边界品位计算报告-陈建宏(20080802)
合理确定低品位铁矿床边界品位的探讨
２０１０年８月
中国矿业
ｖ０１．１９，ｚｋ Ａｕｇｕｓｔ ２０１０
ＣＨ矾Ａ
ＭＤⅡＮＧ ＭＡＧＡＺＤ＿『Ｅ
合理确定低品位铁矿床边界品位的探讨
蒋渊和
（邯邢冶金矿山管理局安徽霍邱诺普矿业有限公司，安徽六安２３７４６４）
摘
要：铁矿是不可再生资源。随着我国高品位铁矿石的大量开采及市场经济的调控，低品位铁矿
第１９卷
中
国
矿业
用。
策。其盈亏平衡品位应满足以下条件：开采盈利＝不 开采盈利；如果该块段予以开采，则其盈利为五一ｚｃ； 如果该块段不予开采，则其盈利为零。即可得： Ｚ卜ｚｃ＝０ 将式（１）、式（２），代人式（３）得： Ｃｐ＝Ｃｄ（Ｓｐ＋＆），乙‰（１一髟） （４） （３）
将表２中数据代人式（６），废石处理运费现价 Ｗｃ为１．８元／ｔ．得 盈亏平衡品位＝精矿品位×（采矿成本＋选矿成 本一废石处理运费）％／精矿售价Ｘ回收率（１一贫化率） ＝０．６６４９ｘ（９５．６０＋４２．７７—１．８）％／９５７．３６ｘＯ．７６１３ （１－０．１３１４）＝１４．３７％ 由以上数据可以看出。由于处理废石成本较 低，开采后的盈亏平衡品位Ｇ为１４．３７％与开采前 的盈亏平衡品位ｃＤ为１４．５３％数据相差无几，因此， 盈亏平衡品位也采用１７％作为盈利指标较为合理。 即当块段品位低于１７％时。产出矿物作为废石直接
床资源越来越受到重视和开发，而边界品位的合理确定，能最大限度地提高经济效益和节约国家资源。本 文从实际出发。考虑地质条件、经济因素、技术水平等前提下，探讨低品位铁矿床边界品位的确定方法，达
到充分利用宝贵资源，延长矿山服务年限的目的。
关键词：合理确定；低品位铁矿床；边界品位
地下开采边界品位动态优化研究及其应用的开题报告
地下开采边界品位动态优化研究及其应用的开题报告一、选题背景与意义随着资源开采的日益深入，地下矿产资源的品位也在逐渐降低，开采难度和成本也越来越高。
因此，为了实现矿产资源的高效利用，地下采矿过程中的优化问题成为了矿产资源开发利用的重要研究方向之一。
其中，针对地下采矿的边界品位动态优化问题是一个重要的研究内容。
通过对边界品位进行合理优化，可以最大程度地提高采矿效率和品位，降低采矿成本，实现矿产资源的高效利用。
二、研究现状目前，国内外学者已经开展了一些关于地下采矿边界品位动态优化的研究。
其中，一些基于数学模型和优化算法的研究成果已经被应用到实际生产中，取得了较好的效果。
但是，目前还存在一些问题，如边界品位的影响因素、优化策略的选择等方面问题有待深入研究。
三、研究内容与目标本课题旨在针对地下开采边界品位动态优化问题，开展深入研究。
具体研究内容包括：1.分析地下采矿边界品位的影响因素，包括矿床地质条件、采矿工艺等因素，建立边界品位的数学模型；2.研究边界品位的优化算法，包括遗传算法、模拟退火算法、遗传-模拟退火混合算法等，比较各种算法的优缺点；3.开发地下采矿边界品位动态优化的应用软件，方便采矿企业实际使用。
本研究的目标是：1.建立地下采矿边界品位优化的数学模型，分析其影响因素，对矿床的开采作出科学的决策；2.研究边界品位优化算法，并比较各种算法的优缺点，为采矿企业提供科学、合理的决策依据；3.开发地下采矿边界品位动态优化的应用软件，提高采矿效率和品位，降低采矿成本，实现矿产资源的高效利用。
四、研究方法与技术路线本研究将采用数学建模和优化算法相结合的方法，建立地下采矿边界品位的数学模型，并研究边界品位的优化算法。
具体技术路线包括：1.收集矿床地质条件、采矿工艺、矿产资源市场需求等相关信息，对边界品位进行影响因素分析；2.基于影响因素建立边界品位的数学模型，包括确定目标函数和约束条件、建立数学模型等；3.研究边界品位的优化算法，包括遗传算法、模拟退火算法、遗传-模拟退火混合算法等，并比较各种算法的优缺点；4.根据优化算法，实现边界品位的动态优化，并开发地下采矿边界品位动态优化的应用软件。
边界品位的确定课件
全球化和国际合作的重要性
全球化趋势
随着全球化进程的不断加速，各国之间的矿产资源开发和品位确定合作将更加紧密。国际合作将有助 于共享资源信息、交流技术经验，共同应对全球矿产资源挑战。
国际标准与规范
在全球范围内推广和应用统一的边界品位确定标准与规范，将有助于提高品位确定的准确性和可比性， 促进国际矿产资源市场的健康发展。
边界品位与资源税费计征的关系
边界品位的确定对于矿产资源税费的 计征具有重要影响。
在资源税费计征过程中，应遵循相关 法律法规和政策规定，确保税费计征 的合法性和合理性。
不同品位的矿石可能适用不同的税率 和计税依据，因此准确确定边界品位 对于合理计征资源税费至关重要。
PART 05
边界品位确定的未来展望
矿石的品位和分布
矿石品位
矿石品位的高低直接决定了边界品位 的确定。品位越高，边界品位的确定 越重要，因为高品位矿石的价值较高。
矿石分布
矿石的分布情况影响采矿的难易程度 和采矿成本，从而影响边界品位的确 定。矿石分布均匀，采矿成本较低， 有利于降低边界品位。
开采技术和经济条件
开采技 术
开采技术的选择对边界品位的确定有重要影响。技术进步可以提高采矿效率和 矿石质量，从而降低边界品位。
ONE
KEEP VIEW
边界品位的确定课件
• 边界品位的基本概念
目 录
PART 01
边界品位的基本概念
边界品位的定义
边界品位：指在矿产资源评价中，用于区分矿与非矿界限的最低品位，即在当前技 术经济条件下，能供开采和利用的矿物的最低品位。
边界品位是衡量矿物含量多少的一个指标，也是衡量矿物经济价值的一个标准。
强化实践应用
加强实践应用方面的研究，不断总 结经验，完善边界品位确定体系， 提高其在矿产资源开发中的指导作用。
地质勘查常用公式
地 学 中 常 用 公 式一、 平均品位的计算公式：1、算术平均：(X 1+X 2-……+Xn)／n X 1、X2、X n 为样品品位 2、加权平均：(X l ×L l +X 2×L 2+……+ X n×Ln)／(L l +L 2+……+L n ) X 1、X 2……X n 。
为样品品位，L l +L 2+……+Ln 为样品长度3、几何平均为Xn X X n ⨯⨯⨯ 21 X 1、X 2、Xn 为样品品位注：品位为正态分布时，处理特高品位时，可用此公式。
二、 矿体厚度(Vm)、品位(Vc)变化系数：—X=(X 1+X 2+……+Xn)／n 计算矿体厚度、品位的平均值∑--=)1/()(2n X Xi σ计算均方差厚度、品位变化系数：Vm 或Vc=⨯÷X σ100％三、 地质剖面岩石厚度计算公式：y=sin α·cos β·cos γ ±cos α·sin βα--导线坡度角 β--地层倾角γ --导线方向与地层倾角的夹角地层倾向与坡向相反取正号，地层倾向与坡向相同取负号；真厚度=L×y四、钻孔矿体厚度的确定矿体的厚度是根据矿体露头上、坑道中和从钻孔中所获得的资料进行的。
(一)坑道中矿体厚度的测定当坑道所揭露的矿体与围岩的接触界线清楚时，取样和编录时可在矿体上用钢尺直接捌量出来。
厚度测量的次数决定于坑道的布置情况，如矿体是用穿脉坑道圈定的，则测量次数与穿脉坑道的数量相符。
如果矿体是用沿脉坑道圈定的，则厚度的测定按一定间隔在取样的位置进行测量。
如果矿体与围岩的界线不清时，矿体厚度的测定必须根据取样结果来确定。
(二)钻孔中矿体厚度的测定因为钻孔中所截穿的矿体均在地下深处、只能间接地去测定矿体的厚度。
当钻孔是垂直矿层钻进时，且岩心采取率为100％，可直接丈量岩心，取得厚度的数据。
若岩心采取率不高，除用钢尺丈量岩心长度外，还要按下式进行换算：L (11-9)mn式中： m——矿体的厚度(米)；L——实测矿心长度(米)In——矿心采取率(％)。
主要金属矿的边界品位及工业品位
主要金属矿的边界品位边界品位实际上与采矿难易程度、储量、和市场价格有关。
这里转载了一些近年来采用的边界品位.元素矿石工业类型品位备注边界品位工业品位黑色金属矿产铁TFe (%) 磁铁矿石20 25 赤铁矿石25 28—30 菱铁矿石20 25 褐铁矿石25 30锰％氧化锰富锰矿I 35 40II 30 35III 18 30贫锰矿石10—15 18 铁锰矿石I 20 25II 15 20III 10 15 碳酸锰富锰矿石贫锰矿石铁锰矿石151010251515含锰灰岩8 12铬％原生矿富矿贫矿≧25≧5—8≧32≧8—10 砂矿≧1.5≧3钛原生矿TiO2％金红石 1 1.5 砂矿（矿物千克/米3金红石≧1≧1.5钛铁矿≧10≧1钒独立矿床V2O5％0.5 0.7 伴生矿床V2O5% ≧0.1-0。
5% 有色金属矿产铜Cu％硫化矿石坑采0.1—0。
3 0.4—0.5露菜0.2 0.4 氧化矿石0。
5 0。
7铅硫化矿0。
3—0.5 0。
7—1。
0% 混合矿0.5-0.7 1。
0—1。
5氧化矿0.5—1。
0 1。
5—2。
0锌% 硫化矿0。
5-1。
0 1.0-2.0 混合矿0。
8-1.5 2。
0-3。
0 氧化矿 1.5—2。
0 3。
0—6.0铝％Al2O3/SiO2露采 1.8-2.6 ≧3.5坑采1。
8-2.6 ≧3.8 Al2O3％露采≧40≧55坑采≧40≧55镁%白云岩（MgO%）≧19菱镁矿（MgO％）42-46镍% 硫化镍矿原生坑采0。
2-0.3 0。
3—0。
5露采氧化矿石0。
7 1氧化镍、硅酸镍矿0。
5 1钴% 硫化钴及砷化钴≧0.02≧0.03—0。
06钴土矿≧0。
3 ≧0.5钨％石英大脉型0。
08—0.10.12-0。
15 石英细脉带型0。
1 0。
15-0.2 石英细脉浸染状0。
1 0.15-0.2 层控型0.1 0。
15—0。
2 矽卡岩型0.08-0.1 0。
15-0.2锡% 原生锡矿0.1-0。
浅谈铁矿勘查中资源量的估算-以原平市某铁矿为例
本次研究铁矿位于山西省原平市东北部。
经勘查，矿区矿体厚度1.10-31.58m，平均厚度4.7m。
受褶皱构造的影响，矿体具有增厚变薄、尖灭再现现象，夹石分布于矿体厚度较大地段，层数1-4层，厚度一般为1.05-5.29m。
1 资源量估算的总体思路在正确圈定矿体、确定资源量类别、划分块段的基础上，分别计算各块段资源量，最后按矿体、资源量级别、品级分别进行资源量统计汇总。
2 矿体圈定2.1 矿体真厚度单工程矿体的真厚度为该工程内圈入该矿体厚度方向上所有样品真厚度之和。
样品真厚度计算公式为：M=L (sinαsinβcosγ+cosαcosβ)式中：M －样品真厚度（m ）；L —样长（m ）；α－钻孔穿过矿体时的天顶角（°）；β－矿体平均倾角（°）；γ－矿体倾向与钻孔方向的锐夹角（°）。
2.2 单工程矿体圈定1）根据一般工业指标，将TFe 品位大于或等于25%，且真厚度大于1m 的样品圈为矿体。
2）边界上TFe 品位大于等于20%样品参与矿体平均品位计算后，整个矿段的平均品位大于或等于25%时，则作为矿体；当整个矿段平均品位小于25%时，则剔除边界上部分TFe 品位在20%-25%间的样品，使整个矿段平均品位不小于25%，以满足矿体圈定的要求。
3）矿体内TFe 品位小于边界品位的样品，真厚度大于1m 者，一律以夹石剔除；真厚度小于1m 的样品，不论品位高低，均参与平均品位计算。
2.3 剖面上和剖面间矿体的对应连接1）剖面上不同工程之间的同一矿体以不同资源量级别对应时，则采用对角对应。
2）剖面间的同一矿体，以不同资源量级别对应时，采用对角对应，以无对应级别剖面为零。
3）相邻两工程间的同一矿体，一个有夹石，一个无夹石，将夹石尖灭于工程间距的1/2处。
2.4 矿体的有限外推和无限外推1）相邻两工程，一工程见矿，而另一工程未见矿，则按两工程间距的1/2尖推尖灭。
2）单工程见矿，按工程间距的1/2尖推尖灭，外推厚度不大于工程见矿厚度。
边界品位的确定课件
净现值法
通过计算矿体的净现值， 评估矿体的经济价值和开 采效益，从而确定合理的 边界品位。
盈亏平衡法
根据盈亏平衡原理，计算 出矿体在达到盈亏平衡时 的品位，作为边界品位的 参考值。
成本分析法
通过对开采、选矿和冶炼 等环节的成本分析，确定 能够实现经济效益的边界 品位。
03
边界品位确定的影响因素
矿床规模
矿床规模越大，边界品位的确定本相对较高，因此边界品位的
确定有助于降低开采成本。
小型矿床中，由于总体储量较小， 边界品位的确定对整体经济效益 的影响相对较小。
矿石质量
矿石质量越高，边界品位的确定越关 键。
低品位矿石的质量较低，其开采成本 相对较高，因此边界品位的确定应充 分考虑经济效益。
经验 法
01
02
03
类比法
通过对比类似矿床或矿体 的品位分布和变化规律， 借鉴已有的经验和数据， 确定矿体的边界品位。
专家评估法
邀请地质专家根据矿体的 实际情况和开采经验，评 估和确定矿体的边界品位。
实践检验法
通过实践开采和选矿试验， 不断调整和修正边界品位， 以符合实际生产和经济效 益的要求。
经济评价法
市场条件的变化会影响边界品位的确定。
在市场需求大时，高品位矿石的需求量较大，因此边界品位的确定应适 当提高。
在市场需求小时，低品位矿石的需求量较小，因此边界品位的确定应适 当降低。
04
边界品位确定的实践应用
边界品位的确定课件
• 边界品位的基本概念 • 确定边界品位的方法 • 边界品位确定的影响因素 • 边界品位确定的实践应用 • 边界品位确定的发展趋势与展望
01
边界品位的基本概念
边界品位的定义
Guidance for Cut-off Grade Determination and Application
