Mass Transfer NTU from a Volumetric Coefficient
Mass Transfer NTU from a Volumetric Coefficient
Number of transfer units (NTU) is the mass-transfer analog of the thermal effectiveness-NTU method used in heat exchangers: it is a dimensionless measure of how much "transfer capacity" a piece of gas-liquid or liquid-liquid contacting equipment provides relative to what is needed, and it appears directly in absorption, stripping, and extraction column design. When the transfer process can be characterized by a single lumped volumetric coefficient — common in agitated vessels and some packed beds — NTU collapses to a simple product of that coefficient and the contact time, letting engineers compare different equipment or operating conditions with one number.
The number of transfer units is NTU = Kya·tau, the volumetric mass-transfer coefficient times the contact time. where Kya is the overall volumetric mass-transfer coefficient and tau is the time the two phases are in contact.
Inputs
Kya_coef := 0.15 min^-1=2.5e-03 Hz
tau_contact := 15 min=900 s
Multiplying the volumetric transfer coefficient by the contact time gives the number of transfer units, a dimensionless measure of how much mass-transfer "work" the equipment has done on the stream.
NTU_mt := Kya_coef·tau_contact=2.25
Results
An NTU of 2.25 corresponds to a moderately effective contactor — as a rough rule of thumb, each transfer unit removes roughly 63% of the remaining driving force, so NTU above about 3 to 4 is usually needed to approach a clean separation. If the process specification calls for a higher recovery than this NTU delivers, the designer would either extend the contact time (a taller column or slower flow) or improve Kya through better mixing or packing. NTU by itself says nothing about equipment size until it is combined with a height-per-transfer-unit value.
Assumptions & limitations
- Kya is treated as constant over the contact time (well-mixed or averaged conditions).
- Single controlling mass-transfer resistance lumped into Kya.
- Applies most directly to well-mixed or dispersed-phase contactors, not staged columns.
- Equilibrium data assumed linear enough for this lumped form to be valid.