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By Fred Bond

THE process of comminution by grinding is properly classified as an art, rather than as a science. Like most other operations concerned in ore dressing, or in the treat-ment of nonmetallic minerals, the mathe-matical relationships of rock breaking are still obscure, and much disputed. If some basic formula exists, comparable for in-stance to E = RI in electricity, it has not yet been placed in common use. The absence of such a comprehensive mathe-matical background undoubtedly is the cause of many inefficient designs and installations, as well as of much poorly oriented experimental work. On the other hand, the mathematical immaturity of the process constitutes an opportunity for a real contribution on the part of those who enjoy mental pioneering. Some of the statements made in any such exploratory work may be little more than opinions, and it is to be expected that some will later be proved untrue; but such an evolutionary development is necessary if we are ever to arrive at the fundamental laws, the discovery of which can change the empirical art into a mathematically exact science. The most significant principle of com-minution that we possess is probably Rittinger's law, which states that the work done in crushing or grinding is proportional to the area of the new surface produced. There is an alternative theory, known as Kick's law, which formerly was preferred to Rittinger's but which now is rather dis-credited. According to Kick, the work done in comminution is proportional to the volume, or weight, of the pieces broken, or to the cube of their diameters, while accord-ing to Rittinger it is proportional to the square of the diameters.

Jan 1, 1940

By ALEC CROWELL

Mississippi has had oil production for only the past six years and natural gas production of minor magnitude since' 1926. The search for oil and gas commenced in 1903 and 1496 wells had been drilled in search of oil and gas up to Jan. 1, 1946. As the year 1945 ended, 659 wells were producing oil and gas from 23 separate reservoirs. The production for the year was 8,353,719,000 standard cubic feet of natural gas measured on a pressure base of 15.025 lb. per sq. in. abs., 15.316,009 bbl. of oil¬field water and 19,093,766 bbl. of crude oil and condensate. Production for the year 1944 was 2,636,067,000 standard cubic feet of gas, 14,979,793 bbl. of salt water and 16,420,346 bbl. of crude oil and condensate.

Jan 1, 1946

No. Place Date Vol. 1. Wilkes-Barre, Pa May, '71 1 2. Bethlehem. Pa Aug., '71 1 3. Troy, N. Y Nov.,'71 1 4. Philadelphia, Pa Feb., '72 5. New York, N. Y.* May, '72 8. Pittsburgh, Pa Oct., '72 7. Boston, Mass Feb., '73 8. Philadelphia, Pa.* May, '73 9. Easton, Pa Oct.. '73 10. New York, N. Y.Feb., '74 11. St. Louis, Mo.* May, '74 12. Hazleton. Pa Oct., '74 13. New Haven, Conn Feb., '75 14. Dover, N. J.* May, '75 15. Cleveland, O Oct., '75

Jan 1, 1929

By Otis W. Freeman

Production of oil in Indiana during 1944 is estimated at approximately 4,950,000 bbl., a decline of 6 per cent from the preceding year. Shortage of labor and material, together with governmental regulations resulting from the war, largely account for the drop in output and limited new developments. Three new pools were discovered in the state during 1944. Two of these, New Harmony, South, and Hovey, West, are in Posey County. Six wells in the New Harmony, South, field produced 66,422 bbl. of oil last year. A third field, Cato, in Pike County, did not market the oil from its discovery well during 1944. Several wells discovered oil in the Henderson field of Jay County along the Ohio state line. An important south extension of the St. Thomas field in Knox County was discovered during the year. Active drilling took place in the Inman, East, and Upton fields, Posey County, both discovered in 1943. Twenty-two wells in Inman, East, produced 151,1gr bbl. in 1944 and 12 in Upton produced 107,052 bbl. Owensville, and especially Owensville, North, in Gibson County, made large gains in production as a result of active drilling. The Dodds Bridge field in Sullivan County continued good production from deep sands reached in 1942. The Griffin continued to be the largest producer among the oil pools of Indiana, accounting for 2,004,180 bbl., over 40 per cent of the state's output. The next largest producing fields are Mt. Vernon and New Harmony, both in Posey County. The largest gas well brought in during 1944 was in the Rockport field, Spencer County, and had an initial output of 2,680,000 cu. ft. per day. The most productive gas fields in Indiana are Rockport, Spencer County, Greensburg, Decatur County, and Unionville, Monroe County. Total production in the state is . hard to estimate, as considerable gas is consumcd in farm homes and for other local uses, and never is reported, but was near 1500 million cubic feet. Some oil from the Trenton field is also used locally and is unreported from pipe-line runs. A total of 606,145 ft. of new hole was drilled in Indiana in 1944. Most of the completions were in Posey and Gibson counties, although wells were drilled in 36 different counties. During the year 331 wells were completed. Of these, 145 found oil in commercial quantities and 28 were gas wells. The initial production of the 145 oil wells was 11,908 bbl. per day. Settled production would be less, of course. The largest wells reported during the year were two on the J. W. Mann farm, in the Mt. Vernon field, with a flush flow of 500 to 800 bbl. each.. Six pools, all small "one well" affairs, were abandoned in 1944; i.e., Fleenor and Patoka in Gibson County, Grafton and Rapture in Posey County, Vaughn in Vandei-bwgh County and Millersburgh, Warrick County.

