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By W. V. Swarzenski

In its effort to combat waterlogging and soil salinity, the Water and Soils Investigation Division of WAPDA (West Pakistan's Water and Power Development Authority) has carried out an extensive program of test drilling andwater sampling since 1954. Data collected during the past ten years have permitted the delineation of fresh and saline groundwater zones in the Punjab Plain. Fresh groundwater containing generally less than 500 ppm of total dissolved solids is found in wide belts paralleling the major rivers and in other areas of fresh-water recharge. Locally, fresh groundwater extends to depths of 1500 ft and more. Saline groundwater occurs down gradient from sources of recharge, particularly in the lower central parts of the interfluvial areas, and presumably underlies most of the Punjab Plain. The groundwaters of the Punjab are characterized by their evolution from calcium, magnesium bicarbonate waters near sources of recharge to waters containing a dominant proportion of sodium. The highly mineralized waters of the Punjab are generally of the sodium chloride type, whereas in the Dera Ismail Khan District, sodium sulfate waters predominate. The pattern of distribution of saline groundwater zones and the observed gradual increase in mineral content, down gradient from sources of recharge, can be explained best by a hypothesis stressing the process of evaporation from the water table and solution of minerals within the alluvial aquifer. In 1954, detailed groundwater surveys in the Punjab Plain were initiated by WASID, the Water and Soils Investigation Division of West Pakistan's Water and Power Development Authority. The investigations, undertaken under a cooperative agreement between the governments of Pakistan and the United States, were aimed at the formulation of reclamation measures to improve waterlogged and saline soils, and to assess the groundwater potential of the Punjab and other areas of West Pakistan. The nature and urgency of WASID's primary task limited the exploration of the alluvial aquifer generally to its uppermost part. About 1030 test holes drilled in 47,000 sq miles of the Punjab defined the nature of the alluvium to depths of about 600 ft and yielded data on water quality to 400 or 500 ft. A report on the hydrology of the Punjab, based on the results of these investigations was published by WASID in 1963.' The present report incorporates data obtained by WASID since 1962 in a program of deep test drilling in the Punjab and the adjacent areas of Bahawalpur and Dera Ismail Khan District, permitting the definition of fresh and saline groundwater zones to depths of 1500 ft in some areas. Groundwater in the Punjab Plain is contained in alluvial deposits, predominantly sand and silt, which extend almost everywhere to depths of 1000 ft and more. The alluvium has been deposited by the Indus River and its tributaries since late Tertiary time and is contiguous with similar deposits in India. The Indo-Gangetic Plain extends from the foothills of the Himalayas to the ancient rocks of the Peninsular Shield in central India and to the ocean. Gradients are generally very low and range from about 1% ft per mile in the upper part of the plain to less than 1 ft per mile in the south and southwest. The monotony of the alluvial plain is broken by scattered bedrock outcrops in two of the interfluvial areas, Chaj Doab and Rechna Doab. The bedrock hills are projections of the northwest-trending Delhi-Shahpur Ridge that is largely buried by alluvium. The rocks of the buried ridge, presumably of Precambrian age, are essentially impermeable and define the lower limit of the alluvial aquifer in parts of Chaj, Rechna, and Bari doabs. Elsewhere in the Punjab, there are no outcrops of other consolidated rocks and their presence below the alluvium is conjectural. The principal areas of bedrock outcrops, near Kirana and Sangla, are shown diagrammatically in Fig. 1. The movement of groundwater through the alluvial aquifer of the Punjab has been described by Green-man and others.' In most of the area, the pre-irriga-tion water table sloped from the rivers downstream and toward the central axes of the doabs, indicating that the rivers were sources of groundwater recharge. As a result of seepage from irrigation canals, water levels have risen as much as 90 ft. In 1960 they were within 5 to 15 ft of the land surface and above the

Jan 1, 1970

In a straight caving system, the ore is first undercut and then broken down by its own weight or .by the weight of the overlying rock, or by a combination of both. Operations that involve the caving of the material overlying an orebody as an essential part of the work are also classed as caving, though practically all the ore is broken by drilling and blasting. Actually there are two distinct methods—sublevel caving and block caving, and modifications thereof. The mines described are Miami and Alaska Juneau.

