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By Jaeheon Lee, Jai‑Won Byeon, Junmo Ahn, Jun‑Jae Lee, Eun‑Woo Kim, Yoo‑Jin Kim, Jiajia Wu, Jae‑Yeon Kim

Growing demand for valuable battery materials and environmental issues from battery disposal make the recycling of spent lithium-ion batteries (LIBs) essential. Specifically, the green approaches using organic reagents have garnered many attentions for battery recycling. In this study, a synergetic organic leaching system using methanesulfonic acid (MSA) of strong organic acid and citric acid (CA) with good chelating ability was investigated to extract valuable metals from LiCoO2. Hydrogen peroxide was used as a reducing agent to enhance leaching kinetics. Cobalt extraction of 98% and lithium extraction of 97 % were achieved in the optimized condition; 2.4M MSA, 1.6M CA, 1.0 vol% H2O2, S/L ratio 80 g/L, 85 °C, and 1 h. The optimal leaching condition of the MSA-CA mixed leaching system exhibited good applicability to various cathode scraps, such as LiCoO2, LiNixMnyCo1- x-yO2, and LiNixCoyO2. The dissolved Co and Li ions in the MSA-CA leachate were selectively recovered with high recovery efficiencies of 99 % and 97 % as Co3O4 and Li3PO4, respectively. The recovered Co3O4 and Li3PO4 were utilized to regenerate cathode materials. LiCoO2 and LiFePO4 were also synthesized through a solid-state reaction and hydrothermal method. The recycling process based on the MSA-CA-H2O2 synergetic leaching system was proposed, and it might be applied as a green and economical organic leaching system for the recycling of various types of spent LIBs.

Sep 20, 2023

By J Hutchings

An essential component to the management of any process is the measurement of key parameters, used to monitor, control, and provide the feedback necessary for improvement. This paper discusses how data collection and analysis can provide a better understanding of the blasting process, as well as additional control and improved outcomes.The drill and blast process involves the generation and use of information at a number of levels. Comparison of historical parameters and results provides a starting point for the development of ongoing blast designs and a baseline against which future results can be compared. The collection of data during implementation provides a quality assurance/quality control (QA/QC) function where potential defects (such as under-drilled or over-charged holes) can be rectified prior to firing. Actual quantities and production rates allow the development of realistic plans and schedules, rather than using inaccurate estimates and targets that lead to unscheduled changes to equipment paths. Over?the past several years there have been a number of technological advances in data collection technology. Drill monitoring instrumentation on blasthole drills provides location information and feedback on rock properties as drilling occurs. Hand held ‘data logger’ technology has also overcome the challenges of working on the bench, such that blasthole measurements can be collected and forwarded directly to the explosive truck. Mine sites are becoming wireless network-enabled allowing the seamless data transfer from the field back to the office, in near real time, as that information is collected. Great strides have also been made in the development of drill and blast software systems which are more user friendly, and yet provide far greater capability to manage the quantity of data generated. The blasting process is critical to the overall mining process and the delivery of a successful blast outcome requires that the blasting process be ‘in control’. The measurement of key parameters can provide the data with which to measure and maintain control of blasting, and allows the validation of performance improvement measures and identification of improvement opportunities.

Nov 8, 2011

By Emanuel Trotz

As the long-felt need of a reliable and easily-managed pyrometer has now been fully supplied, by the latest form of Professor Wiborgh's pyrometer, an account of this instrument will, per-

Jan 1, 1893

By Zhuokun Cao

Manufacture of aluminum foams still suffer from nonuniformity and poor reproductively for there is lack of basic knowledge of foaming process. In this paper, carbon fibers are used as novel stabilizing additive for aluminum foams, and the structure evolution of aluminum foams with different fiber content was studied. A laser rangefinder was used to detect the expansion rate of different al foams. Al foam samples are solidified at different foaming time to determine its relative density and cell size distribution. Results indicate that the cell size of foams linearly increases with the decrease of density, and the slope of the line is influenced by fiber content. The relationship between expansion ratio, density and cell size of the foams is discussed. It is concluded that the density of resulting foam is influenced by the rate of gravity driven drainage, and its cell size is determined by expansion ratio and foaming time.

