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.
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Number of transfer units (NTU)
When the goal is to absorb a pollutant gas in a tower (CO₂, H₂S, SO₂) or to strip a component out of a liquid, one question comes up: how tall must the column be? The HTU-NTU method splits the problem into two independent factors. The NTU (number of transfer units) — here, in the dilute case, NTU = ln(C_inlet/C_outlet) — is the thermodynamic part: it measures the difficulty of the separation, that is, how close to equilibrium the process has to get. Removing 90% calls for a certain NTU; removing 99% calls for a great deal more (the relationship is logarithmic — the last traces are the hardest ones to take out). NTU works like the number of equilibrium stages required, but for packed columns, which operate continuously with no discrete trays. Multiplied by the height of each unit (HTU), it gives the total packing height. Enter the inlet and outlet concentrations.
Related Tools
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.
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.
Zeldovich Number
Computes the Zeldovich number of a flame, β = E_a·(T_b − T_u) ÷ (R·T_b²), the activation energy made dimensionless by the temperature rise across the flame front. It measures how sensitive the reaction rate is to a small temperature change: a high β (typically 8 to 12 for hydrocarbons) means the reaction is concentrated in a very thin layer near the flame temperature, which justifies the large-activation-energy assumption of asymptotic flame theory and the extinction and cellular-instability criteria. The universal gas constant R = 8.314 J/(mol·K) is adopted, with activation energy in J/mol and temperatures in kelvin. Enter the activation energy, the burned gas temperature and the unburned gas temperature.
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.
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.
Elenbaas Number
Computes the Elenbaas number of a channel formed by two heated vertical parallel plates, El = g·β·ΔT·b⁴ ÷ (ν·α·H), which is the Rayleigh number based on the plate spacing b multiplied by the ratio b/H. It governs natural convection in finned heat sinks, electronics enclosures and solar collectors: a very small El means a narrow, tall channel where the boundary layers merge and choke the flow, while a large El means the plates behave as isolated. The spacing that maximises a heat sink's total dissipation falls near El ≈ 46 for isothermal plates, a classic natural-convection fin design criterion. Gravity is taken as 9.80665 m/s², β is the fluid thermal expansion coefficient and H the plate height. Enter the expansion coefficient, the temperature difference, the spacing, the kinematic viscosity, the thermal diffusivity and the plate height.
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