Jan 1, 1945

By H. J. Wasson

At the close of 1927 Venezuela was producing at the rate of 205,000 bbl, per day, making it the third country in the world in point of present daily production. For the year, the total was close to 64,000,000 bbl., representing an increase of about 70 per cent. over the 37,000,000 bbl. in round numbers produced in 1926. All of the 1927 production canie from fields opened up before the beginning of the year. While no new fields were added to the list of shippers, the past 12 months' wildcatting yielded a fair quota of new discoveries which, in the light of prcsent results, may be considered likely sources of production in due time. Altogether three such promising finds were made Of first importance, at least for the immediate future, is the completion by the Lago Petroleum Corpn. of the San Matins well, 4 miles north of the present edge of the Lagunillas field. Although rated as only a 125. bbl. well, at 3217 ft., it indicates a probable extension of the field over the intervening 4 miles between the two. The two other wildcat discoveries of importance were the Los Manueles well in the District of Colon, which has in all probability opened up a new field about 7 miles north of the present Tarra oprations; and the Honibre Pintado well of the Standard Oil Co. of Venezuela,. in the State of Falcon, which is considered to be a promising clc~vc~lop~ncnt. Neither of these last mentioned two discoveries will apprcciably affect production during 1928, as the Manueles area must await the carrying out of a general plan for the exploitation of the District of Colon, a problem requiring time. The Hombre Pintado area is being tested further, but doubtless several wells will be put down before. anything definite will be done towards making the pipe line. arrangements that rnust necessarily precede the commercial exploitation of the field. The San Matias Well The San Matias well is a highly significant dcvelopment,. It is located along the trend of the La Rosa-Ilagunillas producing formations, and when drilling started, production in the Lagunillas field was 4 miles

Jan 1, 1928

Andy H. Vassiliou – Introduction Ladies and gentlemen,.good evening and welcome to the Paul F. Kerr Memorial Symposium dinner. I believe we are all here to honor the memory of a great teacher and advisor, and a true friend -- Professor Kerr, or Dr. Kerr, or to most of us who were his students, "Pappy" Kerr. Most of us who attended the Paul F. Kerr Memorial Symposium earlier today at the New York Hilton had the opportunity to read, or listen to, or discuss scientific papers presented in honor of Dr. Kerr. In addition, all of the speakers had the opportunity to reminisce about their association with Dr. Kerr, who was credited as having contributed substantially to their graduate education and the development of their careers. Dr. Kerr's two daughters -- Ruth and Nancy -- who attended the Symposium at the Hilton are also here with us tonight. I think we should keep tonight's festivities on an informal basis since we are all old friends or former students of Dr. Kerr. Some of us may want to say a few words about our experiences at the time we were students at Columbia, and hopefully include some anecdotes relating to Professor Kerr. I would like to invite everyone to do so, but first we have arranged for two of us to be the lead speakers, whom I will introduce in a few moments.

