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By L. Cortez, Á. Magalhães, F. Durão

Methods based on regionalized variables theory, commonly known as geostatistics, have been widely used since more than three decades to predict/estimate spatial distributed data, namely mineral resources, with quite good results. However, some restrictive theoretical assumptions, such as the need of some kind of stationarity of data and the linearity of the predictor/estimator, are often wrong options in many applications. An alternative approach based on a finite mixture modelling, or cluster weighted modelling (CWM) technique, is presented and compared, in its theoretical and practical aspects, with the geostatistical methodology. CWM is a general non-linear framework based on the estimation of joint density functions allowing the calculation of the conditional probability function of the target values given their locations. Validation tests are performed in a 2D case study, where testing data proceeds from a soil contaminated by a heavy metal. The results of ordinary kriging and CWM estimations show a very good agreement with actual data. Keywords: Non-linear regression, Geostatistics, Ordinary kriging, Finite mixture modelling, Cluster weighted modelling.

Jan 1, 2003

By N Maistry, A Singh

It is estimated that in less than a decade, high-grade iron ore reserves in South Africa will be depleted, leaving only low-grade ores with a dominant lithology of banded iron formation (BIF) hematite. BIF is a complex ore reserve as it is typically liberated below 1 mm, resulting in high energy costs. However, due to its abundance, its beneficiation potential should be evaluated to maximise recovery at an acceptable product grade. To develop a beneficiation program for BIF hematite, the first step is to determine the effect of two laboratory crushing techniques on mineralogical characteristics, specifically liberation and shape. For this study, the cone crusher and high pressure grinding rolls (HPGR) were used. The Electron MicroProbe Analysis (EMPA) and Mineral Liberation Analyser (MLA) were used to compare the mineralogical characteristics. The liberation characteristics for hematite are similar for both crushing techniques; however, HPGR preferentially liberates quartz. HPGR achieved 8– 12 per cent additional quartz liberation in the greater than 80 per cent and 100 per cent liberation classes respectively and specifically in +75 μm size range. Improved quartz liberation is associated with lower energy requirements for downstream milling and improved separation efficiencies for beneficiation units that operate in this size range. Both samples displayed similar shape characteristics; most particles were elongated smooth and the rest were elongated angular. Good hematite liberation is expected at grinds of 212 μm to 150 μm. Further consideration should be given to throughputs, energy efficiency and downstream equipment selection prior to selecting a crushing technique.

Sep 18, 2023

By F. Calizaya

This study summarizes the results of various numerical and laboratory experiments per-formed to study the effect of airflow recirculation on gas concentration. The numerical exercises were carried out on a simulated mine ventilation net-work. The laboratory experiments were conducted at the Mackay School of Mines' airflow monitoring system in Reno, Nevada. In both cases, the airflow was recirculated through the system by means of a main fan and a set of booster fans. The booster fans were positioned to produce two types of recirculation: In line and Cross-cut. For each type, various recirculation conditions were generated by changing the booster fan pressure. During each test, the gas emission rate at the simulated working face was kept constant. The study illustrates the conditions under which controlled airflow recirculation may be used to solve a district ventilation problem.

Jan 1, 1991

By E. V. Lilford

Valuators of mineral properties are faced with a range of valuation methodologies, the most important of which are grouped under the headings of the market approach, the cost approach and the income approach. The way in which value is defined and the detail of the different valuation methodologies is examined here. This paper aims at documenting the variety of valuation procedures and applying each method to a variety of gold projects and comparing the outcomes. Any decision to apply a valuation technique will depend principally on the stage to which the project has been developed. The valuation approach to a greenfield project will be substantially different from that applied to a well-drilled, extensively explored mineral property. Furthermore, a valuation exercise may produce different outcomes for the same gold project depending on which method is applied. In order to investigate the variability in valuation methods and to explore the outcomes of different approaches, a series of five gold projects was analysed. The projects differ in regard to levels of capital application, infrastructural setting, depth below surface, in situ grade, and the stage of development, and were valued using the different methods. The most critical aspect of any valuation is the capacity of the valuer to identify the salient issues and ensure that they are incorporated into the valuation. The danger of simply applying ?black box? solutions to valuation problems without a full understanding of the parameters and the areas of uncertainty is emphasized. The importance of the valuator?s experience, insights into best practice and the ability to recognize and submit to the requirements of compliance within the minerals industry is among the most important characteristics of a valuer.

