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By D. L. Churcher, R. J. Perry

"In recent years much work has been don e to examine alternate underground backfill support systems with the objectives of improving ground support and reducing mining costs. This report deals with the work conducted at Placer Dome Inc.’s Dome Mine to develop a high density backfill system, taking advantage of the unique properties of this fill material, to address a backlog of large open stopes to sustain stable minewide ground conditions for future generations of Dome miners.IntroductionDome Mine began its existence in 1909 with the discovery of visible gold on a dome shaped outcrop located west of Porcupine Lake in northern Ontario. The orebody beneath this outcrop has supported one of Canada’s premier gold mining operations for 80 years. Production during this time of over 46 000 000 tons of ore has resulted in the recovery of II 500 000 ounces of gold and 2 000 000 ounces of silver. Mining continues today at a production rate of 3500 tons per day, with ore coming from both underground and open pit operations.During the life of the mine, different underground mining methods have been used to extract the ore from a complex deposit consisting of single and multiple vein structures.Cut-and-fill mining was introduced in the 1930s using sand fill and later hydraulic fill for support and to provide a working platform. A total of 1 800 000 tons of sand fill and 7 300 000 tons of hydraulic fill have been placed underground in cut-and-fill stopes. Until the late 1960sshrinkage mining was used extensively, particularly in narrow, steeply dipping zones. Bulk mining with small diameter longholes was introduced about this time, to take advantage of low production costs. Longhole blasting has often been used to recover low grade ore from the walls or sills of old shrink stopes, resulting in large open stopes. Backfilling of these open holes has been restricted to smaller stopes and associated with local ground conditions.In the late 1970s it was recognized that the number of large open holes which were being generated presented serious regional and minewide stability problems for future operations. With higher gold prices, economic ore reserves were being tied up in areas adjacent to multi-level open stope complexes. To stabilize these stopes and allow access, backfilling would be required."

Jan 1, 1990

By N. Tassé

Les substrats organiques sont à la base des biofiltres utilisant la réduction des sulfates pour générer de l&apos;alcalinité et diminuer la concentration des métaux dans des effluents contaminés. Afin de tester l&apos;efficacité de résidus forestiers utilisés dans de tels contextes, cinq types d&apos;écorce de nature et d&apos;âge variables ont été placés dans des contenants hermétiques et mis en présence d&apos;une solution synthétique de drainage minier acide. Le pH, l&apos;alcalinité et les concentrations de Fe2+ et SO4 2- ont été mesurés à intervalles réguliers pendant 70 jours. L&apos;importance d&apos;un éventuel neutralisant minéral et du type de souches de bactéries sulfato-réductrices pour l&apos;initiation et l&apos;évolution des réactions d&apos;oxydo-réduction ont été évalués en utilisant de la dolomite ainsi que des inocula de sédiments portuaires réducteurs et de boues d&apos;usine d&apos;épuration. Une augmentation de pH et des diminutions de Fe2+ et SO4 2- ont été notées dans tous les réacteurs. En l&apos;absence de dolomite, le pH augmentait de 1.6 à 5-6, Fe2+ diminuait de 400 à moins de 5-100 mg/L, et SO4 2- diminuait de 2500 à 750-1250 mg/L. Les échantillons inoculés avec des sédiments s&apos;avéraient légèrement plus performants que ceux avec boues. En présence de dolomite, le pH atteignait 6.5-7.0, et Fe2+ et SO4 2- tombaient à <5 et 20-40 mg/L, respectivement. Le degré de réactivité des résidus forestiers n&apos;était pas une simple fonction inverse de leur âge. Les échantillons ayant le mieux réagi, bien que parmi les plus vieux testés (années 1980), étaient ceux contenant une proportion significative d&apos;écorces de feuillus et peu de bran de scie. Les échantillons avec des proportions élevées d&apos;écorce de conifères ou de bran de scie étaient associés à des taux de réduction moindre. Nonobstant l&apos;amélioration rapide des conditions obtenue avec la dolomite, grâce à une neutralisation initiale plus prompte, il s&apos;avère que le type de résidus forestiers éventuellement utilisé dans une barrière réactive est de première importance pour l&apos;efficacité des mécanismes de réduction. Un système basé sur l&apos;utilisation de résidus forestiers devrait utiliser des écorces (plutôt que du bois) provenant de feuillus (plutôt que de conifères).

