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By M. K. Seguin

The study described in this paper is first centered on the determination of the physical properties (gravimetric, magnetic, electrical, and electromagnetic) o f metamorphosed iron ores of the Carol Lake-Labrador City District. Different geophysical surveys available in the Carol Lake-Wabush area were interpreted quantitatively and the dimensions, attitude, and tonnage of the ore bodies investigated were determined. A geophysical-statistical study was undertaken which permitted the determination of the grade of iron, magnetite, and, subsequently, specularite in the ore bodies. A discussion of the theory and logical progression of the study and the application of the results to actual geophysical data is presented. The conclusions, which are of real significance from the economic standpoint, may be predicted from the data obtained from geophysical surveys before any diamond drilling is undertaken. An integrated interpretation of this type is useful in planning future exploration work and selecting the most favorable geological structures. It also serves as a guide to minimize and determine tonnage drilling patterns. The general conclusion that a restricted range of residual gravity and magnetic anomalies are a key to exploration is valid. Indeed large depths to the top of deposits are absent since all the ore bodies are overturned synclinal structures with tops located close to the surface. Certain irregular geometries do occur but they are not common and the alignment of the iron ore bodies is sub parallel so that magnetic anomalies are evenly reduced in the earth's magnetic field vector.

Jan 1, 1975

By Ivan Simon, R. K. McConnell

Anticipating the availability of tiltmeters suitable for use in boreholes, this article proposes a method of using one or more of these meters to determine in situ stress distribution before and after mining operations. Several ways of using relief techniques to measure in situ stresses in rocks have been developed. These techniques, summarized by Merrill,1 involve measuring deformations which take place when a specimen of rock is wholly or partially isolated from the stress field in the surrounding rock. Measurements of rock deformation caused by stress relief from mining operations can, in principle, also be used to estimate in situ stress distributions. Müller2 has mentioned experiments being carried on in Austria with a "deformation indicator" to determine the tilting of holes drilled before a mine opening is made. Similar work using borehole extensometers has been reported by Potts? and Duvall4 has called attention to the possible use of tiltmeters in making these measurements. Considerable attention is now being paid to the use of tiltmeters in detecting rock deformation associated with fault movements, earthquakes, earth tides, etc. The instruments used for these measurements have usually been of the mercury tube, water tube, or quartz fiber type, but because of their large size, and/or fragile nature, such instruments would not be suitable for use in mining stress measurements. Recent instrumentation developments, however, give promise that rugged, sensitive tiltmeters small enough for use in boreholes may soon be available.' In anticipation of these developments, this article presents a number of calculations of the possibility of using one or more tiltmeters emplaced in a drill hole prior to mining operations to determine the in situ stress distribution both before and after a mining operation. Consider point p (x, z) near a tunnel of radius a

Jan 1, 1969

By W. Hurst

The authors of this paper, in substituting values in a material balance equation associated with a gas reserve and a water drive, cannot find sustainment of what the gas in place should be; therefore, their conclusion is that this type of problem dealing with gas reservoirs is insoluble. They have introduced the word, "cybernetics," based on the work of Norbert Wiener, that further extends this line of reasoning, namely, to the effect that the system is a "black box", and that the gas reservoir and aquifer can take on infinite aspects 'based upon their past performance, to quote the authors. The inference is that this black box is an unknown. which permits in computer programming to subscribe as many variables as possible to observe by adjustment of one to another those combinations of conditions that fit field behavior. This may satisfy those in this discipline whose dedication is to programming, but to the others this is a comparison to the rationalization of the combinational results of the throwing of dice—a probability procedure. In reservoir engineering we are more direct. We learn from the examination of individual we'll and field data exactly what is in this black box. I now come to the impasse that has confronted these authors in their machine calculations. In this I have reproduced from their own production data (Tables 1 and 2 of their paper) pressure vs cumulative gas produced. shown as Figs. D-1 through D-5. A perusal of any of these five plots, for the corresponding fields in the Po Valley, shows the straight-line relation of pressure vs gas produced, evidencing pressure depletion. The point I make is that in their fundamental production data, there is no variance from a straight line that can support a water drive.

