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By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By Nikhil Dhawan, Veeranjaneyulu Rayapudi, Singh Rahulkumar Sunil

The ever-increasing demand for steel and the subsequent depletion of high-grade ores requires the massive utilization of low-grade iron ores. In the present study, an iron ore slime sample containing 56.1% Fe was investigated using physical beneficiation, carbothermal reduction, and a microwave-assisted process; however, physical beneficiation and microwave exposure were found to be inefficient as they yielded lower iron recovery. Using coconut shell as an alternative reductant was found to be promising and does not lead to the formation of higher iron oxides, such as fayalite and wustite phases. The microwave-assisted carbothermal reduction was found at par with conventional reduction, saving time and heating. The optimum magnetic concentrate obtained in both carbothermal reduction routes (microwave and muffle furnace: Fe grade, Fe recovery, and yield of 64.3, 97, and 84%, and 67, 99, and 83%, respectively) are suitable for alternative iron-making or blast furnace units.

By P. Hazebroek, M. Prats, E. E. Allen

Well locations in water floods frequently do not coincide with the ideal well locations associated with the flood pattern which is used. A question of importance is. "How much oil is lost because of this?". This is the problem treated in this paper. It is assumed that each pattern in a five-spot flood has the proper number of production and injection wells but that the wells may be off-pattern. The distance by which a well is off-patern is given in terms of the pattern spacing, defined as the length of one side of a five-spot. The influence of off-pattern wells on the performance of a five-spot flood has been investigated mathematically for unit mobility ratio. All production and injection rates are assumed to remain equal. The loss in recovery resulting from pattern irregularitie: has been calculated at a cumulative water injection corresponding to a 98 per cent water-cut in a regular five-spot. Displacing a single production or injection well by about one-third the pattern distance reduces the total field recovery by 4.4/N per cent of the recovery obtainable with regular spacing, where N is the number of five-spots in the flood (assumed large). When off-pattern wells are separated by at least one regular five-spot and are displaced by less than one-third the pattern distance, the total loss in recovery in a large-scale flood is, at most, 1 per cent of the recovery obtainable from that field with a regular five-spot pattern. However, much higher losses may occur if the off-pattern wells are not separated by a regular five-spot, if the rates are imbalanced, or if the mobility of the injected water is higher than that of the crude. Although the loss in oil recovery due to pattern irregularity often may be low, the off-pattern case will always require injection of more water to reach the same final water-cut. The volume of water injected per unit volume of oil displaced has been calculated for each five-spot adjacent to a five-spot containing a single 08-pattern well. The cumulative water injection at the time of 98 per cent water-cut may be increased by as much as 37 per cent when a production well is displaced one-third the pattern distance toward an injection well. The existence of differences between actual subsurface locations and the idealized well patterns used in secondary recovery operations is well recognized. However, the methods commonly used for predicting waterflood behavior ignore such differences, even when subsurface locations are known. The reason for this is simple. The idealized well patterns are highly symmetrical and, as such, the production history of the pattern (and even of the field) can be determined from that of a few production wells—usually from only one. Consideration of the many irregular well spacings found in a specific field would entail a large amount of work, and then the results would be applicable only to that specific field. In an attempt to provide an answer to the more general problem, this paper considers a water flood having an idealized well pattern, except for one well which is not at its regular location. When several off-pattern wells are present, their contributions are assumed to be additive unless the off-pattern wells are close to each other. Only four positions of the off-center well (at x, y. of Fig. 1) are considered in this paper. These are shown

By Christoph Zschiesche

Managing complex material streams within a lead smelting/reduction process has a long history at Aurubis. After modernization of the secondary lead smelter in 1991, Aurubis operates an electric furnace and a Peirce Smith converter to process complex secondary materials. This process links the copper and the lead metallurgy allowing Aurubis to properly combine primary and secondary process lines to optimize the processing of complex raw materials and smelter intermediates. However, combination of copper and lead metallurgy processing requires a continuous evaluation as raw material quality and composition varies. This paper describes Aurubis lead smelter processing and provides some fundamental considerations to optimize the lead processing, in particular with aspects related to speiss formation

