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By Bruno Nordberg

THE high cost of coal in Butte and the development of large amounts of cheap electric power from the Missouri river caused the Anaconda Copper Mining Co. in 1908 to make an investigation as to the possibility of adapting this cheap electric power for the operation of their many large hoisting plants. At this time electric power had already been adopted for practically all other power purposes around the mines, such as pumping, compressing air, etc. The map (Fig. 1) shows the location of the mines of the Butte mining district. These mines are located within a circle of approximately a 1-mile

Jan 9, 1913

By C. G. Dunn

James, Jones, and Leak (JJL) conclude that growth-rate and orientation-distribution data obtained in a steep thermal gradient should be used with caution to account for isothermally produced recrystallization textures. I agree. However, it is not clear whether they conclude a) that the orientation dependence of rate of growth of secondaries in (commercial) silicon iron depends on both temperature and a temperature gradient or b) that, in applying rate data obtained in a steep thermal gradient, the isothermal annealing temperature must be close to the temperature for which the rate data apply. Also, it is not clear what tem-

Jan 1, 1967

By John G. Roscoe

Continental Materials Corp. operates two under- ground uranium mines in the Crooks Gap district of central Wyoming. Both mines are developed as slusher mining operations through vertical shafts with single level haulage to slusher pocket loading stations. In general, operations at both mines are similar except for depth and some minor details. The shafts are identical in cross-section, each with a 4 ½ x 5-ft hoisting compartment and a 4 ½ x 5-ft manway. Kimberley-type skips are loaded from measuring pockets through air-operated guillotine gates. The Seismic shaft is 245 ft deep and the Reserve shaft depth is 585 ft. The Seismic shaft was sunk in 1957 and the mine has been producing 200 tpd since 1958. The Reserve shaft was sunk in 1960 and the mine is still in the development stage. The hoists of both mines are equipped for semi-automatic operation; that is, they are mechanically controlled to perform a certain cycle of duty and then stop until another cycle is manually initiated. The Seismic hoist, however, was originally a conventional, manually controlled unit; the reserve hoist was installed as an automated system.

Jan 7, 1962

By James A. Barr

[CONTENTS PAGE Foreword. By JAMES A. BARRI A New Core Barrel for Prospecting for Phosphate in Florida. By I. M. LEBARON 2 Prospecting for Phosphate in Tennessee. By W. F. GUENTHER 6 Machine Prospecting in Tennessee Brown Phosphate. By H. O. PICKARD, JR8 Diamond Drilling through Flint Horizons in Tennessee. By HENDON R. JOHNSTON9] Foreword PROSPECTING methods used in Tennessee have gradually improved with the years, as required by depletion of the easily accessible and shallow deposits and the universal trend toward mechanization, and as necessitated by exploring deeper beds, often occurring under limestone and flinty overburden. In the early days it was a very simple matter to dig pits by hand, using a plentiful supply of local farm labor to expose relatively shallow deposits of "brown rock" under shallow clayey overburden that would stand up without timbering. Visual inspection of the exposed phosphate and expert judgment of the"grade" analysis, aided by a "biting" test to reveal presence of unwanted silica, furnished most of the information required. All this might be helped by a few samples sent to the local chemist[t] who supplemented his income by judicious trading or tanning a few bear skins. The extra curricula activities did not affect the accuracy of the analysis which hold up even under present day standards. Some shot and core drilling was done in Hickman County, mostly for the limestone-like blue Phosphate deposits. The next step was the use of a 4-in. posthole auger, hand operated as described by Guenther, followed by- a completely mechanized rig, as described by Pickard. Both these methods are practically adapted to the prospecting of the relatively soft brown rock deposits at moderate depths of clay overburden. For prospecting in areas of deeper overburden, such as are often found in Hickman County, up to 150 or even 200-ft depths, a modified core-drilling method is described by Guenther. Johnston describes a special diamond-drilling technique, developed by TVA, to penetrate flint horizons, which was adopted by the International Minerals and Chemical Corporation to prospect in Hickman County where deposits had previously been prospected at considerable expense and with difficulty, by Small, temporary, hand-dug shafts.

