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By J. Murray Riddell

The method of treating hazards wherein value is decreased, is cited by R. D. Parks. Quite properly, the theory of probabilities is made use of when multiple hazards are under consideration. E. F. Fitzhugh, Jr. $ deals with the enhancement phase graphically and uses percentage of expectancy as derived by a study of conditions and the selection of a chance factor. It is believed that both of the authors referred to fully recognize the part which human judgment plays, and as coupled with experience, training, and the application of the theory of probabilities; in that respect the composer of this paper is in accord. Within the past year, the task of arriving at a mathematical method for handling the enhancement phase, and, additionally, coupling the negative and positive phases, was explored. In citing the hazard, or negative phase, reference is made to the text by Parks. Types of Items far Consideration On the hazard, or negative, side some of the common items to be considered are: 1. Subsidence and resulting damage. 2. Flo wage of water above that anticipated. 3. Geological. (a) Decline in quality of probable ore, and/or (b) Decline in quantity of probable ore. 4. Depressed economic conditions. 5. Litigation. Similarly, on the enhancement, or positive, side common items to be considered are: 1. Flo wage of water below that estimated. 2. Geological. (a) Increase in quality of probable ore, and/or (b) Increase in quantity of probable ore. 3. Elevated economic conditions. 4. Litigation. 5. Technological advance in the art. Tn all of the above items no consideration is given to placing a value on, or giving consideration to, possibilities. For example, referring to Table 1, the estimated normal present value (Vp) of a property, exclusive of risk consideration, is taken as $100,000. If subsidence affects the usefulness of the shaft, the present value of the property will decrease to $60,000, and it is judged that there is a 1 in 4 chance that the shaft will be impaired;, consequent.ly, if subsidence took place, the present value would be reduced ($100,000-$60,000) $40,000, but since the chance is 1 in 4, the allowable reduction would be only one-fourth of $40,000, or $10,000, or a discount of 10 pct (hazard factor) of the original value; the related safety factor is taken as unity minus 0.10, or 0.90. Thus, the original Vp, $100,000, multiplied by the safety factor ($100,000 X 0.90) gives $90,000, which is the adjusted present value of the property in this single instance. Additionally, there is a water hazard, which, if encountered, will reduce the present value to $85,000. The chance is 1 in 3. Following through with the same reasoning as shown above, the derived safety factor will be 0.95. To arrive at a single multiplying factor which will express the combined risks, the two safety factors are multiplied together, 0.90 X 0.95 = 0.855. That factor when multiplied by the origirial Vp will give the adjusted, and

Jan 1, 1950

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'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'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. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.' It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch's alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By W. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.' It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch's alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By R. F. Mehl, G. V. Smith

THE decomposition of austenite in steels, because of its immense practical importance, has been subjected to extensive study in recent years from the point of view of the mechanism of the process.1-3 Although much information has been acquired, a number of questions, principally of theoretical interest, remain. One is that of the atomic-crystallographic mechanism by which each of the various reaction products forms. The isothermal reaction products of the eutectoid decomposition in plain carbon steels (to which this study is restricted) have conveniently been classified in three general groupings-pearlite, bainite, and martensite. Of these several products, pearlite and martensite have been studied extensively, but bainite has received only scant attention. As a result, the mechanism of the formation of pearlite and that of martensite are now fairly well understood while a great deal of uncertainty exists regarding bainite. PEARLITE Pearlite forms from austenite by the precipitation of alternate platelets of cementite and ferrite, which grow into the austenite matrix .2-5 The rate of reaction may be described in terms of a rate of nucleation and a rate of growth.2.3 Mehl and Smith6 have attempted to determine the lattice relationships existing between the ferrite in pearlite and the parent austenite. Using a pole-figure method of analysis, it was found that a limited number of ferrite orientations resulted from the decomposition of a single grain of austenite; it was not possible, however, to decide between two assumed ideal relationships, both of which appeared to account for the experimentally determined pole figure. It was definitely shown, however, that the relationship obtaining was quite different from that determined for the proeutectoid separation of ferrite.7 No attempt was made to determine the habit plane (matrix plane to which the precipitate lies parallel) of the pearlite lamellae. Belaiew8 earlier had stated that the number of directions assumed by the pearlite lamellae in a single grain of austenite was 12 (no details were given) and concluded wrongly, as Mehl and Smiths have pointed out, that the lamellae delineate the [210] planes of ferrite.* MARTENSITE It is known that martensite is a transitional constituent of body-centered tetrag-

