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By Allan J. Clark

It may be said that the history of gold in the Black Hills begins with one of South Dakota's most. interesting relics, the so-called Thoen Stone, now in the Adams Memorial Hall at Deadwood. This slab of reddish sandstone, about 14 in. square, was found in by Louis and Ivan Thoen, at the base of Lookout Mountain, near Spearfish, a town in the northern foothills of the Black Hills uplift. Both sides of the stone bear clearly legible inscriptions. One side reads: Came to these hills in 1833. Seven of us, De Lacompt, Ezra Kind, G. W. Wood, T. Brown, R. Kent, Wm. King, Indian Crow. All ded but me, Ezra Kind. Killed by Indians beyond the high hills. Got our gold June 1834. On the reverse side: Got all the gold we could carry. Our ponys all got by the Indians. I hav lost iny gun and nothing to eat, and Indians hunting me. Attempts were made to trace these men. Relatives of Brown were found in Missouri, and it was learned that he had left for the West in 1832, with one Kent. Kind's relatives were also found, and stated that he had started West the same year. None of them had been heard from since their departure. So Kind failed to get out with "all the gold we could carry"; 15 years later California became the center of the first great gold rush, and the Hills waited 40 years for their gold to be rediscovered. It is interesting to speculate on what might have been "the course of Empire" had this little group won through. The history of Dakota, of Montana, indeed, of all the Northwest, might have been very different. When, late in 1875, the goldseekers arrived, they passed quickly northward from the first discovery near Custer, and soon were established on Deadwood Creek, along which, as well as for short distances above the mouths of its tributary streams, Blacktail and Bobtail, placer operations went forward vigorously. These placers were near the northern outcrop of the Homestake ore-body. Their gold was partly derived from this, perhaps in greater quantity from the erosion of the conglomerate or cement deposits, of Potsdam time, themselves a "fossil placer" or beach deposit formed by

Jan 1, 1935

By R. J. Fruehan, F. D. Richardson

Electrochemical measurements have been made of the activity of oxygen in copper and its alloys with silver and tin at 1100" and 1200°C. The galvanic cell used was Pt, Ni + NiO/solid ellectrolyte/[O] in metal, cermet, Pt The results do not support any of the equations so far designed for predicting the activities of dilute solutes in ternary solutions from activities in the corresponding binaries. If, however, a quasichemical equation is used with the coordination number set to unity, agreement between observed and calculated activities shows that this empirical relationship can be useful over a fair range of conditions. SEVERAL solution models have been proposed for predicting the activity coefficients of dilute solutes in ternary alloys from a knowledge of the three binary systems involved. Alcock and Richardson1 have shown that a regular model, and a quasichemical model,' in which the dissolved oxygen is coordinated with eight or so metal atoms, can reasonably predict the behavior of both metal and nonmetal solutes when the heats of solution of the solute in the separate solvent metals are similar. But when this is not so, neither model gives useful predictions unless coordination numbers of one or two are assumed. Wada and Saito3 subsequently adopted a similar model to derive the interaction energies for two dilute solutes in a solvent metal. Belton and Tankins4 Rave proposed both regular and quasichemical type models in which the oxygen is bound into molecular species, such as NiO and CuO in mixtures of Cu + Ni + 0. However, their models have only been tested on systems in which the excess free energies of solution of the solute in the two separate metals differ by a few kilocalories. Ope of the reasons why more advanced models have not been proposed is because few complete sets of data exist for ternary systems in which the solute behaves very differently in the two separate metals. For this reason measurements have been made of the activities of oxygen dissolved in Cu + Ag and Cu + Sn. Measurements on both systems were made by means of the electrochemical cell, Pt, Ni + NiO/solid electrolyte/O(in alloy), cermet,Pt [1] The activity of oxygen was calculated from the electromotive force and the standard free energy of formation of NiO, which is accurately known.5 Before investigating the alloys, studies were made of oxygen in copper to test the reliability of the cell and to check the thermodynamics of the system. Of the previous studies those by Sano and Sakao,6 Tom-linson and Young,7 and Tankins et al.8,7 have been made with gas-metal equilibrium techniques; those by Diaz and Richardson,9 Osterwald,10 wilder," Plusch-kell and Engell,12 Rickert and wagner,13 and Fischer and Ackermann14 have been made by electrochemical methods. EXPERIMENTAL The apparatus employed was the same as described previously,9 apart from slight modification. The molten sample of approximately 40 g was held in a high grade alumina crucible 1.2 in. OD and 1.6 in. long. The solid electrolytes were ZrO2 + 7½ wt pct CaO and ZrO2 + 15 wt pct CaO; the tubes 4 in. OD and 6 in. long were supplied by the Zirconia Corp. of America. They were closed (flat) at one end. In one experiment with Cu + O, both electrolytes were used in the cell at the same time. The reference electrodes inside the electrolyte tubes consisted of a mixture of Ni + NiO. They were made by mixing the powdered materials and pressing them manually into the ends of the tubes, with a platinum lead embedded in them. The tubes were then sintered overnight in the electromotive force apparatus at 1100°C. By sintering the powders inside the tubes (instead of using a presintered pellet9) better contacts were obtained between the electrolyte, the powder, and the platinum lead. Troubles arising from polarization9 were thus much reduced. The electromotive force was measured by a Vibron Electrometer with an input impedence of 1017 ohm; the temperature was measured with a Pt:13 pct Rh + Pt thermocouple protected by an alumina sheath. The couple was calibrated against the melting point of copper. The cermet conducting lead of Cr + 28 pct Al2O3, previously found to be satisfactory9 for use with Cu + 0 was also found satisfactory with Cu + Ag + 0 and Cu + Sn + 0. Superficial oxidation was observed, but it did not interfere with the working of the cell. The reaction tube containing the cell was closed at each end with cooled brass heads and suspended in a platinum resistance furnace. The tube was electrically shielded by a Kanthal A-1 ribbon which was wound round it, and the ribbon was protected by a N2 atmosphere between the furnace and the reaction tube. The cell was protected by a stream of high purity argon which was dried and passed through copper gauze at 450°C and titanium chips at 900°C. All the metals used were of spectrographic standard. Procedure. In studies of the system Cu + 0, be-

