title: "Mass Transfer Calculations in Chemical Engineering Using the Schmidt Number"
slug: "chemical-engineering-mass-transfer-schmidt"
date: "2026-09-29"
author: "Hesaplamasyon Team"
language: "en"
category: "Physics / Fluids and Mass Transfer"
categorySlug: "muhendislik"
calculatorSlug: "schmidt-sayisi-hesaplama"
articleNumber: 2
seo:
title: "Mass Transfer Calculations in Chemical Engineering with Schmidt | Hesaplamasyon"
description: "Learn how the Schmidt number is applied in mass transfer calculations in chemical engineering and reactor design with practical examples."
keywords: "Chemical engineering, mass transfer, Schmidt number, Sherwood number, Reynolds correlation, reactor design"
In the chemical industry, the efficient operation of reactors and the proper functioning of separation processes (distillation, absorption, etc.) rely entirely on mass transfer processes. To determine the rate of mass transfer, engineers rely on experiments and empirical correlations. At the center of these correlations are dimensionless numbers, particularly the Schmidt number.
To speed up your mass diffusion calculations in chemical processes, you can use our Schmidt Number Calculator tool.
Mass Transfer Coefficient and Correlations
The fundamental mass transfer equation in chemical engineering varies depending on the type of flow (laminar or turbulent). Just as the Nusselt, Reynolds, and Prandtl numbers are connected in heat transfer; the Sherwood (Sh), Reynolds (Re), and Schmidt (Sc) numbers are connected in mass transfer.
A general correlation is as follows:
$$Sh = C \cdot Re^m \cdot Sc^n$$
In this equation, $C$, $m$, and $n$ are empirical constants depending on the geometry and turbulence level of the flow. As can be seen, it is mandatory to know the Schmidt number (Sc) to find the mass transfer coefficient (a component of the Sherwood number).
Components of the Schmidt Number: $Sc = \frac{\mu}{\rho \cdot D}$
Since dynamic viscosity ($\mu$) and density ($\rho$) data are generally more accessible in chemical engineering applications, the Schmidt formula is commonly used in this form:
$$Sc = \frac{\mu}{\rho \cdot D}$$
- $\mu$ (Dynamic Viscosity): Internal friction of a liquid or gas (Pa·s).
- $\rho$ (Density): Mass per unit volume ($kg/m^3$).
- D (Mass Diffusion Coefficient): Diffusion rate of substance B into substance A ($m^2/s$).
In industrial reactor design, how fast reactants mix (mass transfer) depends on the turbulence of the system (momentum transfer). The Schmidt number bridges the gap between these two transfer rates.
An Industrial Example
In a bioreactor, oxygen (O2) is fed externally into water (density $\rho \approx 1000 , kg/m^3$, dynamic viscosity $\mu \approx 0.001 , Pa\cdot s$). The mass diffusion coefficient (D) of oxygen in water is approximately $2.0 \times 10^{-9} , m^2/s$.
Let's calculate the Schmidt number:
$$Sc = \frac{0.001}{1000 \times (2.0 \times 10^{-9})}$$
$$Sc = \frac{0.001}{2.0 \times 10^{-6}}$$
$$Sc = 500$$
The resulting $Sc = 500$ indicates that in liquids (Sc $\gg$ 1), momentum diffusion is hundreds of times more dominant than mass diffusion. That is, it is easy to move within the liquid (or at least macroscopic mixing can be achieved) but the diffusion of oxygen into water at the molecular level is a much slower process. Therefore, vigorous mixing or fine bubbles (aeration) must be applied to increase the gas-liquid contact area in bioreactors.
Instead of performing such calculations manually, you can instantly find the Sc number by entering only the $\mu$, $\rho$, and D values into the Schmidt Number Calculator tool in the "Using Dynamic Viscosity & Density" mode.
Critical Warnings and Edge Cases
Here are some important points to consider in chemical process modeling:
- Dependency of the D Value on Environmental Conditions: The mass diffusion coefficient is highly sensitive to the temperature and pressure of the system. For example, as temperature increases, the kinetic energy of molecules increases, and the D coefficient grows. This causes the Schmidt number to drop.
- Mixture Viscosity: The liquid in the reactor might not be simple water; added reactants can change the overall viscosity ($\mu$) and density ($\rho$) of the liquid. When calculating, the current properties of the mixture should be used, not those of the pure fluid.
- Multicomponent Systems: If there are only two components (e.g., air and water), a single D value can be used. However, in multicomponent systems like oil refining, each species has different diffusion coefficients relative to other species in the mixture. In this case, the binary diffusion model is insufficient.
Advanced Process Simulation and the Schmidt Number
Modern chemical plants rely heavily on advanced process simulation software such as Aspen Plus or HYSYS. These platforms use complex thermodynamic models to solve mass transfer processes across entire plants. Within these simulations, the Schmidt number often serves as an intermediate value computed dynamically at thousands of nodes within the reactor model.
The accuracy of these simulations depends entirely on the precision of the fundamental data provided—specifically viscosity, density, and diffusion coefficients. In environments near the critical point (supercritical fluids), thermodynamic properties exhibit sharp, non-linear changes. A static Schmidt number is inadequate here; simulations must compute local Schmidt numbers based on real-time temperature and pressure updates to integrate mass transfer rates accurately. When designing systems, engineers must account for this sensitivity, understanding how much the baseline Schmidt number might deviate under actual operating conditions.
Conclusion
Calculating mass transfer coefficients correctly in chemical engineering increases both production efficiency and saves energy. The dimensionless Schmidt number is an indispensable parameter in Sherwood-Reynolds correlations. When analyzing your system, do not forget to add our Schmidt Number Calculator page to your toolbar to get fast and reliable results using accurate dynamic viscosity, density, and molecular diffusion data.
