartz in fine veinlets. Other minerals are molybdite, pyrite, and chalcopyrite. Although the molybdite may be readily extracted by hydrometallurgical methods, its content is too low to make this profitable. The pyrite ranges from 2 to 5 per cent and the chalcopyrite from 0.03 to 0.05 per cent. There is not enough copper to make its recovery attractive and one of the problems is its elimination, and that of pyrite iron, from the final product. On account of the high degree of dissemination of the molybdenite and the necessity of eliminating the iron and copper, fine-grinding followed by flotation is the only known feasible method of concentration. Two factors, peculiar to Climax ore, have a predominating influence on the metallurgical attack: (1) Molybdenite is one of the most easily floated minerals. High recoveries may be made with pine oil alone if the

Jan 1, 1946

By W. H. Davitt

While it is true that taxes, especially income taxes, whether they be federal, state, or local, are not usually thought of as a "cost" of doing business, it is equally true that these tax costs do reduce the distributable profits just as much as the cost of power, supplies, or labor. Therefore, the consideration given to taxes is often as important as that given to other costs. Hopefully you will recognize that, within certain limits, taxes can be controlled to an economic advantage. The tax laws as now imposed are quite complex. Many of these laws and the regulations thereunder involve many factual determinations, technical considerations, and specialized valuations that can best be made by people trained in the specific area concerned. A substantial amount of a tax liability turns on the proper consideration given to issues involving facts and principles which are peculiarly engineering in nature. The importance of these "engineering" issues in tax administration has been significantly increased in recent years by our rapidly advancing technology, automation, stepped-up mineral and oil exploitation, new industries such as electronics and nuclear power, and the extension of percentage depletion to all minerals. These specialized requirements incorporated in the law are so technical that full consideration can not be given by people with a non-engineering background.

Jan 7, 1974

By R. E. Somers

I. Introduction...........................604 1. Location, Topography, and Climate...............604 2. Scope of Work and Acknowledgments...............606 3. History and Mining......................606 11. General Geology.........................609 1. Introduction...........................609 2. Granite. :..........................610 3. Quartz Porphyry......................... 612 4. Monzonite........................... 614 5. Volcanic Breccia........,................ 618 6. Gravels............................. 619 111. Economic Geology......................... 619 1. Introduction........................... 619 2. Mineralogy........................... 619 3. Occurrence of the Ores...................... 622 4. Oxidation and Downward Enrichment............... 630 5. Rock Alteration........................639 6. Genesis of the Ores........................ 643 I. Introduction 1. Location, Topography, and Climate The Burro Mountains are located in the southwestern part of New Mexico, in Grant county. The group is made up of two distinct mountain masses, known as the Little Burros and the Big Burros, the former lying about 6 miles southwest of Silver City, and the latter about 9 miles farther in the same direction. They are separated by the valley of the Mangas River, a tributary of the Gila, and a stream only in name, except after a heavy downpour of rain. The Little Burros attain an elevation of 6,625 ft. above sea level, and the Big Burros 8,054 ft., with the surrounding country averaging about 6,000 ft. To the south of these mountains stretches the desert plain, while to the north are the more frequent elevations of the mountainous country.

Jan 1, 1916

By AIME AIME

QUALITY and size do not ordinarily go hand in hand, but there is good evidence that both these attributes reached a new peak at the Annual Meeting of the Institute in New York just concluded. Certainly, the total attendance of 2500 was far above any yet attained, as might be expected with the recent rapid growth of Institute member- ship. General comment indicates that the quality of the papers also was notable, though not measurable by so definite a yardstick as attendance. During the meeting 49 technical sessions were held, at which more than 250 formal papers were presented. In addition, there were some thirty special meetings of committees, Divisions, and other Institute groups. In reporting the Annual Meeting eleven years ago the statement was made that "unless the Engineering Societies should build for themselves a new building it is probable that no meeting can be larger," and "the fifth floor, where a buffet lunch is served each day, has reached its full capacity and it seems quite evident that any future development of Institute meetings must be along the lines of quality, not size." Unfortunately the angel to succeed Andrew Carnegie, who financed the building of the present home of the Institute 35 years ago, has not yet ' appeared. Even if some one would merely build another elevator or two in the present building it would help. Fortunately, the modern auditorium of the American Radiator & Standard