Jan 1, 1942

By Michel Daghert, Michel David

In the exploitation of large porphyry type deposits where a cut-off has to be applied and where "internal waste" exists, planning people ask the geologist for the estimated grade of small blocks. Comparison with actual production figures and blast hole assays shows that any kind of weighted average of neighboring DDH (diamond drill hole) samples provides an excessingly smooth picture of reality, resulting most of the time in overevaluation of tons of ore. Solutions based on examination of Past production data exist14 but it would be necessary to have a solution which can be applied before production starts as the preceeding problem also results in an overestimation of the total reserves, often by as much as 20%, thus changing the mine life accordingly and destroying any "optimum planning" which could have been done. The proposed alternative is to forecast the grade distribution of small blocks in a larger block, sufficiently well documented. Several Possible ways to estimate these distributions are reviewed and emphasis is placed on recently developed methods (source G. Matheron) where the coefficients of the orthogonal polynomial series expansion of the distribution of any size of block are directly estimated by kriging. The efficiency of the technique is tested on a level of the Cyprus Pima open pit where the predicted recovery is compared to actual production figures.

Jan 1, 1980

By Neil H. Bostick

A specialized electronic data system processes data taken from normal gologic maps and stratigraphic tables to yield predictions of uranium resource location for an area such as much of the United States. Strata underlying specific quadrangle cells of the earth are evaluated for uranium favorability on the basis of selected criteria of lithology, structure, and stratigraphy but not specific past production in the area. Stored data are computer processed to yield volume of likely host rock beneath each cell to a given depth and at a given favorobility level. Results are plotted by machine directly as maps. A specialized and simplified procedure for predicting approximate uranium resources has been devised at Stanford Research Institute (SRI). The prediction is based on general geology beneath specific area cells of the earth in order to provide complete volume coverage; the strata underlying these areas are evaluated for uranium mineral favorability on the basis of a few selected geologic criteria in order to allow rapid data input. In order that the predictions be generally applicable, they are based on geological factors only, not past ore production of a given cell. Since the bulk of U.S. resources are in elastic host rocks, only such strata are considered in this work. This paper describes the structure and some details of the resource system and how it was tested in an area of the western United States.

Jan 1, 1971

By L. G. Austin, P. T. Luckie, R. R. Klimpel

Application of the Charles and Bond Laws to batch grinding can be deduced as a special case of solution of the first-order batch grinding equation. With additional limitations on the feed size distribution, this special case also gives Rosin-Rammler distributions of constant slope, with the 36.79% retained point a simple function of time. In general, the assumptions concerning the breakage parameters S and B which are necessary to get Charles' and Bond's laws, are not valid except as a crude approximation. With less restrictive assumptions, it is still possible to get approximate Rosin-Rammler distributions, but the slopes change with time of grinding, and the 36.79% retained point is a more complicated function of time. An alternative form to Charles' law is suggested, which accomplishes the same result and has the same errors, but avoids the use of energy of grinding and deals with specific rate of grinding.

Jan 1, 1973

By Alvin W. Schillinger

During the past ten years, the Calumet Div. of Calumet & Hecla, Inc. has conducted extensive exploration and mining in the footwall of the Osceola amygdaloid lode in the native copper district in Michigan's Upper Peninsula. In an attempt to delineate more clearly the extent and nature of high-grade footwall copper mineralization, 876 diamond drill and long steel holes aggregating slightly more than 47,000 ft have thus far been drilled from the accessible hanging-wall workings. Early in this program it became obvious, through inspection of footwall workings in progress, that due to the erratic and bunchy occurrence of the native copper in the footwall zone, the exploration drilling was failing to outline completely the extent of the oreshoots. Early drilling results indicated isolated pockets of ore whereas in actual practice the footwall was found to be fairly thoroughly mineralized in shoots within the ore zone. Based on drill results only, the "success factor" (discovery ratio) was only 34%.