By William E. Ford, Edward Salisbury Dana

Secondary Twinning. - When there is reason to believe that the twinning has been produced subsequently to the original formation of the crystal, or crystalline mass, as, for example, by pressure, it is said to be secondary. Thus the calcite grains of a crystalline limestone often show such secondary twinning lamella?. The same are occasionally observed (Ilc, 001) in pyroxene crystals. Further, the polysynthetic twinning of the triclinic feldspars is often secondary in origin. This subject is further discussed on a later page, where it is also explained that in certain cases twinning may be produced artificially in a crystal individual - e.g., in calcite (see Art. 282).

Jan 1, 1922

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members) Member, Graduate Colorado School of Mines. Four years' experience in West and Northwest. Two years with American Smelting and Refining Co. Wishes to join field party on geological work, mining or areal, where opportunity will be given to be of direct assistance to chief of party in solution of field problems. Age, 26. Unmarried. At liberty June 1. No. 342. Member, technical graduate, aged 30, with' 7 years' experience in concentrating and mining, desires a position of authority with reliable company. At present employed. No. 343. Member. Ambitious, energetic, tactful engineer, college graduate, married, aged 30, desires location with a large coal mining organization. Seven years with present employers -n middle west; has had broad experience in the past eight years on examination, development and construction; successful record in handling men. Position must carry responsible work and a future. Will go anywhere for proper opportunity. Exceptional references as to reliability, character and capacity for work. No. 344.

Jan 3, 1917

THE shipments of high-grade manganese ore, con-taining 35 per cent or more of manganese, from the mines in the United States in 1926 were slightly less than half as large as similar shipments in 1925, accord-ing to the United States Bureau of Mines, Department of Commerce. The shipments in 1926 by 45 producers amounted to 46,258 long tons as compared with 98,324 long tons by 42 producers in 1925. This decrease was due to the falling off of the shipments from Montana. The domestic production of metallurgical ore in 1926 was 26,530 tons; that of chemical ore, 19,728 tons. Montana was the largest shipper with 5713 tons of metallurgical ore and 17,904 tons of chemical ore. The largest individual shipper of metallurgical ore was the Crescent Mine in the Olympic Mountain Region, Clallam Co., Washington, from which the shipments for the year were 3162 tons. The mine was operated by lessees and reverted to the owners in July, and thereafter to the close of the year no .ore was shipped.

Jan 6, 1927

By H. M. Howe

Page 1. Introduction............................514 2. Definitions.............................517 3. Brevity of the Heating........................517 I. THE HARDENING OF THE BORE..............517 4. The Hardening of the Bore.....................517 5. The Thickness of the Hardened Layer.................517 6. Martensitization..........................518 7. The Hardening Repetitive ......................519 8. The Temperature Cycle.......................519 9. The Hardened Layer is the Merged Layer............... 521 10. The Progressiveness of Merging....................521 11. The Progressive Thickening of the Hardened Layer from Round to Round. 523 12. Merging and Hardening are Cumulative................523 13. Three Additional Causes of the Progressive Thickening of the Hardened Layer 525 14. Progressive Roughening of the Bore..................525 15. Avoidance of an Endothermic Transformation.............525 16. Asymptotic Retardation of the Thickening of the Hardened Layer.....527 17. The Troostitic Layer........................ 529 18. The Usual Lack of Martensitic Markings................529 19. The Thickness of the Hardened Layer Should Increase with the Quantity of Heat Taken up by the Walls of the Bore.................530 20. The Decrease of the Thickness of the Hardened Layer from Breech to Muzsle 531 21. Phstic Deformation as a Contributory aCause of Hardening........531 22. In What Way May Plastic Deformation Hasten Hardening?....... 535 23. Possible Need of Coarsening.....................535 24. Carburization as a Cause of Hardening..........:.....536 25. Does Hardening Increase Erosion?..................-538 11. THE CRACKING OF THE BORE ...............539 26. Appearance of the Bore and Cracks in Elevation............539 27. The Cracks in Elevation in the Rear Ring...............539 28. The Cracks in Elevation in the Forward Ring.............540 29. The Copper Network in the Grooves.................540 30. The Cracking of the Lands......................541

