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By R. E. Cech

Metallographic observations on hydrogen-reduced nickel oxide crystals suggest that nucleation of nickel occurs at structural singularities in the oxide. The fully reduced structure contains micron-diameter, worm-like voids occupying 40 to 50 pct of the volume. The crystallographic orientation relationships between nickel oxide and nickel resulting from oxide reduction are recorded and discussed. THE process of reduction of oxide to metal is one of considerable complexity involving a chemical reduction reaction, mass transport of reducing agent to the point of reaction and of reaction product away from it, and finally a transformation whereby metal atoms released from the oxide rearrange to form a stable reduced phase. In addition, nucleation of the reduced phase affects the overall reaction kinetics. Thus far only the thermodynamic aspect of reduction has received the attention warranted by the importance of

Jan 1, 1960

By Mowat D. M., Louis H., Smith W. Mackey W. M., Dron R. W., Ellison C. C., Winmill T. F., Kerr G. L., Haldane J. S., Ashworth J., Garforth W., O'Shea L. T.

Discussion of Winmill's paper, including various anecdotal examples, is presented together with the author's response; topics included: the need to distinguish cubic pyrites from the rapidly decomposing rhombic form known as marcasite; the effects of moisture content in the coal and air; the possible effect of pressure; the heat insulation resulting from heap/stack size; and the means of determining pyrite and moisture contents

Dec 1, 1916

By ROBERT R. ROUGH, FRANK L. BACON, John Dasher

(being shipped as bailast in ocean freighters). Within the last 10 years it has become more economical to use local sands, and there has been a general shift from the Belgian sand. Deposits of purer sand were treated and used for 'some time: but the suprly became limited, and means were sought to beneficiate the more bountiful subpay-f impure beach sands. These sands are composed of, 50 percent feldspar and 50 percent quartz, with small amounts of iron- bearing minerals, The most objectionable impurities in these West coast sands are the oxides of iron and aluminum. The Del Monte (Calif.) beach sand contains about 0.13 percent FeqQg and about 11.0 percent Aig03 (the latter being furnished by the large amount of feldspar present.) For the manufacture of feldspar present.) For the manufacture of flint-glass containers the maximuni quantities of these two impurities permitted in the sand are 0.05 percent F20 and 6 to 8 percent A1203.. The Fe0g occurs in the sand as follows: Traces of iron-bearing minerais resistant to weathering, ferruginous clay stains on the sand grains, and iron minerais not visible and possibly in solid solution or as colloidal incisions in the grains of feidspar or quartz. A good part of the iron in the sand is present in the traces of iron-bearing minerals, biotite, ilmenite, garnet, monazite; and hornblende. Biotite is present in larger quantities than the others. Samples of quartz, were freed of iron-bearing minerais by the use of heavy liquid (sp.gr. 2.70), leached with boiling HCI and SnCl2. Under a microscope a few apparently clean quartz grains were selected, and Fe203 was determined spectrographically to be 0.03 percent. The technique is similar to that described by Gabriel and Slavin. 4/

Dec 1, 1943

By J. H. Craig

As a result of information that the Navy Department was questioning the advisability of raising the maximum allowable exposure temperature for zinc-coated steel parts from 500 to 750 F., it was decided to make a series of high temperature tension tests on several types of uncoated and zinc-coated steels. The objective was to determine at what temperature intergranular penetration of galvanized steel by zinc might take place under conditions of rapidly applied stress and temperature. Tests were conducted in the range from room temperature to 1400 F. In this range, low-carbon and high-carbon steels did not suffer any adverse effects due to zinc coatings. In fact, at 1400 F. the zinc coatings appeared to have a beneficial effect. In stainless steel, the coating had no effect up to 1000 F. Above this temperature, the zinc coating appeared to cause a marked loss in ductility and a less pronounced loss in strength. There was no visible evidence of zinc penetration of the stainless steel structure, but it was assumed that this was the cause of the adverse effect.

Jan 1, 1945

By Jun Li

Rate processes of silver cyanidation were studied with the objective of understanding the reaction mechanism. The research was divided into three sections: anodic dissolution of silver in cyanide solutions, cathodic reduction of oxygen on silver surfaces and the direct leaching of silver in oxygenated cyanide solutions. The charge transfer steps plus the diffusion of reactants from bulk solutions to the silver surface were identified as rate-limiting and the rates of both anodic and cathodic reactions can be calculated using the Butler-Volmer equation and Fick's first law. Based on mixed potential theory and the results of electrochemical studies, a comparison of the rate obtained from direct leaching with that predicted from the calculation is made. Calculated results agree well with the experimental data.

