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By W. R. Reed

The National Institute for Occupational Safety and Health (NIOSH) uses light-scattering dust monitors (nephelometers) in its research to develop dust controls to reduce respirable silica dust overexposures in miners. Recently, the model 1500-pDR, an active nephelometer, was introduced by Thermo Scientific. Testing was completed to ensure compatibility with the metal/nonmetal mine dust personal sampling unit (M/NMDPSU). Results of testing demonstrated that gravimetric concentrations measured from the 1500-pDR are comparable to the gravimetric concentrations measured using the M/NMDPSU, without need for correction, under commonly observed dust loading conditions.

Jan 1, 2012

By J. B. Cohen, O. F. Kimball

Aging of specimens of Au-20 at. pct Ni and Au-40 at. pct Ni has been followed with electron microscopy, resistance, magnetic measurements, and X-ray diffraction. The periodic structures observed by electron microscopy in Au-Ni alloys by Fisher and Embury are shown to be due to nickel-rich prepre-cipitates. Assuming this alloy system undergoes spinodal decomposition, our observations and available data on thermodynamic properties and elastic constants indicate that the gradient energy coefficient in this system is of the order of 10-5 ergs cm-1 . Shifts of X-ray peaks in this system have been found to be due primarily to residual stresses, not faulting. A large effect of applied stress during aging was detected by X-rays and electron microscopy for the Au-20 at. pct Ni alloy. The presence of a preprecipitation stage during aging of gold-rich Au-Ni alloys for short times below 300°C has been indicated by several previous investigations. Changes in electrical resistivity,1"3 elastic modulus,4 superparamagnetisrn,5 positions of X-ray diffraction peaks,6 and hardness7 have been studied. Electron diffraction and microscopic studies by Fukano8 and Fisher and Embury9 respectively showed that the precipitation process resulted in the formation of periodic composition fluctuations—perhaps spinodal decomposition. MOSS10 detected a satellite with X-rays in quenched specimens, but the wavelength was much smallerthan that found by Fukano. Recently Woodilla and Averbac11 detected a modulation similar to that found by Moss, but with electron diffraction. They suggested that the microstructures observed by Fisher and Embury may be simply due to a Moir'e effect from a back deposit of gold during electropolishing. Satellites in electron diffraction can be enhanced by small bends or tilts of a foil. Even if this were not the case, asymmetric satellites, as are found in Au-Ni are difficult to analyze. They are principally influenced by the large differences in atomic size in this system, and obtaining information on the associated composition fluctuations depends on assumptions as to whether or not there are isolated clusters or composition "waves", and in the latter case whether or not the entire specimen has decomposed. Assuming that decomposition was complete in alloys aged at low temperatures, Woodilla and Averbach suggested that the satellites indicated a composition which varied about the average value by only± 5 pct, much less than that predicted from the phase limits, Fig. 1; they attributed this small variation to a cessation of the reaction caused by the loss of mobile vacancies. In Ref. 12 it was shown that vacancies are trapped by the preprecipitate in this system. Furthermore, after reversion, aging proceeds at a much slower rate than immediately after a quench from the solution temperature,5'11,13 indicating the importance of vacancies in the kinetics. In some senses Au-Ni is a favorable system for studying preprecipitation and reversion mechanisms because of the simplicity of the equilibrium diagram14 and the availability of good thermodynamic15 and diffusion data.16,l7 The calculations necessary to relate the decomposition process to classical nucleation and growth or to spinodal decomposition, as well as those necessary for understanding reversion mechanisms, can, therefore, be made. As an example, the position of the chemical spinodal, calculated from the thermo-dynamic data of Sellars and Maak15 with the method described by Rundman and Hilliard,18 is included in Fig. 1. It is compared to the chemical spinodal calculated from the equilibrium miscibility gap by Cook and Hilliard's method.l9 Included is the coherent spinodal suggested by Golding and MOSS," using measured elastic constants for their calculations and the same ther-modynamic data. The spinodal estimated by Woodilla and Averbach,11 by determining the temperature limits for the observation of the satellites discussed above, is also given. Actually this last curve is open to question on the following grounds: As a phase boundary is approached the spacing of particles or the wavelength

