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By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By R. Maddi, I. R. Kramer

C. S. Roberts (Dow Chemical Co., Midland, Mich.)— In this study we have seen another example of how modern electronic instrumentation can be of great value to metallurgical research. The authors have shown much ingenuity in their experimental work. However, I wish to point out that anelasticity theory tells us that we must be cautious when we use pulse methods for measurements which are to be correlated with knowledge of static stress-strain behavior. The basic stress calibrations used by the authors depend on the use of static moduli combined with the pulsed strains. No recognition of a possible modulus defect has been indicated. The general agreement of critical resolved shear stresses may indicate that a

Jan 1, 1953

BEFORE an audience which included many notable members of the engineering profession, the John Fritz Medal was presented to Senator Guglielmo Marconi on July 6, 1922, in the auditorium of the Engineering Societies Building, in New York. The medal was awarded for achievements in the development of wireless telegraphy, but all of the speakers emphasized the inventor's service to mankind, in saving life at sea, especially, as well as his remarkable scientific attainments. SIGNIFICANCE OF THE JOHN FRITZ MEDAL The John Fritz Medal is presented from time to time for notable achievements in applied science, as a memorial to the engineer and metallurgist whose name it bears, one of the charter members of the American Institute of Mining and Metallurgical Engineers. The medal fund, contributed by friends of Mr. Fritz, is administered by representatives of the four national engineering societies. Seventeen awards have been made to men of eminent distinction in the various branches of the profession of engineering, whose names are more familiar to the civilized world than are the names of most of the presidents of the United States. Four of the medallists were present on the evening of July 6: Dr. Elihu Thomson, the dean of the electrical engineers, General Goethals, Orville Wright, and J: Waldo Smith, who developed the New York City water supply, system. In opening the meeting, Dr. Comfort A. Adams, president of the Board of Award, said in part: The profession of engineering knows no national boundaries. That the engineers of this country sense this fact deeply is evi-denced by the absence of any limitations as to nationality in the award of the John Fritz Medal. The engineer is seeking for the truth wherever it may be found, and it frequently happens that the most helpful sugges-tions for the solution of a particular problem are the results of the work of men of other nationalities on the other side of the world, whom we have never seen. Thus through this long range interchange of information and of ideas, there has grown up a feeling of real kinship among the engineers of the civilized world, a sense of interdependence and of the need and value of cooperation, in wide contrast with the all too prevalent sense of conflicting interests, of racial and national antagonisms of bitterness and misunderstanding. We often think of the nations of the earth as separated by walls or barriers, of various kinds and of various heights. Some of these are the natural results of evolution, for example, differences of language, customs and traditions; while others are more artificial, being maintained by law and dictated by fear, greed, and shortsightedness or ignorance. There is deep conviction that the degree in which we can abolish these barriers is a true measure of our progress towards real civilization, and that the destruction of these barriers is the only method of attaining that world-wide peace for which every

Jan 8, 1922

Frank Williams, Johnstown, Pa. (Communicatioll to the Secretary): As the manager of the company which manufactured the " American " magnesite and the silica-brick mentioned by Mr. Pennock, I beg to say that he was quite right in placing a mark of interrogation after " American " (page 268). While the users of magnesite in this country are at a disadvantage as to cost by reason of not having any large bodies of sufficiently pure material at hand, the manufacturing concern referred to has secured an advantage as to quality by a mixture of the different foreign magnesites, which vary considerably in their composition and physical structure. The American (?) magilesite tested was a sample of the next

Jan 1, 1897

INTRODUCTION Engineering studies of many near surface coal deposits that are amenable to strip mining can be enhanced and expedited by the application of computer techniques for defining coal reserves and overburden and intraburden yardage and their stripping ratios. The case study discussed herein could be from the western coalfields of Colorado, Wyoming, or Montana; the lignite deposits of the Dakotas or Texas, or from the strippable coal seams of the midwest. Because the techniques can be applied so universally, the actual map locations are not identified. The same computing principles apply to one seam or multiseam deposits, and the capability of the computing programs and plotting routines to display the coal seams in plan and sections provide excellent base maps for further engineering planning and mine layout studies. MANAGEMENT OF DRILL HOLE DATA Drilling for coalfield information is usually done at much wider centers than for other mineral deposits. The geologic logs of the holes are generally quite simple, and frequently record only major lithologies and depths to the top and bottom of the coal seams, together with hole collar survey information. A header card is prepared for each drill hole showing: Hole ID Northing Fasting Elevation Azimuth Dip The header card can be followed by any number of downhole lithologic intercept records: [Hole Depth Lithology Hole ID From-To Coal] Less data errors occur if the computer cards are punched directly from drill hole logs, thus eliminating opportunities for mistakes in transcribing data. All arithmetic manipulations should be left to the computer to avoid as much human error as possible. The SURVEY program is run over the raw data file and all lithologic intercepts are computed and defined in XYZ space. BOUNDARY SURFACES-COAL SEAMS AND LITHOLOGIC UNITS The most useful computer program for defining coal seams in 3D space is a linear inter-

Jan 1, 1980

By W. B. Watson

IN the USSR considerable technical improvements have been made in hydraulic methods of mining coal. In New Zealand coal mining by these methods is still comparatively crude. The Russian techniques are closely studied in New Zealand, and this description is based mainly on translations of technical articles. Fundamentally the methods in both countries are the same-chief developments in the USSR are the use of high pressure water jets, capable of winning all but the hardest coal without prior blasting, and hydraulic pipeline transportation where the gradient is unsuitable for flume transport.

Jan 4, 1958

By W. A. Schaeffer, M. Albertson

The Yates field is situated in northeastern Pecos County, Texas. Its productive area is about 15,000 acres. Production is chiefly from limestone of Permian age. Depths of wells vary from 1100 to 1800 ft. Initial productions range from a few barrels to 8000 bbl. per hour. The field outlet has always been prorated. Gas-oil ratios originally varied from less than 100 cu. ft. up to 8000 cu. ft. per barrel at allowable production rates. The average ratio was about 500 cu. ft. Fig. 1 shows the structure of the field and the location of the Tippett lease, on which the original experimental tubing work was done. Before the latter part of the year 1929, little actual effort in practice had been given to determination of the conditions under which the highest efficiencies may be realized in naturally flowing wells. For the preceding few years attention had been given to gas-oil ratios and their possible reduction by maintenance of back-pressure by choking at the well head. Some attempts had been made toward reduction of ratio by bottom-hole choking. In late 1929, the Shell Petroleum Corp. started the experimental installation of specially designed flow columns adapted to high-pressure flowing conditions in the Yates field. The objectives in view were the attainment of low gas-oil ratios at low rates of flow and the maintenance of high bottom-hole pressures. All naturally flowing wells should be provided with a suitable eductor string immediately upon completion of the well, so that the benefits of efficient flow will be derived from the beginning. This paper presents a method of tubing for efficient flow and a discussion of some complex factors which influence well behavior. Factors Influencing Gas-oil Ratios Many factors influence the production of gas from naturally flowing wells. The writers believe that in some instances gas control is effected mainly in the reservoir itself, in others in the well bore, and in still others both sets of factors may be significant. Some wells apparently have penetrated productive zones in which practically all of the gas is closely associated with, and mostly dissolved

Jan 1, 1932

By H. R. Hanley, C. Y. Clayton

One of the most important contributions to the art of electrolytic zinc production has been the aluminum cathode. This has been used in all major production since its commercial developmerit in 1916. The literature is replete with important contributions, some of which may have been replaced by better ones, but thus far there appears no other metal to take the place of aluminum as cathode material. Credit for this innovation goes to Sherard Cowper Coles, of England. When experimenting on the extraction of zinc from Broken Hill ore at Hayle, Cornwall, in 1893, he introduced the aluminum cathode, and in 1895 obtained . British Patent No. 20073. The reason for this dominant position of aluminum as cathode material in zinc sulphate electrolytes is its unique surface, to which electro-deposited metals usually do not tightly adhere. The metal must be of high purity for best results. It is possible to develop a starting-sheet method by which thin electro-deposited sheets of cathode zinc are made and stripped from a smooth aluminum plate. Such thin sheets of cathode zinc may be used as are the copper sheets in standard electrolytic copper-refinery practice. However, complications arise because of extreme warping of the zinc starting sheet after a few hours of deposition, and thus special arrangements must be made to compensate for this abnormality. Reasons advanced for the ease with which deposits may be stripped from the aluminum surface are: (1) presence of a permanent oxide coating on the metal, (2) failure of aluminum to alloy with the deposit, (3) differences in coefficient of expansion, (4) high position of aluminum in the electromotive series of metals. Of these reasons for nonadherence, which may have some application in general deposition, probably the oxide coating has the greatest bearing on the subject of zinc deposition. Adherence of zinc deposits has occasionally had serious effect on tonnage and production costs. Opinions have differed as to the specific

