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By H. H. Rachford, J. Douglas, D. W. Peaceman

A numerical solution of equations describing two-phase flow in porous media shows promise in providing a technique for predicting the displacermet from satlds of oil by water or gas. The description includes the influence of relative permeability, fluid viscosities and densities, graviry, and capillary pressure, and, tholrgh tested ortly for two-dimensional cases, should be eqlmlly applicable in three-dimensional geometry. Two memorical methods ore presented: the first method is quite general in its applicability; the second method can be used only with certain types of boundary conditions but requires less computing. Comparisons of computed results with data from Inhoratory models are presented. These data were taken on a water flood of a strarified model and on water floods of a five-spot model for favorable and unfavorable mobility ratios. On the stratified model, excellent agreement with recovery at breakthrough was obtained; agreement with recovery after breakthrough was poor. In the five-spot model, good agreement was obtainecl with recovery at and after breakthrough. The purpose of this paper is twofold: first, to present a reservoir engineering method requiring knowledge only of rock geometry and the normally measured rock and fluid properties for calculating the multi-dimensional flow of water displacing oil from porous, water-wet rock containing connate water; and, second, to investigate the validity of the method by comparing results of calculations with previously observed displacements in laboratory models. The availability of such a verified technique of reservoir analysis would afford major advantages. First, it would demonstrate that the fundamental macroscopic concepts of two-phase fluid mechanics, i.e., relative permeability and capillary pressure, yield an adequate description of the physical process. Also, since most reservoir rocks appear to be water-wet and contain connate water along with oil, it would provide a method of technical and economic value for calculating the course of oil displacement by water directly from measured reservoir and fluid properties. It is important to emphasize that the calculation is subject only to the limitations of detail and precision of reservoir information, but not to limitations introduced by simplifying assumptions. Further, it would providc almost the only means of examining the influence of factors such as the size and extent of reservoir inhomogeneities and uncertainties in the basic reservoir data. Knowledge of this influence is essential in stating quantitatively the detail required to define a reservoir and in establishing the relation between the uncertainty in the definition of reservoir properties and the reliability of predicted performance. Moreover, in the process of solving a particular problem much detailed information would become available about the displacement process. For example, at each point in the reservoir for all stages of the displace ment. the calculations would yield not only the water and oil saturations but also the direction and magnitude of fluid velocities and the local fluid mobilities. Such dctail is potentially of great value in giving insight into the mechanics of particular displacements. The development of such a method has long been the goal of research in the application of numerical an-alysis to petroleum reservoir enginecrinz. The most complete treatment of the displacement process published to date is that of Douglas. Blair, and Wagner,' which, however, was limited to flow in a single dimension. The method presented in the present work is hascd on the numerical solution of a finite difference analogue of the multi-dimensional differential system describing the displacement process. Although current work has considered only displacement of oil by water from water-wet sands, the differential system for other immiscible displacements, such as gas displacing oil with which it is in phase equilibrium, is quite similar. It should therefore be expected that the technique described will be applicable to displacement by gas as well. The description of the simultaneous flow of fluids through porous media in terms of relative perrncability and capillary pressure has been adequately discussed in the literature and standard textbooks. Sec, for exampje, Muskat. Chapter VII.'

