Minimum Reflux (Underwood)
Estimate the minimum reflux ratio of a binary distillation by Underwood's equation (saturated-liquid feed), Rmin = [xD/xF − α·(1−xD)/(1−xF)]/(α − 1), from the relative volatility (α) and the light-component mole fractions in the distillate (xD) and feed (xF). At minimum reflux, the column would need infinite plates; the operating reflux is a multiple of it (1.1–1.5×). It is a key number in column design. Enter α, xD and xF.
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Refluxo mínimo (Underwood)
Toda coluna de destilação recircula parte do produto de topo de volta para a coluna — o refluxo — para melhorar a separação. Há um limite inferior: o refluxo mínimo (Rmin), abaixo do qual a separação desejada é impossível, nem com infinitos pratos. A equação de Underwood (aqui na forma para alimentação líquida saturada e mistura binária) estima esse mínimo a partir da volatilidade relativa α (o quão diferentes são as volatilidades dos dois componentes) e das frações molares do componente leve no destilado (xD, alta pureza desejada) e na alimentação (xF). No refluxo mínimo, formam-se zonas de composição constante (pinch) que exigem pratos infinitos. O refluxo de operação é sempre um múltiplo do mínimo (tipicamente 1,1 a 1,5·Rmin), num compromisso entre número de pratos e gasto de energia. Junto com o número mínimo de pratos (de Fenske), o Rmin de Underwood é a base do método Fenske-Underwood-Gilliland de projeto de colunas. Informe α, xD e xF.
Related Tools
Overall Plate Efficiency (O'Connell Correlation)
Estimates the overall plate efficiency of a distillation column by the O'Connell correlation, the step that converts theoretical stages into actual trays in preliminary design. The correlation uses a single combined variable, the product of liquid viscosity and mean relative volatility, and reads efficiency = 0.492 × (viscosity × relative volatility) raised to −0.245, with viscosity in centipoise. What governs it is the product μ·α: a low-viscosity liquid with relative volatility near 1 lands in the 70 to 80% band, and efficiency falls to 40% or less once the liquid is viscous or the relative volatility is high. Note that a difficult separation, with α close to 1, gives the highest efficiency per tray — that column is tall because of the theoretical stage count, not the efficiency, which there actually dampens the height. The analytical fit 0.492 × (μ·α)^−0.245 was adopted, the usual form for hand calculation; the Kessler and Wankat polynomial on the logarithm of the product differs by a few percentage points at the ends of the range. Enter the liquid viscosity at the mean column temperature and the mean relative volatility.
Optimum Reflux Ratio
Compute a distillation column's operating reflux ratio, R = factor · Rmin, multiplying the minimum reflux by a factor (typically 1.1 to 1.5). There is a classic economic trade-off: a low reflux (near minimum) requires many plates (more column investment); a high reflux requires fewer plates but much more energy in the reboiler and condenser (more operating cost). The optimum balances the two. Enter the minimum reflux and the factor.
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.
Actual Plates (Efficiency)
Compute the number of actual plates of a distillation column, N_actual = N_theoretical / (efficiency/100), from the number of theoretical (equilibrium) plates and the column's overall efficiency (%). Since no real plate reaches perfect equilibrium, more actual plates than theoretical are needed: a 50% efficiency doubles the plate count. It is the step that turns the theoretical design into the physical column. Enter the theoretical plates and the overall efficiency.
Number of Transfer Units (NTU)
Compute the number of transfer units (NTU) of an absorption or stripping column (dilute case), NTU = ln(C_in/C_out), from the inlet and outlet concentrations. NTU measures the 'difficulty' of the separation: the greater the removal desired, the more transfer units are needed. Together with the height of a unit (HTU), it defines the total packing height. Enter the inlet and outlet concentrations.
Packing Height (HTU·NTU)
Compute the packing height of an absorption or distillation column, Z = HTU·NTU, multiplying the height of a transfer unit (HTU, which depends on hydrodynamics and packing type) by the number of transfer units (NTU, which depends on the desired separation). It is the HTU-NTU method of sizing packed columns — it separates the 'kinetic' part (HTU) from the 'thermodynamic' (NTU). Enter the HTU and the NTU.
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