Jan 1, 1970

By D. D. Bolstad, S. M. Dar, T. W. Smelser, H. C. Pettibone

The use of roof bolt supports has reduced the number of fatal and nonfatal roof fall accidents in coal mines. Roof fall accidents, however, still occur far too frequently. Roof bolting plans are based almost entirely on trial and error, which inevitably leads to underdesign or overdesign with regard to bolt length, spacing, tension, and bolt type for the specific conditions. Underdesign poses safety problems, and overdesign leads to unnecessary costs. Guidelines are needed to select and design optimum roof-bolt plans that will maximize safety and minimize cost. Despite the use of 100 million roof bolts per year, the theory of roof bolting remains underdeveloped. Underground tests designed to provide this knowledge have been only partially successful owing to the many uncontrollable geologic variables present in underground mining situations. The Bureau of Mines believes that the best approach is to conduct a laboratory model study in correlation with finite-element analysis (FEA) and field verification, where these variables can be tightly controlled and measured. A physical model allows precise performance measurement of different bolt types as a function of a wide range of precisely measured parameters. Although the model being used is idealized and limited in size, it serves as a reliable basis for confirming the mechanism of rock reinforcement by bolting and the accuracy of the computer FEA approach to modeling mining problems.

Jan 1, 1984

By Colin J. Booth

Hydrogeological impacts of active longwall mining were studied at two sites in Illinois. At the site with the more transmissive sandstone aquifer, aquifer permeabilities increased an order of magnitude due to subsidence. Piezometric levels declined with subsidence due to increased porosity, and ahead of mining due to a transmitted drawdown. Levels recovered rapidly at first and fully over two years. At the site with the less transmissive aquifer, impacts were similar except that recovery has been limited. Local aquifer enhancement through increased yield can occur, but only where the aquifer is transmissive enough for recovery.

Jan 1, 1986

By H. Henao, F. Canales

The present work evaluated the use of copper ore flotation tails as flux in the process of smelting copper concentrates. For this purpose, experimental and simulated liquidus lines were obtained at different ratios of tail/flux. Experimental variables included temperature, partial pressure of oxygen and sulfur dioxide and the conditions of tridymite or spinel saturation. The results indicate the feasibility of replacing the flux by increasing the temperature of the smelting process by 20°C. Results of simulation using FactSage and HSC confirm that the required increase in temperature can be achieved by increasing the flow of concentrate, enrichment of oxygen or increasing the matte grade. INTRODUCTION In the pyro-metallurgical process of copper production, the smelting stage produces two liquid phases, a sulphide phase rich in copper and another composed mainly of oxides called slag. The slag phase is the product of oxidation of the iron contained in the flotation concentrate. The smelting process which is carried out at temperatures of 1250°C, require the addition of silica as a flux and the injection of air enriched in oxygen (Schlesinger 2011). Currently, one of the most important aspects of the mining industry is the minimization of costs, the optimization of the use of available resources and the reduction of environmental impact. Under this context, the use of flotation tails from as a flux in the copper smelting process has the potential of reduced production costs and generate an environmental benefit by reduce the disposal amount of this waste material Regarding the use of copper tails as flux in the copper smelting process, a thermodynamic simulation study using the FactSage software had been reported in the literature (Parra et al., 2011). The results indicated an increase of 35°C in the temperature the liquidus for the equilibrium matte/spinel and a subsequent requirement of energy in the process of approximately 350 [MJ/ton slag]. Given that the calculated viscosity remains in the same order of magnitude, the melting temperature is a more relevant parameter for the evaluation of the use of tailings as flux.

Jan 1, 2019

By AIME AIME

THE American copper mining industry is threatened with disintegration and destruction. This threat is not one which may only materialize in the distant future. The destruction has already commenced. At present, many domestic mines have already closed down. .Others are operating on a greatly curtailed basis. Those operating are doing so only at tremendous loss-because the selling price of copper is below the cost of production and rapidly diminishing financial resources and credit clearly forecast the early suspension of operations in most of the industry. Unemployment in the mining districts is increasing by leaps and bounds. While this condition is due in some measure to the present unsatisfactory state of business in general, the copper industry, unlike other lines of business, sees no possibility of recovery without definite aid. The fundamental, underlying cause of present conditions in the American copper mining industry is the unprecedented rise in foreign production, and the basic change which has taken place in the world copper industry in the last three years. The American industry had begun to feel this change early in 1929 long before the general collapse of business in the fall of that year. While the distress in the industry is undoubtedly aggravated by the present economic depression, it nevertheless would have arrived and. have been present at this time, regardless of general business conditions.