By J. E. Hove

The high temperature physical properties of graphite are reviewed and interpreted in the light of present day knowledge of the mechanisms affecting these properties. The thermal and mechanical behaviors only are discussed and, whenever possible, comparisons are made with other refractory materials. Possible further studies are indicated, including some carbide work. AS long as the term high temperature implied only temperatures up to about 1000°C, the materials problems which arose could usually be handled by fairly conventional metal alloy types, such as the Co-Cr-Ni superalloys, for which there exists a great deal of technology. Perhaps this temperature can still be considered an upper limit for normal applications, but it is certainly true that the number of abnormal applications is increasing rapidly. The advent, in recent years, of ram-jet and rocket missiles and of high power nuclear reactor heat sources has raised a host of questions concerning the basic problem of what material to use in the temperature range up to 2000°C and higher. While there are, of course, many metals, in the second and third transition series, which melt at considerably higher temperatures than this, these metals are, at present, pretty well excluded from practical use by other considerations, such as re-crystallization, chemical activity, or excessive plastic deformation. The behavior of metals, from the standpoint of dislocation theory, is just beginning to be understood and thus there is some hope for the future development of very high temperature metals, but the immediate problems would most logically appear to have solutions involving the nonmetals, such as the refractory ceramics and graphite. For this reason, there is presently a great deal of engineering and experimental research being performed on the latter materials, much of this research being exploratory in the sense of gathering new property data. The situation, so far as graphite is concerned, is somewhat more fortunate than with the other refractory solids in the sense that a great deal is already known about its basic properties. This stems both from the fact that the carbon-carbon bond has been of interest to chemists for a long time (and graphite can be considered as a very large aromatic molecule, if desired) and the fact that its properties, both as a function of temperature and of radiation damage, are of critical importance to nuclear reactor designers. It is still true, of course, that such fundamental questions as why graphite remains solid to such a high temperature and why it has such a high thermal conductivity cannot entirely be answered at the present time. It is, nonetheless, meaningful and instructive to consider such problems in the light of existing knowledge. This is what the present paper will attempt to do. Before going on, it may be appropriate to classify graphite and justify its discussion before readers primarily interested in metals. Graphite is comparatively unique among materials in that there is always a property or group of properties which precludes calling it either a metal, a semiconductor, or a ceramic. It has the high electrical and thermal conductivities of a metal, but the artificial, poly-crystalline types show a negative thermal coefficient of electrical resistivity, generally characteristic of semiconductors. On the other hand, semiconductors, by definition, show an ever increasing resistivity as the temperature is lowered, whereas graphite approaches a finite, and, indeed, a rather low resistivity in the region of 10°K and, furthermore, a good single crystal of graphite has a positive temperature coefficient, as for a metal.' On still another hand, its porosity and brittleness at lower temperatures would put graphite in the ceramic class although, unlike most ceramics, it is readily machinable and has a high resistance to thermal shock. All things considered, it is probably more nearly appropriate to call graphite a metal than anything else. Although certainly outstanding in some ways, graphite has its peculiarities and, especially if the reader is unfamiliar with the data, it is probably valuable to review some representative property variations at high temperature. This review is meant to be mainly illustrative and no attempt has been made to be exhaustive. Review of High Temperature Properties At ordinary pressures, graphite does not melt, but sublimes directly into the gaseous phase at about 3700°C. Although the phase equilibrium diagram is still in some doubt, graphite will melt, at a slightly higher temperature, at pressures in excess of about 100 atm. The chief difficulty of using graphite in an oxidizing atmosphere is that the reaction rate becomes quite high at fairly low temperatures. If a threshold oxidation temperature2 is defined as the temperature at which graphite loses 1 pet of its weight in 24 hr, the value in air is 450°, the value in steam is 700°, and the value in carbon dioxide is 900°C. Efforts are presently being made to raise this threshold temperature either by impregnation with a retardant of some type (sodium tung-state and phosphoric acid, for example) or by a suitable metal or oxide coating. It is probably fair to say that, to date, these attempts have not shown any outstanding success in all respects. Most commercial graphites are fabricated by impregnating a carbon flour (say of coke or lampblack particles) with some type of hydrocarbon