Jan 1, 1947

By Carl E. Johnson

INTRODUCTION A method for predicting water-flood oil recovery was reported by H. Dykstra and R. L. Parsons' in 1950. It is now generally known as the Dykstra-Parsons method and is widely used by petroleum engineers. The method is semiempirical and consists of a correlation of four fundamental variables. These are: V, vertical permeability variation;' a, mobility ratio; Sw initial water saturation; and R, fractional recovery of oil in place at a given producing water-oil ratio. The correlation extends over a wide range in each of these variables, and may be applied to all formations with initial oil saturations of 45 per cent or greater. The method of calculation originally outlined by Dyhtra and Parsons closely follows their derivation. And this is a convenient way of illustrating the development of some rather complicated ideas. However, in actual use it is more cumbersome than necessary. The purpose of this note, therefore, is to provide a simplified method for making Dykstra-Parsons predictions. A SIMPLIFIED GRAPHICAL SOLUTION The correlation between V, a, Sw and R, corresponding to a given producing water-oil ratio, can be shown on a single graph. This is best done by plotting V against a to show lines of constant R(1 - S, . WOR-0.2). Figs. 1, 2, 3, and 4 show these plots

Jan 1, 1957

A. L. FIELD, Cleveland, Ohio (written discussion*.-)In equation 2, B is used to denote the ratio of bases (lime plus magnesia ) to acids (alumina plus silica) it being stated that this ratio gives more concordant results than the ratio either of bases to silica, or of lime to silica. I find, however, that, by making use of the ratio between true CaO (CaO by analysis minus sulfur calculated to CaS) to acids, equation 2 may he modified to agree with the observed facts within an average error of 0.0041 per cent. sulfur instead of 0.0045 per cent. The revised equation is s = 0.072 + 0.01835 - 0.00061 (t - 1400) - 0.0403B where B is the ratio of true CaO to Al2O3 Plus Si02, and the other symbols have the same significance as before. I would not appear to stress too much this slightly better agreement of the revised equation with the observed sulfur. Yet I believe that the use of this ratio of true CaO to acids is to be preferred, if for no other reason than the fact that it is more in harmony with the previous findings of the Bureau of Mines with regard to the effect of magnesia and other impurities on slag viscosity.1

Jan 12, 1919

By Ernest Burchard

A RECONAISSANCE of the chrome and manganese'1ore deposits of Culm was made in the spring of 191s by Albert Burch representative of the U. S. Bureau of Mines and the writer representing the U. S. Geological Survey. The object of the study was to obtain authentic information for use of the: United States Government as to the location, character, size, and availability of the Cuban deposits of the ores of these important steel-alloy metals. The Cuban Government courteously detailed Sr. E. I. Montoulieu, a mining engineer connected with the Treasury Department, to act as escort and associate throughout the work on the Island. Mr. George A. Wright, of Baracoa, Cuba, a mining engineer especially familiar with the chromite deposits of Oriente Province, was a member of the party from Feb. 25 to Mar. 20. It was possible to visit most of, the chrome-ore deposits that seemed to be of promise, but there was not sufficient time to visit all that were brought to our attention, some of which may have merit. Furthermore, no attempt was made to examine the extensive chromiferous iron-ore deposits of the Mayari, Moa, and Cubitas districts, as these deposits cannot be regarded as sources of chromium except indirectly. At the close of the field work the essential data concerning the quantity and quality of ore probably available for shipment during 1918 and 1919, in the event of the continuation of the European war, and of the tonnage of ore in reserve, were furnished to such Government bureaus as were interested, including the Shipping Board and the War Industries Board, and as soon as chemical analyses of the chrome ores could .be obtained, a press bulletin on the subject was published by the Geological Survey. In the present paper the engineering data, and tonnage estimates contained in the unpublished notes of Mr. Burch have been freely used, and their helpfulness is hereby gratefully acknowledged. Many thanks are due Senor Montoulieu and Mr. Wright for their valuable work in the field; to the officials of the Spanish American Iron Co. and of the various other companies; and to individuals holding chromite claims, for courteously facilitating the work of the party. In the study of material for the present paper, chemical analyses have been made by R. C. Wells and petrographic determinations and descriptions were furnished by Miss E. F. Bliss, both of the U. S. Geological Survey.