Jan 1, 1992

By M. Kawakami

In relation to the designing of a new-type blast furnace, the reaction of carbonaceous materials with CO2 is expected to occur at as low temperature as possible. In order to get a highly reaetive carbonaceous material at low temperature, the reaction kinetics was investigated by measuring such quantities as the reaction rate from weight loss, the amount of CO adsorption and specific surface area by BET method. The reaction rates were large in the order of the Bintyo char, metallurgical coke, graphite and glassy carbon. If the rate was converted to the rate per unit area, however, those of the Bintyo char was smaller than that of graphite. Thus, it is suggested that the rate of the Bintyo char is influenced by the pore diffusion of CO2. The rate had a positive relation with the amount of CO adsorption, showing that the rate determining step would be the desorption of CO from the active side on the surface. The rate independent of surface area was derived, combining all the obtained data.

Jan 1, 2003

By Yoshio Waseda, Tetsuya Uda, Tom H. Okabe

"Halide salt has been tested as a reductant for producing titanium powder directly from TiCl4. From the results of thermodynamic investigation for several rare earth chloride systems, DyCl2 was found to be used for the reduction of TiCl4 instead of the conventional metallic reductant. When TiCl4 was fed into molten salts containing DyCl2 at 1073K, titanium powder of several ten micron meters in diameter was obtained. In contrast to the sponge titanium produced by the conventional Kroll process, the present new process using a halidothermic reduction in a reactive molten salt appears to be suitable for producing metal powder. From the thermodynamic point of view, the resultant DyCl3 can be reduced to DyCl2 by magnesium. By utilizing the multivalent halide redox couple, some possible ways of titanium powder production directly from TiCl4 by magnesiothermic reduction are shown to be feasible. This can also be applied to the development of a new continuous titanium reduction process.1 IntroductionTitanium and its alloys show attractive mechanical properties such as strength-to-weight, rigidity-to-weight ratios and excellent corrosion resistance. Nevertheless, the application of titanium alloys is limited compared to other structural materials (e.g. steels, aluminum alloys) because of its high cost of production. Currently, almost all of titanium is produced by metallothermic reduction of TiCl4 by magnesium (Kroll process)[1] in an airtight metallic reactor. This process is batch type and labor intensive. Therefore, many attempts to develop new process for producing titanium are investigated so far."

Jan 1, 2000

By James P. Rider, Jeanne A. Zimmer, Andrew B. Cecala, Robert J. Timko, Earle H. Andrews

Many different types of structures and materials have been used to build mineral processing facilities over the past few decades. Although the structure type and building material were not viewed as significant factors affecting the health of employees in these facilities when they were built, the National Institute for Occupational Safety and Health performed an evaluation to determine to what extent building types could impact respirable dust and noise levels. This report discusses the evaluation of three different types of product sizing silica sand structures: a masonry design, a steel-sided design, and an open structure design. The data obtained in this study indicate that the open structure design (no walls) was superior from both a dust and noise (health) standpoint compared to the other two structures. The open structure design should also be beneficial from a cost standpoint because of lower material and construction costs. Companies and design engineers should consider this open design when building new mineral processing facilities in climates where it could be applicable. Some companies may also want to consider modifying existing structures with a more open design to further reduce dust and noise levels. As the trend continues in lowering allowable dust levels for federal health standards in the U.S. mining industry, the open structure design may be an approach for some companies to consider for their operations.

Jan 11, 2006

By F. Kitzinger

Electromagnetic testing of wire rope has become more and more reliable over the past two decades. This improvement is partly a result of an unprecedented progress of electronic technology, which permitted the development of a new breed of testing instruments. There are two basic methods for the electromagnetic testing of wire ropes, the AC method and the DC method. Both methods rely on magnetic field disturbance caused by mechanical anomalies in the rope structure. The wire rope under test is passed through a magnetic excitation field, which can be a weak alternating field or a strong static field. Because the alternating field is produced by an alternating current, these instruments are of the AC type(l). In the early days of ND-testing, strong permanent magnets were not yet available; therefore, the static magnetic field was produced electromagnetically with direct current. Instruments based on static excitation are still called DC instruments(2), even though the field is now produced by a permanent magnet. Both these methods have certain characteristic features. The AC method can detect loss of metallic area caused by corrosion or other effects, whereas localized faults such as broken wires are better detected by the DC instruments . The basic principles of the wire rope testers have remained unchanged over the years and the improvements present in the new instruments usually reside in the signal processing and recording sections. The Instrumentation Department of the Noranda Research Centre* has been involved in a four-year development program which resulted in a new type of wire rope tester, the Magnographv** . This new instrument in many ways represents a considerable departure from the traditional wire rope testers. The Magnograph has already been patented in Canada and the U.S.A.(3), and patent applications are pending in other countries.