Jan 1, 1959

By E. T. Turkdogan

This paper deals with an analysis of the conditions leading to the formation of blowholes and surface and subsurface defects in cast low-carbon steels. The theoretical analysis of the problem is based on the concept of the occurrence of deoxidation reactions during cooling of liquid steel and during its solidification. The reaction equilibrium data are given on deoxidation of steel by carbon, silicon, and manganese. The details of the calculations are given on the simultaneous deoxidation of steel by silico-manganese additions to produce a desired level of deoxidation at certain residual concentrations. Based on an idealized model, an attempt is made to calculate the enrichment of solutes in the solidifying liquid entrapped within the interdendritic cells which are known to be less than 200 µ thick. Formulae are derived for the calculation of the change in the residual oxygen content of the enriched liquid steel, controlled by Si/Mn deoxidation. It is shown that for every particular initial silicon, manganese, and oxygen concentration in steel (as residuals in liquid solution at the beginning of solidification) there is a particular carbon concentration below which carbon monoxide, leading to blowholes or pinholes, is not expected to form. There are a number of independent variables which have a decisive influence on the formation of blowholes. For example, it is shown that the position of the curve depicting the critical relation between initial silicon and carbon content for suppression of the evolution of carbon monoxide) can be shifted to lower silicon or higher carbon levels by: increasing manganese content; decreasing oxygen, hydrogen, or nitrogen content; or increasing external pressure on the solidifying mass. FOR the production of sound castings it is essential to prevent the formation of interdendritic worm-holes or pinholes brought about by gas evolution during solidification. Another major problem encountered in solidification of ingots is the formation of surface defects. These problems are thought to be closely associated with the deoxidation reaction occurring in liquid steel during cooling and subsequent solidification. As the liquid becomes richer in impurities during dendritic solidification of steel, a series of reactions may occur in the liquid phase trapped within the branches of growing dendrite platelets. Because of the strong interaction between dissolved oxygen and impurities in liquid steel, the reactions most likely to occur are of the deoxidation type. However, inherent to the extreme complexity of the problem in question, numerous simplifying assump-

Jan 1, 1965

By R. P. Alger, C. A. Doh, M. P. Tixier

The principle, the equipment and field operation of sonic logging are described. The tfio-receiver system produces logs independent of hole size and mud. Field experience is given and forms the basis for the interpretation of the log. The derivaiion of porosity values from measured velocities is discussed, according to the type of formations (hard formations, compacted sands, and unconsolidated formations). The time-average equation proposed by M. R. J. Wyllie, A. R. Gregory and L. W. Gardner is uscd as a basis for the computation of porosity in limestones, cemented sandstones and compacted sands. Variations in the lithologic character of limestones do not seem to change the porosity calibration markedly. The compaction of sands is related to the compaction of shale adjacent to them; and, thus, the shale velocity is used for the establishtnent of empirical relations for the computation of porosity in un-consolidated formations. Various forrnu.las are tentatively presented to account for shale and fluid content. Field experience demonstrates that considerable attenuation of sonic energy takes place in unconsolidated formations, particularly when gas bearing, and in fractrured formations. Unusually large attenuation produces skipped cycles, a feature easily recognized. The application of sonic logging to structura1 studies is featured, showing its possible integration with the dipmeter. Correlation and its application to the irrterpretation of seisrmic surveys are reviewed. The paper is illustrated with field examples. Sonic logging is the recording of the time required for a sound wave to traverse a definite length of formation. Sonic travel-times are inversely proportional to the speed of sound in the various formations. The speed of sound in subsurface formations depends upon the elastic properties of the rock matrix, the porosity of the formations and their fluid content and pressure. Below the "weathered" or low-velocity layer extending from 50 to 100 ft or so below the surface, sound velocities may range from about 6,000 ft/sec in shallow shales to as much as 34,000 ft/sec in dolomites. In hard formations (well cemented and/or compacted), the sonic log reflects the amount of fluid in the formations; hence, it correlates well with their porosity. In unconsolidated formations, which are usually of fairly high porosity, the sonic log gives an approach to porosity determination, when its readings are corrected for lack of compaction, shaliness, and fluid content. In such formations the sonic log may also indicate the presence of gas and may distinguish between oil- and water-bearing beds. Field experience with the sonic log in soft formations is more limited than that in hard formations. As a result, interpretation in soft formations is not as well developed at the present time. In all types of formations the sonic log is of considerable value for correlation and for the more detailed and accurate interpretation of seismic data. EQUIPMENT AND PRINCIPLE FIELD OPERATION The basic features of the sonic log" are a two-receiver system and two available short spacings. The log is recorded on film using a standard field unit. An SP curve is run along with the sonic curve to give a more interpretable log and to establish absclute depth control for comparison with other logs run in the same well. If desired, a gamma-ray curve may be recorded simultaneously with the sonic curve. Fig. 1 shows the sonic-gamma ray combination sonde. The sonic portion consists of a sound transmitter and three receivers mounted 3, 4 and 6 ft from the transmitter. When the first and second receivers are used, a sonic log of I -ft spacing (distance between receivers) is obtainea. Use of the first and third receivers provides a 3-ft spacing. The transmitter emits pulses at the rate of l0/sec. After the transmission of a pulse the first arrival of sound energy at each receiver triggers its response system. The differ-

