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By A. A. Dor

Of the numerous methods that have been tested or considered for the beneficiation of low-grade iron ores, this article deals only with proven flowsheets that are adopted in plants in operation or which have been reliably pilot-plant tested. Several recommended layouts are described and discussed. They illustrate recent trends and embody improvements and new features that have resulted from the experience acquired in the operation of the plants already in service. They have been developed, in the last few years, in the course of designing several iron ore beneficiation plants of various types and sizes. Some of the design features in the layouts which are submitted represent, in some respects, personal views and may not meet the full approval of others in this field. It is hoped that this presentation will provide an opportunity for constructive discussion of the problems involved and of suitable solutions.

Jan 6, 1962

By Frank Firmstone

Discussion of the paper of John B. Dilworth, presented at the Pittsburg meeting, March, 1910, and printed in Bulletin No. 35, November, 1909, pp. 1041 to 1043. FRANK FIRMSTONE, Easton, Pa. (communication to the Secretary*) :-Mr. Dilworth's formulas and tables are of course correct, and the extinction will occur as calculated, provided the money periodically set aside for sinking-fund be really invested. and the interest compounded as assumed in the calculation. Actually, in almost all cases, such funds are used "in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must be made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varying and continually increasing one until the date of extinction. On many accounts it seems more natural and convenient to make the extinction by a fixed periodical charge under the legal rule for partial payments, namely, that each payment should apply first to the interest due at the date of payment;: and any remainder, after this is satisfied, be deducted from the principal before the interest for the next period is calculated. The formula below is convenient for such calculations S, Principal to be extinguished. Q, Periodical payment or charge for sinking-fund. B, Balance unpaid at date of nth payment, but before that payment is made. r, Rate of interest per period per cent. n, Number of payments or periods. Then, B=S(1+r)n-Q(1+ r)n-(1+r) Received July 27, 1910.

Apr 1, 1911

By Ashok K. Kakar

THE occurrence of superplasticity in Al-Zn alloys is of interest because of its possible industrial exploitation.' The eutectoid composition (78Zn-22A1) has been the most extensively studied;'-= neck resistant flow and high strain rate sensitivity of flow stress (characteristic of superplasticity) are associated with a micron-size grain conferred on the alloy by an homo-genization and quench.5'6 Compositions away from the eutectoid have received comparatively little attention, especially from the viewpoint of relating the structural

Jan 1, 1969

By Henry Rogatz

During the year 1937, there were 663 oil wells drilled in the Texas Panhandle, making a daily initial production of 322,332 bb1.—that is, 191 more oil wells drilled than in the previous year, with an increase in the total daily initial production of 66,283 bbl. The total daily potential of the field as determined by the Texas Railroad Commission in its Schedule of Dec. 17, 1937, was 1,039,982 bbl., or an increase of 205,094 bbl. over the previous year. On Dec. 17, 1937, the daily allowable of 68,578 bbl. was assigned to the entire field. The total amount

Jan 1, 1938

MOWRY BATES, ? Tulsa, Okla.-In the first part of this paper the author says: "In an unpublished paper on Water Problem in the Augusta Field, S. K. Clark reaches the following conclusions: (1) That the great amount of water present is bottom water, occurring in the Varner sand, the main producing or the 2500-ft. horizon. (2) That the only striking connection between structure and water is in the area of the marked

Jan 4, 1919

By Victor V. Damiano

THOMPSON1 proposed a very convenient nomenclature in which an imaginary regular tetrahedron was used to facilitate the analysis of dislocation interactions in fcc materials. The faces of the tetrahedron were constructed parallel to four different sets of (111) planes, and the six edges of the tetrahedron then represented the six 1/2 [110] Burgers vectors. The lines which joined the midpoint of a tetrahedron face with the ends of one of its edges represented the Burgers vectors of the partial dislocations into which the six 1/2 [I101 Burgers vectors dissociate. Using Frank&apos;s2 notation, all of the dislocations and their partial dislocations were identified and numerous possible interactions were postulated. The case of hexagonal crystals is unfortunately more complex, but it appears convenient to introduce a system similar to that of Thompson1 to describe the various slip planes and Burgers vectors encountered in cph structures. The system proposed has limited application but serves to identify the following slip systems {0001} <l20>, {1010} <1120>,

