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By T. P. Meloy

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,

Jan 1, 1963

By Severn P. Brown

Search for ore continued at a feverish pace-as can be attested to by anyone who has tried to arrange for extensive diamond drilling. The stakes are high, and so is the cost as was indicated by Selco Exploration Ltd. when they announced discovery of base metal sulfides at Uchi Lake in northwestern Ontario. It was apparently their first commercial find after 15 years of exploration at a cost of more than $10 million. For the first time in many, many years the big exploration news has come from east of the Mississippi River. In January, the New Jersey Zinc Co., in an unusually worded press release, stated that they had made a major zinc discovery of 13-50 million tons of ore averaging 5-10% Zn. New Jersey's holdings are said to embrace 500 sq mi. The ore was discovered in eastern Tennessee in the upper part of the Knox dolomite of early Ordovician age. Reportedly the mineralization is at depths of 900 to 2000 ft. Currently about 20 diamond drills are working the area for New Jersey. At least nine other major companies are prospecting the region, which now includes parts of Kentucky. Five hundred thousand acres are said to be under lease. Greatest activity is clustered around Carthage, Tenn. In Missouri, the St. Joseph Lead Co. announced plans to develop a new mine in the Brushy Creek area of the "New Lead Belt." copper and zinc concentrates will be by-products.

Jan 1, 1970

By Edwin Ludlow

THERE has been so much misinformation sent out through the newspapers, and I find so few people who are really acquainted with the true facts in regard to the coal strike, that I feel it would be advan-tageous to present the facts as I have been able to gather them. One of the great points that the miners are now mak-ing is the fact that the operators of the central competi-tive field, consisting of the states of Illinois, Indiana, Ohio and Pennsylvania, have refused to meet them in a joint conference such as has been customary in previous years. There are two reasons why the operators de-clined to hold such a meeting. In the first place, the last time they held a meeting of this kind they were all indicted under the Sherman Act for making an agree-ment in restraint of trade. In the second place, the miners at their convention did not authorize their dele-gates to negotiate a new contract, but instructed them that nothing less than a scale based on the present wage, with the addition that there should be a six-hour day, a five-clay week, time j and a half for over time, and double time for Sundays, would be accepted. These additions would very much increase the cost of coal over the present wage scale. The operators could not consider renewing a contract on the present scale, as it would mean ruin for them, and as the miners were not authorized to negotiate a new scale on a fair basis that would enable the operators to mine coal in competi¬tion, with the open-shop mines the operators did not feel that there was any use in meeting the delegates. Thirty per cent. of the output of bituminous coal comes from the open-shop mines of West Virginia, Alabama and Pennsylvania. During the strike, in 1919, this 30 per cent. was increased to 50 per cent. and it has affected the operations of the union mines to such an extent this year that they have been able to run only 15 to 30 per cent. of their time, while the open shop mines have run from 60 to 80 per cent. as the wages in these mines had been reduced to the 1917 scale.

Jan 5, 1922

• Phelps-Dodge Corp. signed an agreement with the Defense Materials Procurement Agency to increase copper production from the east ore deposit of the company's Copper Queen branch at Bisbee, Ariz. The company agreed to undertake a $25 million expansion program, including construction of a concentrating and leaching plant at the Bisbee mine and enlargement of the Douglas smelter. The Government agreed to buy the first 112,500 tons of the first 150,000 tons produced at 22e per lb if the company could not sell at a higher price. The new facilities will have a yearly capacity of 38,000 tons and should be in production by late 1954 or early 1955. • American Smelting & Refining Co. has started construction of a new building to house the Central Research laboratory at South Plainfield, N. J. It will have approximately 75 individual laboratories and an equal number of offices and shops. Modern apparatus to be installed will include electron microscopes, electric and fuelfired furnaces, miniature copper refineries and zinc plants, wire drawing machinery, and large pilot plant laboratory. In the new building scientists study the base metals, and the development of new uses for a number of Asarco by-products, arsenic, and little