By Carl Pierce

The writer of this article has not attempted to write a technical paper; on the contrary, he has tried to express in "steel-plant English," for steel men, a viewpoint drawn from his practice and experience. It is not his thought that it shall be taken as the "last word" in the making of this class of steel, or that good rimming steel cannot be made by any other practice. The paper was written to serve as the basis of a discussion from which it is hoped much benefit may be derived. The paper deals only with rimming steel made by the open-hearth process, and with the lower carbon steels, such as sheet and tin bar, rivet stock, skelp, etc., although good rimming steel as high as 40 to 50 carbon can be made by having good open slags and giving proper attention to working and tapping temperatures. Definition of Rimmed Steel Rimmed steel is sometimes called open or effervescing steel to differentiate it from killed or partly killed steel. It is steel made by a process which permits the free escape of gases from the metal in the molds. In passing up through the metal, the gases keep it in a rolling action from the walls of the mold inward. The top of the ingot rims in as the metal chills and the walls of the ingot get thicker, the center part remaining fluid until it reaches a pasty condition when it is covered with a cast-iron cap. The Charge In making up a charge for rimming steel, clean stock of a known composition must be selected, special attention being given to the analysis of the materials. The silicon in good rimming steel must be eliminated to a trace, therefore it is advisable to have a uniform amount going into the charge. Too much silicon gives a raw melting heat from which rimming steel is unlikely to result. For this reason a charge containing not to exceed 40 per cent. pig iron and 60 per cent. scrap, with no iron ore, is preferred to the Monell type of charge in which as high as 65 to 70 per cent. pig iron is used with a proportional amount of iron ore for the removal of the excess silicon and carbon. The silicon content of pig iron varies so much from day to day in the average blast-furnace practice that there is danger of getting too much of this element in the latter mixture when

Jan 1, 1926

By D. M. Milne, R. F. Stoner, W. Bakiewicz

The Lower Indus Basin deposits form a substantial unconfined alluvial aquifer of excellent quality. This aquifer contains basically highly saline groundwater, overlain in places by considerable amounts of fresh water whose origin can be traced to the present and historical courses of the River Indus. In the past, the main source of groundwater recharge has been direct river seepage and water tables were generally deep. Since the establishment of a perennial irrigation regime however, deep percolation from the increased irrigation supplies has predominated and the water table has risen to within a few feet of the surface. The river system itself is being progressively devel-oped for irrigation and very shortly a situation will arise where the entire low winter flow will be utilized. Fresh groundwater will then be exploited to supplement the surface supplies, and at the same time a drainage system, mainly based on wells will be used to stabilize the water table at safe depths. This paper discusses some of the methods used to ensure optimum economic development of the fresh groundwater and describes the general design philosophy evolved by the authors' firms for both irrigation and drainage wells, with respect to both well configuration and operation. Water quality standards are discussed insofar as they affect subsequent use of the groundwater. A few particular aspects are considered, including the values of the relevant aquifer constants, the construction of wells, and the determination of screen losses. A major problem solved during the Lower Indus Project investigations has been the design of wells to produce fresh water from layers overlying saline water. This solution is also discussed. The recent interest in the groundwater of the Lower Indus Plains of West Pakistan has two main aspects. Firstly, soil waterlogging and the associated salinity hazards caused by rising water tables are a serious problem in agriculture, and the ease with which drainage requirements can be met by aquifer pumping makes this an obvious solution. The second interest stems from the rapid intensification of irrigation agriculture and the growing shortage of water supplies. In the areas where the groundwater is of suitable quality it can be used immediately for irrigation at relatively small cost and with large financial returns. In addition, the aquifer forms a potential storage reservoir which could be recharged from high river flows and depleted by pumping at times of scarcity. SOURCE OF GROUNDWATER The Lower Indus plain is a relatively long and narrow alluvial basin on a north-south axis, some 23,000 sq miles in area, bounded by higher land to the east and west. One hypothesis to explain the distribution and quality of groundwater in the region1 presupposes a river system considerably larger than, but very similar to the present river. This is characterized by a single mainstream, with subsidiary overspill channels in times of flood, running along the crest of a self-deposited ridge and with an extensive advancing delta. Sea water is contained in the alluvial pores of the advancing delta, forming the native groundwater. This has been partially displaced from two sources, namely direct seepage of fresh water from the river channel in meander flood plain areas and percolation from flood spillage in cover flood plain areas. Percolation has been subject to much re-evaporation and is thus slightly saline even as it reaches the groundwater. The whole complex has been further affected by two main influences: evapotranspiration from the land surface that tends to salinize the groundwater and down-valley flow that tends to bring fresher water

