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By N. S. Stoloff, J. N. Mushovic

Age hardening response of a Mg-Th-Zr alloy has been studied at temperatures in the range 60° to 450°C. Transmission microscopy revealed clustering of thorium atoms at low aging temperatures, supporting a previous report of GP zone formation. Peak strengthening, which is observed at 325°C, is due to the formation of a coherent, ordered, DO19 type superlattice structure, of Hobable composition Mg3Th, as plates parallel to the matrix prism planes. These plates later reveal a Laves phase structure of composition Mg2Th. The equilibrium Mg4Th phase begins to precipitate in two different forms at an early stage, competitively with the Mg2Th plates. RECENT work on the Mg-Th system indicated that, unlike most magnesium-base alloys, complex precipitation phenomena may be occurring. The partial phase diagram of the Mg-Th system indicates that an equilibrium phase, Mg5Th, is the sole intermediate phase.' sturkey,' however, has reported, using X-ray and electron diffraction techniques, that a metastable fcc Laves phase, Mg2Th, precedes the formation of the equilibrium compound, which he identified as closer in composition to Mg4Th. Murakami et al.3 reported that the equilibrium phase precipitates preferentially on grain boundaries and dislocations in a Mg-1.7 wt pct Th alloy; Kent and Kelly4 aged a more dilute alloy, Mg-0.5 wt pct Th, for 4 days at 220°C and found similar results. In addition, they reported that a platelike phase with a structure close to that of the magnesium matrix forms perpendicular to the basal plane and is probably ordered. Research on a Mg-4 wt pct Th alloy by electrical resistance measurements and transmission electron microscopy has suggested that GP zones may form at low aging temperatures.3 However, the electron micrographs purporting to show this phenomenon were not conclusive. In view of the fragmentary evidence concerning the nature of the precipitation processes in the various Mg-Th alloys, an aging study was undertaken to clarify the characteristics of the various precipitates which form and to correlate the mechanical properties of the system with the direct precipitate-dislocation interactions. The latter results are presented elsewhere.' The purpose of this paper is, therefore, to discuss the precipitation sequence in this system. EXPERIMENTAL PROCEDURE Sheet stock (0.060 and 0.010 in. thick) of a commercial Mg-3.93 wt pct Th-0.42 wt pct Zr alloy (designated HK3lA) similar to that studied by sturkey2 was supplied through the courtesy of Dr. S. L. Couling of Dow Metal Products Co. Zirconium does not enter into any precipitation reactions,' but is present primarily as a grain refiner. The alloy was chill cast, warm rolled to 0.090 in. thick stock, and then finally reduced by a combination of hot and cold rolling. The alloy chemistry is given in Table I. This material was solution treated at 580°C for 4 hr in a dry CO2 atmosphere, and then water quenched. Material in this condition was fairly clear of precipitate particles and was fully recrystallized. Aging at temperatures less than 200°C was accomplished by immersing the alloy in a silicone oil bath; for higher temperatures, aging was done in a salt pot. Age hardening treatments were conducted at 60°, 80°, 105°, 135°, 160°, 250°, 325°, 350°, and 450°C for times ranging from 5 min to 400 hr. Hardness tests were performed on chemically polished 0.060-in.-thick blanks of solution treated material which were aged at the various temperatures for increasing lengths of time. For aging temperatures above 150°C the Rockwell Superficial 30T scale was employed, while samples hardened at temperatures below 150°C were monitored with the 45T scale. Each data point consists of at least three separate readings. Yield stresses also were measured at room temperature on both 0.060 and 0.010 in. sheet specimens aged at 325°C. The aged foils were thinned by the window method in a solution of 80 pct absolute alcohol and 20 pct concentrated perchloric acid (70 pct) maintained at 0°C. A stainless steel cathode was used and the applied voltage was 10 to 15 v. Thinned samples were rinsed in distilled water and pure methanol. After the me-thanol rinse the thin foils were quickly dried between filter paper. Foils prepared by the above method were examined in a Hitachi HU11B electron microscope operating at 100 kv. RESULTS A) Hardness. The hardness data are depicted in Figs. 1 and 2. Peak strengthening occurs at 325°C after aging about 6 min, see Fig. 1. Significant strengthening is achieved also at 350°C, but aging at 450°C produces only softening. The stepped curve at 250°C indicates that a complicated precipitation process may be occurring at that temperature. Fig. 2 suggests that at least two hardening mechanisms exist since the lowest temperature hardness peaks are displaced to the left of the peaks obtained at 135° and 105°C. A great deal of scatter is observed at long times in all cases due to magnesium surface degradation caused by the silicone oil bath. B) Identification of the Strengthening Precipitates. The structure formed atlowagingtemperatures (c10O°C) was not clearly resolvable by transmission microscopy. The only bright-field evidence for a change in structure was a mottled appearance which could be observed at extinction contours, as shown in Fig. 3(a), and the disappearance of this effect when dislocations produced under the influence of the electron beam passed through the matrix, as noted in

