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By Leroy W. Weeks, Peter B. Nalle

The rapid growth of the modern electronic computer industry during the past 15 years is, perhaps, the greatest phenomenon that has occurred in American business in this century. This growth is due in part to the new, and in some instances, revolutionary applications of computers instigated and developed by both the manufacturers of such equipment and their customers who search for easier, faster, more accurate methods of conducting their business operations. As in other industries, modern computers are becoming more common in the field of mining. The adaptation of computer analysis to the unique problems of mining companies is undergoing research and development by both electronic and mining companies. However, for those of us in mining who are interested in the possibilities of computer analysis and control, the basic question is Where can a computer system be of use in a mining operation today? Some ideas of such applications follow, as well as a specific example of computer control at the Riverside Cement Co.

Jan 9, 1960

By P. B. Baxendell

The performance of a water-drive reservoir having a gas cap depends primarily on the movement of the gar-oil and oil-water contacts. The movement of the contacts during production depends in turn on fluid withdrawals and how the reservoir pressure changes as fluids are produced from the reservoir; that is, on how effectively the aquifer maintains pressure by replacing withdrawals. inasmuch as pressure changes, fluid withdrawals, contact positions, and produced gas-oil and oil-water ratios are interdependent, the analysis and prediction of the performance of a reservoir produced in a given way must take into account this interdependence throughout depletion. This paper presents an analysis which, within the limitations of the assumptions made, yields an engineering approach to predicting future performance based on reservoir pressure and production history. The most significant assumption is the method of extrapolation of future gas-oil and water-oil ratios. The extrapolation procedure smoothly increases both ratios to preselected values as the remaining oil column undergoes a specified decrease in thickness. This preselection is made on the busis of previous field experience in depletion of similar reservoirs under similar conditions. For computing future performance a vdumebic balance L combined with the differential equation defining pressure distribution in the aquifer to obtain positions of water-oil and gas-oil contacts. From these positions are extrapolated produced water-oil and gas-oil ratios. Reservoir performance can be investigated when oil production rates are dependent upon various factors including the performance of the reservoir itself. Examples of practical application of the procedure are included. INTRODUCTION To predict performance of water-drive reservoirs with gas caps and thin oil columns, it is necessary to describe the motions of the fluids within the reservoir during the entire production period to depletion. These motions depend on the pressure changes and on the withdrawal of oil, gas and water. Production of oil from the oil zone primarily causes water to move in to take its place; production of gas from the cap tends to cause oil to migrate into its place. In addition, the volumes of oil and gas remaining in the reservoir depend on changes in the pressure, since a decrease in pressure causes fluid expansion, gas liberation and oil shrinkage. A method of relating the future pressure to total withdrawals is used to describe the motions of fluids within the reservoir under conditions arising in possible modes of production. The analysis is based on two relationships and will reduce the problem to one amenable to digital computation. The first of these concerns the dependence of the pressure distribution in the entire aquifer furnishing the water drive upon the total reservoir withdrawals. This dependence is dictated by the permeability distribution and the extent of the aquifer; at present, such information is most readily obtained from the performance history by means of the resistancecapacitance reservoir analyzer. The second relation involves withdrawals, pressure in the reservoir, and movement of oil, gas, and water within the reservoir. The analysis is subject to certain simplifying assumptions that are necessary to permit solution of the problem. A comparison of the methods of this paper with those presently practiced is pertinent. One method of analysis is to use the reservoir analyzer to predict reservoir behavior based on aquifer characteristics determined from production history. Inasmuch as the total withdrawal rate depends upon the gas-oil and water-oil ratios, which depend in turn upon, among other things, the positions of the gas-oil and water-oil contacts, these ratios must be assumed in advance. In this paper these ratios are, instead, related to the computed positions of gas-oil and water-oil contacts. Thus, our method can be applied to problems in which the oil production rate is limited by produced gas-oil ratio, or to problems in which it is desired to determine the variable gas injection rate that will maintain the gas-oil or water-oil contact stationary. These problems cannot be worked satisfactorily on the analyzer. Another method presently used is based on a paper by Hurst.' Since his procedure is dependent upon using the solution of the heat flow equation, which requires constant permeability within the aquifer, and our procedure recognizes variations of permeability in