Jan 1, 2010

By R. S. Bigelow

Part 1.- Metal Mines Early experiments with mechanical loaders in metal mines were confined largely to machines of the shovelling type and generally air-operated. Although the first application of the scraper to metal mines dates back to 1910, it was not until about twelve years ago that it came to be used extensively. Generally, the scraper gives better results in metal mines than in coal mines, as degradation due to soft bottom and breakage are not factors, but it has a wide range of application and is successfully used in the mining of salt, potash, gypsum, zinc, copper, and a variety of ores, from soft material to hard chunky ore which settles compactly. Today, the scraper has replaced to a large extent the shovelling type of machine in metal mines. Scrapers have offered an inexpensive solution for the mucking problem and are now employed in most mining districts throughout the world. They are operated by labourers of all colours and degrees of skill. Each installation, however, requires individual study on the part of the mine mechanical department to determine the type of scraper, horsepower of hoist, and most economical speed of rope, as well as method of rope rigging. Unfortunately, the scraper has no power to select pay ore from waste and its suitability for use under circumstances which might require sorting of the ore can only be decided by a weighing of the economic factors involved

Jan 1, 1931

By Sangjian Zhang, Zhu Xiao, Lairong Xiao, Rushi Chen, Mei Fang, Zhou Li

The copper-graphite metal matrix composites were fabricated by two different production methods: directly sintering with copper and graphite (Cu-Gr composite), and in-situ sintering with cuprous copper and graphite (Cu2O-Gr composite). During the in-situ reaction sintering, a redox reaction occurs at the interface of the Cu2O particles and Gr particles, resulting in the improved physical and mechanical properties of Cu2O-Gr composites. Compared with Cu-Gr composite, Cu2O-Gr composite has a higher compression strength at any given graphite content due to the improved interface bonding and uniformly distributed fine graphite particles in the matrix. Increasing graphite content decreases the mechanical properties of the copper-graphite composites. The compression strength of Cu2O-Gr composite is 50-100 MPa higher than that of Cu-Gr composite. INTRODUCTION Copper-graphite composites have been widely used in industry due to their low density, relatively high strength and hardness, good thermal and electrical conductivity, arc ablation resistance and self- lubrication ability (Grandin & Wiklund, 2018; Han & Xu, 1999; Huang et al., 2017). Electric sliding contact friction pair in the high-speed railway system and motor brush in electric contact components have a very high demand on electrical conductivity and self-lubrication ability of materials. The electric devices need to bear both mechanical load and high electric current. Copper-graphite composites with good mechanical, electric and self-lubrication properties are the best candidates for application in multifunctional electric sliding contact frication components. The relative sliding speed of friction pair is developing towards 100 m/s or even faster, which can withstand the electric flow of more than 800 A, and it is often accompanied with vibration and impact (Guo & Ding, 2008). Conventional wear-resistant materials can no longer meet the current requirements and this promotes the development of copper- graphite composites with excellent comprehensive properties (Ding, Chen, Zhu, Zhang, & Zhou, 2009; Yasar, Canakci, & Arslan, 2007). There are many ways to fabricate copper-graphite composites, mainly including powder metallurgy method, liquid immersion infiltration method, rapid sintering method and electrodeposition method (Kalin & Poljanec, 2018; Kim, Lee, & Han, 2014; Liu et al., 2018; Wang et al., 2018). Each method has its own advantages and disadvantages, and the powder metallurgy method is the most commonly used one due to its simple process, high economic benefit, and industrial production applicability. The common steps of the powder metallurgy method are as follows (Samal, Parihar, & Chaira, 2013): firstly mixing the copper (copper alloy) powders and graphite with a certain ratio, following by die-forming, and then sintering at the high temperature with or without pressure. The advantage of copper-graphite composites is that the graphite distributed in the copper matrix uniformly and it can form a carbon diaphragm preventing the wear of the composite (Fu & He, 2010). However, the bonding strength of the interface between the copper matrix and the graphite is relative low as the combination between them is mechanical interlocking but not metallurgical bonding (Ma et al., 2008). It is meaningful to develop new fabrication technology of copper-graphite composites with better interface bonding, which could provide guidance for the design of copper-graphite composites with excellent comprehensive properties.

