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By R. W. Raymond

By the death of Prof. Pettee the Institute has lost one of its earliest, most distinguished, most useful and most beloved members. Among those who survive him there are few who have rendered services of equal professional value or unselfish devotion. The warrant for this statement will be amply furnished in the present brief notice of his life and work. William Henry Pettee was born, January 13,1838, at Newton Upper Falls, Mass., where hie childhood and youth were spent. His father, Otis Pettee, a manufacturer of cotton cloth and of cotton-mill machinery, died in 1853. Up to that time, the son had been educated mainly in the district school; but, being inclined by temperament and constitution rather to books and study than to physical exertion, he had been wisely rest,rained in mental activity, and required, for a season, to work regularly in the foundry and machine-shop of his father. Unquestionably, this discipline not only benefited his health, but also constituted a valoable preparation for his subsequent professional career. In 1857, after suitable preliminary study at various New England academies, he entered Harvard College, where he took high rank in the classical course then required, was selected in his Junior gear to deliver a Latin oration; was elected a mem-

Jan 1, 1905

By C. E. Arnold

In attacking the problems of mining and treating large disseminated copper orebodies such as those occurring in the Miami or the Ray district of Arizona, one of the vital questions to be decided is, "What is the value of the orebody per ton in place?" The importance of this question lies in the fact that its answer helps to reach a decision concerning the method of mining to be employed. Let it be assumed for the moment that milling and smelting practice, especially the latter, is more or less standardized, and has a cost incapable of much variation, while the cost of mining has a considerable range owing to the large number of mining methods by which a mine may be exploited. For instance, a method may be adopted whereby all the available ore can be extracted perfectly clean (i.e., unmixed with barren material) at a relatively high cost; or a method may be used involving the necessary dilution of a portion of the ore with waste, in order to recover that portion, thus giving a relatively poorer extraction but nevertheless a lower working cost than the former method. Naturally, between these two extremes there lie intermediate methods. In order to arrive at a solution of a mining method problem that is of any value, it is necessary that accurate and complete estimates of mining, milling, and smelting performances and costs shall be established. By way of illustration is given a case of mining, by the system of undercutting and caving, a large orebody with an average content of 1.50 per cent. copper supposedly all in sulphide form, to which case has been applied those results in mining operations which one may fairly assume are to be expected when viewed in the light of G. R. Lehman's ore-drawing experiments, which form the subject of a paper to be presented at this meeting. It is assumed that the total costs will be as shown in the table on page 204. To attain these costs, a daily production and treatment of 14,400 tons has been assumed. Other assumptions are as follows: 15 per cent. of orebody is to be extracted clean by development work and undercutting; 63.8 per cent. (75 per cent. of 85 per cent.) is to be extracted clean by caving, leaving 21.2 per cent. part of which is to be extracted by diluting with waste, and the remainder lost. Dilution and extraction are to

Jan 1, 1917

By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,

By William P. Blake

The occurrence and distribution of phosphorus is one of the most important questions with which the steel-maker has to do. Large sums are invested in processes for the removal of this element from ores before they come to the blast-furnace, and much greater sums in freeing the pig-iron from it. Mechanical engineers are becoming more and more critical of the amount of total phosphorus left in structural steel, the tendency being to require that it be reduced to the lowest possible figure. The old maximum of 0.1 per cent. is now considered much too high for first-class structural steel, and demands for 0.03 to 0.01 per cent. are by no means unheard of. The first to speak, in a scientific way, of the harmful effect of phosphorus on iron and steel appears to have been Meyer, who, in 1781, made mention of what we now term "cold-shortness," ascribing it to the presence of this metalloid, but not suggesting any remedy. It is, however, doubtful if a clear idea of this subject was possessed by the scientific world until after the invention of the pneumatic or Bessemer process, in 1855-56. One of the chief obstacles in the way of this renowned metallurgist,—one, indeed, the removal of which was the sine qua non of success,—was the phosphorus in the iron blown. The effect of the phosphorus does not seem to have been apprehended until many and costly experiments had been made, and then the required minimum percentage of it in the iron was secured only by the use of low-phosphorus ores. It was not until '1879-80 that practical success was reached, by the Thomas process, in the actual removal of the phosphorus from the iron. We now know something of the effect of the total amount of phosphorus on iron and steel, but very little as to the effect of the condition of the phosphorus. The state of combination in which