Jan 1, 2005

By Jinung Do, Sung-Ryul Kim, Juhyung Lee

"Model tests have been performed to investigate the vertical, horizontal and cone tip resistances of bucket pile embedded in sand by different installation methods; suction force by pump and jacking force by actuator. Micro-cone penetrometer is used to evaluate the variation of the effective stress inside and outside of the pile after installation. As a result of vertical pull-out test, the jacked pile shows 3 times larger resistance than the suction-installed pile. For horizontal pull-out test, the ultimate horizontal capacity and the slope of load-displacement curve on the suction-installed pile decreases by 22% and 40%, respectively, compared to the jacked pile. In cone penetration test, inside cone tip resistance of the suction-installed pile is about 40% smaller than the jacked pile, which indicates that the effective stress is reduced due to upward seepage of bucket pile in sand by suction force. Therefore, installation methods can affect the behavior of the bucket pile significantly.INTRODUCTIONA suction force occurred when bucket pile penetrates into sandy soils induces seepage flow into the bucket pile so downward seepage near the outside of bucket pile causes to increases the effective stress, while upward seepage inside the bucket pile decreases the effective stress (Mahn, 2005; Fig. 1). The effect of induced seepage causes to reduce the penetration resistance during installation. On the other hand, reduced effective stress can decrease the horizontal and vertical capacities of bucket pile by significant disturbance at the tip of the bucket pile due to the flow net. Due to the complexity and difficulty considering the effects of suction installation, many previous researchers generally have neglected the effect of suction installation in their experiments. Therefore in this study, the effects of suction installation on resistance of bucket pile is examined."

Jan 1, 2016

By B Hu, B Zhang, J Wang, H Ma, D Liu, L Han

Zeolites are potential carriers of slow release fertilisers due to their unique phenomenon for salt occlusion. A comparative study was performed on the capacities of potassium nitrate (KNO3) occlusion in molten KNO3 treated synthetic 4A and 13X zeolite molecular sieves with main channel sizes of 0.41 x 0.41 nm and 0.74 x 0.74 nm respectively. The results show that in a laboratory setting, the treated zeolite 4A contained 13.57 per cent of occluded KNO3 and the treated zeolite 13X did not contain any. This was confirmed by the regular release of K+ and NO3- during washing both treated mixed samples with water and by their IR spectra and TG analysis. There are also changes of the relative intensities of peaks in X-ray diffractograms of both treated zeolite samples. K+ release from molten-KNO3 treated zeolites in deionised water and simulated soil solution shows that release of K+ from KNO3 occluded in zeolite 4A are slow and steady. Proper size fit between the channel size of zeolites pore and the size of K+-NO3- ion pair of KNO3 is the decisive factor for zeolites to occlude KNO3.

Jan 1, 2008

By R. K. Rath

The low-grade iron ore sample contains both lumps and fines. It is mostly hematitic iron ore and considerable amount of goethitic/limonitic material is present in it. The major impurities present were quartz and clay. It is observed that the iron bearing phases are poorly liberated above 300 µm and the liberation improves below 300 µm. More than 80% liberation is achieved below 106 µm. Based on the liberation data, the feed for the different beneficiation methods was prepared by stage crushed the ROM followed by grinding passing to 106µm and the ground material (-106µm) was deslimed. The underflow was subjected to various beneficiation techniques such as tabling, enhanced gravity separator (EGS), wet high intensity magnetic separation (WHIMS), and flotation and the results are discussed. All the methods studied could able to produce pellet grade concentrate with iron content of 64.5%, however, a marginal higher yield was observed for WHIMS (81%). Keywords: beneficiation, gravity, magnetic, enhanced gravity separation, flotation, low-grade iron ore, desliming