Jan 1, 1970

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman's arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman's paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman's work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"'. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963

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 A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,' who first dealt with the coning problem; (2) Chaney, et al,' who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.' Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,' and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy's law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

By Chester Wells Purington

Situation.—The Camp Bird mine is in Imogene basin† (Fig. 1) at the head-waters of Canon creek, a branch of the Gunnison, in the southern part of Ouray county, Colorado, towards the northern edge of the region known as the San Juan mountains, and about 10 miles W. of the continental divide. It is 8 miles by wagon-road from Ouray, the terminus of a branch of the Rio Grande' Southern railway. The distance from Denver to Ouray is 387 miles by rail. In an air-line, the mine is 190 miles SW. of Denver. The altitude of the town, tunnel and buildings is 11,200 ft., and level No. 2 is 11,500 ft., and No. 1 is 11,670 ft., above sea-level. The lowest point of the lode-ontcrop, which crosses the basin E. and W., has an elevation of 11,850 ft., and that of the highest point, on the divide between Imogene and Tomboy basins, is 13,250 ft. On the eastern slope of the Imogene basin (towards Ironton) the vein is less clearly defined on the surface. Ownership and Extent.—At the time of the writing of this paper, the property is owned by Mr. Thomas I?. Walsh, and operated under the management of Mr. J. W. Benson. It

Jan 1, 1903

By H. H. Campbell

The following pages discuss some problems connected with the manufacture of steel by the open-hearth process. The methods employed necessarily enter into the domain of what is called theory; but the results are eminently practical. The determination of the various losses of thermal power and the investigation into the chemical reactions in the bath, are important to every manufacturer. It will be understood that definite figures concerning one furnace and one system, will not apply to all other furnaces and systems; but it is hoped that methods are developed, which are capable of general application and which will shorten the labors of others. The gas-calculations contain nothing entirely novel; but certain methods appeared to be very convenient and they are here elaborated in order that others may have a model to follow. The determination of the loss of iron by weighing the slag and finding the percentage of iron therein, is probably unusual. If so, the fact is to be regretted, since this is the only way that an accurate result can be obtained. The common method of estimating the loss in open-hearth work, is to subtract the weight of metallic products from that of the materials charged. Nothing could be more unsatisfactory, inaccurate and meaningless. Pig-iron, steel, wrought-iron and ore are charged into the furnace; complicated chemical reactions occur; the sand of the pig-iron, the slag from the wrought-iron, the gangue of the ore, all rise to the top ; the silicon, manganese and carbon burn and leave the metal; some of the iron oxidizes and goes into the slag; some of the ore is reduced and gives up metallic iron ; the recarbonizer is added, the mission of which is to waste itself; in the pouring of the steel, pit-scrap is made in the ladles, around the moulds and under the spout; the errors in weighing the products join hands to make accuracy impossible; and then the " loss" is determined by diffrence !