Jan 11, 1951

By G. C. Gester

With the exception of exploration geological work that is being prosecuted in various parts of the mainland of Arabia, the only new developments in Arabia during 1934 were on Bahrein Island, which is in the southwestern portion of the Persian Gulf, approximately 25 miles from the mainland of Arabia. Here the Standard Oil Co. of California, through its wholly owned subsidiary, The Bahrein Petroleum Co., Limited, has continued to carry on a systematic drilling campaign and has constructed camps, pipe line and marine loading facilities. During 1934 eight wells have been completed at depths ranging from 2058 to 2253 ft. These wells have shown average initial productions ranging from 1500 to 5000 bbl., with one, No. 15, estimated as being capable of flowing as much as 11,000 bbl. per day. The oil is asphaltic in character and has a gravity range of from 32' to 34' A.P.I. The locating of all new wells has followed a plan of orderly development, with the ultimate object of obtaining efficiency of operation and maximum production. The wells are taking a penetration of 200 to 250 ft. of the lower or so-called Main productive zone. The upper oil zone, which is cased off, includes 300 to 400 ft. of alternating limestones, clays and shales and carries a heavier oil under lower pressures. The Main zone is similar lithologically to the upper zone. Micro-fauna collected from cores have shown that the oil occurs in formations of lower Eocene and Cretaceous age. Development to date has not progressed sufficiently so that either the maximum thickness of the oil-bearing horizons or the limits of the field can be determined. Something over 10,000 acres has been proven to date. Among other developments leading toward the marketing of oil from Bahrein during 1934 was the construction of a marine loading terminal. This included the laying of over 3 miles of 12-in. submarine pipe line from the small island of Sitra out into the harbor, terminating in 50 ft. of water; also the laying of more than 10 miles of gathering lines from the producing area to the terminal. Three crude oil working tanks with floating roofs were erected on Sitra Island, having a capacity of 250,000 bbl. A pumping plant was provided having a capacity of 5700 bbl. of oil per hour. This is housed in a dustproof building, as rather severe

Jan 1, 1935

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons. ) The governing body of the Imperial College of Technology, London, S. W. (Royal School of Mines), will shortly proceed to the appointment of a Professor of Metallurgy. This important Chair has been filled in the past by such eminent metallurgists as John Percy, Sir William C. Roberts-Austen, and others. A large manufacturing company having two iron foundries, blast furnace, etc., requires the services of a chemist, metallographist, and metallurgical engineer qualified to give advice on cast iron practice, and to prescribe remedies for difficulties often met with in the usual iron foundry. The position of converter blower at a side-blow Bessemer steel casting plant is vacant.

Jan 5, 1913

By AIME AIME

YALE UNIVERSITY looked like a top-notch school to "Bert" Phillips in spite of the belief that the college in the home town sometimes looks less attractive than a more distant campus. So Bert, a native of New Haven, earned his B.S., M.S., and Ph.D. degrees from Yale. Immediately after Yale days lie served as metallurgist of the Scovill Manufacturing Co., Waterbury, and then went to the Central Research Laboratories of the American Smelting and Refining Co. at Maurer, N. J., where since 1931 he has been superintendent of research. Bert has contributed to metallurgical literature many reports of studies on the constitution and the physical, metallurgy of copper and copper alloys as well as papers on general nonferrous physical metallurgy.

Jan 1, 1938

By Robert H. Richards

It has long been known to boiler makers and to the users of cylindrical pipes of many kinds that when a tube is exposed to internal fluid pressure the resolution of forces is such that the material of the walls of the tube is exposed to twice the stress in the direction tending to produce longitudinal rupture, as it is in the direction to produce circumferential fracture. By longitudinal fracture is meant the fracture by a rent parallel to the axis; by circumferential fracture is meant fracture by rents running round the cylinder. In consequence of this the makers of boilers always lay the fibre of their metal in direction round the boiler, and the same is true with the makers of gun-barrels. I have never seen any good and simple illustration of this law until I met with it in blowing glass. If a thin bubble of glass be blown out in a spherical form and then exploded it will be found that the particles tumble into totally irregular shapes, showing no special direction in the molecular structure of the material. If now a bubble of glass be blown out and so manipulated that it will take a cylindrical form (see accompanying illustration), and then be exploded, it will drop into ribbon-shaped pieces from end to end, and the only parts that will be found to differ from this form will be the two hemispherical ends which will remain whole, having a fringe of ribbons representing the line of their fracture from the cylinder. The main point of difference between this experiment and the