Jan 1, 1985

By W. J. O'CONNOR

THE production of lead in the United States for the period from 1720 to 1912 was 10,432,668 tons valued at $924,600,000. The average price during this period was 4.4c. a pound, although lead sold at times below 3 cents. We know that in the early days of lead smelting in Montana lead was deliberately lost in the slag and only enough reduced as bullion to collect the silver. This bullion was freighted by ox team to Corinne, Utah, the terminus of the railroad at that time, and shipped to Swansea or Omaha, Neb., for refining. The slag from some of the above mentioned operations contained as much as 15 per cent lead and has since been resmelted. Since 1921 the production of lead has increased each year and the price and tonnage have been as follows :

Jan 1, 1926

By John M. Kelly

New Mexico produced 38,882,342 bbl. of oil in 1943, and regained seventh place among the oil-producing states. This production was an increase of 6,968,526 bbl., or 21.8 per cent, over the figure for 1942. The maximum per-well allowable on Jan. I, 1943, was 38 bbl. daily and at the end of the year this figure had been increased to 48 bbl. Allocations as set by the New Mexico Oil Conservation Commission closely followed recommendations by the Petroleum Administrator for War and the average daily pipe-line runs were 106,476 bbl., being within 2.2 per cent of these allocations. Production for Lea County was 33,043,925 bbl.; Eddy County, 5,405,-967 bbl.; northwestern New Mexico, 432,070 bbl., and Chaves County, 380 barrels. Drilling activity for New Mexico in 1943 was only 75 per cent of that in 1942, with 255 completions. Of these completions 180 were oil wells, 10 gas wells and 65 dry holes. The ratio of dry holes to producers, more than I to 3, was the greatest in recent years. Of these dry holes, 46 were drilled within the boundaries of proven . areas while 19 were wildcats. Wildcat drilling during 1943 was responsible for the discovery of four new oil fields and one new gas field, as well as three extensions to existing proration areas. At the close of the year the New Mexico Oil Conservation Commission had designated 64 areas as proven for oil and/or gas. The Monument area was again New Mexico's largest producing oil field, with an annual production of 7,228,855 bbl. Next was Eunice, with 6,461,044 bbl., followed by Vacuum with 4,946,110 bbl. IIobbs, ranking fourth, with 3,799,114 bbl., was the leader in total recovery with an accumulated production of 104,180,53I bbl., or more than 10,000 bbl. per acre to date. Drilling activity in Lea County accounted for completion of 67 oil wells, 2 gas wells and 24 dry holes. One of these oil wells was the discovery well of a new area and three extended proven areas. The most active drilling campaign in the county was again in the Maljamar area, where 18 oil wells were completed. The Maljamar Cooperative Repressuring Agreement affected 141 producing wells, and operations were a decided success, more than 85 per cent of the gas produced being returned to formation. The new oil field for Lea County was designated as the San Simon area although boundaries have not been established to date. Discovery well for this area was the Skelly Oil Company's State U. No. I, in theNE. NE. K of sec. 5, T.22 S.,R.ssE. This well was drilled to a total depth of 4183 ft. and plugged back to 4138 ft. after encountering bottom-hole water. Initial production was 124 bbl. per day on the pump. This oil is 37.4' gravity and has a sulphur content of I per cent. Productian is from Yates sand of Permian age. The Lynn area of southern Lea cbunty was extended 145 miles to the northwest

Jan 1, 1944

By John M. Kelly

New Mexico produced 38,882,342 bbl. of oil in 1943, and regained seventh place among the oil-producing states. This production was an increase of 6,968,526 bbl., or 21.8 per cent, over the figure for 1942. The maximum per-well allowable on Jan. I, 1943, was 38 bbl. daily and at the end of the year this figure had been increased to 48 bbl. Allocations as set by the New Mexico Oil Conservation Commission closely followed recommendations by the Petroleum Administrator for War and the average daily pipe-line runs were 106,476 bbl., being within 2.2 per cent of these allocations. Production for Lea County was 33,043,925 bbl.; Eddy County, 5,405,-967 bbl.; northwestern New Mexico, 432,070 bbl., and Chaves County, 380 barrels. Drilling activity for New Mexico in 1943 was only 75 per cent of that in 1942, with 255 completions. Of these completions 180 were oil wells, 10 gas wells and 65 dry holes. The ratio of dry holes to producers, more than I to 3, was the greatest in recent years. Of these dry holes, 46 were drilled within the boundaries of proven . areas while 19 were wildcats. Wildcat drilling during 1943 was responsible for the discovery of four new oil fields and one new gas field, as well as three extensions to existing proration areas. At the close of the year the New Mexico Oil Conservation Commission had designated 64 areas as proven for oil and/or gas. The Monument area was again New Mexico's largest producing oil field, with an annual production of 7,228,855 bbl. Next was Eunice, with 6,461,044 bbl., followed by Vacuum with 4,946,110 bbl. IIobbs, ranking fourth, with 3,799,114 bbl., was the leader in total recovery with an accumulated production of 104,180,53I bbl., or more than 10,000 bbl. per acre to date. Drilling activity in Lea County accounted for completion of 67 oil wells, 2 gas wells and 24 dry holes. One of these oil wells was the discovery well of a new area and three extended proven areas. The most active drilling campaign in the county was again in the Maljamar area, where 18 oil wells were completed. The Maljamar Cooperative Repressuring Agreement affected 141 producing wells, and operations were a decided success, more than 85 per cent of the gas produced being returned to formation. The new oil field for Lea County was designated as the San Simon area although boundaries have not been established to date. Discovery well for this area was the Skelly Oil Company's State U. No. I, in theNE. NE. K of sec. 5, T.22 S.,R.ssE. This well was drilled to a total depth of 4183 ft. and plugged back to 4138 ft. after encountering bottom-hole water. Initial production was 124 bbl. per day on the pump. This oil is 37.4' gravity and has a sulphur content of I per cent. Productian is from Yates sand of Permian age. The Lynn area of southern Lea cbunty was extended 145 miles to the northwest