Jan 1, 1918

Jan 1, 1968

By Ö. Valla, A. Muan, K. Grjotheim

The solid miscibility gap between CaO and "FeO" in the system CaO-"FeO" in contact with metallic iron gradually closes as MnO is added as a third component. On the liquidus surface of the system CaO-"FeO"-MnO, this situation gives rise to a boundary curve which originates in the bounding system CaO-''FeO", proceeds a short distance into the composition triangle of the ternary system, and then vanishes. A new approach has been used to follow the course of this boundary curve. It is shown that the curve vanishes at a much lower temperature and at much lower MnO contents than has been inferred previously. The oxides CaO, "FeO", and MnO together with SiO2 are the major components of the slag phase formed in the basic oxygen process. Hence, the system CaO-"Fe0"-MnO is of considerable technological interest. In addition, the system is theoretically interesting. The three oxides above all have sodium chloride structure. The size differences among the cations are such that in the bounding "binary"* systems CaO-MnO and "FeO"-MnO complete solid-solution series are formed,1,2 whereas in the system CaO-"FeO" there is only limited mutual solubility in the solid state,3 see Fig. 1. Hence, a solid miscibility gap exists in a part of the "ternary"* system Ca0-"Fe0"-Mn0, and a liquidus boundary curve originates at the peritectic point, point a in the insert in Fig. 1, in the system CaO-"FeO", extends a certain distance into the ternary system, and then vanishes. Very little quantitative information on the system Ca0-"Fe0"-Mn0 is available in previous literature. Fischer and Feischer4 sketched isothermal sections at 1600° and 1700°C, and estimated that the vanishing boundary curve extends to approximately 1650°C and a composition of 42 wt pct MnO. The work to be described in the following was aimed at locating experimentally the "vanishing" liquidus boundary curve, determining its end point, and deriving representative isothermal sections below and above the temperature of the end point of this curve. EXPERIMENTAL METHODS The phase relations were determined by the well-known quenching method. (For a description of this method as applied to oxide systems, see the original paper of Shepherd, Rankin, and wright.5) Prereacted oxide mixtures of desired compositions were contained in iron crucibles and heated in a vertical tube furnace in an atmosphere of purified nitrogen. After equilibrium was judged to have been attained, the samples were quenched to room temperature, the phases present were identified by microscopic and X-ray examination, and total iron oxide contents were determined by chemical analysis. "Fisher Certified" reagents (MnCO3, CaCO3, Fe2O3, and Fe) served as starting materials. The calcium carbonate and ferric oxide were heated in air at 400° and 800°C, respectively, for 24 hr prior to use. Manganese oxide was prepared by decomposing the carbonate in a graphite crucible in hydrogen atmosphere at 1000°C. The product was ground under acetone to -100 mesh. The iron powder was used directly without any preparation. Dicalcium ferrite was used as a starting material for some mixtures. It was made by mixing some of the above prepared CaCO3 and Fe2O3 in proportions corresponding to the formula 2CaO. Fe2O3. This mixture was then fired in air for

Jan 1, 1969

By Martin G. Castro, Renato G. Bautista, Morton Smutz

During the last 25 years, multistage mixer-settlers have been used extensively for liquid ion exchange work. The mixer-settler has the advantage of being a compact device in which a large number of stages can be assembled in a relatively small area. They are particularly advantageous for the separation of rare earths. Most of the adjacent rare earths have separation factors which are near one, which means that a large number of stages are needed to produce a good separation. When two elements (m, n) are extracted simultaneously, the separation factor (ßm, n) is defined as: [ ] where Ym, Yn are the molarities of the respective elements in the organic phase and Xm, Xn, are their molarities in the aqueous phase at equilibrium. The industrial consumption of rare earth oxides rose to over 6800 tons in 1968, an increase of 33% over 1967.1 The increased production and demand for rare earth and lanthanum chlorides for petroleum cracking catalysts was one of the principal factors in this increased consumption of rare earths. In 1968 approximately 59% of the rare earth oxides produced were used for gasoline cracking catalysts in the form of rare earth and lanthanum chlorides. There was also an increase in the sales of lanthanum oxides for use in optical lenses and in fiber optics. The future looks good for the rare earth industry. The rare earths can be expected to be used in many new products which are being developed. Until the late 1950's tributyl phosphate (TBP) was the principal solvent used in rare earth liquid ion exchange. In 1957 Peppard3 reported the use of di (2-ethyl-hexyl) phosphoric acid (D2EHPA) as a solvent for separating the rare earths. Rare earth separation factors of up to 2.5 were obtained in nitrate and chloride systems while the maximum separation factor using the

