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The Henderson Mine is a large underground panel cave molybdenum mine located near Empire, Colorado. Secondary blasting requirements have varied from one shot per 27 tonnes (30 tons) to one shot per 900 tonnes (1,000 tons) of ore. Geology, structure, cave abutment loads, and location of the ore in the column all affect the amount of oversize boulders (greater than three-fourths cubic meter or one cubic yard) that require secondary breakage. The primary method of breakage utilizes cone charges (plastic funnels filled with an emulsion) placed on accessible oversize rocks. Hangups in the brow area of the drawpoint are drilled with a self contained diesel hydraulic drill and loaded with gelatin dynamite. High hang-ups located beyond the reach of the secondary drill are "bombed" in with strategically placed emulsion bundles or ANFO bags loaded in place though a sectioned aluminum pipe.

Jan 1, 1994

By Jian Zhang

From the standpoint of quality, surface cracks normally pose more of a problem than internal cracks. Hypo-peritectic (HP) steel grades are well known for their proneness to surface longitudinal cracking (SLC) during continuous casting. This study analyzed the influences of chemical composition, technique parameter and secondary cooling on the surface longitudinal cracks. Based on the optimized the first and secondary cooling zone water distribution in the process of continuous casting, low cooling water distribution at solidification initial stages and uniform cooling at secondary cooling zone were suggested, which can be used to effectively control the surface longitudinal cracks.

Jan 1, 2010

By LUDWIG VOGELSTEIN

WE are indebted to Mr. Barbour for his valuable contribution to the literature on copper statistics; it is to my knowledge the only intelligent attempt to throw light on a much misunderstood subject. If I should appear to criticize some of his findings and arguments, I do not want to leave the impression that I do not appreciate the article; I think Mr. Barbour has been painstaking, and even where one might not agree with his conclusions, he has opened our eyes and stimulated us in our search for the truth.' It might be well to define the term "secondary copper" and to make a few remarks about the origin and the reasons for the variation of the supply. Mr. Barbour has touched on these points, but not sufficiently to make them clear to those not in the business.

Jan 1, 1931

By J Wood

Steady depletion of the world’s primary copper reserves coupled with a meteoric rise in electronic waste (e-waste) generation has led to secondary copper processing assuming an ever-increasing importance within the global copper industry. Treatment of secondary copper feeds at existing smelting operations has traditionally been performed in the Blast furnace, Peirce-Smith converter and/or anode furnace. In the past decade or more, bath smelting technologies have been preferred for the processing of these materials due to their superior environmental performance and flexibility to operate under a wide range of conditions. This paper focuses on the pyrometallurgical processing of copper secondaries in the Outotec Ausmelt TSL Furnace and some of the unique issues facing secondary copper smelters and downstream gas handling/cleaning equipment.

Aug 8, 2011

By W. R. Opie

Fundamentals of blast furnace smelting of low grade copper and precious metal scrap and residues are reviewed with emphasis on emission control, by-products produced, slag cleaning for high recovery of metal values and the evolution of an off-gas system to eliminate hydrocarbons that result from decomposition of plastics in the blast furnace- charge. Problems with tin, antimony and nickel in the smelter-refining cycle are discussed.

Jan 1, 1985

By A. P. Svenningsen

DURING the work at the test mill in Morenci, it was determined that a suitable feed for the ball mills could be made by a single pass through a short-head cone crusher. These crushers did not require a closed circuit delivering only a screen product to the mills, such as is the practice in some concentrators. By no means does this mean that the practice in these other concentrators is wrong, but just that the Morenci ore can be most economically crushed and ground in this manner. Therefore, the design of the secondary crushing plant was simply a problem of taking 25,000 tons of ore per 16 hour day from the primary crusher, this ore ranging in size from fine particles to 10 or 12 in., and reducing it to minus 3/4 in. Inasmuch as outages must be contended with in any crushing plant, it was assumed that the crusher would operate at full capacity for approximately only twleve hours per day, which is three-quarter capacity for the 16-hour shift. With this in mind, it was necessary to design a crushing plant which would average approximately 1600 tones per hour for the 16-hour day, or 2000 tons per hour for slightly over 12 hours per day.