Jan 9, 1919

By L. J. Ebert, G. Sachs, W. F. Brown

Isothermal transformation, or "aus-tempering," of a carbon-containing aus-tenite at elevated temperatures yields so-called "intermediate products." Their structure and properties are, for a given hardness, rather different from those of "tempered martensite" obtained on conventional quenching and tempering.' Several investigators2,3 have found that for high carbon and slightly alloyed steels the intermediate products formed at temperatures close to that of the martensite reaction possess strength properties superior to those of tempered martensite. The structure of these low temperature, intermediate products is generally acicular (bainite) but clearly different from that of martensite. However, at higher austempering temperatures, between 1000 and 1300°F (540 and 700°C) carbon steels were found to exhibit a rather low ductility.4,5 Thus notch bar tensile tests showed the ratio between notch strength and regular tensile strength to decrease with increasing austempering temperature. For ductilities below a few percent this notch strength ratio is a measure of ductility, according to investigations on low alloy steels.637 Furthermore the presence of intermediate products formed unintentionally on quenching was considered as responsible for the low ductility and impact energy of some heat treated steels,8 These intermediate products could result from partial transformation at the so-called "nose-temperature" where the rate of the transformation is a maximum. Tempering improved such mixtures of martensite and intermediate products, their properties approaching those of tempered martensite of equal hardness. The following investigation constitutes an attempt to determine certain strength properties of a partially austempered and subsequently quenched low alloy steel, namely, a chromium steel (SAE 5140) The structures formed by such a treatment should consist of a mixture of intermediate products formed on austempering and a martensite formed on oil quenching from the austempering temperature. It was intended, by varying the austempering time, to vary the quantity of the intermediate products between zero and 100 pct. The austempering temperature of 860°F was selected after extensive preliminary tests close to the nose-temperature. Austempering at this temperature yielded an acicular intermediate product. .Additional tests under less exacting conditions were made for an austempering temperature of 950°F where the intermediate product appeared to be very fine pearlite. To determine the effects of tempering on structures containing various amounts of

Jan 1, 1949

By G. Sachs, L. J. Ebert, W. F. Brown

Isothermal transformation, or "aus-tempering," of a carbon-containing aus-tenite at elevated temperatures yields so-called "intermediate products." Their structure and properties are, for a given hardness, rather different from those of "tempered martensite" obtained on conventional quenching and tempering.' Several investigators2,3 have found that for high carbon and slightly alloyed steels the intermediate products formed at temperatures close to that of the martensite reaction possess strength properties superior to those of tempered martensite. The structure of these low temperature, intermediate products is generally acicular (bainite) but clearly different from that of martensite. However, at higher austempering temperatures, between 1000 and 1300°F (540 and 700°C) carbon steels were found to exhibit a rather low ductility.4,5 Thus notch bar tensile tests showed the ratio between notch strength and regular tensile strength to decrease with increasing austempering temperature. For ductilities below a few percent this notch strength ratio is a measure of ductility, according to investigations on low alloy steels.637 Furthermore the presence of intermediate products formed unintentionally on quenching was considered as responsible for the low ductility and impact energy of some heat treated steels,8 These intermediate products could result from partial transformation at the so-called "nose-temperature" where the rate of the transformation is a maximum. Tempering improved such mixtures of martensite and intermediate products, their properties approaching those of tempered martensite of equal hardness. The following investigation constitutes an attempt to determine certain strength properties of a partially austempered and subsequently quenched low alloy steel, namely, a chromium steel (SAE 5140) The structures formed by such a treatment should consist of a mixture of intermediate products formed on austempering and a martensite formed on oil quenching from the austempering temperature. It was intended, by varying the austempering time, to vary the quantity of the intermediate products between zero and 100 pct. The austempering temperature of 860°F was selected after extensive preliminary tests close to the nose-temperature. Austempering at this temperature yielded an acicular intermediate product. .Additional tests under less exacting conditions were made for an austempering temperature of 950°F where the intermediate product appeared to be very fine pearlite. To determine the effects of tempering on structures containing various amounts of