Jan 1, 1944

By HUBERT O. De

IN December, 1936, several drilling tests were made at the Hubert O. De Beck feldspar mine at Green Mountain, N. C., to determine the most efficient type of hammier-drill bit and drilling method for use at this particular property. This mine is well recognized as having the hardest rock in the Burnsville - Spruce Pine feldspar district and drilling costs always have been high. Local structural deformation has greatly distorted and warped the normal crystalline structure of the feldspar so the rock is much tougher than usual. In studying drilling methods and bit types, available literature was re¬viewed but little specific data could be found on the direct comparison of four-point and six-point drill bits so the following results may be of some interest.

Jan 1, 1937

At a special inaugural ceremony in Blue Hill, Maine on August 3rd, Governor John H. Reed detonated the first blast to signify the beginning of development work on a new copper-zinc mining venture that seems destined to focus increased interest in the mineral potential of that State. The property which is the first new base metal mine to be discovered in the northern Appalachians in 30 years, is owned by Black Hawk Mining Co., a subsidiary of Denison Mines Ltd. of Toronto. When it goes on-stream in 1966, it will join Ducktown, Tenn., as the only active copper producing region, east of the Mississippi River. According to official reports submitted by the Company to Robert G. Doyle, Maine's State Geologist, Black Hawk has found ore reserves totalling 4.5 million tons. Assays show 2.8 million tons of 2.0'; copper and 0.4 oz. of silver per ton; 1.2 million tons of 16.75% zinc and 0.58% copper; and 0.5 million tons of 6.75% lead with 4.25 oz. of silver per toil and some zinc.

Jan 9, 1964

By L. W. Legerwood

During the past three decades, the oil industry has expended increasing eflorts seeking improved drilling tools or systems to reduce drilling costs. The total cost of these efforts is unknown, but it certainly amounts 10 tens of millions of dollars. Most of the "new" system that past and present investigators have sought to develop actually are old public information. In seeking to implement new-systern concepts, investigators have tested the following: impact at frequencies ranging from 6 to 300 cycles per second; electrical, mechanical and hydraulic meam of actuating percussors; bit rotary speeds up to 2,000 rpm; electric and hydraulic bottom-hole means of rotating bits; bottom-hole machines with power outputs up to 400 hp; shock waves; explosives; high-velocity pellets; flame; arc; grinding wheels; abrasive jets; erosion by high-velocity gases; chemical attack; electric current; magnetic waves; retractable rock bits; reelable drill pipe; continuous coring with reverse circulation; and automation of drilling rigs. Table I shows how these investigations are grouped for discussion purposes in this paper. In spite of these efforts to discover new and improved systems, rotary drilling main;aim its economic leadership. Undoubtedly, rotary drilling costs will continue to be reduced by rigid application of the best available technology and by development of new rotary technology. In view of the extensive past development programs, however, significant long-range improvement appears to be a research, not a development problem. Research must postulate and prove theories and principles governing variour subsurface rock-failure processes pertinent to both rotary and new systems. Ah, research must produce physical and engineering data relative to these processes. When such information is available, earth boring will graduate from an art to a science. Major improvements in rotary drilling can then be expected, and the systematic evolution of an improved drilling method can be initiated—with a strong probability for success. Development of drilling methods other than rotary drilling has been one approach investigated by the industry as a means for reducing drilling costs. Major cost-reduction efforts, however, have been centered on engineering development work aimed at incremental improvements in rotary drilling. A relatively minor effort has been expended to establish basic physical principles and engineering data pertaining to the earth-boring process which can serve as a foundation for the development of cost-cutting drilling hardware. Current oil-industry economic trends have added impetus to the need for effective programs to reduce drilling costs. However, areas for expanded future efforts should be selected only after careful study of past investigations. It is the purpose of this paper to review past and Dresent industry efforts to develop new drilling tools or systems and to suggest areas where additional science is needed. Past reviews of drilling methods have been limited to a few processes prominent at the time the reviews were made. This paper seeks to present a concise, well organized review of all methods that have received actual development or test work. The preparation of a paper seeking to review all past developments is fraught with many difficulties, not the least of which are errors in or obsolesence of printed matter used as source material and the lack of data on industry developments which have not been published. Since de-