Jan 1, 1970

By C. B. Dudley

In a work published in 1838, De Morgan, the author of the article on " Probabilities," in the Encyclopedia Metropolltimn, says: " The method of least squares is not yet introduced iutb the affairs of common life,.....that many thi~gs which are denlonstrable only by the higher branches of mathematics are looked upon as useless." And he mentions an instance in which "a method was suggested for estimating the relative importance of boroughs, by considering their population and ~wntributions to the revenue con)-

Jan 1, 1881

By David Harrison, Brian Harrison

The Army Corps of Engineers completed the Charleroi Lock and Dam in 1932. It is located on the Monongahela river approximately 22 miles (35k) south of Pittsburgh in Charleroi, Pennsylvania. It is comprised of a 420-foot (128m) gated dam, and a 720-foot (219m) by 56-foot (17m) land side lock, which provides for a 16.6 foot (5m) vertical lift.

Jan 1, 2018

By Simon Houlding

"The objective of Part J of this paper is to identify the limitations of the traditional modelling methods and to illustrate, by example, the potential for error created by their application to complex deposits and mining situations. Part 2 describes the evolution of new, proven technology which eliminates these deficiencies and provides precise and practical alternatives. These promote the use of realistic geological and mining shapes and eliminate altogether the rectangular approximations of traditional methods.The Case for Precision ModellingIt is not the intent of this paper to promote the benefits of computer modelling per se. It is assumed that these are recognized by the mining industry in general. The concern of Part 1 is to identify, qualify and quantify (where possible) the limitations of the tractitional modelling methods. In many instances these methods continue to be applied to complex geological and mining situations for which they were never intended nor designed. The source and magnitude of the resulting errors, conflicts and inefficiencies are not always obvious, however, they can have far-reaching effects on the efficiency and profitability of mining operations.The conclusions support a rapidly growing demand by industry for practical, precise modelling technology which eliminates the deficiencies and can be applied with confidence to evaluation, design, planning and control of mine production in all situations. Part 2 describes new technology which has evolved in response to these industry pressures and has already been successfully applied to complex mining situations. This new technology can aptly be described as appropriate technology for the 1990s."

Jan 1, 1991

By J. E. Chilton

The Bureau of Mines has examined the operation of an oxygen sensor manufactured by the City University, London, England. The sensor produces a current proportional to the oxygen concentration by reacting oxygen at a nonconsumable cathode. The sensor design is unique in that the primary mode of oxygen transport to the cathode is by diffusion through a capillary, The sensor using this design has a stability of 0- to 0.02-pct reading change per day over a 4.7-month test, small temperature coefficient of 0.29-pct reading change per °C, and small pressure coefficient of 0.34-pct reading change per 1,000-ft altitude change, If this sensor were incorporated into an oxygen detector or monitor, this would be a distinct improvement in electrochemical-type oxygen analyzers and would be useful to the mining industry.

Jan 1, 1983

By F. K. McKean

Introduction The present paper may be considered as a sequel to a paper, A Process for Cleaning Molybdenite .Concentrate, which was presented by the author at the annual meeting of the Institute last year. In that paper, a description was given of the laboratory work leading up to the adoption of a new process for treating complex molybdenite ores of the Molybdenite Corporation of Canada. A bare outline of mill performance with the new flow-sheet was included. With this writing, the purpose is to describe the highly interesting work of translating laboratory experience into mill practice, to show what changes were required in design to put the scheme on an operational basis, and to point out the gratifying improvements in mill products which resulted from the new procedure. The process has been placed in operation at the La Corne mine of the Molybdenite Corporation of Canada. This mine was operated during the war by Wartime Metals Corporation, and, earlier, by the Molybdenite Reduction Company, which installed a small plant. The property is situated on the highway from Amos to Val d'Or, Quebec. The claims held by the Company are at the boundary between La Corne and Vassan townships.