Jan 1, 1963

By T. M. Olson, B. G. Lewis

The adsorption of selenite on bentonite, kaolinite, and an iron--coated illite was studied to determine the importance of several soil variables on selenite removal from uranium mill tailings pond seepage. Adsorption capacities of the clays of selenite varied by orders of magnitude and decreased in the following order: illite > kaolinite > bentonite. Maximum adsorption of selenite on the clays was observed between pH 2.5 and the clay&apos;s zero-point-of-charge. Substantially less selenite was adsorbed on these clays in actual mill tailings solutions than in model systems. Virtually all selenite was removed from the tailings at pH 7. The principal removal mechanism at this pH is suggested to be the adsorption of selenite on freshly precipitated metal hydroxides. It is concluded that selenite can be removed from tailings seepage in soil or in clay liners in the presence of kaolinitic clays and iron oxides. Selenite would also tend to be removed from tailings seepage in calcareous strata.

Jan 1, 1984

By A. D. Hill, R. S. Schechter, M. P. Walsh, I. H. Silberberg, M. J. Humenick

There are many uranium deposits which are too deep, too poor in quality or too small in extent to be economically strip mined. It now appears that this uranium can be mined using in situ leaching processes. A number of field tests have been, are being or will be conducted to demonstrate the feasibility of In site leaching. Preliminary results are encouraging, but a major question concerns the restoration of the mine site, which is generally contained within an aquifer. It is necessary to ensure that the quality of the water is not adversely affected by the mining operation. One component of the lixiviant is necessarily a cation and, during the course of mining, the ion exchange sites of the minerals in the mine zone become saturated with this cation. Ammonium is the cation now commonly used. Clearly, any restoration procedure or question involving the rate of cation migration with the groundwater all necessarily involve the process of ion exchange coupled with flow in porous media. The equations describing this process are presented in this paper and numerical solutions obtained. Preliminary results showing the effect of isotherm shape, cation exchange capacity, flow and dispersion are presented. These results demonstrate that in many situations cation migration in ground water will be slow.

Jan 1, 1979

By J. H. Johnson, H. J. Schock

The cases of no auxiliary ventilation and ventilation with tubing were mathematically modeled, using a turbulent dispersion model. The Scooptram® used to load is modeled as a variable-speed, variable-strength source of pollutants moving in and out of the dead-ended drift. Model predictions are compared to experimental measurements. A parametric analysis was performed to determine If a relationship existed between C02 and NO levels. It was concluded from this analysis that when modeling a load-haul-dump cycle, it is necessary to use a model that can predict changes in source strength as well as source location. Carbon dioxide was used as a tracer to calibrate the model since, knowing the fuel flow rate, it is possible to calculate C02 production. The model was then verified after this calibration process using additional experimental results. With the calibrated model, it is possible to predict pollutant concentrations at any location in the heading using an engine map and the previously calculated flow field.

Jan 1, 1984

By W. H. Emmons

ALTHOUGH gold is one of the rarer metals, it is widely distributed; it is found on all of the continents and in each of the grand metallogenic provinces of the earth. It is prominent particularly in the shield areas of the earth; these areas have produced a large part of the world&apos;s lode gold and in most of them gold lodes are more important than the lodes of other metals. The Scandinavian shield is the only one that has not produced much gold. Nearly all of the world&apos;s gold has been derived from lodes and from sands and gravels where gold placers formed by the destruction of lodes. The gold derived from magmatic segregations, from pegmatites and from contact metamorphic deposits is quite subordinate to that derived from auriferous lodes. The lodes include all veins and related deposits that are formed by hot waters that move along fissures or other openings and that deposit vein matter in the fissures and by replacement of the country rocks along the fissures. All of the shield areas of the earth are characterized by large areas of granitic rocks including granitic gneisses, granodiorites and other acid intrusives which here are included in the general term "granite." The granites are intruded into schists, ancient lavas and other rocks which here are designated as the "invaded" rocks. The granites are parts of what once were great batholiths: that is, they are the remaining portions of great deep-seated bodies that slope outward, have very irregular roofs and so far as known have no floors but extend downward to great though unknown depths. Some of them are scores or hundreds of miles across and contain islands or "roof pendants" of the invaded rocks at places where the roofs of the batholiths were low-that is, where erosion has not yet completely unroofed the batholiths.