Jan 1, 1932

By Robert Warner

The growing importance of screening makes an accurate measure of the quality of a sizing operation desirable. Screen efficiency is considered equal to the percentage of true undersize in the feed obtained as undersize from the screen. This method is unreliable, as it gives the same credit for removing minus 200-mesh material as for removing material just able to pass the aperature of the screen. A more accurate measure of screen efficiency is to consider only the work done on the "difficult" grains, that is, those grains of which the intermediate diameters closely approach the screen aperture.. The application of this method is given, together with the derivation of formulas and an example of their use. Is AN accurate measurement of the efficiency of a screen under a given set of operating conditions valuable? If so, what is the efficiency; of, a screen and how can it be measured? Sizing, especially of the finer sizes of material, has increased in importance in the development of flow sheets as a result of the perfecting of the rapid vibrating screens. More consideration should be given screens in the preparation of ball-mill feed, where they permit the admission of a dryer feed than, the classifier. Where possible, the introduction of a screen ahead of the primary ball-mill, and the diverting of ore below, say, 4 mm. to a secondary mill, might result in a greater overall economy because of the thicker feed and the better, adjustment of crushing media and mill operation to the reduction demanded. With the present trend back toward a combination of gravity methods and flotation, rather than flotation alone, the accurate, economical sizing possible with the new screens makes fine jigging a method to be considered. W. 0. Borcherdt1 and John Bland2 discuss the screening problem and also the value of close sizing in the concentration of some of the rare-metal ores. If a screen is to be used, it should be selected in competition with others; other things being equal, that screen which makes the cleanest oversize should be preferred. The quality of the screening and the tons

Jan 1, 1924

ATHOUGH the open-hearth charge contributes CO, CO2, and water vapor to the combustion gases and absorbs oxygen from them, in the main the thermal effects in the melting charge and molten bath can be considered independently of those in fuel combustion, the latter being regarded simply as the source of any extra heat required to finish a heat of steel. First of all, it should be remembered that a large percentage of the heat supplied to the bath is furnished by oxidation of the various elements in the charge itself. If this charge consisted of 80 to 100 per cent of hot metal and the oxidation were obtained by blowing in air or oxygen, as is the case in the Bessemer converter, then the net heat absorption would be negative, that is, the bath would contribute part of the heat required to keep the melting chamber hot, in addition to that contained in the finished steel and slag. In actual open-hearth practices, probably the nearest approach to this is in the duplex furnace, charged with Bessemer-blown metal and some hot metal, where very little heat is required to complete the refining and nearly all the heat energy from fuel combustion is used to keep the roof and walls of the melting chamber up to around 2900 to 3000°F. (1600 to 1650°C.) so that the bath will not cool off during the refining. The other extreme is with all-cold charges containing around 80 per cent steel scrap and 20 per cent cast iron or cold pig iron, in which case a very large proportion of the heat in the bath at tap is supplied from the fuel combustion. THERMAL EFFECTS IN MELTTNG In the previous chapter it was pointed out that in a typical heat, the fuel furnishes about four million B.t.u. per ton of steel produced. The heat required for the metallurgical processes is not easily defined in useful manner (as is shown later), but it ranges downward from about one million B.t.u., depending not only on the charge but on the manner of calculation. In any event this requirement appears quite small in comparison with the heat furnished by the fuel and invites

Jan 1, 1944

By E. B. Hunt, T. M. Geffen, C. R. Stewart, V. J. Berry

Laboratory data .show that the gas-oil ratio performance of non-uniform porosity limestones produced by solution gas drive is sensitive to producing rate and to fluid properties. Nan-uniform porosity limestones are those for which laboratcry solution and external gas drive tests yield considerably different relative permeability ratio characterislics. The oil recovery performance by solution gas drive depends directly on the number of gas bubbles formed. Laboratory rates of pressure decline, which are 100 to 10,000 times greater than normal field rates. cause the formation of an unusually large number of gas bubbles. This results in abnormally high oil recovery efficiencies. Since it is impractical to reproduce the number of bubbles formed under field conditions, laboratory solution gas drive data on non-uniform porosity limestones are therefore not directly applicable to field operations. However, certain laboratory data can be used to make a conservative estimate of field performance. The concepts presented in this paper indicate the possibility that increased field oil recoveries may he obtained from non-uniform porosity limestones by rap- idly reducing reservoir pressure for a short interval of time. It has yet to be established that significant improvements in oil recovery from such reservoirs can he realized by varying the pressure decline rate within limits possible in the field. However, the possibility that recovery may be increased in this manner warrants further study. INTRODUCTION Limestone reservoir rocks can be divided into two general classes according to the nature of their pore space. One class has a comparatively uniform pore system composed mainly of voids between grains of the rock (intergranular type porosity). The other class, in addition to having intergranular porosity, has a secondary pore system composed of combinations of solution cavities, fractures, etc., and is considered to have non-uniform porosity. It has been shown in a previous publication' that the laboratory measured gas-oil flow behavior of uniform type porosity limestones is essentially the same for a test simulating a field solution gas drive as for one simulating an external gas drive. For non-uniform porosity type limestones a significant difference in gas-oil flow behavior was found. More efficient behavior was