Jan 1, 1947

By Shadia J. Ikhmayies

In this work the equilibrium temperature-composition phase diagrams of the Si-O2 system were calculated using Thermo-Calc software in the temperature range 500–3000 K. Constituents of stable phases were obtained, and the amounts of certain phases where investigated with the variations in the composition of oxygen and temperature. It is found that quartz with silicon represent a stable phase in the temperature range 500–1150 K, while tridymite with silicon represent a stable phase in the temperature range 1150–1700 K. A liquid phase is found besides tridymite in the temperature range 1700–1750 K, and a stable phase of cristobalite with liquid appears in the temperature range 1750–2000. The maximum amounts of quartz, tridymite, and cristobalite are found at oxygen mole percent of 67.7%.

Mar 1, 2017

One of the most important parameters in rock/resin/bolt load transfer mechanism is the surface property of the bolt. Although there are various bolt surface configurations available in the market, very little work is reported on the bolt/resin interface failure mechanism. This paper examines the behaviour of bolt surface roughness under constant normal stiffness conditions which is considered as being a realistic way of evaluating bolt surface roughness. A series of shear tests have been conducted on the flattened bolt surface to study the shear behaviour of bolt/resin interface. Based on the experimental results, a mathematical model has been developed to predict the shear resistance of the bolt/resin interface at various normal stress levels for the bolt types used in the study.

Jan 1, 1999

By Ning Yu

There are about 1.341 trillion tons (t) of proven coal reserves in China, of which 279.58 billion t are available for mine well construction basis. Thick coal seams are 44% of the reserves. The production of thick coal seams exploitation is over 45% of the total coal production. Full-seam mining and fully-mechanized mining for large mining height is the technology development direction of thick and extra thick seam mining. It is also the important way to achieve efficient and intensive mining with the characteristics of high production, high mechanization, high efficiency and low energy consumption, etc. Complete set of technology and equipment of fully-mechanized top caving for large mining height of full-seam (7m) mining and extra thick seam ( 14-20m) has been gradually mature and for demonstration application by the joint research of government, enterprises, universities, scientific research organizations and users. It has solved some technical problems of coal face for large mining height (over 7m) such as the coal wall spalling control, stability of support, wall rock coupling, cooperation work of mining and caving, full roadway support for super large section, end support, equipment matching of coal shearers, hydraulic support and scraper conveyor. It has developed key equipments including powerful hydraulic support of fully-mechanized mining and fully-mechanized top caving for large mining height, electrically-driven coal shearer with high speed and reliability, scraper and belt conveyer with big capacity, soft-start and high reliability, automatic control system of coal face with the core of electric-hydraulic control, bolting drill boom large section coal roadway shearer, heavy auxiliary transport equipment. The operation rates of fully-mechanized top caving equipment for full-seam and large mining height are 94% and 92.1%, and recovery ratios are 93.6% and 88.9% respectively. The annual raw coal production of single work face is over 10 Mt. The automation and intelligentization level have been clearly improved. The exploitation of thick and extra thick coal seam that is safe and efficient has been achieved in China.