Jan 1, 1979

By D. Laguitton

"Mathematics, process theory, process practice and computer applications are the main disciplines that contribute to developing useful techniques for computer simulation of mineral and coal processing plants. As in any multidisciplinary effort, communication or transfer mechanisms must be developed to facilitate the flow of experience between participants of different backgrounds. These mechanisms include written reports, verbal communications, workshops and transfer of computer programs. The SPOC project at CANMET is devoted to computer simulation and as such has addressed, or will address in the near future, problems inherent to methodology transfer. The first major output of the project was the material balance program, MATBAL2, which has been acquired by over 30 organizations. Program documentation, industrial workshops and summer student programs have been used to effect the transfer. This experience is discussed and the future outlined.IntroductionComputer simulation has become a common tool in many different fields of human activity during the past two decades, as illustrated in Figure 1. The total number of articles abstracted in Chemical Abstracts under the general subject entry of “Simulation"" has been following a pseudo-exponential growth since 1972 and was approaching 5000 in 1980, whereas no such entry was even used prior to 1967. This represents over a dozen papers published daily on the subject and should continue to grow to higher figures. Still, progress toward accepting modelling and simulation in mineral and coal processing has been very slow. It will be shown later that this slow acceptance is a cause rather than a consequence of the limited success of the various attempts made so far to draw unambiguous benefits from simulation applications. The real cause of the difficulties in fully accepting the new methodology lies in the multidisciplinary aspect of modelling and simulation, which does not suit the traditionally conservative approach that prevails in designing and operating large and costly processing plants."

Jan 1, 1982

Investigation on Sheelite Floatability by Particle Size Fraction

Sep 13, 2010

By Peter C. Finlayson

Rapidly rising gas and oil prices and the falling quality of coal is forcing energy users in many parts of the world to consider the application of low grade fuel, particularly coal, for steam raising and power generation. However, the use of such low grade coal is normally resisted by the consumer because of operational problems associated with high ash content, sulfur emission and, in some instances, slagging problems caused by low melting temperature constituents in the ash. Recently developed technology involving 'fluidized bed combustion' offers a potential solution to these operational problems. Much of the early work was conducted in Britain, where rig tests were commenced during the early 1960's. This has led on to the successful conversion and operation of a fluidized bed fired industrial boiler at the Renfrew works of Babcock & Wilcox Ltd. Orders for the first commercial boilers incorporating this technology have recently been announced. Significant development work on fluidized combustion is now being undertaken in various parts of the world, in particular North America, Germany and Japan, and the first large scale units are under construction or being commissioned. This paper concentrates on the development of the technology in Britain, outlines the reasons for applying fluidized bed combustion and de-scribes its application at atmospheric pressure for steam raising and at elevated pressure for power generation . Coal Processing Consultants is a Partnership between the National Coal Board and Babcock & Wilcox Ltd. of Britain and has been established in order to provide technical advice and economic evaluations on all aspects of coal processing and utilization. In view of the involvement of its Parents in the development and exploitation of fluidized bed combustion technology, Coal Processing Consultants has been retained by clients in various parts of the world to provide expert advice on the application of fluidized combustion for particular coals and project situations.

Jan 1, 1978

By Caibin Wu, Chengfang Yuan, Jiaqi Tong, Zhilong Cheng, Ningning Liao, Chong Zeng

In a series of Julius Kruttschnitt size-dependent breakage models, the cumulative percentage passing 1/10 of the initial size is used as a fineness indicator for scientific research and the selection of grinding equipment. However, in industrial practice, it is quite customary to use the mass percentage passing 75 μm as the indicator. In this paper, based on the energy-particle size model, quartz and calcite, two materials with distinctly different hardness, were used as test samples in a conical ball mill. At the same specific energy, the value of the cumulative percentage passing 1/10 of the initial size decreased while that of the mass percentage passing 75 μm increased with finer feed size. The experimental test values of the mass percentage passing 75 μm have a good linear relationship with the model predictions, which suggests that the particle size energy relationship of the mass percentage passing 75 μm and Ecs can be used instead of the cumulative percentage passing 1/10 of the initial size and Ecs. By building family curves, when particle size x < 300 μm, the family curve can be well fitted, and the fine particle size distribution of the whole product can be reconstructed.