Jan 1, 1942

By Peter L. Siems

Humid tropical environments pose many problems for mineral exploration. The problems result from thick lateritic soils, dense vegetation, seasonally heavy rains, deep chemical weathering, few outcrops and thick saprolites. Although geochemical exploration should be potentially a useful technique in these environments, it appears from the scarcity of reports in the literature that insufficient attention has been paid to developing procedures that are specific to the needs of humid tropical areas. For this reason, the authors believe that this account of a geochemical study in a tropical coastal area on the edge of the Brazilian shield is of general interest and importance for potential geochemical exploration surveys in similar areas within the tropics. The objective of the geochemical study was to develop a practical technique of reconnaissance geochemical prospecting for copper deposits in Brazilian tropical coastal lowland areas. In order to achieve this objective, information concerning the secondary dispersion of copper in these areas was required. Consequently, an orientation survey was designed to provide this information. The present account contains details of the geochemical study and the information about the secondary dispersion of copper that was acquired during the course of the orientation survey. Location and Climate The field area is on the Atlantic coastal lowland of Brazil at latitude 13°S. It lies approximately 10 kilometers south of Maragojipe, a city of 15,000 inhabitants; this city is on the western side of the Bay de Todos os Santos about 45 airline kilo¬meters northwest of Salvador. (See Fig. 1) A good gravel road from Sao Felipe to Sao Roque do Paraguay crosses the southern part of the field area. The climate of the area is hot and moist, and is without prolonged dry periods. The mean annual rainfall is about 1600 mm (63 in.) and the greatest precipitation occurs during the winter months of May and June and the summer months of December

Jan 1, 1972

By Kenneth N. Pike

The need to comply with environmental regulations and increase production has resulted in modifications to the East Penn blast furnace operation. Changes made include furnace design modifications, closed loop water cooling with heat recovery, automated weighing and charging, automated tuyere punching, ammonia scrubbing of tail gases and improved metal and slag handling to minimize environmental impact. These changes have resulted in a marked increase in yearly production and compliance with many of the air, water and solid waste regulations.

Jan 1, 1990

By Michael E. Stout

M.A. Industries, Inc. has developed and is now offering on a commercially available basis, complete systems to recover and recycle lead from spent SLI batteries. The system begins with the breaking and separation of the component parts of the batteries and subsequent treatment of the effluent water produced by this operation. The recyclable materials recovered from this process are metallic lead, lead paste and polypropylene. The lead paste is introduced into a process to convert it from a lead sulfate to a lead carbonate. The process also regenerates the salt solutions into reusable carbonate. The lead carbonate is then leached into an acid bath where it is later recovered by a proprietary electrolytic process. The metallic lead is recovered in a short rotary furnace producing metal for further refining and alloying. The polypropylene is further washed and then introduced to a reclaim extruder along with the proper modifiers and additives. The resulting resin can then be sold on the open market to injection molding processors. This complete system greatly reduces the amount of waste to be disposed of and completely complies with all applicable EPA guidelines.

Jan 1, 1993

By Richard A. Leiby

The recycling of lead-acid batteries in the United States has become a challenge as to how to balance ever increasing environmental regulation and cost with efficient operations. East Penn's captive secondary lead smelter has developed into a recycling facility producing lead, polypropylene, sulfuric acid, ammonium bisulfite, and non-hazardous discard slag. The emphasis has been to design a facility to comply with environmental regulations, to eliminate wastes, and to produce products, while at the same time, continuing to supply the company's battery manufacturing raw material needs.

Jan 1, 1993

By Charles E. Nelson

In considering the types of scrap that are processed into secondary magnesium, it is important to point out that the greatest proportion of this material is fabrication, foundry and machine shop scrap that is generated during the conversion of magnesium products into the finished article. This material, then, is largely of the same composition and quality as the original ingot or heat of metal except as it may be mixed with other compositions or metals in the fabricating process. Insofar as such materials can be processed back into secondary ingots or final products which meet the composition and property standards required of the original virgin stocks, then it seems reasonable that such products are fully equivalent to the primary products. With these premises then, it is the intent of the present discussion to consider briefly some of the methods whereby scrap may be generated, segregated, shipped, and processed in such a manner that the final products will be equivalent to virgin materials. Some information on the effects of impurities will be given in order to aid in the evaluation of these products. SCRAP GENERATION The method by which scrap is generated serves in a rough way to classify the resulting materials in terms of how they may be handled and recovered. These methods will be dealt with briefly. Machining operations such as milling and turning undoubtedly provide the great-

