Mass Transfer Coefficient Calculator
Compute the convective mass transfer coefficient (k) for packed columns, bubble columns, or stirred reactors using dimensionless Reynolds and Schmidt number correlations. Used by chemical engineers sizing gas-liquid contactors.
About this calculator
The mass transfer coefficient k (m/s) is estimated from the Sherwood number correlation: k = A · Re⁰·⁸ · Sc⁰·³³ · (D / L), where Re = v·L / ν is the Reynolds number, Sc = ν / D is the Schmidt number, D is molecular diffusivity (m²/s), L is the characteristic length (m), ν is kinematic viscosity (m²/s), and v is fluid velocity (m/s). The pre-factor A depends on system geometry: 0.25 for packed columns, 0.31 for bubble columns, and 0.20 for other configurations. Re⁰·⁸ captures turbulence-driven convection, while Sc⁰·³³ accounts for the relative thickness of the velocity and concentration boundary layers. Higher velocity, smaller characteristic length, or lower viscosity all increase k.
How to use
Consider a packed column with D = 2×10⁻⁹ m²/s, v = 0.5 m/s, L = 0.01 m, ν = 1×10⁻⁶ m²/s. Step 1 — Re = (0.5 × 0.01) / 1×10⁻⁶ = 5,000. Step 2 — Re⁰·⁸ = 5000⁰·⁸ ≈ 549.5. Step 3 — Sc = 1×10⁻⁶ / 2×10⁻⁹ = 500. Step 4 — Sc⁰·³³ ≈ 500⁰·³³ ≈ 6.30. Step 5 — D/L = 2×10⁻⁹ / 0.01 = 2×10⁻⁷. Step 6 — k = 0.25 × 549.5 × 6.30 × 2×10⁻⁷ ≈ 1.73×10⁻⁴ m/s.
Frequently asked questions
What is the difference between the mass transfer coefficient for packed vs bubble columns?
The pre-factor A in the Sherwood correlation reflects how efficiently each system generates interfacial turbulence. Bubble columns use A = 0.31 because rising bubbles continuously renew the gas-liquid interface, enhancing mass transfer relative to a stagnant film. Packed columns use A = 0.25 because the packing distributes liquid but provides less active interface renewal. Other geometries default to A = 0.20 as a conservative estimate. Selecting the correct system type is critical for accurate sizing of industrial contactors.
How does molecular diffusivity affect the mass transfer coefficient?
Diffusivity D appears in two places in the correlation: through the Schmidt number Sc = ν/D (with an exponent of −0.33) and directly in the D/L term (with an exponent of 1). The net effect is that k scales approximately as D⁰·⁶⁷, meaning higher diffusivity significantly increases the mass transfer coefficient. Gases have diffusivities around 10⁻⁵ m²/s, roughly 10,000 times larger than liquids (10⁻⁹ m²/s), which is why gas-phase mass transfer coefficients are much larger than liquid-phase ones.
When should I use a more detailed model instead of this dimensionless correlation?
This correlation is suitable for preliminary design and order-of-magnitude estimates in turbulent flow regimes (Re > 1,000). For laminar flow, non-Newtonian fluids, or highly concentrated systems where the driving force is not dilute, more rigorous models such as penetration theory or surface renewal theory are recommended. Reactive absorption systems also require incorporating enhancement factors. Experimental validation with pilot data is always advisable before finalizing column specifications for production-scale equipment.