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By E. Miller, K. L. Komarek

Equatiorzs have been derived which related maximum solid solubilities in semicondcting compounds having retvograde solidus curves with 1iqllidus data. Liquidus curves in Lke Pb-Te, Pb-Se, ard PB-S systetris have been defermined by thertrzal aralyses. Fvotrz expevimental maximum solibilities ia CdTe, PbTe, uxd PbS vetvograde tetrperatures hale beep1 calculated. TIze resllts support the concept that under certaiz conditiots pronounced itjlections in the liquidis curves arc indzcatiz:e of retropade solidus curves and that the tenlperatltre of the lmaximum solid solubility will be close to the temperature of the point of inflection in the liquidus curve. The maximum solid solihility within a gvoup of homologous cottrpoods SeetlLs to increase with increasing flatness ol the liquidus curvres. The phenomenon of retrograde solubility in metals, i.e., maximum solubility in a solid terminal phase in equilibrium with a liquid phase, has been theoretically predicted by Van aar' in his calculations of hypothetical binary phase diagrams. It was not until 1926, however, that retrograde solubility was experimentally verified in the Zn-Cd system.' Since then many sys- tems with retrograde solubility have been found, so that at present approximately fifty binary diagrams with a retrograde solidus curve are known.3 Meijering4 has critically appraised the accumulated data and has presented calculations which alloy predictions as to whether or not a solidus line will be retrograde. Interest in retrograde solubility increased when it was found that the solidus curves of germanium and silicon alloyed with a great many doping elements are retrrade. The problem was treated thermody-namically by odkinson,% d all available data on solid solutions in germanium and silicon were summarized by Trumbore.7 Although it is to be expected that intermetallic compounds will also exhibit retrograde solubility, experimental evidence is much more limited. Until now retrograde solidus curves have been reported for the compounds de,' be, Ps:" ne," SnSe," and SnS.13 All these compounds are semiconductors, and the solidus curves were usually obtained by determining the carrier concentration at room temperature of samples equilibrated at elevated temperatures and then quenched. It has been hown,'' however, that it is not always possible to quench in the equilibrium compositions from above a certain temperature. Theoretical discussions have either explicitly excluded intermetallic compounds4 or not treated them with respect to retrograde slubilit.j In the following a thermodynamic treatment of retrograde solu-

Jan 1, 1967

By Norman F. Schulz

The technical excellence of separation achieved in a mineral concentration process, or any other process where two constituents of any kind are physically separated from each other, is expressed uniquely and quantitatively by the separation efficiency (E,): E. = (R - R,), where R is the percentage of the valuable constituent and R, the percentage of the waste appearing in the concentrate. The separation efficiency meets all the usual requirements of a true efficiency and is independent of the nature of the process used. It can be visualized as the percentage of the feed material that, in effect, actually undergoes complete separation while the rest of the feed is distributed randomly and unchanged into the two separation products. The problem of quantitatively assessing the results of a mineral concentration process recurs whenever one tries to decide which of two similar test results is more desirable. Although economic factors may greatly influence the eventual choice of process, they usually have very little to do with the technical excellence of a separation and are, therefore, not a consideration at this point. Concentrate grade and recovery, used simultaneously are the most widely accepted measures of performance, and if both the grade and the recovery are greater for one case than for another, the choice is simple. However, when the results of closely competitive operations are compared, it often occurs that one set of test results shows a higher grade and a lower recovery than another and the choice is no longer obvious. Laboratory investigations of a mineral concentration process applied to a given feed material can often be designed to yield successive paired values of concentrate grade and recovery over the practical range of the course of a separation process.' These results may be plotted as some combination of the cumulative values of grade, weight recovery, or unit recovery in the concentrate. The resulting correlations for two slightly different sets of conditions can then be compared qualitatively, or even quantitatively in particular cases.2 Such comparisons are not applicable, however, to individual concentration test results. The reduction of a separation test result to a single efficiency figure, preferably as a percentage of ideality, would afford the simplest and most precise means for comparing the results of competitive tests. The effective proportion of feed material that undergoes complete separation in any real concentration process, hereafter referred to as "separation efficiency," is such a figure. It is essily calculated from the usual feed and product data and can even be evaluated, in many cases, from data in publications describing various concentration processes. Mineral Concentration Processes and Their Evaluation Mineral Concentration Processes: The overall concentration process may be subdivided into a liberation process which severs the bonds between unlike mineral species, and a separation process, which sorts the resulting liberated particles into two products—a concentrate rich in mineral A and a tailing lean in mineral A. A perfect mineral concentration process is represented by the idealized scheme shown in Fig. 1 in which liberation and separation are not differentiated. The feed mixture consists of two mineral types which are completely liberated early in the process and then sorted by type. All the mineral particles of type A which respond uniquely to the selection forces acting in the ideal separator, report to the concentrate, while all the mineral particles of type non-A report to the tail-