Jan 1, 1893

By Mohamed Mortada

A practical analytical method is developed in this paper which provides the practicing reservoir engineer with a handy method for analyzing oilfield interference problems. The procedure employed entails the principle of superposition of individual eflects. A set of charts has been developed and can be used to evaluate the individual effects. The charts represent non-steady state pressure distribution in an extensive aquifer due to a constant rate of production from an oilfield which can be approximated by circular geometry; they are constructed from solutions to the diffusivity equation considering a circular sink as distinguished from a point sink. The solutions are obtained partially from mathenlatical considerations and partially from analog and digital computations. By virtue of the method of images, the charts can be used also to treat the case of production near a fault. In addition, provisions are made for treating oil fields, which are produced by partial water-drive. Treating an actual field case is deferred to a subyequent writing; however, illustrative example is presented to demonstrate the method of application. The pressure distribution in linear and limited radial aquifers is currently under study. INTRODUCTION With the increasing difficulty of discovering new oil reserves, attention is necessarily focused on the efficient development and production of existing reservoirs. Efficient production depends on the availability of reliable means for predicting the pressure-production behavior of oil fields. The prediction is usually performed by analytical methods or computers. Analytical methods are often limited to systems which can be approximated by simple geometry. However, analytical methods have the distinct advantage of being readily performed without special equipment. Analog and digital computers lend themselves to a variety of problems, but are not always locally available and consequently their use is limited. One particular situation in which analytical techniques are needed involves studies of multiple, water-drive oil fields sharing a common aquifer. Such oil fields are in hydrodynamic communication. Therefore, production from any of the oil fields is accompanied by a pressure decline which is transmitted through the aquifer to the other oil fields and manifested as pressure interference. The rate of propagation of the pressure decline is such that the pressure may be significantly reduced many miles away from a producing pool. An example of pressure interference is found in the Woodbine formation in East Texas. There. a dozen or more pools, including several of major size, draw on the Woodbine formation for water drive. The pressure in the water-bearing portion of the formation has been significantly reduced over an area of several thousand square miles. This reduction of pressure has been such that when the Hawkins pool was discovered in 1940, the pressure in it had already been reduced 280 psi below the initial value in the aquifer. This resulted from prior production from other Woodbine sand pools, including, in particular, the East Texas field some 20 miles to the east of Hawkins.' The above example indicates that the interference effect can be significant and should be taken into con-

Jan 1, 1956

ASIDE from the John Fritz Medal, in which the Institute participates through its representation on the John Fritz Medal Board, the Institute itself has three major awards to make annually and one special prize for excellence in technical papers, as follows: The Robert W. Hunt Medal and- Prize, The J. E. Johnson, Jr., Award, the James Douglas Medal, and The Lewisohn Platinum Prize to senior members. ROBERT W. HUNT MEDAL AND PRIZE The partners of Robert. W. Hunt established a fund which was presented to the Institute at a fitting ceremony on May 27, 1920, to establish an annual medal and a sum of money to be awarded under the following rules: 1. The award shall consist of two prizes; first of a gold medal, second of a sum of money; a certificate to accompany each prize. The money prize shall not be awarded to a member over 40 years of age, but under unusual circumstances, both prizes may be allotted to one person provided that he is not over 40 years of age. In general it will be understood that the Committee shall award the money prize to the younger men, rather than the medal. 2. The awards shall be made not oftener than once a year to that person or persons contributing to the Institute the best on al paper or papers on iron and steel. The scope of the term "iron and steel" shall determined by the sub-committee considering the awards. In general, papers dealing with the practical side of the subject have preference over those dealing with the theoretical side in recognition of the fact that Captain Hunt's main contributions to the industry have been in the improvement of production and quality of material. 3. A sub-committee of three to five, including the Chairman of the Iron and Steel Committee, shall be appointed by the Iron and Steel Committee annually to adjudge the award subject to approval. 4. The awarding committee shall submit its report to the Iron and Steel Committee at its October Meeting, and the award be certified to the Secretary of the Institute in time to permit the presentation to be made at the Annual Meeting of the Institute. 5. The recipient of the award shall be designated "The Hunt Medallist." This prize is administered by the Iron and Steel Committee. J. E. JOHNSON, JR., AWARD This award is made from' the income of a. fund of $3000 donated by Mrs. Margaret Hilles Johnson in memory of her husband, J. E. Johnson, Jr., who was a prominent engineer, author of two valuable volumes on iron blast-furnace construction and practise, vice-chairman of the Institute's Iron and Steel Committee, and a frequent contributor of papers. to the Institute's Transactions. This prize is administered by the Iron and Steel Committee. The intent of the donor is to encourage young men in creative work in branches of the metallurgy or manufacture of pig iron with which the professional activities of Mr. Johnson were chiefly concerned. The control of the fund and distribution of the awards having been vested in the Board of Directors of the Institute, this Board has made the following regulations concerning it:

Jan 1, 1925

By David R. Maneval, Ralph A. Lambert, H. B. Charmbury

Subsidence, although it may or may not be apparent on the surface, is an inevitable consequence of deep coal mining and a frequent cause of damage to surface structures. Efforts to prevent subsidence go back many years, but there is still only one known antidote that is both technically feasible and predictable. This is the hydraulic or pneumatic stowing of solids-or flushing. In coal mines, however, flushing has been rarely used because it is considered the most expensive method of filling such mines, even though the reverse is true for ore mines. It is thus significant that the method has found favor in a comprehensive program the Commonwealth of Pennsylvania has undertaken to eliminate the hazards of abandoned coal mines within its jurisdiction. In "Operation Backfill," as the program is known, the Commonwealth has successfully used hydraulic flushing and fully justified the method economically.

Jan 4, 1967

By Bruce A. Lamberton

In U. S. underground mines concrete work is not widely used. Timber and steel are cheaper, and there are few serious water problems. But in the Union of south Africa men dig deeper, more persistently, and probably more profitably than anywhere else on earth. Some gold mines near Johannesburg are below the 10,000 level and employ as many as 35,000 natives on a single property. Underground substations, pump chambers, and air conditioning plants have capacity to serve small cities. The complexity and extent of underground operations and the heavy subsurface water flows, especially in the new Free State gold fields, require heavy in a Deep concrete installations.

Oct 1, 1956

By Charles W. Goodale, William A. Akers

The treatment of silver-ores of too low a grade to justify either smelting or preliminary roasting, and yet not " free" enough to permit of raw amalgamation, has ever been a serious problem. As bearing upon it, the operations of the Combination Mining and Milling Company of Black Pine, Deer Lodge county, Montana, during the past year may not be without interest. It is not claimed that the process to be described is not susceptible of great improvement, nor is any claim of originality made for it; but its use is, as yet, not very general, and it seems to offer a means of profitably working the large class of partially-decomposed argentiferous ores which, by reason

Jan 1, 1890

By Pedro G. Salmon

The broad general distinction between primary and secondary batteries lies in the fact that in the former the current is produced by the consumption of one or both of the elements composing the cell, while in the latter the elements retain their form as such, and merely pass from one state of chemical combination to another. Much has been said in condemnation and but little in praise of storage-batteries; yet, notwithstanding the severe criticisms passed upon them, the skepticism with which electricians have viewed them, and the ignorance with which they have been handled, they continue to push their way into use. Their manufacture has now become a well-defined and established industry.

Jan 1, 1890

By Harry P. Hohenadel

DURING the past few years the amazing developments of the chemical industry have inspired so much publicity that the feature writers assure us that we are entering a "Chemical Age," industrially as important as the "Steel Age" and the "Electric Age," so-called. Whether or not these assurances are overstatements, it is a fact that the expansion of the chemical industry during the past 25 years has been enormous. The Chemical Bureau of the War Production Board calculates the value of chemicals produced during 1944 at $8,300,000,000, no small sum even in inflated dollars. As concerns us of the Southwest oil and gas country, four significant trends of the chemical industry are most important. (1) Many of the recently developed chemical products are new creations, not substitutes,. as new and original as the invention of the light bulb, and with a field for exploitation almost as wide. (2) Many of these chemical products will enter the mass consuming markets, which require enormous tonnages of products, and such markets are setting up an industrial demand for chemicals on a mass volume basis, compared to the relatively high-priced low-volume basis ordinarily considered as the chemical outlet of the past. (3) Most of the processes involved in producing these chemicals are adapt. able to the use, all or in part, of natural gas, oil, or refinery gases as raw mate-