Jan 1, 2019

By Arkady Senchenko

At present, there are different traditional and modern methods for ore grindability evaluation. The correct and rational approach to sampling, testing methods and mill sizing enables one to design a workable technology. This paper contains TOMS institute experience in different grinding indices determination over the last 7 years (SAG Design Test, BWi, CWi, RWi, and other). Mill sizing examples and circuits modeling for the projects in Russia and Kazakhstan are considered. Keywords: ore grindability, SAG Design Test

Sep 1, 2012

By Daniel Lachapelle, Nuri Hmidi, Turgut Yalcin

"Simulation can serve as a convenient tool in studying the behaviour and performance of grinding circuits by facilitating the evaluation of various scenarios and identification of optimum operating conditions. This technique was applied to the St Andrew Goldfields Ltd.’s Stock Mine Mill which is a 1300 tpd gold milling facility, offering custom milling services as well as processing the Company’s own ores. Lack of adequate instrumentation in the mill poses a challenge in attaining optimum performance especially with changing ore types and characteristics. The grinding process is monitored essentially by manual measurement and adjustment of pulp densities at various streams. A simulation program was designed to assist in the effective implementation of this mode of grinding control. Product sizes from both the primary and secondary grinding circuits were correlated empirically to relevant process variables using a database formed from the results of past sampling campaigns. The simulator was created in Microsoft Excel whose data analysis and optimization tools coupled with its Visual Basic Programming capabilities were found to provide an excellent environment for the development of a cost-effective, efficient and user-friendly simulation program.INTRODUCTIONGrinding is often a very costly unit process in milling operations, mainly due to the excessive energy consumption associated with it. For example, for a Canadian copper-zinc flotation mill, grinding was listed as being the most costly item taking up 30.4% of the total milling expenses, followed by the flotation cost at 2 1 .O% (Kidd Creek Mines Ltd., 1982). A survey on 45 copper flotation mills around the world showed the average grinding cost to be 34.5% of the total milling cost (Weiss, 1985).Overgrinding aggravates the cost issue, while insufficient grinding either causes loss of valuable minerals to tails or results in low-grade concentrates. Therefore, it is essential that grinding circuits be carefully controlled and monitored. To this end, a great deal of effort has been devoted over the years to the modelling and simulation of grinding systems in order to assist in the efficient running of these processes."

Jan 1, 2001

By Fred Horne

1N THIS PAPER, the writer proposes to limit his comments to few generalized phases of the subject, based on his personal experience in the midwestern United 'States and in one section .of the Coal Branch in Western Alberta. The following statistics are submitted to show the importance that strip mining has assumed in the coal mining industry of the United States. In 1914, 1,281,000 tons of strip coal were produced, amounting to 0.3 per cent of the total production. In 1948, the total was 13~,505,000 tons, representing 23.3 per cent. In 1949, the percentage figure dropped slightly and this can be partially accounted for by the labour disturbances prevalent throughout the year. In 1914, there were 48 power shovels and draglines being used in the stripping of coal; in 1949 there were 3,712, not to mention other types of coal stripping equipment such as bulldozers, tractors and scrapers, rotary excavators, and stackers. At the bituminous coal mines in Western Canada, strip mining was introduced only a few years ago, two of the major reasons for its development being the need for increased production during the war and post-war years and the need to hold the line on increasing production costs, but even in these few years the percentage of strip production has in-creased to such an extent that some mines that, five or six years ago, were producing all their tonnage from underground operations are today obtaining up to 80 per cent of their total output from strip mines.

Jan 1, 1951

By A. R. Taylor

In recent years, thermodynamic data have been used to a greater degree than ever by the chemical and metallurgical engineer as a means of predicting and controlling chemical reactions. To satisfy the spiraling demand for basic physical data needed for the calculations, the Bureau of Mines is studying the heat capacities of a variety of chemical compounds at high and low temperatures. This paper is one of a series presenting such data. The heat capacities of two alkaline earth compounds, strontium bromide and strontium nitrate, were measured in a temperature range of 60° to 300° K. in an adiabatic calorimeter and at temperatures of 300° to about 1,200° K. in a Bunsen ice calorimeter. The construction and operation of the calorimeters are discussed in other reports.3 4 The heat-capacity data presented in this report were extrapolated to 0° K., and smooth values of heat capacity, entropy, enthalpy function, and free-energy function were calculated and tabulated at even 10-degree intervals. The enthalpy data were fitted with algebraic equations by applying the method of least squares; calculations a£ heat-capacity values, entropy, enthalpy function, and free-energy function were made at even 50-degree intervals. The heat and entropy of fusion of strontium bromide were calculated from the enthalpy measurements.