By Hans Smit

The face of mining as we know it is set to change in the very near future as mining companies all over the globe realize the implications of accessing the vast mineral wealth contained on, and under, our ocean floors. With some land based mineral deposits being fully exploited across the world, deep sea mining is set to revolutionize global approaches to the search for precious metals and other sought after minerals. [ ] Previously, the financial implications of deep sea mining outweighed the benefits of access to the mineral rich deposits identified all around the world. The process of marine diamond mining off the west coast of southern Africa started in the late 1950?s by a Texan, Sammy Collins, and subsequently continued by De Beers to the present day, has proven to be an excellent proving ground for the development of technology and mining systems that ensure a sustainable and financially viable business. [ ]

Jan 1, 2008

By I. M. Ahmed, R. S. Hassan, M. I. Aly

Extraction and separation of La, Sm and Dy ions from acidic sulfate-phosphate solutions was investigated using a cation exchange extractant, bis(2,4,4-trimethylpentyl) phosphinic acid, CYANEX 272, in kerosene. The influence of shaking time, equilibrium pH, extractant, sulfate and phosphate ion concentrations, diluent type and temperature was studied. The extraction was found to be pH-dependent, and increasing the phosphate ion concentration inhibited the extraction which was found to be endothermic. The stoichiometry of the extracted metal species was found to be MOH.H2OHSO4H2A.A2. Aliphatic diluents were found to enhance the extraction compared to aromatic diluents. The results showed that there was a separation mode between the metal ions when varying the hydrogen ion and sulfate ion concentrations, under the used experimental conditions. The investigated process was used for the recovery of La, Sm and Dy from the acid solution resulting from the leaching of low-grade monazite.

By Kenneth B. Higbie

PRESIDENT LYNDON B. JOHNSON announced at midyear that the test flight of the A-It plane, the world's first super-sonic aircraft capable of flying 2,000 miles per hour, was made possible by "the mastery of the metallurgy 'and fabrication of titanium." Not all of the contributions made by the mineral industry in 1964 were acknowledged so widely. Yet the contributions were significant as the search continued for new and improved methods for providing metals and mineral products to meet the ever-expanding requirements of the world economy. This chapter reviews only a few of the metallurgical developments that resulted from U.S. and foreign research efforts. MINERAL BENEFICIATION Up-to-date theory 'and practice in the mineral ,Processing field in 1963 involved subjects such as autogenous grinding, high-intensity magnetic separation, and mill control by computers. These subjects were fully discussed at the Seventh International Minerals Processing Congress held in New York City during September.

Jan 1, 1965

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By I. I. Inculet, M. A. Bergougnou, J. D. Brown, R. M. Quigley, D. K. Faurschou

"Coal from Hat Creek, B. C., has been successfully beneficiated to remove ash while retaining calorific value by a dry electrostatic separation process using a fluidized bed for triboelectrification. Two samples of Hat Creek coal used in the beneficiation experiments have been characterized particularly with respect to their mineral and clay content. The calorific value recovery exceeds the simple dry coal recovery because of the heat lost in altering the clay minerals of the ash fraction during burning. Recoveries and ash contents of the beneficiated coal are comparable to recoveries by water washing, but the dry process avoids the potential water pollution problems.IntroductionProposals have been made which suggest an interim Canadian coal production target for the end of the century which will require a four- to fivefold increase over the 1977 production. This implies a nominal annual growth rate of about 6070 to achieve a production rate of 115 to 140 million tonnes/year. Whether or not this target is realistic, it is becoming increasingly evident that coal must be utilized more fully on a world-wide basis. The crisis in Iran has provided the latest stimulus to renewed interest in Canadian coals for domestic use and export.The emerging new era of coal utilization for fuel and chemical feedstock will not, however, generally tolerate the level of coal technology which prevailed prior to the availability of abundant cheap oil and natural gas. Economic, environmental and resource management considerations will necessitate, for example, the use of improved methods of beneficiating coal. Continued development and application of conventional processes, principally aqueous, involving heavy media and cyclones will solve many of the problems. However, less conventional processes may be preferable or necessary in certain applications."