Cut-off Grade Determination and Application(Draft)March, 2014TABLE OF CONTENTS1INTRODUCTION (1)2CUT-OFF GRADE DEFINITIONS (1)2.1Breakeven Cut-off Grade (1)2.2Incremental Cut-off Grade (2)2.3Mill Cut-off Grade (3)2.4Cut-off grade for an orebody with multiple metals (4)2.5Discussion (4)3CONCEPT OF NEXT BEST ORE (5)4COST ESTIMATION (6)5METALLURGICAL RECOVERY (6)6CUT-OFF GRADE REPORT REQUIREMENTS (7)7LIMITING CAPACITIES AND SUBSEQUENT STRATEGIES (8)7.1The Role of Stockpiles (8)7.2Possible Scenarios (8)No table of figures entries found.No table of figures entries found.1 INTRODUCTIONThis document is to provide a useful reference guide to enable consistent calculation of cut-off grades, encourage optimal strategy usage and communicate general stockpile philosophy among Huaao operations. Cut-off grades are used as the basis of mineral reserve estimations and for decisions influencing operating strategy, mine planning and design. In an effort to provide consistency between Huaao operations, there is a need to understand at least three distinct types of cut-off grades:• Break-even Cut-off Grade (BCOG) – is the grade of material, which will generate revenue from sale of the finished product that is equal to the cost of mining, transporting (including stockpiling and rehandling costs that may apply), processing and final refining of contained metal(s). (Underground and open pit BCOGs are derived somewhat differently; further discussion will appear later in this document).• Incremental Cut-off Grade (ICOG) – is the grade of material which will generate revenue from sale of the finished product that is equal to the further required variable costs to transport, stockpile, rehandle and process (including all necessary royalties, smelter fees and any other requisite expenses).• Mill Cut-off Grade (MCOG) –is the grade of the already mined material, which will generate revenue from sale of the finished product that is equal to that of the remaining processing and refining costs necessary to produce the final product. All applicable rehandling costs as well as royalties and relevant variable costs must be included in MCOG calculations.The following definitions attempt to unify and clarify industry standard nomenclature within the context of Huaao operations and development projects.2 CUT-OFF GRADE DEFINITIONS2.1Breakeven Cut-off GradeAlso referred to as a “fully-costed” or “site” cut-off, this calculation is used exclusive of other cut-off's when there is no excess mining or milling capacity (which is rarely the case). For an underground operation, a break-even cut-off must cover all fixed and variable costs (including mining, milling, general and administration [G&A], gross royalties, transport and shipping costs, smelting and refining costs, limits to payable metals and refining penalties for deleterious metals). In the case of an open pit, all mining costs as listed above are accounted for during the optimization phase of pit limit planning. This assumes, of course, that pit optimization is an ongoing process and takes place at least annually, or any time that costs, recoveries, actual results and/or other factors affecting the ultimate pit shell change. Ideally, the optimization process should use the same costs, recoveries and assumptions as used for cut-off grade calculations. Once the optimum pit extents have been determined the mining cost should not be included in the cut-off calculation. The decision to mine the material has been made, the cost incurred; the only task remaining then is to determine the routing of the material. Routing may be based on contained grade and mineralogy assuming contained value is sufficient to pay for the remaining costs to process and, if necessary, to stockpile and subsequently rehandle.A break-even cut-off calculation for an underground mine should not include sustaining capital (other than as noted below), capital development or taxes but must cover total site costs. Capital items or expenses deemed to be directly proportional to ore tonnage (tailings dam or leach pad expansions, for example) must be fully accounted for in the calculation of cut-off grade. The break-even cut-off grade will vary across a given site, depending on mining methods and their respectivecosts, transport distances, metallurgy, differing royalty regimes and/or other characteristics affecting the final costs of production.It is important to note that calculations of break-even cut-off grades contain no profit assumptions (hence the “break-even” designation). Because break-even cut-off grades are the basis for the estimation of mineral reserves, it is technically possible (although highly unlikely) to have an ore reserve that generates no profit to the company.The following is a simple example of the method used to calculate a break-even cut-off at an underground mine (g/t):U/G Break-Even Cut-off Grade (BCOG) is calculated from the following equation:Where:∙Revenue = BCOG x Recovery x (Metal Price – Refining Costs – Gross Royalties)∙Operating Costs = Mining Costs + Process Costs + G&A CostsThus,()Where:∙Mining Costs = total mine operating costs (include operating development costs, exclude capital development costs)∙Process Costs = total process operating costs∙G&A Costs = total general and administrative costs∙Recovery = planned recovery of metal∙Metal Price = gold price in $/oz.∙Refining Costs = smelter, refinery and transportation costs in $/oz.∙Gross Royalties = non-NSR or net profits royalties (if applicable) in $/oz.