Jan 1, 1945

By P. B. Butler

IN common with others, the zinc industry found itself after the war largely over-capitalized, a condi-tion which still exists notwithstanding that Tri-State production has doubled since prewar days. This is partly due to the abnormal war demands and partly because of the war impetus given to research, a stim-ulus that because of its success has persisted (and probably will persist) constantly since then. Improved practice and metallurgy resulting from research are today responsible for an increased pro-duction in the Tri-State district of 15 per cent over the practice of five years ago, and the giant strides in this respect in the western states together with the more moderate advance in the Tri-State district has thrown out of equilibrium the more or less balanced production of before the war and production has con-sequently gained on consumption, a condition resulting in rapidly narrowing profits in the Tri-State field, where the present average cost is actually greater than the price received for our product. Despite this condition, no thinking person will de-plore the cause or means used to achieve a greater production and, as this progress is merely the economic application of intelligent thought, it follows that equal effort and thought may be expected to produce the remedy. It has been suggested that the practical application of research has resulted in less need for man-power and consequently in the lessening of employment to common labor and to engineers. I cannot think that such is the case although personally I have received more ap-plications for employment during the last two years than ever before. But when one considers the strides production of all commodities has taken, it is difficult to reconcile this immense development with the possible increase in pop-ulation especially in view of our stringent immigration laws. Whether or not improved industrial methods are responsible for the lessening of employment the ques-tion as to the wisdom of such improvement is hardly debatable. While the Tri-State district of Oklahoma, Kansas and Missouri continues to be the leading factor in the zinc¬mining industry, gradually lowering prices during 1925 and 1926 and a. decided drop during 1927, have de-creased its production almost 20 per cent, this tonnage having largely been replaced by western concentrates.

Jan 4, 1928

By C. L. Dake

AN insistent and steadily growing demand is evident for the broadening of undergraduate curricula in engineering. Among suggested additions are training in public speaking, report writing, business law and contracts, accounting, finance, money and banking, scientific management, economics, social and labor problems, psychology, and ethics. The demand for these subjects comes from the older engineers and from the industries that employ our graduates. Of course, many of the men who suggest such changes are influenced largely by their personal needs and contacts, but the demand is sufficiently widespread to merit serious study by educators. In fact, many educators themselves concur in the proposals for broader training. These matters were examined intensively a few years ago in an exhaustive study of engineering education. Opinion at that time was rather strongly against any profound change. Since then, however, the whole economic system has undergone violent disruption. Even if recommendations made a few years ago were appropriate to the conditions then- obtaining, the enormously changed conditions of the present make advisable a further careful study of this problem. In recent years, mergers, to reduce costs, have sharply limited the number of engineers employed and have thereby intensified the struggle to secure positions. In this stiffer competition, engineers with the most adequate training undoubtedly fare the best.

Jan 1, 1934

By M. Gensamer

THE stresses which initiate deformation processes in metals are funda-mentally important in the study of the mechanical properties of metals. A point of inflection in the load-elongation curves obtained for single crystals1 has been rather too readily interpreted as a true yield point, and the critical resolved shearing stress on the plane of slip taken as a material constant. Even early work showed that the stress at this point varies with rate of loading, but it has not been generally appreciated that creep tests under static loads alone are suited for determining the existence or nonexistence of a yield point.2 It has now been shown by Miller that single crystals of zinc3 when loaded statically begin to yield at loads too small to measure; as a result there is no case now known, apart from that cited in the present paper, in which a true critical stress for yielding has been demonstrated for single crystals of metals. The case of iron has especial interest: the existence of an upper and lower yield point and of an elongation at the yield point in ordinary iron and steel marks this substance as unusual, though the effects have been found to a very minor degree in other metals and alloys. ? Most alloys do not show such marked phenomena when appreciable yielding begins, and accordingly modern practice is to speak of the yield strength of such materials, a stress read from the load-elongation curve after elongation has begun, rather than yield point. The special behavior of iron suggests that it is more likely that single crystals of iron should have a true yield point than other metals.

Jan 1, 1938

By E. B. Thornhill

In this paper on the recovery of mercury as sulphide, from the residues from the amalgamation and cyanide treatment of high-grade ores and concentrates, I will not discuss the many reactions, chemical and other- wise, that take place in the general process, but confine myself more particularly to the methods of recovering the mercury. I submit charts of two amalgamation-barrel charges, Figs. 1 and 2, which are self-explanatory. The flow sheet of the high-grade and the mercury extraction plants is showh in Fig. 3.

