Search Documents

By Robert Mehl

THE purpose of this investigation was to prepare high-purity iron-carbon alloys, to determine as precisely as possible the A3(GOS), the Acm(SE), and the A1(PSK) transformation temperatures in the meta-stable iron-iron carbide system (up to 1.4 per cent C), and to study the influence of carefully controlled and constant rates of heating and cooling (1/8 to 2° C. per minute) upon the transformation temperature and upon the resulting microstructure. Apart from the general metallurgical importance attending the completion of such a task, it will be noted that highly precise transformation temperatures are of interest and importance in the thermodynamic study of this system1. Several determinations of the iron-iron carbide diagram have been made. These suffer generally from the low purity of the alloys used, and from the application of methods of investigation of low sensitivity. Attempts to compare and weight the many data available in an effort to construct as accurate a diagram as possible have, in the main, been unsuccessful. In general, the wide differences in the results of different workers, the lack of complete analytical data, the omission of important details relating to the heat-treatment of the alloys, and the meager description of the methods of investigation applied, render such a process of averaging nearly meaningless. It may be seen from the summaries by Epstein2 and Körber and Oelsen1 that variations as great as 30° C. exist in the reported data on the A3 temperatures in iron-carbon alloys. For-tunately, the A3 temperature in pure iron is now known to be 910° C. ± 1° C.3 The best recent work on iron-carbon alloys is that of Esser4 on hypoeutectoid steels and that of Sato' on both hypoeutectoid and hyper-eutectoid steels.

Jan 1, 1937

Jan 1, 1968

By B. N. Das, P. A. Beck

THE o phases have a complex tetragonal structure with Lo/ao = 0.52 and 30 atoms per unit cell.1 A large number of such phases are now known to occur in various binary systems of the transition elements and they exhibit the following typical features: 2,3 The composition of binary o phases is variable, ranging from approximately A4B to ABI. With only a few exceptions, in the o phases the A-ele-ment comes from the V- or Cr- group of the periodic table, while the B-elements are from the Mn-, Fe-, Co-, or Ni- group. In the first long period the corresponding o phases of the V- and Cr-series have approximately the same compositions. However, as the B-element changes from Mn to Fe to Co to Ni, the mean composition shifts monotonously toward higher A-contents.2-4 For example, if the mean compositions of the various o phases with vanadium are compared with each other, the composition shift mentioned above becomes plainly visible: V 30Mn0 80 Vo.45Feo..,, Vo .,Coo. 45 and Vo.5Nio.3. Similiar composition shifts, although not the same composition values, were observed in u phases formed by second and by third long-period transition elements.3'4 This behavior, very characteristic of o phases, is in rather sharp contrast to the usually quite well-behaved stoichi-ometry of the Laves phases. In the latter, the AB2 stoichiometry predominates, with A the large atom and B the small atom.= The p phase occurs in the four binary systems of Mo or W with Fe or Co. On the basis of their crystal structure determination, Arnfelt and westgren6 ascribed to the p phase in the Co-W system the ideal composition W,Co7. Since all four binary pphases have nearly the same composition, it would seem quite plausible that some definite stoichiometry such as A6B7, might be characteristic of this phase, as AB2 is of the Laves phases. On the other hand, it has been noted,7 that the phases occur at average electron concentrations near to those at which the various cr phases are found. Also, it has been pointed out by Shoemaker and associates8 that structurally the a phases and the p phases are somewhat related to each other; both of these structures may be described in terms of suitable stackings of quasi-hexagonal layers'of atoms. By studying a suitably chosen ter- nary phase diagram, one might expect to be able to find out which one of the two conditions, the analogy with the o phase or the constant ratio between the number of large atoms and the number of small atoms in effect governs the behavior of the p phase. Several isothermal sections of ternary systems containing o phases have been investigated. In all cases where two binary o phases occur, these were found to be connected b a more or less straight ternary o phase field.7' '10 Such elongated o phase fields were also found in ternary systems in which only one of the limiting binaries is known to contain o phase. In this manner a latent o forming tendency could be detected and the virtual composition of a "binary o phase", which does not actually occur as such was approximately determined by extrapolation. The behavior of the phases, including their composition shift, is analogous to that of the classical electron compounds, as described by Hume-Rothery.11 In order to decide whether the p phase is essentially a "size compound" like the Laves phases, where a fixed stoichiometric ratio is quite generally maintained between the "large atoms" and the "small atoms", or whether the p phase is typically an "electron compound" in the same sense as ois, it was decided to investigate an isothermal section of the Mo-Mn-Co system. The Mo-Co system12 and the Mo-Mn system13 each are known to have a binary o phase. It could be therefore expected that a ternary o phase field will connect these two binary cr-phase fields. The p phase is known to occur in the Mo-Co system. If the p phase should turn out to form an elongated phase field extending deep into the ternary system, the following considerations mighto apply. The atomic radius of manganese (1.314for C.N.12) is between the va,lues for Mo (1.40Afor C.N.12) and for Co (1.26Afor C.N.12). If it is assumed that p is a "size compound", and that Mn is substituting for the smaller Co atoms in the p-structure in the ternary system, the y-phase field might be expected to extend parallel to the Mn-Co binary line. If Mn is substituting for the large Mo atoms in the p-structure, the p-phase field may be expected to extend parallel to the Mn-Mo binary line. On the other hand, if the p-phase turns out to be an "electron compound" like o, the ternary p-phase field should extend parallel to the ternary o -phase field connecting (Mo,Mn)owith (Mo, Co) a