Jan 1, 1943

By R Austerberry, S Green

The discovery of the Cuffley Lode at Mandalay Resources Costerfield Operations provided an opportunity to extend mine life via mining the offset depth extension of the previously worked Alison Mine. Access from the existing Augusta Mine placed the initial Cuffley underground workings at approximately 250 metres depth from surface. As the new orebody transitioned towards production, a secondary means of egress needed to be established. The depth of the initial capital development presented a challenge in establishing a secondary means of egress that could be confidently relied on. The availability of land to locate a surface shaft collar further reduced available options and geotechnical drilling further limited suitable shaft locations. Time limiting factors such as permitting and having a secondary means of egress in as soon as possible, further highlighted that an innovative secondary means of egress was needed. A consideration of using an emergency gig lowered by a suitable sized crane supplied by an external crane contractor was investigated and found to be a suitable outcome. This Emergency Gig was deployed via the Cuffley Return Air Raise. When trialled, the emergency gig was found to provide a reliable, repeatable extraction method with an acceptable level of risk. Issues discovered during such trials further improved the process to a point where this extraction method became the adopted secondary means of egress for additional lodes that existed at depth. When assessing possible methods of secondary means of egress, the use of a third-party crane and custom designed and fabricated emergency gig should not be discounted. Where a crane can be sourced within an acceptable timeframe, the emergency gig extraction method provides a reliable safe and cost-effective means of secondary means of egress, especially when multiple shafts are to be developed. Local laws may negate the ability to employ such a system, although it is believed with good communication and well-constructed risk assessments, this system can be safely deployed.

Mar 15, 2021

By A. A. Novoselov, U. Kelm

"Large volumes of mine tailings accumulated in surroundings of porphyry copper deposits represent a growing threat to environment. They contain significant concentrations of toxic metal and metalloids which can contaminate river runoff, ground waters or can be transported by wind. Both extreme pH of fluids in tailings impoundments and high surface areas of processed mineral grains provide their increased reactivity. As a result, during only a few decades, As, Cu, and Mo can be mobilized, redistributed through the tailing column and accumulated through post-deposition leaching, evaporation and contamination with natural fluids. Those processes are reflected in the forming of secondary minerals. Gypsum, Fe oxides/hydroxides, efflorescent salts and clay minerals are typical alteration products in tailings. Here we present the results of reactive transport simulations implemented on the base of PHREEQC and SUTRA codes. The one-dimension model emulates the mass balance between rainfall, evaporation and subsurface runoff, the kinetically- and thermodynamically-driven dissolution of tailing minerals, advective and diffusive transport of tailing fluids, and precipitation of secondary phases. A typical tailing column is composed of four unequal layers with predominance of (i) evaporation, (ii) secondary mineralization above, (iii) below water table, and (iv) near the bottom of dump. Those horizons are characterized by contrasting pH, chemical composition and bulk mineralization of pore fluids, distinct accessibility of atmospheric oxygen and, as a consequence, distinct intensity of sulfide oxidation. The modeling and its verification on Chilean tailings impoundments reveal the complexity and high rates of secondary mineralization. The accumulation of toxic alteration products is controlled by fluid transport through the tailing column induced by both rainfall/evaporation and exchange with subsurface runoff. The geochemical modeling is a powerful approach which allows comparing the processes in tailing deposits produced by distinct flotation regimes and providing the long-term predictions of their environmental impact as well as identifying sectors of tailings for possible re-processing."