Jan 1, 1962

By John Jermain Porter

The chief purpose of this paper is to indicate the laws governing the fuel-economy of the cupola, to examine the feasibility of some of the proposals for increasing its fuel-economy, and to show that the conditions limiting fuel-economy here are altogether different from those prevailing in the blast-furnace. The two methods available for studying the thermal efficiency of the cupola and determining the factors limiting fuel-economy are: 1, by the determination of the total heat-balance; and 2, by the application of the theory of critical temperatures. The case selected as an example represents a cupola operating under fairly efficient conditions. The data are as follows : Cupola, GO in. in diameter, 15 ft. high to the charging-door, with a 9-in. lining. Bed-charge, 2,000 lb. of coke and 4,000 lb. of iron. Subsequent charges, 400 lb. of coke and 4,000 Ib. of iron. Total number of charges, 20. There was 800 lb. of coke recovered from the drop, hence the total coke burned is 8,800 lb., or 0.11 lb. of coke per Ib. of iron. Coke contains 90 per cent. of fixed carbon and 2 per cent. of moisture. 300 1b. of kindling-wood is used in lighting. 80 lb. of limestone (95 per cent. of CaCO,) is used per charge, or 0.02 lb. per Ib. of iron. Melting-loss, 4 per cent.; distributed thus : Fe, 3.5; Si, 0.25; Mn, 0.25 per cent. Average analysis of top-gases : CO2, 15.1; CO, 10.0 per cent. Average temperature of top-gases, 1,600" F. Temperature of air and stock charged, 60" F. Dew-point of air, 50 F. The items entering into the total heat-balance and their calculation are as follows: 1. Heat of combustion of fuel.—Total heat evolved = 14,580 x lb. of carbon burned + 7,200 X Ib. of wood burned. Hence B.t.u. per lb. of iron charged =

Jan 1, 1913

By Sutham Niyomwas

The Fe-TiC composite powder was synthesized in situ by carbothermal reduction of ilmenite. The standard Gibbs energy minimization method was used to calculate the equilibrium composition of the reacting species. The effects of the reaction temperature (1300 °C - 1500°C) and milling time of precursors on the Fe-TiC conversion and powder morphologies were investigated using XRD and SEM method. The synthesized products showed that composite with iron matrix and titanium carbide as a reinforced phase was formed.

Jan 1, 2006

By H M. Parker, G Verly, T Postolski

Assessing the uncertainty and risk in mineral resource estimation is required for best practice and is implied by the public reporting codes in the categorisation of mineral resources and reserves. One industry best practice is quantifying the risk on future production for a given period, which can be done using two geostatistical approaches: conditional simulation and drill hole spacing studies based on estimation variances. Conditional simulation can provide a more complete and flexible answer to the problem, but it takes a fair amount of time to complete. Drill hole spacing studies are simpler, faster and can provide reasonable assessments of mineral resource uncertainty.This paper is a presentation of the principles, theory and practice of drill hole spacing studies. Various types of risk assessment are considered. Difficulties encountered in practice are discussed, and solutions are proposed. The important parameters impacting the results are reviewed. Examples of results and sensitivities are shown.CITATION:Verly, G, Postolski, T and Parker, H M, 2014. Assessing uncertainty with drill hole spacing studies – applications to mineral resources, in Proceedings Orebody Modelling and Strategic Mine Planning Symposium 2014, pp 109–118 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 24, 2014

By L. Martins

To increase zinc recovery in the concentrate, this investigation performed mineralogical characterization, dispersion studies, bench and pilot-scale flotation experiments and an industrial flotation trial. The objective was to verify the flotation behavior of the silicate zinc ore (calamine type) in the presence of slimes, with the aid of dispersing agents. Characterization studies identified the major minerals in the flotation feed as hemimorphite (calamine), quartz and dolomite. Dispersion tests showed that enhanced dispersion of the particles in the pulp in the absence of reagents occured at a pH range between 8.5 and 12.0. Bench-scale flotation experiments were planned using the statistical tool of complete factorial design at two levels, replicated once. These experiments showed, and were confirmed at the pilot-plant scale, that higher doses of sodium sulfide and polymeric dispersant combined with sodium silicate favored a higher metallurgical recovery. At 6,800 g/t (218 oz/st) sodium sulfide and 6,992 g/t (224 oz/st) polymeric dispersing agent combined with sodium silicate, a zinc grade of 38.4% in the final concentrate was achieved, at an average metallurgical recovery of 72.4%. The industrial trial confirmed the pilot scale results, leading to zinc recovery of 76.1% and a 37.3% zinc grade in the concentrate. Key words: Froth flotation; Flotation reagents; Flotation depressants; Zinc/ zinc ores