Jan 1, 1961

By John V. Beall

Copper production in the. United States in 1972 amounted to 1,658,000 tons according to the USBM. This figure is up over 1971 but falls below 1970 production of 1,719,101 tons. This report is essentially about the status of copper mining operations in the U.S. and is an update and expansion of the report "Southwest Copper-A Position Survey" published in [A=], October 1965. At that time, the trend was toward using larger equipment to mine lower grade ore and toward the expansion of dump leaching practice. That trend continues today but, it is overlain by intensive activity to comply with existing environ¬mental legislation and uncertainty over proposed revisions of venerable laws governing mining. In the U.S. today there is, practically speaking, no excess smelting capacity so that expansion of copper production through the startup of new mines is inhibited. Owners of a large undeveloped orebody would have to decide before going into production whether to sell the concentrates offshore, which has many problems, whether to try one of several unproved chemical processes for producing refined metal from concentrates or embarking on the construction of a traditional pyrometallurgical plant in the face of considerable uncertainty over the pollution standards that eventually must be met. The situation is such that not only is the present rate of U.S. copper production threatened but the ability to meet projected increased demand in the years ahead may have been severely retarded.

Jan 4, 1973

By W. M. Bertholf

To establish the minimum or break-even efficiency of a preparation plant it is necessary to determine the ratio of production costs per ton of run-of-mine coal to sale price per ton of clean coal. This ratio is then divided by the percentage of plant recovery. Assume, for example, that washability data indicate that 80 pct of the run-of-mine coal may be recovered as clean coal selling for $5.50 per ton. If the same plant incurs $4.00 per ton mining costs and $0.25 per ton preparation costs, the cost to sale price ratio would be 4.25/5.50, or 77.3 pct. Since the plant is capable of recovering 80 pct of the run-of-mine coal the minimum plant efficiency would be 77.3/80, or 96.6 pct. If the plant efficiency were increased to 100 pct the limit on preparation costs would be increased to $0.40. Therefore, the washing operation must be accomplished at a cost of $0.25 to $0.40 per ton and the efficiency must be 96.6 pct or higher. By plotting a curve of efficiency vs preparation costs and taking into consideration the plant cost, feed rate, operating costs, and yields of the various flowsheets it is possible to select a financially sound process. Table I classifies preparation processes according to their nature of separation. It must be remembered that what is thought to be ideal does not always prove practical under actual operation. An outstanding example is the work done on the plunger-type jig. It was determined by the law of equivalence that this unit could treat satisfactorily only sizes differing by no more than a ratio of 2. Yet these same plunger-type jigs are successfully treating sizes considerably greater than this ratio.