Sep 1, 2012

By C. W. Lee

"Introduction of diesel engines in underground mines may generate severe health hazards associated with exhaust contaminants. One of the most important parameter in determining the optimal air quantity for hazard reduction is the exhaust dispersion. Through analyzing the exact solution of the diffusion equation and its approximation by finite difference method(FDM) , this paper aims at doing a fundamental research to find an efficient dispersion model suitable to the domestic mines. Diffusion coefficients are likely to be small in the underground airways with high ventilation resistance. This makes concentration profiles similar to the convection-based step functions. It is the case for fixed as well as moving engines. Concentration estimation by exact solution is almost impossible in the case of either a single engine moving at a variable speed or the existence of multiple engines. Application of FDM to the diffusion equation including turbulent dispersion results in the various problems; unstable concentration profiles depending on the engine location, nuctuating concentrations near the engine, and overestimation of the dispersion region of which error grows with waning diffusion coefficient.Convection-based dispersion model is found to fit well for dynamic simulation of exhaust dispersion from multiple diesel engines in the airways showing low diffusion coefficients. Its suitability is more likely in the regions with frequent equipment passage. Published"

Nov 1, 1995

By Q. Zhang, X. C. Wang, X. Q. Ao

The flotation separation of apatite and calcium-bearing gangue minerals (dolomite and calcite) has always been a problem in phosphate ore mineral processing research. The crystal structure and surface properties of minerals have an important influence on their floatability. In this paper, the theoretical and comparative analysis of the crystal structure and surface electronic properties of apatite, dolomite and calcite were carried out using the first principle calculation based on density functional theory. As a supplement and validation, the surface wettability of three minerals under different flotation conditions were compared and analysed by contact angle test. The results theoretically revealed that the three calcium-bearing mineral surfaces have similar surface electronic properties and thus exhibit similar floatability. In the flotation process, the anion difference between apatite and carbonate gangue should be fully utilised, and the minerals can be separated only after surface modification by flotation reagent. The contact angle test shows that phosphate and carbonate can be separated by using anion flotation collector after surface modification with acid. It is expected that this research is of interest for understanding the surface structure and electronic properties of apatite and carbonate gangue minerals and providing the theoretical basis for surface interaction. Keywords: Apatite, dolomite, calcite, surface structure, electronic property, density functional theory

Jan 1, 2020

By Husamuddin Ahmadzai

A survey of regulations and state of the art control technologies is presented relating to the smelting of primary aluminium, copper and recycling of residues. Some costs associated with the alternatives and trends for the coming decade in this. sector are identified.

Jan 1, 1992

By Robert L. Davidoff

INTRODUCTION The impact of taxation differs substantially from state to state in a complex fashion that depends on both the physical characteristics of a mineral deposit and on the price of the mineral commodity relative to its costs of production. A comparative analysis of the tax structures of eight states (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah and Wisconsin) showed wide variations in rates of return for any given type of mineral property, with no state having either the most burdensome or least burdensome tax structure under all circumstances. Three hypothetical mineral operations were analyzed: a producing open-pit copper property, a non-producing underground platinum operation, and a non-producing underground gold operation. None of them corresponds exactly to an existing property. Each of these property types is further defined to have ore feed grades at three different levels, leading to three potential profitability levels, referred to in this paper as "economic", "marginal" and "subeconomic". Thus the differential impact of state tax structures is measured for mineral properties of different types, as well as for different profitability levels. Montana is used as the base case. This study does not address the topic of corporate structures or tax consolidation. There are no costs assumed external to the operation of the deposit (e.g. exploration to locate additional deposits). Two types of analyses were performed for this study. The first calculates the total cumulative tax payments in each state using all applicable taxes (including U.S. federal income taxes and examines the resultant differences in discounted cash-flows rate of returns DCFROR's amoung the eight states. The second is a sensitivity analysis that examines each type of state tax separately (i.e. state income, property, and severance taxes) in order to isolate and examine the differences in tax payments that are due to the difference in rates and methods of computing specific types of taxes in each state. The results of this study serve to illustrate the complex nature of interactions among various taxes. For example, property tax is a deduction in calculating severance tax in some state. Changes in property-tax and severance-tax payments both enter into the calculation of state and federal income-tax liability. This, in turn, could change the timing and usage of tax-loss carry forward amounts and investment tax credits. Additionally, the physical characteristics of a property, the method and costs at which the mineral will be extracted, and the profitability level at which each property operates will affect tax treatment. Each mineral operation was evaluated at three different predetermined profitability levels, referred to using the terms economic, marginal and sub-economic. These three profitability levels are defined by the ore feed grades of the primary commodity that yield in constant terms, approximately an "economic" 18% DCFROR, "a marginal." 10% DCFROR, and a "sub-economic" 5% DCFROR, respectively, under the Montana tax structure. In the analyses, the mining and processing parameters for each of the three types of properties were assumed to be identical for each of the eight states. It was assumed that each operation produces at full operating capacity throughout its life. This implies the level of mineral commodity demand will support the inferred commodity price, such that each operation will be able to sell all its output. The analyses performed for this study were done using a comprehensive economic evaluation simulator that is used in the Bureau of Mines, Division of Minerals Availability MAS program to perform DCFROR analyses. All economic evaluations performed upon these data (see appendix 2) were in constant January 1981 dollars. By-product prices used for the analyses were: [Gold $425.00/troy ounce Palladium$200.00/troy ounce Silver $ 10.00/troy ounce] Typical cash-flow calculation layout is given in Appendix 3. The initial step for each evaluation is to define an "economic" profitability level scenario. An 18% DCFROR rate in Montana was considered the