Jan 1, 1949

Edward Keller, Baltimore, Md. (communicatioin to the Secretary*):—It is pleasing to note the increasing amount of work on metallurgical problems that is being carried on by exact scientific methods, and the results of such labor issued by the laboratories of our universities. Without doubt, Mr. Bolles's paper will be welcomed by all progressive practitioners. Many of the results which Mr. Bolles presents to as are new; and I take exceptioil to a few minor points only. The first of his concluding remarks is as follows: "Mattes are not homogeneous, but are composed of distinct mineral entitier, and may be likened to igneous rocks, in which the mineral constituents fall out upon the lowering of the temperature and ensuing solidification." He quotes an introductory remark to a paper1 of mine, as follows: "The true chemical character of copper-mattes does not yet seem to have been definitely determined, i.e, it is still more or less of an open question whether they are true chemical compounds, or mixtures, such as igneous rocks." This quotation, taken alone, would convey the impression that Mr. Bolles's conclusion is entirely new. Had he quoted also another paragraph from my paper in question, it would be clear that he was, to a certain extent at least, anticipated. I take the liberty, therefore, to state the substance of my own work. In the paper referred to, I showed the existence of the phenomenon of liquation in mattes, and, continuing, said: " A more direct method to test whether a matte is a compound sulphide or a mixture of individual sulphides was attempted by applying hydraulic separation. A clean piece of matte was selected containing practically no magnetic oxide and of the following composition: Cu, 37.96; S, 24.45; Fe, 33.63; Zn, 1.25; Pb, 1.02 ; Sb, 0.26 ; As, 0.065 ; insoluble, 1.15 per cent. ; Ag, 26.7 ; Au, 0.04 oz. per ton. For such a test it is essential to select a chemically uniform piece, other-

Jan 1, 1905

By R. F. Nielsen, R. G. Bentsen

Jan 1, 1966

By Wolfgang Hermann

The ancit-process of the Eschweiler Bergwerks-Verein, an affiliate Company of ARBED S.A., Luxembourg, was developed in its principles by the Dutch State Mines, Limburg, in the mid-50's with the aim of producing a smokeless domestic fuel on the basis of low volatile hard coal. In 1967, the EBV erected a 10 t/h large- size pilot plant along these principles in the Aachen mining district and further developed the acquired know-how. In hardly 10 years more than 650 000 t of ancit briquettes with unit weights between 17 and 100 grams were produced and in the meantime stream rates of over 85 % of the yearly utilization hours have been reached. In more than 10 blast furnace trial runs involving substitution rates up to 100 p. c. ancit have proved the suitability of ancit as a metallurgical fuel both for a burden with a high and a poor iron content. Construction work for a minor process-step to enable processing of coal with a higher content of volatile matters is finished and first results are expected by summer this year. A pilot plant with a 30 t/h capacity working on a low-volatile coal basis is being planned. Engineering and construction are supervised by MecanARBED. Luxembourg, as responsible contractors.