Jan 12, 1957

FOLLOWING the presentation of the papers by Messrs. Mahan and Butler, the discussion printed below ensued. A. C. LANE* With particular reference to the New England con-sumer, I entirely agree with Mr. Mahan that intelli-gent marketing methods will do a good deal, but there is more than one way of improving them. For instance, coal can be shipped best to New England about this time of year-after the storms of the winter and before the movement of crops in the summer. For that reason there ought to be seasonal freight rates. This will be agreed to by most coal men if you will ask them, especially those who are connected with large concerns like the Metropolitan Coal Co., and yet they do not get seasonal freight rates partly because the railroads are afraid if they once reduce them they will never have a chance to get them back again. But it would be an improvement to have seasonal freight rates. Another thing: When we are buying in New England we want really a certain amount of heat value in our coal. There is no great advantage in our buying ash, nor is there any particular advantage in the railroad shipping ash and clogging the circulatory system of the body politic any more than clogging the circulatory system of the physical body. It would be desirable if the wholesaler, and to some extent the retailer, could guarantee the amount of ash or sell their coal on heating value. If you are interested in that you will find some interesting charts, in "Anthracite Coal Costs Analyzed," a pamphlet issued by the Anthracite Coal Consumers Association, Inc., New York City, as to rates from various and sundry points for bituminous and anthra-cite coal from the field to New York, Buffalo and Chi-cago. Here in New England they are both up against the competition of oil. About 3 or 3 1/2 bbl. oil will do the work of a ton of coal. One of my millionaire friends who is well posted on the situation is putting oil in his Commonwealth Avenue house because it is the most economical. Moreover, we can get Welsh coal from across the water (and help equalize this matter of exchange with Europe) in close competition with Penn-sylvania coal.

Jan 4, 1928

By L. C. Raymond

Valuations in the mineral industry differ from those of other enterprises because mines and oil wells have a definitive life so cannot be considered a perpetuity. This requires that in any mineral-property evaluation the recovery of invested capital is necessary during the life of the property. Capital writeoffs for nonextractive industries are assumed to be continuously plowed back to sustain the operation and produce yields on the capital invested. The extractive or mineral industry, however, generally attempts to return to the investor both interest and principal during the life of a property. Normally this is done currently and the dividend includes both items. Where the mineral properly possesses large reserves and the life factor approximates a perpetuity, the return on investment is generally comparable to that of industrial stocks. The valuation of a mineral property, at best, is based on educated estimates and judgment factors. This is particularly true as it relates to estimating selling prices over a long term or assessing the quality of management. Also, it is possible to make various assumptions as to rapidity of working out the deposit, varying time for start-up of operations, varying earning rates, so as to obtain different results with the same basic facts. Thus it is not surprising that two engineers, irrespective of their abilities, may not agree exactly even when given the same facts, but their results should be close enough to be used in establishing a fair value for trading purposes. The valuation is no better than the source of basic data and the soundness of judgment factors. Fundamentally the basic principles of mineral valuation are similar for base metals, sulphur, oil, or any other mineral. Each mineral, however, requires an engineer to have a knowledge of such factors as its occurrence, distribution, mining and processing methods, and marketing problems in order to gather and analyze all the facts and data that have a bearing on the earning potential of the property. PRESENTVALUEOFAMINERALPROPERTY In essence the present value of a mineral property is a sum of money in today's dollars that future earnings from the property are worth. It differs

Jan 1, 1959

Jan 1, 1967

By F. P. Peterson

The manufacture of gasoline by extraction or precipitation from the natural gases in which it is found, the present status of the industry, its past development and future extensions, offer a subject which is so broad that to handle it in its entirety would require a voluminous paper. The writer will, therefore, attempt to concentrate the essential matter of the subject for a general presentation, giving some of the most interesting details of the factors that are important to the industry. This industry has drawn liberally on the principles of physics and chemistry, and, to a large extent, has had to adapt such information as is most useful—not from data recorded with reference to petroleum, but from data recorded with reference to general treatment of other materials. Because of the complex character of the petroleum series of hydrocarbons and the fact that data, such as solubilities, 'vapor pressures, etc., . of the different petroleum compounds have not been determined, we are still working by rule of thumb in some essential phases of the industry. Furthermore, the difficulties of determining such data are almost insurmountable. We have not one, but two butanes to deal with—not one, but several, pentanes, hexanes, heptanes, and, as we ascend in the series the complexity and multiplication of isomers increases at such a rate as to make the task of isolating and studying their physical characteristics almost beyond the hope of possible attainment. The industry is the connecting link knitting the interests of oil producers and refiners into a much closer relationship than ever existed prior to its inception and development. The relation between the producer and the refiner of petroleum prior to 1910 was a rather antagonistic one in a commercial sense. It was to the interest of the producer of crude petroleum to sell it for a maximum consideration; the refiner's interest was to obtain the same product for a minimum consideration; therefore, each side of the business transaction retained within his own hands as far as possible the trade secrets of his business. Each side maintained an attitude of cold-blooded business sympathy only for the other. Cas-

