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By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By D. G. Oss, S. E. Erickson

An automatic control method for the ferrosilicon heavy media process maintains media density within 0.01 specific gravity points. Continued demands for higher grade, competitive products from the Mesabi Range have resulted in experimental work such as that detailed for one concentrator. Various methods, step by step procedures and instruments used at an iron ore beneficiation plant in the development of an automatic control system are described. Work continues and it is hoped that further applications of control instrumentation can be made in the next operating season. The need for instrumentation and automatic control of the various parameters in the heavy media process of iron ore beneficiation has been apparent for some time. Continued demands for higher grade, competitive products from the Mesabi Range have made it necessary to increase the efficiency of the process in every possible way. In a typical heavy media flow scheme for iron ore beneficiation (Fig. 1) a sized, prepared feed (generally about —1% in. to +% in.) is fed to a heavy media separatory vessel, along with a ferrosilicon slurry. A separation of the feed is made on the basis of specific gravity. Low density particles overflow a tailings discharge weir, while high density ore particles sink to the bottom of the high density pool and are moved away to the concentrate discharge chute. Both products are passed over drainage screens and then are cleaned thoroughly of attached ferrosilicon on wash screens. Float material is generally stockpiled, while the sink product is shipped as a final concentrate. Undersize from the drain screens is returned directly to the circulating media sump. Wash screen undersize is cleaned of contaminating ore particles and slimes by passing through magnetic separators. Provision is also made for splitting a portion of the tailings drain undersize into the cleaning circuit if necessary for control of depth of tailings overflow, or for additional cleaning as required. Cleaned ferrosilicon is stored in a densifier and returned to the Circulating media sump as make-up material. Dilution water is also added to this sump to maintain a desired specific gravity of the circulating media. As in any process, operational intelligence is secured only by keeping records of the process variables. Generally apeaking, plant operators have neither the inclination nor the time to keep complete and detailed records of these variables over the course of their shift. Before instrumentation was added to aid the operator, specific gravity was measured by weighing a given volume of pulp at intervals of from 30 to 60 min. Scale readings were made at the beginning and end of each shift. No records were kept of operating conditions, such as rpm of the separatory ves-sel, media level in the machine, tons per hour of the products, and so forth. These items were recorded only when spot checks were made by the metallurgical staff. CONTlNlJOUS DENSITY RECORDING The first process instrument used, other than the usual ammeter on the drive motor of the separatory vessel, was a nuclear density gauge and its associated circular chart recorder. These instruments were used to indicate and record specific gravity of the circulating media. This was a tremendous aid to the operator in that tie was able to observe and correct the specific gravity at any time. There was also added incentive to make frequent corrections because of the permanent record made by the recorder of the densities. The addition of the nuclear density gauge was influential in securing optimum quality and recovery of the heavy media product. Manual control was improved, and it became possible for a good operator to main control within f.05 specific gravity units. This compares with an unknown quantity, estimated at f0.15 gravity units, when manual measurement and control was used. An example of the improvement in manual control over the course of one season's operations is shown in Fig. 2. Chart A is typical of the records made shortly after the gauge was installed. Needless to say, it was difficult for operators and foremen alike

Jan 1, 1962

By Carl Scholz

FROM the engineer's standpoint, labor organizations are of interest in so far as they 'affect efficiency, maximum production and unit cost, and in this respect the earlier labor organizations' which existed in the age of the Guilds were ideal, inasmuch as they stood ' for competency of the apprentice and close cooperation ' between employers and employees. In later years the tendencies of the labor organizations have gone in the opposite direction and, instead of cooperating 'with the engineer, they usually oppose him on the mistaken theory, that labor-saving devices reduce forces, and costs; in this respect, the united Mine Workers of America have been particularly active and, to a very great extent, successful.