Jan 1, 1985

By Takayoshi Otsuka, Taher Elsamni, Ashraf Bou-Krisha, Takaya Takimoto

"INTRODUCTION Tunnel is a closed space structure and it is necessary to ensure the sufficient time and route for safe evacuation for the tunnel users in case of a tunnel fire. In order to do so, damages and collapse of the tunnel linings and the secondary disasters can be avoided. Furthermore, the road tunnel is one of important infrastructural facilities and stopping its function for a long time for a tunnel fire could cause a great economic loss. Therefore, the tunnel structure shall be the one which can be repaired as soon as possible, and the fire protection methods need to be selected among those which enable the service to start as early as possible. The necessity of the fire protection works is evaluated for the tunnel structure with the consideration of the expensive tunnel construction cost and the economic effects of the tunnel service. Naturally, the fire protection works, which can protect the tunnel linings from the tunnel fire with small repairs, are inevitable. Design engineers of the fire protection works estimate the scale of fire from the degree of damages on the linings and its repair cost, the effect of fire extinguishers placed inside of the tunnel, the secondary disasters in accordance with the tunnel lining damages if any, and the ratio of fire protection cost calculated from tunnel operation cost. Based on this information, the engineers design the fire protection works according to the permissible limits Among the design cases of the tunnel fire protection in Japan, as shown in Table 1, there is no cases that used the fire temperature-time curve to design the fire protection works for large fire caused by vehicles catching fire. However, the most of cases used 30-60 minutes for fire duration based on the entry prohibition of dangerous goods carrying vehicles or the effect of early fire fighting. This paper will study the variation between different methods used for fire protection in road tunnel in Japan to evaluate them and try to found some recommendations. Especial l care will be attention to Polypropylenes (PP) which is starting to be applied lately."

Jan 1, 2016

By K L. C Gontalves

In 1999, the Mineral Development Centre of CVRD (CDM) acquired a flotation device referred to as Mini Pilot Plant (MPP), which is able to run continuous flotation tests with drill core samples. Since then this equipment has been used to define the flotation circuit and process conditions during the pre-feasibility phase of CVRDÆs copper sulfide projects. Until now, the MPP results had not been validated for an industrial flotation operation. The present work consists of a comparison and correlation of the results from a flotation MPP and an industrial plant. In order to make this comparison, an industrial plant was completely sampled and the feed ore was tested on bench scale and on a MPP. The metallurgical and mass balances of each test were used for the comparison.

Jan 1, 2005

By Peng Zhang

In previous research, the laminated overburden model from the LaModel program was effectively integrated with Analysis of Retreat Mining Pillar Stability (ARMPS) through ARMPS-like input to create a laboratory version of the new ?ARMPS-LAM? program. This program takes the basic ARMPS geometric input for defining the mining plan and loading condition, and then automatically develops, grids, runs, and analyzes a full LaModel analysis of the mining geometry to output the section stability factor (SF), all without further user input. The initial ARMPS-LAM results were encouraging with a case history classification accuracy of 55% to 71%; however, a few of the input variables that were nominally included in the SF calculation showed independent significance in the classification accuracy. Therefore, in order to further improve the accuracy of the ARMPS-LAM program, an investigation of the SFs calculated by the new ARMPS-LAM program and the ARMPS program is detailed in this paper. The initial results of a linear correlation between the ARMPS-LAM SF and the ARMPS SF showed a strong correlation (R2 = 0.88), with the ARMPS-LAM SF averaging about 8% higher. The difference in SFs between the programs were further investigated, and, ultimately, the results indicated that the laminated overburden model as implemented in ARMPS-LAM distributes relatively more load on the section pillars for depths less than about 1,000 ft and less load for depths more than 1,000 ft. The results of this research highlight the potential for improving the ARMPS-LAM program in the future by implementing a more accurate loading calculation on the section pillars.

Jan 1, 2014

By Farzaneh Sadri

After water leaching of an acid baked REE concentrate, impurities such as Fe, Al, Th, and Cu are removed by neutralization with different reagents such as NaOH, Mg(OH)2, MgCO3, CaO, and CaCO3. Among these chemicals, lime (CaO) and limestone (CaCO3) are the preferred reagents due to their low costs. However, because of calcium sulfate dihydrate (gypsum) precipitation, they are not so common in industry. One of the disadvantages of gypsum precipitation is the adsorption of REE to the precipitates, losing a fraction of REE to gypsum which is hard to recover. In this paper, batch and continuous conditions in the impurity removal process using limestone are investigated and the differences between these two processes are examined. Based on the experiments, REE uptake by gypsum significantly increases in continuous processes, and different gypsum morphologies are observed.

By Saeed Zandi, Kazem Oraee

"Tunnels and galleries are the most important structures in coal mines. They are used for variety of purposes, such as transporting ore and people and for ventilation. A well-designed support system is necessary to stabilize structures and prevent collapse.Using rock bolts increases the strength of the rock in which tunnels are made. Rock bolts are used extensively in most underground mines today, and coal mines are no exception. Almost all galleries in a typical coal mine use some type of rock bolt, at least, as a means of partial or supplementary support.In this research, changing the support system from expensive methods to the use of rock bolts as the primary means of support is discussed, with the focus on a particular gallery in Hejdak coal mine. Visionary design methods, in conjunction with rock mass classification schedules, were used to determine an optimal rock bolt pattern. For this purpose, rock mass rating (RlVIR) and quality index (Q) classification systems were used. Several empirical methods were also used to design an optimal pattern for rock bolt installation in the particular tunnel under analysis.As such, the tunnel support system was designed using both finite element and empirical methods. Finally, the results obtained from both numerical and empirical methods were compared under different load conditions. The methodology prescribed in this paper, together with the comparison, can be a useful tool when selecting a support system. The results can also be used to design a support system in this and any other coal mine with similar conditions.INTRODUCTIONSince the advent of underground excavation techniques, one of the biggest challenges has been stabilizing tunnel walls and preventing roof collapse in tunnels and other underground openings, such as galleries. Loose rocks and layers drop into tunnels and galleries, except in very hard rock. Underground roof collapse and falling rocks can have devastating effects on the safety of operation personnel and equipment and can seriously affect production. When designing an underground coal mine, the stability of tunnels and galleries is an important parameter that should be studied carefully because it has an important role in the production process of the mine. Therefore, an appropriate and well-designed support system is necessary for preventing collapse and helping to stabilize the tunnels and galleries."

Jan 1, 2016

By P. Jacquin

Many a deposit estimation has been carried out since geostatistical methods were first implemented. To date however few mining programs have totally been completed and even fewer comparisons can be drawn between estimated reserves and extracted ore tonnages. Aluminium Pechiney work a number of bauxite mines in Southern France. As from 1969 they modified their deposit estimation methods, giving up traditional approaches and opting for geostatistics. At that time, the authors of this paper were entrusted with the first geostatistical estimations and in particular, those concerning the deposits mentioned herein. Over the past decade a number of deposits have been worked out and we thought it interesting to report about comparative results. French bauxite deposits are of the karstic, as opposed to the lateritic, type. The bauxite, formed at some distance of the present-day deposit, was brought to and trapped in limestone karst pits. Subsequent physical and chemical alterations may have taken place : silica and carbonate drifts, recent karst slips. The morphology of these deposits is often rather complicated. The deposits are small from a few hundred thousand to a few million tons at the most. The overburden thickness usually precludes open mining. Mining investments and financial risks are often high, making it necessary to obtain optimal information on the deposit considered for mining. For the three cases brought up in this paper, deposit sizes, exploration methods and conclusions differ. They are brought up mainly to show the advantages inherent to a quality geostatistical study and the lessons drawn by Aluminium Pechiney.