Aug 1, 2013

By Günther M. Volkmann

"INTRODUCTION The construction of the BAB 44 motorway between Kassel and Herleshausen (both Germany) is an important part of the trans-European road network. After its completion, the A 44 will permit an efficient connection of the Benelux States in the West and Poland in the East. In the section between Eschenstruth and Hessisch Lichtenau the Hirschhagen Tunnel is constructed with a length of 4.1km. Most sections of the tunnel are situated in weak ground conditions. Hence a combination of face bolts with spiles (short forepoling) or pipe umbrellas (long forepoling) additionally support the tunnel heading on a regular basis This article will focus on the application of a newly developed method to connect the pipe umbrella support, which is mostly installed by conventional drilling machines nowadays. The installation method limits the outer diameter to a maximum of 168mm and a pipe wall thickness of 12.5mm because workers must be able to handle pipes and its drill steel. Typically these pipes are connected with threads that create a weak link in the support system so during the last decade alternative connection systems were developed to overcome this disadvantage. One of these alternative coupling systems is the so called Squeezed Connection, which will be explained in this article followed by a discussion of its advantages and disadvantages regarding technical specifications, construction time, and safety issues. THE HIRSCHHAGEN HIGHWAY TUNNEL The German highway A 44 directs from Aachen through the Ruhrgebiet to Kassel (all Germany) and it is extended to Herleshausen (Germany). The new section connects the A 7 to the A 4 after completion. This upgrades the east-west highway connection starting at the Benelux Union and heading to Poland so it is an important part of the trans-European road network. The newly constructed section has a total length of approximately 63 km and comprises 13 tunnels. All tunnels are constructed as double tube tunnels with 2 lanes and emergency sidewalks on both sides and 14 emergency cross passages. The Tunnel Hirschhagen starts in the north of Eschenstruth and ends near Hessisch Lichtenau (Figure 1). The length of the northern tube is 4,147 m and that one of the southern tube is 4,204 m. So it is the longest tunnel of the A 44 and the second longest highway tunnel in Germany when it is put into operation. On its alignment it crosses underground the Losse valley with the state road 7, the streetcar Kassel-Hessisch Lichtenau and the Losse stream. The cover above crown varies from 10 m to 95m and it is the lowest when crossing the Losse stream."

Jan 1, 2016

By P. Jordan

The practice of ilmenite smelting in electric arc furnaces has been researched and published over the last few decades. An issue that has not been addressed is the understanding of the properties of ilmenite smelting reductants, and linking these properties to the subsequent smelting behaviour in the furnace. The reduction mechanism of ilmenite smelting is not fully understood, but it is believed that the Boudouard reaction plays a role. This paper investigates the behaviour of a number of reductants when reacted with CO2 at different temperatures. Keywords Boudouard reaction, carbon reactivity, reductants, ilmenite smelting.

Jan 1, 2011

By Wilfred Walker

With the advent of the New Global Tectonics a coherent pattern of geology is emerging. To the economic geologist this is of vital concern because the type of mineralization in particular environments is predictable. Developments in geological reasoning now take their place beside developments in geochemistry and geophysics. Much is known of the worldwide geography of the Alpine orogenic period because it is now ending its 200 million years of existence, starting with the Jurassic, and we can see the mid-ocean rises and the down flow zones, and between them the stable oceanic and continental platforms. The concepts of mantle cells, the spreading sea floor, and continental drift have gained general acceptance. The oceanographers have demonstrated the uprises like that in the mid-Atlantic. In this paper it is suggested that down flows in the oceans are marked by island arcs, like the West Indies; and down flows in the continents are marked by orogens like the American Cordillera. The number and position of mantle cells is controversial: a total of about 16 cells is suggested in this paper. Certain cells expand, and as they carry continents with them give rise to concepts of plate tectonics. Specific types of mineral deposits are associated with the uprises, oceanic and continental platforms, and down flows. The uprises are accompanied by the currently described Red Sea and Salton Sea deposits, the oceanic parts of the platform have the nodular deposits, and the continental platforms have the post-tectonic deposits. However, most economic metal deposits are associated with the down flow zones in which the stage of geosynclinal development controls the type of deposit: (1) In the initial development stage the simatic upper mantle may be tapped and give rise to the volcanogenic massive base metal sulfide deposits and to the ophiolite suite which characteristically carries nickel, chrome, and cupreous pyrite. (2) In the early geosynclinal stage sialic crust is driven down into the simatic magma of the upper mantle and basic to acidic differentiates give rise to stocks accompanied by skarn and hydrothermal deposits. (3) The intermediate stage of geosynclinal development gives rise to tin-tungsten, lithium, and beryllium deposits as the magma chamber rises above the level of the upper mantle and there is no simatic component. (4) The late stage is one of regenerated deposits. The porphyry deposits are not restricted to stages but only by the time of generation of acid magma. As the geosynclinal system dies, the mantle is again the source of magma, giving rise to gabbro and diabase dykes and sills: in this last, post-tectonic, continental platform environment are found the Mississippi Valley type lead-zinc deposits, the Blind River and Witwatersrand type of sedimentary uranium and gold deposits, and also Sudbury's nickel. The key relationship of major ore deposits generated by downflows is depicted herein on a framework of uprises, platforms, and downflows in the Alpine orogenic period. There is evidence for nine orogenic periods, of which the Alpine period is the latest, having taken place from 3500 million years ago to the present. Each period was characterized by its own worldwide mantle cell system and associated uprises, platforms, and down flows. The cycle of geosynclinal development, including corresponding cycles of mineralization, can be precisely defined in relation to each of these orogenic periods. The development of the Alpine orogenic period therefore can be used as a guide to the study of the earlier orogenic periods which comprise well known periods: Kenoran, Hudsonian, Grenville, and Paleozoic; and less well known: Konkian, Aulian, Belomorian, and Elsonian [(Table 1)]. Each name is used for the period as a whole, and not for the main orogenic event.