Jan 1, 1925

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By J. T. Crawford

ALTHOUGH nearly 10 pct of the total tonnage of coal produced annually within the United States is handled by bulk freighters on the Great Lakes, very little of the detail connected with it has been published other than occasional newspaper stories and publication of tonnage statistics. Of the total tonnage floated on the Lakes each year some 10,000,000 is stored and distributed from the port of Duluth Superior, at the western end of Lake Superior commonly known as the Head of the Lakes. This port has the largest single area concentration of coal docks in the world. Since this area contains the largest ore docks, the largest movable material handling bridge, the largest and highest grain elevator and the largest coal briquetting plant in the world, it is entirely fitting and proper that here also should be located the largest coal dock and what we believe to be the worlds largest clam shell. Of the sixteen coal docks operated by ten companies, five are owned and operated by the North Western-Hanna Fuel Co. which has two docks on the Superior, Wis. water-front and three docks in Duluth, Minn. It is with these five docks that we are primarily concerned. GENERAL HISTORY In the summer of 1871 a small sailing vessel entered the harbor of Duluth Superior with the first commercial coal cargo. All the coal brought up that first year did not amount to more than 3000 tons. During the year 1877 the first dock equipped for handling coal was built in Duluth. Coal receipts increased to 52,785 tons in 1879 the first year for which an official record was kept. Since then the volume of water-borne coal to the Head of the Lakes steadily increased to a maximum of 12,688,321 tons in the year 1923. This tonnage was nearly equalled in the year 1927 and the next highest tonnage recent year was in 1946 when 10,105,703 tons were unloaded. The average annual bring-up over a ten year period 1938 to 1947 was 8,605,231 tons. Approximately 30 pct of the coal unloaded at the Head of the Lakes is handled over the docks of the North Western-Hanna Fuel Co. Competition of other fuels coupled with expansion of coal fields in the mid-west have held coal receipts for Duluth-Superior at a relatively constant figure during the last eight years although the total tonnage of coal floated on the Great Lakes has more than doubled in the past 25 years. From the shovel and wheelbarrow method of unloading early cargoes to the horsepowered windlass derrick with a wooden tub was but a short step. The first movable coal handling, steam operated,

Jan 1, 1948

By C. E. Sims, H. M. Banta, S. L. Hoyt

OVER the past few years, metallic arc welding has been extended to steels of the hardenable type. As compared with other methods of fabrication, production has been facilitated, service performance frequently has been improved, and the overall results have been so favorable that engineers and production men have placed great emphasis on this application of welding. The metallurgist and welding engineer, however, have been confronted with new problems, since, for one reason, the harder steels are more apt to crack and special precautions must be taken if sound joints are to be procured. Some of the factors that are pertinent to this problem are metallurgical, and it is an object of this contribution to discuss steel manufacture and processing methods and to show how their control assists in reducing the hazard of cracking. By this time, the problem of cracking specifically underbead cracking, or "hard cracks," or parent-metal cracks-is well known, and a large amount of work has been published, both here and abroad, dealing with this subject.1 The tests described are made under restraint to facilitate cracking and, are so designed that a semiquantitative, or at least a relative, value of the cracking tendency is obtained. As one would expect, it has been reported that the incidence of cracking increases with the carbon and alloy content of the steel. More specifically, the cracking tendency is said to increase with the hardenability of the steel, though it is now recognized that the situation is not so simple. The phenomenon itself, on the other hand, has been but loosely described, and it is in only broad generalizations that this cracking has been related to steel metallurgy. Thus, while it has been abundantly demonstrated that the hardenable aircraft steel, S.A.E. 4130, must tend to crack when arc-welded, the problem still remains of why two lots of the same composition and the same hardenability can vary so greatly in cracking tendency, or what it is about the prior metallurgical history that so strongly affects the results. Further, while the efficacy of preheating and postheating in preventing cracking is recognized and utilized in production, the mechanism by which they function seems not to have been described. These points are thought to be significant in the production of steel for fabrication by metallic arc welding and, hence, of interest to mill and process metallurgists and welding engineers. Consequently, it is another object of this paper to discuss the mechanism of parent-metal cracking, including the influence of the condition of the steel and the control of cracking by manipulation of the time-temperature conditions during and after welding. A new method of rating the cracking. tendency is also discussed, and the results of the test are related to steel composition and structure or prior history. The work to be described was the outgrowth of work in 1940-41 at Battelle Memorial Institute 0n two projects, one