Jan 1, 1970

By H. M. Chance

Discussion of the paper of H. M. Chance, Bi-Monthly Bulletin, No. 23, September, 190S, pp. 791-808. CHARLES CATLETT, Staunton,Va. (communication to the Secretary *):-Mr. Chance's suggestions that the brown hematite ores of the Potsdam formation are due to the alteration in place of iron sulphide, and that their extension may reasonably be expected to contain valuable deposits of unaltered sulphide, are interesting; but the facts marshaled by him are too limited to justify more than the hope that they may serve as a commercial source of sulphur. It is true that these deposits have been the source of large amounts of iron-ore; and it. is common, as stated by him, for the mining operations to extend to a shallow depth only; but this is largely due to the fact that the surface-material represents an accumulation from the breaking down and collection of the ore which formerly reached a much higher level. With, increasing depth comes a decreasing thickness of valuable material. This is especially appreciated by a glance at Mr. Chance's drawings. This is the reason why so many disappointments have resulted when these ores have been followed to greater depths. Even if the ore is largely derived from oxidation in place, it is impossible to ignore the great number of concretionary forms, as well as those showing the evidence of secondary solution and deposition now taking place, such, for instance, as the part replacements of fragments of quartzite derived from the underlying beds. Concretionary form does not necessarily mean long transportation, and may be a variation of material in place; but commonly it is an evidence of collection, and tends to imply that more or less concentration has taken place. This fact would also argue against an equally extensive develop¬-

Nov 1, 1908

As already announced, the Arizona Meeting of the Institute is to be held from the 18th to the "25th of September. There will be a special train from New York City to Arizona and return, to take members and guests of the Institute to the meeting., The Committee in charge consists of Walter Douglas, Chairman, Cleveland E. Dodge, John C. Greenway, Arthur S. Dwight and Julius Kruttschnitt, Jr., and while the plans of this Committee are not complete, it may he announced that 'the train will be run with the requisite number of Pullman, dining and baggage cars to accommodate those who desire to go, which will accompany the party during the entire week of the Arizona Meeting as per the following program, including, of course, the visit to the Grand Canyon. It is especially desirable that the Committee should know, at as early a date as possible, the number of those who desire to make the trip; and those who desire special accommodations such as drawing rooms, state rooms, etc., are especially requested to communicate as soon as possible with the Secretary of the Institute, stating the number in their party.