Jan 1, 1980

By Jun Wang, Bo Zhang, Wenqing Qin, Guanzhou Qiu, Xiaozhen Ma, Key Lab of Biohydrometallurgy of Ministry of Education, Fen Jiao, Central South University, Yansheng Zhang

"Arsenic contained in minerals sulphides such as enargite and tennantite can represent not only a significant penalty element in base metals production, but also a disadvantage to the environment through producing the toxic emissions to the atmosphere. The achieving separation of arsenic bearing minerals either at an early stage in floatation or from the floatation concentration is significantly beneficial to the economic. However, there was no feasible commercial method of separation at the flotation stage because of its similar flotation properties with many other copper sulphides. In this work, the selective floatation of enargite from copper sulphide concentrate containing maily covllite, chalcoctie, bornite and enargite was investigated. A low arsenic concentrate with As 0.2%, Cu 22% and a high arsenic bulk concentrate with As 7.65%,Cu 33.65% were obtained. It was indicated that Ca(ClO)2 is the effective depressor and the optimum floatation condition was obtained. Most enargite could be floated at pH 11 and controlling the pulp potential at 290 mV SHE. Furthermore, the arsenic removal from the high arsenic bulk concentrate by hydrometallurgy methods was study. The results showed that the reaction temperature and the concentrations of NaOH were the most important variables affecting the rate of arsenic removal. A low arsenic concentrate with As 0.24%, Cu 37.80% was obtained in the optimum leaching condition.INTRODUCTIONArsenic is mainly produced as a by-product of base metals smelting, in particular copper concentrate. China has imposed an upper limit of 0.50% arsenic for concentrates entering (Long et al., 2012). Arsenic amount of copper concentrate within 0.40% has also been imposed in China, and above which will be introduced about 50 RMB penalties per ton for each 0.10% increasing by smelters now. Therefore, it is necessary to remove arsenic from the copper concentrate.In copper concentrate, arsenic is mainly in the form of arsenopyrite (FeAsS), enargite (Cu3AsS4) or tennantite (Cu12As4S13). There are two types of arsenic in the separation of copper and arsenic: arsenopyrite and arsenic bearing copper mineral. It is easier to separate arsenopyrite from the copper sulphide by flotation in comparsion with the separation of enargite or tennantite from non-arsenic copper minerals (Pineda et al., 2015). The main difficulty in the separation of arsenic copper mineral from non-arsenic copper sulphides is their extremely similar floatability, which depends on the fact that tennantite and enargite contain high copper content (Pineda et al., 2015)."

Jan 1, 2016

By Juan L. Luque Lanza

Durante las fases de minado como la exploración, desarrollo, preparación y explotación de una zona mineralizada, surgió la necesidad de clasificar geomecánicamente el terreno a través del uso los conceptos básicos de la mecánica de rocas y la integración de dicha disciplina al planeamiento del minado de una mina subterránea. Por ello, el presente texto describe el proceso de esta metodología que consiste en la clasificación del terreno según los grupos de similar comportamiento y la elaboración de planos geomecánicos, con la finalidad de encontrar la relación existente entre el tiempo límite y el espacio activo para una excavación subterránea, diseño y cámaras pilares en la mina subterránea de Yauricocha.