Jan 1, 2010

By E. McCullough, S. Gaillard

"Diesel particulate matter (DPM) remains a health concern in many underground metal/nonmetal mines, and has been regulated by the Mine Safety and Health Administration since 2002. While the NIOSH 5040 standard method for DPM monitoring is required to demonstrate regulatory compliance, the FLIR Airtec DPM Monitor can serve as complementary engineering tool. It is a handheld instrument that offers near real-time measurements. As part of an ongoing field study, the Airtec has been used to survey elemental carbon concentrations (a proxy for DPM) in an underground stone mine. Via “spot-checking” and more prolonged area monitoring, this effort was aimed at determining spatial and temporal DPM variation in several key locations. INTRODUCTION Diesel particulate matter (DPM) is the solid fraction of the exhaust emissions from a diesel engine. It is largely made up of elemental and organic carbon (EC and OC, respectively), which can be measured as proxies for estimating mass concentrations of DPM. The National Institute for Occupational Safety and Health (NIOSH) considers DPM to be a health hazard and potential carcinogen [1]. It is believed to cause and/or exacerbate respiratory illness upon inhalation, deposition, and retention in lung tissue [2]. Since DPM exists in both the micro- and nano-particulate ranges, it can surpass typical auto-immuno defense mechanisms that keep larger particles out of the respiratory system [2]. Relative to other occupations, the DPM exposure potential for underground miners is high because these individuals work in enclosed environments where diesel powered equipment is frequently used [3,4]. A variety of engineering and administrative controls have been devised to reduce DPM exposures in underground mines, and increased airflow is often a key component of control strategies. In large-opening mines, which are most common in the metal/nonmetal sector, DPM abatement via increased ventilation can be especially complex due to moving and controlling the large air quantities [5]. The Mine Safety and Health Administration (MSHA) has regulated DPM exposure in metal/nonmetal mines since 2002. The final rule limits personal exposure to total carbon (TC, which is the sum of EC and OC) to an eight-hour time weighted average (TWA) of 160 µg/m3. To demonstrate compliance, operators must use the NIOSH 5040 Method [6]. However, the Airtec DPM Monitor (FLIR Systems, Inc., Nashua, NH) was developed as an engineering tool to provide near real-time measurements of both EC and TC for tracking personal exposures [7]. The portable Airtec works by capturing DPM on a filter and successively measuring laser extinction on the filter as DPM accumulates; the EC fraction of the DPM is dark, and so as it accumulates the filter becomes darker and absorbs more laser light [8]. The laser extinction value is directly correlated to EC, but since EC and TC are generally observed in consistent proportions (i.e., TC = EC*1.3), the Airtec is also programmed to display TC as a TWA [9]. There have been multiple studies conducted to validate the Airtec and the instrument has been adopted by some mine operators as a tool for their health and safety programs [3,8]."

Jan 1, 2016

By Takashi Furuyama, Sukeyuki Mori, Abel Bissombolo

"In flotation practice, a good recovery of minerals largely depends on the degree to which the valuable minerals have been liberated from the associated gangue during the grinding process. Therefore, a regular measurement of the degree of liberation can provide data for the assessment of the quality of separation and predicts the effect of changes in the grinding-classifying circuit on flotation process. Generally, the standard procedure for measuring the degree of liberation requires the preparation of polished sections - a time consuming operation that also has the disadvantage of providing an overestimated number of free particles because of the stereological nature of produced samples.The present work is an alternative approach to avoid these miscalculations and establish a system of control for fluorite flotation plants. The system deals no only with the state of liberation but also the dynamic behavior of individuals particles and mineral components within the grinding-classifying and flotation circuits. It involves methods such as sieving, x-ray diffraction analysis, study of polished sections and microscopic counting of preliminarily sieved minerals particles from a fluorite processing plant, randomly dispersed on a glass slide, but not embedded in a resin mounting medium. If a complete information on the textural properties of minerals in the ore (including its mineral components distribution) can be obtained through x-ray diffraction analysis and study of polished sections, the microscopic counting is used to determinate with enough accuracy the mineral liberation, estimate the grade of fluorite ore and products, determinate the deportment and approximate recovery of individuals particles and mineral components within the investigated circuit. For a count of 100-1000 particles in each n-size range, the counting method was found to be a particularly reliable and less time consuming operation that could substitute the chemical analysis of fluorite ore for an estimate of the grade:"