Nov 1, 2002

By T. Patching

"MINING operations at the Star Key Mine provided an example of a small-scale prairie-type coal mine that employed several interesting procedures and achieved good productivity with low capital expenditures. The mine was located about 11 miles north of the city of Edmonton, on the north side of the Sturgeon River valley. It opened in 1945 and operated until 1979. Output in the winters reached about 500 tons a day in the late 1940s, but in the spring and summer periods activity was usually limited to only servicing and development work. In the later years of the mine's life sales fell to less than 100 tons per day. Most of its output was bought for domestic use in furnaces and stoves so production of large sizes was desired. A modest market for stoker coal did exist for a time. Screenings (-5 / 8 in.) were sold to the city's power plant until it converted to natural gas and were also used for thawing frozen ground for work on pipelines. These markets were comparatively small and the small sizes did not command as high a price as did the larger sizes. However the extension of natural gas services to rural markets cut into the domestic heating market and finally led to closure of the mine. The coal was strong when freshly mined, but because of its high inherent moisture content, about 25%, it did not store well on surface but tended to disintegrate. It was of subbituminous Crank with a heating value of about 8000 Btu per pound and burned with a clean flame. The seam mined was in the Edmonton Formation, of Upper Cretaceous age, at a depth of 60 to 80 ft below the surface. The seam in the mine area was about 11 feet in thickness but thinned gradually to the north and south and split to the west (1). It was approximately horizontal but gentle rolls in the floor of several feet in height necessitated brushing in places to produce suitable haulage grades. The floor material was of bone and clay, overlying a thin layer of coal. Above the seam there were only a few feet of mudstones and weak sandy shales while the remainder of the overburden was clay and unconsolidated glacial till and surface soil. Because of the soft floor and weak roof material the miners usually left about a foot of coal in the floor to provide a firm working surface and about a foot of coal above the rooms and two feet of coal above the entries to provide a competent roof."

Jan 1, 1985

By A. Mcdonald

"An X-Met Analyzer was purchased from Outokumpu in late 1983for use in the Hudson Bay Mining and Smelting smelter. Its first use was in the fuming plant to give zinc assays of each charge of slag tapped from the fuming furnaces. This quickly told the operators exactly when each charge had reached its economic tap-out point, and gave supervision a fool-proof method of identifying good operation. These and other factors led to major improvements in coal utilization in the fumers and to major increases in zinc oxide production. A second unit was later purchased for the reverberatory furnace to give silica and iron assays of the slag, and these were used to make adjustments in the feed composition to maintain the desired SiO2:Fe ratio in the slag. Since purchasing the units for the furnace, the oil consumption and copper content of the slag have dropped significantly. IntroductionSmelters have lagged far behind concentrators in process control by mean s of rapid product analysis. The on-stream X-ray analyzer was developed about seventeen years ago, and soon concentrators around the world were getting assays of the incoming ore, .concentrates and tailings every fifteen minutes, and using these to control reagent additions and other process variables. Almost always, the concentrate grade and recovery improved.In smelters, product streams are solids or molten materials, not the more easily handled slurries, and until seven years ago no inexpensive equipment was available to provide rapid analysis of this type of material. In approximately 1980, several companies developed instruments based on irradiating solid samples with low-intensity gamma rays from radio-isotope sources, and measuring the secondary X-rays emitted from different elements in the sample to provide an analysis of the elements desired.The smelter staff had a close look at what was needed and listed the following points as being critical:1. ability to provide Zn assays of a sample of slag within 15 minutes of taking it, in order to achieve optimum fuming times (zinc fuming , being a batch process, had the greatest potential benefit from rapid slag analysis);2. ability to give Cu and Fe assays on the slag, and on other smelter products, such as matte and converter slag;3. ability to give Si02 assays since the SiO2 content of the slag has a strong effect on fuming rate; and4. ability to stand up to an industrial atmosphere such as exists in the fuming plant."