Jan 11, 1964

By P. Greenfield, P. A. Beck

RECENT work by J. Darby, Jr. in this laboratory has shown that the reported vanadium-rich limit of the s phase in the Co-V system at 1200°C is in error. The appearance of a second phase in s actually is restricted to alloys containing over 68 atomic pct V. The error in the original value is due apparently to a reaction that takes place along the numerous cracks in the s specimens between the alloy and the impurities present in the He + 8 pct H atmosphere in the annealing furnace. Such a reaction and the consequent appearance of a second phase can be suppressed if the alloys are sealed under vacuum in Vycor tubing. The new value of 68 atomic pct V for the vana-dium-rich limit of the s phase in the Co-V system effects slightly the s compositions calculated from average values of N, and N,. for various s phases. The standard deviation between experimental mean compositions and those calculated from the assumption that s is characterized by a constant number of 3d + 4s electrons per atom (N,), is slightly reduced from 9.1 to 8.8 pct. The maximum divergence for the V-Mn s phase is reduced from 15.5 to 14 atomic pct. The standard deviation calculated from constant electron vacancy numbers given by N.. = 4.66 (Mo + Cr + V) + 3.2 (Mn) + 2.2(Fe) + 1.71(Co) + 1.6(Ni) is now greatly reduced, as the maximum divergence for this correlation previously occurred in the V-Co system. This maximum divergence is reduced from 7.6 to 2.3 pct, and the standard deviation for all s- phases is reduced from 4.1 to only 2.9 pct. The correlation for electron vacancy numbers given by N. 5.66 (V when with Ni or Co) + 4.88 (V when with Mn or Fe) + 4.66 (Cr + Mn) + 3.3 (Mn) + 2.66 (Fe) + 1.71 (Co) + 0.61 (Ni) is made slightly worse, and the standard deviation increases from 2.8 to 3.9 pct. These changes, however, do not affect the conclusions of the paper.' The deviation between calculated and experimental s compositions is much less for either one of the electron vacancy correlations than for the correlation with the number of 3d + 4s electrons.

Jan 1, 1955

By S. M. Marshall, A. C. Richardson, H. Y. Yancey

A year ago, Marshall and Bird presented a paper in which a new method of measuring the agglutinating power of coal was described.' The procedure used was to determine the strength of a button containing 10 parts sand and one part coal, formed by carbonizing the mixture in a crucible in an electric furnace. The result of the determination was reported as the total weight in grams required to bring about complete destruction of the button. Correlations were shown between the agglutinating value and some of the characteristics of the different coals that were investigated. This agglutinating test has been in use fairly continuously during the past five years for coals of widely differing coking qualities, and it has shown reasonably concordant results accurate enough for commercial use, although there are many features of the test which should have further scientific study. During the past year a study has been made of some coals of low coking strengths, and incidental to the main investigation some data which appear to be of interest and value were obtained on the loss in agglutinating power caused by exposure to the air. Three coals were investigated, all of which were of the Tertiary age; two were from one field in Asia, and one from a field in the United States. The three were similar, as shown by the proximate and ultimate analyses in Table 1 (moisture-free basis). Coals SA and RA generally contain about 5 per cent. moisture and coal P about 3.5 per cent. moisture on the as-received basis. The large difference in the ash contents of the coals, amounting to practically 10 per cent. between SA and RA, and P, makes difficult a direct comparison of their qualities. In the second section of Table 1 the figures have been put upon an ash-free basis., This table shows that these coals are closely alike. The ultimate analyses are almost identical except for the higher nitrogen content of

Jan 1, 1930

By Carl Beal

IN February, 1918, the conclusion was published by Lewis and Beal1 "that wells of equal output on the average will produce equal amounts of oil in the future, regardless of the ages of the wells." This conclusion was based upon the study of data collected principally in Oklahoma and was not known at that time to be true for other oil fields. An abundance of statistical proof was later, collected by the senior author of the present paper, which showed that the conclusion was undoubtedly well founded and that it applied to other fields as well. Accordingly, it was later restated2 as the "law of equal expectations" as follows: "If two wells under similar conditions .produce equal amounts during any given year, the amounts they will produce thereafter, on the average, will be approximately equal, regardless of their relative ages." Although only scanty data from the California oil fields were available at the time this publication was prepared, sufficient information was analyzed upon which to base the insert on Fig. 80, which showed beyond a doubt that the law held at least for a part of the Midway oil field in California. Recently the authors have collected more complete data in California, and it is the purpose of this paper to explain the method used in demonstrating the truth of the law and, in addition, to give several methods by which curves constructed in accordance with this law can be used in a practical way with ease and accuracy.