∙Recovery = metallurgical recovery as a percentage2.2Incremental Cut-off GradeAn incremental cut-off grade, also referred to as “Marginal Cut-off Grade”, is applied if either of the mill or mine is not operating at full capacity or if the concept of “next best ore” applies.At an underground operation, incremental material must carry only the variable portion of mining costs (drilling, blasting, mucking, hoisting haulage), process operating costs, G&A costs, gross royalties and, if stockpiled, the associated rehandling costs. Development costs, both capital and operating, should only be included in incremental cut-off grade calculations if the development is necessary only to mine the incremental ore and would not be carried out otherwise. Any incremental process capital costs required to process the incremental ore (i.e. tailings dam expansions) must be considered as well, if applicable, and be included in incremental cut-off grade calculations. Incremental grade ore should never displace the processing of break even cut-off grade ore if it is available. If the mill is operating at capacity and the mine has the ability to provide material for placement in stockpiles, then incremental grade material can be set aside for later processing, provided it can additionally bear the fixed portion of processing and G&A costs, as well as the costs associated with rehandling.In the case of an open pit, Incremental Grade ore must carry any incrementaltransport costs (i.e. any haulage and/or conveying costs over and above the cost required to move the material to the appropriate waste dump), incremental capital costs (tailings dam and/or leach pad expansions), gross royalties, and only the variable portions of process operating costs and G&A costs. In a similar fashion, if haulage costs to process facilities or stockpiles are lower than the haulage costs to waste pads the savings should appear in the ICOG calculation as a credit. If the pit is capable of producing more incremental grade material than the mill is able to process, the incremental grade material can be placed in stockpiles if it can bear the associated portion of the cost of stockpile construction, maintenance and future rehandling. In the case of long-term stockpiles (i.e. those that are planned to be processed once mining has been completed) the material must additionally be able to bear the fixed costs related to processing and G & A.The following is an example of a simple incremental cut-off grade (ICOG) calculation (expressed in units of gram/tonne) for short term stockpiling (variable cost inclusion only shown):Where:∙Revenue = ICOG x Recovery x (Metal Price – Refining Costs – Gross Royalties)∙Operating Costs = Variable Mine Costs + Variable Process Costs + Variable G&A Costs Where:∙Mine Costs = all direct mining operating costs beyond pit crest + variable mine support costs∙Variable Process Cost = portion of process operating costs attributable to incremental ore ∙Variable G&A Costs = portion of G&A costs attributable to incremental ore∙Recovery = planned recovery of metal∙Metal Price = gold price in $/oz.As discussed above, depending on U/G mining statuses, there could be several incremental cut-off grades for the same mining area.2.3Mill Cut-off GradeAs with an incremental cut-off grade, a mill cut-off grade is applied if the mine or mill are not at capacity or if the concept of “next best ore” applies. This cut-off grade is applied to low grade material that must be broken and removed from the mine but which does not meet either break-even or incremental cut-off grade criteria.In an underground mine, it is usually comprised of material from development headings. In order to qualify for milling, such material must be able to bear the additional portion of the variable costs incurred by additional material handling needs which would not be required if the material were to be treated as waste. Underground costs might include additional transport costs due to increased hauling or tramming distances, additional equipment operating expense, underground crushing, hoisting and others. Surface handling, process and refining expenses must be included in mill cut-off grade calculations as well. If the mill is operating at capacity with material at or above the break-even cut-off grade and the mine has the ability to provide material to stockpile, then the MCOG material can be set aside for later processing, provided it can bear the additional cost ofrehandling. Mill cut-off grade material should never displace break-even cut-off gradematerial as mill feed.The following is an example of a simple underground mill cut-off grade (MCOG) calculation expressed in gram per tonne:Where:∙Revenue = MCOG x Recovery x (Metal Price – Refining Costs – Gross Royalties)∙Operating Costs = Variable Mine Costs + Variable Process Costs + Variable G&A Costs()( ) Where:∙Variable Mine Costs = (ore handling costs – waste handling costs) + surface rehandle costs ∙Variable Process Costs = portion of processing operating costs attributable to incremental ore∙Variable G&A Costs = portion of G&A costs attributable to incremental ore∙Recovery = metallurgical recovery expressed as a percentage∙Metal Price = gold price in $/oz.∙Refining Costs = smelter, refinery and transportation costs in $/oz.∙Gross Royalties = non-NSR royalties (if applicable) in $/oz.For an Open Pit mining, MCOG is used for reporting reserves within an optimised pit.2.4Cut-off grade for an orebody with multiple metalsWhen significant revenue is recovered and received from more than one metal in the same orebody it is often convenient to use the concept of “an equivalent grade”. Ideally, an equivalent grade is expressed through the primary metal that is recovered (i.e., copper equivalent grades in Cu-Au deposits). In practice the preferred methodology is based on deriving the contained metal values per tonne of finished product (generally per tonne of concentrate) using the appropriate representative recovery rates for each metal and deducting the applicable penalties, smelter charges, transportation costs, refining fees and assay costs. When this is the case, the equivalent combined metal cut-off grade is calculated by relating the value of the two or more contained metals to each other.2.5DiscussionThe cut-off grades and concepts described apply across the full spectrum of reserve accounting, from summarizing global resources for an exploration project to making daily production calls in an operating mine. It is common to define a cut-off grade for ore reserves which is quite different for the actual cut-off grade applied to the operations. Usually the operational COG reflects the economic realities and the reserve COG reflects long term strategic