Jan 1, 1916

By Martin Coryell, Eckley Coxe, R. P. Rothwell

WILKES-BARRE, PA., April, 1871. THE great development of the mines and metallurgical works of this country during the last few years, accompanied as it has been by the investment of enor¬mous sums of money in purchasing lands, and in the erection of improvements, requires that advantage should be taken of the accumulated knowledge of engi¬neers, superintendents, and others, in mastering the problems which are con¬stantly presenting themselves for our action. Among those may be mentioned the consideration of more economical systems of mining in our coal and metal¬liferous mines, improved methods of transportation above and below ground, unwatering and ventilating mines, the mechanical preparation of coal and other minerals, the various metallurgical processes, and, in fact, every question tending to the attainment of two great objects 1st. The more economical production of the useful minerals and metals. 2d. The greater safety and welfare of those employed in these industries. In European countries, where the arts of mining and metallurgy have long been the subject of the most careful study, no means have been found so effectual in attaining the end above proposed as the free interchange of experience among those actually engaged in these industries, and this object has been accomplished, mainly, through the medium of institutes, associations or societies, composed of those engaged in these occupations, and by the- periodical publication of essays or papers, communicated to such societies by their members. It must be evident to all practical men that the interchange of the varied experience of those engaged in such occupations in this country could not fail to advance very materially the desired objects; it is, therefore, proposed to establish an American Institute of Mining Engineers, which will hold its meetings periodically in the great mining and metallurgical centres, where works of interest, such as mines, machine shops, furnaces, and other metallurgical works, can be inspected, and the members exchange their views, and consult for mutual advantage upon the difficulties encountered by each; these transactions or proceedings, when published, would form a most valuable and greatly-needed addition to our professional literature. It is proposed that a meeting of those sympathizing with the object above men¬tioned shall be called for the purpose of organizing such an association, the place and time of meeting being Wilkes-Barre, Pa., and the month of April or May. Communications indicating the opinion and wishes of all, both as to these points, and also as to the organization and objects of the Institute, will be gladly received by any of the undersigned, and a notice of the date of meeting, which will be arranged to suit the greater number, will be duly communicated. Any

Jan 1, 1873

By Simon D. Strauss

INTRODUCTION The changes in ownership, management, and operation of the non-fuel minerals industry since the Second World War have been dramatic. World-leading enterprises have lost their identity; host countries have taken over operations from multi-national firms; marketing practices have been drastically altered - and yet the world industry is supplying minerals on a scale far greater than had been anticipated in projections made at mid-century. The world's known mineral resources have been enormously expanded, despite the doom sayers who for decades have been predicting that depletion of non-renewable resources would impose limits to growth. PALEY REPORT One can set the stage by reviewing how the minerals outlook was regarded in a thoughtful and comprehensive analysis made in the years 1950 and 1951. During the War years, President Harry Truman of the United States had come to appreciate the decisive role played by minerals resources through his chairmanship as a U.S Senator of a committee that investigated the procurement and allocation of natural resources. In 1950, in the Cold War era that resulted in actual military conflict in Korea, he appointed a prestigious five-man commission to study the problems of Materials Policy over the following quarter century. Their findings, published in five impressive volumes in early 1952, became known as the Paley report. The text was prepared by expert scientists and economists who spent 18 months assembling statistics, making projections of future demand, and interviewing leaders in industry, academia, and government. [ ] The Commission had correctly foreseen that aluminum would replace copper as the largest volume non-ferrous metal, but it had fallen short of reality by a wide margin indeed for all three materials. Even though the Commission's expectations for growth proved to be extremely understated, it had concluded its report with grave foreboding about the effect of its estimates of demand in relation to supply, as follows: "Consumption of almost all materials is expanding at compound rates and is thus pressing harder and harder against resources which, whatever else they may be doing, are not similarly expanding. This materials problem is thus not the kind of 'shortage' problem, local and transient, which in the past has found its solution in price changes which have brought supply and demand back into balance. The terms of the materials problem we face today are larger and more pervasive." With respect to some minerals, the Paley Report expressed scepticism that, in fact, supplies would be forthcoming regardless of price. Because the Paley demand forecasts understated the actual growth in demand for virtually every mineral, one could logically have expected frequent and protracted shortages in the years since 1950.