Jan 1, 1918

By N. A. Gokeen, M. Ohtani

EFFECT of elements on the solubility of carbon in liquid iron is useful in calculating and correlating a number of thermodynamic properties as shown elsewhere in detail.' Kitchener, Bockris, and spratt2, and later Turkdogan and Hancock3 have investigated the effect of sulfur on the solubility of carbon at various temperatures and concentrations. For any chosen sulfur concentration, the solubility of carbon reported by Kitchener et al. is considerably lower than that by Turkdogan and Hancock. It was therefore felt that a reinvestigation of this problem was necessary. EXPERIMENTAL METHOD An alloy of Fe-C-S .was prepared with electrolytic iron and ferrous sulfide melted by induction in a graphite crucible, 4 in. high 1 1/2 in. ID under a CO-atmosphere. The temperature, held at 1500" ± 5°C in all experiments, was measured with a Pt-Pt + 10 pct Rh thermocouple immersed into the melt. In order to assure saturation with carbon, the melt was stirred with a graphite rod. After approximately 1 hr at 1500 °C, a sample was obtained by sucking the melt into a silica tube, 4 mm ID. The sample was then analyzed for carbon and sulfur by usual methods. RESULTS The results are presented in Table I and plotted in Fig. 1 with the individual values of Turkdogan and Hancock.3 Scattering in the data is equivalent to 3 pct or less in carbon analysis. The broken line represents the empirical equation obtained by Kitchener et al. from their data. It is evident that the present data are in good agreement with those of the former investigators but in disagreement with the latter. The cause for this discrepancy cannot be readily offered since the experimental methods in the three investigations were nearly identical. Additional evidence corroborating the author's results may be presented in the following manner. The difference between the solubilities of carbon in the ternary Fe-C-X melt with a small concentration of any element X, and in the binary Fe-C melt is %?C = %CIII-%CII [1] where %?C is the change in solubility, and %CIII and %CII are the solubilities in the ternary and the binary systems respectively. The value of %Cii

Jan 1, 1961

Jan 1, 1970

By A. H. Bell

Continued low prices and restricted markets for crude oil discouraged drilling activity in Illinois oil fields during 1933. Only 36 wells were completed in the state, the smallest number since 1904, and of these the majority were scattered wildcat wells, only 10 having been drilled in producing fields (Table 2). Production was curtailed approximately 40 per cent for the first half of the year. During July, August, and the early part of September there was no restriction on production. On Sept. 8, under the "code of fair competition for the petroleum industry," the quota of allowable production for Illinois was fixed at 12,000 bbl. per day. The state's production in 1933 was 9 per cent less than in 1932. What it would have been had there been no curtailment of production and if economic conditions had permitted a normal amount of cleaning out and repairs to wells, it is not possible to estimate, but it would no doubt have been considerably more than the actual figure. No new pools or new producing horizons were discovered in 1933, but the deepening of a Robinson sand well in Crawford County to the McClosky "sand" horizon (St. Genevieve limestone of the Lower Mississippian) resulted in a production of 3 bbl. per day (Fred Patchel, Savilla Shipman No. 5, NE. 1/4, SW. 1/4, sec. 26, T.6N., R.l3W., deepened from 1122 to 1388 ft., to be tested to the McClosky horizon, and, owing to the rapid variations in porosity within short distances, as shown in the Lawrence County field to the south, one test may not be considered as proving or condemning any large area. The average price of Illinois crude oil in 1933, calculated from the posted prices as published in the Oil and Gas Journal and Oil Weekly, was $0.862 per barrel. This compares with a calculated average price of $1.032 in 1932 and 0.852 in 1931. The total value of Illinois crude oil produced in 1933 obtained by multiplying the average price (0.862) by the total production (4,227,000 bbl.) was $3,643,674. Of the 26 wildcat wells drilled in 1933, only one was drilled on known favorable structure. This was the Walmar Oil Company's William Pepple well No. 1, sec. 12, T.4N., R.12W., Hancock County, which tested