Jan 1, 1940

By IRVING H. WENTIVORTII

(New York Meeting, February, 1912.) THE little town of San Nicolás, Tamaulipas, Mexico, lies approximately 60 miles east of Linares, situated in the State of Nuevo Leon, and 150 miles SE. of Monterey, as shown in the sketch-map. Fig. 1. The place is reached from Monterey by the Tampico train as far as Linares, a distance of 92 miles, and then by coach the rest of the way. It is situated in a narrow valley between low hills, the houses forming one main street and a plaza. It is peopled by about 500 inhabitants. The climate is temperate, the thermometer ranging from 90° in summer to a few degrees below freezing-point in winter; but this severe weather only lasts a day or two at a time, when the " northers " blow. There are no streams in the vicinity, but water sufficient for the use of the people is obtained from wells. The rainfall is about the same as that in the rest of NE. Mexico. The rainy months are July, August, and September. The rest of the year is practically dry, with an occasional showery day or two during the winter, when a " norther " is blowing. Timber is abundant in many localities. There are two varieties of oak, besides mesquite, ebony, "maguira," "patol," and a number of other kinds of trees indigenous to this region. I. HISTORY. On the discovery of the silver-lead hearing veins occurring in this district, the mining-camp of San Nicolás was founded in 1767 by the Spaniards, and numerous mines were opened and worked for a distance of abort 3 miles east and 5 miles west of the town. At the western extremity and near the Carrolena mine, a small town called San Pedro was built. The ruined walls of the houses form a single street, and all is over-

Aug 1, 1912

By J. A. Retty

IN the Labrador iron fields two concessions, totaling nearly 24,000 square miles, have been staked out and commercial-grade deposits delineated. The Newfoundland-Labrador concession, owned by the Labrador Mining and Exploration Co. Ltd., is a 20,000-square-mile tract in the upper basins of the Hamilton and N askaupi Rivers which drain into Lake Melville. The New Quebec licensed area is 3900 square miles, owned by the Hollinger North Shore Exploration Co. Ltd., lying to the northwest of the northwestern part of the Labrador concession. It includes the upper basin of the Swampy Bay River and part of the upper basin of the Whale River, both of which drain into Ungava Bay. Both of the above-named companies are controlled by Hollinger Consolidated Gold Mines Ltd. with The M. A. Hanna Co., of Cleveland, holding a minority interest. When exploration was first undertaken in 1936, the only published map of the area was that prepared by A. P. Low in 1895. It showed only the main watercourses and gave only a rough, general idea of the geology. The numerous lakes of this vast area had to be first sketched and then mapped. Since then, extensive geological and topographical surveys have been conducted by the Labrador company, work which is normally done by Government branches. The object of the work was to examine the area and gradually eliminate unfavorable or less favorable prospecting ground. With this object in view, geological

Jan 1, 1948

By Robert E. Sorenson

EXPLORATION for deep-seated orebodies in the Silver Belt area of the Coeur d'Alene mining district is complicated by meager surface expressions of diagnostic criteria, lack of knowledge of the significance of specific alteration phenomena, and the great expense involved in the exploration for ore shoots, the tops of which often occur near sea level elevation or below and as much as 4000 ft or more below the surface. Except for the early studies of Ransome and Calkins in 1903 and 1904,[1] little geological work was done in the Coeur d'Alene district for many years, and it is only during the last 15 to 20 years that complete and careful geological mapping has been applied to most of the mines in the area. Much early information, which now would prove invaluable, is lost in hundreds of miles of caved and inaccessible mine openings not mapped by mining geologists. In more recent years mining geology has become a tool of greater use in the district, and some measurable progress is being made in the accumulation of observations that are adding gradually to the knowledge of ore deposits in the district.

Jan 7, 1951

By L. S. Richardson, N. J. Grant

REACTIONS of oxygen and nitrogen at low pressures with titanium have recently been studied by a number of investigators.1-3 Gulbransen and Andrew' noted that the reaction with nitrogen followed the parabolic rate law whereas the reaction with oxygen deviated slightly from this law in the temperature range 300° to 800°C. In the work reported here, commercial titanium (75 A) was used as the test material. Cylinders 2.5 in. long and 0.25 in. in diameter were machined from heavier bar stock. The test pieces were given a metallographic finish, immersed for 30 min in cold concentrated HC1, washed in water, then acetone, and dried with lint-free cloth. Reaction rates were determined in a modified Sieverts type apparatus by measuring the decrease in gas pressure of the reacting gas contained in a constant volume. The amount of gas added could be measured in a calibrated gas burette to an accuracy of 0.01 mm. During the course of a run the temperature never varied by more than 10°C and then only for brief moments. After placing the specimen in the furnace, the system was first evacuated for 12 hr at room temperature, and then flushed with purified argon five times, adsorbed gases being discharged during this period from the glass system with a high frequency spark coil. The flushing and discharging were repeated at 400°C. This rather involved procedure was found necessary after a number of trial runs indicated extraneous effects traceable to the system. Reaction periods up to 2 hr were used, at initial gas pressures of 0.2 to 0.5 atm. Experimental Results Fig. 1 shows the decrease in oxygen pressure for tests at 0.5 atm at various temperatures as a function of the square root of the time. Deviations from linearity are minor and the parabolic rate law is obeyed. Fig. 2 shows the same plot for the nitrogen reaction. A definite deviation from linearity is noted; however, it is probable that the higher initial rates are caused by the presence of small amounts of oxygen contamination, the initial faster rate changing to the slower rate after about 5 to 10 min. Calculations of the rate constants were made on the basis of the latter portion of the curves. The parabolic rate law constants calculated from these curves are shown for oxygen and nitrogen in Fig. 3. In spite of some scatter the average curves are quite definite. Changes in gas pressure of the order of 20 pct did not result in a measurable change in the rate law constants. The activation energy for the oxygen reaction was calculated to be 47,400 cal per mol (above 700°C), which is not in agreement with the value quoted by Gulbransen and Andrew' for lower temperatures, their value being 26,000 cal below 600°C. The activation energy for the nitrogen reaction was calculated to be 45,400 cal per mol above about