Jan 1, 1944

By N. A. Ziegler

THE present publication is a continuation of the work on gas analysis, described in a paper presented before the Institute of Metals Division a year ago.1 While that paper was largely descriptive in character, dealing with the various parts of the apparatus and method of operations, the present one gives numerical data obtained as a result of a series of experiments with iron-carbon alloys. The apparatus and the methods applied are essentially the same as previously described, changes being only in minor details. Attention should be called to the fact that in the present work we are dealing with the gaseous mixtures obtained as a result of vacuum melting of various ferrous alloys. It should be understood that when the terms "degasified sample" and "products of degasification" are used, they refer to the sample remaining after the vacuum fusion of the alloy and the gaseous products removed therefrom, respectively. The writer does not wish to create the impression that the metallic products of this process are absolutely free from any gaseous elements, nor that the gases obtained are present as such in the original sample. These two points are not yet definitely known and are subjects for future investigation. The point, however, which has been established beyond doubt, is that all the gases dealt with come from the metallic charge and are present either in the charge as such, or are produced as a result of chemical reactions going on within the charge. The suggestion that the gases are due to the reactions between the metallic charge and the refractory materials has no valid basis.

Jan 1, 1929

By John Dasher, M. C. Chang

The Crucible mine in Pennsylvania, operating on Pittsburgh seam coal, is rated at 5000 tpd. The washing plant, built in 1943, is rated at about 400 tph, using hydroseparator boxes to wash the coarse coal (4 x 5/16 in.) and hydrotator units for the fine coal (5/16 x 0). It is generally acknowledged that gravity concentration equipment cannot be used efficiently to beneficiate coal finer than about 65 mesh. Before the present flotation circuit was installed, Crucible recovered its fine coal slurry, predominantly -24 mesh material, by passing it through a battery of five 14-in. and one hundred and ten 3-in. Hey1 & Patterson cyclones in parallel with a 75-ft Dorr thickener. About two thirds went to the cyclones and one third to the thickener. Underflows from cyclones and thickener were filtered, respectively, in one 12-disk Eimco and two 4-disk Oliver filters fitted with stainless steel cloth. The resulting cakes were added to the coarse metallurgical coal. The filtrates, overflow from the 3-in. cyclones, and thickener overflow were recycled to the coarse coal plant.

Jan 3, 1959

By Gen-Hua Shi, William Boyle, Richard E. Goodman

This keynote paper calls attention to two critically important issues relating to selecting supports for excavations in hard rock. The first is the proportion of the ultimate sliding volume that needs to be stabilized by the support system. Some excavations can be imagined to liberate very large rock volumes, whose weight can not be assigned to supports without severe economic penalty. Using the keyblock principle, it is argued that only the most critically oriented and finite blocks right on the periphery of the opening have to be supported; if these are retained by the support system, or by self resistance due to friction on the sliding faces, then the blocks behind will remain in place. As all concepts, this one has bounds and limits. Since the keyblock analysis for rock engineering is very new, these limits are not yet understood ... The second issue is the degree to which possibly stabilizing forces associated with the in-situ stress field ought to be accepted as support for potential keyblocks. It is shown that the initial stress can be effective in stabilizing rock wedges whose faces are nearly perpendicular to the excavation surface. It is too early to decide this issue but important to consider it.

Jan 1, 1982

Jan 1, 1932

By C. E. Reinhard

A useful accelerated weathering test should be capable of placing any series of metals quantitatively in the same order of endurance as that noted under a particular set of actual exposure conditions. The development of such a test must necessarily depend to a considerable extent upon data obtained from a wide variety of exposures. This paper offers preliminary data from exposure tests on nine metals placed in 11 locations in the Lehigh Valley, within a radius of 20 miles from Palmerton. The exposure conditions vary from a severe industrial atmosphere to a pure rural atmosphere. The data are offered as evidence of the necessity for the identification and evaluation of the variables of corrosion and as illustration of some of the variations to be considered in the development of a useful accelerated test. It is quite clear, from this evidence, that a useful accelerated test must be versatile to the extent of showing the probable variations of corrosion resulting from differences in atmosphere as well as from differences in the metals. The paper is presented solely with the object of pointing out the wide variations in relative merits of several common metals in resisting corrosion and without any thought of initiating controversy regarding the merits of particular metals. For this reason the metals are designated only by symbols in the tables and no key is given to these symbols. Test Procedure Specimens, 4 by 6 in., were cut to accurate dimensions from each of the following metals or alloys: aluminum, ascoloy, copper, copper steel, galvanized iron, and zinc. Additional grades of these metals bring the total to nine types. Since it was impossible to obtain the required number of copper-steel specimens having equal surface conditions of rust and scale, it was thought advisable to pickle these specimens in a hot solution of 10 per cent. sulfuric acid. All other specimens were carefully cleaned in ether and alcohol and weighed just prior to exposure. Four specimens of each type of metal were mounted on a test rack by means of porcelain insulators. The racks were so constructed that