Jan 8, 1919

By W. A. Boyer

If the safety factor of a mine hoisting rope is checked for the lowest depth, is the rope then safe for all levels? The answer here is no. A new set of volues is proposed. HOISTS for metal mines are seldom designed for one particular depth. They are intended for an ultimate load and depth with a given speed but are first used to hoist from a shallower depth, gradually working to the ultimate as development progresses. Sometimes the mine is not worked on the upper levels because of the kind and grade of ore, the mining of which depends on market conditions. In this case the hoist may be used in the same working shift to lift ore, for example, from the 1200 and the 4400-ft level. This means that the safety factor of the rope should be considered not only when it hoists from the greatest depth, but also when it hoists from the upper levels. According to present safety factor standards, a hoisting rope can have ample safety margin when hoisting from the lower or lowest level and still be shy of sufficient safety margin when hoisting from the upper levels. This will be shown by curves presented in this paper. The safety factor of a hoisting rope as defined by the U. S. Bureau of Mines' is the ratio of the static load to the tensile strength of the rope. It is calculated by dividing the breaking strength of the rope* In Fig. 1 curves A and B are plotted against the vertical suspended distance, which is the abscissa, and the factor of safety, the ordinates. Curve C is a smooth curve drawn through the midpoints of the steps of curve A and would more closely represent the minimum factor of safety for new rope for any particular depth. Curve D is a smooth curve drawn through the midpoints of the steps of Curve B and would more closely represent the minimum factor of safety when ropes should be discarded for any particular depth. If a new rope were applied with a minimum factor of safety, then the vertical distance or ordinate under curve D for any particular depth, divided by the vertical distance or ordinate under curve C, would represent the minimum percent of remaining area intact that could be allowed before the rope would be discarded. Also, that section of the ordinate between curve C and curve D is proportional to the section of the area of the new rope that could be allowed for wear and broken wires. Considering that point at 2500 ft on the chart, the ratio do to co would be the minimum percent of rope area remaining at the point of discard. The ratio of that portion of the ordinate cd to co would represent maximum percent of area of a new rope available for wear and broken wires.

Jan 1, 1955

By Bruce T. Stanley

The concepts of ore reserve estimation at the Henderson mine are reviewed presenting a geostatistical approach and procedure as applied. Specific problems encountered are recapped and explained as to the nature and resolution thereof. The methodology and results are shown, along with an approximation of computer usage and capacities needed. The scope of the paper is to set forth an example of actual application, usage, and benefits realized from such a procedure. Local Conditions The Henderson molybdenite deposit is located in central Colorado about 69 kilometers west of Denver. The geology consists of a classic subvolcanic ryolite porphyry sequence with quartz-molybdenite mineralization occurring in an extensively fractured granite stock complex. Being assymetric and bilobate in section, the orebody measures approximately 300 meters thick and 600 meters by 1200 meters in plan. The orebody is sampled by means of underground drill holes which create an east-west fan pattern spaced roughly 60 meters apart in the north-south direction. Approximately 27,000 meters of drill hole assayed on 3.04-meter intervals were available for analysis. Recovery on the core is about 95 to 100 percent, thereby affording us with reliable data all prepared to the same standards.

Jan 1, 1977

By Robert Stefanko

Roof bolting in coal mines has progressed very rapidly in the last decade, and today this method of support is in general use. There are many theories concerning the functions of roof bolts, but the importance of beam building is indisputable. Proper tension in the bolts minimizes shearing along bedding planes and creates a thick, competent beam from individually weak layers. Bolting must be accomplished immediately upon exposure of the roof, and bolt tension must be maintained if roof failure is to be prevented. Seams are being mined today with roof bolt support where conventional timbering was not effective1. The widespread use of continuous mining equipment was made possible by roof bolts which permit long supported spans free of obstructions.2 Since adequate anchorage is the key to successful bolting, better methods for determining the efficiency of anchorage are continually being sought. Attempts have been made to measure bolt loads, thus assessing anchorage efficiency by employing sensing devices between the bolt head and roof. 3,4,5 None of the techniques appears to be very accurate, and all have at least one serious deficiency.

Jan 5, 1962

By R. R. Goddard

By use of the frequency response method with a radioactive tracer, it was possible to determine fluid dispersion and distribution in a natural consolidated and an unconsolidated medium. Measurements were made in a linear flow system at oleic saturations of 69 per cent in the consolidated medium, and 100 per cent in both media. Dispersion and distribution were obtained by measuring the amplitude attenuation and the phase velocity of sinusoidal waves with a dual monitor apparatus. The gamma ray emissions permitted in situ measurements at any distance along the porous samples. One result of importance was that the effective diffusivity increased as the wave length increased. As a consequence, a dispersion coefficient appropriate for the injection of large slugs might exceed the value measured by use of small slugs. Since flow models based solely on fluid velocity and an effective diffusivity coefficient imply that the diffusivity should be independent of frequency, such representations were not adequate for the data of this study. A comparison was made with a capacitance model of porous media with deadend PVs, but even this model was not completely adequate. By using attenuation and phase velocity data, fluid dispersion can be predicted without postulating a differential equation satisfied by the tracer concentration, thereby eliminating the need of a complicated model to represent dispersion. INTRODUCTION The flow of similar miscible fluids through a porous medium can be fairly adequately described by two parameters: the average fluid velocity and the effective diffusivity.1-3 It has been pointed out recently, however, that significant discrepancies exist between this representation and the experimental data.4-7 An improved agreement can be obtained by introducing additional parameters based on the concept of dead-end pores. The purpose of the present investigation was to find out whether the frequency response method could be used to measure the relevant parameters. The method was used in the following form. A stream of fluid was flowed at a constant rate through a sample of porous material and the concentration of a radioactive tracer in the fluid was varied sinusoidally at a fixed frequency. The effects of flow through a porous medium are a decrease in the amplitude of the concentration wave and an increase in the velocity of the peaks of the waves above the average velocity. Attenuation and phase veIocity of the waves were measured as a function of frequency and fluid velocity. The simple two-parameter model implies that the diffusivity should be independent of frequency. Data reported in this paper show that the diffusivity decreases as the frequency increases. Hence, as shown also by many others, the two-parameter model is not completely adequate. Coats and Smith 5 used two additional parameters in their model: the volume of the dead-end pores and the rate of mass transfer between dead-end pores and the flowing stream. Their capacitance model of a porous medium containing some stagnant fluid, to which transfer occurs by molecular diffusion, did not explain the dispersion results of either the present study or of theirs. Instead, the capacitance effect can be better described as the result of extreme velocity variations within the pores of the medium, with transfer between the velocity zones by convection. EXPERIMENTAL PREPARATION OF POROUS MEDIA Data reported here were obtained with a natural Berea sandstone, and with two packings of 20/25 mesh sand. Pertinent information about these media is listed in Table 1. The sandstone core was first sealed with a non-

Jan 1, 1967

By R. E. Shinkosk

This paper outlines the development of a program for increasing the life of woolen bags used for filtering Dwight-Lloyd gases by treating the bags and gases with hydrated lime. Methods and apparatus are described for determining alkalinity of dusts, acidity and breaking strength of bag cloth. Procedure and results, based on several years of operation, are presented. DURING 1939, additional facilities were constructed in the Dwight-Lloyd Blast Furnace and Baghouse departments at the Selby, California, Plant of the American Smelting and Refining Co. In order to handle adequately the increased volume of gases from the resultant increase in production, it was necessary to increase gradually the amount of water used for cooling gases ahead of the sinter machine baghouse. As a result of this increased water cooling, the average bag life dropped from 27 months in 1939 to 14 months in 1941. (Table I). This drop in life meant an increased. bag cost, as well as lower recovery of dust and some curtailment of operation. During 1941, it was found new bags showed as high as 0.3 pct acidity* after two weeks of opera- tion and as much as 2.0 pct acidity after some months of operation. This high acidity was present in spite of the fact that free oxide or relative alkalinity of the unburned dust ran from 5 to 6 pct. In view of these circumstances, a twofold program was started in Nov. 1941.t Part one of this program consisted of vigorously dipping all new bags in a weak lime solution, containing 50 lb of hydrated lime per 50 gal of water. Part two consisted of feeding fine, dry, hydrated lime into the gas stream intake of the sinter baghouse fan. Apparatus for feeding this lime is shown in fig. 1. All baghouse chambers are shaken in rotation about once each hour. On alternate hours, the baghouse operator places 50 lb of hydrated lime (one sack) into the lime feeder, starts feeder and immediately starts the bag shaking machinery. The rate at which lime is fed is set to coincide with the approximate time necessary to shake all sinter bag-house chambers, or about 15 min. It is felt this method of lime addition is most effective for getting lime into the woolen bag fabric. The amount of lime so fed averages about 600 lb per day. The amount of lime fed per day is varied to keep a minimum relative alkalinity of 9 pct in the unburned sinter dust. A daily dust sample is taken for alkalinity by allowing dust to accumulate in a sample pipe over a 24-hr period. This sample pipe, placed in any chamber cellar, is 2 in. in diam, 4 ft long, is sealed on the inner end, and capped on the outer end. It has a 1/2 in. slot cut for 18 in. along the tip end. This slot faces upward and allows the pipe to fill gradually with dust as bags are shaken. Breaking strength of bags has, in most cases, been the deciding factor in bag replacement. Bags that normally test 100 psi breaking strength when new are replaced when they test under 35 lb. The method for determining breaking strength is shown in the description accompanying fig. 2. Since the start of the liming program in 1941, bag life has increased from 14 months to an average of over 23 months, with a consequent material decrease in bag cost per year. Acidity, as per cent sulphuric acid, may be determined by means of a Beckman pH meter as follows: From a piece of bag cloth. which has been thoroughly cleaned of dust, a 5 g sample is weighed on a balance. Cut the sample into fine pieces and place in a 400 cc beaker. Add 100 cc (measured) of distilled water and stir vigorously. Filter on suction funnel, holding cloth pulp in beaker with a stirring rod. Wash cloth sample and filter wash water four additional times, each time with 20 cc distilled water, the last time squeezing cloth pulp over funnel. Discard pulp and rinse funnel and filter paper. Pour wash solution jnto measuring graduate and make up to exactly 300 cc with distilled water. Place into clean 600 cc beaker and measure the pH on meter. The per cent acid in bag cloth is read from the following table:—

Jan 1, 1951

By S. Skowronski

OvErpolEd copper, as commonly defined,- is copper which has been excessively reduced during the poling period of the refining process. Owing to its porosity, such coppcr is unfit for commercial purposes. The cause of this phenomenon is undoubtedly the lack of oxides in the copper, yet this does not completely explain it. Refined copper of the same "pitch" and "set" varies considerably in oxygen contents, and analyses of overpoled bars also show similar wide differences; moreover, it is possible to melt copper in 'crucibles so as to obtain bars that are practically free from oxygen although they show a "tough pitch" and "level set" surface. Frederick Johnson advances the following theory: The regulation of the quantity of oxygen in copper is the keynote of all copper refining. It is the presence of a well defined proportion of oxygen in the form of cuprous oxide, forming a copper-cuprous oxide eutectic, which enablcs copper to be cast free from blowholes. It seems that when oxygen is present, other gases are less soluble in molten copper; when oxygen is absent, or is present in insufficient quantity, the copper dissolves other gases, such as hydrogen and carbon monoxide, which are insoluble in the copper when solid, and, being rejected during the process of solidification, causes internal porosity and external ridges and excrescences.1 The "level set" of wire bars, etc., is entirely the result of a compromise between the occluded gases and cuprous oxide. With excess of the former the metal would be "overpitch" and spongy, while an excess of the latter would result in the metal being "underpitch" and brittle.2 The result of the absorption and subsequent expulsion of reducing gases, carbon monoxide and hydrogen,' and the effect of this action on the overpoling of copper are in dispute; the literature on the subject is full of contradictory statements and will continue to be so until better analytical methods have been developed. Sulfur, however, is tangible. The refiner can see it in his button sample and consequently attributes to it any trouble that may happen during the melting of the copper.

Jan 1, 1919

By Frank Reiber

The study of earthquakes long ago developed the fact that by study-ing the travel .times of the various groups of waves from the same earthquake, as received on seismographs :it varying distances, major discont'inuities in the earth's crust, could be reasonably well defined. Using this original discovery, and adapting the mathematical methods originally devised in seismology for determining the depth below the surface at which such discontinuities occur, other investigators were able to develop a new branch of seismology which promises to be extremely useful in extending the boundaries of our information on local conditions Below the earth's surface. As an outstanding example of the applications of this work, we have the so-called " seismograph " exploration of the Gulf Coastal region, which has resulted in the discovery of a large number of salt domes, from many of which oil fields may be developed. The original seismological investigations, from which different major discontinuities in the earth's crust were deduced, as well as these later successful experiments in locating salt-dome structures, involve relatively simple problems. In each case we arc dealing with surface materials in which elastic waves will be propagated with a fairly definite velocity. Under this material we have something quite different', in which the elastic waves will be propagated with a much higher velocity. The transition from one medium to the other is likewise relativtly abrupt. For example, in the Gulf Coastal region the sedimentary formations have a velocity of 6000 or 7000 ft. per sec., while the velocity of elastic waves in the cap rock of a salt dome may exceed 15,000 ft. per sec. Under such conditions, delineation of the formation is a relatively simple matter, and, furthermore, there is very little opportunity for ambiguous results. Development of Elastic-wave Method The success of this Gulf Coast work immediately suggested the advisability of attempting to extend elastic-wave methods to a point

Jan 1, 1929