Jan 1, 1987

By R. J. Brailey

"A USER'S VIEW OF CONVEYOR WEIGH SCALESThe Sudbury Operations of Falconbridge Nickel Mines Limited includes seven mines, three concentrators and a smelter. The flow of ore, concentrates, fuel and fluxes between and within these plants requires measurement for accounting and control. The design, installation and maintenance .of weighing systems falls within the responsibility of the Instrumentation Department of Falconbridge Nickel Mines thus al lowing a common approach to conveyor weighing problems and the benefit of a common spares supply. This paper gives a brief overview of the recent experience with conveyor scales within the Sudbury Operations and discusses the problem areas.GeneralThe best way to establish the total amount of material going to or from a process is with a bucket and a stop watch. Unfortunately the flowrates involved in mining plants make the buckets very large, but wherever it is feasible static weighing is the preferred method of determining total quantity. This applies particularly to batch systems, where the material can be brought to rest long enough to allow a very accurate weight determination. Any form of weighing in motion is susceptible to variations in the forces of the transporting system. A belt scale is affected by its position on the belt, idler alignment, support stiffness, variations in belt tension, material spills and build-up, and a host of other factors all of which require careful consideration in any installation.As with instrumentation applied to any system the plant should be designed to ensure that the best results can be obtained from the equipment. This means getting the scale supplier together with the conveyor supplier as early as possible in the designing of a new plant. Any corners cut in scale installation will be paid for later in poor results and/or increased maintenance."

Jan 1, 1975

By Jinsuo Zhang

Investment in coal resource development is affected by a variety of uncertain factors. Investors can make a flexible, strategic decision to achieve the value of risk implicated in those uncertain factors. Therefore, based on real-option theory, we identified key uncertain factors that affect a coal resource investment project, and revealed the formation mechanism of option value in coal resource developing investment project. Then, a multi-factor decision making model was established for a coal resource development investment project with random changes of coal price, interest rate, convenience yield and production cost. Finally, we tested the model and analyzed relevant parameters by applying living data. Our results indicate this model reflects the value of risk implicated in uncertain factors for coal resource development investment, and is able to determine a critical point of decision making change when coal price and production cost varym respectively. By means of parameters analysis, the convenience yield has a positive effect on the project value. The interest rate has a negative effect.

Aug 1, 2013

By L. A. Nazarova, M. Vandamme, L. A. Nazarov, R. I. Rodin

"The paper describes a new method of interpreting the “canister test” data for the quantitative estimation of gas-kinetic parameters of coal bed based on the developed model of gas emission from coal sample placed in a sealed container. The model accounts for grain-size composition of the sample, initial gas content S, as well as coefficients of diffusion D and mass transfer ?. The inverse coefficient problem is formulated to find S, D and ??from the data of pressure measurements in the sealed container. It is shown that the inverse problem is uniquely solvable if the pressure is dropped during the experiment. The method has been tested using the data from an underground coal mine in the Kuznetsk Basin.Based on the poroelastic model of a coal bed and Khristianovich’s concept about origination and evolution of the filtration zone F in the neighborhood of a degassing borehole the authors considered the corresponding direct problem on rock mass geomechanical state. It was offered interpretation method for data on pressure measurements in a plugged degassing borehole allows evaluation of the diffusion coefficient, the horizontal component of natural stress field and parameters of F. The related inverse problem of the mixed type is formulated, and the cost function is constructed. The analysis using synthetic input data has shown that the cost function has a number of local minimums arranged on the same straight line, one of the minimums being the inverse problem solution. INTRODUCTIONPre-mine degassing is an integral part of coal mining. It allows mitigation of induced accidents in mines (coal and gas outbursts, rock bursts) (Guide, 1990; Malyshev & Airuni, 1999; Seidle, 2011) and also furnishes an alternative and ecology-friendly energy source—methane (Rice, 1997; Nambo, 2001). Choosing an optimized pattern of degassing boreholes, as well as estimating degassing time and amount of gas recovered requires data on gas-kinetics indices of coal beds out of which the key parameter is a gas content S. According to the latest guidelines for coal mines in Russia (Ruban et al, 2012), mining is allowed if S in a coal bed section is under 7 kg/m3."

Jan 1, 2015

By L. A. Anestiev

A method based on use of calorimetric data for the determination of solidification kinetic parameters is proposed. The method incorporates recent theories of nucleation and growth and allows modeling heat fluxes observed in calorimetric experiment. Statistically optimal estimations of the kinetic parameters, which include the activation&apos;s energies of nucleation and growth, are derived from experimental data by means of nonlinear regression analysis. The method is applicable to pure substances and alloys. The evaluation of the kinetic parameters characterizing solidification of pure Al is used for clarifying and exemplifying the method.