Dec 22, 2022

By H. C. Goodrich

At the Utah Copper mine, steam shovels were first used, in 1906, for the removal of overburden, and in June, 1907, for the mining of ore. Prior to 1907, the ore came from underground development work and from stoping. The use of the steam shovel gradually increased until 1914; since then all material, both overburden and ore, has been loaded by power shovels operating on the various benches of the mine. During these 19 years, there has been a great improvement in open-pit mining, largely in the use of equipment having greater capacity and dependability. The history of the development of mechanical shovels and related equipment, as affecting the Utah Copper Co., would be interesting and would justify considerable space; but of greater interest at this time is the operation of the equipment now in use. The Utah Copper mine is in a great deposit of copper-bearing monzo-nite, which occurs as a prominent headland of the Oquirrh range of

Jan 1, 1925

By J. M. Callow

THe results obtained by pneumatic flotation throughout the country on all classes of ore, and the tonnage now being treated by this particular method, speak for themselves. Its advantages over the so-called agitation process are now established by facts and data from practicc. The comparative efficiency of a rapidly revolving paddle, as a means for aerating an ore pulp, and of a cyeloidal or turbine blower for the same purpose, would seem to be so obvious as to leave no room for discussion. Practitioners in this art are to be congratulated on the acquisition of the valuable literary contributions that have recently been made on the theory of flotation by Messrs. Ralston, Van Arsdale, Taggart and Beach, and others, and the very valuable and able articles by Messrs. Laist and Wiggin on "Flotation Concentration at Anaconda, Mont.," by Dr. Rudolf Gahl on the "History of Flotation at Inspiration," and by David Cole on "The Advent of Flotation in the Morenci District." It is not within the province of this article to attempt an answer to the various issues raised in regard to the theory, or to defend the one advanced by me a year ago. But since discussion usually benefits the profession, a reply will be made to some of the statements made by the last-named writers. CoMPABATIVE SENSITIVENESS AND ATTENDANCE Concerning the article, "Flotation Concentration at Anaconda, Mont.," by Laist and Wiggin, a little explanation is in order. It should be stated that, with the exception of about 24 days at the end of the testing period, the Callow experimental plant at Anaconda was not run under my direction. This perhaps accounts for some of the concIusions drawn on page 499 of the descriptive paper. The conclusion that the use of acid seems to be of considerable advantage, calls for some comment. While the tests conducted by the Anaconda Copper Co. do show acid to be of considerable benefit, this is a consequence of using acid sludge as a flotation agent. My belief has always been that the Anaconda