Lead-zinc production in Canada accounted for 19% of the total value of metals and minerals produced in 1976, says Keith C. Hendrick, president of Noranda Sides Corp. Mine production of recoverable zinc w as 1. 158 million toils of 27.4% of free world production in 1976. Slab zinc pro¬duction was placed at 472,000 tons that year. Canadian mine production of recoverable lead was 247,000 tons or 10.6% of the free world production. Refined lead that year was at 177,000 tons.

Jan 11, 1977

By P. S. Miller, S. H. Ash

EXTENSIVE and diversified resources justify large populations and great industries. To carry on the business of commerce and meet the demands of large populations, the utilization of tunnels in some form for transportation purposes constitutes an important link in modern civilization. The driving of tunnels has been appropriated by the tunneling branch of the heavy-construction industry, and the progressive steps taken by modern tunnel builders were not even dreamed of 50 years ago. Great strides have been made toward more rapid progress in tunneling in the United States during the past 10 years. Tunneling consists of a definite cycle of operations developed from ideas that are crystallized and translated into action programs through various engineering phases that begin with the first preliminary survey and do not end until the job is completed. Once the line of the bore is established and a time set for the completion of the work, the face must advance according to estimates prepared before the work commences. This schedule must be followed in regular sequence from the moment the drills start against a new face of rock until they are ready again to drill the succeeding face, constituting a round.1 Mining is largely tunneling carried on under conditions often more inherently hazardous than actual tunnel construction, but for various reasons1 tunneling is more hazardous than mining in any branch of the mineral industry, On the other hand, obstacles are sometimes encountered in heavy-construction tunneling projects that when met in mining enterprises do not offer comparable tasks to avoid or overcome them. One of these is the existence of water under high pressures. In mining enterprises, various alternatives offer a solution in driving a tunnel, even to the extent of its discontinuance or the abandonment of the mine, but a "construction" tunnel usually must go forward because some important project depends largely if not entirely upon it. This paper describes an unusual method of driving a water-supply tunnel through rock carrying water under pressures and conditions that did not permit the use of ordinary tunneling methods. THE DELAWARE AQUEDUCT The new Delaware aqueduct is a Manhattan project of some magnitude; when completed, it will contain what probably will be, for some time to come, the longest tunnel in the world. Various features in its construction are currently described in the trade journals of the construction industry, and informative engineering details are given in the Delaware Water Supply News, published twice a month by the Board of Water Supply of the City of New York. Work was begun on this project on March 24, 1937. The tunnel will convey water from reservoirs at the headwaters of the Delaware River to the City of New York.

Jan 1, 1942

By J. Holms Pollok

The determination of specific gravity dates from such antiquity, and the various published methods of determining it are so numerous, that one may well be skeptical as to the value of a new means of obtaining so well-known a quantity. I make no claim to any great novelty for the little device here described, the principles, though not the convenient details, of which are more or less embodied in the publications of Mr.