By J. C. Cawley, G. T. Homce, M. R. Yenchek, H. K. Sacks

As in many other industries, such as construction and agriculture, overhead electric power lines are a serious hazard at mining and mining-related operations. Even when excluding injuries that occur during electrical maintenance work, over one fourth of electrical fatalities in the mining industry are due to accidental overhead line contacts, and for each fatality nearly two serious non-fatal injuries occur due to such contacts. In incidents involving high-reaching mobile equipment, many of the victims touched the equipment after the fact, unaware that the machine frame had become energized by the line contact. MSHA data for accidents involving overhead power line contacts in the mining industry between 1980 and 1997 reveal that in 57% of the cases personnel were unaware of the accidental line contact until after one or more workers touched the equipment or a hoisted load and were injured. The situation is similar in the construction industry, where according to the National Institute for Occupational Safety and Health (NIOSH) data at least 20% of such victims are unaware of the line contact. This suggests that a device that alerts workers when a power line has been contacted could help prevent many of these injuries. Such a device would not prevent power line contacts, yet if widely employed could yield a significant reduction in the number of resulting injuries. Researchers at the NIOSH Pittsburgh Research Laboratory are attempting to develop such a device. The approach being investigated is based on measuring electric current flow to ground through a machine during a line contact. The specific technique being tested involves the diversion of some part of this current through a shunt cable mounted on board the machine, to provide a point at which to install a current sensor. Experiments thus far indicate that this approach is feasible. Ongoing research is better defining electric current flow through mobile equipment, refining techniques for measuring this current, and identifying factors that could limit the effectiveness of the proposed alarm.

By Gregor Kücher

Lack of basic knowledge on the semi-direct recycling methods for hard metals hinders the application on an industrial scale. However, advantages like reduced expenses and lower environmental impact draw interest at future potentials. Consequently, this report aims to offer insight into the influence of varying bulky hard metal substrates during their lixiviation in acidic media with an oxidant. The statistical software Modde 11 assisted in the development of a design of experiments (DOE) for evaluation of the impact of average grain size, binder and tantalum carbide (TaC) content on the leaching characteristics. The other experimental parameters were constant. Among them were temperature, solution concentration and quantity, duration and substrate surface exposed to liquid volume. Eventually, prediction plots and factors of the computed model equation describe the effects of varying substrate qualities on leached binder metal and selectivity.

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By Donald P. Tuchman, Robert P. Vinson, Steven J. Page, Linda J. McWilliams, Gerald J. Joy, Steven E. Mischler, Jon C. Volkwein

The United States National Institute for Occupational Safety and Health, through an informal partnership with industry, labor, and the United States Mine Safety and Health Administration, has developed and tested a new instrument known as the Personal Dust Monitor (PDM). The new dust monitor is an integral part of the cap lamp that coal miners normally carry to work and provides continuous information about the concentration of respirable coal mine dust within the breathing zone of that individual. Previous laboratory testing demonstrated that there is a 95% con?dence that greater than 95% of individual PDM measurements fall within ±25% of reference measurements. The work presented in this paper focuses on the relationship between the PDM and respirable dust concentrations currently measured by a coal mine dust personal sampler unit utilizing a 10 mm Dorr Oliver nylon cyclone. The United Kingdom Mining Research Establishment instrument, used as the basis for coal mine respirable dust standards, had been designed speci?cally to match the United Kingdom British Medical Research Council (BMRC) criterion. The personal sampler is used with a 1.38 multiplier to convert readings to the BMRC criterion. A strati?ed random sampling design incorporating a proportionate allocation strategy was used to select a sample of mechanized mining units representative of all US underground coal mines. A sample of 180 mechanized mining units was chosen, representing approximately 20% of the mechanized mining units in production at the time the sample was selected. A total of 129 valid PDM/personal sampler dust sample sets were obtained. A weighted linear regression analysis of this data base shows that, in comparison with the personal sampler, the PDM requires a mass equivalency conversion multiplier of 1.05 [95% C.I. (1.03, 1.08)] when the small intercept term is removed from the analysis. Removal of the intercept term results in a personal sampler equivalent concentration increase of 2.9% at a PDM measurement of 2.0 mg m-3.

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy's Law is valid. 4. The formation is saturated with a single homogeneous fluid.