Jan 1, 2003

By Webster S. Anderson

The design, development, and testing of hydraulic props to provide a lightweight, high strength, recoverable unit is described. Modifications in design incorporating threaded components resulted in the development of a lightweight hydraulic prop fabricated from aluminum alloy tubing. This new design facilitates interchange and replacement of component parts, and the physical properties of the material are not changed as they are when welding is required. The new prop is 65,000 pounds and has a maximum load capacity of a lower weight-to-load capacity ratio than the hydraulic props now available.

Jan 1, 1967

By Oliver Bowles

"Asbestos" is not the name of a distinct mineral species but is rather a commercial term applied to fibrous varieties of several minerals. The origin and significance of names applied to asbestos by early writers are discussed in the section devoted to sources of supply and terms employed in ancient times. VARIETIES The most useful variety of asbestos is chrysotile, a fibrous serpentine the composition of which is expressed by the formula H4Mg3Si209. Chrysotile is characterized by a strength and flexibility that permit the use of the longer fibers for spinning. The bulk of the world production of both long and short fibers, is of this variety.

Jan 1, 1935

By T Akiyama, J A. de Castro, H Nogami

Blast furnace is a countercurrent moving bed reactor that produces pig iron from iron bearing materials like pellet, sinter or lump ore. The furnace has cylindrical shape and the lump solid materials are alternatively charged onto the top of the furnace. Hot air is introduced through tuyeres that are set on the lower furnace wall. Auxiliary fuels (pulverised coal, oil or natural gas) and raw materials (fine ore or fluxes) are injected into the furnace with blast air from the tuyeres. In front of the tuyeres, coke particles react with oxygen in the blast air and generate carbon monoxide. The hot reacting gas heats up the lump solids and reduces iron oxides in the upper furnace. In the middle height of the furnace, the reduced iron and slag are fused by the combustion heat and form the cohesive zone. The molten iron and slag that are generated in this region trickle down through the packed bed of coke particles and flow into the bottom of the furnace. Therefore, the flows of gas, lump solids and liquids exist at the same time in the lower part of the blast furnace.

Jan 1, 2000

By J. W. Marx, R. H. Langenheim

The authors are to he complimented for a timely presentation of useful information concerning application of heat to oil reservoirs to increase the rate and ultimate recovery of oil. The solution for heated area resulting from constant rate injection of a hot fluid, presented by the authors, and the fluid-flow analogy, solved by Carter,' are particularly interesting in that 110 restriction is placed on the direction of development of the heated area. It is not necessary that the heated area grow radially. Thus the solution could provide useful information for heat injection in any type of well pattern with any specified swept area data. However, it was assumed in the development that the heated region would remain at a constant clevatcd temperature. Vertical heat losses were computed on this basis. Physically. the assumption that the heated region will remain at a constant temperature (independent of distance from the injection point) appears to require that the heat injection medium be stcam, or other condensible gases near the boding point at injection pressure. If a hot liquid below the boiling point or a hot gas considerably above saturation temperature were used, the temperature of the heated region would decrease with distance from the injection well. Lauwerier2 has discussed this problem for a linear system. (See also Jenkins and Aronolsky; and McNiel and Nelson.') Thus, the authors' solution applies more nearly to steam injection than to hot water injection or hot, non-condensable gas injection. Assuming steam as the injection medium, it appears that steam would pass through the constant-temperature heated region and condense upon contact with the unheated sand. The tempcrature in the condensing region would probably be governed by the release of heat of vaporization required for phase equilibrium at the existing pressure distribution. Temperatures in the region would also be influenced by vaporization of hydrocarbon. Thus, it is doubtful that an expression for radial temperature distribution based on heat conduction only (such as the authors' Eq. 9) would have practical significance. As pointed out by Marx and Langenheim, the growth of the heated area under constant rate steam drive will eventually be limited economically by vertical heat loss. The possibility of continuing to move heat economically by cold water injection or by increasing the steam injection rate appears to be a very important consideration. (Movement of liquids away from the injection well should increase injectivity.) Fortunately, the solution presented by the authors may be generalized to thc case of a variable heat injection rate. The general solution is: