By Gregory T. Benz, Lee Enterprises Consulting
Fermentation processes, both aerobic and anaerobic, have been successful on an industrial scale for quite a long time, producing a wide variety of products. In most of these processes, if any gas has been added, it has been either air or oxygen-enriched air. In the advanced bioeconomy, organisms are now being studied that metabolize other gasses. One example is the category of bacteria that are called methanotrophs, which metabolize methane. Other organisms are known which metabolize carbon dioxide, carbon monoxide and hydrogen, and there are sure to be others. This article seeks to summarize what is similar in designing agitation systems for such organisms, and to identify what is different and what needs to be done to assure a successful installation.
Basic Mass Transfer Relationship
Generally speaking, the most important role of the agitation system is to disperse gas into the liquid, thereby promoting interphase mass transfer. Other roles include reducing concentration gradients and enhancing heat transfer. We will focus solely on mass transfer in this article. The simplified form of the mass transfer relationship can be written as follows:
1) MTR (mass transfer rate) = kla*(Csat-C)
Where kl is the liquid film coefficient, a is the interfacial area per volume, Csat is the saturation value of the gas in the liquid at local gas concentration, temperature and pressure, and C is the actual dissolved concentration of the gas in the liquid. For a tall vessel, the term in brackets, known as the driving force, is more properly written as a log mean. However, to illustrate concepts clearly for this article, we will just use the simple form above.
For an aerobic fermentation, equation 1 is normally written as OTR (oxygen transfer rate), and is usually in units of mmol/l-h. The combined term kla is normally treated as a single variable, as it is hard to separate the two terms experimentally. When the gas is not oxygen, there are some significant differences affecting mass transfer. We will first look at driving force and then the mass transfer coefficient.
Driving force effects
Oxygen is a gas which is sparingly soluble in water. All gasses have a temperature effect on their solubility, so to compare gasses we will just use relative solubility at a fixed temperature of 30C in this article. Below is a table comparing the solubility of the previously mentioned gasses in water.
One can see that there is quite a range of solubilities for these gasses. Carbon dioxide is so soluble that it is easy to achieve a high driving force. The other gasses are less soluble than oxygen; hydrogen is much less soluble. This means that high dissolved concentrations of such gasses will require more back pressure to achieve than would be needed with oxygen. Not all organisms need high concentrations, however. The goal is to keep the dissolved concentration in the range that will satisfy the metabolic needs of the organism. Often, mixtures of gasses are used. The saturation value depends on the absolute partial pressure of the gas species, including consumption of the gas in the process. Calculation of the mass balance and driving force principles is illustrated in Reference 1.
Mass Transfer Coefficient Effects
The overall mass transfer coefficient, kla, depends on several things. It is normally correlated as a function of gas flow and agitation in the following form, though others are possible:
2) kla = A(P/V)B(US)C
where P/V is agitator power per volume, US is superficial gas velocity, and A,B and C are empirically determined constants. Clearly, the mass transfer coefficient depends on agitator power input and gas flow. The constants are broth-specific, and may depend on such things as temperature, viscosity, ionic strength, surface tension, dissolved solids, suspended solids, reactions near the gas-liquid interface and maybe a number of other variables. Reference 2 gives guidance on how to develop an experimental protocol to determine these constants.
As stated previously, kla is normally treated as a single entity, as it is hard to experimentally separate the film coefficient from the interfacial area per volume, and because the agitation effects are similar on both the film coefficient and the interfacial area. However, caution is advised when attempting to take a kla correlation developed for one gas and applying it to another. The hydrodynamic effects are probably the same, so the “a” term, or interfacial area per volume, will likely be close to the same for a given broth. And the agitation and air flow effects on the kl terms are probably the same. However, the diffusivity of the different gasses will be different, and this will directly affect the value of kl. In general, kl is proportional to the square root of the diffusion coefficient. Below is a table comparing relative diffusion coefficients and the resultant effect on kl (and probably the same effect on kla) at a temperature of 25C. Results should be fairly similar at other temperatures, but it is prudent to look up comparative results at actual process temperatures.
Table 2 Comparative Diffusivity and Liquid Film Coefficients
One can readily see that carbon dioxide and carbon monoxide should have similar overall mass transfer coefficients to oxygen. Hydrogen should be higher, though not enough to offset its very low solubility in water. Methane has both a lower solubility and a lower mass transfer coefficient, so its overall mass transfer rate will generally be quite a bit lower than would be obtained with oxygen under similar conditions.
It is expected that the same kinds of calculations used to predict oxygen transfer rates for an air-water system can also be used to predict the mass transfer rates of other gasses into water. However, the differences in solubility and diffusivity must be taken into account. For best results, a broth-specific experimental protocol should be developed for the actual gasses in use.
- “Optimize Power Consumption in Aerobic Fermenters”, G. Benz, Chemical Engineering Progress, May 2003, pp 100-103
- “Piloting Bioreactors for Agitation Scale-Up”, G. Benz, Chemical Engineering Progress, February 2008, pp32-34
About the Author
Gregory Benz is a member of Lee Enterprises Consulting, the world’s premier bioeconomy consulting group, with more than 100 consultants and experts worldwide who collaborate on interdisciplinary projects, including those requiring the technologies discussed in this article. The opinions expressed herein are those the author, and do not necessarily express the views of Lee Enterprises Consulting.