plans.In practice, operations are likely to require more than one cut-off grade for each of these types due to differing mining and processing costs. Factors including the mining methods in use, variable ore types and mineralogy, different process streams and metallurgical recoveries, changes in work indices, ore source locations, related haulage distances and multiple royalty regimes can all cause significant variability in mining, milling and smelting costs. In order to obtain relevant cut-off grades to maximize NPV and optimize mine life we must ensure that costs are calculated accurately and fully for each of the combinations of factors throughout the mining cycle.All cut-off grades assume fully diluted and actual ore values that are deliverable to themill, not in-situ values. If planned grades are used in calculations but are not being achieved in mill feed, maximal NPV is not going to be obtained and possibly significantly reduced. It is imperative therefore that planned or designed grades be compared to those actually achieved and suitable adjustments be made to ensure that the most appropriate grade value be used for cut off grade calculations. Additionally, when more than one mining method is used at an operation, an accurate dilution factor should be applied per method, and, when adequate grade reconciliation data exists, should be adjusted to reflect actual results rather than assume that planned dilution properly represents actual results.There are a number of limitations, using cut-off grade for reserve estimation, including:∙Various categories of cost are totalled without consideration of timing. As the expenditure on underground development can precede the cost of stoping (and recognition of revenue from ore contained in stopes) by in excess of a year, the present value of this expenditure is larger than would be considered in a cut-off grade calculation.∙The tax implications of various categories of expenditure are not considered. Depreciation and amortisation of capital expenditures (including capitalized waste stripping and development) can have a significant impact on the magnitude and timing of cash taxes paid.∙Cost elements are seldom 100% fixed or variable. It is difficult to accurately estimate the true incremental costs associated with mining a particular stope without use of a bottom up cost model from which an incremental analysis of costs can be made.Consequently, best practice in reserve estimation should involve the following iterative approach, where the cut-off grade(s) is used only to identify potentially economic material.∙Cut-off grades are applied to the mineral resource model, based on the expected cost structure for the strategic option selected. These define resource blocks that are potentially economic.∙Stope outlines are designed for potentially economic resource blocks that are classified as measured or indicated. These outlines must take account of factors for mining recovery and dilution.∙An LOM schedule is generated for potentially economic stopes.∙Operating and capital cost estimates are prepared for the schedule and economic analysis performed. Stopes that are not economic are removed from the schedule and the remaining material is re-evaluated. This process should be repeated until no uneconomic material is included in the LOM schedule.∙The material included in the LOM schedule is classified as proven or probable reserves, based on the confidence of geological and economic estimates.∙Risk analysis should be performed to determine the sensitivity of reserve tonnage to factors such as metal price.It is the simplest way to use cut-off grades for reserve evaluation. One of the key assumption is the mine is mostly (if not totally) developed for an underground mine. If there is a new and isolated ore zone, which requires significant decline/incline developments and/or ventilation shafts, then a proper pre-feasibility (or feasibility study) is required.3 CONCEPT OF NEXT BEST ORETo maximize the value of mining/processing operations it is necessary to maximise the output of recovered metal as early as possible in the life of the mine. While it is normally not feasible to schedule mine production to deliver the highest production grades early on in the mine life followed by declining head grades as the mine matures and reserves are depleted, it should always be attempted (provided this strategy does not reduce operating efficiency or the optimal recovery of ore). The ongoing goal is to follow sound mining and processing strategies to make the highest grade material available and enable the most effective cashflow possible. This is significantly aided with the creation and utilization of graded stockpiles and well considered stockpile strategies.For an underground mine, the mining strategy/sequence must be thoroughly analysedbefore any detailed scheduling starts by using any schedule package. In general, the mine development is usually the critical path, which is required for stoping and diamond drilling. Once mine design is done, the in-situ oz per jumbo development metre may be used for determining the mining strategy/sequence. The higher priority should be given to the area with higher Oz per development metre.4 COST ESTIMATIONOperational costs fall into two categories, variable and fixed, so that the appropriate expenses can be suitably applied for cut off grade purposes. The following general definitions and examples are included to demonstrate the difference between fixed and variable costs and their inclusion in the calculation of appropriate cut off grades.Fixed Costs –Those costs which do not change directly with a change in production or throughput. Examples of fixed costs include labour, G&A costs (assuming extra staffing is not required as a result of increased throughput), overheads and others. BCOG calculations must include all fixed costs considerations, calculations of ICOG and MCOG should not except at the end of mine life when all site costs must borne by the remaining stockpiled material.Variable Costs –Any portion of operating costs that vary with a change in production or throughput. Examples of variable costs are power sources (e.g., diesel fuel consumption increases as tonnage moved rises), consumables, and equipment operating and maintenance costs among many others. It is noted that, in some cases, certain costs have both a fixed and a variable component and care must be taken to ensure that both are considered and used in cut-off grade calculations accordingly. An example of this instance is the case of electrical power consumption –the fixed portion of the electrical cost is that which would normally be incurred with lighting and heating power consumption while the variable portion is that which is additionally consumed with increased throughput due to the processing of incremental ore. Any changes in costs should be followed by recalculation of Cut-off Grades. For the calculation of incremental COGs, only variable costs should be included in calculation as it is considered that the fixed costs are borne by the material at or above BCOG. In essence then, any additional throughput, provided the material can cover all the variable costs associated with it, has the potential to add to the NPV of the operation and therefore should be segregated, stored and processed whenever possible, as long as it does not replace higher-grade material at BCOG or above. The exception, as previously noted, is when mining operations have ceased and no more BCOG material is produced. At this point in time, and beyond, the remaining material being processed must bear both variable AND fixed costs.It is critical that the costs used in cut-off grade calculations are as accurate as possible using current consumable pricing, labour rates, equipment operating and maintenance costs. Future price increases, as may be known or can be projected reasonably, should be considered as well.5 METALLURGICAL RECOVERYMetallurgical recovery is a critical variable in cut-off grade calculations as inaccurate values used in cut-off grade calculations will lead to misrepresentative COGs and could ultimately affect NPV and mine life. Metallurgical recovery is expressed as a percentage that indicates the portion of the contained metal mined and sent to the mill that may be recovered through processing. It is very important to monitor feed grade and throughput tonnages as best as possible so that recovery calculations are based on accurate data. Sampling techniques should be reviewed on a regular basis, an adequate number of samples to obtain representative results must be taken and weightometers and other instrumentation should be calibrated regularly to ensure valid results. Recovery is typically dependent on the type of ore, and it may be quite variable throughout a given deposit. When historical data does not exist, metallurgical recovery estimates are based on results from test work or pilot plant processing studies. In some cases, and with proper justification preferably based on full-scale experience, bench and/or pilot plant results may be adjusted(upwards or downwards) to reflect such experience. Proper supporting documentationis required. When, for the same ore body, historical data is available, efforts should be made to "calibrate" the laboratory procedures to simulate the actual plant performance. These models/procedures should be updated periodically. On that basis, plant historical performance can be taken into account to predict recovery and costs, while ensuring that the ores to be fed have been tested and it appears reasonable to use such database interpretation to confirm expected performance. In other words, ores to be fed to the plant that are included in the LOM and Reserve/Resources calculation should be tested to compare their response to the models and ensure that there is no significant deviation. Should significant deviation exist, further investigation to determine the nature and root causes must take place so that the best estimation of predicted recovery may be used for COG calculations.Typically, recovery is also dependent on grade, and therefore grade-recovery curves should be developed and utilized. Accurate definition of the recovery at and near the actual COG is very important and must be emphasized. The work index, the mineralogy and blending of the various ore types all affect metallurgical recovery. In addition, test work should focus on optimising recovery and thoroughly understanding the metallurgical characteristics within different areas and zones throughout the ore deposit. Cut-off grade calculations should be made and reported for all ore types which result in significantly different recoveries; if processing methods used vary with ore characteristics, appropriate costs and recoveries must be used for the determination of the best and most representative cut-off grades for each of the specific process methods.Personnel responsible for reporting resources and reserves must diligently monitor actual processing plant recoveries and compare them with the recovery parameters used for prior estimates to assure that they correlate. When reconciliations between the resource model and plant production indicate that adjustments are necessary, these must be communicated and implemented prior to the next reporting deadline.6 CUT-OFF GRADE REPORT REQUIREMENTSFor Cut-Off Grade reporting the following items must be included as appropriate, for both underground and open pit operations (and, if not applicable for a given site, it should be stated that the requirement does not apply, and why):•Concise mention of metal prices, and exchange rates used for both reserve and resource calculations.•Cut-off grades summarized in table format including O/P and U/G cut off grades with all pertinent cut-off grades included (BCOG, ICOG, MCOG) for all relevant locations (i.e.different pits, mine zones, mineralogy, mining methods etc.) for both reserve AND resource metal prices, sensitivities for based on dollar values (i.e., +/- $50/oz Au) or a percentage difference.