Jan 1, 1932

By M. W. Fabjanczyk, E. G. Alexander

INTRODUCTION The purpose of this paper is to summarise development of design processes used in the 1100 oreoody as a result of experience encountered. Design methods have been developed as a result of the history of ground behaviour, free-standing qualities of cemented back fill and mass blasting techniques. This paper contains an historical review of design methods previously described by Matthews ( 1972 ) , Hornsby and Sullivan (1977 and 19781, Kirkby, Blair and Hutton (19781, and Stewart (1980). The reasoning behind design philosphy changes are discussed and placed into context with methods now adopted. The 1100 orebody is Mount Isa&apos;s main producer of copper ore (5 million tonnes per year ) . Proven reserves are 120 million tonnes at 3.2% Cu. Location of the 1100 orebody in relation to overall mine geometry was well described by Dayton (1976). Geology The orebody is located in a series of massive brecciated shale lenses, in either a siliceous or dolomitic matrix, surrounded and separated by a uniform shale sequence. The whole formation is truncated at depth by a faulted contact with a greenschist facies metamorphic sequence below (Figure 1 and Figure 2) Mathias and Clark (1976). The breccia is known locally as silica dolomite and contains nearly all the economic mineralisation. Interfingering of shale and breccia often results in irregular boundaries to the silica dolomite and the ore limits. Geometry The geometry of the orebodies is shown by Figures 1, 2 and 3. Figure 3 also shows the location of the copper orebodies in relation to the lead orebodies. Structure Although the orebody is contained within the massive breccia (u.c.s. 150-250 MPa), it is cut by shear zones sub-parallel to the regional bedding (north-south striking, dipping approximately 60o to the west), and diagonally by major transverse faults (Figure A). These major faults have continuity in excess of 300 metres, with varying amounts of displacement up to 200 metres, and are zones of potential movement.

Jan 1, 1981

By Paul A. Beck

THE occurrence of the (100) [lOO] or "cube" texture upon annealing of cold-rolled copper has been much investigated.&apos; The conditions favorable for its formation were found to be a high final annealing temperaturez or long annealing time," a high reduction of area in cold rolling prior to the final anneal,&apos; and a small penultimate grain size." The effects of penultimate grain size and of rolling reduction were found by Cook and Richards4 to be interrelated in such a way that any combination of them giving lower than a certain value of the final average thickness of the grains in the rolled material leads to a fairly complete cube texture with a given final annealing time and temperature. Also, according to the same authors, at a higher final annealing temperature a larger average rolled grain thickness, i.e., a lower final rolling reduction, is sufficient than at a lower temperature. These somewhat involved conditions can be understood readily on the basis of recent results obtained at this laboratory. Hsun Hu was able to show recently by means of quantitative pole figure determinations that the rolling texture of tough pitch copper, which is almost identical with that of 2s aluminum: may be described roughly as a scatter around four symmetrical "ideal" orientations not very far from (123) [112]. In the case of aluminum, annealing leads to retain-ment of the rolling texture with some decrease of the scatter around the four "ideal" orientations, and to the appearance of a new texture component, namely the cube texture." A microscopic technique, revealing grain orientations by means of oxide film and polarized light, showed that the retainment of the rolling texture is achieved through two different mechanisms operating simultaneously, namely "re-crystallization in situ," and the formation of strain-free grains in orientations different from their local surroundings, but identical with that of another component of the rolling texture. Thus, a local area in the rolled material, having approximately the orientation of one of the four "ideal" components of the texture, partly retains its orientation during annealing, while recovering from its cold-worked condition, and it is partially absorbed at the same time by invading strain-free grains of an orientation approximately corresponding to that of another "ideal" texture component. The reorientation here, as well as in the formation of the strain-free grains of "cube" orientation, may be described as a [Ill] rotation of about 40°, see Fig. 1 of ref. 6. The preferential growth of grains in such orientations is a result of the high mobility of grain boundaries corresponding to this relative orientation.&apos; " It appears very likely that in copper the mechanism of the structural changes during annealing is similar to that observed in aluminum (except for the much greater frequency of formation of annealing twins in copper). In both metals the new grains of cube orientation have a great advantage over the new grains with orientations close to one of the four components of the rolling texture. This advantage stems from their symmetrical orientation with respect to all four retained rolling texture components of the matrix; they are oriented favorably for growth at the expense of all of these four orientations. As a result, the growth of the "cube grains" is favored over the growth of the others, as soon as the new grains have grown large enough to be in contact with portions of the matrix containing elements of more than one, and preferably of all four component textures. It is clear that this critical size is smaller and, therefore, attained earlier in the annealing process if the structural units, such as grains and kink bands, representing the four matrix orientations are smaller, i. e., if the average thickness of the rolled grains is smaller. Hence, for a given annealing time and temperature, a smaller penultimate grain size and a higher rolling reduction both tend to increase that fraction of the annealing period during which the above condition is satisfied. Consequently, the percentage volume of material assuming the cube orientation increases. The same is true also for increasing time and temperature of annealing when the penultimate grain size and the final rolling reduction are constant, since the average size attained by the new grains during annealing increases with the annealing time and temperature. For the same reason, at higher annealing temperatures a given volume percentage of cube texture can be obtained with larger rolled grain thickness (larger penultimate grain size, or smaller rolling reduction) than at lower annealing temperatures. The well-known conspicuous sharpness of the cube texture may be interpreted as a result of the fact that selective growth of only those grains is favored that have an orientation closely symmetrical with respect to all four components of the deformation texture and exhibit, therefore, a high boundary mobility in contact with each. The effect of alloying elements in suppressing the cube texture, as described by Dahl and Pawlek,&apos; appears to be associated with a change in the rolling texture. For face-centered cubic metals, such as copper, which do exhibit the cube texture upon annealing, the rolling texture is always of the type described above, i. e., scattered around four "ideal orientations" of approximately (123) [112]. The addition of certain alloying elements, such as about 5 pct Zn or 0.05 pct P in copper, has the as yet unexplained effect of changing the rolling texture into the (110) 11121 type. This texture consists of two fairly sharply developed, twin related components. In such cases, as in 70-30 brass and in silver, the annealing texture again is related to the rolling texture by a [lll] rotation of about 30°, however, because of the different rolling texture to start from, it has no cube texture component. At higher temperatures, both in brassm and in silver," grain growth leads to a further change in texture: A [lll] rotation of the same amount, but in reversed direction, back to the original rolling texture.