Jan 6, 1916

By R. M. Schuster, F. M. Benavides

A plan is prepared to develop and operate a four mine complex over a 30-year period. The mining complex is in the vicinity of two existing processing plants and the most economical means of transporting the raw minerals to either or both of these processing plants is sought. The mines and processing plants are all within a radius of 5.6 km (3.5 miles). Existing transportation facilities consist of county and state roads and federal highways as well as haul roads in some areas. A navigable river meanders through the area under study and there are two railroad systems servicing the area. The analysis shows the economic and operational feasibility of using an overland conveyor in lieu of other means of transportation.

Jan 1, 1983

By Henry M. Howe, Joseph Winlock, Francis B. Foley

This investigation was undertaken for the purpose of determining, in a systematic way, the effect of the rate of cooling of steels, heated to above the transformation range, on their various mechanical properties. This paper gives the results obtained in the investigation of the heat treatment of carbon steels carried out under the auspices of the Committee on The Heat Treatment of Carbon Steels of the Engineering Division, National Research Council. The objects of this committee, of which Dr. Henry M. Howe was chairman, were to increase knowledge of the influence of heat treatment on the mechanical properties of carbon steel. The mcthod pursued was to subject specimens of steel of the carbon contents most used for engineering work, 0.34 per cent., 0.52 per cent., and 0.75 per cent., to various heat treatments, and to test the mechanical properties thus induced. The steels were the same as were used by the committee on fatigue phenomena. This project was financed jointly by the U. S. Bureaus of Mines and Standards; industries and university laboratories have cooperated. A large part of the work was done at Doctor Howe's private laboratory. The committee consisted of F. B. Foley, H. AT. Boylston, H. C. Boynton, G. K. Burgess, H. J. French, J. H. Hall, Zay Jeffries, R. S. Johnston, F. C. Langenberg, H. F. Moore, E. H. Yeirce, H. S. Rawdon, W. E. Ruder and 11. J. Stagg. The work was undertaken at the suggestion of Doctor Howe, who thought, at the outset, that steel in the sorbitic state might have properties which, for most engineering purposes, would be better than those of the usual or pearlitic state. By a systematic variation in the heating

Jan 1, 1923

By Joseph Winlock, Francis B. Foley, Henry M. Howe

This investigation was undertaken for the purpose of determining, in a systematic way, the effect of the rate of cooling of steels, heated to above the transformation range, on their various mechanical properties. This paper gives the results obtained in the investigation of the heat treatment of carbon steels carried out under the auspices of the Committee on The Heat Treatment of Carbon Steels of the Engineering Division, National Research Council. The objects of this committee, of which Dr. Henry M. Howe was chairman, were to increase knowledge of the influence of heat treatment on the mechanical properties of carbon steel. The mcthod pursued was to subject specimens of steel of the carbon contents most used for engineering work, 0.34 per cent., 0.52 per cent., and 0.75 per cent., to various heat treatments, and to test the mechanical properties thus induced. The steels were the same as were used by the committee on fatigue phenomena. This project was financed jointly by the U. S. Bureaus of Mines and Standards; industries and university laboratories have cooperated. A large part of the work was done at Doctor Howe's private laboratory. The committee consisted of F. B. Foley, H. AT. Boylston, H. C. Boynton, G. K. Burgess, H. J. French, J. H. Hall, Zay Jeffries, R. S. Johnston, F. C. Langenberg, H. F. Moore, E. H. Yeirce, H. S. Rawdon, W. E. Ruder and 11. J. Stagg. The work was undertaken at the suggestion of Doctor Howe, who thought, at the outset, that steel in the sorbitic state might have properties which, for most engineering purposes, would be better than those of the usual or pearlitic state. By a systematic variation in the heating

Jan 1, 1923

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of September, 1913: Members. ANDERSON, ANDREW P., Min. Engr 908 Story Bldg., Los Angeles, Cal. ANDROS, STEPHEN 0., Min. Engr University of Illinois, Urbana, Ill. BECKETT, PERCY G., Min. Engr Globe, Ariz. BLAIR, THOMAS S., JR., Prest. Blair Engrg. Co 343 S. Dearborn St., Chicago, Ill. BOYLE, HARRY, Min. Engr S07 Lowman Bldg., Seattle, Wash. BRADEN, EUGENE B., Vice-Prest., Selby Smelting & Lead Co., Merchants Exchange Bldg., San Francisco, Cal. CHALMERS, JOHN W., Min. and Elec. Engr., Morro Velho, Villa Nova de Lima, Honorio Becalho Minas Geraes, Brazil, So. America.