Jan 1, 1982

By D. Clement

A comparison between hydraulic and pneumatic rockdrills by D. CLEMENT The regulation of compressed-air reticulation systems is very poor compared with that of electrical systems; this means that electrohydraulic rockdrill systems offer greater flexibility, additional power being readily available at the working face. Hydrometallurgy A new journal devoted to all aspects of the aqueous processing of metals is scheduled to appear this year. Entitled Hydrometallurgy, the journal will be published in quarterly issues, one volume per year. Mineral dressing Contributions are invited for the Symposium on Recent Progress in Mineral Dressing in South Africa, which is to be arranged jointly by the South African Institute of Mining and Metallurgy and the National Institute for Metallurgy. Mineraalbereiding Bydraes word verlang tot die Simposium oor Onlangse Vordering met Mineraalbereiding in Suid-Afrika wat gesamentlik deur die Suid- Afrikaanse Instituut vir Mynbou en Metallurgie en die Nasionale Instituut vir Metallurgie gereel gaan word. Rock mechanics The Sixteenth Symposium on Rock Mechanics is to be held at the University of Minnesota from 22nd to 24th September, 1975. The Symposium is the official Symposium for 1975 of the International Society for Rock Mechanics (I.S.R.M.), and the Council for I.S.R.M., consisting of members from 25 countries, will meet during the Symposium. Powder metallurgy The annual meeting on powder metallurgy organized by The Metals Society is this year to be held at the Stratford Hilton Hotel, Stratford-upon-Avon (the notification did not include the date of the meeting). Vacation School The South African Institute of Mining and Metallurgy has great pleasure in announcing its intention of holding a vacation school on the topic of electric-furnace melting. NIM reports Report no. 1681 The determination of sulphur and phosphorus in chromite. Report no. 1687 The viscosities and electrical conductivities of slags associated with the production of high-carbon ferromanganese alloys.

Jan 3, 1975

By Mark Flower

A 20L ignition test chamber has been used to test suspensions of 7 UK and world traded coals in air and O2/CO2 mixtures typical of oxy-combustion conditions. The coals varied in rank from sub-bituminous to bituminous and were tested in varying concentrations from the ignition limit to 400g/m3. Following each successful test the combustion residue was collected, weighed and analysed within a thermogravimetric analyser, allowing Q factors to be estimated. The ignition limit varied slightly in air, but was mostly around the 200g/m3 level. With the exception of Coal C, which was much harder to ignite, it correlated roughly with coal rank. The ignition limit changed significantly with O2 concentration when in mixed O2/CO2 gases. Only a few high volatile coals ignited in 21% O2/CO2 v/v, and then only with a 2500 J, rather than a 1000J, igniter. An increase in O2/CO2 levels to 30 or 35% gave ignition patterns similar to those carried out in air with a further increase to 40% having little additional effect. In addition the minimum ignition concentration decreased with increase in O2. Heterogeneous combustion or gasification of the coal by CO2 appears to be confirmed by comparing weight loss results for air and O2/CO2 mixtures respectively for an equivalent peak pressure rise.

Jan 1, 2009

By Larry G. Stolarczyk

1.0 FRAMEWORK FOR COMPARISON This document describes the decision factors that bear on the selection of the modulation process for the wireless underground medium frequency (MF) communication system. The selected modulation process must satisfy the Bureau of Mines stated objective of improving general communications within an underground mine. The improvement being sought includes the development of a wireless communication technology of measurable benefit to both mine safety and mine productivity. The improvement will allow wireless communications paths to exist between roving miners. The wireless communication paths will also be made compatible with the existing underground telephone system to extend paging and voice communication throughout the underground mine. The new wireless equipment will include man-pack, vehicular, repeater, and base station transceivers. Repeaters and base stations will feature coupling networks for interfacing with the existing telephone circuits. Frequency modulation (FM) and single sideband (SSB) modulation processes are analyzed in view of the special conditions associated with underground mining. Of primary importance is the tremendous electrical noise generated in an operating mine that could adversely affect communications quality. High noise coupled with high attenuation rate of near field signals forces the communication system to be inherently short range. Fortunately, near field signals can propagate over great distances on underground wires and cables. The framework for comparison is generated by presenting all factors that