Jan 1, 1945

By B. G. Agnew

In evaluating fracture treatments, the need to answer such questions as "What zone or zones were actually treated?" and "What was the vertical extent of the treatment" is necessary, since determining effectiveness of the fracture treatwrent depends on knowledge of the reservoir portions stimulated and the vertical extent of the fracture system or systems. Injection of hot or cold fluids during fracturing operations will transfer heat to the surrounding formations and fracture faces mainly by heat conduction. Once injection ceases, temperature anomalies will develop opposite the zone fractured because the rate of temperature decay is less than that opposite zones heated or cooled by flow inside the wellbore or along the cement sheath. Thus, temperature surveys can he used to determine where fractures were generated outside the wellbore and to reasonahly estimate the vertical extent of the fractrires. This technique has been used successfully to evaluate over 344 fracture treatments at depths ranging from 1,500 to 15,700 ft. Examples of actual temperature surveys are presented to show how this method of fracture treatment evaluation can be used effectively and beneficially. INTRODUCTION Stimulation of producing or injection wells by fracturing is commonplace in the industry today. In evaluating these treatments, two basic questions which arise are "What zone or zones were actually stimulated?" and "What was the vertical extent of the treatment?". Knowledge of the reservoir portions stimulated and vertical extent of the fracture system or systems is vital to effect efficient and economical well completions and to assure maximum recovery from reservoirs. Not all fracture treatments are successful and many times the desired or anticipated results are not achieved. When this occurs, it is in most cases the engineer's job to determine why. The answer to this problem forms the primary basis for deciding whether to spend more money for development drilling and/or completion attempts or to forego additional expenditures to improve the particular zone. Also, knowledge of the reservoir portion actually stimulated is invaluable in planning future workovers. This is especially true in wells producing from reservoirs containing multiple porosity stringers or zones. For various reasons, all zones within a reservoir may not be perforated on initial completion with the thought of developing remaining zones through future workover operations. Because particular zones are perforated and fracturing fluid pumped down the wellbore, it cannot be assumed that all perforated zones are stimulated, and in turn drained. Occasionally, unperforated zones which are planned for future development are actually stimulated on initial completion. eliminating the need for future recompletion attempts or all zones perforated initially are not stimulated, thus requiring additional completion work to insure that these zones are adequately drained. In most cases, it is costly. if not impossible, to determine with assurance why a fracture treatment is unsuccessful after the job has been completed and the results tested. Further, unpredictable upper and lower fracture barriers. as well as possible borehole communications (cement channels), do not permit it to be taken for granted that the formation opposite the perforations is the only zone receiving the fracture treatment. Thus. evaluation of fracture treatments is necessary for efficient and prudent well completion practices and should be done simultaneously with the fracture job. Several methods have been used to locate fractured zones, all of which are based on detection of radioactive tracer materials added to either the fracturing fluid or the propping agent. These methods have been helpful in increasing knowledge of fracturing operations; however, they are seriously limited because of cost and inability to detect accurately radioactive tracer material more than a few inches away from the borehole. To develop a better diagnostic tool to pinpoint which zone or zones had actually been fractured, temperature surveys were run after fracturing with heated and cooled fluids. Significant temperature anomalies were found to exist opposite zones suspected of receiving the fracture treatment. From the analysis and examples to be shown, it can be seen that temperature surveys run in a stabilized wellbore several hours after a fracture treatment using hot or cold fluid will yield temperature anomalies which show the actual reservoir portion stimulated, the vertical extent of the fracture system or systems and a qualitative indication of the portion of fracture-fluid volume entering a given depth interval. The experience and illustrations used in this paper are based on evaluation of over 344 fracture treatments during the past three years using this diagnostic tool at depths ranging from 1.500 to 15,700 ft and fracture volumes ranging from 2.000 to 110.000 gal. Based on analyses of these temperature surveys, analyses of fracture gradients and evaluation of several open-hole packer impressions in the West Texas area,' vertical fracturing is the predominant mechanism and horizontal fractures occurred frequently, if at all.