Jan 1, 2018

By E. Guerrini, M. Maccagni, J. Nielsen

"Lead is the most important material able to meet the current demand for energy storage. The lead acid battery is reliable, efficient and inexpensive. Continuous developments in battery construction are providing improvements in all aspects of the batteries’ performance. The lead acid battery is both the main lead product and the main raw material for lead production. More than half of the lead produced is from secondary smelters where batteries are the most important feed material. The environmental pressure on lead production has been increasing for many years, and continues to become stronger and stronger. The lead production processes and technologies themselves will require updating to meet the new regulations. Although they are very strict now, they will become even more so and current technologies may not be sufficient. Because recyclability is a strong point for the lead acid battery, the secondary smelters need to reduce the environmental impact as much as possible. In recent years, the secondary smelters underwent impressive changes in this direction, but some more improvements are possible. Electrochemistry can offer a step change improvement in making secondary lead production more environmentally friendly. Engitec has developed an electrochemical process base on a very high current density (high productivity) cell using an inexpensive electrolyte and at a relatively low cost. In this paper, the latest update on the technology is provided. INTRODUCTION The lead acid battery is considered the “walking dead” by some new technologies trying to replace it. It has played and will continue to play a very important role in our lives because it is inexpensive, fully recyclable and the existing lead and the mine reserves guaranty enough material for the extended future. According to the life cycle, the lead acid battery is the cheapest and the most effective system to store energy. Lead is practically a close loop where lead battery production consumes more than 80 % of the produced lead but contemporarily it is the most important raw material for the production of metallic lead. In fact, nowadays, the secondary production has overcome primary production and this trend is expected to continue. Primary lead is the make-up material for the existing battery production and the source of lead for the construction of the new ones."

Jan 1, 2018

By Ludwig Hermann

"Phosphorus is required by every cell of living organisms and essential for plant growth. It is a non-renewable resource that must be mined from natural deposits, going gradually into depletion. Abundant secondary resources are available in sewage sludge and meat and bone meal, with the highest exploitable P concentrations in ashes that remain from their widely used combustion with energy recovery. ASH DEC has successfully removed heavy metals and transformed sewage sludge ash into a marketable P fertilizer by application of a thermo-chemical treatment process. Pilot scale investigations in which ash was treated proved that generally heavy metal limits required by fertilizer legislation can be attained. To achieve a high P availability for crops – an essential fertilizer quality feature – was a more challenging R&D task. Our presentation demonstrates the scientific approach and R&D results that lead from assessment of market requirements to licensed products.IntroductionPhosphorus (P) is required by every cell of living organisms. It is one of the major elements for plant nutrition and therefore essential for crop production. P supply in plant nutrition depends entirely on external inputs into soils [1]. This is achieved by P-fertilizers deriving from rock phosphate deposits that are gradually going into depletion. Serious prognoses anticipate that rock phosphate will be the first low running resource in the world [2]. In the EU, last year 2.530 kt of phosphorus (P2O5 in fertilizers) was consumed and only 313 kt (P2O5 in rock phosphate) was mined. Since 2007, rock phosphate prices have increased by 500% because of a tight supply situation [3].For these reasons, P recycling is becoming an increasingly important issue. Suitable secondary raw materials with regard to their high P-content and abundance are sewage sludge and meat and bone meal. In the EU 989 kt P2O5 are accumulated annually in theses materials, of which 632 kt P2O5 are permanently lost to landfills and other forms of disposal. The main reasons for their limited recycling are concerns on heavy metal contents and organic pollutants that may incite health hazards. As an additional shortcoming, the availability of P from these materials to plants is poor and storage and transportation are problematic issues [4, 5]."