Jan 1, 1955

A comprehensive, systematically structured mineral evaluation system is a prime requirement for objectively assessing mineral supply impacts on the economy. The Minerals Availability System developed by the US Bureau of Mines is a step in the right direction-a well-organized unraveling of the mineral supply network, structured in format to allow quick retrieval for rapid listing, supply analysis, and other uses.

Jan 9, 1977

By Henry E. Wood

Cleveland Meeting, October, 1912.) IN my opinion, the concentration of minerals by flotation is the most interesting problem in ore-dressing, and will command eventually far more consideration than it has at present. For many ores it furnishes a complete method of concentration absolutely independent of specific gravity, and thus simplifies the milling of many difficult combinations. Not having to recognize the influence of specific gravity, we are also able to dispense with some of the complications resulting from classifying-conditions. Where flotation cannot be used for a complete separation of the minerals from the gangue, it will be found, in nearly all cases, to save those portions which are generally lost by reason of their fine state of division. For this reason, it should be looked upon mainly as an aid to general concentration, although there are many ores so well adapted to flotation that more than 90 per cent. of the valuable metals can be recovered from them in one operation by this process. In presenting the results of my investigations in. flotation, I have endeavored to theorize as little as possible. That side of the subject has been extensively discussed by others. My earliest work with flotation was done in 1895, when I used various oils, grease, soap, etc., with results that were remarkable. I did not realize then that with water alone equally good separations could be made. Up to 1906, my endeavors were confined to attempts to keep the concentrates on the tables well wetted and away from exposure to the air. In common with others, I observed that when there was any obstruction in. the wash-water on the table of sufficient size to divert the water to either side, the concentrates collected, and, on exposure to the air, would promptly float away. This convinced me that the sulphides were all good " swimmers," and that if,

Nov 1, 1912

By F. W. Lee

Historical-From the beginning of time, all ingenuity of mankind has been concentrated upon the methods of finding gold and unusual deposits in the earth. An illustration (Fig. 1) from the old treatise by Agricola, "De Re Metallica," published in 1580, will serve to show the im-plicit faith of that generation in divining methods. However, it was not until 1920 that real progress was made in prospecting by using the latest advances of the physical sciences. The public interest was stimulated by the successes of these methods on the part of commercial oper-ators, and governmental agencies received many requests for information concerning their relia-bility. There were also, in the late 1920's.high- pressure mine-promotion schemes which used geophysical methods in a very questionable manner, symbolized in Figure 2 as of 1928 by an elec-trified forked stick. Authoritative information concerning such practices for public protection was needed to curb such notorious undertakings. Dr. Scott Turner, then Director of the United States Bureau of Mines, thoroughly understood the situation and was first in the governmental de-partments to recognize the possible value of a study of modern prospecting methods. The Bureau of Mines began this investigation by employing Drs. A. S. Eve and D. A. Keys of McGill University for short periods in the summer in 1927. Their first publication [see 1 of "References" at end of paper] served to illustrate the fundamental scientific principles which underlie geophysical prospecting. This was followed by a second publication [21 giving the results of field-tests. In the light of the rapid improvements during the intervening ten years, these two papers take a historical position. Later a full-time position under Civil Service was planned by the Bureau of Mines for con-tinuous investigations and research concerning geophysics and its applications to prospecting. It was Turner's idea that. since the oil-industry had been making very rapid progress with good results, if mineral mining could also benefit to the same degree, it would be of great help to that industry.