Jan 1, 2004

By I. Stefanou, J. Sulem

"In the last thirty years, the study of earthquake mechanisms has emphasized the major role of rock friction. Earthquakes appear to be the result of a frictional instability and occur by sudden slippage along a pre-existing fault or a plate interface. Multiphysics couplings play a major role in earthquake nucleation and seismic slip. The effect of shear heating and thermal pressurization may be of prime importance in the control of the stability of shear deformation inside the slipping zone. Other mechanisms in relation with thermal decomposition of minerals affect the pore pressure and the temperature evolution of the system, and can play a significant role in the extreme strain localization observed in field. The actual width of the localized zone is a key parameter for understanding fault weakening mechanisms. On the basis of field observations, laboratory experiments and recent advanced modeling, these phenomena are analyzed and discussed in order to bring some new insights in the understanding of earthquakes nucleation.INTRODUCTIONIn the last thirty years, the study of earthquake mechanisms has emphasized the major role of rock friction. Earthquakes appear to be the result of a frictional instability and occur by sudden slippage along a pre-existing fault or a plate interface (Scholz, 1998; Sykes, 1978). The conceptual model of spring slider system is commonly used to represent the interaction between an elastic crustal block and a fault zone. Stick-slip instability is possible if the softening rate of the shear resistance of the fault zone is high enough as compared to the stiffness of the crustal block. Therefore, weakening mechanisms that can explain how the frictional resistance of a fault decreases with slip and/or slip rate is of prime importance to understand how an earthquake nucleates. In recent years, several drilling programs in active faults (e.g. the Nojima fault in Japan, Boullier, 2011; the Aigion Fault in Greece, Cornet et al. 2004, the Chelungpu fault in Taiwan, Ma et al. 2006, and the San Andreas fault in the U.S.A. Ellsworth et al. 2000) as well as high velocity friction experiments (e.g. Tanikawa et al 2012a; Tanikawa et al. 2012b) have highlighted the physico-chemical processes involved in the nucleation of seismic slip (see for the example the review paper of Niemeijer et al. 2012)."

Jan 1, 2015

By W. G. Schultz

"Sylvite's potash mine, which produces 8,000 tons of ore per day, probably ranks as one of the most highly mechanized and automated mining operations in the world. Employing, on a normal 10-hour production shift, one supervisor and a crew of seven operators, Sylvite is able to mine at an average rate in excess of 600 tons per hour. The ore is produced by two Marietta miners weighing 258 tons, the largest and heaviest pieces of equipment ever taken underground. The ore produced by these two Marietta miners is conveyed to the shaft area, cycled through a 15,000-ton storage system and hoisted to surface completely automatically. The operation of all equipment in the mine can be monitored and controlled from a central control panel located underground. Because Sylvite's mine is a new operation with equipment of a new design, the full potential of the operation has not yet been realized. The ultimate capability is clearly evident from the success Sylvite has had over the past year as the average mining capability has risen from 100 tons per hour to 600 tons per hour."

Jan 1, 1973

By R. M. T. Raja Ismail

Shipping and stevedoring industry is going to witness a massive increase in the amount of containers to be handled while land constraints become more critical. Offshore transfer operations hence offer a preferable solution to deal with the surge in cargos rather than to expand the port outwards. Recently, there has been increasing research interests on offshore crane automation. Suspended cargos in a ship-mounted crane system are caused to swing due to the vibratory motion of the ship induced by ocean waves, which can lead to collision between cargos and deck. Therefore, it is vital for offshore crane systems to satisfy rigorous requirements in terms of safety and efficiency. This paper presents the modelling and control development for offshore boom crane systems. A second-order sliding mode control law is proposed for trajectory tracking and sway suppression control, making use of its capability of actuator chattering alleviation while achieving high tracking performance and preserving strong robustness. The asymptotic stability of the closed-loop system is guaranteed in the Lyapunov sense. Simulation results indicate that the proposed controller can significantly reduce the effect of disturbances coming from gusty waves and other dynamic loadings.