Jan 1, 1921

By C. A. Heiland

WITH seventeen papers submitted. and thirteen presented in three sessions, the geophysicists had a most successful meeting at New York in February. The first paper on Monday morning dealt with the location of a diabase dike near Chapel Hill, N. C., by magnetic and resistivity methods. The magnetic indications were pronounced directly over the dike. whereas the anomalies of apparent resistivity were less distinct and displaced away from the dike. In the second paper, Professor Keys reported on the results obtained with four different methods of depth calculation on known portions of the Falconbridge

Jan 1, 1937

By WM. P. BLAKE

THE salt-beds at Salton, on the line of the Southern Pacific railway, in San Diego county, California, have been successfully worked for many years by the corporation known as the East Liverpool Salt Co., and the salt has been largely used upon the Pacific coast generally and in the interior. But the industry has lately been destroyed by the overflow from the Colorado river. The salt is dissolved, and the waves of the Salton sea now roll 50 ft. above the site of this once thriving and growing business. The salt-bed was evidently the residual accumulation from the waters of an ancient lake, which I have named Cahuilla, from the name by which a large part of the valley-the home of the Cahuilla tribe of Indians-is known. The deposit covered a comparatively small area in the lowest part of the valley, 280 ft. or more below the sea-level. This depressed area is now generally known as the Colorado desert, but has a soil of wonderful fertility wherever water can be had on its surface. The deserted beaches, and the water-lines, only a few feet above tide-level, upon the rocks of the bordering mountains, as well as a great abundance of shells in the soil, all bear decisive testimony to the former occupation of the valley by water. The depression is topographically the northern end of the Gulf of California, from which it is now separated by the delta of the Colorado river, extending practically from the mouth of the Gila river across the valley to the coast mountains on the west side. We may conclude that the imprisoned salt water was gradually displaced and freshened by the inflow and outflow of the river, so that the lake was changed to fresh or brackish water, with enough salt in it to give a bed at the bottom upon

Jan 1, 1908

By Albert S. Trube

Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of reservoir fluids well in advance of more accurate laboratory data. One such factor is the isothermal coefficient of expansion of an undersaturated hydrocarbon liquid which may be contained in a particular reservoir. This coefficient, or liquid "compressibility", has often been assumed to be relatively insensitive and nearly constant. Although this assumption may be nearly correct in the case of high specific gravity liquids, it cannot apply in the case of medium to low specific gravity liquids. Any treatment of the nature of liquid compressibilities must give consideration to the variable nature of the isothermal expansion coefficient and the fact that it can be both pressure sensitive and temperature sensitive. The isothermal coefficient of expansion, or compressibility, of a substance is defined as -c = 1/V (?V/?p)T......(1) The value of Eq. 1 may be approximated for a finite pressure change by using the well-known relation, c = V1 - V1/Ve (p2-p1), ........(2) in which p1 > p1 and V2 > V2 and V1 + V2/2. The instantaneous compressibility may also be estimated from the slope of a curve on which log V is plotted vs pa. In this instance, it has been shown that c = In V1/V2/p2-p1 ...........(3) Eq. 3 may be used for variable compressibilities by plot-ting V vs p on semi-log paper. In this case, the instan-taneous or point compressibility is c = 2.303 m.......... . (4) in which m is the slope of the curve at a point in log cycles per psi. ISOTHERMAL COMPRESSIBILITY OF UNDERSATURATED LIQUID In the case of gases, the compressibility has been defined by Muskat' and others as Co = 1/p - ?z/z?p ..........(5) This was later generalized through application of the theorem of corresponding states' to co = 1/pr - (?z/z?pr) T8 ........(6) in which c, is defined as the pseudo-reduced compres-sibility and is numerically equal to (c.p,) and the sign is arbitrarily changed for mathematical convenience. Eq. 6 is general and applies to gases and liquids. In the case of liquids, c. = c1,pe, but if Eq. 6 is used, values of z and ?z/?p, must be determined for the liquid in question. The difficulty of obtaining accurate values of ?z/?p,, particularly in the region where T, is approaching 1.00, was pointed out in the previous paper'. This method of approach is unreliable for extension into computations of liquid compressibilities. On the other hand, c, can also be defined as follows: - Cr = 1/Vr (?Vr/?pr) Tr ......(7) and from which, Cr = 1/pr (?pr/?pr) Tr .....(8) In accordance with the theorem of corresponding states, Vr = V/Vr, p, = p/pr and pr = p/pr. Ref. 2 pro-vides an excellent source of reduced density, reduced pressure and reduced temperature data for a wide variety of fluids. For the purpose of this investigation, the set of fluids2 having ze = 0.27 was chosen because it in-cludes most of the heavier hydrocarbons usually found in those complex mixtures loosely defined as "reservoir oils". Data on undersaturated liquids in Ref. 2 were rearranged to conform with Eq. 8. To simplify the computation of cr, the isothermal p, data were plotted vs the log of pr, in which case for any straight line or tangent cr = 1/M pr pr .....(9)