Jan 1, 1883

By Fred D. DeVaney

W. O. Philbrook (Carnegie Institute of Technology, Phila.)—Mr. DeVaney's paper is a valuable addition to the growing technology of the magnetic roasting of lean iron ores. His furnace is ingeniously designed to permit close control of the process and to achieve high thermal efficiency by counter-current heat exchange and the withdrawal of both solid and gaseous products at relatively low temperatures. The principle of using a lean reducing gas to avoid over-reduction of the ore even at high operating temperatures (for rapid re-action rate) is thoroughly sound. The gas analyses and flow rates reported, however, are internally incon- sistent and render suspect any details of a heat balance based upon them. While it is entirely proper to consider the entrant gas as a reagent and to account only for the heat evolved by consuming a portion of the gas, many operators are accustomed to a heat balance using the total calorific value of the reagent supplied; and comparison of heat balances made with different bases of calculation can be quite misleading. Since Mr. DeVaney's paper is likely to be cited frequently in future discussions of magnetic roasting processes, it seems worth while to point out the internal discrepancies and to give alternate values of heat requirements for different bases of calculation.

Jan 1, 1954

By Harry H. Nowlan

A heavy development campaign progressed during the year 1936 in South Texas1, following up important discoveries made in 1935. Oil and gas wells completed during the year were 1473 against 704 in 1935. The drilling program reached its peak of operations in June in consequence of offset requirements made necessary principally in Duval County in the Seven Sisters, Loma Novio, Lopez and Cole fields. There were six new fields discovered during 1936 as follows: Rhode in McMullen County; Peters, El Mesquite and North Kohler in Duval County; Wood in Starr County and Colorado in Jim Hogg County. No discovery of unusual consequence was made during the year. The pools mentioned above are simply in the primary stages of development. The most intensive exploratory work during the year was in Duval, Webb and Zapata Counties. Considerable activity also prevailed in Starr and Brooks Counties. Much significance is attached to the California Company's discovery in the Alta Mesa field in Brooks County, which is considered to be a deep-seated salt dome. The Comitas field, in Zapata County, developed some surprisingly good production in a shallow sand at 900 ft. and is being followed by a heavy wildcat campaign throughout that area in search of like production. In Starr County an active wildcat campaign is in progress in a continued effort to find new fields northwest of the Sam Fordyce field, in Hidalgo County. This play continues in a northerly direction through Starr and Jim Hogg Counties. New Fields Rhode.—The Rhode field, in southeastern McMullen County, was opened in May by the Magnolia Petroleum Co. with a gas well in the Whitsett (Upper Jackson) sand at a depth of 1810 to 1822 ft., this test is located in the southeast corner of sec. 86 on the Rhode ranch. Four gas wells have been completed, proving up a gas area of 1000 acres, more or less. Development will be slow because of lack of market for the gas.

Jan 1, 1937

By Joseph E. Pogue

Price is a complicated concept, for price is both a cause and an effect. This reciprocal aspect is commonly overlooked and the oversight is the source of many economic maladjustments. Price is the resultant of the ratio between supply and demand, but it differs from a mathematical concept of a proportion, by itself constituting an economic force which continuously alters the elements that determine the relationship. Price, therefore, is not merely the outcome of other forces but is in its own right one of the most powerful of economic agents. Price accordingly does not play a passive role; nor can it be sterilized or rendered inactive. In consequence, price cannot be fixed or at least kept fixed, except by the elimination of all freedom of choice on the part of producers and consumers. A primary objective of all economic activity is equilibrium. The same is true of a unit of economic activity, the single industry. The plane upon which equilibrium centers may shift in the course of time, but equilibrium itself is the point of departure and the point of return. If an industry is in equilibrium, that industry is operating effectively. The motivating forces of an industry—profits or the common good—are not to be confused with the prerequisite of equilibrium, but this mistake is often made. The producer is dominated by the profit motive; the consumer, or his collective representative, by the general welfare motive. No one is the advocate for equilibrium; that status is supposed to be arrived at automatically. If the forces of competition are perfectly free, such is the tendency. Equilibrium For the purposes of this analysis, equilibrium needs to be broadly defined and is conceived to involve: (1) balance between supply and demand; (2) internal equipoise amongst the elements within an industry; and (3) symmetry in respect to the whole economy. This definition implies flexibility and case of adjustment; a ready accommodation to change. Equilibrium does not postulate profits or nonprofits, social objectives or the lack of them. A decadent industry may be in equilib-