•Multi metal mines, equivalent grade calculation methodology.•Tabular summary of cost centres (mining methods, locations, processing circuits, recoveries, G&A and smelting, refining, royalties information) for significant cost regimes.•Comments, explanations and rationale for price / breakdown of variable and fixed cost components, which are used for ICOG and MCOG along with implications at end of mine life for O/P stockpiles.•Mine, mill and, if appropriate, smelting/refining capacities stated with historical and projected throughputs stated, as well as reasons for changes included (i.e. upcoming mill expansions, equipment downtime impacts on past performance etc.). What is constraint at MCOG? How close are mill/mine outputs, rated and actual throughputs?•Stockpile strategies employed, past, present and upcoming changes based on current COG calculation.•Comparison of past, current and future COGS, both calculated and those used for operating strategies with clear rationale included.•Major cost drivers, consumable pricing strategy (upcoming more important than historical, though both should be included for comparison sake) with clearly stated currency unitsused, best estimates of future pricing based on material supply contracts,labour agreements etc.•When consumable pricing varies from corporate guidelines, explain reasoning for the variance.•Sustaining capital – perceived definition, upcoming needs and why?•Mining dilution factors used, as well as comparison of planned vs. actual dilution (with brief description of reconciliation methodology used).•Actual mill grade vs. planned mill grade with explanation of variances.•Process recoveries, actual performance, variances and rationale for values being used, Grade and recovery curves included, for varying process methods, mineralogy and for each valued contained metal.•Clear statement of royalties, royalty cost / oz., applicable local, regional (state) taxes, smelter charges, penalties, how by-product credits are handled in COG calculations, transportation costs, all other relevant expenses and costs.• A brief statement about development costs for u/g mines, what is considered capital and operating development, what determines if operating development costs are included and when, how operating costs are calculated and what is the strategy / decision making process regarding identification and pursuit of incremental ore?•Costs, often actual and 3 year averages should be stated consistently, currencies and units (metric or imperial) stated explicitly in every table.7 LIMITING CAPACITIES AND SUBSEQUENT STRATEGIES7.1The Role of StockpilesProvided space is available, material should be stockpiled when mine ore output exceeds the mill capacity to process ore at or above Break-Even Cut-off Grade. In this case the excess mine capacity is most efficiently used to create stockpiles. The following three cases may exist:The mine is producing all available break-even ore, but the total amount of break-even ore produced is less than the total ore producing capacity of the mine. Emphasis should be to increase availability of BCOG ore supply and use excess capacity in the short term to stockpile ICOG, then MCOG materials. In line with the “Next Best Ore” concept, the lowest grade or lowest net revenue material should be stockpiled and highest grade material available processed preferentially.If any stockpiled material remains unprocessed at the end of mining activities, this material must also bear the full burden of the remaining site costs (both fixed and variable). The quality of the ore after being in the stockpile must also be considered if, for example, the stockpiled material oxidizes and recovery will be reduced.A potential third case is the stockpiling of mineralized material that is below the mill cut-off grade in anticipation of an increase in metal prices and/or improvements in processing costs or recoveries that could make the material economic at some point in the future. Stockpiles containing material below the current mill cut-off grade should not be reported as reserves because the material is not economic and, thus should not carry non-cash costs, including depreciation and depletion. If the mill consistently runs at capacity while processing underground ore with grades at or above, the break-even cut-off and the mine frequently encounters material between the incremental cut-off grade and the break-even cut-off grade that is left unmined a potential opportunity may be lost. When this occurs, the feasibility of increasing mine production and expanding the mill should be considered.7.2Possible ScenariosMine limited production: Most underground mines fall into this category. Processing facilities are able to process as much tonnage as the mining operation can deliver due to mine production and materials handling limitations. In this case, operational strategy should be to keep the process facility operating at, or as near as possible, to full throughput. To achieve maximum metal recovery any material meeting at or above BCOG should be prioritized and delivered for processing,。
地质勘查常用公式
地学中常用公式一、平均品位的计算公式：1、算术平均：(X1+X2-……+Xn)／n X1、X2、X n为样品品位2、加权平均：(X l×L l+X2×L2+……+ X n×Ln)／(L l+L2+……+L n) X1、X2……X n。
为样品品位，L l+L2+……+Ln为样品长度3、几何平均为Xn2⨯1 X1、X2、Xn为样品品位X⨯n⨯X注：品位为正态分布时，处理特高品位时，可用此公式。
二、矿体厚度(Vm)、品位(Vc)变化系数：—X=(X1+X2+……+Xn)／n 计算矿体厚度、品位的平均值∑-σ计算均方差XXi(2n=)1-/()厚度、品位变化系数：Vm或Vc=⨯σ100％÷X三、地质剖面岩石厚度计算公式：y=sinα·cosβ·cosγ±cosα·sinβα--导线坡度角β--地层倾角γ --导线方向与地层倾角的夹角地层倾向与坡向相反取正号，地层倾向与坡向相同取负号；真厚度=L×y四、钻孔矿体厚度的确定矿体的厚度是根据矿体露头上、坑道中和从钻孔中所获得的资料进行的。
(一)坑道中矿体厚度的测定当坑道所揭露的矿体与围岩的接触界线清楚时，取样和编录时可在矿体上用钢尺直接捌量出来。
厚度测量的次数决定于坑道的布置情况，如矿体是用穿脉坑道圈定的，则测量次数与穿脉坑道的数量相符。
如果矿体是用沿脉坑道圈定的，则厚度的测定按一定间隔在取样的位置进行测量。
如果矿体与围岩的界线不清时，矿体厚度的测定必须根据取样结果来确定。
(二)钻孔中矿体厚度的测定因为钻孔中所截穿的矿体均在地下深处、只能间接地去测定矿体的厚度。
当钻孔是垂直矿层钻进时，且岩心采取率为100％，可直接丈量岩心，取得厚度的数据。
若岩心采取率不高，除用钢尺丈量岩心长度外，还要按下式进行换算：L (11-9)mn式中： m——矿体的厚度(米)；L——实测矿心长度(米)In——矿心采取率(％)。
陈志康 勘界测量报告书