Aug 26, 1988

By A. Sobhy

Froth flotation is a widely used, cost effective coal cleaning process. However, its high process efficiency is limited to a narrow particle size range between approximately 50 to 600 µm for coal and 10 to 100 µm for minerals. Beyond this range, the efficiency of froth flotation decreases sharply, especially for difficult-to-float coal fines of weak hydrophobicity (e.g., oxidized coal). This study was aimed at enhancing recovery of an Illinois fine coal sample using a flotation column featuring a hydrodynamic cavitation nanobubble generator. Nanobubbles that are mostly smaller than 1 µm can be formed selectively on hydrophobic coal particles from dissolved air in fine coal slurry. Results indicate that combustible recovery of a -150 µm coal was increased by 5-50% for different size fractions in presence of nanobubbles, depending on process operating conditions. Other major advantages of the nanobubble flotation process include lower collector dosage and air consumption since nanobubbles are produced from air naturally dissolved in water and they act as a secondary collector on particle surfaces, thereby resulting in considerably lower operating costs. Key words: Cavitation; coal; froth flotation; nanobubble.

Feb 27, 2013

By Maurice Deul

For the first half of the 21st century, the United States will rely on the same mix of fuels it has for the past 50 years. Petroleum for the United States will cost more and availability will decline as developing nations modernize. Increased use of natural gas for electric power generation will result in stress on the gas supply. Coal will be the fuel of last resort. More than half the petroleum used is imported, about the same amount as used for transportation. Only coal can provide relief by fueling railroads through electrification while encouraging “piggy-back” trailer haulage, co-generation for manufacturing and expanded passenger service.

Jan 1, 2002

By R. Winand, P. Harlet

he cathodes produced are of electrorefined grade; metallographic structure and surface roughness are controlled to a depth of 1.3 cm (single-side deposits); silver levels in the cathode are regulated by the presence in solution of Cl- and Br- ions; organics must be used at very low concentrations (around 0.1 mg/l with a consumption of about 0.01 mg/l/hr). The required concentrations of additives were established according to a well-defined strategy based on the consumption of organics at the cathode by a mass transfer limited-process.

Jan 4, 1992

By A. E. Isaacson

The U.S. Bureau of Mines determined the effect of common sulfide minerals on the corrosion rates of various types of ferrous alloy grinding media. Data obtained from this study will aid in determining the contribution of any electrochemical reactions between sulfide minerals and grinding media to the total grinding media consumption. Common sulfide minerals used in this study were chalcopyrite, galena, and sphalerite. In the presence of oxygen, chalcopyrite was found to increase the corrosion rate, galena was found to decrease the corrosion rate, and the effect of sphalerite was dependent upon the type of grinding media. Possible electrochemical reactions of these minerals in the presence of grinding media are suggested.

Jan 1, 1989

By Derek E. McBride

"Exploration work in the Beardmore - Tashota area has led to a reinterpretation of relationships between gold mineralization and the geologicalevolution ofthe area. The host volcanic rocks form two parallel volcanic belts connected by a much smaller cross-cutting band, which trends northeast from Beardmore to Tashota. This connecting band consists of mafic and felsic volcanic, plus clastic sedimentary rocks in a sequence conformable with the contact of the Onaman Lake Batholith to the east. A metamorphic aureole or incorporated xenoliths are lacking along this major contact and the only intrusive relationship observed is chilling between mafic dikes and a cold host granite in proximity to it. Granite dikes are totally lacking in the volcanic succession, or the overlying sedimentary sequence. A major part of this sequence consists of a polymict basal conglomerate with granite boulders and volcanic clasts in a fine-grained chloritic matrix. The nearest source for these boulders is the Onaman Lake batholith.Gold mineralization in significant economic quantities (+ 50 000 ounces) occurs at the top or above the mafic volcanic succession as quartz bands. In the Northern Empire Mine, the band is conformable, folded, boudinaged and the mineral zoning shows a relationship to variations in the host rock, not structural overprinting. In general, where the host mafic tuff is medium-grained, the quartz band is thicker, up to a metre wide, and carries economic grade; where the tuff is finer-grained and bedded, the band is very thin and low grade.Stratigraphic control and metal zoning shows that the mineralization formed as part of the development of the volcano- sedimentary succession. The other major deposits in the area (Leitch and Sturgeon River) have a similar structural history suggesting that they are also syngenetic in terms of the stratigraphic development. Regionally, these deposits were emplaced prior to any significant tectonic deformation but at the end of the mafic volcanic event.The mafic activity was related 10 a period ofextension which caused the volcanic troughs to develop along centres of rifting. The hiatus at the end of this event permitted extensive hydrothermal systems to form and deposit siliceous exhalite bands within sedimentary or terminal mafic volcanic environments in promixity to major thermal sources. Subsequently, the Kenoran Orogeny deformed the entire succession into upright folds with a sub-vertical schistosity. Evidence shows that the deposits have remained intact since deposition."