Jan 1, 1972

By E. A. Gulbransen, J. W. Hickman

DURING the past two decades considerable progress has been made in the art of manufacturing heater alloys. The conventional iron-chromium-nickel alloys have been improved by the addition of small quantities of other elements. Up to the present time, to our knowledge, there has not appeared a systematic study of these alloys where the newer tools of investigation have been brought to bear on the problem. It is not yet clear what roles the additional elements play in increasing life time in usage. As a first approximation one might guess that elements such as manganese, silicon, zirconium, calcium and aluminum would aid in the formation of a protective film on the alloy surface, thus retarding the oxidation rate and increasing lifetime. If these additional elements do form protective oxides in the outer surface of the oxide film, it may be possible to identify them by means of reflection electron diffraction. It is also possible that the additional elements may not diffuse to the surface but may remain at the interface between the oxide and the metal. Then, too, the major elements in the alloys undoubtedly form oxides which are stratified on the surface. If the minor elements concentrate in a layer in contact with the substrate where they undergo oxidation and if this oxide film offers resistance to the diffusion of iron, chromium and nickel ions, then the lifetime of the heater element might be expected to increase. It is also possible that preferential reduction in the diffusion rates of the several ions may Occur to such a degree that oxides may form in the body Of the film and On the outer surface which are different from those that would normally form if the additional elements were not present. The use Of transmisson electron diffraction may aid us in jnterpreting these phenomena. UP to the Present time all Of the factors which influence the lifetime of a given heater element are not definitely known. Among these are: (I) The rate of oxidation of the alloy. This may be dependent upon the composition and the physica1 state of the "alloy. (2) The stability of the structure of the coating which forms. Transitions from one structure to another or solid phase reactions resulting in a change of composition may occur. The tendency of the film to adhere to the substrate when heated and cooled successively will be important. (3) The evaporation of various constituents from the alloy such as the remova1 of carbon by Oxygen in a decar-burization reaction. With these possibilities in view, an electron diffraction study of the oxides occurring on six different nickel-chromium alloys was undertaken with the hope that the results of this study could be correlated with oxidation rate studies as determined by means of the vacuum microbalance method1 and with lifetime tests carried

Jan 1, 1949

Jan 1, 1967

By T. K. Smith

The comments contained in the discussion of the paper concerning the prediction of fracture gradients are of considerable interest, since the subject is of a very controversial and timely nature. It is regrettable and Fairhurst2 contradicts the author's statement in the third paragraph of Other Applications. These references create significant doubt that Eaton's Eq. 1 predicts fracture pressure during the injection of fluid into old wells. 3. No evidence is presented in this paper to support the author's Conclusions 2 and 3. While an empirical coefficient related to back-calculated field data is correlated with depth (Eaton's Fig. 4), there is no reason to suspect that this coefficient might be the Poisson's ratio of the various formations involved. 4. Until the field data supporting the empirical approach proposed by the author are presented and evaluated, the accuracy claimed in Conclusion 5 is without substantiation. References 1. Geertsma, J.: "Problems of Rock Mechanics in Petroleum Production Engineering", Proc., First Intl. Symposium on Rock Mechanics, Lisbon (1966) 585. 2. Haimson, B. and Fairhurst, C.: "Hydraulic Fracturing in Porous-Permeable Materials", I. Pet Tech. (July, 1969) 811-817. that the comments are those of a critic and do not offer an alternative and better method for the prediction of fracture gradients. Nevertheless, a reply is in order.

Jan 1, 1970

By M. ROWE, H. E. Gilliland, L. BARNES

The authors of this paper are to be commended for a clear exposition of a timely subject. However, some important conclusions, in addition to those presented in the paper, can be drawn from the results of their elaborate and rather complete numerical computations. First of all, the major part of the calculations presented in the paper are for semi-infinite slabs of oil shale (the authors designate this as Model I) and a question must be posed — Are these elaborate computations needed to arrive at realistic estimates of the shale oil displaced. Consider the model of Lauwerier* that corresponds to the authors Model I if thermal conduction parallel to the fracture be neglected. If one also neglects the finite (but relatively small) heat capacity of the material in the fracture, it is easily shown from Lauwerier's solution that the cumulative oil production would be:

Jan 1, 1969

By Hewitt Wilson

CHALK is soft, pulverulent limestone formed from calcareous remains of microscopic organisms. Whiting is the powder made by the fine- grinding of limestone. Although European chalk dominated the early American market and is still shipped to the eastern and western seaboards, the domestic producer, by new technical processing, improved equipment, and proper selection and mixing of raw materials has shown that the United States can be independent of foreign sources. DISTRIBUTION European Chalk-Outcrops of Cretaceous chalk are found in the area roughly bounded by Antrim, Ireland, on the east, East Prussia on the west, Sweden and Scotland on the north, and Nice, France, on the south. Commercial chalk is mined from the chalk cliffs between Dover and Hull, England; from deposits near Mons, in the Departments of Pas de Calais and Nord in northern France; and from similar de- posits in Denmark and Belgium. United States-Some grade of limestone is found in every state of the Union, but true chalk of Cretaceous age is limited to three large areas in the central and southern states. Niobrara (Cretaceous) chalk outcrops are found as a narrow band encircling the Black Hills in South Dakota, Wyoming, and Nebraska, and in much larger exposures in southeastern South Dakota, eastern Nebraska, and western Kansas. A third chalk belt extends from west central Arkansas into Oklahoma and connects with the Austin beds, which almost cross Texas. In the southeastern states, the Selma chalk extends from western Tennessee south through northern Mississippi and turns east across central Alabama. Most of the domestic chalks are discolored with iron oxide or carbon. Some marls can be included with chalks of commercial possibilities. Some of the soft, cream-colored limestones of northern Florida, Georgia,

Jan 1, 1949

By Ray W. Ballmer

"For his leadership in developing and managing large, complex, and technically innovative mines, particularly the outstanding and successful Bougainville mine and for his lecture, 'The Moving Targets of Mine Development '. " Recipient of the 1981 D. C. Jackling Award

Jan 1, 1982

By H. Jehn

Like some other Pt-group metals palladium shows a low but considerable solid solubility of oxygen, which was found already from oxidation studies. The oxygen solid solubility of palladium in equilibrium with gaseous oxygen has been investigated at 900 - 1300 °C in oxygen (665 mbar) and air by gassing and analyzing polycrystalline samples. The 0-concentrations range from 40 to 90 ppm and decrease with rising temperature. The isobaric solubility can be represented by the least-squares fit log c0 = 0.5 log p02- 0.32 + 920/T (c0 in wt. ppm, p02 in mbar, T in K). The thermodynamic data of the exothermic solution reaction are calculated to ?H°= -17.6 kJ?mol-1 and ?S° -76.5 J?mol ? K-1. The behaviour of palladium in an oxygen atmosphere is characterized by the simultaneous reactions of the solution of oxygen in the metal and the formation and evaporation of volatile oxides besides the pure metal evaporation.

Jan 1, 1984

By M. W. Von Bernewitz

AN important regional meeting of the American Institute of Mining and Metallurgical Engineers was held, at Salt Lake City on Aug. 22 to 26, jointly with the fifth annual meeting of the Western Division of the American Mining Congress. The whole meeting was marked by enthusiasm, keen attention to the subjects under discussion, and many renewals of personal contacts. The trips to the various plants were well attended and the local press paid much attention to the meeting. The A. I. M. E. sessions began Aug. 23, with a non-technical morning session. J. 0. Elton, manager for the International Smelting Co., presided. The purpose of this session was to present in a non-technical manner the relation of flotation to mining, smelting, and the State. Ernest Gayford, metallurgist with the General En-gineering Co. of Salt Lake City, gave the definitions of flotation as suggested by Rickard, the dictionary, Weinig, and Taggart. The active agent in flotation is the air bubble, and the two prime requisites are the formation of bubbles and the creation of selective action of the bubbles for metallic particles instead of for gangue particles. Broadly, all the sulfides are floatable minerals, but the oxides, carbonates, silicates and sulfates are not. As far as Utah is concerned, flotation has been one of the greatest means of conserving its natural re-sources, because it has converted millions of tons of waste rock into pay ore; it is recovering millions of pounds of metal formerly lost in tailings; it has con-verted the zinc from a liability into an asset; and has kept thousands of men at work and distributed millions in dividends for the benefit of the State. As to the future of flotation, Mr. Gayford can con-ceive that the next 5 or 10 years may see as much, if not more, advance than was made in the preceding period. The big problem is dressing oxides, carbonates, silicates, and sulfates, and simplification of the number of reagents, also the separation of different gangue min-erals from one another.

