Total Reduction Ratio
Calculate the total reduction ratio of a three-stage comminution circuit, RR_total = RR₁ × RR₂ × RR₃, multiplying the reduction ratios of each crusher/mill in series. The dimensionless result is the circuit's overall size reduction — from bench rock blocks (hundreds of mm) to fine particles (mm or µm). Since each stage has a limited reduction ratio (4 to 10 for crushers), large total reductions (100, 1000 or more) require several stages in series: primary, secondary, tertiary crushing and milling. Enter the reduction ratios of the three stages.
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Razão de redução total
Reduzir rocha de bancada (blocos de centenas de milímetros, ou até maiores) até o pó fino necessário para o beneficiamento mineral (frações de milímetro ou micrômetros) representa uma razão de redução total enorme — frequentemente de 100, 1000 ou mais. Mas, como cada equipamento de cominuição tem uma razão de redução limitada (4 a 10 para britadores), essa redução gigantesca é alcançada por vários estágios em série, e a razão total é o produto das razões de cada estágio: RR_total = RR₁ × RR₂ × RR₃ × … Um circuito típico de britagem com três estágios (RR de 4, 5 e 5) atinge uma redução total de 4 × 5 × 5 = 100. O conceito explica a arquitetura das plantas de processamento mineral, que têm uma sequência característica: britagem primária (britador de mandíbula ou giratório, recebe a rocha da mina e a reduz a ~150-200 mm), secundária e terciária (britadores cônicos, reduzem progressivamente a ~10-25 mm), e finalmente moagem (moinhos de bolas, barras ou SAG, que levam a partículas finas para a flotação ou lixiviação). Cada estágio é dimensionado para uma razão de redução dentro da capacidade do equipamento, e o conjunto entrega a redução total necessária. Conhecer a razão total e distribuí-la entre os estágios (nem sobrecarregar um equipamento, nem ter estágios demais) é uma decisão central do projeto do circuito, que afeta o número de máquinas, o consumo de energia (lei de Bond) e o custo de capital e operação. Informe as razões de redução dos três estágios.
Related Tools
Crushing Reduction Ratio
Calculate the reduction ratio of a crusher or mill, RR = F ÷ P, dividing the feed size F by the product size P (usually F₈₀/P₈₀ or crusher openings). The dimensionless result shows how many times the material was reduced in size in one stage. Each equipment type has a typical reduction ratio range: jaw crushers 4-7, cone crushers 5-8, ball mills up to 100 or more. Since each stage has a limited ratio, reducing large blocks to fine powder requires several stages in series, whose product of ratios gives the total reduction. Enter the feed and product sizes.
Grinding Energy (Bond Work Index)
Calculate the specific comminution (grinding/crushing) energy by Bond's law, W = 10 × Wi × (1/√P₈₀ − 1/√F₈₀), from the ore's Bond work index Wi (kWh/t), and the particle sizes passing 80% of the product (P₈₀) and feed (F₈₀), in micrometers. The result, in kWh per tonne, is the energy needed to reduce the ore from feed to product size. Comminution is mining's largest energy consumer (up to 50% of the plant). The Wi index characterizes the ore's resistance to fragmentation. It is the basis for sizing mills and energy consumption. Enter the Wi, P₈₀ and F₈₀.
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Calculate the total cholesterol to HDL ratio, an indicator of cardiovascular risk. Below 3.5 is ideal; above 5 points to high risk for your heart.
Stripping Ratio (SR)
Compute the stripping ratio (SR) of an open-pit mine by dividing the amount of waste (worthless rock that must be removed) by the ore extracted. It is the central economic indicator of open-pit mining: the higher the SR, the more useless material is moved per tonne of ore, and the higher the cost. It defines the pit limit and the viability of the operation. Enter the waste and ore quantities.
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Compute the concentration ratio of a processing operation, CR = feed mass / concentrate mass, how many tonnes of raw ore are needed to produce one tonne of concentrate. It measures the degree of upgrade: high ratios indicate lean ores that require heavy processing. It is useful in the mass balance and plant sizing. Enter the feed mass and the concentrate mass.
Number of Stages by the Gilliland Correlation
Estimates the number of theoretical stages of a distillation column with the Gilliland correlation, which links excess reflux to excess stages: with X = (R − R_min)/(R + 1) and Y = (N − N_min)/(N + 1), you get N = (Y + N_min)/(1 − Y). It is the third step of the FUG shortcut method, after N_min from the Fenske equation and R_min from Underwood, and it settles in one line the preliminary sizing that would otherwise need a McCabe-Thiele diagram or a simulator. Eduljee's analytical fit is adopted, Y = 0.75·(1 − X^0.5668), the usual form for hand calculation; the Molokanov correlation is more accurate at the extremes and gives a result a few percent different. Enter the operating reflux ratio, the minimum reflux ratio and the minimum number of stages.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.