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By M. P. Tixier, M. Gondouin, G. L. Simard

In the quantitative interpretation of the SP logs, the electrochemical component is generally taken equal to — K log Rm /Rw where K has the theoretical value corresponding to solutions of pure sodium chloride. This method may be misleading when relatively large quantities of salts other than NaCl are present in form-rrtion waters—as is generally the case for low salinities —or in gyp-base muds. In such cases recourse is made in the field to changing the K value or to adding a correction term to the equation on the basis of local experience. An investigation has been made in the laboratory of the influence of HCO3, SO4=, Ca++, and Mg++ on the amplitude of the SP deflection, which included in par-ricular determinations of the activity coefficients of Ca++ and Mg++. The theory, the experimental techniques and a tentative method for applying the results are described. So far, applications to actual field cases where chemical analyses of waters were available have provided an excellent confirmation of the proposed method. The case of the SP in very salty brines is also considered and it is shown that the use of activity data for sodium gives satisfactory results. HISTORICAL In early times of electrical logging, the SP curve was used exclusively as a tool for the location of permeable beds and the definition of their boundaries. Later, with the introduction of methods of quantitative analysis, attention was called to the possibility of deriving from the SP log some information on the formation water resistivity, which constitutes one essential element for the computation of water saturation from log data. The first laboratory experiments' in 1932 had shown that, as a result of electrochemical phenomena arising at the contact of the niud and the formation, the amplitude of the deflection of the SP curve was, at least partly, a function of the salt concentration of interstitial water and accordingly of its resistivity. It was indicated that the amplitude of the electrochemical component of the SP should be equal to K log R1/R2, R1 and R2 being the resistivities of the mud and of the formation water respectively. However, the exact value of the K coefficient was not determined at that time because the surface clay used for a laboratory model was far from an ideal shale membrane. Consequently, the way was not yet open towards quantitative interpretation. In the early forties, Tixier reported2, on the basis of field log observations, the following equation for the case of NaCl solutions, SP = -71 log f1c1/f2c2, c1 and c2 being the concentrations and f1, f2 the mean activity coefficients. The local variations observed in the empirical values of K, chiefly in the Rocky Mountains, led him to advance the opinion that, besides the relative amounts, the nature of the salts present in the solutions had a bearing on the magnitude of the SP. At about the same time Mounce and Rust- ad published laboratory results which emphasized the part played by the shale in the generation of the SP. On the basis of laboratory tests and theoretical considerations, Wyllie in 1948' published the following equation of the electrochemical SP for the case of NaCl solutions, SP= - 71 log (a1)m/(a2)m

Jan 1, 1958

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman's paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author's comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman's paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author's comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By H. I. Aaronson, H. A. Domian, A. D. Brailsford

A current study of the growth kinetics of k (hcp) plates in a Cu-Si (fcc)&apos; has generated a requirement for data 02 the chemical interdiffusion coefficient in a (termed D,) as a function of temperature at the composition of the a/a + k pJase boundary. Rhines and Mehl 2 have determined D, as a function of composition at lower silicon contents by making Matano analyses of concentration-penetration curves. However, the accelerating increase in B, which they demonstrated as the phase boundary composition is approached at constant temperature and the rapidly diminishing accuracy of this analysis as the limiting compositions of a diffusion couple are approached (the silicon-rich component of their couples contained appreciably less silicon than is permitted by the solubility limit) indicate that the required information cannot be safely obtained by extrapolation of their data. Although the quite different method employed in this study is not exact, it will be shown that the approximations made are not serious ones, particularly from the viewpoint of the prgcipal application anticipated for these data. D, was determined from the migration kinetics of the a :k boundaries formed in sandwich-type diffusion couples produced by welding a block of high-purity copper to opposite sides of a cube (* in. on edge) of homogenized high-purity Cu-5.82 wt pct Si alloy. The alloy is pure k in the temperature range employed. The surfaces of the couple components which were normal to the diffusion direction were machined accurately flat and parallel, lightly polished, and carefully cleaned. Welding was then accomplished by means of the vacuum-encapsulated pressure jig technique previously employed.3 Welding was always conducted at the intended diffusion temperature; thus the welding anneal also served as the first diffusion anneal. Subsequent diffusion anneals were performed in evacuated Vycor capsules. Following the welding anneal, one of the surfaces parallel to the diffusion direction was machined, ground, and polished flat; additional material was removed from this surface after each diffusion anneal in order to avoid any effects of composition changes. After etching,4 the average distance between a : k boundaries was measured by means of a traveling microscope with an accuracy (per measurement) of better than 1 p. Satisfactory results were obtained at four temperatures in the range 775° to 655°C; attempts to obtain data at two lower temperatures were unsuccessful, evidently as the result of the interference of surface contamination during the welding process.

Jan 1, 1969

By George Bell

THE mine and milling plant of Demonstration Gold Mines, Ltd., is near the city limits of Baguio, Mt. Province, P. I. The mine road connects with the main highway to Manila. The nearest railway point is near sea level, approximately 40 miles distant. The Baguio district is very mountainous and has one of the heaviest rainfalls in the world. It is therefore difficult to maintain roads or to impound tailings and mine dumps. All supplies are trucked into the district direct from Manila or the nearest railway point, which means uncertain deliveries and high freight rates. Installation of equipment is difficult and costly. The average elevation at the mine is 4000 ft. and the climatic condi-tions.are ideal except for a three months rainy season. The company generates its own power for mining and milling opera-tions with three 400-hp. Ruston Diesel engines direct connected to 250-kw. General Electric alternating current generators. Labor conditions have been excellent, although at present social security laws are causing some unrest. Labor receives a higher average wage rate in this district than other labor in the Islands. The com-pany also furnishes free living quarters, hospitalization and work-men&apos;s compensation. Taxation has been reasonable up to the present time, but some of the new mining legislation may make it difficult to operate and pay dividends. The future depends largely upon the continuation of $35 gold and the political outcome in the Islands.

Jan 1, 1939

By L. P. Teas

In spite of the influx of operators into the Gulf Coast anxious to retrieve their depleted production in other fields, and in spite of very active application of the most scientific geophysical methods to locate new producing areas, the results have been very discouraging and the year has failed to produce more than the average results for a Gulf Coast year. During the year seven new oil fields, some of which are still of very little importance, and one new gas area have been discovered. These fields are Tom Ball, Greta, Cleveland, Raisin and Garwood in Colorado County; Louise and Premont in Jim Wells County, and the new producing gas area near Ace in southern Polk County. During the year salt has been found for the first time at Carlos and Esperson. New producing areas have been developed on East Stratton Ridge, Hockley, Hull, Port Neches, near Pettus in Bee County, and on the O&apos;Connor Ranch in Victoria County. The total production for the Gulf Coast for the year was 62,837,435 bbl., an increase of 18,589,000 bbl. over 1932. During the year, 1307 wells have been drilled of which 207 were wildcats, compared with 653 wells and 141 wildcats the previous year. The total daily production at the end of the year was 165,201 bbl. At present there are 3100 oil wells producing. The average production per well is 55.5 bbl. per day. The price of crude fluctuated considerably during the year, beginning at 80c per barrel and closing the year at $1.04 per barrel. Completion data for 1933 are as follows:

Jan 1, 1934

By Otis W. Freeman

Production of oil in Indiana during 1944 is estimated at approximately 4,950,000 bbl., a decline of 6 per cent from the preceding year. Shortage of labor and material, together with governmental regulations resulting from the war, largely account for the drop in output and limited new developments. Three new pools were discovered in the state during 1944. Two of these, New Harmony, South, and Hovey, West, are in Posey County. Six wells in the New Harmony, South, field produced 66,422 bbl. of oil last year. A third field, Cato, in Pike County, did not market the oil from its discovery well during 1944. Several wells discovered oil in the Henderson field of Jay County along the Ohio state line. An important south extension of the St. Thomas field in Knox County was discovered during the year. Active drilling took place in the Inman, East, and Upton fields, Posey County, both discovered in 1943. Twenty-two wells in Inman, East, produced 151,1gr bbl. in 1944 and 12 in Upton produced 107,052 bbl. Owensville, and especially Owensville, North, in Gibson County, made large gains in production as a result of active drilling. The Dodds Bridge field in Sullivan County continued good production from deep sands reached in 1942. The Griffin continued to be the largest producer among the oil pools of Indiana, accounting for 2,004,180 bbl., over 40 per cent of the state&apos;s output. The next largest producing fields are Mt. Vernon and New Harmony, both in Posey County. The largest gas well brought in during 1944 was in the Rockport field, Spencer County, and had an initial output of 2,680,000 cu. ft. per day. The most productive gas fields in Indiana are Rockport, Spencer County, Greensburg, Decatur County, and Unionville, Monroe County. Total production in the state is . hard to estimate, as considerable gas is consumcd in farm homes and for other local uses, and never is reported, but was near 1500 million cubic feet. Some oil from the Trenton field is also used locally and is unreported from pipe-line runs. A total of 606,145 ft. of new hole was drilled in Indiana in 1944. Most of the completions were in Posey and Gibson counties, although wells were drilled in 36 different counties. During the year 331 wells were completed. Of these, 145 found oil in commercial quantities and 28 were gas wells. The initial production of the 145 oil wells was 11,908 bbl. per day. Settled production would be less, of course. The largest wells reported during the year were two on the J. W. Mann farm, in the Mt. Vernon field, with a flush flow of 500 to 800 bbl. each.. Six pools, all small "one well" affairs, were abandoned in 1944; i.e., Fleenor and Patoka in Gibson County, Grafton and Rapture in Posey County, Vaughn in Vandei-bwgh County and Millersburgh, Warrick County.

Jan 1, 1945

By M. A. Mahtab

When characterizing orientations of rock joints in an engineering site with respect to mean values of the existing clusters or joint sets, a need may arise for a similarity test that allows grouping of observations from several adjacent sampling stations. Subjective judgment, though based on experience, may not produce realistic groupings in the data. A similarity test is developed in this paper for objective grouping of samples of joint orientations in engineering sites. The test is applied to the data from a large, geologically complex site of a potential open pit mine.

Jan 1, 1984

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy&apos;s law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy&apos;s law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By W. E. Bonini, E. A. Hickok

IN the course of an investigation directed toward expanding ground-water facilities in Essex and Morris counties, New Jersey, the Board of Water Commissioners of the city of East Orange authorized a seismic-refraction survey&apos; for the purpose of de-lineating bedrock topography below unconsolidated overburden. Results of the survey were highly satisfactory and led to the preparation of a comparatively detailed bedrock contour map. Knowledge of the bedrock depth and configuration was an important aid in selection of sites for test drilling. The portion of the East Orange Water Reserve under consideration is in the flood plain of the Pas-saic River about 10 miles west of Newark, N. J. The flood plain is about 175 ft above mean sea level and is bordered by low hills rising to elevations of approximately 250 ft. The bedrock underlying the Water Reserve consists of sandstone and shale of the Triassic Brunswick formation and is covered everywhere by deposits of unconsolidated glacial outwash sand and gravel, lacustrine clay, and recent river silt as much as 150 ft thick. Yield of wells in the sandstone and shale averages 100 to 200 gpm. Since production wells constructed in the sand and gravel aquifer in the buried river valley shown on the contour map (Fig. 1) yield 300 to 1400 gpm, it was proposed to locate additional production wells in this buried valley, where the yields per well would be maximum. In 1939 and 1946 the East Orange Water Dept. had electrical-resistivity surveys made to determine depths to bedrock. From the resistivity data the exploration company prepared a bedrock contour map. A well field expansion program begun in 1955 utilized this information to locate sites for test wells along a predicted northward extension of the buried valley in which existing production wells are located. After several test wells (wells 201-205) had been drilled, it became apparent that the resistivity information was unreliable." For example, test well 201 recorded bedrock at a depth of 72 ft, whereas the resistivity depth determination was 130 ft. As a consequence, the test drilling program was temporarily suspended and a seismic survey was under- taken to determine the topography and extent of the buried valley known from well records to underlie the existing well field. In the first phase of this study, several seismic shot point locations were placed at sites where well logs had been obtained previously. This procedure is necessary in a new area to determine whether the seismic method is applicable and what degree of accuracy is to be expected. At the East Orange Water Reserve, depths obtained from the shot points near test wells 202, 203, and 204 were within 8 to 11 pct of the depths logged (Table I). With this assurance that accurate results could be obtained, additional seismic spreads were located on the Water Reserve. Using a portable refraction seismograph, in the fall of 1955 a crew of four men shot a total of 29 reversed seismic spreads in a period equivalent to six field days. Charges as heavy as 3 1b of 40 pct dynamite were necessary at a few places to overcome ground vibrations caused by traffic on nearby highways. At most other sites, a 1-1b charge was sufficient. Travel-time plots were made for all spreads, and depths and true velocities were calculated according to formulas for multiple sloping layers by Ewing, Woollard, and Vine.&apos; The plot of spread 7 (Fig. 2) is typical of the short spreads in which bedrock was shallow—about 50 ft in this case. Where there were not enough arrivals through the bedrock to define the high velocity bedrock line, the spreads were lengthened. This was done by placing shots on line several hundred feet away from each end of the line of geophones. It was then possible to construct complete reverse plots for both short and extended shot points (see spread 27, Fig. 3). Four individual depths were calculated from each extended spread. Three and in some cases four seismic layers were observed. The surficial layer had a velocity range of 900 to 1200 fps, the lowest velocity recorded. This seismic layer is above the water table and is interpreted as recent river silt. The bedrock had the highest velocities, which ranged from 10,600 to 16,400 fps. Intermediate velocities ranged from 4500 to 6800 fps. In every case the intermediate layer was within

Jan 1, 1959

By P. W. Bridgman

IT is characteristic of most scientific investigators that they are not satisfied with the discovery of new facts, no matter how curious or unexpected, but that along with the factual discovery there is a constant effort to understand It appears that. one&apos;s interest in, and satisfaction with, the discovery of an array of news experimental facts is enormously increased if one has at the same time a theory or hypothesis guiding one&apos;s expectation of what sort of new experimental discovery may lie around the corner Conversely, as a theoretical physicist one&apos;s satisfaction with his theory is greatly enhanced if along with the development of the theory can go the discovery of new experimental facts, confirming or perhaps modifying the theory as it grows Of course, there have been long and stretches in the history of physics in which new data of unquestioned ultimate importance ham e piled up, without much inspiration or illumination in the way of understanding For 50 years spectroscopy had such an and history, but how irksome this was felt to be is plainly shown by the almost audible relief that greeted the first success by Bohr in injecting understanding into the situation, and by the fresh rush of experimenters into this field when the prospect of understanding had once been offered The investigations in the field of high pressure, which have occupied me for a long time,1 until the last few years have been in very much the Same sort of situation as spectroscopy before the advent of Bohr A great many kids, of data were collected for a great many solid and liquid substances, and there could be no question of the importance of these data, because the uniform change of dimensions produced by hydrostatic pressure is perhaps the simplest conceivable type of alteration to which a body can be subjected But except for a few isolated flashes, there was no theoretical illumination, so that it had to be to a large extent the enthusiasm of the collector that kept me going However, within the last few years the wave-mechanics theory of solids has progressed so rapidly that

Jan 1, 1938

By H. T. Hildage

Although Greater New York does not bear any resemblance to a great mining district, the mining operations that are being conducted in and about the city are both extensive and interesting in character. With regard to the extent, it may be mentioned that, at present, there is more dynamite used in New York than in any mining district in the United States; that there are under construction about 38 miles of tunnel, and that 66 miles more are projected, most of which must be constructed .in the near future; that since 1903 at least 2,000,000 tons of earth has been removed in underground work, in addition to about 3,500,000 tons that has been removed in open-cut in connection with tunnel-work, and many times this quantity that has been removed in excavating foundations for buildings not connected with tunnel-work; and that there are to-day probably more than 5,000 men engaged in mining-work in and about New lrork City. These undertakings include almost every operation connected with underground work, from exploration by means of trench and boring, to the sinking of large shafts and the driving of large tunnels through every kind of ground from hard rock to soft, semi-fluid silt and quicksand. It is proposed in this paper to give a general description of some of the methods and appliances used in the opening-up of a " mine " in a large city, and a brief description of some of the &&apos;mines" now being developed in New York, connecting as far as possible the methods described with the particular work for which they were designed, in order to give a general idea of the

Jan 1, 1908

By P. S. Miller, S. H. Ash

EXTENSIVE and diversified resources justify large populations and great industries. To carry on the business of commerce and meet the demands of large populations, the utilization of tunnels in some form for transportation purposes constitutes an important link in modern civilization. The driving of tunnels has been appropriated by the tunneling branch of the heavy-construction industry, and the progressive steps taken by modern tunnel builders were not even dreamed of 50 years ago. Great strides have been made toward more rapid progress in tunneling in the United States during the past 10 years. Tunneling consists of a definite cycle of operations developed from ideas that are crystallized and translated into action programs through various engineering phases that begin with the first preliminary survey and do not end until the job is completed. Once the line of the bore is established and a time set for the completion of the work, the face must advance according to estimates prepared before the work commences. This schedule must be followed in regular sequence from the moment the drills start against a new face of rock until they are ready again to drill the succeeding face, constituting a round.1 Mining is largely tunneling carried on under conditions often more inherently hazardous than actual tunnel construction, but for various reasons1 tunneling is more hazardous than mining in any branch of the mineral industry, On the other hand, obstacles are sometimes encountered in heavy-construction tunneling projects that when met in mining enterprises do not offer comparable tasks to avoid or overcome them. One of these is the existence of water under high pressures. In mining enterprises, various alternatives offer a solution in driving a tunnel, even to the extent of its discontinuance or the abandonment of the mine, but a "construction" tunnel usually must go forward because some important project depends largely if not entirely upon it. This paper describes an unusual method of driving a water-supply tunnel through rock carrying water under pressures and conditions that did not permit the use of ordinary tunneling methods. THE DELAWARE AQUEDUCT The new Delaware aqueduct is a Manhattan project of some magnitude; when completed, it will contain what probably will be, for some time to come, the longest tunnel in the world. Various features in its construction are currently described in the trade journals of the construction industry, and informative engineering details are given in the Delaware Water Supply News, published twice a month by the Board of Water Supply of the City of New York. Work was begun on this project on March 24, 1937. The tunnel will convey water from reservoirs at the headwaters of the Delaware River to the City of New York.

Jan 1, 1942

By Richard H. Mote

The endlessly changing pattern of mineral supply and demand offers opportunity to the alert and can bring disaster to the unwary. The discovery of ore bodies, the invention of extractive processes, the provision of new transport facilities, the political stabilization of underdeveloped areas, and many other changes can increase supply dramatically. Such new outpourings of mineral wealth from ore bodies bring fortunes to their developers, and consumers frequently find their competitive positions decidedly improved by new and cheap sources of supply. On the other hand, operators of marginal properties can find competition from newly opened high-grade mines intolerable. Consumers that have depended on the products of nearby, high-cost mines may find new, remote, low-cost supplies advantageous only to their competitors. The invention of new prospecting methods can have spectacular effects. Shortly after World War I the discovery rate of petroleum pools began to decline. The leading prospecting technique of that day, the projection downward of surface reflections of geologic structure, was proving less rewarding. Prophets foretold an oil shortage in the near future. But at that very moment scientists were perfecting the application of seismic waves to reveal underground oil-bearing geologic structures. As these geophysical methods were put into commercial use the whole outlook changed-the problem of the 1930&apos;s became how to cope with the surplus from discovery, not how to meet the ever rising demand. Many lead mines were being abandoned as unprofitable about this same time because the penalties charged by smelters for the zinc in the ores and concentrates more than counterbalanced the payments for lead and silver. Then selective flotation (at the time called differential flotation) appeared,

Jan 1, 1964

By Notman, Arthur

THIS is a day of surpluses, some good and some not so good. One can hardly pick up a newspaper, magazine, review or economic treatise without confronting the fact that we have or are threatened with more .of certain goods than we have use for, whether it be corn, wheat, cotton, coal or oil, -lumber, &apos;leather, newsprint, automobiles, zinc, lead, copper or what not. How did this unprecedented state of affairs arise? Who is to blame? How shall we avoid smothering ourselves in our own production? The voice of the farmer is raised in appeal to the Government to relieve him from the dilemma of his own fertility. In answer the Government employs thousands of experts and spends millions of dollars to aid the farmer. But to what end? To make him still more efficient so that he may produce even greater surpluses? Not satisfied with the result, it spends other millions to prepare vast areas of the arid land of the West for more farmers to cultivate and insure yet larger surpluses. Then what? Naturally another appeal to the Government to fix prices by financing the

Jan 1, 1928

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By J. J. Jonas, J. L. Uvira

Equipment was constructed which permitted the hot compression of 99.8 pct Armco iron and 2.8 pct Si steel at constant true strain rates of 0.05 to 1 per sec over the temperature range 600" to 1000°C. A maximum true strain of 1.9 could be attained, followed by immediate quenching or by isothermal annealing. True stress-true strain curves were obtained, and the steady-state flout stress, a, strain rate, i, and temperature, T, were found to fit the following expression: The constants A, a, n&apos;, and AH were determined for the two ,materials. The activation energies obtained for Arrnco iron and silicon steel are 66 and 80 kcal per mole, respectively, and approximate those for seu- diffusion and for creep. This indicates that hot compression is a diffusion-controlled thermally activated process. THE hot compression of iron and steel is usually carried out in the austenite temperature range,1"7 as this is the one of greatest interest with respect to industrial hot working. However, a disadvantage of testing in the austenite range is that the hot-worked structure is destroyed by the phase transformations taking place during cooling. The present study was therefore carried out in the ferritic temperature range, and the hot-worked substructures were preserved by rapid quenching after deformation. The substructural results will be described in a separate paper, and the present communication is restricted to the strain rate/stress/temperature relationship observed during hot working. The results of hot-compression testing are usually given in the form of true stress/true strain curves, with a different curve for each temperature/strain rate ~ornbination.&apos;,~,~ Sometimes simple algebraic equations are fitted to the curves, so that certain extrapolations or interpolations can be performed.1&apos;2&apos;5 These equations are, however, devoid of mechanistic interpretations. The present study was undertaken to show that hot compression can be described by an equation of the type used in creep studies. That is, it will be shown that the temperature dependence of the strain rate in hot working is well-represented by an Arrhenius term, with an activation energy similar to that for creep. Also it will be seen that the stress dependence of the strain rate is similar to that for creep EXPERIMENTAL METHOD AND MATERIALS The investigation was carried out with the following three ferrous materials: 1) Armco iron; 2) Armco iron with 0.26 pct Mn; 3) 2.8 pct Si steel. The first two materials were utilized for investigations performed in the temperature range 600" to 800°C; the last one was used for tests at temperatures from 600" to 1000°C. The materials were of commercial purity,* as shown in Table I. Cylinders of five different sizes were prepared by strain annealing. The resulting mean grain diameter was 3 mm in the 1-in. Armco iron and 2 mm in the other sizes and grades. Different ratios of diameter/height were used to enable the determination of the coefficient of friction. The specimen faces were provided with concentric grooves, which acted as lubricant holders during compression, as recommended by English and ~ackofen&apos; and others.2&apos;9 Powdered glass lubricants were applied to the samples before hot compression to decrease friction and barreling, following the practice of previous investigator~.~~~~~~~~ Different mixtures of glass powder were used for each temperature, after the determination of suitable compositions by experiment.&apos;&apos; Equipment for Hot Compression. Hot-compression tests were carried out on an adapted 150-ton vertical hydraulic extrusion press and also on a modified high-temperature creep machine. The modified extrusion press was used for temperatures up to 800°C. The following items were added to the press: a) a high-temperature furnace with built-in upper and lower platens; and b) a transmission assembly, which permitted the attainment of logarithmically decreasing crosshead speeds. These accessories are described in detail in Ref. 11.

Jan 1, 1969