Jan 10, 1913

By Roshan B. Bhappu, Milton F. Lewis, Jean A. McAllister

Several alternatives are available for treating lower grade gold ores averaging 0.04 to 0.10 oz per ton. These include heap, vat, and agitation leaching and may involve conventional zinc precipitation or carbon adsorption-electrowinning systems. Each of these processes have their inherent economic and operating advantages and disadvantages and the selection of the optimum method for a given gold ore is solely based on economic evaluation of the applicable processes. In this paper an effort is made to provide engineering feasibility estimates for the above processes under varying operational conditions such as ore grade and price of gold.

Jan 1, 1974

By Eugene N. Cameron

Pegmatites occur in abundance in certain areas of South West Africa and in adjacent parts of northern Cape Province in the Union of South Africa. Some of the pegmatite deposits were prospected before World War I, and intermittent mining was done during the period between the two World Wars. The deposits of the Jooste lithium mines became an important source of lepidolite, and beryl, columbite-tantalite, wolframite, and other minerals were produced. Since World War I1 prospecting and mining have been carried on vigorously, with the result that South West Africa produced nearly 3000 tons of beryl during 1949 through 1953, together with more than 40,000 tons of lithium minerals, chiefly lepidolite and petalite. Small amounts of tantalite, columbite, and other minerals have also been produced during the postwar period. Most of this mineral production has come from two pegmatite areas roughly outlined in Fig. 1. One is the Karibib-Omaruru area of north central South West Africa. The second is the northeastern part of the Orange River pegmatite area, which extends into adjacent parts of Namaqualand, in northern Cape Province of the Union of South Africa

Sep 1, 1955

By J. H. Pratt

In a recent paper* on the origin of corundum associated with the peridotites of North Carolina, attention was called to the constant occurrence of the mineral, chromite, in these rocks. The field-data obtained during the preparation of that paper have been used largely in the present paper. During the past summer the general occurrences of chromite have been carefully studied, and those in North Carolina have been especially examined in the field. It is purposed to give, in this paper, the reasons why the chromite should be regarded as having been formed at the same time with the peridotites, having been held in solution by the molten mass of the peridotite, and crystallizing out among the first minerals as the mass began to cool. This theory is essentially the same as that advanced by me for the origin of the corundum associated with the peridotite rocks, and a similar line of reasoning has been used to substantiate the theory proposed. Investigations concerning the igneous origin of some of the ores have been materially aided, during recent years, by the skillful experiments of Morozewicz and Lagorio,§ and by researches that show us, more clearly, why we should regard a fused mass of rock as a liquid, having similar properties to an ordinary solution. These experiments have shown that a molten basic glass, similar in composition to the basic magnesian rocks, dissolves alumina readily, and that upon cooling, the first minerals to separate out are corundum and spinel.

Jan 1, 1900

THE annual winter meeting of the A.I.M.E., which is to open in New York on Feb. 14, will be charac-terized by a number of novel features. The most important is that the technical sessions will be dis-tributed over four days instead of three as heretofore. This makes it possible to reduce the number of conflicts between sessions and also will enable each member to attend a larger number. At the same time the ses-sions are so arranged by groups that those interested only in one or more that are related can, if necessary, cover all in that group in three days as heretofore. The general excursion to which the fourth day has, for some years, been devoted has been regretfully given up, mainly because of the uncertainties of the weather in New York in February. In its place a series of group excursions are being offered at various times during the meeting, arranged, so far as possible, so as not to con-flict with any technical session likely to be of interest to those taking part in a particular excursion. Among the places to be shown the visitors are: the construction work on the Eighth Avenue subway, a real mining job; the Vehicular Tunnel, the world's greatest ventilating project; the manufacture of 42-in. conveying belts; one of the largest and most modern steam plants; a coal terminal; manufacture of mining equipment; a cable-making plant; an oil terminal and refinery. Other en-tertainment features include a smoker Monday evening with a real chance to get together and talk; an informal dance and entertainment given by the Woman's Auxiliary on Tuesday evening; the dinner-dance at the Waldorf Wednesday evening, with no long speeches; a general session Thursday evening when the Petroleum Division will present a series of important reviews of the year. An extensive program has been arranged for enter-taining the ladies, and members are urged to bring their wives. There will be dinners, teas, theater parties, shopping and sight-seeing excursions as well as the dances. The usual general luncheons for members, guests and ladies will be served each day at headquar-ters, and various committees and groups will hold lunch-eons, dinners, and round table conferences as indicated in the schedule on the page opposite. The Mining and Metallurgical Society of America and the American Society of Steel Treaters are participat-ing in this meeting and their members will be welcome as guests at any session or function. A joint conference of the Mining and Metallurgical Society and the A.I.M.E. has been arranged for Tuesday afternoon, under the chairmanship of Clinton H. Crane, at which the whole matter of the mineral reserves of this country is to be up for discussion.