On the more important mines it is almost essential to have a general plan of the surface. A special feature of this plan should be the indication thereon of a suitable arrangement of contour lines, either wholly over the surface of the property or at parts where may seem most useful. The importance of having these contours marked on the plan will be best appreciated by the engineer, in selecting the best available site for a proposed new plant, in locating a tramway, in connecting the surface with the underground workings to the best advantage, or in solving many similar problems that come within his province. The closer the contours are together vertically the better, the limitation being the trouble and expense of getting them on to the plan. They may range from five to fifty feet apart but a distance of ten feet will be found, in most cases, to be the most useful.In deciding the datum level from which these contours are to be measured, it is best to depart from the ordinary sea level datum, and use instead the highest available point on the property. This datum will be called zero and all levels will be reckoned so many feet below it; thus by a contour marked 160 on the plan, it will be understood that the level of the plane of the contour is 160 feet below the highest available point on the property. This system of measuring levels downward is readily suggested from measuring the depths of shafts from the brace or of excavations from the original surface.

By J. E. Fox Jr., J. L. Lummus, J. P. Gallus

Fresh water or brine drilling fluids may be kept free of suspended drilled solids by the addition of a water soluble acrylamide-carboxylic acid copolymer at the flowline. Addition of from .01 to 0.2 lblbbl of the polymer solution to drilling fluids containing less than 5 per cent clay solids by weight causes the solids to flocculate and settle rapidly to the bottom of the pits. Solutions of the polymer injected at the pump suction reduce the loss of water to permeable formations without impairing the permeability to oil. The use of drill-itlg fluids clarified with the polymer has resulted in increased drilling rates, extended bit life, and lower drilling fluid costs. INTRODUCTION Field experience and the results of a number of investigations have established that the accumulation of solids in drilling fluid reduces drilling rate.'-' Drilling with water makes possible higher drilling rates than can be achieved with mud but in many areas drilling with water may not be feasible because of the possibility of encountering high formation pressures or by-dratable formations. To combat these conditions, the drilling fluid must possess certain physical properties such as viscosity, density, fluid loss, etc., which require the presence of solids. The current trend in drilling fluid treatment is to maintain as low a percentage of solids as is possible without harmfully affecting the mud properties needed for drilling. Mechanical separating devices such as wet cyclones and decanting-type centrifuges are proving to be an economical means of controlling the percentage of solids and thereby maintaining low solids muds. Also: special muds have been developed for the purpose of retarding the hydration of drilled solids so that they may be more easily removed by shale shakers or settling pits. In some areas, such as West Texas, the characteristics of some formations will permit drilling with water. However, because of the dispersion of drilled solids, it is usually not possible to maintain clear water even with the aid of mechanical separators, or by utilizing large settling pits. For this reason the commonly used term "water drilling" is a misnomer since the water usually contains some solids. Because of the improved drilling rates and other benefits which might be effected, a laboratory and field study was made of the use of flocculating agents for maintaining clear water for drilling. PROCEDURE Laboratory—Solids Settling Two techniques were employed to determine the effectiveness of flocculating agents in settling solids from drilling mud. First, the rate of fall of solids was measured in graduated beakers containing mud treated with various flocculating agents. Natural gum, oil-in-water emulsions prepared with ethoxylated nonyl phenols and diesel oil. and a powdered synthetic acrylamide-carboxylic acid copolymer* (hereinafter referred to as "polymer") were tested as flocculating agents in both fresh water and salt saturated muds containing 4 per cent solids. The polymer was not added in the powder form directly to the muds but was first dissolved in water in a concentration of 3.5 lb/bbl. The polymer solution was then added directly to the mud. The concentration of the flocculating agents, including the polymer, was varied. High rates of fall of the solids indicated high flocculating efficiency. A second technique consisted of measuring the time in minutes required to obtain clear water at the pump suction after addition of the various flocculating agents at the flowline. These tests were made using a model mud circulating system having a total volume of approximately 10 gal. The natural fresh water and brine muds used contained 4 per cent solids. A sketch of the circulating system appears in Fig. 1. The circulating rate

By R. J. Sandrea, S. M. Farouq Ali

The results of an experimental and theoretical study of the effects of rectilinear impermeable barriers and highly permeable channels on the sweep efficiency and conductivity of a five-spot network are presented. The study was carried out using Hele-Shaw, and conductive sheet analogs for both. normal and inverted flood patterns. A functional relationship was developed which provides quantitative prediction of the above parameters; i.e., sweep efficiency and conductivity, for the nonhomogeneous system. To evaluate this, it is necessary only to measure the interference modulus of the obstacle using a simple expression. The results indicate that impermeable barriers, with an interference modulus greater than zero, always cause a decrease in the conductivity and the sweep efficiency of the pattern. On the other hand, permeability channels do not have a significant effect on these parameters, unless they are located along the streamlines. The study also discusses a method of formulating the difference equations pertaining to the two-dimensional Laplacian in a system containing rectilinear barriers. In addition, a technique is described for tracing the progress of a free surface, using marked particles, in a stream containing discontinuities SuCh as those occurring at the extremities of barriers. The above computational scheme was used in a digital computer program to simulate results of the Hele-Shaw analog. The computed values of sweep efficiency mere in good agreement with the experimental values. INTRODUCTION At the present time waterflooding remains the most widely used technique for the secondary recovery of oil. Among the numerous factors that affect the performance of a waterflood, the areal sweep efficiency constitutes one of the most critical parameters. It is a function only of the geometric distribution of the wells for a homogeneous medium and unit mobility ratio. Geological considerations, however, such as the presence of sealing faults or solution channels in the rock matrix, would generally exert an adverse effect on the areal sweep efficiency of a waterflood network. Surprisingly little information is presently available on the quantitative implications of such permeability interferences. It was the object of this investigation to consider the presence of rectilinear, impermeable and highly permeable interferences in an otherwise homogeneous five-spot pattern, and to analyze their effects on the resulting sweep efficiency and pattern conductivity. The experimental phase of the study was conducted using two different models: the Hele-Shaw flow cell and the field plotter. For experimental convenience, the geometric boundaries of the five-spot were assumed to constitute streamlines even in the case where the interference was asymmetrically placed with respect to a repeated five-spot pattern. A second object of the study was to develop a computational scheme for numerically calculating the pressure distribution in a five-spot flow pattern containing rectilinear, impermeable barriers, and to use this distribution to compute the sweep efficiency. EXPERIMENTAL PROCEDURE HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remains valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates. The model used in this study was composed of

By K. Hodgson, J. P. M. Hojem, N. G. W. Cook

Already about one-third of South Africa's coal is mined at depths exceeding 100 metres. Almost all this mining is done by the bord and pillar method. Conventional design procedures call for ever larger pillars as depths of workings increase, resulting in the loss of large amounts of coal and reductions in productivity. Barrier pillars are in general use to ensure against large collapses. The presence of these strong pillars would allow a more efficient design of the bord and pillar layout to yield improved extraction ratios by using smaller, yielding, pillars between the bords. Knowledge of the complete load- displacement curves for such pillars is a prerequisite for the design of such a system. A 100-MN, stiff jacking system for measuring the complete load-displacement curves of pillars with cross-sections of up to 2 m X 2 m is described. The jacks are installed in a slot cut across the central plane of symmetry of a pillar, thereby ensuring that the stress distribution in the pillar during a test, especially at its contacts with the roof and floor, is identical to that caused in a similar pillar by convergence across the seam. Preliminary results in the form of complete load-displacement curves for test pillars of about 1.5 metre square section are given.

