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By W. T. Cardwell, R. L. Parsons

This paper discusses the practical problem of estimating a single equivalent permeability for an oil reservoir, or a portion thereof, whose actual permeability varies in an irregular manner. Limiting averages for general types of permeability variation are developed, and illustrated by examples involving important, specific types of variation. Introduction The theory of the flow of fluids through porous media1"4 is becoming increasingly important in predictions of oil-reservoir behavior. In practical applications, however, reservoirs are seldom found to which simple theory strictly applies. Actual reservoirs have complicated shapes and nonuniform permeabilities and porosities. This paper discusses the problem of estimating a single equivalent permeability for an oil reservoir, or a segment of an oil reservoir, whose actual permeability varies in an irregular manner. The equivalent permeability of a reservoir segment is defined as the permeability of a homogeneous segment of the same dimensions that would pass the same flux under the same pressure drop- It is the permeability value that can be used in simple theoretical formulas to calculate the reservoir behavior. To the authors' knowledge, previous theoretical calculationst on systems of nonuniform permeability have been carried out only by Muskat'"; and he has not dealt with irregular variations, except in writing down the general differential equation for the pressure in variably permeable systems.lb In practical work, many calculations necessarily have been made to estimate equivalent permeabilities from the permeabiiity profiles obtained by core analyses. Regarding such calculations, Johnston and Sherborne6 say: Simple arithmetic and weighted averages have been tried on many wells and it has been found that, where frequent sampling has occurred, the arithmetic average is as satis- factory as a weighted average. It is possible that the application of statistical methods to the analysis of permeability data as recently presented by Law8 may prove fruitful. L,, has made a valuable contribution in showing how statistical analyses may aid in picturing the characteristics of a reservoir from those of a necessarily limited number of core samples. It is believed however that the particular problem of the estimation of equivalent permeabilities can be most directly approached from a fluid dynamical viewpoint as given in the present paper. An example is presented of the use of the conclusions herein in conjunction with Law's method. Theory In order to approach the problem of heterogeneity simply, it is interesting to consider a square block composed of four smaller, homogeneous, square blocks of porous medium, two of which have a

Jan 1, 1945

By S. R. Gilbert, B. W. Burdett, L. B. Hales

A brief review of grinding control systems is given with a review of the most popularly reported control loops. The trend toward more sophisticated control systems in terms of control strategies and control equipment is discussed, and the reasons for the popularity of distributed control equipment are outlined. The evolution of the interface between the operator and the process and its importance in plant control is described. Finally, the authors' view is given as to the future of grinding control.

Jan 1, 1984

The Anglovaal Group has released details concerning its new processes for recovering platinum group metals, stating that the Group's system, which involves batch processing and precipitation methods for these metals (PGM's), leads to faster recovery times, increased recoveries, and higher purities than the conventional process. Insofar as South Africa's Merensky Reef is concerned, the Anglovaal method of recovering palladium first (as opposed to platinum in the conventional process) enables it to use a much simpler process in the subsequent recovery of platinum and other metals. Because the processes give cleaner separations, the volume of material to be recirculated -and therefore the total volume of material in the recovery circuits- is reduced substantially.

Jan 3, 1976

By P. B. Liebermann

THE resistance to motion offered by mine cars is caused principally by: Rolling friction, flange friction, bending rails, bearing friction and wind resistance. With proper construction and with a fair amount of attention and care, that is, under favorable conditions, the first three items cannot be greatly improved. The wind resistance ordinarily is negligible on account of the slow speeds commonly used. The bearing friction, however, is a variable item, depending upon the design, the bearing material, the lubrication, the location (whether in wheel-hub or on car-body) and the alignment. Under the most favorable conditions the bearing friction will reach a lowest possible value. By the development of a successful anti-friction mine-car bearing this lowest value has been improved to such an extent as to affect the whole system of mine haulage. After being satisfied of their durability and certainty of operation, any investigation into the advantages of anti-friction bearings for mine cars will have to be based upon reliable information as to the saving in power of such bearings. While numerous tests have been made in this direction, the results have not always been convincing, principally because of the rather crude methods that were employed. These crude methods are the main cause of the wide variations existing in regard to the exact amount of the frictional resistance. Frequently an ordinary spring balance is used and the pull necessary to move a certain car or train of cars is obtained by a number of readings. Such spring balances necessarily have a coarse graduation and the continuous vibration and fluctuations to which they are subjected make them highly dependent upon the individual observer. Further, they must be frequently calibrated. Sometimes these tests were made without regard to acceleration, speed or even grade.

Jan 6, 1916

By W. A. Backofen, D. Lee, F. S. Jabara

THE empirical character of plasticity analysis insures a continuing need for measurements of the yield surfaces of anisotropic materials. Recently, Wheeler and Ireland (W-I) proposed that an octahedral yield locus could be constructed on the basis of six Knoop hardness indentations. Such simplicity would have obvious appeal, if it led to consistently dependable results. In other recent work, a much more straightforward (and more tedious) method of measurement was used to establish all quadrants of the plane-stress yield loci for two substantially anisotropic titanium alloys.2,3 The same materials have since been reex-amined by the W-I method with results being reported here. A full description of the stress state under a Knoop indentor would be complex. In principle, however, this can be avoided in relating the hardness number to a plane-stress yield locus, by the expedient of superimposing the appropriate hydrostatic component on that state of stress. Six possible orientations of in-dentor on orthogonal (symmetry) planes, along (principal) coordinate directions, are illustrated in Fig. 1(0). Pictured in Fig. l(b) are normal-stress components nominally associated with indentation n: o2(H), directly proportional to the Khn in this case, together with By overlaying a hydrostatic tension, ah, that in general is equal to the stress state around the indentation is reduced to one of plane stress in the x-y plane for which the stress ratio is a The key step in the W-I yield-locus construction is to represent the Khn for any indentor orientation as a vector quantity on the octahedral plane. In the plotting, the vector is given as deviatoric stress components along the principal axes in the ratio , where represents the direction of the minor (width) diagonal and 1 that of the major (length) diagonal. There is no attempt by W-I to justify the 7/1, although it might be supposed that the value originates in the usual ratio of major to minor diagonals in a Knoop indentation of about 7/1. If that were its origin, the link to the deviatoric stress ratio would presumably be made by first taking 7/1 and then turning to the Levy-Mises equation for isotropic material: Interpreted in this way, the W-1 approach seems arbitrary and even contradictory. Yet it would still be favored by two circumstances: the deformation under a Knoop indentor approaches plane strain: when dcw/del =a; and the shape of the locus where plane strain is represented is not overly sensitive either to the exact value of dc,/dcl or to the degree of anisotropy, within a rather wide range of both variables. The second point is illustrated below, after a few additional comments on applying hardness

Jan 1, 1968

By Klaus Schoenert

In the analysis of comminution processes, it is necessary to have a detailed knowledge of such subprocesses as: transportation of the particles to the zone where they are stressed; the stressing of particles to a level high enough for breakage; removal of the fragments that are smaller than the limit size from the grinding zone; and prevention of agglomeration of the fine fragments. Breakage phenomena of particles is the most difficult subprocess to understand. It can be understood only by applying the principles of fracture physics to obtain information about the stress-strain field in particles which are loaded either by compression or by impact, and by using this theoretical knowledge to interpret experimental results obtained from single particle crushing studies. Two important features of the "Science of Communition" are discussed: the fracture physics and crushing under controlled conditions with special reference to single particle crushing, packed bed crushing, measurement of energy needed for fracture, fragment size distribution, and new surface area produced. The important features of these aspects are detailed, namely, energy balance of a crack, influence of environment, specimen size problems, and energy utilization in single particle crushing.

Jan 1, 1973

The Institute has no available copies of Bulletin No. 7, January, 1906, and Bulletin No. 105, September, 191.5. The sum of 30.50 per copy will be paid for these Bulletins.

Jan 6, 1917

By M. J. Mullikin, J. B. Conway

Several different equation forms were studied to determine the extent to which each particular equation type yielded an accurate representation of a given set of first-stage creep data. Specially developed least-squares computer programs were employed to obtain unique solutions for the creep-equation constants. In studies of creep data for lead at 14.5"C, nickel at 70OCC, and arc-cast tungsten at 2400°C consistently good representations were afforded by a third-degvee polynomial in t113. Other effective correlations were obtained with the Andrade, Cottrell-Aytekin, and de Lacombe equations along with a third-degree polynomial in t112. A newly proposed creep equation involving a hyperbolic-sine term in t1'3 was also found to yield very satisfactory results. This appears to be the first use of such a functional relationship in the analysis of transient creep behavior. In general, the deformation behavior of a material subjected to a tensile load is described in a strain-time plot. Experiments have shown that, following the instantaneous elongation which results on loading, the instantaneous slope (i.e., creep rate) of the strain-time curve decreases gradually with time and approaches what appears to be a constant value. Equations, therefore, which are proposed to provide an analytical representation of such first-stage or transient creep behavior must be consistent with these observations. In other words, at time zero, these equations must yield a finite deformation value corresponding to the elongation on loading. Furthermore, the first derivative of these equations must exhibit a fairly high although finite value at time zero, and then values which decrease with time. It is also preferable, in general, that the derivative eventually assume a constant value at high time values. Although many studies of first-stage creep behavior have been made and numerous equation forms have been proposed for expressing this type of deformation behavior, it is still not possible to state with any assurance which functional relationship will be adequate for a given set of measurements. Parabolic relationships have been employed most extensively although logarithmic expressions have been shown to be applicable in some instances. Combined forms1 have been studied in considerable detail and have on occasion been found to be very effective. One such expression is that of iXndradea and involves a modified parabolic expression: where 1 is the instantaneous length, lo is the length immediately following load application, t is the time, and p and k are constants. Another combined form has been proposed by weaver3 as follows: where E is the instantaneous strain, is is the linear creep rate, t is the time, and a and b are constants.