Jan 1, 1958

By A. M. Gsudin, F. W. Bloecher, C. S. Chan-s, P. L. De Bruyn

M ANY elements can now be obtained in radioactive form. The radioisotopes have the same chemical properties as the corresponding inactive forms, differing from them only by their nuclear instability. This combination of properties permits radioelements to act as atomic tracers, the tracer atoms revealing themselves at the time of their decay with emission of electrons and positrons (beta radiation), helium nuclei (alpha radiation), or electromagnetic radiation (gamma radiation). The tracer technique is particularly attractive for the study of surface chemistry problems in general and flotation problems in particular because of its extreme sensitivity. A large proportion of the ionizing events, initiated by the characteristic decay emissions in a radioactive sample, can be recorded by radiation probes of suitable design and geometry. An idea of this sensitivity can be gathered from the following example: assume that 0.001 mg of pure RaD (radiolead), a beta-ray emitter, is used in a flota¬tion tracer experiment. This is 1210 X 10-1 mole; since the fraction trans¬formed per second (the so-called decay constant), is 9.92 X 10-10, the number of ionizing events per second would be (6.023 X 1023 X y,,, X 10-1) X 9.92 X 10-10 = 2.845 X 106. (The decay constant is expressed in sec-'. Its product with the half life, expressed in seconds, is the pure number, natural logarithm of 2 = 0.693. The half life is the length of time required for decay of one half of the total number of radioactive atoms of one particular type.) (See reference (1) at the end of this article.)

Jan 1, 1948

By D. R. Parrish, W. E. Lamoreaux, W. W. Owens

Several methods are now being used by the industry for determining the gas-oil flow characteristics of reservoir rock samples. Most of the laboratory experirnerltal rlzethods can be classified either as steady-state, unsteady-state, or Hassler-type tests. Although the validity of the results obtained by any specific method is not questiorzed, in general, the complexity of these methods leaves much to be desired. This investigation dealt primarily with the development of a simplified unsteady-state (gas drive) laboratory test method for measuring kg/ko re1ationships of small core samples. A procedure for selecting uniform and representative sandstone rock samples was developetl since it was observed that the reliability of the test resu1ts was dependent upon having a sample which was uniform in porosity and permeability. The importance of factors known to influence the results of this type test, such as oil viscosity, gas expansion, and pressure differential were eva/uated. The method of calculating the test results was found to give valid data over a wide range of gas expansion. The limits of pressure differential and oil viscosity which would insure reliable results were defined. In cornparisorz with other presently used testing methods, the gar drive method requires considerably less apparatus, is less time consuming, and is more readily adaptable to a routine type core test. INTRODUCTION The detcrmination of the gas-oil flow characteristics of reservoir rocks has been given concentrated study by the oil industry for the past decade. Both analytical and experimental methods have been considered. The analytical methods have generally relied on a simplified characterization of porous materials in order that the fundamental laws of fluid flow and capillarity could be utilized. More direct experimental methods have been proposed by numerous production research laboratories with the primary goal being a simple and inexpensive, yet reliable method for measuring the gas-oil flow characteristics of reservoir rock samples. The experimental methods which have been reported in the literature generally can be grouped into one of the following classifications: 1. Steady state1,2,3,4 in which a fixed ratio of flowing fluids is forced through the test sample until equilibrium conditions of saturation and pressure gradient are established. 2. Hassler or stationary liquid method5,6,7 in which a uniform liquid saturation is attained, usually through capillary desaturation, then gas or oil is flowed through the sample at a pressure drop insufficient to disturb the pre-established saturation. :. Non-steady state method1,8,9,10 In which only the gas phase is injected into the sample, causing displacement of the oil phase and resulting in a system of continually changing average saturation and saturation gradient. The steady-state and Hassler methods have been most popular because, no doubt, of the simplicity of the actual relative permeability calculations. The problems involved in these methods were limited to apparatus design and measurement techniques. In the steady-state method, for instance, a constant flowing fluid ratio is established which, at equilibrium, results in an essentially uniform saturation over the entire length of the test sample. Therefore, the basic flow characteristics could be obtained by correlating the average saturation of the test sample with the kg/ko determined at various flowing gas-oil ratios.

Jan 1, 1957

By RALPH HAYES SWEETSER

IRON ore and bituminous coal are the two basic raw materials for the whole iron and steel industry. The ore furnishes the iron and is absolutely necessary-all iron and steel products come directly or in- directly from the iron ores. The bituminous coal furnishes the carbon needed for the smelting of the ores and for the fuel used in all the processes of iron and steel manufacture. The necessary carbon could be furnished in some other form besides bituminous coal. In fact, it is only since the Civil War that bituminous coal has been the chief source of the carbon for metallurgical fuel. For many years only charcoal made from the forests furnished the carbon for smelting iron ores. About 90 years ago, anthracite coal was first used as blast-furnace fuel and for many years continued to be the chief blast furnace and steel making source for carbon. Even in my own blast-furnace experience, I have used charcoal in Canada and anthracite in Pennsylvania for smelting ores in an iron blast furnace. Bituminous coal, now almost exclusively the source for the carbon used in smelting iron ores, also furnishes most of the heat used in the steel-making processes. It is seldom used in blast furnaces in its natural condition, hut is first coked in beehive, or in by-product coke ovens; such bituminous coal is called "coking coal." Bituminous coal that is suitable for making the producer gas used in the open-hearth steel process is called gas coal. Any bituminous coals suitable for making blast-furnace coke or foundry coke, or that can be satisfactorily used for making producer gas, are classed as metallurgical coals and as such are to be considered in my proposed plan for the evaluation of metallurgical coals. According to Bureau of Mines Bulletin No. 449 these coals comprised 22 per cent of the bituminous coals mined in this country in 1923.

Jan 1, 1926

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By Donald L. Katz

FIFTEEN years ago Dr. Manning published a paper in "Petroleum Development and Technology" on '.Fundamental Research Relating to Petroleum." He tabulated for several industries "the proportion of their present success which can be fairly attributed to the application of information and processes obtained by scientific research," giving petroleum a score of 7 compared to 100 for the electrical and coal-tar industries. Today the petroleum industry as a whole and the producing groups both have raised their score beyond the majority and are climbing toward the top. Present practices are being developed both by fundamental research and the application of the research method in field operation.

Jan 1, 1941

By H. D. Yoo, M. R. Tek, D. L. Katz

The behavior of gas-storage reservoirs subject to water drive is investigated through analog simulation on an electronic differential analyzer. The simulation technique developed on an LM-10 computer permits the prediction of reservoir volume or pressure resulting from the movement of water in the surrounding aquifer. The method developed on the analog computer consists of setting up an appropriate transfer-function circuit and feeding the arbitrary time-varying boundary conditions as an input signal. The input may be specified as gas reservoir pressure, pore volume or the water flux. Several cases studied include an isolated gas reservoir on a limited aquifer, interference among three reservoirs adjacent to a common aquifer and the growth of gas-storage volume on an aquifer. It is concluded that the method developed on an electronic differential analyzer provides an excellent technique to simulate and investigate the behavior of gas reservoirs subject to water drive. The agreement between the reservoir performance as predicted from the simulation technique and as measured from actual field data is found to be better than the range usually encountered in predicting water-drive behavior. INTRODUCTION It is generally known that some gas-storage reservoirs are located on top of blanket sands of large extent, saturated with brine called aquifers. Because the volume of the body of water associated with aquifers is usually very large and water is compressible, the cyclic pressure variations encountered in normal storage service inevitably cause unsteady, compressible flow conditions in the adjacent aquifers. The solution to radial diffusivity equation for a limited aquifer for constant terminal conditions has been know111 since the early 1930's. The solution for the constant terminal conditions for an infinite aquifer was puhlished in 1949.2 The proldem of handling the unsteady flow of water through a porous medium with time-varying boundary conditions has been studied by many investigators through the use of graphical,3 digital4 computing techniques or on an R-C type of electrical analog called a reservoir analyzer.5 The digital computer performs a series of arithmetic calculations to superimpose the solutions of constant terminal conditions, while the R-C type of analyzer permits the simulation of the continuous medium by means of "lumped-cell" electrical resistance and capacitance elements based on finite-difference approximations. The graphical method is based on the convolution integral solution of the partial differential equalion. The purpose of the present study was to simulate the behavior of an aquifer on a general-purpose, electronic differential analyzer to obtain the influx of water or the change in pressure at the reservoir continuous1r and quickly. The use of the electronic differential analyzer was based on well known solutions for the constant terminal conditions already available in the literature.2,6-8 THEORETICAL DEVELOPMENT MODEL. The gas reservoir (R) is described in relation to an aquifer in Fig. 1. The permeability and porosity of an aquifer sand, the viscosity of the brine, and the compressibility of the brine and the formation are assumed to be constant. It further is assumed that the blanket sand is not thick enough to give appreciable vertical pressure distribution. The model in consideration is circular with radial geometry. The aquifer radius can be of limited or infinite extent. The gas-water interface is assumed to be fully segregated, and the displacement of the gas by

By Lyon F. Terry

IN contemplating the prospects of natural gas being transported from the fields where it is produced to such distant points as Philadelphia, New Jersey, New York City, and New England, let us review the advance that natural gas has made and the projects currently scheduled for construction. This may give us a perspective of the point in the long-range development of the natural gas business in which we now find ourselves, and some basis for judging the further expansion of the industry. Authentic statistics of the total marketed production of natural gas in the United States have been compiled by the Bureau of Mines since the year 1906. The growth of the business is indicated by the following data on marketed production for each ten-year interval since 1906:

Jan 1, 1947

By Simon D. Strauss

Production and consumption of nonferrous metals in the United States during 1950 were at peak levels for the postwar period, as is shown in Tables I, II, and III. The trend of production was upward through most of the year. At the year end, with the possible exception of the Tri-State zinc-lead district, the large mining operations in the country were running at capacity. The absence of serious labor interruptions during the year was an important contributing factor in the increased out-put of metals, since in each of the previous postwar years there had been a number of major strikes which affected production adversely.

Jan 2, 1951

By K. Aoki, N. Kameda, T. Esaki

The shortage of adequate construction sites and their difficult location has compelled many engineering structures to be planned in old mining areas in Japan. This paper shows, first, the characteristics of the excavated underground environment and next, the necessary preventive measures during construction of surface structures. Where the depth of a mined out area is relatively shallow, there is a tendency of cave-in consequent to surface loadings. The effect of surface loadings is inversely proportional to the depth of goals. Finally, a power plant project is studied as an example.