Jan 1, 1940

By John Griffen, David H. Davis

Much of the ground to be covered by this paper was ably covered by a paper presented by Messrs. Morrow and Jordan1 before a joint meeting of the Iron and Steel Section of the Engineers Society of West-ern Pennsylvania and the A.I.M.E. Pitts-burgh Section at Pittsburgh in the spring of 1940. As that paper was not published, the present authors have availed them-selves of Mr. Morrow's kind permission to use information given therein. Similar figures for the latest years available have been added to many statistics originally presented. It is unfortunate that Mr. Jordan's death removes his stimulating guidance and help, which the authors would have welcomed and have found invaluable in the past. One interested in the Pittsburgh seam should not fail to read the exhaustive and authoritative paper by Eavenson2 presented in 1938. As Allegheny, Fayette, Greene, Washington, and Westmoreland Counties contain practically all the reserves and furnish nearly all of the production from the Pittsburgh seam in Pennsylvania at the present time, this area only is intended when reference is made to the Pittsburgh seam in Pennsylvania. On much of the seam in Greene and Washington Counties, which contain a large proportion of the total reserves, insufficient data are available to determine the detailed characteristics of the seam with any degree of finality. It is hoped that the data presented here will fairly well indicate the probable characteristics. Economic Importance of the Pittsburgh Seam The Pittsburgh seam in Pennsylvania is of primary importance as a coal resource, not only because of its substantial reserves but because it contributes such a large proportion of the coal used in the country and an even larger proportion of that used in the manufacture of coke. Mr. Ashley3 placed the estimated recoverable reserves (1935) of the Pittsburgh coal bed in Pennsylvania at 7,500,000,000 tons.* Although a considerable portion of this tonnage is not now suitable for coking coal, because of its high sulphur content, undoubtedly the supply of coking coal will last for many years and that not suitable for coking will furnish industry with an ample supply of energy. In attempting to assess the contribution of the Pittsburgh seam to total coal production and to that of coal used in making coke, one finds that the statistics published annually by the U. S. Bureau of Mines, Minerals Yearbook, do not give tonnages classified as to seams but only as to districts or states and counties. However, it happens that, at present and during much of the

Jan 1, 1944

By David H. Davis, John Griffen

Much of the ground to be covered by this paper was ably covered by a paper presented by Messrs. Morrow and Jordan1 before a joint meeting of the Iron and Steel Section of the Engineers Society of West-ern Pennsylvania and the A.I.M.E. Pitts-burgh Section at Pittsburgh in the spring of 1940. As that paper was not published, the present authors have availed them-selves of Mr. Morrow's kind permission to use information given therein. Similar figures for the latest years available have been added to many statistics originally presented. It is unfortunate that Mr. Jordan's death removes his stimulating guidance and help, which the authors would have welcomed and have found invaluable in the past. One interested in the Pittsburgh seam should not fail to read the exhaustive and authoritative paper by Eavenson2 presented in 1938. As Allegheny, Fayette, Greene, Washington, and Westmoreland Counties contain practically all the reserves and furnish nearly all of the production from the Pittsburgh seam in Pennsylvania at the present time, this area only is intended when reference is made to the Pittsburgh seam in Pennsylvania. On much of the seam in Greene and Washington Counties, which contain a large proportion of the total reserves, insufficient data are available to determine the detailed characteristics of the seam with any degree of finality. It is hoped that the data presented here will fairly well indicate the probable characteristics. Economic Importance of the Pittsburgh Seam The Pittsburgh seam in Pennsylvania is of primary importance as a coal resource, not only because of its substantial reserves but because it contributes such a large proportion of the coal used in the country and an even larger proportion of that used in the manufacture of coke. Mr. Ashley3 placed the estimated recoverable reserves (1935) of the Pittsburgh coal bed in Pennsylvania at 7,500,000,000 tons.* Although a considerable portion of this tonnage is not now suitable for coking coal, because of its high sulphur content, undoubtedly the supply of coking coal will last for many years and that not suitable for coking will furnish industry with an ample supply of energy. In attempting to assess the contribution of the Pittsburgh seam to total coal production and to that of coal used in making coke, one finds that the statistics published annually by the U. S. Bureau of Mines, Minerals Yearbook, do not give tonnages classified as to seams but only as to districts or states and counties. However, it happens that, at present and during much of the