Jan 1, 1955

The control objectives and constraints for grinding circuits are ana- lysed, taking a single-stage ballmill-cyclone circuit as an example. The design of a hierarchical modular control system is described, for implemen- tation on modern microprocessor-based control systems. Product sizing measurement is identified as a problem area, and a new approach to product sizing inference, from on-line cyclone feed and overflow measure- ments, is presented. The procedure over-comes several practical difficulties of a previously proposed inferential method and is therefore expected to find application in more advanced grinding circuit control systems.

Jan 1, 1988

By J. J. Mather

NEPHELINE SYENITE is a feldspathic rock resembling granite in texture and hardness but it is white in colour and contains appreciable quantities of the mineral nepheline, the result of a silica deficiency. It is relatively common, with known occurrences in Russia, Scandinavia, India, Canada, United States, and other parts of the world. However, the particular deposit being mined at Nephton, Ontario, by American Nepheline Limited is unique in its remarkable uniformity and low content of iron bearing minerals, both qualities essential in a ceramic raw material. The orebody is a pear-shaped mass over five miles in length, up to a mile in width, rising in three prominent ridges as much as 300 feet above the surrounding lakestudded terrain. American Nepheline holdings, consisting of 2,200 acres, comprise some 85 per cent of the total mass.

Jan 1, 1957

By Paul Gordon

The distribution coefficient, k, of interest in zone refining is generally defined as the ratio of the solid to the liquid solubilities of one element in another at the normal melting point of the solvent. In practice, distribution coefficients are frequently calculated from solubilities at temperatures well below the melting point of the solvent, e.g., at a eutectic temperature. This is done because of the general lack of accurate data on the liquidus and solidus curves in most phase diagrams. The practice is equivalent to assuming that the liquidus and solidus curves are straight lines in the temperature range between the melting point of the solvent and the temperature at which data for the solubilities are known. It is recognized that the k values so derived may be in serious error; we have found evidence in recent zone-refining operations that a case in point is silicon in aluminum. The phase diagram found in the literature for silicon in aluminum indicates a eutectic on the aluminum-rich side at 12.5 at. pct Si and at 577°C,1 and a solid solubility of silicon in aluminum at this temperature of 1.59 pct.2 It also shows the liquidus and solidus as nearly straight lines from 577°C to the melting point of aluminum (660°C)1,2 The k value obtained from this data is 0.13. This is almost exactly the same as the k value (about 0.14)' obtained in a similar way for copper in aluminum. Yet we have found by mass-spectrograph analyses* of three bars of zone-refined aluminum that copper is efficiently removed from aluminum by zone refining but silicon is not. Two of the three bars of aluminum were zone-refined in our laboratories, the other in the laboratories of AIAG Metals, Inc. The former two bars, designated bars PG2 and PG3, were 30 in. long by 1 in. in diameter during refining; each was processed in a high-purity graphite boat* and kept under refining stage of the process consisted of thirty unidirectional zone traverses at rates of about 1 to 2 in. per hr, with a zone length of 1 to 2 in. At approximately the middle of the refining period a 6-in. piece of the impurity-laden finishing end of the bar* was cut off and replaced with new start- ing material. Following refining, the purest 20-in. section of the bar (obtained by discarding approximately 2 in. of the starting end and 8 in. of the finishing end of the bar) was leveled and then analyzed. The AIAG bar was 16 in. long and about 1.2 in. in diameter; it was purified by eight passes of a 2-in. zone at a rate of 1.6 in. per hr, the bar being contained in a sintered alumina boat lined with loose alumina powder of the highest purity. Data for the silicon and copper contents of the three refined bars are given in Table I. Derived data for the efficiencies of the zone-refining operations are listed in Table 11. It is clear from these two tables that the copper is removed much more efficiently—by a factor of 10 to 50 times—from aluminum during zone refining than is silicon. For example, in bar PG3 the thirty zone passes reduced the copper content from 10 to 0.02 ppm, i.e., by 500 times, whereas the same treatment lowered the silicon content by only a factor of about 16. It seem virtually certain, therefore, that the distribution co efficient, k, for silicon in aluminum is well above that for copper and is very likely not much below unity. This also implies that the solidus line on the aluminum-rich side of the A1-Si phase diagram is very probably appreciably curved near the aluminum melting point since the phase-diagram data indicate such curvature is unlikely in the liquidus.