Jan 1, 1917

By L Richards, R L. Brathwaite, C Mazenga

Underground mining of gold-silver bearing quartz lodes was carried out in the great mines at Martha Hill, Waihi over 70 years from 1882 until 1952. Shafts and stopes reached a total depth of 600 m on 16 levels, with workings extending laterally some 1.6 km, and as new reefs were discovered the workings extended beneath parts of the township. Over their long life the mines produced 1217 tonnes of gold-silver bullion from processing 12.2 million tonnes of mined ore. In the early-1980s drilling proved large reserves of gold and silver ore remaining in stock-work zones between the previously mined lodes. This led to a new era of mining at Waihi with the opening of the Martha Hill open pit in 1988. A series of three sink holes have formed above unfilled stopes of the Royal lode. In 1999 a sudden collapse crater 40 m in diameter occurred near an occupied part of Waihi, placing in danger several houses and a busy street. This crater formed close to a similar crater that occurred in 1961. The 1999 collapse resulted in subsurface investigations and risk assessment studies being commissioned by the local Hauraki District Council. However, a further 50 m diameter collapse crater in December 2001 formed in a residential area, swallowing and wrecking an occupied house, fortunately without injuring its five occupants. Two other houses were perched on the crater rim. The 2001 collapse led to an acceleration of the work being carried out by the Institute of Geological and Nuclear Sciences Ltd. (GNS) to identify the extent of the old underground workings at Waihi. For the risk assessment detailed rock mechanics analyses were made to consider the stability of the underground mine stopes, in terms of the stope back, hangingwall, footwall and crown pillar failure mechanisms, as well as void migration. The collapse crater areas were analysed using using several methods, including analysis to simulate the probability of void migration from unfilled stopes to the surface using the @Risk program. The analyses show that in the cases of the actual collapse craters, the voids have a high probability of migrating to the surface, thus providing a method of testing the void migration modelling. Modelling analysis applied to the remaining stopes of the old underground mines show there are further areas where void migration from unfilled stopes has a high, medium and low probability of reaching the surface as a collapse crater. The locations of these probabilistic hazard zones were outlined using the @Risk modelling and deterministically by using the dimensions of the historical collapses applied along the length of the stopes. Consideration of the æincubation periodÆ (the time interval between the cessation of mining and the occurrence of collapse) and comparisons with mine subsidence histories overseas, indicates that further collapses are likely to occur over the next 50 years. Risk assessment estimates made using property values and occupancy levels within the three hazard zones, were compared with Societal and Individual Risk criteria. Results indicate that safety within the high and medium zones may be unacceptable.

Jan 1, 2003

By M. Ashraf Mahtab

A feature of interest in stability of excavations in domal salt is the phenomenon of gas outbursts which has occurred in five of the six mines in Louisiana salt domes. Gas outbursts are sudden erruptions of salt and gas from the face or roof of a mine opening. They are associated with anomalous zones in salt, depth of mining, and the method of excavation. Potential risks from gas outbursts include an unplanned connection to a reservoir of water or hydrocarbons and, possibly, a loss of the mine. It is proposed that a gas outburst is initiated by disking in biaxial compression and propagates by spalling of the cavity walls and further disking. The outburst is terminated by a combination of dilatancy hardening, increase in stress along the cavity axis, and enlargement of the cavity to the boundaries of the pressure pocket. Identification of burst- prone areas will require research into in situ measurement of material characteristics and further under- standing of the mechanism of gas outbursts. Shock blasting in advance of mining appears to be a promising technique for controlling gas outbursts.

Jan 1, 1981

By G. S. Adisoma

To address the problem of grade estimation in a general three-dimensional shape and the uncertainty associated with the estimate, the technique of jackknifing/block kriging short-cut is proposed. A new estimator called jackknife kriging is introduced first. Through the jackknife variance, a confidence limit for the reserve grade estimate can be calculated. Unlike the kriging variance, which is more a measure of data configuration and is independent of data values, the jackknife variance reflects the true variability of the data. This approach provides a simple way to set a confidence level for global estimation of resources.

Jan 1, 1995

By I. Stefanou, J. Sulem

"In the last thirty years, the study of earthquake mechanisms has emphasized the major role of rock friction. Earthquakes appear to be the result of a frictional instability and occur by sudden slippage along a pre-existing fault or a plate interface. Multiphysics couplings play a major role in earthquake nucleation and seismic slip. The effect of shear heating and thermal pressurization may be of prime importance in the control of the stability of shear deformation inside the slipping zone. Other mechanisms in relation with thermal decomposition of minerals affect the pore pressure and the temperature evolution of the system, and can play a significant role in the extreme strain localization observed in field. The actual width of the localized zone is a key parameter for understanding fault weakening mechanisms. On the basis of field observations, laboratory experiments and recent advanced modeling, these phenomena are analyzed and discussed in order to bring some new insights in the understanding of earthquakes nucleation.INTRODUCTIONIn the last thirty years, the study of earthquake mechanisms has emphasized the major role of rock friction. Earthquakes appear to be the result of a frictional instability and occur by sudden slippage along a pre-existing fault or a plate interface (Scholz, 1998; Sykes, 1978). The conceptual model of spring slider system is commonly used to represent the interaction between an elastic crustal block and a fault zone. Stick-slip instability is possible if the softening rate of the shear resistance of the fault zone is high enough as compared to the stiffness of the crustal block. Therefore, weakening mechanisms that can explain how the frictional resistance of a fault decreases with slip and/or slip rate is of prime importance to understand how an earthquake nucleates. In recent years, several drilling programs in active faults (e.g. the Nojima fault in Japan, Boullier, 2011; the Aigion Fault in Greece, Cornet et al. 2004, the Chelungpu fault in Taiwan, Ma et al. 2006, and the San Andreas fault in the U.S.A. Ellsworth et al. 2000) as well as high velocity friction experiments (e.g. Tanikawa et al 2012a; Tanikawa et al. 2012b) have highlighted the physico-chemical processes involved in the nucleation of seismic slip (see for the example the review paper of Niemeijer et al. 2012)."