Jan 1, 1987

By N. Sloan Dworian, Alyssa Smith, Ian Kellogg

Many studies have utilized magnetic susceptibility data to fingerprint porphyry copper centers; however, usage of magnetic susceptibility data to identify trends in a Climaxtype molybdenum porphyry deposit is limited. To better understand potential petrophysical signatures in a Climaxtype Mo porphyry deposit, magnetic susceptibility data was gathered at regular intervals from core holes across the Climax Mine, targeting major lithologies and styles of alteration. Preliminary analysis suggests that there are quantifiable patterns which may correspond with the mineralizing intrusions. This data can complement current mapping and exploration techniques to identify Climax-type molybdenum porphyry centers and likewise further the exploration potential for this deposit type.

Feb 22, 2026

By Shu Yamaguchi

The behavior of halide impurities in pyrometallurgical processes such as Wealtz kiln and MF process has been discussed based on the thermochemical data and the reported data of PbO activity in PbCl2-PbO melts. The role of PbCl(g) has been estimated to be significant in the chloridization evaporation reaction. From reported data on the PbO activity in PbC12-PbO melts, activity of PbCl2 has been calculated by the numerical integration of Gibbs-Duhem equation, and the stability domains and the composition of the liquid phase as well as the vapor pressure of PbCl2 have been estimated as functions of log P2HCI/PH2O and temperature. From the discussion of the path during cooling process on the log P2 HCI . PH2O vs. temperature diagram, the authors proposed a possible dechioridization process that utilize water vapor as a dechloridizer for the direct precipitation of PbO from gas phase.

Jan 1, 2003

By Ernest Baafi

A simulation model RoadSIM using the ARENA modelling system has been developed to evaluate roadway development options for a given development panel configuration. The RoadSIM simulation system has provisions for variability/randomness in operations including cutting and loading at the face, tramming and discharge of coal to the boot end and availability of equipment. The modelling system provides a means for assessing the operational limitations of roadway development practices at a particular coalmine. It is a ?what if? tool that allows a range of equipment, configurations and operating practices to be assessed in terms of achievable advance rates and equipment utilisation. Output from the system is in the form of a dynamic visualisation as well as summary reports and detailed logs of operations over time.

Oct 1, 2009

By Daniel T. O’Brian

Mineral exploration activities are benefiting from new interpretive techniques which have become economically practical with computers. Government agencies, educational institutions, and industry have each contributed research and development efforts for improving the mathematical analysis and graphical display of exploration data, resulting in operational aids not foreseeable a decade ago. Progress has been worldwide and is expanding rapidly. Books 1-10 are supplementing the periodic literature, at least one abstracting service is now active, 11 and an association has recently been formed to encourage and publicize advances in this field. 12 With the diversity of applications, only partial coverage of the subject can be made at any single symposium. Four of the six papers in this section report on the current state-of-the-art in selected areas of interest: graphics, time-sharing, mathematics, and economic analysis. The remaining two papers are descriptions of advanced statistical techniques for gaining additional information during exploration, and illustrate methods which will become more commonly applied in the future. "Computer Graphics: A New Tool for Exploration and Mining" describes the use of a computer and accessory equipment as an information retrieval device, graphically merging and displaying pertinent information for visual inspection and interpretation. This is a rapid means of studying information which has been pre-stored in a form accessible to the computer. Time-sharing is a means of achieving a comparable rapid response when calculations are being performed. The paper, "Some Applications of Time-Sharing in Mining Geophysics," describes the experience of one company using a time-sharing facility for geophysical computations. Another paper on this subject, stressing mining applications, has recently been published. 13