Jan 1, 1944

By T. B. Counselman

PROBABLY the earliest concentration of iron ore in this country was carried on in the northeastern magnetite areas. Magnetic concentration was relatively simple and gave a concentrate that, after agglomeration, and in spite of being high in phosphorus because of the dry concentrating methods then in use, was satisfactory blast-furnace feed. Production from the northeastern magnetite area languished after the discovery and development of the Lake Superior ores, where there was seemingly an unlimited tonnage of high-grade ore, first the Michigan ores, and subsequently the still larger deposits of Minnesota. For years only the higher grade, direct shipping ores of the Lake Superior district were mined. Those of Michigan, and of the Vermilion Range in Minnesota, were hard ores and came principally from underground mines. The softer ores of the Mesabi came partly from underground mines, but mostly from the enormous deposits that could be worked by open-pit methods. The costs of ore from these open-pit deposits, even with the high initial cost of stripping, were so low that the underground mines of the Mesabi could hardly compete. The so-called Old Range ores, of Michigan and of the Vermilion Range of Minnesota, were hard and lumpy, and opened up the burden in the blast furnace, therefore making possible harder driving with greater output. Also, some of these ores were of such grade and physical characteristics that they were suitable for charge ore in the open hearth. These ores, therefore, commanded a price premium, and could compete with the softer, finer, but cheaper, Mesabi ores. The big tonnage reserves, however, are on the Mesabi, and it is these big open-pit deposits that constitute our stock pile of iron ore, from which we are drawing so heavily during this war period. On the western end of the Mesabi the ore was found to be high in silica, and not suitable as furnace feed. As early as 1902, attempts were made to concentrate this so-called wash ore and by 1910 the first washing plant was put into operation. The process was very simple, consisting essentially of a sizing and washing operation, with scalping screens, logwashers, and tables, which later were replaced by classifiers. Ore particles finer than 100 mesh were deliberately wasted, because these fines were undesirable in the furnace. Fortunately, these tailings were impounded, and already are being reworked. Before long some of the low-grade ores began to require more elaborate treatment than the simple washing operation and, tables having been discarded because of their low capacity, in favor of classifiers, jigs were next introduced. These were able to discard coarser pieces of tailing than classifiers. Jigs are in active use today, various improvements having been made in their design and application. Various other machines and methods of concentration have been tried from time to time, and have in turn been discarded for more improved processes. The latest and most important process that has been

Jan 1, 1943

By AIME AIME

T. E. PURCELL, general chairman . of the local committee, opened the seventh meeting of the Fuels Division A.S.M.E. and the Coal Division A.I.M.E., at the William Penn Hotel, Pittsburgh, Oct. 28-29, by introducing Harry M. Moses, president, H. C. Frick Coke Co., who welcomed the 500 registrants to "our town." Mr. Moses, in his brief talk, declared that in the postwar period each of the new centers must have a reason for existence. Pittsburgh, he said, has no iron ore, or bauxite, and limestone is scattered and not near by; but Pittsburgh does have low-cost fuel within reasonable distance. Its problem is the economical utilization of the low-cost fuels that remain, as the high-quality fuels are gone. Mr. Moses expressed confidence in this group in the solution of the problem and looked forward to what they would do. Harold V. Coes, the first A.S.M.E. president to attend one of these conferences, responded. He thoroughly believed in these joint meetings - in the cross-fertilization of ideas. Each Division learns from the other. Mr. Purcell then turned the meeting over to J. E. Tobey who presided over the coal research session that followed.

Jan 1, 1943

By Donald H. McLaughlin, John H. Moses

IN the latitude of Lima, the broad uplifted block that forms the Andes is made up of a complex sequence of folded and faulted sediments and volcanics, broken by large and small bodies of granitic rocks and porphyries with which the principal mineral deposits are closely associated in both time and space. The intrusives are a final episode in the geologic history as revealed by the consolidated rocks, for after their emplacement and after the formation of the primary ore deposits in and about them the record is simply one of long continued erosion and uplift.

Jan 1, 1945

By AIME AIME

INDUSTRIAL Pittsburgh, the center of the coal and iron and steel industry of the world, was host to the Coal Division at its Fall Meeting held there on Oct. 21 and 22 at the William Penn Hotel. The past year has witnessed remarkable progress in new methods of mining and burning of coal and many of the papers on the program discussed these developments. Nearly 100 had registered at the time of the first session on Wednesday morning and this number increased to 168 on Thursday. Owing to the large number of papers on the program, eighteen in all, it was necessary to hold group meetings on Thursday morning, with a capacity attendance at each meeting. . Chairman McAuliffe was on hand early Wednesday morning to open the meeting. George Otis Smith, representing President Lovejoy, came over from Cleveland where he attended the meetings of the Institute of Metals Division. Secretary Parsons arrived later from Cleveland and spent the whole morning with the executive committee of the Division. Doctor Smith, Secretary Parsons, and J. T. Breunich were the official representatives from Institute headquarters.

Jan 1, 1936

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model