Jan 1, 1900

By P. W. Bridgman

IT is characteristic of most scientific investigators that they are not satisfied with the discovery of new facts, no matter how curious or unexpected, but that along with the factual discovery there is a constant effort to understand It appears that. one's interest in, and satisfaction with, the discovery of an array of news experimental facts is enormously increased if one has at the same time a theory or hypothesis guiding one's expectation of what sort of new experimental discovery may lie around the corner Conversely, as a theoretical physicist one's satisfaction with his theory is greatly enhanced if along with the development of the theory can go the discovery of new experimental facts, confirming or perhaps modifying the theory as it grows Of course, there have been long and stretches in the history of physics in which new data of unquestioned ultimate importance ham e piled up, without much inspiration or illumination in the way of understanding For 50 years spectroscopy had such an and history, but how irksome this was felt to be is plainly shown by the almost audible relief that greeted the first success by Bohr in injecting understanding into the situation, and by the fresh rush of experimenters into this field when the prospect of understanding had once been offered The investigations in the field of high pressure, which have occupied me for a long time,1 until the last few years have been in very much the Same sort of situation as spectroscopy before the advent of Bohr A great many kids, of data were collected for a great many solid and liquid substances, and there could be no question of the importance of these data, because the uniform change of dimensions produced by hydrostatic pressure is perhaps the simplest conceivable type of alteration to which a body can be subjected But except for a few isolated flashes, there was no theoretical illumination, so that it had to be to a large extent the enthusiasm of the collector that kept me going However, within the last few years the wave-mechanics theory of solids has progressed so rapidly that

Jan 1, 1938

SUDBURY ore processed by International Nickel Co. of Canada Ltd. was recovered for many years as two mill concentrates, one primarily of copper, and the other mixed pentlandite-pyrrhotite, But, Since iron content of the nickeliferous pyrrhotite concentrate was ten times its nickel value, capacity of smelting was limited by the need for slagging the excess iron. A process for recovering the iron con- tent was developed after some years of research and a $20-million plant was constructed to employ the new method. Built near Copper Cliff, Ont., the plant started operation early in 1956, scheduled for separate treatment of 365,000 tons of pyrrhotite each year. It is only the first unit of an installation which will have a capacity of more than 1 million tons per year of pyrrhotite. By early 1958, production totaled more than 200,000 long tons of 68 pct Fe pellets containing 0.003 pct P, 1.5 pct SiO2, 0.01 pct S, and 0.15 pct Ni.

Jan 8, 1958

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

[Trans. No. Place Date Vol. Page 1. Wilkes-Barre, Pa May, '71.. 1 3 2. Bethlehem, I's Aug., '71.. 110 3. Troy, N. Y Nov., '71.. 113 4. Philadelphia, PaFeb., '72.. 117 5. New York, N. YMay, '72120 6. Pittsburgh, Pa Oct., '72.. 125 7. Boston, MassFeb., '73.. 128 8. Philadelphia, Pa.*May, '73.. 23 9. Easton, PaOct., '73.. 27 10. New York, N. Y Feb., '74211] [ ]

Jan 1, 1925

By Richard H. Mote

The endlessly changing pattern of mineral supply and demand offers opportunity to the alert and can bring disaster to the unwary. The discovery of ore bodies, the invention of extractive processes, the provision of new transport facilities, the political stabilization of underdeveloped areas, and many other changes can increase supply dramatically. Such new outpourings of mineral wealth from ore bodies bring fortunes to their developers, and consumers frequently find their competitive positions decidedly improved by new and cheap sources of supply. On the other hand, operators of marginal properties can find competition from newly opened high-grade mines intolerable. Consumers that have depended on the products of nearby, high-cost mines may find new, remote, low-cost supplies advantageous only to their competitors. The invention of new prospecting methods can have spectacular effects. Shortly after World War I the discovery rate of petroleum pools began to decline. The leading prospecting technique of that day, the projection downward of surface reflections of geologic structure, was proving less rewarding. Prophets foretold an oil shortage in the near future. But at that very moment scientists were perfecting the application of seismic waves to reveal underground oil-bearing geologic structures. As these geophysical methods were put into commercial use the whole outlook changed-the problem of the 1930's became how to cope with the surplus from discovery, not how to meet the ever rising demand. Many lead mines were being abandoned as unprofitable about this same time because the penalties charged by smelters for the zinc in the ores and concentrates more than counterbalanced the payments for lead and silver. Then selective flotation (at the time called differential flotation) appeared,

Jan 1, 1964