编号: 001土地勘测定界技术报告书用地单位: 贵州大学项目用地名称: 贵大勘界测量书勘测定界单位: 贵州大学2012-12-20目录土地勘测定界技术说明 (3)勘测定界表 (5)勘测面积表 (6)宗地分类面积表 (7)土地分类面积表（集体） (7)地块面积及界址点坐标成果表 (10)外围界址点成果表..................... 错误!未定义书签。
项目用地地理位置图. (14)界址点点之记 (14)贵大勘界测量书用地土地勘测定界技术说明为测定贵大勘界测量书建设项目用地的面积、土地利用现状和使用土地的界址, 受贵州大学的委托, 由贵州大学对该项目进行土地勘测定界。
一、工程项目勘测定界依据1. 关于贵大勘界测量书项目初步设计的批复（批复文号）；2. 《土地勘测定界规程》；3. 《土地利用现状调查技术规程》；4. 《城镇地籍调查规程》；5. 《全国土地分类》（过渡时期适用）6. 贵州大学提供的工程总平面设计图、测量控制点成果等。
二、施测单位及日期该项目勘测定界由贵州大学承担, 2012-12-20至2012-12-20完成外业作业及内业整理。
三、勘测定界工作情况1. 外业调查情况(1)权属调查情况从当地国土资源管理部门搜集用地范围内土地利用现状调查及土地登记中的权属资料, 并对分幅权属界线图、权属来源证明文件等进行了审核, 将审核合格的行政界线、权属界线转绘到工作底图上；对无上述权属证明材料或权属界线模糊、不清的, 在各级国土资源管理部门的配合下, 组织原权属单位有关人员按《土地利用现状调查技术规程》和《城镇地籍调查规程》要求现场指界, 并将用地范围内的权属界线测绘到工作底图上。
(2)地类调查情况依据《全国土地分类》（过渡时期适用）、《全国土地分类》（试行以地籍图、土地利用现状图以及地形图上的地类界线, 通过现场调查及实地判读, 将用地范围内及其附近的各地类界线测绘或转绘在工作底图上, 并标注三级地类编号。
露天开采境界边界品位的合理确定
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维普资讯
第３ Ｏ卷 第 ６期 ２０ ０ ６年 １ ２月
中 国
钼
业
Ｖ ｌ３ ｏ ６ ｏ ＿０ Ｎ ．
Ｄ ｃ ｍｂ ｒ ２ ｏ ｅ ｅ ｅ ｏ ６
Ｃ ＮＡ Ｍ０Ｌ ＨＩ ＹＢＤＥＮＵＭ ＮＤＵＳ Ｉ ＴＲＹ
露 天 开 采 境 界 边 界 品位 的合 理 确 定
（ ． ｈｎ ｓ ｃｄｍｙｏ Ｌ ｎ ｎ ｅｏ ｒｅ ｃｎｍｉ ，ａ ｈ ６ ２ ， ｅ ｅ ， ｈｎ ） １ Ｃ ｉｅｅＡ ａ ｅ ｆ ａ ｄａ ｄＲ ｓｕｃｓＥ ｏ ｏ ｃ Ｓｎ ｅ０ ５ ０ Ｈ ｂｉＣ ｉａ ｓ １
（ ． ａ ｃａ ｇＥ ｇｎ ｅ ｎ ２ Ｎ ｎｈ ｎ ｎ ｉｅｒ ｇ＆ Ｒ ｓａｃ ｎｔｕｅｏ ｏ ｆ ｒｕ ｔ ｓ Ｎ ｎ ｈ ｎ ３ ０ ０ Ｊ ｎｘ ， ｈｎ ） ｉ ｅｅｒ Ｉｓ ｔｔ ｆ ｎｅ ｏ ｓＭｅ ｌ， ａ ｃａ ｇ３ ０ ０ ，ｉ ｇｉＣ ｉａ ｈ ｉ Ｎ ｒ ａ ａ
起到重要作用 ， 但是 随着我 国市场经济体制 的改变 和产品售价与成本的变化 ， 原有 的工业指标越来越
矿区边界数据分析报告
矿区边界数据分析报告1. 引言矿区边界的准确定义是矿区管理和规划中的重要环节。
矿区边界准确定位与确定涉及矿区管理、矿权划定、环境保护等问题的重要。
本文通过对矿区边界相关数据的收集和分析，旨在为相关决策提供科学依据。
2. 数据来源与收集本次矿区边界数据分析的数据主要来源于地理信息系统（GIS）技术和遥感卫星图像。
通过遥感手段获取高分辨率卫星图像，以及地面实地勘察、测绘等，获取矿区范围的相关信息。
3. 数据处理与分析方法在数据处理方面，对采集到的卫星图像进行了影像处理和地物分类。
通过卫星影像的几何校正、辐射定标和拼接等步骤，获得高质量的图像。
同时，使用GIS软件对地物进行划分和分类，对矿区地物和非矿区地物进行准确的分类。
在数据分析方面，从以下几个方面对矿区边界数据进行了分析：3.1 地理空间分析通过GIS技术将矿区边界数据与其他与其相关的地理数据进行叠加分析，揭示矿区边界的地理分布规律。
同时，可以对矿区边界周边的地理环境进行评估和预测，为矿区管理和环境保护提供科学依据。
3.2 空间统计分析通过统计学方法对矿区边界范围进行了分析，包括面积、周长、形状等参数的计算和统计。
通过这些统计参数，可以进一步评估矿区的规模和形态，并与相关规划和管理标准进行比对。
3.3 遥感影像分析通过遥感影像的解译和分析，确定矿区边界的具体位置，并提取矿区内、外的地物信息。
通过对矿区内的地物类型、分布情况和变化趋势进行分析，可以更加全面地了解矿区的开发和利用情况。
3.4 时间序列分析通过对历史遥感数据的分析，可以得到矿区边界在一定时间段内的演变与变化情况。
通过时间序列分析，可以揭示矿区开采活动对边界的影响，并对未来矿区边界的变化进行预测。
4. 数据分析结果通过对矿区边界的数据处理和分析，得到了以下结果：4.1 矿区边界的空间分布规律明显，与地质构造和矿产资源分布存在一定的关联性。
4.2 矿区边界的形状多样，但整体上呈现出一定的规则性。
基于蒙特卡洛模拟的有色多金属矿山边界品位动态优化管理
基于蒙特卡洛模拟的有色多金属矿山边界品位动态优化管理钟旭东;陈建宏;刘浪
【期刊名称】《黄金科学技术》
【年(卷),期】2014(000)002
【摘要】为了充分利用矿产资源，提高多金属共伴生矿企业的经济和社会效益，提出了运用蒙特卡洛模拟数学方法，结合计算机技术进行边界品位测算的新方法，并简述了实现过程。
通过系统地研究矿山生产投入参数，建立相关数学模型，最后利用SQL Server 2008数据库软件和.NET 4.0软件开发平台，研发了一套多金属矿边界品位动态优化管理系统。
通过在某多金属矿的应用，该系统实现了矿山技术经济指标和生产成本的动态管理，并得出了最优边界品位。
【总页数】5页(P55-59)
【作者】钟旭东;陈建宏;刘浪
【作者单位】中南大学资源与安全工程学院，湖南长沙 410083;中南大学资源与安全工程学院，湖南长沙 410083;中南大学资源与安全工程学院，湖南长沙410083
【正文语种】中文
【中图分类】TD9
【相关文献】
1.基于蒙特卡洛模拟的矿山投资风险分析 [J], 金胜;胡福祥
2.基于MATLAB的铀矿山井底车场列车排队系统蒙特卡洛模拟 [J], 洪昌寿;李向
阳;胡鹏华;李先杰;叶勇军;谢东
3.基于蒙特卡洛模拟的Z水电项目进度与费用偏差\r分析动态仿真 [J], 李咏梅;赵正佳
4.基于蒙特卡洛模拟的Z水电项目进度与费用偏差分析动态仿真 [J], 李咏梅; 赵正佳
5.基于蒙特卡洛模拟信息不完全下双寡头垄断市场动态研究 [J], 刘曌[1]
因版权原因，仅展示原文概要，查看原文内容请购买。
露天开采时矿体边界品位动态优化的神经网络方法
露天开采时矿体边界品位动态优化的神经网络方法
黄光球;桂中岳
【期刊名称】《中国矿业》
【年(卷),期】1996(005)004
【总页数】6页(P65-70)
【作者】黄光球;桂中岳
【作者单位】不详;不详
【正文语种】中文
【中图分类】TD854
【相关文献】
1.沙溪铜矿开采边界品位动态优化方法 [J], 蒋成荣;彭平安;王李管
2.露天开采矿体边界品位动态优化新方法 [J], 黄光球
3.地下开采时矿体最小工业品位动态优化的神经网络方法 [J], 黄光球;桂中岳
4.地下开采矿体边界品位的确定方法 [J], 初道忠;王青;丁一;刘建兴
5.中厚缓倾斜矿体露天开采顶底板三角体处理方法 [J], 周文勇
因版权原因，仅展示原文概要，查看原文内容请购买。
边界品位计算报告-陈建宏(20080802)
1.3 国外边际品位研究和应用现状
（1）Ulf Henning。首次对Berry所述的用单一
值的动态盈亏平衡品位指标来指导整个矿山服务
年限内的开采活动的做法提出了质疑。他认为： “为了使矿山开采的净现值达到最大化，必须在
整个开采时期不断地调整其最优边际品位，而这
种指标系列是逐步递减的”，他用一个数值案例 证明了这一点。它所分析的案例是以地下开采为 研究对象，所做的成本分析过于粗略。
项目背景
生产矿山边界品位的测算是一个非常复杂的课题，涉
及地质、采矿、测量、选矿、冶炼及市场营销、国家政策 等多方面因素。制定理论先进、可操作性强的边界品位测 算实施方案是一项理论性较强、工作量很大的困难工作， 它不仅在理论上需要进行论证和突破，在传统观念和习惯 上也需要突破，这些工作必须通过大量的调研，在充分收 集资料的前提下，建立资源数据库和矿山企业技术经济指 标数据库，在此基础上，制定边界品位测算办法实施细则， 最终建立适应市场经济的资源/储量的动态管理系统，到达 充分利用资源，保证企业有良好的经济效益的目的。
5. 随着计算机应用的发展和应用数学的发展，边际品位最优化方 法与模型将越来越具有可应用性。
1.3 国外边际品位研究和应用现状
西方国家实行市场经济，矿山企业对其效益极为关 心，因此，对品位问题的研究起步也很早，并逐步取得 了显著的成果，形成了一套完善单指标体系，对边际品 位实行动态管理。 我国长期以来实行计划经济，而且采用与西方不同 的双指标体系，加之西方国家边际品位研究发展迅猛时 期正值我国的文革期间，因此，我国研究人员在对西方 边际品位研究思想与方法演变的分析评论方面的工作做 得较少。下面对西方国家有关品位优化研究主要成果进 行简要评述。
1.3 国外边际品位研究和应用现状 3、上世纪60年代中期至70年代中期 这一时期的研究，从其理论上来说，可以说达 到了一定的高度，其分析内容上考虑了诸多的影响 因素，从其分析的逻辑上看，更具系统性。这一时 期研究的显著特点是将品位分布、成本收益结构、 资金时间价值、生产能力平衡关系等，统一地纳入 到边际分析的框架下来，是边际分析法形成的主要 时期。
边界品位的确定
G m c g m
= g c = g m c
if
i f i f
g g m c m g m c g c g g g m m c c
二、最大现值法(Lane 法）确定 边界品位
最佳边界品位
Vm Vc Vm Vc
gmc
gm
gc
边界品位
图16 - 5 Vm与Vc随边界品位变化示意图(情形II)
g r p ' Cr Cr gp
(16 - 12)
一、盈亏平衡品位计算
•价值与成本计算 ：
故：
gr p M C C C c m p r g p
Mv = rp rr Pr
(16 - 13)
若金属的售价为Pr，Mv可用下式计算
(16 - 14) (16 - 15)
(16 - 16)
(16 - 21)
gp C C Wg m p c p 当最终产品为精矿时： g c r p p p
(16 - 22)
因此，当块段品位高于gc时，将其作为矿石送往选厂要 比作为废石送往排土场更为有利。值得注意的是，当块段的 品位刚刚高于gc时，将其作为矿石并不能获得盈利， 然 而 既 然 块 段 必 须 采 出， 将 其 作 为 矿 石 处 理 的 亏 损 小 于 作 为 废 石 处 理 的 成 本， 故 仍 然 将 其 划 为 矿 石。
二、最大现值法(Lane 法）确定 边界品位
最佳边界品位
Vm
Vc Vm Vc
gm
gmc
gc
边界品位
图16 - 4 Vm与Vc随边界品位变化示意图(情形I)
二、最大现值法(Lane 法）确定 边界品位
最佳边界品位
还 可 能 出 现 图16 - 5 和 图16 - 6 所 示 的 两 种 情 形。 在 图16-5所 示 的 情 形 中， 最 终 边 界 品 位 为 g m； 在 图16 - 6所 示 的 情 形 中， 最 终 边 界 品 位 为 g c。总 结 上 述 讨 论， 当 同 时 考 虑 采 场 与 选 厂 时 ， 最 佳 边 界 品 位 Gmc 可 用 下 式 求 得：
460FLAC3D应用於地下储集层岩盘应之分析
第二屆資源工程研討會論文集460FLAC 3D 應用於地下儲集層岩盤應力之分析陳建宏1、丁原智2摘要國內位於苗栗之鐵砧山油氣田為臺灣最大的油氣田，自1965年開始生產以來，歷經30餘年的開採已漸枯竭。
因此目前利用此氣田作為地下儲氣窖，目的為儲存天然氣，就近調節北部天然氣尖峰、離峰時段之用氣需要。
本研究之目的即在於了解儲氣層之應力狀態，以確保地下儲氣窖之有效儲氣能力及產能。
研究架構主要分為三個部分，分別為：(一)應用井孔崩落(Borehole Breakouts)分析，找出儲氣層中水平最大主應力(H σ)之方向；(二)應用有限差分軟體FLAC3D ，評估地層應力大小；(三)應用倒傳遞類神經網路分析，找出影響地層應力方向及大小之重要因子。
蒐集充足且合適之鑽井電測資料(Caliper log)為本研究最重要的工作之一，目前共蒐集有六口井之電測資料，經研究結果發現，鐵砧山地下油氣田的水平最大主應力方向介於N80.1W 至28.5W 之間，而地層中之側向最大水平壓力係數H K 的範圍約介於2至1之間，而側向最小水平壓力系數h K 的範圍約介於0.8至0.4之間，至於影響該地層應力大小最重要的因子，以目前電測資料來說是井徑(1-3)軸的大小。