Jan 10, 1927

By R. W. Hertzberg, F. D. Lemkey, J. A. Ford

The technique of unidirectional solidification has been applied to the A1-AI3Ni and A1-CuAl2 ezltectic alloy systems; the controlled microstructure of A1-A3Ni consists of parallel A13Ni whiskers emhedded in an aluminum matrix while the Al-CuAl2, system solidifies as parallel alternate lamellae of aluminm and CuAl2. Mechanical tests (tension and flexure) have shown that the particle-matrix interface bond formed during unidirectional solidification allowes for efficient load transfer from the matrix to the reinforcing phase. Strength and fracture characterstics of the alloys were studied as a function of phase orientation; the tensile strength of controlled Al-Al3Ni samples was 43,000 psi (three times greater than that of as-cast specime~s). The strength of the Al-CIA2, cutectic was studied as a function of lamellae-flexure stress-axis orientation using a microbend apparatus. A twofold increase in outer fiber stress was observed as the lamellae were rotated from a position of no reinforcing (perpendicular to the stress axis) to one of maximum reinforcing (parallel to the stress axis), The brittle reinforcing constituent in each alloy (A13Ni and CuAl2) was observed to he the nucleating phase for fracture. It is to be concluded from this investigation that unidirectionally solidified eutectic alloys have a potential use as reinforcing coniposite) materials. In a recent review article, Chadwick1 has described the work of many investigators in the area of controlled solidification of binary eutectic alloys. Thus far, more than twenty eutectic alloys have been unidirectionally solidified to produce structures consisting of two phases in the form of alternating lamellae or as whiskers embedded within a continuous matrix; in either case, the phases are aligned parallel to the growth direction. In particular, Kraft and Albright2 have shown that the Al-CuA1, eutectic alloy exhibits a lamellar microstruc- ture as a result of unidirectional solidification while Lemkey, Hertzberg, and Ford3 have studied the A13Ni whisker-aluminum matrix morphology in the A1-A13Ni system. Whether these alloys could exhibit reinforcing behavior would have to depend upon the strength and volume fraction of the reinforcing phase (AI3Ni and CuA12) and the nature of the bond between the reinforcing phase and the matrix. Hertzberg and Kraft4 have shown that the interface bond between chromium whiskers and a copper matrix in unidirectionally solidified Cu-Cr is particularly good while Lemkey and Kraft5 have reported chromium-whisker tensile strengths in excess of 1,000,000 psi. However, with the chromium volume fraction being less than 2 pct, no reinforcing behavior was displayed by the Cu-Cr alloy.6 In view of the encouraging results concerning the good interfacial bond and high strength of the reinforcing phase in the Cu-Cr system and preliminary mechanical test data reported by Lemkey et al.3 for the A1-A13Ni system, the A1-CuA1, and A1-A13Ni eutectic alloys containing 50 and 10 vol pct, respectively, of the reinforcing phase give promise of possessing mechanical reinforcing behavior. Based on this premise, the objective of the investigation was to study the strength and fracture behavior exhibited by these anisotropic microstructures. EXPERIMENTAL PROCEDURE Controlled Solidification Procedure. An extensive description of the technique of unidirectional solidification has been presented elsewhere.' However, the pertinent details for each eutectic system studied are discussed below. Al-A13Ni System. Several master heats of this alloy were prepared by vacuum-induction melting in an A12O3crucible and casting in SiO2 mold or by induction melting in alumina crucibles under argon. The initial heats were prepared from 99.99 pct A1 and 99.99+ pct Ni, while later heats used 99.999+ pct A1 and 99.99+ pct Ni. Specimens of these master heats were unidirectionally solidified using induction and resistance heating sources and argon atmospheres at growth rates from 1.1 to 28.7 cm per hr. The thermal gradients in the liquid were controlled in the range of 26" to 36°C per cm for these runs. Al-CuA12 System. The master heat and controlled

Jan 1, 1965

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970