Jan 1, 1973

Mt. Whaleback is in the Pilbara region of Western Australia approximately 1200 kilometers north of Perth, the State capital. In this deposit the Mt. Newman Joint Venturers are mining ore reserves totalling 1500 million tonnes of high grade hematite averaging 64.0% Fe. In addition to Mt. Whaleback, 38 ore bodies have so far been identified outside Mt. Whaleback on the Company's remaining 75,000 hectares of lease area. These ore bodies contain major tonnages of iron ore. Extraction at present is planned at a rate of 37 million tonnes per annum at an ore-to-waste ratio of approximately 1 to 1.4. The ore is railed north to Port Hedland on the Indian Ocean where the different products are screened, crushed and blended prior to shipping. The purpose of this paper is to acquaint the reader with the facilities installed in the Mt. Newman operation to form a background to the sampling techniques employed, describe the precisions which were achieved in experiments conducted February through June, 1976 and also to assess the degree of blending which takes place during the various processes and to put a quantitative measure to the degree of blending. There have been many excellent papers written on the more theoretical aspects

Jan 1, 1976

By Burgess JM

Research on gas distribution in the iron- making blast furnace has been conducted in three separate areas. Firstly, experimental work has been conducted to determine the important parameters which dictate the pressure losses in homogeneous and heterogen- eous packed beds. Secondly, a theoretical analysis of gas flow through the furnace softening-melting zone has been undertaken to determine the effect of the shape of the zone on the distribution of gas flow towards the furnace walls. Thirdly, a theoretical programme has been undertaken to develop methods for the prediction of furnace soften- ing-melting zone shape from furnace tempera- ture and gas composition measurements.

Jan 1, 1980

By Ulrich Leiste, Andrew Wardlaw, William Fourney

This paper describes the loading on a plate suspended directly over an explosive charge submerged in water. This problem is of interest because it yields results similar to those obtained in the detonation of an explosive buried in saturated soil and thus it is associated with landmines. Recent experiments [1] indicate that plate loading from a submerged charge is similar to that for a buried one, with respect to impulse and pressure. Compared to the buried explosive problem, the submerged explosive case is attractive from a computational point of view; it replaces sand, which is diffi cult to simulate, with water, whose properties are well known. Studying this problem allows modeling uncertainties to be separated from sand simulation issues.

Jan 1, 2008

By Eckersley J, Boyd G

A brief review is presented of the mechanisms and causes of spoil pile failures which have occurred at the Goonyella Mine. In particular, the results of a recent geo- technical investigation of the spoil dumps in the Cleanskin pit are briefly presented. Spoil pile hydrology is discussed in relation to the use of effective stress concepts in the analysis of spoil pile stability. Experience in relation to stabilisation of dragline dumps is discussed as well as the likelihood of current techniques being success- ful in the prevention of gross failures if prestrip material is placed in existing spoil piles. Parameters exerting a major control on dump stability are outlined.

Jan 1, 1981

By B. C. Blakey

The economic feasibility of the sulphuric acid pressure leaching route for the extraction of nickel and cobalt values from limonitic ores is highly dependent upon the behavior of aqueous aluminium. This is primarily due to its precipitation as hydronium alunite ((H30)A13(S04)2(OH)6), which is one of the major scale-forming compounds found in autoclaves used for pressure leaching. As a result of renewed interest in the pressure leaching process, an investigation of the aqueous-solid eqilibria in the aluminium-sulphate-water system under acidic (< pH l), high temperature (230 to 270°C) conditions has been conducted. Pure hydronium alunite was synthesized in an autoclave by leaching boehmite (A100H) at elevated temperatures in sulphuric acid solutions initially 0.25 to 0.75 m H2S04 in concentration. Spontaneous, in situ precipitation of hydronium alunite followed. A high temperature solution speciation model was used for the analysis of the resulting solubility data in order to calculate equilibrium constants for the precipitation reaction.