Jan 1, 1967

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

By William B. Plank

THE growing dependence of our vast industrial civilization (:n mineral products demands today, as never before, the highest technical skill in those who produce these product-;. That the duty of training the engineers, whose responsibility it is to produce these mineral products efficiently and in sufficient amount, falls directly on the schools of mining is beginning to be more fully recognized. The Institute, realizing this fact and that its future membership depends largely on the annual accretion of young men, is showing a keen interest in the problems of the mining schools and in the work of its Committee on Engineering Education. The Committee has, during the past several years, considered the problems connected with the training of men for the mineral industry, whether these have been problems of college training, or placement of the young engineer in the industry, or personnel training after he enters the industry. The field of interest and discussion has been as broad and varied as the mineral industry itself. Coal mining, metal mining and metallurgy have been discussed and the papers on these subjects have been outstanding contributions to the literature on mineral education.

Jan 1, 1931

NEW MEMBERS The following list comprises the names of those persons who became members during the period Apr. 10 to May 10, 1915: Members ADMAN, WILLIAM, Supt., Susquehanna Coal Co Lykens, Pa. BARTH, CARL G., JR., Min. Engr 6151 Columbia Ave., Philadelphia, Pa. BOOTH, ERIC EDWIN, Min. Engr., Mount Elliott Mine, Selwyn via Cloncurry, North Queensland, Australia. BOYDELL, HARRY CYRIL, Asst. Mgr., Randfontein Central Gold Min. Co., Box 42, Randfontein, Transvaal, South Africa. BRADY, SAMUEL HOWARD, Mine Supt Bohemian Club, .San Francisco, Cal. Buses, HARRY EDWARD, Mine Supt., Engels Copper MiningCo Keddie, Cal.

Jan 6, 1915

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889 ADAM S HEWITT 1890 JOHN BIRKINBINE 1891-1892 H M HOWE 1893 JOHN FRITZ 1894 J D WEEKS 1895 E G SPILSBURY 1896

Jan 1, 1923

In the Philippines, where distances are spoken of in terms off fight time, the Sipalay copper mines are two flight hours southeast of Manila on the island of Negros. After landing at the airport in Bacolod, it is then 170 km (106 milers) by surface transportation to Marinduque Mining and Industrial Corp.'s expanding copper operation. While copper deposits were discovered in the area in 1936-and one mine, the Binulig, began operations soon after-it wasn't until 1956 that stripping at Sipalay and construction of a 4000-t/d (4400-stpd) mill began. The mill went into operation in May 1957, and the first shipment of copper concentrate was made three months later.