Jan 1, 1929

By C. E. Reinhard

A useful accelerated weathering test should be capable of placing any series of metals quantitatively in the same order of endurance as that noted under a particular set of actual exposure conditions. The development of such a test must necessarily depend to a considerable extent upon data obtained from a wide variety of exposures. This paper offers preliminary data from exposure tests on nine metals placed in 11 locations in the Lehigh Valley, within a radius of 20 miles from Palmerton. The exposure conditions vary from a severe industrial atmosphere to a pure rural atmosphere. The data are offered as evidence of the necessity for the identification and evaluation of the variables of corrosion and as illustration of some of the variations to be considered in the development of a useful accelerated test. It is quite clear, from this evidence, that a useful accelerated test must be versatile to the extent of showing the probable variations of corrosion resulting from differences in atmosphere as well as from differences in the metals. The paper is presented solely with the object of pointing out the wide variations in relative merits of several common metals in resisting corrosion and without any thought of initiating controversy regarding the merits of particular metals. For this reason the metals are designated only by symbols in the tables and no key is given to these symbols. Test Procedure Specimens, 4 by 6 in., were cut to accurate dimensions from each of the following metals or alloys: aluminum, ascoloy, copper, copper steel, galvanized iron, and zinc. Additional grades of these metals bring the total to nine types. Since it was impossible to obtain the required number of copper-steel specimens having equal surface conditions of rust and scale, it was thought advisable to pickle these specimens in a hot solution of 10 per cent. sulfuric acid. All other specimens were carefully cleaned in ether and alcohol and weighed just prior to exposure. Four specimens of each type of metal were mounted on a test rack by means of porcelain insulators. The racks were so constructed that

Jan 1, 1929

By H. W. Johnson

DURING part of the year 1932, conditions at the plant of the Inland Steel Co. made possible the collection of data on two of the variables of blast-furnace operation, between which we observed an interesting correlation. The variation in percentage of coke ash in the coke seemed to be reflected in the variations in percentage of silicon and sulfur present in the iron. This subject is of particular interest during this period of low production because of its effect on quality and cost of pig iron. The consumers of pig iron are now more exacting in their requirements. Formerly 0.050 per cent sulfur was considered satisfactory; now many foundries and steel plants insist on iron under 0.030 per cent sulfur and expect it to average 0.025 per cent sulfur. To attempt to produce iron so low in sulfur and still have reasonably good furnace operation means that everything possible must be done to minimize all variations. This subject is also directly connected with the cost of producing iron. A blast furnace operates most economically and efficiently in rather narrow limits and so any variable that has range enough to disturb regular operation must be moderated. The importance of regularity is accepted and the methods followed to eliminate variations in materials such as coke and iron ore are recognized as indispensable. Uniformity of Ore and Variations in Coke Ash The delivering of uniform cargoes of well mixed ore to the blast furnace involves much handling and expense, but it is accepted that the trouble and expenditure are justified. After the ore reaches the dock, further mixing is assured by spreading ore in thin layers, preventing segregation by keeping piles level, variations in digging, and the use of several bins for one ore. And finally, the fact that the furnace burden generally contains three or more ores, together with several miscellaneous materials, eliminates the possibility of ill effects due to variations in any one. Thus, much effort is made to insure a uniform ore. But a variation in the percentage of silicon in ore is less detrimental than a variation in the percentage of ash in coke. The former affects