Jan 1, 1977

Jan 1, 1923

By James B. Graham, Earle E. Smith

The value of all minerals produced in the United States for the years 1930 to 1932 averaged $3,460,000,000 annually, according to Bureau of Mines reports. Of this amount, approximately $1,280,000,000 represents nonmetallic substances, such as petroleum, gas, sulfur and salt produced as fluids. Thus, about.37 per cent of the country's mineral wealth is procured through wells drilled in the earth, which require casing to keep them open throughout their life. Deep well drilling has increased greatly in the last few years. Several strings of casing have been set deeper than 9000 ft.—one, a string of 7?-in. O.D. casing, 10,301 ft. long, run in a well drilled by the Gulf Production Co. in West Texas, holds the record up to this time. These are longer strings than were contemplated when the American Petroleum Institute Specifications were adopted 10 years ago, therefore it is necessary to consider whether the present joint standards are adequate for such strings, or for even longer strings that may be called for in the future. Petroleum engineers are asking: Is there a possibility that stronger joints can be designed without going to stronger and more costly steels than offered in present specifications? Without sacrificing too greatly the tensile properties of the joint, can its design be changed to allow more clearance in the open hole below the next larger string of casing, and thus avoid costly underreaming? What can manufacturers offer for drilling through heaving shale? Fundamentals of the Problem During the last few years considerable study has been given to casing joints and their limitations, and since attention must be given to this subject by those who will be required to drill deeper holes, it is timely to review the fundamentals of the problem. These will be recognized generally as the following: 1. No threaded joint can be stronger than the area of metal under the root of the first perfect thread, and this area must be large enough

Jan 1, 1935

By Jasper L. Stuckey

PYROPHYLLITE, first identified as soapstone,1 later as agalmatolite,2 and finally as pyrophyllite,3 has been known to occur in North Carolina for more than 130 years and has been produced intermittently in commercial amounts for the past 100 years. Pyrophyllite mining, however, has become a major industry in North Carolina only during the past 25 years. North Carolina and California are the chief producing states. Current annual production averages 125,000 tons, of which slightly more than 90 pct comes from North Carolina. Distribution and Geologic Setting: All known pyrophyllite deposits in North Carolina are associated with rocks of the Carolina Slate Belt,4 which is composed of a vast series of metamorphosed volcanic and sedimentary materials, occurring as two zones extending in a northeast-southwest direction across the state. The larger of these zones, lying in the central Piedmont region, varies from 8 to 50 miles wide. The smaller zone lies along the eastern edge of the Piedmont region and is partly covered by coastal plain sediments.

Jan 1, 1958

By P. Somasundaran, D. W. Fuerstenau

This article presents the results of an analysis of grinding of 1:1 mixtures of 4x8-mesh quartz and limestone in laboratory ball and rod mills. From these experiments, the amount of energy consumed in grinding each component of the mixture was determined. In the ball mill, limestone consumes slightly more energy than quartz in the initial stages of grinding, but as the grinding proceeds quartz begins to consume a slightly greater fraction of the energy. The postulate that the fraction of energy consumed by any material in a ball mill is proportional to its volume fraction has been shown to be approximately true. On the other hand, in a rod mill energy consumption by quartz and limestone is equal only in the initial stages of grinding, with energy consumption by quartz greatly exceeding that by limestone as rod milling proceeds. Preferential energy consumption in tumbling mills has been discussed in a number of papers. For example, from an analysis of the kinetics of comminu- tion in ball mills, Arbiter and Bhrany' obtained rate equations based on the postulate that only coarse particles are ground, indicating that fine particles are protected from the action of the balls by coarser particles. In rod mills this protective action is much more pronounced than in ball mills. Recent studies on the rod milling of limestone-quartz mixtures have shown that this protective action causes the mineral with the lowest grindability (quartz in this instance) to consume the greater fraction of energy. 2 However, in the ball milling of mixtures it has been postulated that the consumption of energy by one of the constituents is determined by its volume fraction within the mill. 3 Possibly this hypothesis may be a simplification of the ball milling of mixtures since the protective action suggested by Arbiter and Bhrany may result in some preferential energy consumption by one of the constituents of a mixture. The objective of this study has been to determine preferential energy consumption in laboratory ball and rod mills by analyzing size distributions of each material in the products obtained from grinding 1:l mixtures of quartz and limestone. MATERIALS AND METHOD The procedure for carrying out the tests on wet grinding quartz-limestone mixtures has already been described.'r3 In the present investigation, 1:l mix-