Jan 8, 1978

By F. Habashi

Conclusive evidence is given showing that the dissolution of gold in cyanide solution follows mainly the over-all equation A similar equation can also be written for the dissolution of silver. Theoretical derivation of the velocity equation for this reaction has been obtained, which describes quantitatively the experimental facts. The equation is as follows: where [CN-] and [O2] = the concentrations (in moles/ml) of cyanide and dissolved oxygen, respectively. DcN- and Do2 = the diffusion coefficients of cyanide and dissolved oxygen; 1.83 x 10-5 and 2.76 x 10-5 cm2 sec-1, respectively. A = the surface area of the metal in contact with the aqueous phase, in cm S = the thickness of the boundary layer; varies between 2 and 9 x 10-3 cm, depending on the speed and method of agitation. Rate being expressed in g. equiv. sec-1. INTRODUCTION During recent years a number of papers have been published on the kinetics of dissolution of gold and silver in cyanide solution.1,6 The authors agree that the rate of dissolution is diffusion-controlled, but disagree regarding the mechanism of the reaction. Some authors'-3 support the Bodlander equations: The apparently conflicting results, when critically reviewed, are concordant and lead to the conclusion that the proper equation for the dissolution reaction should be only Eq. 1. This conclusion is based on the following facts: 1) For every 2.2 equivalents of metal dissolved one mole O2 was consumed. 2) For every 1 equivalent of metal dissolved, 2 moles of cyanide were consumed.' 3) Hydrogen peroxide is formed during the dissolution of gold or silver, and for every 2.2 equivalents of metal dissolved, one mole H2O2 was produced.1,2 The fact that Kudryk and Kellogg4 did not detect H2O2 during the dissolution of gold should not throw doubt on the many affirmative reports of other investigators. Lund2 has shown that depending on the crystalline nature of the silver surface, (e.g. method of etching the sample) H2O2 may undergo catalytic decomposition heterogeneously according to: Further Kudryk and Kellogg4 carried out their experiments in the presence of 0.5% KC1 to achieve a greater electrolytic conductivity, and Matsudaira7 has shown that H2O2 is catalytically decomposed (homogeneously) in the presence of C1- ion in alkaline solution. 4) Experiments carried out by Boonstra8 and Lund2 showed that the dissolution of gold and silver respectively in KCN + H2O2 in the absence of oxygen was a slow process. Thus the reaction takes place to a minor extent only. Further kinetic studies showed that: 1) The rate of dissolution depends on the surface area of the metal in contact with the liquid phase, thus indicating that the process of dissolution is a heterogeneous process. 2) The rate of dissolution depends on the speed of stirring,5,6 thus indicating that the process is controlled by a physical phenomenon.

Jan 1, 1967

By AIME AIME

M ALBERTSON is research engineer for the Shell Petroleum COT. He joined the Roxana Petroleum Corp. (later the Shell) in 1920, at Hanger, Texas, became district geologist at Shreveport, and after two years was transferred to the production department, where he has been for the past fifteen years. His jobs have ranged from a modest field engineer up to assistant production manager. During this time hc has successively resided in Texas, Louisiana, Missouri, Louisiana, Oklahoma, Missouri, Texas, The Hague (Holland), and Texas. II? the Yates Pool, Texas, in 1929, "Al" initiated' the tubing of wells under pressure to control gas-oil ratios, particularly at restricted rates of flow. This led to the compulsory tubing of all oil wells drilled in the State

Jan 1, 1937

By D. L. King, B. A. Schepman

A number of unique thickener mechanism designs with the operating results achieved in various installations are discussed. These unusual designs include new types of raking arms, lifting devices, and feed-wells employed to obtain higher underflow densities and minimum operator control or improved overflow clarity. Several installations of large thickeners in which the underflow lines pass upward through the center to eliminate tunnels are reviewed. The location of the lines and pumps with the maintenance and operating records are included. Several types of automatic lifting device controls are used to provide storage in the thickener. Some of the installations employing underflow density controls are achieving excellent operating results. Thickeners or sedimentation basins are used in minerals beneficiation plants for three basic purposes. These are 1) Concentration, or to raise the density of a liquid-solids slurry. 2) Clarification, or removal of finely divided solids from a slurry. 3) Hydroseparation, or removal of a specific fraction of solids from a slurry. The concepts that control the size and configuration of basins used for these purposes are different. Likewise, different equipment is properly employed to accomplish these various objectives. The pattern of liquid and solids flow in the clarification zone of a sedimentation basin used for thickening or raising the density of a pulp normally is not critical. That is, the solids normally will drop or plunge to the bottom quite readily, and the liquid separates itself from these solids so as to overflow the basin in a relatively clear condition. When clarification or removal of finely divided particles is to be accomplished, the flow patterns in the basin are extremely important. The velocity of the incoming stream must be dissipated and the liquid flow distributed ]In the tank so that the feed is not divided into streams that flow directly to the overflow carrying the fine:ly divided solids that are to be removed. Similarly, the configuration of the arms that provide the raking and thickening of the pulp is not as important in basins primarily devoted to clarification. In thickening, the design of the arms and the manner in which the pulp is moved or worked, can contribute appreciably to the thickening process and achievement of a higher density underflow. THICKENING As the grade oi ore bodies throughout the world generally decreases, and chemical processes, hydro-metallurgy, and other more refined methods of minerals beneficiation are required, problems in thickening become more acute. Difficult operating conditions, previously encountered only occasionally in thickening metallurgical slurries, or clarifying process streams in the mill, are now the rule rather than the exception. Fig. 1 illustrates some of the different types of raking arms that are successfully achieving the desired goals in pulp thickening. The conventional raking arms consist of a relatively simple truss with the blades attached to the bottom chords. This design provides proper Concentration of many 'normal' slurries. A modificaiion of this design as shown in the center is being used with excellent results on large thickener basins where it is desirable to have a