Jan 1, 2008

By J. L. Fitch, B. G. Hurd

The presence of gypsum in samples subjected to standard core analysis introduces serious errors in the measurement of water saturation and porosity. The magnitude of these errors, depending upon the type of analysis procedure used, has been evaluated experimentally and theoretically. Water-saturated pore volumes determined by vacuum distillation or retort procedures may be too high by as much as 48 per cent of the volume of gypsum present. The maximum error in this value determined by Dean-Stark extraction with toluene is 36 per cent of the gypsum volume. If pore space is measured by a Boyle's law type porosimeter the maximum erorr due to gypsum is 38 per cent of the original gypsum volume present. The conscientious core analyst may eliminate the errors caused by gypsum by either of two methods. He may apply suitable corrections for the water of crystallization removed from gypsum, or take special precautions to prevent dehydration of gypsum during core cleaning and alzalysis procedures. These alternatives are discussed and methods for obtaining reliable core analysis data are proposed. Gypsum (CaSO4 . 2H2O) occurs as a common mineral in many of the world's sedimentary basins. In addition to its presence as primary bedded evaporitic deposits, it is often found as secondary replacement zones and pore-fillings in host rocks. That it may cause false indications in porosity, both on neutron logs and in standard core analysis, has been generally recognized. False porosity interpretations from neutron logs result because the chemically bound water in gypsum attenuates neutrons as effectively as free water. Errors in core analysis result when gypsum is dehydrated prior to or during the analysis. Vacuum retort procedures used by many laboratories to determine fluid saturation and porosity effect a complete removal of water of crystallization from gypsum. The crystal water, distilled and collected with free water from the sample, is counted as water-sat11rated pore space. Dehydration of gypsum results in a decrease in volume occupied by calcium sulfate and a corresponding increase in pore volume. Thus, if gypsum is dehydrated by sample cleaning and drying procedures, subsequent porosity measurements with gas expansion or compression instruments will be high. The qualitative effect of gypsum on porosity determinations by retort procedures was discussed in a recent article by Bynum and Koepl3. They concluded that since false porosity was interpreted as being water saturated, determinations of oil content were not affected. Others in the industry, however, have pointed out that porosity values are often used with values of water saturation determined independently, e.g., from electric resistivity logs in making reserve estimates. Values of water saturation calculated from the formation resistivity using the Archie equation, S4= are actually low if values of are high due to gypsum. In this case, false porosity values due to gypsum could cause serious errors in calculations of oil-in-place. This investigation was made to determine quantitatively the effect of gypsum on porosity values determined by different core analysis procedures. EXPERIMENTAL PROCEDURES Dehydration of Gypsum The extent and rate of removal of water of crystallization from gypsum under conditions encountered in core analysis procedures were studied. Taken for the experiments were three types of relatively pure, naturally occurring gypsum, viz. selenite, satin spar and massive gypsum. Although all samples probably contained trace chemical impurities, each type lost the theoretical amount of water upon complete dehydration. An automatic recording thermobalance, similar to one described by Mauer2, was used to obtain dehydration rate data for samples heated in dry air. Water

By H. C. Johnson, J. K. Elliott

One of the primary requirements for successful operation of an enriched gas-drive project is to control the composition of injection gas. This can become a serious and difficult problem, particularly in cases where the enrichment material is being furnished from a number of field -produced gas streams. It is possible to effect control of the injection gas composition through frequent or continuous sampling; however, this can be extremely costly and, in many cases, impractical due to laboratory requirements of time. Another alternative would be to provide a calculation technique which would be flexible and sufficiently accurate to predict composition of the liquid and gas streams of interest at any point in the system. The purpose of this paper is to discuss a technique that was used successfully on an operating enriched gas-drive project for developing information which could be used for controlling composition of the injected gas. FIELD OPERATIONS The particular field (hereafter called Example field) in the example operation being discussed is composed of four oil reservoirs (A. B, C and E) and one gas condensate reservoir (D). Casinghead gas from the oil reservoirs and gas from the gas condensate reservoir are gathered through a field gathering system as shown in Fig. I for injection into Reservoir C. The gas mixture which is recovered from the five reservoirs for injection purposes is composed of gases liberated in 19 individual separators, each operating at a separate temperature and pressure. PROPOSED CALCULATION TECHNIQUE It is well known that vapor-liquid equilibrium calculations in general use throughout the petroleum industry can be used to predict reliably the phase behavior of hydrocarbon mixtures, particularly at pressures less than 1,000 psig. It is then a simple matter to account for the material on a ComPonent basis by m''ing flash and material balance calculations at each separation point in a hydrocarbon system. Accordingly, it was proposed to use vapor-liquid equilibrium and material balance cal- culations with a medium-sized electronic digital computer as a basis for developing a control procedure for use in controlling injection gas composition in the enriched gas-drive project. Although the approach is a simple one, the numerous vapor-liquid equilibrium calculations involved make the problem laborious; in this particular case, it would have been impractical to make sutficiently complete analysis without the aid of digital computing equipment. SAMPLING AND VERIFICATION OF CALCULATION PROCEDURE To obtain representative gas and liquid stream samples and to provide a quantitative measure of overall system Performance for comDarative purpLses, a thorough test of the field and plant system was conducted in the summer of 1957. Oil production at each battery was sta-