Jan 1, 1969

By William L. Grube

PECIMEN preparation for electron metallography involves several steps, such as polishing, etching, replicating, mounting, and shadowing. Although each step must be done with care, the operation requiring the utmost attention is etching. Proper etching is important because the relief pattern developed on the surface of the specimen by the etchant, and reproduced as minute differences in thickness of the replica, determines entirely the amount of detail seen in the final micrograph. The characteristic colored stains, sometimes used in light metallography to simplify identification of certain microconstituents, cannot be tolerated because there is danger of introducing artifacts in the replicating operation. It is also quite difficult to remove plastic replicas from stained specimens. A suitable etchant for electron metallography must, therefore, in all cases exhibit a preferential attack upon each of the microconstituents present sufficient to result in a difference in surface elevation. When only two microconstituents are present, it is not too difficult to find a suitable etchant since their physical or chemical properties are generally sufficiently different to result in a marked difference in attack by the etchant. For example, picral (a saturated solution of picric acid in methanol used as an immersion etch) is a satisfactory etchant for the specimen shown in Fig. 1 consisting of iron carbide particles embedded in a ferrite matrix.'

Jan 1, 1952

By P. E. Baker

Approximate solutions are presented for the heat-flow equations in a loss-free linear system with a moving source and with heat transfer by convection and conduction, representing in situ combustion in an oil reservoir. The rate of heat generation and the velocity vf of the source (flame front) are assumed constant. A cold front or convection front caused by the cooling effect of in-jected air develops behind the flame front and moves with velocity vc, which is determined by the thermal properties of the air and rock. Because of thermal conduction the fronts are not sharp; i.e., they do not represent temperature discontinuities. The following solutions apply after a sufficiently long time. where Q is heat generated per unit volume of formation, k is thermal conductivity, CF is volumetric heat capacity, a is thermal diffusivity, and subscripts 1 and 2 refer to values behind and ahead of the flame front, respectively. The parameter CF2 is contained in v . Te is initial reservoir temper- . C2 e ature and air-injection temperature. Other mathematically possible solutions are presented. The different solutions result from the use of different values for various physical parameters. The solution just presented is thought to be most commonly applicable. INTRODUCTION In this paper, approximate analytical expressions are derived for the temperature profile developed in the underground combustion method of oil recovery. A qualitative description of the process may be found in a paper by Tadema.1 The flame front is regarded as a moving source with a constant rate of heat generation. Heat transfer is by conduction and convection. Previous publications, of which a few are cited here, 2-5 have also attacked this problem and have presented solutions pertaining to different methods of approximating or idealizing the process studied. The present paper also treats an idealized case: linear flow is assumed for heat and fluids, and vaporization and condensation effects are neglected. The results obtained are similar to those derived by Bailey and Larkin,3 but are obtained by an entirely different procedure. The method used here should give considerably greater insight into the physics of the in situ combustion process. Four types of cases are considered, distinguished by thermal and fluid-flow properties of the system. A constant rate of heat generation and constant rate of flame-front advance are assumed. Flame-front temperature is determined for each case using a heat balance which involves the entire temperature profile. The applicability of the different solutions to real systems is discussed after they are all presented. Again, this is done for the purpose of understanding better the physics of the process. Consideration of the nonapplicable solutions and of the reasons for their not applying is significant. In a paper by Cooperman,4 the only case solved is one considered here as not applicable. Fluid flow, as such (pressures, saturations, oil recovery, etc.), is not treated. This subject has been covered in a paper by Wilson, et al.6 Also, we are not concerned with requirements for continuance of the process; we only attempt to determine the temperature history for cases where the process has continued for some time. PHYSICAL SYSTEM AND APPROACH TO PROBLEM A linear flow (heat and fluid) system is assumed and the x-axis is taken parallel to the flow direction. The combustion zone (flame front) is vertical,