Jan 1, 1994

By B. M. Larsen, T. E. Brower

In an earlier paper1 we discussed a simple, rapid method of taking samples of liquid steel and analyzing them for oxygen, which, though possibly not absolutely accurate (as is likewise true of all other methods), certainly yields results that are satisfactorily consistent. Accordingly, samples from hundreds of heats ill different shops were analyzed for oxygen, with results sufficient in number to be handled statistically and permit estimation of some general trends. Measurements were made in acid as well as in basic open hearths, throughout the refining period, to learn how stirring, blocking, adding ore or lime or sand, affects the oxygen content of the bath; we also followed the changes brought about by tapping, teeming, and deoxidizing. Some of these results, discussed in an earlier paper,2 bring out the dominant role of the carbon-oxygen reaction in regulating degree of oxidation both of metal and of slag, also the marked variability of concentration of dissolved oxygen [0] in excess of that which would be in equilibrium with carbon and with carbon monoxide at a partial pressure of one atmosphere. As a logical beginning on this complex problem, we take up in the present paper the variability of this excess oxygen, A[O], when other factors are as constant as they ever are in open-hearth operation; namely, toward the end of the refining period, when the bath may be regarded as in the comparatively steady state it approaches in absence of disturbing factors. This condition was chosen because by that time the significant reactions, except carbon oxidation, between slag and metal have come to substantial equilibrium; this facilitates interpretation of the complex situation and thus perinits more definite conclusions to be drawn. This excess concentration of oxygen, A[O], in the metal is needed, of course, to make the steelmaking process go at a reasonable rate; alternatively it may be regarded as a measure of the virtual pressure increment above one atmosphere, or of the degree of supersaturation, of carbon monoxide in the metal. According to our measurements, the excess concentration A[0] in liquid steel varies from about 0.009 to 0,035 per cent oxygen by weight. It is quite sensitive to change of conditions, being altered temporarily by operations such as stirring with green poles, additions of ore, lime, or sand; but as the disturbance works itself out, it resumes a level within the intermediate range characteristic of the steady state. The conditions most common in average furnace practice are covered by the following: i[O] Usual Per Cent Oxygen by Conditions Weight 1. Vigorous lime boil........... o.oog-0.01s 2. Steady state................ o.or;-0.025 3. Working of ore.............. o.023-0.035 Thus when the bath can be regarded as in a reasonably steady state—that is, when it is boiling normally, is at proper temperature with a well-shaped slag, and has been free from disturbing effects during the preceding half hour—A[0] returns from

Jan 1, 1948

By B. M. Larsen, T. E. Brower

In an earlier paper1 we discussed a simple, rapid method of taking samples of liquid steel and analyzing them for oxygen, which, though possibly not absolutely accurate (as is likewise true of all other methods), certainly yields results that are satisfactorily consistent. Accordingly, samples from hundreds of heats ill different shops were analyzed for oxygen, with results sufficient in number to be handled statistically and permit estimation of some general trends. Measurements were made in acid as well as in basic open hearths, throughout the refining period, to learn how stirring, blocking, adding ore or lime or sand, affects the oxygen content of the bath; we also followed the changes brought about by tapping, teeming, and deoxidizing. Some of these results, discussed in an earlier paper,2 bring out the dominant role of the carbon-oxygen reaction in regulating degree of oxidation both of metal and of slag, also the marked variability of concentration of dissolved oxygen [0] in excess of that which would be in equilibrium with carbon and with carbon monoxide at a partial pressure of one atmosphere. As a logical beginning on this complex problem, we take up in the present paper the variability of this excess oxygen, A[O], when other factors are as constant as they ever are in open-hearth operation; namely, toward the end of the refining period, when the bath may be regarded as in the comparatively steady state it approaches in absence of disturbing factors. This condition was chosen because by that time the significant reactions, except carbon oxidation, between slag and metal have come to substantial equilibrium; this facilitates interpretation of the complex situation and thus perinits more definite conclusions to be drawn. This excess concentration of oxygen, A[O], in the metal is needed, of course, to make the steelmaking process go at a reasonable rate; alternatively it may be regarded as a measure of the virtual pressure increment above one atmosphere, or of the degree of supersaturation, of carbon monoxide in the metal. According to our measurements, the excess concentration A[0] in liquid steel varies from about 0.009 to 0,035 per cent oxygen by weight. It is quite sensitive to change of conditions, being altered temporarily by operations such as stirring with green poles, additions of ore, lime, or sand; but as the disturbance works itself out, it resumes a level within the intermediate range characteristic of the steady state. The conditions most common in average furnace practice are covered by the following: i[O] Usual Per Cent Oxygen by Conditions Weight 1. Vigorous lime boil........... o.oog-0.01s 2. Steady state................ o.or;-0.025 3. Working of ore.............. o.023-0.035 Thus when the bath can be regarded as in a reasonably steady state—that is, when it is boiling normally, is at proper temperature with a well-shaped slag, and has been free from disturbing effects during the preceding half hour—A[0] returns from