Jan 1, 1891

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By D. N. Collins, J. R. Stevens

New expressions in the technical assessment of mineral concentration processes have been defined as Concentration Efficiency: Concentration Index: where h is the percentage of head grade; c, percentage of concentrate grade; maximum percentage of concentrate grade obtainable at 100 pct recovery; and R, percentage of recovery. In developing these expressions, the basic requirements for the technical assessment of concentration operations have been defined and the various expressions suggested by others for asses-sing the results of such operations reviewed and criticized. The derived expression for E, depends on a simple combination of recovery (R) and a new term selectivity (s), where S is (c-h)/(c,,, -h), by definition. Limitations of the new expressions are discussed and examples given of applications to concentration operations. It is also shown that the formulae for E, and I, can be applied to scatter diagrams, multi-component systems, size-assay analyses, and classification data. Many methods of quantifying concentrating operations have been proposed. These include direct presentation of weights and assays together with the derived data for other items such as ratio of concentration, recovery, rejection losses, and enrichment ratio. These terms are now accepted mineral dressing nomenclature, and in the assessment of the results of concentration processes, concentrate grade and recovery are together the most widely accepted measures of concentration efficiency. For practical purposes when the concentrate grade is equal to or greater than a predetermined acceptable value, test or operation results may be assessed by the recovery figures alone. Similarly when recovery is within specification, the operation can be assessed by concentrate grade. The ultimate assessment and selection of a concentration operation is—admittedly with a few ex-ceptions—a matter of economics. There is however an intermediate stage in laboratory and pilot plant testing when evaluations must be made without the assistance of an economic yardstick. Numerous techniques are employed to facilitate such evaluations among which may be mentioned graphical plots of grade vs recovery, cumulative weight vs cumulative recovery, scatter diagrams, etc. The desirability of combining metallurgical results and product weights and assays into a single value has been recognized and discussed by many workers1-" with the resultant suggestion and use of such terms as Metallurgical Efficiency ,' Summation Index,' Selectivity Index,'- and Absolute Efficiency B None of these expressions completely satisfies all the requirements of a selectivity or efficiency formula and it is proposed in this report to define the terms, relating to the technical efficiency of a concentrating operation, concentration index and concentration efficiency. Examples are given of their application and a comparison is made of their use in relation to other formulae. All product grades in this paper will be referred to in terms of mineral percentages and a list of symbols is given in Table I. CONSIDERATION OF EXISTING FORMULAE A number of the existing efficiency and index terms used in quantifying concentrating operations are considered below. Metallurgical Efficiency:

Jan 1, 1961

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967

By P. W. Rainier

THE Chivor emerald field is situated on the eastern slope of the Andes in the Department of Boyacá, at an elevation of about 8000 ft. above sea level. It overlooks the Llanos (plains) of the Orinoco and is watered by many streams flowing into the Rio Meta, the Orinoco's largest tributary. The Rio Meta is navigable from the Orinoco to a point within about 50 miles of the Chivor district and may eventually prove to be the reasonable outlet for the future development of this part of the country. The topography of the district is extremely rugged and mountainous (Fig. 1), the difference in elevation between two points on a mining claim 1 km. square being sometimes as much as 4000 ft. The ground is covered with dense forest growth and the available timber is suitable and sufficient for mining purposes, but it is becoming gradually depleted by Indian clearings as the country around the mines becomes settled. The many streams combined with the rough topography give good possi-bilities for hydroelectric power. The center of population nearest to Chivor is Bogota, the capital of the republic and a city of some 300,000 inhabitants; the distance is two and one-half days' travel. The first stage of the journey from Bogota, is accomplished by rail to Chocontá, some 4 hr. travel. From Chocontá the journey is made in the saddle, one night being spent in Guateque. The latter is a small town and the nearest post office to the mines, being some 10 hr. ride distant. The roads are mere bridle paths, in parts hazardous and almost impassable in the wet season. All supplies brought to the mines, other than those produced locally, are carried by pack mule; mule freight from Chocontá costs 3 centavos1 per pound. The climate of the Chivor district is healthful and bracing. The wet season begins in March and concludes in November, the remaining months being dry. The annual precipitation is about 150 in. The temperature throughout the year is nearly constant, varying from about 45° F. to about 65° F. shade temperature. The rains are cold and unpleasant, and for the greater part of each day in the wet season the country is shrouded in dense mist. A fire can with comfort be kept burning in a living room all the year round. There are a few slight

Jan 1, 1929

By Richard H. Jahns

Gem materials, comprising those minerals and closely allied natural substances used for personal adornment, for the fashioning of ornamental objects, or for other decorative purposes, have been valued in human commerce for thousands of years. Amber, jet, natural glasses, and at least 15 mineral species were sought and used by primitive man, and most of the materials in common use today were known well before the time of Christ. Their variety is remarkably great, and the traceable relationships among their respective sources, modes of occurrence, properties, and histories of production, preparation, and valuation are extremely complex. Their uses have been affected by numerous shifts in fashion, and from time to time by superstition, by decrees of church and state, by personal interpretations of religious significance, and by various presumptions concerning medicinal value and influence on human behavior (Ball, 1935, 1950; Kunz, 1913; Pogue, 1915, Whitlock, 1946). Thanks to their durability, portability, and relative scarcity, some gem stones have been employed as media of exchange, and the investment value of the more precious stones has long been recognized and exploited, especially in Asiatic and European countries. Demands for gem materials have stimulated trade among various peoples for centuries, and they also were responsible for much early geographic exploration. During more recent times they have prompted numerous geological studies and a considerable amount of research on the growth and properties of crystals. Apart from decorative uses, some naturally occurring gem materials also are employed directly in numerous fields of industry. Substances that are manufactured for gem or industrial uses are termed synthetic gem materials; most of these correspond in composition and crystal structure to certain minerals found in nature. Imitation materials are those whose use is based upon their resemblance to substances of different composition and greater intrinsic value. Gem stone is a designation commonly restricted to those materials suitable for personal adornment, and the complementary term ornamental stone is applied to the remaining materials not used industrially. This distinction is arbitrary and somewhat inconsistent, owing to numerous geographic differences and historical shifts in end uses. Further, there is a complete gradation between the category of ornamental stones and that of dimension stone. Substances that lose their identity in use are excluded from the gem category; thus a transparent crystal of beryl would not be classified as a gem stone if it were processed as a source of beryllium metal. The adjectives precious and semiprecious have been employed as a means for distinguishing different gem materials on the basis of recognized value. Diamond, emerald, ruby, and sapphire consistently have been regarded as precious stones, and in cut form they commonly are referred to as the noble gems. Opal, pearl, turquoise, and chrysoberyl also have been classed as precious at various times. In recent years, however, it has been increasingly recognized that no satisfactory distinction can be based upon assessed value or any group of specific properties, and now all gem stones normally are referred to as precious. Indeed, the tendency is to extend this term to include many of the so-called ornamental stones, and the designation semi- precious has been essentially discontinued. Unlike most mineral commodities of economic value, gem materials are little altered in processing for end uses. Some stones are used in essentially their natural form, and most are reshaped and polished without significant changes in their fundamental properties. Thus the preparation of gem and ornamental stones is intended chiefly to emphasize or enhance

Jan 1, 1975

By Haydn H. Murray

The term clay is somewhat ambiguous unless specifically defined because it is used both as a rock term and as a particle size term. Actually most persons using the term clay realize that it has a double meaning and in most instances define it. As a rock term, clay is difficult to define because of the wide variety of materials that compose it so that the definition has to be general. Clay is a natural, earthy, fine-grained material composed largely of a limited group of crystalline minerals known as the clay minerals. Many definitions state that a clay has the property of plasticity when wet, but some clays are not plastic, i.e., halloysite and flint clay; however, most clay materials are plastic when wet. As a particle size term, clay is used for the category that includes the smallest particles. The maximum size particles in the clay size grade are defined differently on some grade scales. Soil investigators and mineralogists generally use 2 microns as the maximum size. The Wentworth scale' defines clay as material finer than approximately 4 microns. Grim' has found it convenient to use the term clay material for any fine-grained, natural, earthy, argillaceous material and in this way can include clays, shales, or argillites, and some soils if they are argillaceous. Even though no standard definition of the term clay is accepted by geologists, agronomists, engineers, and others, still the term is generally understood by all who use it. Clay is an abundant natural raw material and has an amazing variety of uses and properties which will be discussed in this chapter. In order to understand better the relationships between the clays and their uses, a brief discussion of the structure, chemical composition, and identification of the clay minerals is given. Mineralogical Composition of Clays Clays are composed of certain groups of hydrous aluminum, magnesium, and iron silicates that may contain calcium, potassium, and other ions, which are called the clay minerals, and other minerals of variable composition, which are nonclay minerals. Both clay minerals and nonclay minerals influence the properties of a clay material. In order to understand the relationship between clay minerals and the properties of a clay material, a short summary of the structure and composition of clay minerals is necessary. Any scheme of classification tends to impose a certain rigidity and as new and additional data become available it is necessary to revise classifications. Brindley3 has discussed the classification and structural mineralogy of clays in very lucid fashion and chose a classification based on structural features and chemical composition. Grim2 proposed a tentative classification which is based on the structural attributes of the various clay minerals. This classification is relatively simple and workable, and is shown as follows: I. Amorphous Allophane group II. Crystalline A. Two-layer types (sheet structures composed of units of one layer of silica tetrahedrons and one layer of alumina octahedrons). 1. Equidimensional Kaolin group kaolinite, dickite, nacrite 2. Elongate Halloysite group

Jan 1, 1960

By E. C. Bain, E. S. Davenport

When annealed carbon, or low-alloy, steels are suitably heated the ferrite (alpha iron solid solution) and the carbide, of which they are composed, react together to form a single solid solution of carbon (and other elements) in gamma iron (austenite). This reaction may begin only at a certain minimum temperature called the eutectoid temperature. The first ferrite and carbide thus to react together do so in definite proportions known as the eutectoid composition. With further heating the original constituent that is present in excess is dissolved in the austenite until exhausted. Whether the excess constituent be ferrite (hypoeutectoid steels) or carbide (hypereutectoid steels) the procedure is much the same, and upon slow cooling the homogeneous austenite expels the excess of either (proeutectoid ferrite or carbide) until the eutectoid composition is reached. Thus the reaction upon heating is strictly reversed upon cooling and accordingly an equilibrium diagram of this process may be constructed. Such an equilibrium diagram concerns itself only with the temperatures involved and with the proportions and compositions of the phases developed under conditions that suffice to permit equilibrium. Specifically it has no concern for the type or mode of distribution of these constituents nor with any extra-equilibrium conditions such as undercooling, which is almost universally encountered in metals. Actually, however, of great importance is the sluggishness toward equilibration caused by the not inconsiderable time involved in diffusion. Thus instead of the theoretical transformation point AF, we find for a certain rate of heating or cooling the use of the designations Ar and Ac (transformation temperature found on cooling and upon heating). These figures obviously have no particular meaning except as measured and expressed for a definite heating or cooling rate, and represent the apparent temperature displacement caused by an inadequate time allowance. In this paper are presented the results of a study of the time required for the transformation of austenite to ferrite and carbide at a variety of temperatures and also of the time required for the reaction austenite? martensite at the temperatures at which this reaction occurs instead of

Jan 1, 1930

By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection' at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969

By N. A. Ziegler

IN every research it is desirable to eliminate as many variables as possible and to leave only a few to be investigated one at a time. Metallurgical problems are no exception. Some of the variables that are difficult to control are the size, the distribution, and the orientation of the grains in a metallic test piece. It is therefore very desirable to obtain isolated metallic grains (single crystals, as they are commonly called) large enough to enable one to study their mechanical and physical properties. The present investigation is a part of magnetic research work on iron and iron alloys, undertaken to obtain, if possible, the magnetic properties of pure iron (Fe). This paper will deal primarily with the preparation of single crystals of iron and their mechanical properties, while another paper, by T. D. Yensen, now in preparation, will deal specifically with their magnetic properties. The work with "single crystals" is attracting more attention every year among the investigators in metallurgy. Van Liempt1 gives an interesting summary of the work done and the different methods used in the preparation of metallic single crystals. Briefly stated, the four principal methods used are the following: 1. The cooling of a liquid metal in such a way that the crystallization would start at one point only, causing the entire liquid to solidify as one crystalline unit. This method can be successfully applied to the majority of the metals that do not have any allotropic transformations in the solid state. It has been used and described by a number of investigators,2 but it has never been successfully applied to iron on account of allotropic transformations.

Jan 1, 1930