Jan 1, 1933

By Dennis V. D’Andrea, Robert C. Steckley, William C. Larson, Richard A. Dick

A fragmentation experiment was performed in cooperation with Duval Corporation in a porphyry copper molybdenum deposit near the Sierrita pit south of Tucson, Ariz. A 10-hole test blast was detonated to establish relationships between blasthole spacing and the resulting fragmentation. Blastholes were 9 in. in diameter and 110 ft deep. The 10 blastholes contained a total of 17,400 lb of aluminized slurry blasting agent in 50-ft columns with 60 ft of stemming. Blasthole spacings of 25, 20, and 15 ft were tested. Diamond drill core examination was the primary method used to determine the condition of the rock before and after blasting. Topographic surveys were used to measure the rock swell produced by the blast and a fragment size distribution was obtained for the rubblized material on the surface. The rubble zone at the surface was ideal for in situ leaching. Fragmentation to depths of 110 ft was excellent from the 15- to 20-ft blasthole spacing patterns. Good breakage was also produced by the 25-ft pattern although the effects of the blast were not as obvious. In situ leaching tests were not conducted. However, based on size consideration only, all three blasting patterns produced adequate breakage for successful leaching.

Jan 1, 1974

Jan 1, 1916

By W. A. West

ONE who attempts to collect and classify equilibrium data from various iron-alloy systems is soon struck with the absence of any quantitative theory that can serve as a general background against which to compare and contrast results from different systems, at different temperatures, and with different concentrations. It is not necessary to wait for a perfect theory; investigation of divergences of theory from observation may prove of great value in acquiring understanding of the subject. For example, one has only to think of Raoult's law as applied to aqueous solutions. The equations developed by Zener1 represent an effort to provide such a quantitative theoretical background, and it is therefore desirable to subject this theory to such tests as can be applied. The present article is intended to be an application of available tests, and may thus be considered as a supplement to Zener's paper. It is assumed that this paper is available to the reader. The equations make it possible to calculate the effect on the equilibrium concentration of one alloying element due to the presence of one or more other elements. In particular they are intended to give, for alloy steels, the carbon concentrations in alpha and gamma phases in equilibrium with each other, and in gamma in equilibrium with cementite. They may, however, be modified for use for carbon-free alloys. A summary is given later of the equations used in analyzing the data in this paper, and the symbols are there defined. About 125 papers have been examined for experimental data suitable for this investigation. An effort was made to look up all available reports of ternary systems including iron and carbon, as well as similar systems of higher order. Supplementary material was also obtained from a number of binary systems. A few noncarbon ternary systems were also found to which these methods could be applied. A comparatively small proportion of the papers read provided usable material. In many systems the number of quantitative observations made in the iron-rich region is extremely small, and the smoothed curves to be found in most published phase diagrams are entirely useless for quantitative treatment. This opinion is confirmed by the authors of the series on Alloys of Iron Research, whose remarks show clearly that they have no illusions as to the accuracy of many diagrams that they present. A further difficulty arises from the fact that these equations apply only to rather low percentages of alloying elements. The result is that at the lowest concentrations, where the best agreement might be hoped for, the errors of observation become relatively very large. The experimental difficulties in measurements of this kind of equilibrium are, of course, an old story.

Jan 1, 1946

By B., Hoyaux

A first requirement for assessing the safety of a rock slope, either artificial or natural, particularly if the rock behaves in an elastic-brittle manner, is a proper knowledge of the distribution of stresses within the slope and their development with time and advancement of workings.

Jan 1, 1972

By Kenneth L. Adams

10.3-1. Introduction. Equipment replacement or maintenance is of major concern to every company today. It can be the difference between an efficient and profitable operation or an inefficient and struggling one. Mining equipment, as everyone knows, will not last forever. Some equipment becomes obsolete before it wears out while some may be doing its intended job, yet not economically. It is a major problem for management to make the decision as to whether a piece of equipment should be repaired or replaced. There are numerous approaches to this problem; using formulas, charts, and graphs. These would be very good if all conditions were stable. Since conditions and requirements are constantly changing, an accurate observation cannot be derived from a set formula. A formula does, however, serve as a reminder to include most of the items that should be considered when evaluating old and new equipment. In the field of mining there are several questions which enter into the reasoning that are difficult to put into an equation. Some of these are: 1. Will the present equipment produce the required output of the mine, or an increase if necessary? 2. Are reserves adequate to support the purchase of new equipment? 3. Can the old equipment be repaired to efficiently continue the mining operation? 4. What is the stability of future markets for the product? Depreciation rate, or the write-off life, is a factor that can directly effect decisions on replacement. If the initial life expectancy is too long and the price of equipment is not written off when discarded, then the original investment has not been recovered. If the write-off time is too short, then the equipment is written off before replacement is even considered. In this case, the depreciation accrual is usually used to finance some other phase of the operation. In view of the increasing prices, the amount of depreciation fund is generally too small for much incentive to replace an older unit

Jan 1, 1968