Jan 1, 1963

By F. J. Longworth

For a number of years an intensive study has been made to improve the blast-furnace practice at Copperhill not only as to costs but to provide a good grade of gas for the acid plants. This study, took us back to the fundamentals of successful pyrite smelting; namely, a blast furnace working on a clean sulfide ore, free from fines, and the use of quartz high in silica as a flux. In 1919, the quality of the flux was improved and its effect on the metallurgy was very marked. To improve the practice further, it was necessary to work out some method of treatment for the sulfide fines and the siliceous and refractory ores, other than in the blast furnace. A series of milling tests indicated that these products could be successfully treated by differential flotation, and in 1922 plans were made and a flotation plant built. It was estimated that the flotation plant would deliver to the smelter 40 to 50 tons of concentrates per day; the problem was what to do with these concentrates. It was out of the question to attempt to smelt them in a blast furnace because of the dust losses and, because our practice demands a charge free from fines for satisfactory operation. There is no custom smelter in the vicinity to which concentrates may be sold, pending the time when the tonnage will be sufficient to warrant roasters and a reverbatory furnace. Sintering and nodulizing were investigated but neither method fitted into our scheme of metallurgy. A close study of the converter practice was then made to see if some method could not be evolved to smelt this tonnage of concentrates in a converter without preliminary treatment. At that time, the converter installation consisted of two 12-ft. Great Falls converters, which were handling 12 to 14 per cent. matte. The heat balance of the converters working with 12 to 14 per cent. matte was more than sufficient to smelt the contemplated tonnage of concentrates but the mechanical difficulties. of feeding fines into the Great Falls converter made the use of this type of converter impractical.

Jan 9, 1924

By O. W. Ellis

THE writer has dealt with the effect of various methods of melting copper upon the gas content of the metal.1 The copper referred to in his in his earlier paper was melted in the foundry both in the oil furnace and the electric furnace. As the metal, did not measure up to conductivity FIG. L -INGOT OF OVERPOLEP COPPER. standard, the term "casting copper" was applied to the material in the title of the paper. It was thought that some information in regard to the gases in a sample of overpoled copper might also be of interest, and through the courtesy of C. R. Stevens, superintendent of the copper mill of the Westinghouse Elec. & Mfg. Co., such a sample was obtained. The metal was chill-cast in the form of an ingot about 7 in. long, 2 ½ in. deep (from the base to the raised surface of the ingot) and from 1 3/8 to 1 7/8 in. wide. A photograph of part of the ingot is shown in Fig. 1. The effect of overpoling on the surface of the metal is here quite clearly shown.

Jan 1, 1929

John Chipman (Massachusetts Institute of Technology, Cambridge, Mass.)—After looking over the authors' shoulders for several years and after many discussions on the interesting diagrams of the types shown, it is a pleasure to see a formal paper published on this subject. There can be no doubt of the practical usefulness of the concepts shown. Inclusion formation in steel is such a highly complex matter that any system for understanding the subject is bound to be welcomed by those who must work with steels and who see in their day-to-day experience the good and evil effects of inclusions. A feature of the work with which the discusser has been concerned, and which he would now like to attempt to explain, is the relation between the schematic diagrams which the authors use and the phase diagrams for related systems. Obviously, the authors' diagrams are in no sense complete phase diagrams. However, there is a relation between this type of diagram and the true phase diagram, and the understand- ing of this relation ought to help in understanding the general picture which the authors are presenting. Consider the authors' Fig. 4, which shows the liqui-dus relations in the Fe-Mn-S-0 system. To show the complete relations between temperature and composition in these four ternary systems would require four triangular prisms, the vertical axes of which would represent temperature. The four triangles of Fig. 4 represent basal projections of certain lines from the four prismatic phase diagrams. Readers of the paper are all more or less acquainted with this type of projection and its usefulness and limitations are generally understood. In order to concentrate on the interesting parts and to minimize the less interesting features, the composition scale may be shifted to de-emphasize regions containing gaseous sulphur and oxygen. Such a diagram is shown in Fig. 16, which is a distorted version of the authors' Fig. 4. Here the oxide of iron is wiistite, denoted by W, and it is to be noted that between W and MnO lies the entire MnO-FeO "binary" system. Similarly, between MnS and FeS lies another binary whose

Jan 1, 1956

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958