Aug 1, 2013

By T. H. Adair

"IntroductionCONTINUOUS casting of ferrous and non-ferrous metals is not a new innovation. Patents describing machines for continuous casting are on file as far back as the year 1842. In the middle of the last century, Sir Henry Bessemer conceived and built a continuous casting• machine for the production of mild steel sheet.The production of billets and slabs of both non-ferrous and ferrous metals is being carried out by the continuous method on a fairly large scale on this continent and abroad. At present, the volume of production of •copper and aluminum and their alloys in billet and slab form is much greater than the continuous casting of steel products. The new installation of a continuous casting unit at Atlas Steels, Limited, is designed primarily for the casting of alloy steel billets and slabs.As an introduction to the art of continuous .casting of metals, it is interesting to examine a few of the many devices which have been developed. As previously mentioned, Sir Henry Bessemer constructed a machine for the direct casting of mild steel sheet. His discoveries and ideas of continuously casting steel formed the foundation for the work of other pioneers in this field, all of whom have contributed to the improvement of this art through the ensuing years. The machines which will be selected for examination are those of Bessemer, Poland-Lindner, Williams, Ennor, and Junghans. The last unit to be discussed will be a modification of the Junghans machine recently installed at Atlas Steels."

Jan 1, 1954

By J. D. Zhu

A numerical model for predicting microporosity formation in aluminum castings has been developed, which describes the redistribution of hydrogen between solid and liquid phases, the transport of hydrogen in liquid by diffusion and Darcy flow in the mushy zone, One of the key features of the model is that it uses a two-stage approach for porosity prediction, In the first stage, the volume fraction of porosity is calculated based on the reduced pressure, whereas, in the second stage, at fractions solid greater than the liquid encapsulation point, the fraction porosity is calculated based on the volume of liquid trapped within the continuous solid network, which is estimated using a correlation based on the Niyama parameter, The porosity model uses thermal data calculated using the commercial finite element package ABAQUSTM. The model has been applied to examine the evolution of porosity in a series of experimental samples cast using unmodified A356 in which the initial hydrogen content was varied from 0,048 to 0.137 [cc/100g], A comparison between the model predictions and the experimental measurements indicates good agreement in terms of the variation in porosity with distance from the chill and the variation resulting from initial hydrogen content.

Jan 1, 2005

By Baisheng Nie

The process of gas diffusion through coal particles and the mathematical physical model under the third kind boundary condition was determined to obtain the rules of gas diffusion through coal particles of different sizes. The analytical solution of the equation was obtained by the Method of Mathematical Physics. The parameters of analytical solutions and the implications of parameters were analyzed. The Biot criterion (Bi) and the Fourier criterion (F0) of mass transfer can represent and reflect the features of gas diffusion field of coal particles. Moreover, the measurement method of gas diffusion coefficient and surface mass transfer coefficient is introduced and an example of measurement is given. The achievement can provide the support to prevent disasters related to methane in coal mines.

Aug 1, 2013

By Zhibao Li, Lanmu Zeng

The behavior of dicalcium silicate in NaOH-NaAl(OH)4-Na2CO3 solution is of significance for controlling the silica level in the production of alumina via the sintering process. Dicalcium silicate samples were obtained through a twostep approach: coprecipitation of calcium and silicate from CaCl2-Na2SiO3-NaOH solutions; and calcination of the hydrated precursor at 1200°C for 4 hours. The optimization of the synthesis parameters including temperature, solution concentrations and aging time was also investigated. Xray diffraction (XRD) and chemical analysis show that the calcined solids include dicalcium silicate with trace amounts of wollastonite. The solubility of the synthesized dicalcium silicate in HCl, NaOH, mixed NaOH-NaAl(OH)4 and NaOH-NaAl(OH)4-Na2CO3 solutions was determined. It was found that the solubility increases with increasing HCl and NaOH concentration. The effect of temperature on the solubility in HCl solutions is limited, but the solubility decreases with increasing temperature in NaOH solutions. The solubility of dicalcium silicate in NaOH-NaAl(OH)4 and NaOH-NaAl(OH)4-Na2CO3 solutions was shown to increase with increased temperature, Al(OH)3 and Na2CO3 concentration. The BromleyZemaitis model for the aqueous electrolyte system was selected to predict the solubility of dicalcium silicate. The model’s predictions yielded certain success compared with experimental solubility data.