By Bruce F. Grant, Stefan F. Szasz

During 1947, a Sinclair research team was assigned to investigate thermal methods of oil recovery. The assignment was recommended by a survey of possible research approaches to increase the amount of oil that ultimately can be recovered from oil producing reservoirs. The use of heat to stimulate oil production rates by the melting of paraffin deposited in well bores can be traced back to within one or two decades of the drilling of the Drake well. The application of heat on a larger scale has been discussed by generations of oil producers. Shortly after the turn of the century, one intrepid operator is reported to have injected steam into a Pennsylvania property. After a few weeks, he apparently became discouraged and terminated his experiment. Subsequently, the literature contains references to several well-developed techniques for supplying heat to a producing well bore to melt paraffin or to reduce the viscosity of oil contained in the formation immediately around the well bore.1.?.3.4 Some early references discuss procedures to furnish heat to the reservoir,5,6 with the injection well as the heat source, thus obligating the process to maintain the entire rock mass at a temperature above that at which the desired improvement in oil recovery would occur. Another approach to reservoir heating was reported by a group of Russian technologists in 1935.7,8,9 They definitely demonstrated that combustion can occur within the porous structure of an oil-bearing sandstone. Their field experiments, however, relied less on combustion within the rock than on heat furnished by combustion of oil supplied to the injection well bore. Ignition of the air-oil mixtures in the well bore was found very difficult, and the field tests were carried on for only short periods of time. Publication of the Russian work spurred at least one independent operator in this country to try firing an air-gas injection well, on for only short periods of time. Publication of the Russian work spurred at least one independent operator in this country to try firing an air-gas injection well. The Brundred Oil Corp. reportedly obtained combustion in the sand immediately around the injection well bore, but the experiment was abandoned because of interference with normal production schedules. Injection capacity of the experimental well was greatly reduced by firing. The well was reshot and pieces of sand showing partial fusing of the quartz matrix were recovered. To the authors' knowledge no other field experiments utilizing combustion techniques for formation heating were undertaken prior to 1948, although the patent literature evidences continued interest in formation heating."'," CONCEPT OF COMBUSTION-SUPPORTED HEAT WAVE The references cited were in agreement that heat applied to a reservoir would increase recovery, but there

Jan 1, 1955

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By L. D. Wooddy, W D. Moore

Water drives may be natural or artificial. For the case of a natural water-drive reservoir, the volume of water influx corresponding to reservoir pressuve-production history may be calculated by means of the material bal-ance-unsteady state equation. For the artificial water drive or pattern injection water flood, the material balance equation is sufficient to determine the reservoir pressure-production, injection history. However, for both cases to reliably predict reservoir performance, it is necessary to calculate the saturation distribution of the reservoir fluids at different stages of depletion. This paper consolidates the various equations used to determine the performance of water-drive reservoirs into one approach that is applicable to any reservoir that has a natural water drive or is to be produced by water injection. The numerical procedure has been simplified considerably, and the solution is adaptable to either hand calculations or digital computer operation. INTRODUCTION A water-drive reservoir is one in which the predominant source of energy for production of oil results from the encroachment of water into the oil zone. The water drive may be either natural or artificial. Water invasion takes place by expansion of water in the aquifer as a result of the pressure decline transmitted from the oil reservoir. Because water is practically incompressible, a natural water drive requires an extensive aquifer containing a volume of water many times the volume of oil in the reservoir. Provided the permeability of the formation is reasonably high, a moderate decline of reservoir pressure usually causes adequate water influx. If the reservoir pressure decline becomes excessive because of low permeability or a high rate of production, part of the oil production may result from the liberation of dissolved gas which may cause excessive quantities of free gas to be produced along with the oil. In extreme cases, reservoir pressure may decline so rapidly as to cause the oil to be produced predominantly by dissolved gas drive, leading to abandonment of the reservoir before the advancing water has had a chance to flush the entire reservoir. In reservoirs that are not connected to extensive aquifers, an artificial water drive may be created by injecting water into or around the lower edges of a reservoir. Sometimes water is injected within the reservoir through wells interspersed among the producing wells. When injection is carried out in such fashion, the reservoir is in effect subdivided into a number of separate producing segments, in each of which the displacement of oil is simultaneously taking place, and the shapes of which are fixed by the well patterns employed. Because of the natural tendency of oil and water to segregate according to their relative densities, water will tend to migrate downdip regardless of where injected. Accordingly, the injected fluids can be retained within the intended reservoir segments only when conditions are unfavorable to their migration under the force of gravity. Pattern injections are usually confined, therefore, to reservoirs having low structural relief, or low permeability, or when production and injection rates are such that fluid movements in the reservoir are dominated by the pressure gradients rather than by the force of gravity. In the case of natural water-drive reservoirs and artificial water-drive reservoirs in which the water is in-

Jan 1, 1958