Jan 1, 1965

By David R. Morrey

During the past 50 years, significant research has been performed in the ecology and physiology of plants that colonize soils containing elevated concentrations of heavy metals. Similar work has also been performed on plants that are able to survive acidic and saline environments. Efforts have focused on the ecological analysis of plant communities that occur over a range of metalliferous mining wastes. Investigations have been performed on the mechanisms that allow selected varieties of plant species to survive in normally phytotoxic environments and on the potential applications of metal-tolerant varieties of plant species. The purpose is the remediation and reclamation of mining wastes and soils that contain unusually high concentrations of so-called heavy metals. Characteristics of some mineral wastes Metalliferous mining wastes present special environmental restoration problems because of their toxicity. Potential toxicities are mostly caused by residual metals derived from weathering of low-grade ore or the waste products of mineral processing. In cases where pyrite forms a part of the mining waste, acid generation by oxidation may exacerbate the toxicity problem by promoting heavy-metal mobilization in aqueous solution.

Jan 1, 1995

By M. A. W. Bryson

Platinum group metals are extracted almost exclusively in South Africa from three very different zones in the Bushveld Igneous Complex, called the Plat, Merensky, and the UG-2 reefs. The Plat reef is currently being exploited only by Anglo American Platinum, whereas the Merensky reef is exploited by them, Impala Platinum, Northam, and Lonplats. The UG-2 reef, on the other hand, is also processed by these producers, but Kroondal and Barplats have operations that exclusively treat ore from this reef. At present the extraction of pgms from ores in South Africa follows the traditional route of upgrading to a concentrate in a minerals processing circuit, further upgrading to a matte in a smelter, and final upgrading and separation of the individual metals in a refinery. Thus all operations that extract pgms require a minerals processing circuit, the design and performance of which is a topic of much interest, as it is a poorly understood and not a very efficient process in relative terms, compared to the other processes. Recoveries across the minerals processing circuit of between 75 and 90% are the norm.

Jan 1, 2004

POSITIONS VACANT (Under this heading will he published notes sent to the Secretary of the Institute by members or other persons.) Mine and mill accountant for Mexico. Knowledge of Spanish desirable. Salary $150 to $200 gold per month with living quarters. No. 60. Master mechanic familiar with mine and cyanide plant machinery for Mexico, $200 gold per month and living quarters. No. 61. Electro-metallurgist for production of ferro-alloys, salary $200 to $400 depending on experience. No. 62. Man familiar with ferro-tungsten products of electric furnaces to draw up specifications for machine tools, to watch these tools in service and revise specifications accordingly. Salary $150 to $200 per month. No. 63. Man to take entire charge of the sales of a steel company making electric alloy steels in the shape of ingots, billets and bars. To the right man an opportunity will be offered for taking a leading position in the management of the company and of participating in its results. No. 68. Chemist wanted by Electric Steel concern in the East. Must be fully acquainted with alloy steel analysis. Send full particulars and references. No. 73.

Jan 3, 1916

By Franklin Allison

THE influence of cobalt and nickel on the properties of steel might be readily expected to be very similar. The two elements occupy close and somewhat unusual positions in the periodic table, their chemical behavior and compounds are so completely analogous and their various physical properties, including the ferro-magnetic characteristic, show such a remarkable correspondence, that there is no doubt of a strong resemblance existing between these two metals. However, the variety of, properties that are obtained from steel is due, largely to the fact that the element iron possesses allotropic forms. Alloying elements that affect these allotropic forms, or alter the nature of the allotropic changes, exert a profound influence on the resulting steel. In the case of nickel and cobalt, although these elements are very similar chemically and physically, it is found that they differ distinctly in their individual effects on the critical points of iron. Both nickel and cobalt form a series of homogeneous solid solutions with iron at temperatures above 1800° F. The difference in their behavior does not occur until changes begin to take place in the solid state below this temperature. An inspection of the respective thermal equilibrium diagrams at the lower temperatures makes the opposite effects of nickel and cobalt clearly evident.