Jan 2, 1927

By C. A. Stetefeldt

It will be of interest to compare the statistics of the gas-producer plant at Aspen, Colorado (recorded by Mr. W. S. Morse in a paper read at the Montreal Meeting, February, 1893*), with those at the Marsac mill, Park City, Utah, where such a plant was first introduced by the writer in July, 1890. In both mills a Stetefeldt furnace is used for roasting; but the Marsac mill has the old-fidsdshioned revolving dryers, while at Aspen, shelf-dryers are at hand. At Aspen, separate Taylor-producers are provided for the Stetefeldt furnace and the shelf-dryers; at the Marsac mill one 7-foot producer supplies gas to both the furnace and the dryers. Hence, in the latter case, the quantity of coal consumed for each apparatus can only be estimated, based upon the relative consumption of wood before gas was introduced. According to Mr. Wilson's statement, the relative consumption of wood in the Stetefeldt furnace and the revolving dryers was as 3 to 2. In the year 1892 the Marsac mill put through the dryers and the Stetefeldt furnace the following quantities of ore and salt (approximate dry weights) : ore, 22,800 tons; salt, 2262 tons. There were consumed in the Taylor-producer 2,714 tons of Rock Springs coal. We may thus make the comparative estimate as follows: Table Showing the Consumption of Coal per Ton Of Ore and Salt at the Marsac and Aspen Mills. Marsac. Aspen. Difference. Pounds. Pounds. Pounds. Drying ore and salt,.... 86.63 72.22 14.41 Roasting ore,.....142.40 117.44 24.96 Total,.....229.03 189.66 39.37 In making a just comparison a number of items must be taken

Jan 1, 1894

PRESIDENT HORACE V. WINCHELL MINNEAPOLIS, MINN. PAST PRESIDENTS PHILIP N. MOORE ST. Louis, Mo. SIDNEY J. JENNINGS NEW YORK, N. Y. FIRST VICE-PRESIDENT A. R. LEDOUX NEW YORK, N. Y. TREASURER GEORGE D. BARRON NEW YORK, N. Y.

Jan 1, 1923

By K. F. Veit, R. L. Marovelli, T. S. Chen

There is an error at the bottom of the right-hand column of p. 11, and the top left-hand column of p. 12. The first paragraph of the section EXPERIMENTAL RESULTS should read: "Thermal shock tests were conducted on circular discs of basalt, quartzite, and taconite. Average grain sizes ranged between 0.10 and 0.25 mm. Individual discs were tested only once, either in a cooling or heating shock. Several discs of the same rock type were shocked at a temperature, and the temperature level then was increased for another test by 10° to 20°F until complete fracture occurred when a specimen was quenched. The minimum temperature difference required to initiate cracking, TmiN was observed and used, together with other property values, to compute the dimensionless stress o*max . The observed ?Tmin for cooling shock in different media is tabulated in Table I. The property values E, St, a, and K are shown in Figs. 6, 8, 10, and 11, respectively. Discs of various rocks shocked in different isothermal baths gave o*max values for a wide range of Biot numbers. These o*max values were then compared with the theoretically predicted values."