Jan 1, 1934

By Fernando A. Buttazzoni, Jorge C. Munita

INTRODUCTION To provide a background for discussing long-range financial and operational planning in the mining industry, we would like to begin by describing the role of planning in Codelco. Having taken part in Codelco's planning process since its inception in 1976, we believe that useful conclusions may be drawn for the experience we shall relate. Although Codelco is a state-owned copper producer with an important role in the Chilean economy, and is consequently very much at the core of national economic planning, the following discussion is not related to government planning but to planning in an operationally and commercially autonomous business concern with all the characteristics of a private enterprise. The only way in which Codelco differs from private business is that its financial successes or failures have a more direct impact on the countryls ability to participate in international trade, to meet its international financial commitments and to achieve economic and social growth. Thus, what follows is a presentation of the conceptual features of the planning process at Codelco and a description of the current state of planning in the company. It is understood that certain conceptual components are basic to any formal strategic planning process, and that the components of Codelco's planning process are therefore generally applicable in similar companies. First, the mission and scope of operation of the company must be defined, and goals must be set to achieve leadership in the business activities in which it engages. Having set this framework, the company must constantly scrutinize those internal elements and conditions that are essential to fulfill its mission and achieve leadership. In Codelco this means considering the actions which can best serve to define future capacities, taking into account declining ore grades and determining optimal production levels; watching over the productivity and skills of its labor force, and; keeping abreast of technological developments in non-ferrous mining and processing. If the company is proficient in these three areas, it will be cost efficient and there- fore competitive. Codelco must also watch over the business environment in which it operates. The company sells concentrate, blister and fire-refined copper, wirebar, cathodes and wire rod and must study the behavior of the market to attune its product mix to the demand existing for these various commodities in the international market and the copper consuming industries in general. By examining the internal and external environment in which the company conducts its production and commercial operations, it is able to diagnose its strengths and weaknesses, to identify the hazards it must overcome to stay ahead in the copper trade, and to take full advantage of business opportunities as they arise. CHARACTERISTICS OF CODELCO-CHILE Although our subject is Codelco, readers should keep in mind that there are many other copper producing operations in Chile, all in the private sector, and many valuable deposits that may be exploited in the future. Codelco is the only public sector copper producer, although there is one other state enterprise that operates smelting and refining facilities principally to serve a large number of very small producers of copper concentrate. In the mid-19801s, Codelco is the largest copper mining company of the world and the largest producer and exporter of copper with yearly sales totalling close to US$ 1.8 billion in 1983. Moreover, it is a highly profitable copper company at a time when the world copper industry as a whole has reported losses for several years. Codelco-Chile is a fairly new organization. The history of the four mining operations it manages is much longer: El Teniente was opened in 1912, Chuquicamata in 1915, Salavador in 1959 -- with installations of the old Potrerillos mine dating from 1927 -- and Andina in 1970. Having had separate owners, the management systems of the

Jan 1, 1985

By G. W. Josephson

SINCE the earliest years of recorded history the durability and protective qualities of asphalt and tar have been known and utilized. The mummies of early Egyptian kings were coated with asphaltic materials, and asphalt mastics were common in Babylon. However, according to various authorities, it was not until 1780 that the first forerunner of present-day composition roofing was discovered,1 and the large-scale expansion of the industry has taken place since 1900. HISTORICAL BACKGROUND Development was stimulated by the growing popularity of manufactured gas. The by-product tars from these operations accumulated in large waste piles that had no commercial value and were a source of annoyance and expense to the gas companies. These tars were offered at very attractive terms to anyone who would take them away, and the infant "composition" roofing industry benefited accordingly. At first the process consisted simply of dipping sheets of burlap or other fabric in a tank of molten tar or asphalt. The long strip of roofing was rolled up for convenient handling, and the early experimenters soon found that it was necessary to dust the surface of their new "roll roofing" with some kind of material that would prevent the tarred surfaces from sticking together. Any finely divided, low priced local material like sand or fine gravel served this purpose and from its application the roofing-granule industry grew. As time went on other characteristics of a properly applied mineral surfacing were recognized. As with wooden shingles, tar and asphalt can be ignited by flying embers from near-by fires. It was found that by increasing the largest particle size to the maximum that could be successfully embedded, and by properly controlling the amount of smaller fractions retained in the grade so as to cover the asphalt completely a Nigh degree of resistance to fire was attained. Needless to say, in this early period asphaltic roofing needed such selling points to gain acceptance in a field dominated by wood, slate, and tile. When asphalt is protected from the sun's rays it is extremely durable, but when exposed to sunlight its surface is comparatively rapidly decomposed. Completely covering asphalt roofing with mineral surfacing protects the asphalt and adds materially to the life of the roof-conservatively, 500 per cent. Slate Granules In the production of split slate shingles a large quantity of waste slate is accumulated, as 60 to go per cent of the rock quarried is discarded. This waste was a continuing burden on the industry. Some was marketed as ground slate flour for filler in paint and linoleum, and there is a record that as early as 1906 two carloads of coarse screenings from slate flour were marketed as granules for surfacing roofing. This new field appeared to the slate pro-