Jan 1, 1952

By R. W. Raymond

ALEXANDER BRINTON COXE was born in Philadelphia, Pa., Jan. 19, 1838, the second of five sons of lion. Charles Sidney Core and Ann Maria Brinton. A more extended history of his family and its important relations to the development of the United States will be found in my Biographical Notice of his younger brother, Eckley B. Coxe, published in 1895. It is therefore sufficient to say here that Dr. Daniel Coxe, a distinguished physician and surgeon of London, and a medical attendant of Charles II and Queen Anne, purchased, in 1684 and 1686, lands in East and West Jersey from grantees of the Duke of York, and became Governor of West Jersey, in which capacity he did much to develop the provincial fisheries, the manufacture of marine salt and pottery, the exportation of tim¬ber and the West India trade. In 1698, having acquired the royal patent of the Province of " Carolana," covering (with some reservations) the territory extending from the Atlantic to the Pacific, between the 31st and 36th parallels of N. latitude, Gov. Cole sent an expedition from Charleston, S. C., to the Mississippi. In 1769, seventy years later, his grandchildren surrendered to the Crown their title under this vast and vague patent, receiving in return a grant of 100,000 acres in the Colony of New York. The line of his descendants, so far as they concern this sketch, is as follows 1. Col. Daniel Core, his son, b. 1673, who came to New Jersey in 1700; resided there until his death (1730); held many high offices; and issued in London (1722) A Description of the Provinces of Carolana, containing probably the earliest published plan of political union for the British Colonies in North America.

Sep 1, 1906

By E. P. Humphrey

The Lehigh Valley Coal Co. finished the rebuilding of its Drifton No. 2 breaker at Drifton, Pa., in the summer of 1917. The new construction comprises an addition and the complete remodeling of the old breaker. It is of interest to note that the old structure was the first iron breaker erected in the anthracite region. The Old Breaker This old breaker was built by the Cross Creek Coal Co., under the direction of the late Eckley B. Coxe, in 1888-89, and was fully described by him in the Transactions1. The columns were cast iron, 8, 10 and 12 in. square. The floors and partitions in pockets were cast-iron ribbed plates. The struts were cast iron of "H" section; the other members were of structural iron either rolled I-beams or built-up sections. The sizes of the rolled beams varied from 6 to 20 in. deep, while the built-up sections, made of plates and angles, varied from 6 to 63 in. in depth, so that there apparently was no rule to determine the type of section used. In the remodeling of the old structure, practically everything was taken down excepting the columns and roof, and such beams as were necessary for temporary construction purposes, and, therefore, a close inspection of the old structural members could be made and the effect of the acid water on them could be noted. The cast-iron members were but slightly attacked by the water, while the wrought-iron beams, in the wet places, were corroded almost to failure. The following are analyses of cast-iron, wrought-iron, and structural-steel samples taken from the old and the new structure.