Jan 1, 1968

By Alfred Weiss

When I first received the announcement of this meeting I was pleased to see that this 14th APCOM Symposium had expanded its range of interest. One new topic to be considered this year is long range or strategic planning--the continuous process by which current risk taking decisions are made systematically, and with the greatest knowledge of future impact. Long range planning should receive our attention. It is the first step in the management process and the foundation of many--if not all --key managerial decisions. Improvements made at this stage of managing are almost certain to be of benefit in later stages of decision making. It is obvious to many of us that in a physical process such as mineral beneficiation, one does not concentrate all of one's attention on the flotation design without also considering the grinding, cycloning, and desliming stages of the process. Taking this a step further it would be equally erroneous to find a mineral engineer designing a mill without due consideration for mine, smelter and refinery and beyond that the sales goals, growth and profit objectives of the firm itself. And yet, how many times have we seen organizations staff and reorganize without consideration of an overall plan; without adherence to the management process which by its definition, calls for a plan first, followed by the appropriate organization and staff. The computer applications traditionally discussed at APCOM meetings have concentrated on areas dealing with things and people-- the implementation of the plan, rather than with concepts and ideas, the formulation of the plan.

Jan 1, 1977

By L. R. Flint, W. L. Freyberger, W. J. Howarth

W. L. Freyberger (Director, Institute of Mineral Research, Michigan Technological University, Houghton, Mich.)-The authors are to be complimented on their theoretical analysis of a column flotation process, and the comment I wish to make is not related to that analysis, but to the use of the word "countercurrent" to describe that process. Strictly speaking, the process the authors have described is countercurrent only in the sense of particle-bubble contact. That is, as solid particles and air bubbles pass through the column, the leanest flotation feed (the tailing) comes in contact with the greatest concentration of mineral-free bubbles. However, air bubbles alone do not comprise the complete extracting phase in a flotation system. A second component of this extracting phase is the collector, which is really the extractant inducing transfer of mat-

Jan 1, 1972

By G. L. Oldright

THE development of the reverberatory furnace for smelting copper ores up to 1912 was described by E. P. Mathewson1 with details concerning the great changes in dimensions of the furnace. Hayward2 tabulated similar data, giving developments up to about 1924, in his revision of Hofman's Metallurgy of Copper. DEVELOPMENT OF PRESENT SMELTING PRACTICE Dimensions of Furnace Very great changes were made in the dimensions of the smelting hearths of the furnaces in the period from about 1800 to 1906, the length increasing from about 11 to 116 ft., and the width from 8 to 19 ft. During this time the tonnage smelted increased from about 9 to 250 tons per 24 hr., and the tons of charge smelted per ton of coal increased from 0.77 to 4.3. Dr. Mathewson3 noted no great difference in the "fuel ratio" (i. e., the amount of charge smelted per ton of coal) as the furnace at Anaconda was increased in length by stages from 85 to 116 ft. (The percentage of copper in the slag, however, was lowered from 0.42 to 0.36 per cent. The other components of the slag were not given.) Lump coal fired on grates was the fuel used during this period. The practice in operating the furnaces over such a length of time naturally varied considerably, and there were differences in composition and nature of the charge, yet it may be considered that the improvements made were due largely to increases in the size of the furnace used. Doubt-less some credit should be given to improvements in operating technique, like changes in the methods of firing the lump coal. However, the greater part of the advance was probably due to factors influencing the

Jan 1, 1928

By W. E. Foreman, James A. Redding

INTRODUCTION Screening is a mechanical process that separates particles by size. Modern coal preparation is made possible by efficient sizing. Sizing of coal is defined in terms of the opening through which an individual particle will or will not pass, or as two openings, the larger of which passes the particle and the smaller of which retains the particle. Screening accomplishes sizing by passing coal of a wide range of sizes through a series of screens, each of a decreasing size. The individual screen discharges are then directed into different screen products for subsequent sale or processing. Screening in modern preparation plants is done for the following reasons: 1 ) Removal of fine coal before a size reduction step. 2) Size separation of the coal into a coarse and fine fraction for sized products or processing in coarse and fine coal circuits. 3) Recovery of heavy media from heavy media coal cleaning circuits. 4) Dewatering. 5) Rock and trash removal by handpicking on a screen. Fig. 8-1 is a generalized flowsheet of a plant showing the use of screens in the coal preparation process. Table 8-1 shows the vibrating screen equipment utilized in Fig. 8-1

Jan 1, 1979

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is 'uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b'e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970