Jan 1, 1944

By John H. Schissler

INTRODUCTION AND SUMMARY Complex copper-lead-zinc ore is mined from underground workings high in the Western Cordillera of the Andes mountains about 100 km in a stralght line north of the city of Arequipa in southern Peru. The Madrigal mine is situated in a steep-walled canyon into which the six operating levels "daylight". Production is from cut-and-fill stopes currently producing approximately 740 dry metric tons per day. The Santa Rosa vein, the most important producer in the district, outcrops for a distance of about 4 km, bearing N 75º W and dipping about 70º NE. In places the vein splits into two or three branches; widths of each vary between 1 and 4 m and total mineralized widths of up to over 8 m occur. Principal ore minerals are chalcopyrite, galena and sphalerite. Ore reserve grades for the Madrigal mine average about 1.45% Cu, 2.6% Pb and 5.0% Zn, 2.9 ozAg per metric ton. [Compania] Minera del Madrigal is a California limited partnership; the general partner and operator is [Compania] Madrigal, a wholly-owned subsidiary of Homestake Mining Company. HISTORY Shallow workings found on the Santa Rosa vein were probably made by the Spaniards during colonial times in their search for

Jan 1, 1977

By John C. Calhoun, Frank T. Bethel

The application of a method for analyzing pressure build-up curves to determine the effective permeability in the Spraberry is presented. Sixteen upper Spraberry wells of the Driver area arc analyzed and show variations in the in-place effective permeability of 2 to 183 md. Since these value- are much larger than the .5 md. or less reported for the matrix rock. a large part of the vertical fractures noted in Spraberry cores- must be considered native to the formation. The effectiveness of the well fracture treatment in connecting the well bore to the native fracture system is analyzed by comparison of the effective permeability as determined from the PI test to that obtained from a pressure build-up curve. These results show that the fracture treatment is sufficiently effective in connecting tile well bore to the native fractrure system to yield a flow capacity within about 50 per cent of that dictated by the native fracture system About two-thirds of the wells show some degree of local blockage. INTRODUCTION Fractured reservoirs have been known in the past.' However, during the past two years the Spraberry formation has directed the attention of the petroleum industry to a study of the performance of a fractured reservoir. The large variation in the number of fractures noted in Spraberry cores rile large variation in the producing ability of offset well.. the dramatic effect of well treatment on well ,productivity. the unknown quantity of oil stored in the fractures and matrix rock. and the unknown oil to be recovered were part of the initial Spraberry puzzle. In this type reservoir where the well treatment is an important factor in determining the productivity. it i- particularly desirable to determine the in-place flow capacity of the drainage area at distance* far removed from the well bore. This value. when compared to the flow capacity obtained from a PI measurement, will show the effectiveness of the well treatment (completion. fracture treatment, acidization. etc. in establishing a flow capacity in the vicinity of the well bore equal to that in the more remote region. The object of this paper i.; to show the application of a method of pressure build-up analysis for this purpose in studying the Upper Spraberry formation in the Driver area. STATEMENT OF THEORY The theoretical basis for the application of a pressure buildup curve to show the effective permeability of the rock at distances far removed from the well bore has been presented in detail in earlier publications.', in the previous development it was shown that pressure build-up behavior of all wells could be reduced to the same dimensionless build-up curve of Fig. 1. This mean.; that the bottom hole pressure of a well after hut-in will rise in such a manner that a plot of pressure against the logaritllm of time yields a straight line. The slope of this linp can be rlzed to calculate the effective permeability as expressed by the following equation: where: effective oil permeability md oil production rate prior to shnt in. STB/I) In practice the flow which occurs into the well bore after shut in and the variation in flow capacity in the immediate vicinity of the well bore usually cause the early part of the build-up curve to be unsatisfactory in the determination of permeability. In general the effect of these factors on the straight line section will become negligible after a time when the of the following equation is equal to 0.1. and the preferred section Of the curve for use in defining the slope lie-

Jan 1, 1953

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

Jan 1, 1967