Jan 1, 1985

By W. M. McKewan

Jan 1, 1961

By Gregory Dybalski

The purpose of this paper is to illustrate the forecast capability of the econometric model of the cobalt industry1/ as utilized by the Federal Preparedness Agency. Forecasts from this model are illustrated from the premise that the leading producer continues production of cobalt. An alternate forecast is presented where the model structure is altered to reflect the condition where the leading producer leaves the market. All estimations and forecasts presented here are shown for illustrative purposes. The cobalt industry is highly concentrated; one company, owned by the Zaire government, accounts for approximately three-fifths of world production. The cobalt supply outside of Zaire is determined by the level of activity of copper or nickel markets, as cobalt is mined as a by-product of copper or nickel. The demand for cobalt reflects a diversified usage pattern; cobalt is used mainly in heat and corrosion-resistant materials, high- strength materials and permanent magnets. According to 1974 U.S. consumption data superalloys accounted for 22%, magnetic alloys 18%, cutting and wear-resistant materials 13%, and catalyst 7%. Foreign consumption is probably similar in terms of usage categories, but the relative order of the categories is in variance.2/ The Cobalt Model The cobalt model's object is to explain consumption, supply and price movements by utilizing statistically estimated equations. Central to the econometric model is the role of Zaire as the profit-maximizing "dominant firm". Zaire sets the price that is most profitable for itself. The price of cobalt depends on industrial demand, production of other firms, and net exogenous purchases, such as government

Jan 1, 1977

By J. C. Martin

A theoretical analysis of steam stimulation is presented for single sands. The analysis includes the effect of steam production and most of the effects of heat conduction. The results show the effects of a number of important variables on the performance of an idealized well under steam stimulation. Calculated responses are presented which indicate the effects of steam production, amount of steam injected, water production, formation thickness and formation damage. Results indicate that steam production can cause large reductions in the heat contained in the formation. This effect can be eliminated by drawdown control. Water production reduces the amount of oil produced during stimulation. The optimum amount of steam to inject depends on economic factors as well as the well response. In many cases, the increased temperature resulting from stimulation reduces oil viscosity near the well sufficiently to overcome the effects of formation damage even if the damage is not removed during steam injection. Calculated responses for thin sands are more favorable than anticipated. INTRODUCTION Little has been published on the theory of steam stimulation'-' despite the interest it has created and the wide variation in well responses. The results of the present analysis provide an insight into steam stimulation, and the methods employed provide a foundation for future work. Analyses presented in Refs. 1 and 2 are very limited and apply to gravity drainage conditions. Ref. 3 contains an analysis similar to the one presented here. The idealized models used and the assumptions made in Ref. 3 are different from those used in this paper. The analysis assumes that after steam injection has heated a small portion of the volume within the radius of drainage of a single uniform sand, a shut-in soaking period is allowed before returning the well to production. The effects of gravity, capillarity, transient pressure and water-sensitive sands are neglected. The injection and soaking times are assumed short compared to the stimulated production time. The initial temperature is assumed uniform; thus, the results apply primarily to first-cycle stimulation. The effects of gas production other than steam are neglected, and the water-oil ratio during production is assumed constant. Steam stimulation involves the simultaneous variation of the temperature, pressure and saturations. General mathematical equations for these variations are complicated and can be very difficult to solve. Simplified equations based on idealized models are used to reduce the mathematics sufficiently to allow approximate solutions to be obtained. DISCUSSION INJECTION An idealized model for which heat conduction is neglected is used to represent the behavior of a well during steam injection. The mathematics for this model is presented in Appendix A which also contains an approximate solution for the behavior of the no-conduction model. SOAKING During soaking, the well is shut in. Only the temperature, pressure and saturation distributions at the end of soaking are needed in the analysis. During soaking the heat is considered to be conducted in a uniform medium from an initially uniformly-heated circular cylinder confined to the producing interval. At the end of soaking the saturations and pressures are assumed to correspond to the cold zone. Analysis of the heat flow during soaking is included in the next section. The radius of the heated cylinder is calculated from the following heat balance (for constant quality steam injection). At the end of the soaking period it is assumed that little or no free gas is present near the well, and that the soaking period has been sufficiently long that the steam zone has had time to expand and the steam has condensed. The condition where there is no soaking is considered in the next section. PRODUCTION In this section, an approximate method is presented for solving the equations of heat and fluid flow associated with the production of oil and water during steam stimulation. Where initial pressure drawdowns are sufficient to cause steam to flow into the wellbore, steam production is assumed to occur within a short initial adjustment period (Appendix B). The production practices followed soon after the well is returned to production can have a large influence on the amount of oil produced during the stimulation cycle. Under most conditions, there is a period of time in which some or all of the water in the heated zone is converted into steam and produced. This flashing of hot water is caused by the pressure in the heated zone dropping below