Jan 1, 1971

By Albert F. J. Bordeaux

INTRODUCTION. THE following general survey of the character and present condition of the silver-mines of Mexico, though not offered as a detailed treatise, has been prepared with care, is believed to he generally up-to-date, and is offered as a summary which may be found useful by mining engineers. Mexico has ranked for several centuries first among the silver-producing countries. It is now second as copper-producer, and seventh as gold-producer, with a fast-increasing output every year. The total amount of capital invested in its mining- and smelting-works is more than $250,000,000, while the yearly metallic production is $160,000,000. There are more than 20,000 recorded mining properties. The silver-mines of Mexico represent deposits of three principal classes: (1) veins and stock-works in eruptive rocks; (2) fissure-veins crossing the crystalline schists, granite, diorite, etc. ; and (3) veins and replacement-deposits in limestone. The true fissure-veins in some districts contain (in value) more gold than silver. In other deposits, the silver is decreasing in depth, leaving galena and zinc-blende as the principal ores.

Jan 9, 1908

By Herbert Hoover

THE time has arrived in our national development when we must have- a definite national- program in the development of our great engineering problems. Our rail and water transport, our water supplies for irrigation, our reclamation, the provision of future' fuel resources, the development and distribution of electrical power, all 'cry out for some broad-visioned national guidance. We must create a national engineering sense of provision for the nation as a whole. If we are to develop this national sense of engineering wand its relations to our great human problems, it must receive the advocacy of such institutions as this. We, together with our sister engineering societies, represent the engineers of the United States. It is our duty as citizens to give voice to those critical matters of national policy which our daily contact with this, the fundamentally constructive profession, illuminates to us. Just as our medical associations voice the necessity of -safeguards to national health; as the bar associations of safeguards to our judiciary, so the engineers should exert themselves in our national engineering policies. We have none; but we need some, or the next generation will face a lower instead of a higher standard of living than ours.

Jan 1, 1920

By Joseph E. Pogue

THE period of new oil discoveries in Illinois began in February 1937, when The Pure Oil Co. found the Clay City field the forerunner of a number of limestone pools. The importance of the area was emphasized greatly in December of the same year with the discovery of excellent sand production by The Carter Oil Co. at Louden and in June, 1938, with the discovery by The Texas Co. of the Salem field producing from two sands and one lime- stone horizon. By September, 1939, new discoveries in Illinois were estimated to have added, under prevailing production practices, some 500,000,000 barrels to the crude oil reserves of the United States and to have produced to that date some 63,000,000 barrels with daily production passing the 300,000-barrel mark by Sept. 1.

Jan 1, 1939

By Sheldon P. Wirnpfen

AN extensive study of German underground manufacturing experience is being undertaken by the Air Materiel Command. Headquarters officials consider completely underground facilities one of the most effective means of protecting aircraft production against air attacks of the strength and type employed in World War II. Advantages accruing to underground manufacturing installations other than protection are, perhaps, a smaller maintenance problem and the possibility of using gravity flow on some production lines. Offsetting these advantages are the high cost of construction, problems of ventilation, and poor acoustics. Excavation costs might well be less than the cost of enclosing the same area on the surface, as new and better methods of rock drilling and transportation are developed. Certainly the amount of building materials used would be far less than in constructing a surface plant of the same dimensions. A fewer number of skilled workers would be required to perform the labor of excavation. Underground construction would

Jan 1, 1947

By R. S. Shoemaker, F. W. McQuiston

REFINERY SECURITY "Highgrading, " a polite word for stealing gold and silver, has been a way of life since the metals in native form have been mined or produced. Unfortunately, in the past, highgraders were not always severely prosecuted or even looked upon unfavorably in their communities. Recent high metal prices with attendent world wide publicity, however, has made highgrading or thievery again a serious problem in mines and plants. When a small button of gold the size of the end of ones little finger has a value equal to about one week's wages, the safe-guarding of gold production by enforcing tight security measures becomes a prime responsibility of management. The higher the gold price, coupled with unrestricted owner- ship, the greater the temptation to “get-your-cut”, and diligence by management must become an integral part of plant security. Primary security begins by knowing the expected gold production and the sampling of a gold ore mill feed for this determination has proved not reliable. However, solution flows can be accurately sampled and measured thereby closely predicting the gold recovered each day as precipitate. The progressive record of total ounces of gold contained in the precipitation press, referred to in cyanidation plants as I1solution calll1 predicts the accumulated production. The "callH is an important adjunct to security and extreme caution must be used so that the pregnant solution meter and sample are confined in a security area. It should be recognized that this key sample may be the target for Ifdoctoring" by trusted insiders (assay office employees) as a preliminary step for stealing precipitates and/or metal. Security measures similar to the following were adopted after one operation experienced a sizeable theft of gold precipitate and metal by trusted employees. The refinery area where precipitates are handled and melted to bullion and all other gold products are kept should be completely enclosed with a tight security fence preferably of solid construction. Access to this enclosure should be through one of two electrically controlled gates, one for personnel and another for occasional truck entrance. Admittance should be restricted to essential personnel who are required to sign a register in and out with the date and time. I£ there is a "back gate" to the restricted fenced area, it should remain locked except in an emergency and then opened only by a supervisor. Television monitoring cameras viewing the gate entrance and other sensitive areas connected to a viewing screen located in the general office afford visual observation at all times.

Jan 1, 1975

By J. B. Morrow, D. H. Davis

THERE are two general approaches to the problem of increasing profits from an operation. One is to lower expense; the other is to raise income. Mechanical preparation of coal may be used for either purpose but a prudent consideration of many details must precede any decision lest the results be negative instead of positive. It is quite possible that any net gain will result from a combination of the two. Since mechanically prepared coal invariably is a better product qualitatively than a hand-picked coal from the same mine, it is a reason- able expectation that the customer will be willing to increase the producer's income by paying a higher price. Or there may be the possibility that a combination of mechanical mining plus mechanical cleaning will give a lower over-all production cost for the coal in the railroad car. More likely, there will be found a combination of these two factors. From the customer's point of view, the competitive delivered cost per B.t.u. considered in relation to such incidental factors as dust nuisance, handling properties, ash disposal, and ash fusibility determines what he will pay. In a bulk tonnage product such as coal, freight is a very considerable part of the delivered fuel cost, and obviously freight paid on incombustible ash has no economic attractions. INCENTIVE FOR CLEANING Coal is prepared in four major ways: 1 (I) by screening or sizing, (a) by mixing or blending, (3) by cleaning, including hand picking and mechanical cleaning, (4) by dustless treatment. By a combination of any or all of these methods, coal can be prepared to standard specifications. It is easily possible to have good cleaning and still get a poor final product because of faulty screening or mixing,

Jan 1, 1943

By Oswald J. Heinrich

(Read at the Amenia Meeting, October, 1877.) THE deposit of rock salt along the shores of Lake Huron, in Canada, has been brought before the public during the last six months, in consequence of the developments made by the diamond drill at Goderich. It is likely to be of more than common interest in the future, since now actual operations have been commenced to exploit the deposit and work it by regular mining. The methods of mining rock salt being but little known in this country, it may be of interest to make a few general remarks in regard to them before entering, upon the description of this new mining enterprise. According to the conditions under which salt is found in nature, various methods have been resorted to, in course of time, to make it available for the human race. They consist in : A. Natural or solar evaporation. B. Artificial evaporation, either exclusively or in connection with the former. C. Mining the rock salt in its natural state, and converting it to a marketable product, if need be, by simply pulverizing it. Without going into the details of the various methods of making salt available in an economical point of view, dependent on its degree of purity, or on various local influences, we cannot refrain from. alluding to the general principles which influence the mining and manufacturing of salt in countries where they have been carried on for hundreds of years. ECONOMICAL CONDITIONS FOR SUCCESS. Salt being one of the articles of prime necessity, and one universally distributed throughout nature, it must always be sold at a comparatively low price. It would even be quoted in the market at prices far below those now ruling, if it were not for the high duties generally imposed upon it, for purposes of state revenues. But looking closer into the subject, it will be found that this duty is probably one of the least oppressive, although in some countries it exceeds sixfold the cost of profitable production. To produce the article at the lowest possible cost requires, therefore, a

Jan 1, 1878

Jan 1, 1881

By Oswald J. Heinrich

The deposit of rock salt along the shores of Lake Huron, in Canada, has been brought before the public during the last six months, in consequence of the developments made by the diamond drill at Goderich. It is likely to be of more than common interest in the future, since now actual operations have been commenced to exploit the deposit and work it by regular mining. The methods of mining rock salt being but little known in this country, it may be of interest to make a few general remarks in regard to them before entering, upon the description of this new mining enterprise. According to the conditions under which salt is .found in nature, various methods have been resorted to, in course of time, to make it available for the human race. They consist in: A. Natural or solar evaporation. B. Artificial evaporation, either exclusively or in connection with the former. C. Mining the rock salt in its natural state, and converting it to a marketable product, if need be, by simply pulverizing it. Without going into the details of the various methods of making salt available in an economical point of view, dependent on its degree of pority, or on various local influences, we cannot refrain from alluding to the general principles which influence the mining and manufacturing of salt in countries where they have been carried on for hundreds of years. ECONOMICAL CONDITIONS FOR SUCCESS. Salt being one of the articles of prime necessity, and one universally distributed throughout nature, it must always be sold at a comparatively low price. It would even be quoted in the market at prices far below those now ruling, if it were not for the high duties generally imposed upon it, for purposes of state revenues. But looking closer into the subject, it will be found that this duty is probably one of the least oppressive, although in some countries it exceeds sixfold the cost of profitable production. To produce the article at the lowest possible cost requires, therefore, a

Jan 1, 1879

By A. T. Miesch, L. B. Riley

Distribution of minor elements in sandstone-type uranium deposits of the Colorado Plateau is being studied by the USGS on behalf of the A EC. A primary objective has been to provide basic data which could be useful in geo-chemical exploration for new deposits. The basic statistical measures — similar to those used in sedimentary petrology—are described. The underlying principle is that the frequency distributions fit or approach the log-normal form. Since 1952 the U. S. Geological Survey on behalf of the U. S. Atomic Energy Commission has conducted a study of the distribution of minor elements in sands tone-type uranium deposits of the Colorado Plateau. A primary objective in this study has been to provide basic data which could be useful in geo-chemical exploration for new deposits. Among the basic data considered important are estimates of the abundance and habit of each element in the ore and in the host rocks. It has been found that a few basic statistical techniques, and variations of these techniques, are useful in this type of study. Some of the basic techniques have been used to advantage by researchers in geochemistry and in other fields of geology, especially sedimentary petrology; others have been used to only a limited extent. Among the latter is the linear correlation coefficient, which has proved useful in assessing the element associations in a particular rock type without analysing individual mineral separates. In computing the basic statistical measures a scale has been used which is, in some ways, similar to the phi ($) scale used by sedimentary petrol-ogists in grain-size studies.' FREQUENCY DISTRIBUTIONS It has been recognized for some time that the results of analyses for a given minor element in a suite of samples of rocks or ores yield frequency distribution curves which are approximately normal when the curves are plotted on logarithmic or geometric scales. In other words, the analytical results give an approximate lognormal frequency distribution. A classical example is given by D. G. Krige2 in the study of the distribution of gold values from a mine on the Witwatersrand. Another example is shown in Fig. 1, the distribution of barium concentrations in samples of uranium ore from the Chinle formation. The geochemical data are analogous to grain-size data gathered by the sedimentary petrologist. Both types of data, after simple logarithmic transformations, may be treated by conventional statistical methods based on the normal distribution. This is not to say that other types of transformations may not serve equally well or better for particular element distributions.3 Spectrographers and other analysts are quite aware of the dependence of their precision on the concentration of the element present.4 For example, in the part per million range the variation may

Jan 1, 1961

By F. W. Jessen, C. C. Patton

Adsorbed films were formed on polished stainless steel specimens from dilute benzene solutions of two crude oil distillation residua. Although the two residua were extremely dissimilar in composition, contact angle measurements showed that the two films increased the wettability of the steel specimens to oil by equal amounts. Furthermore, the wettability of the films was essentially unaffected by the desorption techniques used. Paraffin deposits were formed from heptane-wax solutions on the same stainless steel specimens. These deposits definitely adhered to the surface. Presence of an adsorbed crude oil film on the metal surface increased its free surface energy and resulted in increased deposition of paraffin. The addition to the heptane - wax solution of small amounts of the same distillation residua that were used to form the adsorbed films resulted in decreased cohesive strength in the deposits formed, which resulted in decreased deposition. The presence of a crude oil fraction both in the solution and as a preadsorbed film eliminated the adherence of a deposit of any kind. A mechanism of deposition is proposed which explains the results obtained. INTRODUCTION The natural formation of any predominantly organic accumulation in oilwell tubing, surface flow lines or other production and storage facilities is called a paraffin deposit. These deposits restrict the production of crude oil, causing a substantial increase in production costs because of decreased flow capacity, expense for periodic deposit removal and unproductive downtime. The conditions under which such deposits form, their physical characteristics and the nature and severity of the problem created are extremely varied. Over the past several years, much progress has been made in developing and utilizing methods to remove accumulated paraffin deposition. However, like so many other problems, the basic stumbling block appears to be a lack of understanding of the fundamental mechanism involved in the formation of such deposits. Crude petroleum is known to contain considerable quantities of polar, surface active substances which Doddl has shown to be present at the oil-water interface. Denekas, Mattax and Davis2 observed that the wettability of reservoir rocks was drastically altered by exposure to crude oil fractions; and Zisman, et a1.3 showed that the nature of the compounds adsorbed on a surface would determine its wettability characteristics. Cole and Jessen4 and Ehrig5showed that surface wettability can have a profound effect on the magnitude of paraffin deposition, and Parks6 demonstrated chat the presence of certain adsorbed films on a metal surface would reduce the adherence of paraffin to that surface. Zisman7 has since advanced the theory that the conditions for adhesion are the same as for wetting. Therefore, it was felt that there was adequate evidence to support the supposition that adsorption of compounds from a crude oil might play an important part in paraffin deposition. ADSORPTION-WETTABILITY EXPERIMENTS Initial experiments were conducted to determine the effects of adsorption from solution of crude oil residua on the wettability of a polished stainless steel surface. Distillation residua with initial atmospheric boiling points of 700F were used in preference to the whole crudes in order to concentrate on the molecular weight range of interest, and to eliminate the possibility of composition change due to evaporation of the light ends. Also, these high boiling materials would be expected to be adsorbed from the whole oil in preference to similar compounds of lower molecular weight.

Jan 1, 1966

By D. B. Hobbs, L. W. Kempf, R. S. Archer

SILICON is one of the most important elements in the metallurgy of aluminum. It is always present in small amounts in the ordinary grades of "pure" aluminum, and hence in all alloys made therefrom. Within the last few years binary alloys containing up to 13 per cent. of silicon have come into extensive use for castings. Silicon is also added, beyond the amount present as an impurity, in alloys containing one or more other elements such as copper, manganese, magnesium and nickel. The binary aluminum-silicon alloys are not yet heat treated to any extent in commercial practice, although, as will be shown, their properties are affected to a very considerable degree by heat treatment. There are other aluminum alloys that develop higher strength, but the special characteristics of the silicon alloys may well lead to the application of heat-treating processes on a commercial scale. The role of silicon in the heat treatment of aluminum alloys is more important than would be indicated by consideration of the binary alloys alone, because many of the alloys that are heat treated in regular commercial practice contain some silicon in addition to that derived from the aluminum ingot as an impurity. Among these may be mentioned the heat-treated 195 alloy castings, and the wrought alloys 25S, Special 17S and 51S of the Aluminum Co. of America, and the German wrought alloy, Lautal. It is the purpose of this paper to present the results of experimental work and the conclusions derived therefrom regarding the heat treatment of the binary aluminum-silicon alloys. The products heat treated included forgings, chill castings and both "normal" and "modified" sand castings. REVIEW OF LITERATURE The literature on the heat treatment of aluminum-silicon alloys is not very extensive. The following review gives the principal references of which the authors are aware, in which appreciable information may be found.

Jan 1, 1928

By Goerge F. Weaton

Since 1909, when an agreement between Minnesota's Tax Commission and the University of Minnesota's School of Mines was worked out, it has been the annual responsibility of the School to evaluate and classify the iron ore deposits within the State. These unique duties of an academic institution have provided School officials with an excellent view of the past, present and probable future of the mining industry in Minnesota as the average grade of iron ore (excluding taconite) * diminishes while at the same time it competes with beneficiated taconites and foreign high-grade ores for use in America's eastern blast furnaces. SYSTEM OF EVALUATION In the latter part of November of each year, the Mining Division of the Department of Taxation makes a preliminary study of the active mines which the Department wants the School of Mines to review. These are discussed with the engineers of the Ore Estimate Division of the School of Mines and with the mining companies. After these discussions, a list of the mines of each of the major operating companies is submitted to the Ore Estimate Division of the School of Mines with the request that these properties be reviewed by them as of the next assessment date (May 1st). At the same time, a letter is sent to the mining companies requesting that they submit to the Division their own estimates on the selected mines operated by them, together with all computations, drill records, maps and cross-sections. The mining companies are re- quested to send in this information during the first half of the year, and, as far as is possible, they have always complied with this request promptly. Much of this information received by the School of Mines is of a confidential nature and is treated as such.

Jan 1, 1965

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales: If members have copies of these volumes which they can spare, the price of $3 per volume will be paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will he given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will be sent and the balance will be credited to the payment of clues.

Jan 12, 1918

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales. If members have copies of these volumes which they can spare, the price of $3 per volume will he paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will be given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will he sent and the balance will be credited to the payment of dues.

Jan 1, 1919

By J. B. Fletcher

The Miami mine first started operations in 1910. For convenience, the history of the orebody can be divided into the following categories (Fig. 1): 1) 1910 to 1925: 24.4 million tons of high grade ore, mined by top slicing, sublevel caving, etc. 2) 1926 to 1954: 102 million tons of low grade ore, mined by block caving.

Jan 1, 1961

By Dr. O’Neil Thomas J., Donald W. Gentry

Introduction “A Western mine is a hole in the ground owned by a liar. . ." -Mark Twain THE CAPITAL INVESTMENT DECISION Decisions pertaining to a firm's proposed capital investments can have vital short- and long-term consequences on the organization's ability to compete, and even survive.Capita1 investment decisions, in general, center around two fundamental activities: (1) allocating capital funds to specific investment projects or assets, and (2) obtaining necessary financing in such proportion as to increase the overall value of the firm. In essence these activities or decisions describe the science of finance (as contrasted with economics). Fimnce has been described in general terms as the study of how a present, known amount of cash is converted into a future, perhaps unknown, amount of cash (Archer, Choate, and Racette, 1979). Fundamental to understanding the science of finance and the capital investment decision process in general are the basic concepts relating to cash flow transactions, time, income generation (markets), expected returns, and risk. The functions of finance may be segregated into three fundamental decisions which a firm must address: (1) the dividend decision, (2) the financing decision, and (3) the investment decision. These decisions are interdependent and their joint impact on the objective of the firm must be considered. This book primarily addresses the concepts and components associated with the investment and financing decisions as they affect the practice of mine valuation. Responsibilities of Management A primary assumption incorporated in this book is that the fundamental objective of any firm is to maximize its value, or wealth of its owners (stock- holders). Here, the term wealth refers to the total current market value of the firm's assets. In the case of corporations, the wealth or value is considered to be represented by the market price of the firm's common stock. The price of the firm's common stock obviously will be affected by its investment, financing, and dividend decisions. Consequently, an optimal combination of these three decisions should maximize the value of the firm to its stockholders. It is important to point out that wealth maximization is a more appropriate and inclusive goal for the firm than profit maximization. Indeed, there is a difference between the two objectives in most situations. For instance, a firm can always raise profits by selling stock and investing the proceeds in treasury bills or certificates of deposit. This type of activity, however, would rarely cause net shareholder wealth

Jan 1, 1984

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in