(1f) Improvement in Understanding of the Sodium Sulfite Steady-State Method for Gas-Liquid Mass Transfer Measurement in Precision Fermentation Applications

One of the recognized methods for mass transfer measurements in Gas-Liquid systems is the excess sodium sulfite method catalyzed by cobalt. In this method, the stoichiometric sodium sulfite required to consume the dissolved oxygen from a system is calculated and a specific quantity larger than this is added to the gas-liquid system. The time taken to consume this known quantity of excess sulfite can then be equated to a mass transfer rate of oxygen into the system. This measured mass transfer must be corrected to represent the system of interest for the following reasons:

• Addition of ionic components is known to influence the mass transfer rate (1). This effect must be corrected for as additional sulfite is added. Dissolved ions also affect the interfacial tension and the gas molecule solubility. This also limits the number of experiments which can be performed before replacing the bulk liquid.
• Variation of temperature in the gas-liquid system is also known to influence the mass transfer rate. There is an ASCE (ASCE, American Society of Civil Engineers, 2022) correction factor for this for the standard sulfite method (2).

A full understanding of the effect of these variables is key to:

• Accurately representing the baseline mass transfer rate and drawing the correct conclusions from the results of the experiments.
• Maximizing the number of trials per volume of bulk liquid while ensuring that accuracy is maintained.

As a solution provider and researcher for Gas-Liquid mixing processes, SPX FLOW has an interest in understanding these effects further. While there are other methods that do not suffer the same drawbacks of the sulfite method, the sulfite method remains a very cost effective and quick technique for assessing the mass transfer potential of a system. The effects of temperature and total dissolved solids or ionic strength can be accounted for and thus eliminated from the data. An analysis of recent mass transfer measurement experiments was conducted to investigate the effects of these variables and improve the sulfite technique for measuring mass transfer in gas-liquid stirred tank reactor systems.

The testing was performed at a single scale (T = 0.46m, H/T = 2.5) with technical grade sodium sulfite over a period of weeks. The water temperature was not controlled and varied between 10 – 17°C. Regression models were fit using R statistical programming language and different regression models were compared using Leave One Out Cross Validation (LOOCV) to prevent overfitting.

It was concluded that the effect of temperature is not fully represented by the ASCE correction factor. By including temperature as a power law variable, the model RMSPE (root mean square percentage error) was reduced from 5.9% to 3.5% (Approx 40% reduction). This reduction in error led to more robust interpretation of the impact of other variables in precision fermentation processes.

It was also concluded that the effect of sulfite concentration varied when measured on different dates for different physical setups. This effect could not be explained by the additional temperature correction factor. A custom polynomial fit for sulfite correction was used for some sets of trials due to this variation. It was noted that using a power-law variable to represent this in regression resulted in only a minor effect on accuracy.

References:

1. Van’t Riet, “Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels” Industrial & Engineering Chemistry Process Design and Development, vol. 18, 1979.
2. ASCE, American Society of Civil Engineers. (2022). Measurement of Oxygen Transfer in Clean Water. Reston, Virginia: ASCE/EWRI.