Jan 1, 1948

By J. M. Mutmansky

Introduction Since the Hardy Cross numerical algorithm was applied to the solution of mine ventilation networks, numerous developments have taken place in ventilation network analysis procedures. The Newton-Raphson method, the linear theory method and the second-order approximation method are three of the additional approaches that have been applied. The efficiency of a ventilation network analysis procedure depends not only on the method of solving the system of equations derived from ventilation networks but also on the method of deriving the equations through selection of the meshes. This paper investigates the impacts of three mesh selection methods on the efficiencies of four ventilation network procedures. The minimum-resistance spanning tree method is the most popular procedure for selecting meshes. The shortest-path method was suggested by Epp and Fowler (1970) for improvement of the Newton-Raphson method. The minimum-resistance-path method is suggested here as the third method of selecting meshes. The effects of these three methods on the Hardy Cross method, the Newton-Raphson method, the linear theory method and the second-order approximation method are analyzed in this paper. These network analysis methods have been summarized in the paper by Kim and Mutmansky (1991). Mesh selection methods A procedure for mine ventilation network solution based on mesh equations typically consists of two steps: • the mesh selection step and • the network solution step. The mesh selection step establishes a set of independent equations to solve the network. The resulting equations are nonlinear. One method of solving nonlinear equations is to linearize the equations and iteratively solve these linear equations. The four analysis methods previously discussed in this paper use this approach. The linear equations required for solution can be written in matrix form as: P•dQ = dF (1) where P is the pseudo-resistance matrix, Q is the quantity matrix, and F is the Jacobian matrix (Kim and Mutmansky, 1991). The efficiency of the solution method depends on the characteristics of the P matrix, which in turn depend on the method of selecting meshes. To understand the impacts of the mesh selection methods on the efficiency of the ventilation network analysis procedures, the characteristics of the P matrix must be understood first. The diagonal elements of the P matrix, m in number, are the sums of the pseudo-resistances of the branches contained in the m meshes necessary for solution. The off-diagonal elements are the sums of the pseudo-resistances of the branches shared by two meshes. For example, P12 (first row, second column element of the P matrix) is the sum of the pseudo-resistances of the branches common to mesh 1 and mesh 2. When solving the system of equations expressed in Eq. (1), three of the iterative procedures (the Newton-Raphson, the linear theory and the second-order approximation methods) use the direct factorization method (Burden and Faires, 1985) on the P matrix. When the direct factorization method is used, the computational efficiency is enhanced by larger diagonal elements and a sparser P matrix. Generally, the sparsity of the P matrix is more important than the size of the diagonal elements. There is no known mathematical method of predicting the efficiency of these procedures, but heuristic methods can be used to study the efficiency. The Hardy Cross algorithm applies the Gauss-Seidel method of splitting the P matrix and applies the Newton-Raphson procedure. The efficiency of the Hardy Cross method depends on the spectral radius of the matrix[[D-L]-1U], where D is the diagonal, L is the lower triangle and U is the upper triangle of the P matrix for the Newton-Raphson method (Ortega, 1972). The smaller the value of the spectral radius, the faster the convergence. As with the other three methods, larger diagonal elements and a sparser matrix aid in faster convergence. With the Hardy Cross method, however, the size of the diagonal elements is more important than the sparsity of the matrix. Remembering that each of the diagonal elements of the P matrix is the sum of the pseudo-resistances of the branches in a mesh and that each off-diagonal element is the sum of the pseudo-resistances of the branches shared by two different meshes, the following strategies can be used: • Avoid having branches with larger resistance values shared by multiple meshes. This increases the size of the diagonal elements and reduces the chance of off-diagonal elements being large.

Jan 1, 1993