Jan 1, 1937

By Julian Kennedy

THINKING that it may prove of interest to the Institute, 1 have prepared a short; account of the blowing in and subsequent working of the "A" furnace of the Edgar Thomson Steel Works. This furnace was built for the purpose of making spiegel, but has been started and is now running on Bessemer iron. The shape and size of the furnace are shown in the accompanying drawing. It will be seen that the section is formed of lines making very small angles with each other. In fact, an arc of a circle can be drawn, from the top to the tuyeres, which will nowhere deviate more than two inches from the lines given. In building, also, great pains were taken to gradually round the angles, so that the most careful observer, standing in the crucible and looking upward, could not tell at what points the slopes changed. It will also be seen that the widest part of the furnace is almost exactly midway between the bottom and the stock line. The flattest slope is maintained for 20 feet above the crucible, and is about 18 inch to the foot from the perpendicular. The furnace is lined with small brick throughout, and has six tuyeres four inches in diameter, which project seven inches inside of crucible. There are three Siemens-Cowper-Cochrane stoves, each 15 feet in diameter by 50 feet high. Blast is furnished by an upright engine with 32-inch steam cylinder, 84-inch air cylinder, and 48-inch stroke. The steam cylinder has balanced poppet valves, working horizontally. The steam valves are worked by a Porter link-movement in order to obtain a variable cut-off. The exhaust valves are worked by a separate eccentric. It is intended to attach a governor to the cut-off, but at present it is set by hand. The steam cylinder is

Jan 1, 1880

By D. C. Anderson

Utah Construction & Mining Co.'s Lucky Mc mine is one of the major uranium producers in the United States. It is located near the geographic center of Wyoming in Fremont County. The climate is middle-latitude steppe, with an average annual precipitation amount of 10 in.; the temperature varies from 40º below zero to 100º above. The land surface is moundlike, rolling terrain, with sparse grass and sagebrush. The northern slopes of the higher ridges support a scattering of juniper and pi[n]ion growth. DISCOVERY The discovery was made by Neil E. McNeice, of Riverton, Wyo., on Sept. 13, 1953. After prospecting the area and staking a few claims, McNeice reported his findings to geologists of the Atomic Energy Commission (AEC), who immediately began preliminary studies of the numerous surface uranium exposures of the district. The discovery received widespread publicity, resulting in an intensive search for uranium throughout the region ; thousands of claims were staked. The AEC drilled several shallow holes near the discovery outcrop. Assays of cuttings from these holes confirmed the presence of a low-grade, oxidized uranium deposit. McNeice and his partner, L. A. Morfeld, tried to start a mining operation but were plagued by a lack of capital and technical know-how. They sought assistance from a Salt-Lake-City-based mining firm, the New Park Mining Co., engaged in underground base-metal mining in the Park City district of Utah. After a period of negotiations, New Park initiated activities that led to the forming of the original Lucky Mc Uranium Corp. The company started limited development drilling and mining operations in the summer of 1954, with the first ore production being shipped by truck to the Vitro mill in Salt Lake City. The mining

Jan 1, 1969

By Bruce H. Gardner, Stephen A. Miller, Shosei Serata

The Bryan Mound salt dome in Freeport, Texas, has some of the largest and oldest solution caverns in the U.S. There are a total of five caverns of varying shapes and sizes randomly distributed throughout the salt dome. When the caverns were converted from a brine production to an oil storage operation, the effects on long-term stability of the caverns and inter-cavern behavior were analyzed to evaluate the future safety of the storage operation. The analysis was based on a worst-possible-case scenario, including accidental wellhead pressure loss. The impact of this pressure loss upon the thinnest partition between the two closest caverns was analyzed, using a case example of storing lightest weight LPG, thereby creating maximum differential pressures between these two caverns. The finite element method with the REM computer code was utilized for this analysis. Results of the analysis illustrate the basic mechanisms of the long-term behavior of the multiple caverns in the LPG storage operation.

Jan 1, 1985

By G. E. Archie

Data given in this paper indicate that certain relations exist between different characteristics of sandstone. These relations are not rigid, for all sandstones are more or less heterogeneous. Not every increment of a given horizon follows exactly the relationship; however, studying a reservoir as a whole from a large number of samples, definite trends are found to exist. Apparently nature's processes of sedimentation and diagenesis are such as to give some degree of uniformity. Average relationships are valuable because electrical measurements in a borehole comprise a considerable volume of rock near the hole. Also, it is desirable that a given producing reservoir be studied as a unit. In a permeable reservoir whose pores are filled with a saline solution, it was found that the total porosity and the type of sandstone influence the relationship between its electrical resistivity and the RO and the resistivity of the brine R,. The relation can be expressed by the following empirical equation, Ro = R10O— [i] where 0 is the porosity expressed as a fraction and the numerical value of the exponent lies between 1.8 to 2.0 for consolidated sandstones, and is about 1.3 for clean, unconsolidated packs. This equation indicates that an appropriate electrical log can be used to estimate the porosity of a saline water-bearing reservoir when Rw and the type of rock are known. The fraction R0rw, is called the "formation resistivity factor." It reflects the effect of the nonconducting rock structure on the resistivity of the salt water that fills the tortuous paths through which the electricity must pass. The formation resistivity factor F is found to be related to permeability k. In this case the type of rock plays an important role, as shown by the relation F = ak-b [2] where the values of a and b must be determined experimentally for each horizon. Therefore Eq. I rather than Eq. 2 is used when it is desired to determine the value of F, because small changes in rock structure particularly in the pore size are not critical. Another useful relation, R = R0S- [3] where R = resistivity of rock when partially saturated with brine and partly with oil or gas, S = fraction of the pore space filled with brine, and n equals approximately 2 for both unconsolidated and consolidated sandstone, shows that the connate water of an oil or gas reservoir can be estimated in situ from a resistivity log. Equation 3 shows that in order to estimate the water content of a reservoir a knowledge of R and Ro is essential. The first value can be obtained from the electrical log when all factors influencing the resistivity curve can be properly taken into account. The latter may be obtained when a log is available on the same horizon where it is entirely water-bearing and has

Jan 1, 1946

By G. E. Archie

Data given in this paper indicate that certain relations exist between different characteristics of sandstone. These relations are not rigid, for all sandstones are more or less heterogeneous. Not every increment of a given horizon follows exactly the relationship; however, studying a reservoir as a whole from a large number of samples, definite trends are found to exist. Apparently nature's processes of sedimentation and diagenesis are such as to give some degree of uniformity. Average relationships are valuable because electrical measurements in a borehole comprise a considerable volume of rock near the hole. Also, it is desirable that a given producing reservoir be studied as a unit. In a permeable reservoir whose pores are filled with a saline solution, it was found that the total porosity and the type of sandstone influence the relationship between its electrical resistivity and the RO and the resistivity of the brine R,. The relation can be expressed by the following empirical equation, Ro = R10O— [i] where 0 is the porosity expressed as a fraction and the numerical value of the exponent lies between 1.8 to 2.0 for consolidated sandstones, and is about 1.3 for clean, unconsolidated packs. This equation indicates that an appropriate electrical log can be used to estimate the porosity of a saline water-bearing reservoir when Rw and the type of rock are known. The fraction R0rw, is called the "formation resistivity factor." It reflects the effect of the nonconducting rock structure on the resistivity of the salt water that fills the tortuous paths through which the electricity must pass. The formation resistivity factor F is found to be related to permeability k. In this case the type of rock plays an important role, as shown by the relation F = ak-b [2] where the values of a and b must be determined experimentally for each horizon. Therefore Eq. I rather than Eq. 2 is used when it is desired to determine the value of F, because small changes in rock structure particularly in the pore size are not critical. Another useful relation, R = R0S- [3] where R = resistivity of rock when partially saturated with brine and partly with oil or gas, S = fraction of the pore space filled with brine, and n equals approximately 2 for both unconsolidated and consolidated sandstone, shows that the connate water of an oil or gas reservoir can be estimated in situ from a resistivity log. Equation 3 shows that in order to estimate the water content of a reservoir a knowledge of R and Ro is essential. The first value can be obtained from the electrical log when all factors influencing the resistivity curve can be properly taken into account. The latter may be obtained when a log is available on the same horizon where it is entirely water-bearing and has

Jan 1, 1946

By J. Douglas Gibson

In Canada, the economic climate for mining is still warm, but a noticeable chill set in last November when the Government published a White Paper on tax reform known as the Carter Report. Moreover, this chill could drop to a freeze injurious to the whole Canadian economy if two of the proposals in the Carter Report are adopted. The offending suggestions call for an end to (1) the depletion allowance and (2) the three-year tax holiday for new mines. Both of these tax incentives have played a major role in the postwar development of the Canadian economy and will, if undisturbed, play an even more important role in the future. The fact that they have worked and worked well is evident from the record. Fruits of an Industrial Beanstalk Excluding fuels, the value of Canadian mineral production was just under $3 billion in 1968-almost nine times as much as in 1946. With fuels included, the figure is $4.25 billion, or almost ten times as much as in 1946. Proportionately, this growth far exceeds that of Canada's manufacturers or of her economy as a whole. Table I traces the overall mineral production growth by principal products. Of particular interest here are petroleum, iron ore, natural gas, sulfur and potash, the combined production of which has grown from little or nil to a point where it now accounts for more than 40% of Canada's mineral output.

Jan 1, 1970

By Bernard York, John J. Reed

W. 0. Philbrook (Carnegie Institute of Technology, Phila.)—Mr. DeVaney's paper is a valuable addition to the growing technology of the magnetic roasting of lean iron ores. His furnace is ingeniously designed to permit close control of the process and to achieve high thermal efficiency by counter-current heat exchange and the withdrawal of both solid and gaseous products at relatively low temperatures. The principle of using a lean reducing gas to avoid over-reduction of the ore even at high operating temperatures (for rapid reaction rate) is thoroughly sound. The gas analyses and flow rates reported, however, are internally incon- sistent and render suspect any details of a heat balance based upon them. While it is entirely proper to consider the entrant gas as a reagent and to account only for the heat evolved by consuming a portion of the gas, many operators are accustomed to a heat balance using the total calorific value of the reagent supplied; and comparison of heat balances made with different bases of calculation can be quite misleading. Since Mr. DeVaney's paper is likely to be cited frequently in future discussions of magnetic roasting processes, it seems worth while to point out the internal discrepancies and to give alternate values of heat requirements for different bases of calculation.

Jan 1, 1954

By Cyril Stanley Smith

BETA brass (consisting of approximately equal atomic proportions of copper and zinc) exists as a random solid solution at high temperatures, but at low temperatures [ ] an ordered structure is stable, with the copper and zinc atoms occupying alternate sites on the body-centered-cubic lattice. On cooling, ordering commences at a temperature of 450° to 490°C., depending on the composition. The degree of ordering progressively increases at lower temperatures until it becomes virtually complete at about 100°C. The electrical resistivity of the alloy illustrates the changes clearly (Fig. I). This type of reaction has been a favored subject for study by physicists. An [ ] excellent summary of the theory is to be found in a paper by F. C. Nix and W. Shockley.1 All published data on electrical conductivity, specific heat and other properties agree in indicating that the ordering reaction in beta brass takes place so rapidly that it cannot be prevented or even retarded by quenching. With most ordered alloys, cold-working induces disorder and

Jan 1, 1942

By John C. Calhoun, Raymond G. Loper

Theoretical calculations for the decline of pressure and the variation of instantaneous producing gas-oil ratio with increased cumulative production have been made for reservoir systems under various producing drawdown values and for various spacings. These variables have been included by a modification of previously Published techniques. This consists essentially of utilizing a radial system flowing gas and oil in a succession of steady state calculations. The results of the calculations do not show any variation in the predicted behavior of the internal gas drive reservoir when either the drawdown or the spacing are changed. The prediction of performance on an internal gas drive reservoir has been presented by various authors. ',"' These predictions are in the form of a pressure decline and an instantaneous producing gas-oil ratio as a function of cumulative oil withdrawal. In making these predictions a basic assumption has been that the saturation of the reservoir is uniform throughout at any time, or that the pressure differential imposed on the reservoir system is zero. Because of these assumptions the validity of such predictions has been questioned. Their application to actual systems, where saturations are not uniform and where producing differentials exist, has been a hazardous procedure. The authors cited have used different methods of approach to the derivation of equations for making their predictions and for arriving at a solution of both equations, but basically the same relationships are utilized in each case. In all instances the instantaneous producing gas-oil ratio is calculated from the equation: In utilizing this equation an average reservoir pressure and an average reservoir saturation must be known, the former to define ß, v, s, and uo/ug and the latter to define kg/ko. Predictions can be made, therefore, only for the conditions of a uniform reservoir saturation and a uniform reservoir pressure. This restriction of requiring a uniform oil saturation can be resolved by applying two-phase steady state flow for the radial system to the reservoir's history. Radial steady state flow is defined when the ratio of phases flowing,

Jan 1, 1949