Jan 1, 2014

By Y. M. Shneerson, E. E. Zhmarin, E. M. Vigdorchik

One of the Gipronickel Institute activities is research and development of customized leaching technologies. The work is performed in several steps. Leaching kinetics are studied on a lab-scale according to a special procedure. Experimental data are processed using mathematical models of batch and continuous processes. Reliability of kinetic data and preliminary calculations is verified experimentally in laboratory reactors of various capacities. If necessary, certain parameters of the mathematical model are adjusted after pilot plant tests in continuous mode ( 4-reactor train, each with 25 L capacity). The specified kinetic characteristics along with the mathematical model are used for further development of industrial leaching technology.

Jan 1, 2005

By C. O. Staples, J. G. Morrow

The application of cationic flotation to the upgrading of magnetic concentrates was investigated in the laboratory by both batch and continuous test procedures. It was found that the collection of coarse gangue particles with amine, heretofore considered a serious obstacle to this particular application of cationic flotation, is greatly enhanced by a drastic reduction in what might otherwise be considered normal impeller speed. Gangue flotation is in-dependent of variations in the rate of aeration. The collector and Crother additions and the impeller speed which favour the formation of a matte froth yield optimum results.

Jan 1, 1966

The original JKMRC AG/SAG mill model was developed over 30 years ago and has been upgraded a number of times since then, with the current published version being the Variable Rates model that is now over 15 years old. Since this model was developed further enhancements have been derived, some of which are applied in-house and some which have yet to be incorporated. The published and the commercially available model in JKSimMet is currently undergoing a comprehensive overhaul with a vastly extended data base for model evolution and validation. Improvements developed within the AMIRA P9 project, in-house development and a number of collaborative projects, are being incorporated into the upgraded model structure. Enhanced capabilities will include: power-based breakage rates scaling; a far wider mill filling range (from 10% to 40%) that exhibits peak in throughput as mill filling increases; higher ball loads; improved pebble discharge function; improved slurry discharge function incorporating important mill design and operational influences; and the new size dependent breakage function. The model will also be able to accommodate some influence of liner design and multi-component ores (blends of hard and soft components). This upgrade is still a work in progress but substantial changes have been made to date. This paper presents some of the new improvements and their influence on the predictive capability of the model.

Jan 1, 2012

By K. C. Corin, M. S. Manono, J. G. Wiese

Depressants play a crucial role in the flotation of PGM bearing ores as they prevent naturally floatable gangue (NFG) from reporting to the concentrate. This action is regarded as critically important because less dilution of the concentrate means lower costs for downstream processes. However, abnormal water conditions (such as high concentrations of ions) in the flotation system can modify the selectivity of these depressants. It is well known that the existence of selected electrolytes in water can alter the behaviour of some polysaccharide depressants by enhancing their adsorption onto gangue minerals and thereby prevent naturally floatable gangue from moving into the froth phase. Concurrently these same electrolytes may enhance frothability, owing to their stabilising effect on the bubbles within the system. Plant water at various ionic strengths was investigated against depressant type and dosage in order to understand electrolyte-depressant interactive effects during the flotation of a Merensky ore, using entrainment, rate of NFG recovery, and total gangue recovery as proxies. The study showed that the rate of NFG recovery per unit mass of water decreased with increasing ionic strength at all dosages, however the total amount of gangue reporting to the concentrate increased with increasing ionic strength at all depressant dosages. Thus, this paper attempts to consider the effects of both ionic strength and depressant dosage as individual factors within flotation. It further looks to investigate whether any interactive effects exists between these two factors when considered simultaneously.

Jan 1, 2016

By J. B. Evans

"NORMALLY the duties of the exploration engineer and geologist cover the initial, and possibly, the most important phase of mining property evaluation; that phase being the presentation of an opinion of the property's ore reserve potential in terms of tonnage and grade. The prime objective of this pa-per is to outline one method of bridging the wide gap that lies between a know ledge of a property' s tonnage and grade potential and an appreciation of the value of that property in dollars and cents.THE PRESENTATION OF PROPERTY EVALUATIONThe engineer engaged on a mining property evaluation, regardless of whether he be an independent consultant, or a company employee, has as his goal, the presentation of his appreciation of the property's potential value or worth within terms of reference acceptable to his principal.To furnish a complete evaluation report, the evaluator must firstly study all aspects pertaining to the particular property under consideration, then present his appreciation of the property's worth in some tangible form. The ultimate presentation is one giving a Present Value of the pro pert y in terms of monetary exchange. Such an idealistic presentation is not always possible; typical preventives being -insufficient reliable information, limited time, Jack of ability and absence of definite direction."

Jan 1, 1960