Jan 1, 2015

By M. H. Harris

A solution has been obtained to the problem of calculating flow into a cased and perforated well. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. Computer experimentation indicated that the results are within 3 per cent of the exact solution. Computed results are presented as an apparent skin effect, on a series of dimensionless working curves. Productivity ratios can be rapidly calculated from these data for the wide range of wellbore and reservoir properties actually encountered in field practice. Any reasonable vertical unisotropy ratio can be included in the computation. Productivities can be calculated for wells perforated in a regular pattern, a single horizontal plane or a vertical line on one side of the casing. Solutions for asymmetrical perforation patterns can he easily obtained from the working curves. Solutions for flow into sells completed with a horizontal notch are also provided. Results show that productivity can be increased by extending perforation penetration. This is especially true for shallow penetrations. The highest productivity is obtained when perforations are arranged in horizontal planes, as opposed to a vertical line on one side of the casing. Four or five perforations in one plane will approach the maximum productivity. The effect of perforation hole diameter is small, and is rioticeable only in shallow penetrations. INTRODUCTION The perforating method of well completion has been successfully and widely used in most producing areas. In the past, the desired perforation results were achieved by simply shooting numerous large holes in the casing. A perforating scheme for an area, or particular well, was established by evaluating two types of experimental data: the well flow index and the productivity ratio.&apos; 3 The well flow index test is a means of determining the relative flow capacity of perforations in a linear system. This test also gives information on the perforation size, shape and hole damage which can be expected under well-bore conditions. However, relative flow data from this test cannot be accurately tarnsformed into the radial wellbore system. Thus, no true indication of the productive capacity of a perforated well can be obtained from the well flow index test. A well productivity ratio is derived from electrolytic models built to simulate perforated wells. Available productivity ratio data 2,3 are limited in that all important variables are not extensively evaluated. For example, data are limited to well radii of 3 and 6 in., and to maximum perforation penetration of 1 ft. Practically no information is available on the pattern of flow into a perforation. The effect of various perforation patterns on well productivity has not yet been determined and the effect of perforation diameter has not been thoroughly studied. Also, it will be shown that this type of electrolytic model data is probably in error by as much as 10 per cent or more. Modern completion techniques such as limited-entry perforating, single-plane fracturing, steam and hot air injection and chemical consolidation of incompetent formations all rely on injection and/or production from a limited type of completion. These completions may consist of several high-capacity perforations or a horizontal notch which is equivalent to an infinite number of perforations in one plane. Proper design of these new completion techniques requires, in part, accurate estimates of a well&apos;s productive capacity. Data on perforated and notched well productivity have been determined in this investigation. Results are presented as a function of the pertinent variables. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. DESCRIPTION OF PROBLEM PRACTICAL APPLICATION The computed results can be applied to wells which meet several general specifications. An external drainage radius of the well must be known or assumed, but the well need not be drilled on a regular pattern. The well must be cased and cemented through the entire producing interval. And, the casing must be perforated with one or more horizontal planes of perforations. The perforation pattern itself must conform to three geometrical requirements. 1. The perforations in a plane must divide the plane into equal angular segments (Fig. 1). Four perforations per plane would be 90" apart. 2. Perforations in a plane must be directly above or beneath perforations in adjacent planes. For two shots per plane, perforations would lie in the BB&apos; plane (Fig. 1). 3. Horizontal planes must have equal vertical spacing and be separated from the top and bottom of the formation by one half the spacing interval. Single planes of perforations should be in the middle of the formation. This is shown in Fig. 2 where h is the formation thickness in a single plane conlpletion or the spacnig interval in a multiple plane completion. The spacing interval at the top and bottom of the formation may vary somewhat without causing an appreciable error in the productivity calculation if the formation is reasonably thick and there are many horizontal planes of perforations. A special provision has been made to calculate the productivity ratios of wells with uneven spacing intervals, or for the case where a single plane of perfora-

Jan 1, 1967