Jan 3, 1927

By Miguel Araos

The aim of this study was to understand clearly how VOD of emulsion-based gassed explosives is influenced by parameters such as nitrate salt composition in the oxidizing phase, product density, blend composition, gassing rate, type of sensitization, etc. Also some VOD testing was performed on watergel-based gassed explosives in order to compare the results with those obtained for emulsions. VOD measurements were conducted in the surface blasting facility at the Research and Development laboratory of ENAEX SA (Calama, Chile). Despite the fact that the influences of some parameters on VOD of emulsion-based gassed explosives are easily predicted, there was found to be an unexpected correlation. Although it is commonly believed that the VOD of gassed explosives depends on the density, this study found that the VOD depends on the both size and the amount of gas bubbles incorporated into the product as well as type of sensitisation, regardless of whether the explosive was straight emulsion or a blend. Density is just a consequence of the incorporation of voids into the explosive. Future work in this area may examine variation of other parameters, in order to obtain a greater knowledge of detonation properties and therefore to design more efficient explosives.

Jan 1, 2002

By F. R. Morral

INDUSTRY has yet to find a universal solution to the problem of engineer personnel selection. Today, the choice of the right man for the right job is even more pressing than ever before. The age of the hard apprenticeship seems to have passed. In its place one finds the interviewer who must determine through personal contact and evaluation of college grades whether a graduate engineer will fit into his company's scheme. The problem, as it is constituted today, may be broken into four parts: Need for better use of human resources (there is a shortage of engineers, scientists, and skilled workers), productivity with higher efficiency, encouragement of personal pride in work performed, and employee's happiness on the job and away from it.

Jan 4, 1953

By J. E. Hilliard

AS is well-known, the length per unit volume, Lv, of any lineal feature (such as grain edges in a polycrys-talline specimen) can be estimated from a count of the number of point intersections with a random plane of polish. Specifically:' Lv = 2NA in which NA is the expected number of intersections per unit area of the plane. As with all other measurements in quantitative metallography, the estimation of Lv is subject to a sampling error, the magnitude of which will depend on the number of observations. The analysis is usually performed by counting the number of intersections falling within a closed test figure of known area applied to a succession of different areas on the plane of polish. The test figure can be drawn directly on the screen of a projection microscope or else superimposed on the image of the structure by means of a reticule in a focusing eyepiece of an ordinary microscope. The use of micrographs is very inefficient unless, as in the present study, these are also needed for some other purpose. Consider an analysis in which n applications are made of a test figure within which the expected number of intersections is N. The expected total number of intersections counted is then given by NT = nN If (N) is the standard deviation in N for one application of the figure and if the latter is applied to non-overlapping regions so that the N's are independent in the statistical sense, then the standard deviation in Nt is given by: a(NT) = a(N)vn Eliminating n from Eqs. [2] and [3] we obtain: Thus, k will be a constant for a given specimen and test figure. From Eqs. [ I] and [4] we find As is to be expected, therefore, the fractional error in the estimation of Lv is inversely proportional to the square root of the total number of intersections counted. It is very desirable to have at least a rough estimate of k before starting an analysis, since it will then be possible to decide in advance by use of Eq. [5J how many counts should be made in order to achieve the desired accuracy in Lv. Without such information the investigator, unless lucky, will either do needless (and tedious) work or else obtain a result with too large an error. It is very easy to calculate k for the limiting case of N — 0, i.e., when the test figure is vanishingly small. In this case there is a negligible probability of two or more intersections falling within the figure. There are therefore only two possible outcomes: a count of one with a probability of, say, p and a zero count with a probability of (I-p). Thus and Therefore: We might expect k to depend on N and therefore on the size of the test figure. Such a dependence was observed2 in the analogous case involving the estimation of grain-boundary area per unit volume by a count of the number of intersections of a test circle with traces of the boundaries on the plane of polish. In this case the theoretical value of k at the limit N — 0 was 1.41. It was also predicted that k would display an initial sharp decrease with increasing N. Experimentally, k was observed to decrease to a value of 0.62 at N - 6 and thereafter remain approximately constant. Furthermore, the value of k for N > 6 was found to be insensitive to the form of the structure provided no pronounced anisotropy or grain-size variation was present. In order to determinewhether k would exhibit a similar dependence on N in the estimation of grain-

Jan 1, 1967

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949