關鍵詞：井徑電測資料、FLAC 3D 、井孔崩落、應力分佈ABSTRACTThe largest oil gas field located in Mount anvil of Miao Li in Taiwan. It’s been more than thirty years since the field began to produce oil gas in 1965. Due to it’s depletion, the gas field is now utilized as an underground gas storage reservoir to regulate the need of gas supply during peak and off-peak demand in northern Taiwan. The purpose of this research is to analyze the stress distribution of the underground NG storage reservoir formations. For securing the effective capacity and production of gas. The structure of this research is divided into three parts including: (1) breakout data analysis obtained from oriented four-arms caliper logs in 6 wells to provid the orientation of maximum horizontal stress (H σ); (2) estimate the stress distribution of the gas reservoir by finite-difference model FLAC 3D ; (3) apply Artificial Neural Networks (ANN) to reveal the factors that influence the stress distribution. The borehole breakouts and tensile fractures analysis results indicate that the average direction of the maximum horizontal stress,Hσ, is oriented approximately in N80.1˚W for TCS-A3 and N28.5W for TCS-B3 well. At 2700 m depth of theunderground NG reservoir the maximum horizontal stress is approximately between 1 and 2 of the vertical stress . The borehole diameter variation of the caliper(1-3) is the most important factor affecting the scale and directions of the stress of the reservoir.Keywords: heterogeneous, geophysical well logging, Chou-Shui-Shi alluvial fan, Levy-stable distribution.1 國立台北科技大學材料及資源工程系碩士班研究生 2國立台北科技大學材料及資源工程系副教授第二屆資源工程研討會論文集461一、前言舊氣田規劃或開發地下水層為地下儲氣窖早已行之有年，其主要目的為將天然氣注入地下儲氣層儲存並調節供氣生產。
采矿方法数值优化选择的直观表示法——蛛网图法
采矿方法数值优化选择的直观表示法——蛛网图法
陈建宏;林成义
【期刊名称】《有色金属：矿山部分》
【年(卷),期】1999(000)006
【摘要】针对采矿方法数值优化选择的不足，本文提出一种采矿方法数值优化选择的直观表示法－＝－蛛网图法，并通过实例进行了验证。
【总页数】3页(P12-14)
【作者】陈建宏;林成义
【作者单位】中南工业大学;中国有色金属工业总公司
【正文语种】中文
【中图分类】TD853.3
【相关文献】
1.确定核心期刊的直观表示法--蛛网图法 [J], 黄瑞金
2.计量经济学的几何直观化分析研究——直观几何方法及与巴伦坦图法的比较 [J], 董志勇;王丛
3.截面表示法柱平面图的自动识别方法 [J], 罗志伟;颜巍;蔡士杰
4.基于层次分析和灰色关联法优选采矿方法--以云南省某铁矿山的采矿方法选择为例 [J], 肖婷;陈玉明;杨仁华;杨宫印;朱宁
5.绘制扭矩图的一种简易方法——“直观绘图法” [J], 高庆华
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项目背景
目前，国内大部分矿山采用前苏联的双指标体系，西
方国家采用单指标体系，双指标体系侧重于资源的回 收，单指标体系侧重于获得最大的经济效益。
随着我国市场经济的深入以及矿业权市场的完善，资
源充分利用与企业经济效益，两者正在取得一致。
采用市场经济的手段代替政策手段保证资源的最大程 度的利用，这是本项目研究和实施的目的所在，它符 合当今矿产资源管理的发展趋势，具有重要的社会效 益和经济效益。
1.3 国外边际品位研究和应用现状
（2）Lane K.是近三十年来西方国家在边际品位经济优化研究中 具有代表性的人物之一。1964年，他曾经对传统的露天矿爆堆收 支盈亏平衡品位(要求选矿费用与精矿销售收入相平衡)的优缺点 作了系统的分析。他认为，收支平衡品位指标只能保证每吨矿石 的收入与露天矿境界内的生产费用之差不小于零，从而有可能使 逐年累计的精矿产量和矿山未贴现的总利润极大化，但由于平均 品位逐日的变化会使采、选、冶能力不相平衡，而且早期多利用 贫矿意味着推迟利用富矿，尤其是在价格上涨时也不能利用富矿 多产多销金属，经营者并不能充分发挥资源潜力。他主张先求出 可以充分发挥采、选、冶三种能力的三项经济上的极限品位指标 和使这三种能力两两均衡的三项均衡品位指标，然后从这六项品 位指标中选出最佳品位指标。至于收支平衡品位，他认为只是在 贴现率为零和采矿能力不足时的最佳品位指标。
2、上世纪20年代初至60年代中期 （1）资金时间价值的引入
1922 年， Berry 首先提出要用净现值来计算边际品位。并以资金时间 价值理论证明在传统盈亏平衡分析的基础上永久性地提高矿床边际品位 的合理性，其根据是以矿山企业利润最大化为目标，提高品位指标可以 尽早取得效益，从而带来时间价值。
（2）沉没成本概念的引入
1.3 国外边际品位研究和应用现状
（3）关于边际品位指标定义问题的研究 边际品位作为指导开采活动的指示器，它本身的含义就必 须很明确。Mortimer，Musgrove和Krige等人在此方面做了大量 的研讨。讨论的焦点是围绕着开采矿石所获收益对于它相应的 开采加工的成本补偿问题而展开的。Mortimer认为:“采出矿石 的平均品位应是能够提供某一最低额度的利润，而采出矿石的 最小品位应能抵偿其自身的开支。”这一简洁的思路，至今在 许多矿山的开采实践中得以体现。 （4）边际分析法的初步引入 边际分析法是新古典经济学的一个重要分析工具。在这一 时期里，研究者应用边际分析法研究矿石开采成本对边际品位 决策的影响，与边际分析法相联系的增量分析也得到了应用。
1.2 边界品位经济分析的意义
1. 从微观的角度来看，边际品位对矿山经济效益影响很 大。现实采矿作业中有时边际品位在高达士50%的范 围中调整，其对效益的影响十分敏感，它直接影响到 精矿产出量和相应的成本支出，品位的变化还会影响 储量，进而影响矿山寿命，因而它还与矿山的持续发 展问题相关。
2. 从宏观上看，边际品位的高低，影响到一个国家资源 量的多少，因此它还与国民经济发展规划、自然资源 有效利用等问题紧密相联系。 3. 从应用广泛性看，边际品位问题在矿业中非常普遍， 在黑色冶金矿山、有色金属矿山、黄金矿山都有边际 品位的经济优化问题，在化工矿山、非金属矿山中的 许多矿山中也有品位优化问题。
1.2 边际品位经济分析的意义
4. 从紧迫性看，国外市场经济国家对边际品位优化问题 一直非常重视，并通过合理优化取得了良好的经济效 益。而在我国，由于长期受计划经济的影响，这一领 域研究还没有受到足够的重视，需要深入研究和规范 化管理。尤其是，我们现在颁布了新固体矿产资源储 量计算标准，它要求从经济上深入考察矿产资源的经 济性，在边际品位上加强理论和方法研究。
项目背景
生产矿山边界品位的测算是一个非常复杂的课题，涉
及地质、采矿、测量、选矿、冶炼及市场营销、国家政策 等多方面因素。制定理论先进、可操作性强的边界品位测 算实施方案是一项理论性较强、工作量很大的困难工作， 它不仅在理论上需要进行论证和突破，在传统观念和习惯 上也需要突破，这些工作必须通过大量的调研，在充分收 集资料的前提下，建立资源数据库和矿山企业技术经济指 标数据库，在此基础上，制定边界品位测算办法实施细则， 最终建立适应市场经济的资源/储量的动态管理系统，到达 充分利用资源，保证企业有良好的经济效益的目的。
1918年，经济学家G卡塞尔在他所著的《社会经济原理》中 提出：计算矿石总量的价值要引入折现的方法。1919年，H.D霍 斯尔德在《工程师评价手册》也提出，估算矿石储量价值要考虑 资金的时间价值。这些早期的思想对矿石品位指标的研究极富启 发性，其影响是非常深刻的。
1.3 国外边际品位研究和应用现状
1.3 国外边际品位研究和应用现状
（1）Ulf Henning。首次对Berry所述的用单一
值的动态盈亏平衡品位指标来指导整个矿山服务
年限内的开采活动的做法提出了质疑。他认为： “为了使矿山开采的净现值达到最大化，必须在
整个开采时期不断地调整其最优边际品位，而这
种指标系列Байду номын сангаас逐步递减的”，他用一个数值案例 证明了这一点。它所分析的案例是以地下开采为 研究对象，所做的成本分析过于粗略。
5. 随着计算机应用的发展和应用数学的发展，边际品位最优化方 法与模型将越来越具有可应用性。
1.3 国外边际品位研究和应用现状
西方国家实行市场经济，矿山企业对其效益极为关 心，因此，对品位问题的研究起步也很早，并逐步取得 了显著的成果，形成了一套完善单指标体系，对边际品 位实行动态管理。 我国长期以来实行计划经济，而且采用与西方不同 的双指标体系，加之西方国家边际品位研究发展迅猛时 期正值我国的文革期间，因此，我国研究人员在对西方 边际品位研究思想与方法演变的分析评论方面的工作做 得较少。下面对西方国家有关品位优化研究主要成果进 行简要评述。
一、绪论
边际品位确定的经济问题 边际品位经济分析的意义 边际品位研究的学术意义和应用前景 国外边际品位研究和应用现状 我国开采品位指标的研究现状
1.1 边际品位确定的经济问题
边际品位最优化经济分析研究的基本问题，就是要 选择最优的品位指标，使矿山生产的利润最大化。这是 边际品位经济最优化问题的基本结构，涉及到自然、技 术、经济等因素的影响，对于社会主义市场经济国家， 矿产资源属国家所有，因此，其经济分析研究还要涉及 到国民经济的边际效率问题。
生产矿山边界品位测算与论证
（国内外品位经济学研究进展）
中南大学 陈建宏 教授
二○○八年七月
汇报内容
项目背景及绪论 国内外品位指标体系 经济品位的含义及计算 最低工业品位的确定 合理出矿品位测算方法 边际品位理论及计算方法
生产矿山边界品位测算
基于新分类的矿体圈定及经济性判断 结论和建议
1.1 边际品位确定的经济问题
矿山生产的利润最大化是从经济学的角度来定义的， 它不是企业通常的会计核算的利润形式，而是经济利润。 作为衡量动态经济利润的有效手段，人们通常使用现值 (NPV)来进行计算。因此，经济利润最大化问题就转换为矿 山生产寿命期的NPV最大化问题。从宏观经济的角度来看， 所谓矿石开采的边际性效率，就是要考察其对国民收入增 加的贡献如何。 在最优化研究的基础上，考虑到矿山开采过程中技术 经济各因素及其关系的复杂性和模型求解的便利性，应注 意研究生产矿山边际品位的准优化问题或称次优化问题。
1.3 国外边际品位研究和应用现状
（3）Taylor. H.K。Taylor也是西方矿物工程经济研究中具有代 表性的人物之一，1972年，他发表了《边际品位的基础理论》 一文，他的研究成果主要有4个方面： ① 他为边际分析法的应用铺垫了广泛的基础，在这种基础上可以 对各种采矿方法的边际品位指标问题进行研讨(Lane的理论主要 是针对露天开采而展开的)； ② 对长期以来在边际品位定义上含混不清的问题进行了进一步的 澄清，为此，他提出应区分“边际品位”与“盈亏平衡品 位”(或极限品位)，后者是由某一特定的财务需求所决定的； ③ 对采掘活动制约和经济性制约与品位优化的关系进行了分析； ④ 在最优边际品位的计算方面，其基本思路沿用了Lane的方法， 但他在许多方面作了扩展以使其更具一般性。
1.2 边际品位经济分析的意义
5. 边际品位优化问题研究应用领域： (1)它是矿山生产计划编制的重要依据(长期计划，短期采矿计划)。 (2)它是矿山企业战略管理中，企业内部优势分析的一个重要方面， 因为边际品位决定着矿山的资源基础。 (3)矿山建设可行性研究中，在生产能力设计、开采境界设计、服务 年限设计等方面，都必须与边际品位的优化问题一起共同考虑。 (4)在矿业权评估中，要求通过合理分析矿山的现金流来为矿业权定 价，矿山品位策略是影响现金流的一个重要因素，因此，只有科 学地分析其相互关系，才能为矿业权合理定价。 (5)在地质勘探中，需要合理的边界品位指标来圈定矿体。 (6)国家有关政府部门在矿产资源政策形成中，需要充分考虑边际品 位的经济学问题。比如，我国铁矿和铜矿都是紧缺资源，目前都 需从国外大量进口，同时在国内存在大量的低品位铁矿和低品位 铜矿没有得到开发利用。是用外汇进口外国矿石？还是通过一些 优惠政策使国内低品位矿石得以利用，何者更具经济性?这些问 题与边界品位是密不可分的。
项目背景
应核工业第四研究设计院邀请，中南大学资源经济
研究室就《边界品位测试与论证项目》的相关研究与核
四院进行合作。负责对目前国内外边界品位测算的研究 现状进行文献调研，对国内外边界品位理论研究的最新
情况，国内外资源/储量估算方法、矿体经济性判断及储
量分类方法进行分析，为核四院制定生产铀矿山边界品 位测算方案提供理论上的支持和帮助。
在经济学的决策成本问题研究中，有一个著名的沉没成本概念，它 是指在决策分析之前已经发生的资源投入，并且已经不可挽回，因此它 与决策分析无关。在这种思想指导下， Carlisle 首先对盈亏平衡分析中 的呆板的平均成本计算方法提出了异议，并把沉没成本的理念引入到边 际品位的研究中来。他明确地指出，在矿石开采中的许多场合下包含沉 没成本，这些成本与边际品位决策分析无关。