Jan 1, 1984

By Peter F. Weiss, H. Riedler, I. M. Moschitz, A. Olsacher, G. B. Fettweis

CONTENTS : 1. NATURAL FACTORS Geology Petrography and Rock Mechanics Mining System Orientation Rock Bolting System Movability of the Ore Grain Size Distribution Permeability Contamination Value of the Ore Hydrology 2. TECHNICAL FACTORS Height Length and Width Drawing Areas Time Factor Water Predrainage Surf ace Draining Underground Draining Advancing Slitting Sequence of Development Initiation of the Caving Process Drawing Rate 3. SPECIFIC MINING RULES Advancing Development Drawing Rate Interruption of Drawing (Water Distribution, Concentration of Mud, Dilution) Blasting 4. CONTROLS Safety Controls for Operation Computerised Drawing Control Structure of the Computer Program Hard Ware Print Outs 5. SUMMARY 6. ACKNOWLEDGEMENTS 7. REFERENCES Under the heading "Development System for Block Caving under Severe Conditions" a report was presented to this congress regarding a magnesite mine using block caving for several years. On account of the experience gathered in this mine and the results of far reaching exchange of experience, as well as under due consideration of the international literature it is tried to systematically list and briefly discuss the following factors that have to be considered for development and draw control of block caving. 1. NATURAL FACTORS It is self evident that this implies all those circumstances given by nature and which cannot be altered by man. Any mining activity is subjected to those and the success is depending on how far technology can be adjusted to those conditions. Geology Deposits of considerable thickness with rather steeply inclined flat-faced contacts are optimal for block caving. While vertically there is practically no limitation- for the deposit, theoretically, the smallest horizontal basis apt for operating block caving is the minimum area necessary to get the rock to completely cave in by undercutting and drawing. Practically, only consider- ably bigger main dimensions are found, mainly because of technical factors (machinery and equipment) and economic factors (cost ratio of exploration vs. development, danger of contamination).

Jan 1, 1981

By M. Cross

INTRODUCTION The development of refining processes involving gas injection into liquid metals has seen the evolution of a variety of designs [I]. During the last few years or so the top, bottom and side blown processes have, essentially, been combined to produce a series of mixed gas blowing schemes (eg. the LBE [2,3] and LD-OB processes [4,5]). Although, a variety of mixed gas blowing processes have been carefully engineered and recorded operational experience now attests to their effectiveness, optimising their design and operational performance is another matter. Detailed process analysis of such operations is impeded by the complex nature of the physical and chemical processes involved: . fluid flow behaviour of the liquid metal and injected gases, . chemical reactions in the vessel, . mass and heat transfer within the fluid phases in the vessel, . influence of the geometry (eg. location of the tuyeres, etc.), . monitoring the operational performance. By and large, design and operating parameters evolve from a combination of laboratory scale experiments, pilot plant work and, of course, practical engineering experience. Conventionally, the gas-liquid system used to model the industrial process is air-water, for a number of valid reasons including – . visual demonstration plus geometric and (to some extent) dynamic similarity, . the fact that the system demonstrates, at least, qualitatively many of the complex features of gas injection - interaction between the gas and the liquid - the nature of the gas flow behaviour - qualitative indications of mass transfer rates Important experimental contributions to the understanding of gas liquid systems include the work of Brimacombe [6], Wraith [7], T.Robertson [8], D.Robertson [9], Guthrie [10] and Szekely [11] (these references provide starting points to identify the major published work in this area). Although air-water systems have been instrumental in providing a great deal of qualitative insight into the fluid flow behaviour of the processes, reliable quantitative predictions are more problematic. A number of workers (notably Brimacombe and colleagues [6, 12])have demonstrated that different gas-liquid systems can lead to wide variations in behaviour. Other limitations of physical modelling include the assumptions of isothermal flow, scale- up of turbulent flow behaviour and the inability to directly include the effects of chemical reactions. The above limitations in physical modelling, therefore, yield a natural role for mathematical modelling provided that it can be made comprehensive enough whilst remaining cost-effective. The major physical processes involved in gas injection systems may be summarised as . behaviour of the gas envelope structure in moving through the liquid metal . the global movement of the liquid metal . momentum interaction between the liquid metal and the injected gas . heat transfer and mass exchange via the chemical react ions. The behaviour of gas envelopes forming at a tuyere and then moving through the liquid has been investigated thoroughly by a large number of workers. Such models are generally based upon simple physic- al concepts derived from visual observation. An early model by Davidson and Schuler (DS), based upon a force balance between the liquid inertia and a combination of the bouyancy and momentum forces on the envelope, has proved to be a useful tool in predicting bubble volumes at detachment [13]. The DS model has been successfully modified in a number of ways [14-17] to cope with heat transfer and reactive transfer rates, etc. Furthermore, the basic ideas summarised above have also been confirmed on industrial converters by both Guthrie [I8] and Brimacombe [19]. Models have also been developed to predict the behaviour of the "chemical" component of some gas-liquid systems. However, one thing is clear; all gas-liquid reactive systems are governed by the degree to which effective mixing occurs. As such, the processes are dominated by the behaviour of the heat and mass exchange of the two phase fluid flow system. It is the pattern of movement of the turbulent liquid metal plus its interaction with the injected gas which must be predicted reliably, if sufficiently comprehensive comp-

Jan 1, 1984

By A. S. Odeh

ABSTRACT A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs fram pressure build-up and/or drawdown plots. INTRODUCTION The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard,l Freeman and Natanson,2 and Samara.3 The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results,4 Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a fractured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. TO understand the behavior of the pressure buildup and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions: 1. The matrix blocks act like sources which feed the fractures with fluid; 2. The net fluid movement toward the wellbore obtains only in the fractures; and 3. The fractures' flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures' bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady -state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. la this paper, the fundamental equation of flow

Jan 1, 1966

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By Francis Donaldson

THE direct injection of cement grout into water-bearing fissures as a means of checking or stopping the flow of water into shafts and tunnels has been experimented with for a decade or longer and seems to have been first attempted in Europe. The earliest application of which the writer has found a record was at a shaft sunk by the Mining Society of Lens; this is described by C. Dinoire in the Transactions of the Institution of Mining Engineers.1. It is only lately, however, that the process has been entirely successful. This success has been accomplished on the Catskill Aqueduct, now under construction by the city of New York. This aqueduct includes a number of deep pressure tunnels, reached by shafts for both waterway and construction purposes. In portions of these shafts and tunnels considerable underground water was met. The contract for the first of these deep pressure tunnels was let to the T. A. Gillespie Co.; this section is known as the Rondout Siphon. It leads under the Rondout valley at a depth of from 400 to 800 ft. and is about 5 miles long. The engineers expected that considerable water would be encountered, but fortunately this was not the case except at one shaft, known as No. 4, which penetrated the rock at a junction between limestone and conglomerate. Water-bearing fissures were encountered almost immediately. At a depth of about 200 ft. a flow of 1,500 gal. per minute was struck. The shaft then contained as many pumps as could be used, and it seemed impossible to sink it further. After vain efforts had been made to proceed, John P. Hogan, a division engineer of the Board of Water Supply, suggested that cementation of the fissures be tried. The process was attempted for the first time in this country. Since the shaft was partly full of water it was necessary to drill grout holes with a diamond drill. Platforms were placed on the timbers at the water level, the diamond drill was installed and six 90-ft. holes were drilled in the bottom of the shaft. Several car loads of cement were pumped through these holes into the fissures, the drill casings being used for grout pipes. This largely cut off the flow of water from the bottom and sinking could then

Jan 1, 1914