Jan 1, 1967

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.' They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan'gin' using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By A. S. Richardson

THe conditions that make necessary the mechanical ventilation of the Butte mines of the Anaconda Copper Mining Go. are due to a number of causes, all of which are incidental to the depth at which mining operations are now carried on, The main object to be accomplished, of course, is the reduction of the temperature and humidity of the air in the working places. Ventilation fans, both surface and underground, have been used for many years, but increasing depth has made the problem much more difficult. Further improvement in both ventilation equipment and methods, therefore, became necessary; and it is the purpose of this paper to describe the work planned and done under the improvement program. The mines of the district have been frequently described in various technical publications, so a description is unnecessary here. From a mine-ventilation viewpoint, compared with coal-mine ventilation systems, the problem is complicated by the fact that the workings to be ventilated are situated on a large number of steeply dipping veins which frequently intersect and are faulted, and also by the fact that the extent, or existence, of orebodies is not definitely known in advance of actual development work. For these reasons ventilation work cannot be planned in advance of actual operations, nor can such regular systems of ventilation as are used in working the more uniform and continuous bodies of coal be developed. When operations are conducted at a normal rate, about 10,000 miners are employed on two shifts, so that about 5000 men will be underground at one time. But as ventilation is necessary to reduce high temperature and humidity due, mainly, to natural causes, the quantity of air per man per minute is not a governing consideration in determining ventilation requirements. Most important among the numerous sources of heat and humidity in the mines are: heat generated during decay of mine timber; heat and humidity given off by mine rock and water; heat generated by oxidation of sulfide minerals; heat given off by electrical equipment; heat generated by mine fires (in certain localities).

Jan 1, 1923

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By A. S. Richardson

THe conditions that make necessary the mechanical ventilation of the Butte mines of the Anaconda Copper Mining Go. are due to a number of causes, all of which are incidental to the depth at which mining operations are now carried on, The main object to be accomplished, of course, is the reduction of the temperature and humidity of the air in the working places. Ventilation fans, both surface and underground, have been used for many years, but increasing depth has made the problem much more difficult. Further improvement in both ventilation equipment and methods, therefore, became necessary; and it is the purpose of this paper to describe the work planned and done under the improvement program. The mines of the district have been frequently described in various technical publications, so a description is unnecessary here. From a mine-ventilation viewpoint, compared with coal-mine ventilation systems, the problem is complicated by the fact that the workings to be ventilated are situated on a large number of steeply dipping veins which frequently intersect and are faulted, and also by the fact that the extent, or existence, of orebodies is not definitely known in advance of actual development work. For these reasons ventilation work cannot be planned in advance of actual operations, nor can such regular systems of ventilation as are used in working the more uniform and continuous bodies of coal be developed. When operations are conducted at a normal rate, about 10,000 miners are employed on two shifts, so that about 5000 men will be underground at one time. But as ventilation is necessary to reduce high temperature and humidity due, mainly, to natural causes, the quantity of air per man per minute is not a governing consideration in determining ventilation requirements. Most important among the numerous sources of heat and humidity in the mines are: heat generated during decay of mine timber; heat and humidity given off by mine rock and water; heat generated by oxidation of sulfide minerals; heat given off by electrical equipment; heat generated by mine fires (in certain localities).

Jan 1, 1923

By George Frederick Kunz

Mexico has been famous for its silver-mines ever since the Spanish conquest; but in respect to gems, although many varieties occur, yet only a few have been obtained in any important amount. Considering the extent of country in Mexico and ill the adjoining States of the Central American Republics, and the richness of mineral wealth that must surely exist there, our present knowledge of the occurrence of precious stones is remarkably small. The great prevalence of igneous rocks would lead us to anticipate the future discovery of many localities of gems and ornamental stones, when fuller scientific exploration shall have taken place.* At the present time the only gem-stone that is systematically mined in Mexico is opal, and the only important ornamental stone is tecali, the so-called Mexican onyx. In addition to these may be mentioned the pink garnet, or rosolite, found in one

Jan 1, 1902

By J. H. Nead, J. W. Halley

The new low-alloy high-strength steels are obviously here to stay. With 75 per cent higher yield strength and 50 per cent higher tensile strength than plain carbon structural steel, they permit 20 to 40 per cent weight savings and 10 per cent or more increase in pay load in the construction of railroad cars, buses, trucks, and a great variety of material-handling equipment. Their cost is low enough so that the extra cost of the new lighter construction over that with carbon steel offers an attractive self-liquidating investment; in some instances new construction with these low-alloy steels may even be as cheap as with plain carbon steel. A considerable and rapidly growing demand for the low-alloy steels has already sprung up. The many steel compositions that have appeared on the market lately18, 27, 28, 29, 30 to meet this demand would seem to indicate that no single composition is uniquely fitted for the purpose. However, no doubt some compositions are more suitable than others. The purpose of this study was, therefore, to compare the effects of the various alloying elements that might be used in the low-alloy steels in order to choose the metallurgically most logical composition, paying due regard, of course, to the economic aspects involved. Properties Desired in Low-alloy Steel A distinction between the new low-alloy steels and the common alloy steels is that the latter are generally used in the heat-treated (that is, quenched and tempered) conditions, whereas the new low-alloy steels are not only not heat-treated but are not susceptible to heat-treatment in the ordinary sense of the term. In this lies one of their chief advantages. Their properties can be obtained in the as-rolled, air-cooled, or annealed condition, just as with mild plain carbon structural steel. There is no need for heat-treating. Such steels can be readily formed hot or cold, and their properties are not appreciably changed by hot

Jan 1, 1936

By J. H. Nead, J. W. Halley

The new low-alloy high-strength steels are obviously here to stay. With 75 per cent higher yield strength and 50 per cent higher tensile strength than plain carbon structural steel, they permit 20 to 40 per cent weight savings and 10 per cent or more increase in pay load in the construction of railroad cars, buses, trucks, and a great variety of material-handling equipment. Their cost is low enough so that the extra cost of the new lighter construction over that with carbon steel offers an attractive self-liquidating investment; in some instances new construction with these low-alloy steels may even be as cheap as with plain carbon steel. A considerable and rapidly growing demand for the low-alloy steels has already sprung up. The many steel compositions that have appeared on the market lately18, 27, 28, 29, 30 to meet this demand would seem to indicate that no single composition is uniquely fitted for the purpose. However, no doubt some compositions are more suitable than others. The purpose of this study was, therefore, to compare the effects of the various alloying elements that might be used in the low-alloy steels in order to choose the metallurgically most logical composition, paying due regard, of course, to the economic aspects involved. Properties Desired in Low-alloy Steel A distinction between the new low-alloy steels and the common alloy steels is that the latter are generally used in the heat-treated (that is, quenched and tempered) conditions, whereas the new low-alloy steels are not only not heat-treated but are not susceptible to heat-treatment in the ordinary sense of the term. In this lies one of their chief advantages. Their properties can be obtained in the as-rolled, air-cooled, or annealed condition, just as with mild plain carbon structural steel. There is no need for heat-treating. Such steels can be readily formed hot or cold, and their properties are not appreciably changed by hot

Jan 1, 1936

By Edgar Shepard

THE interest of the Federal Government in improvement of water-ways dates from 1820, when Congress appropriated $5000 for making a survey of the Mississippi and Ohio Rivers and assigned this work to the Corps of Engineers of the Army. Since that time the Government has gradually assumed increasing jurisdiction in the matter of improvement and control of inland waterways until, by the River and Harbor Act of Jan. 21, 1927, Congress assigned to the Secretary of War and to the Chief of Engineers the duty of making surveys, in accordance with House Document No. 308, 69th Congress, to formulate plans for the most effective improvement of the navigable streams of the United States and their tributaries, for navigation, development of water power, control of floods, and the needs of irrigation. Virtually all the preliminary investi-gations and surveys required by this act have been completed. The reports made to Congress have been published and often are referred to as "308 Reports." The map shown in Fig. 1 is merely a skeleton distribution of the projects covered by these reports, but it serves to indicate the magnitude of the proposed undertaking. In many instances, a single character on the map stands for a major development involving several dams and reservoirs or many miles of canals or levees. The devastating floods of 1936, and the need for worthy public works to take up the slack in employment, gave further impetus to this program and in 1936 led to the enactment of a bill authorizing a large number of these projects.

Jan 1, 1940

By D. Gupta, S. Weinig

This investigation comprises the study of dislocation-oxygen interactions in a! titanium and its effect on the ductile to brittle transition in titanium. Internal friction techniques using a low-frequency lorsion pendulum were used to study the oxygen atom interactions with dislocations in "superpurity" titanium. A calculation of the interaction energy between an oxygen atom and a dislocation, based on the "breakaway" strain resulted in a value of 0.015 ev as compared to theoretical values of 0.022 and 0.035 ev for edge and screw dislocations, respectively. Both the saturation of the room temperature decrement and the transition from ductile to brittle behavior occurred at 1.5 at. pct 0. It was proposed that the embrittlement was due to oxygen atoms immobilizing the dislocations. It was possible to increase the ductility of the Ti-0 binary alloys by decreasing the oxygen pinning. The increase in uniform elongation was 30 pct for an increase in the preanneal temperature of 300°C. ThE room-temperature ductility of a titanium is significantly affected by interstitial solutes. Although oxygen has a solid solubility of 15.5 pct by weight, the room-temperature ductility extends only to 0.6 pct.' The ductility precipitously falls at this concentration and the fracture characteristics change from ductile to brittle.2 The small effective bulk composition of solute required to destroy the room-temperature ductility of the titanium must be indicative of an in-homogeneous distribution of solute atoms. Internal friction techniques were used in this investigation to

Jan 1, 1960

By N. P. Goss

ASTERISM appearing in X-ray Laue dia-grams is an extremely sensitive index of changes in the internal structures of indi-vidual grains of polycrystalline metals. It indicates the existence of various forms of subboundary structure or subdivision within the grain. The present viewpoint is that the grain is made up of lattice blocks having substantially the same size and shape.1-4 When these blocks all assume exactly the same orientation, the crystal is perfect and asterism is absent. Cleaves and Thompson5 observed that the hardness of iron is virtually constant over a range of grain sizes. It is quite possible that the subboundary structure caused this, and that the latter is just as important as grain size itself. While the experiments reported here are not con-clusive, they do support this viewpoint. Metals can, under certain conditions, be prepared entirely free from asterism, but this preparation does not necessarily require long heating or slow cooling, as will be shown here. In this paper a distinction is made be-tween mosaic and distorted grain struc-tures but the difference is only a matter of degree. In a previous paper9 it was shown that the grains can become distorted even during heat-treatment. The block structure exists inherently, even in a perfect crystal; the size and shape of these crystallites, or lattice blocks, varies, depending upon a number of factors. Goetz, for example,7 has shown that a metal before crystallizing from the molten state must go through a paracrystalline phase with oriented groups of atoms about 10-14 to 10-15 c.c., or 10-5 cm. in size.

Jan 1, 1940

By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967

By T. B. Counselman, T. B.

Continuous countercurrent decantation calculations have always been a headache to the cyanide man (and the chemical engineer) because of the simultaneous equations involved. These are tedious to solve, and there is considerable opportunity for mathematical error. This paper presents a shortcut method for making these calculations, which has been in successful use for twenty years by the author, and which is particularly valuable in selecting the best of several possible flowsheets, or evaluating the effect of various assumptions.

Jan 1, 1950