Jan 1, 1962

By H. Reinhardt, P. Haglund, J. Rydberg, B. Lunden

As legislation to minimize pollution in effluent streams becomes stricter, it is important to treat used acid pickling baths before discharge. This is usually achieved by neutralization of the acids and precipitation of the dissolved metals in such a way that neither acids nor metals can be re-used. A process has been designed and tested on a pilot plant scale to recover both acids and metals from a stainless steel pickling bath leaving only Na2SOs in the effluent. In this process, H2SOr is added to the spent pickling liquor and the recovery of the pickling acids HN03 and HF is achieved by solvent extraction, using TBP in kerosene as the organic solvent. The extracted acids are stripped with water, giving an acid concentration high enough for direct use in the pickling bath. Molybdenum is also extracted by TBP and is recovered in a separate step. The other metals, Fe, Cr and Ni, are precipitated from the raffinate as hydroxides, dried and recycled to the metal process. In evaluating this process, comparative experiments with mixer-settler and pulsed column have been performed. The process described is being considered for use by a Swedish company pickling 70,000 tons per annum of stainless steel.

Jan 1, 1973

The Joint Economic Committee's subcommittee on international payments and exchange has recommended that, following international monetary reforms, the law which prohibits private possession of gold by American citizens be repealed. The subcommittee recommendation called for reforms to enhance the role of special drawing rights in international monetary affairs and downgrade the role of gold. Special drawing rights, also known as "paper gold", are on artificial reserve with the International Monetary Fund (IMF) which distributes them to member nations in proportion to their economic importance in the world economy. The special drawing rights are then used to settle debts between nations in the same manner as gold or currency. The subcommittee said that under the reforms now being discussed special drawing rights would be acceptable in lieu of gold among the member countries of the IMF.

Jan 1, 1973

By Fred H. Poettmann, A. L. Benham

correlation of waters and identification of mixtures of two and three waters is important in secondary recovery evaluation studies and studies involving underground movement of waters. The importance of such studies suggests the need for a method to correlate a great number of water analyses to accurately identify and improve the understanding of mixtures of waters. Geochemical analyses of waters furnish a quantitative measure of each of the ions present in a water. Table L shows a portion of the data on many oilfield water analysis report forms in use today. Under "parts per million" are listed the quantitative amounts of each ion in milligrams per liter. Following the work of Stabler' and Palmer", some laboratories have reported additional data to indicate the reaction capacity, or reacting value of each ion. Table I lists data under two subheads for the "reacting value". Under the first subhead, the reacting value is reported in gram equivalents per million, hereinafter called equivalents per million. This value is determined by multiplying milligrams per liter of the ion by a factor equal to the reciprocal of the equivalent weight of the ion. Under the second subhead (per cent) is listed the percentage of each ion based on the total equivalents per million. Sodium is not usually an analyzed value in routine analyses, but is determined by the difference between total negative equivalent per million values and the sum of all of positive ion values for which analyses were made. This difference is reported as sodium, hereafter labelled "sodium". On this basis, the subtotals of the equivalent per million and per cent reacting values of the positive and negative ions are equal. CORRELATION OF WATER ANALYSES DATA Previously reported methods for correlating oilfield waters have used part of the data in Table 1, and can be classified into two categories. Correlation by Chemical Character Correlation methods using the chemical character of waters, as represented by the per cent reacting values of the ionic constituents, have been used by Palmer2 and Tickell. These methods have the limitation of neglecting the ionic concentration of the waters. This limitation can be serious in areas where waters have the same chemical character, but differ in concentration. Correlation by Concentration of the Ionic Constituents The Reistle' and the Stiff methods use the ionic concentration in parts per million and equivalents per million. These methods are effective in differentiating waters of similar chemical character and varying concentration, as in the highly saline waters of the Mid-Continent area. These methods have the disadvantage that they correlate waters by comparing many graphs of individual water analyses to determine the similarity to, or the variance from "type" waters. PROPOSED METHOD OF CORRELATING WATER ANALYSES DATA Correlation graphs presented in Fig. 1 represent water analyses data as points to facilitate the correlation of waters. The graph on the left of Fig. 1 is a plot of per cent reacting value of magnesium vs calcium. The right