By C. D. Stahl, E. E. Templeton, R. F. Nielsen

It has been customary, in predicting saturation changes, to use the Leverett fractional flow formula", obtained by eliminating the unknown pressure gradient from the generalized Darcy equations for the separate phases. The formula presents difficulties in the case of counterflow, since the "fractional" flow may be negative, greater than unity, or, in the case of a closed system, infinite. Recently, it has been shown by several authors that the corresponding equations (with capillary pressure and gravity terms) for actual flow of the phase may be used just as well. These equations are in agreement with Pirson's1 statement that, if the two mobilities differ considerably from each other in a closed system, the flow is largely governed by the lower value. The present study was undertaken because of an apparent lack of experimental data on gravity counter-/low with which to test the theory. A 4-ft sand-packed tube in a vertical position was employed. Electrodes for determining saturations by resistivity were spaced along the tube, one phase being always an aqueous salt solution. Air, heptane, naphtha, or Bradford crude oil was used for the other phase. A reasonably uniform initial saturation was set up by pumping the phases through the system, alter which the tube was shut in and saturation profiles obtained at definite intervals. Cumulative flows over certain horizontal levels were obtained by integration of the distributions; hence, differentiation of the cumulative flows with respect to time gave instantaneous flow rates. To compare experimental and theoretical flow values, capillary pressures were assumed given by the final saturation-distribution curve. The upper part corresponds to the "drainage" region and the lower part to the "imbibition" region, where trapping of the nonwetting phase occurred. While calculations indicated that the capillary pressure saturation function and, probably, the relative permeability saturation functions changed during the segregation, the relation of the measured rates to saturation distributions are in general accord with the frontal-advance equation. It appears that the Darcy equations, as modified for the separate phases, are generally valid for counterflow due to density differences. The usual method of predicting saturation changes, which involves a continuity equation and the elimination of the unknown pressure gradient from the flow equations, should therefore be applicable. However, the need for advance knowledge of drainage and and imbibition "capillary pressures" and relative permeabilities during various stages presents difficulties. INTRODUCTION The present study was undertaken because of a seeming lack of experimental data relating to vertical counterflow of fluids of different densities in porous media. In particular, it was desired to determine whether data obtained from these laboratory tests were in accordance with certain mathematical treatments of counterflow which have been proposed. The gravity "correction" has been incorporated into the flow equations (and, hence, into displacement theory) nearly as long as both have been used. field4 and laboratory5 data have generally borne out the validity of the theory as applied, for instance, to downward displacement by gas, with all fluids moving downward. However, the modifications for counterflow have only recently been pointed out. 2-3 It has been customary to use fractional flow rates instead of actual flow rates in displacement calcuIations. In the case of counterflow, this results in negative values, values greater than unity and, when rates are equal and opposite, in infinite values. As pointed out by Sheldon, et a1,3 and by Fayers and sheldon,2 actual flow rates may be used just as well. The fact that these may be of opposite signs for the two fluids does not present any difficulty.

Minutes of meeting held at the Moth Hall, Witbank on 13th November, 1969. There were present eleven members: Mr J. Meintjes (in the chair); Messrs I. E. van Aswegen, O. T. Wright, A. W. L. Brereton, A. Bain, J. Brook, P. J. Beukes, C. H. Coxon, B. F. v.d. Merwe, A. C. Hofmeyer, G. E. Carlyon. Six Associate Members: Messrs E. J. Jackson, J. N. H. Pritchard, R. E. Powell, W. Weber, R. Smith, B. T. Hosking. One Student Member Mr M. J. de Beer. Seven visitors. The Chairman reminded members of the intended visit to Barberton. Dr Stander, Director of the National Institute for Water Research, gave an interesting talk, illustrated with slides and a short film, on the conservation and reclamation of water in South Africa. After question time, Mr Hector, Witbank Town Engineer (visitor) thanked Dr Stander. The meeting closed at 7.10 p.m.

By J. Duran

Mining at Newmont Mining?s Phoenix?s Mine is currently done by surface operation in the Fortitude and Bonanza pits at a combined rate of approximately 100 kt/d (110,000 stpd). A portion of the orebodies targeted by these pits was mined previously by underground mining methods, dating back to the mid-to late-1800s. Most of the underground workings (voids) are located in the west central area of the Bonanza pit. The surface operation requires excavation through voids, and there is a risk of pit floor subsidence that has to be addressed. This article presents a review of the risk mitigation measures that were implemented to reduce risks to people and equipment working in the area.

The sphere of operations of dry crushing has been so much enlarged of late years that the following notes with reference to its advantages and limitations, and also some practical results in connection with the crushing of gold ores will probably be of service to the members of the Institute. Until recently, with one notable exception that of the Mt. Morgan Gold Mine, dry crushing has only been practiced to a very limited extent in Australasia, and elsewhere it might be said to belong to industries other than mining Its sphere of usefulness depends on the fact that the' product is delivered in a dry state without the separation of the finer particles from the coarser to any appreciable extent, thus enabling the following advantages to be achieved with different ores.

By R. S. Conti

The US Bureau of Mines (USBM) has developed an inflatable feed-tube seal (IFTS) for high-expansion foam generators. The IFTS is a lightweight, portable, rectangular inflatable bag that can be used by firefighters to rapidly seal large openings, such as those in underground mines, and to simultaneously provide a feed-tube for a high- expansion foam generator. Thus allows fire-fighting foam to freely flow to the fire site and control or extinguish the fire. Studies indicated that a high-expansion foam plug will travel 183 m (600ft) down an entry with a 4.5% rise in elevation, before leakage of foam from around the inflatable partition.