Jan 1, 1918

By G. R. Mansfield

THE third year of Government exploration for potash by the U. S. Geological Survey and the U. S. Bureau of Mines under the authorization of the act approved June 25, 1926 (Public 424-69th Cong.) is drawing to a close. The results thus far obtained are thought to be sufficiently interesting and satisfactory to justify the presentation of a brief pre¬liminary account of the work. REVIEW OF EARLIER EXPLORATION The general geologic similarity of the Permian basin of Texas and New Mexico to the potash field of Germany had long ago suggested the possibility of the presence of potash salts somewhere in that basin, but petroleum exploration was then making little headway there and the necessary data could not be obtained. The discovery by Udden in 1912 of potash in brine from the Spur well in Dickens County, Texas, was the first direct evidence of its presence. In 1915-17 the U. S. Geological Survey drilled a test well with standard tools at Cliffside near Amarillo, but failed to find potash. Nevertheless, an observer has been kept in the field, at first in cooperation with the Texas Bureau of Economic Geology but since 1922 by the Survey alone, to secure data and samples from oil and gas tests. Since the discovery of oil in Reagan County in 1923 exploration by drilling has been rapidly extended to many parts of western Texas and southeastern New Mexico. The identification of the potash-bearing mineral polyhalite was first announced by the Geological Survey in June, 1921, the material having come from cuttings from the Bryant well in Midland County and the Burns well in Dawson County, Texas. Successive discoveries and announcements of similar purport aroused widespread interest in potash exploration, which culminated in the action by Congress already noted.

Jan 1, 1929

R. W. NEWCOMB,* New York, N. Y. (written discussiont).-On page 1638 mention is made of a new -instrument with an exceptionally high resistance that has been developed by Charles Engelhard. All friction and wear of moving parts of the moving system has been elimi-nated by replacing the hardened steel pivots and jeweled bearings, commonly used on other instruments, by a double metallic filament, one at the top and One at the bottom, under slight tension. Any pos-sible distortion of the moving coil, because of tension, has been eliminated by introducing a solid spindle as the axis of the coil between the points on the coil where the metallic filament is attached. The filaments serve not only as a support for the moving coil; but also to lead in the current from the binding posts to the moving coil, and as a source of counter-torque; instruments so constructed, do not require leveling, and are mechanically very robust. The clock of the recorder serves only to drive the chart at its specified rate and -to operate a small contact-making device; i.e., there is no other mechanical load on the clockworks. The contact-making de-vice is so constructed that there is a quick-make, a quick-break, and a wiping effect while the contact is being made. Contact surfaces on this switch are of platinum platinum-iridium. The operation of this contact, which occurs once each minute, sends a current, from a 6-volt supply; through a solenoid magnet, which operates the depressor bar mechanism in the case of the single-record instrument; in the case of the multiple-record instrument, it operates the automatic switch and color-changing features, as well as the depressor bar.

Jan 12, 1919

A MINING institute open to all men interested in any branch of the mining industry will be held at the Col-lege of Mines, University of Washington, Seattle, during the week beginning March 5. Prospectors, miners, mine owners, persons interested in metallurgy, investors in min-ing enterprises, and the public generally are invited to at-tend. This institute will take the place of the Winter Min-ing Session which originated at Seattle in 1897 and con-tinued for twenty-eight years. The complete new equip-ment of the Mines Laboratory will be used to give demon-strations of new machines and processes of mining, ore dressing, and metallurgy. This year the ceramic industry, including cement and branches of clay working of special Importance in the Northwest, will be included in the insti-tute. All instruction will be given by specialists. Prominent technical men and managers will give lectures on their special subjects. Among the speakers engaged are G. T. Jackson, formerly superintendent of the Alaska-Gas-tineau and the Chichagof mines, who will speak on the mining of large bodies of low-grade ore; R. F. McElvenny, superintendent of the Tacoma Smelter, on the nature of contracts that a smelter can offer to mines and prospects; M. D. Leehey, mining lawyer, on some popular errors re-garding the mining law; H. H. Townsend, on the explora-tion and purchase of prospects by operating companies; J. L. McAllen, on quartz mining in the Willow Creek dis-trict, Alaska; F. Powell, on gold dredging. In the evenings, lectures illustrated by stereopticon views and moving pic-tures will be given. The week will close with an excursion o mines and plants.

Jan 3, 1928

The problems associated with the processing of the Tilden ore are very much representative of the problems encountered in plants processing fine grained magnetic and nonmagnetic iron ores. I would like to comment on some of the problems mentioned in Dr. Nummela&apos;spaper and add to his list of research opportunities in the processing of iron ores. Grinding, the most important step in the processing of fine grained iron ores, is synonymous with liberation. One grinds to separate discrete grains of minerals from the gangue. By convention- al grinding in tumbling mills, mostly random size reduction is achieved with relatively little preferential liberation of minerals. Not only are discrete particles broken that should not be broken, but damage is done to the mineral surfaces. The combination of over- grinding and surface damage shows up in lower recovery figures and higher grinding costs. What is obviously needed is a better comminution process that is more discriminating and that would permit liberating mineral particles at the coarsest possible size with a minimum production of fines. Laboratory attempts at such preferential grinding have been quite successful, but technological difficulties have unfortunately prevented its use. Impact grinding is a good example of a new comminution process that has not been accepted because of equipment problems. Either these problems have to be solved or new comminution systems have to be developed to reduce grinding costs and improve liberation. In his paper Dr. Nummela mentions the change in the primary mill throughput that occurs during the winter months. Seasonal changes in the operation of the grinding circuit and other unit operations have been observed in many plants, and many explanations for this phenomenon have been advanced. The fact is that we do not fully

Jan 1, 1979

ANDES, lying south of Chuquicamata and north of Braden on the western slope of Chile&apos;s cordillera, can best be described as a big well-managed copper-mining enterprise without any peculiarly outstanding features. In point of copper produced, since output started in 1927, it ranks fifth among the Porphyries, being exceeded only by its two Chilean contemporaries and by Utah Copper and Morenci in the United States. Even so, there is little to distinguish it from other properties. It does not have the phenomenally rich ore (better than 2 per cent copper) that characterizes Braden; and it is not in the same class as Chuquicamata whose ore has the excellent tenor of around 1.7 per cent, nor has it Chuqui&apos;s immense tonnage of proven ore reserves and potential ore resources. One might say the operations are standard in that there are no basic or radical departures from established practice. A letter from New York supplying me with sundry pertinent facts for which I had asked, makes this comment regarding the answer to one inquiry: "omitted because it is the ordinary equipment found in any well-run mine." The substance of that remark applies generally to the other operations, plants, and facilities. One interesting fact that helps explain this situation should not be overlooked. Until the "new" Morenci in 1942, Andes was the last of the Porphyry copper mines to come into production. It did not do much pioneering because other companies had, of necessity, charted the way in many particulars. The company was organized by the Anaconda Copper interests in 1916 to take over a, group of claims held under option by William Braden who, a few years earlier, had interested

Jan 1, 1957

By Murray F. Hawkins

One problem of reservoir engineering is the early estimation of the size of newly discovered reservoirs. Often these reservoirs are the expansion type in which sizeable pressure drops occur incident to the production of small fractions of the oil reserve, above the bubble point, and a material balance equation may be solved to find the reserve. The early form of this equation&apos; considered only the compressibility of the oil. Later Hall2 showed that the compressible nature of the formation rock is a significant factor in production above the bubble point, and he presented a new equation which includes a formation (rock) compressibility term. This note presents a further extension of the material balance equation as applied to volumetric, unsat-urated reservoirs above the bubble point by including a term for the presence and compressible nature of the interstitial water. DERIVATION OF EQUATION During a decline in average reservoir pressure, ?p ?p, — p1 the initial reservoir volume V,, will decrease to some value V, due to the reduction in pore volume as a result of a decline in the hydrostatic pressure within the formation, and v, = V,, [l — cr ?p]......(1) The formation compressibility c, is expressed in terms of change in pore volume per unit pore volume per psi. Simultaneously the connate water within the formation expands from an original volume V,, = S,V,, to a new volume V,, V, = s,v,, [I + c,npl.....(2) The difference [Vp — V,] is the hydrocarbon pore volume at pressure p and may be equated to the volume of the remaining oil, or [N — N,] B, = V,,, [I - C~A;] - S,.Vpi [l + cwnjl.........(3) But the initial oil in place in terms of the initial reservoir volume, connate water, and formation volume factor is Ilividing Equation 3 by Equation 4 eliminates V,, to give,

Jan 1, 1956