Carbon dioxide stripping in aquaculture – Part II: Development of gas transfer models
Highlights
► It is proposed that the standard condition for carbon dioxide stripping should be 20 °C, 1 atm, , and . ► This standard condition will ensure transfer rates will be comparable even though the value of in the atmosphere is increasing with time. ► The computation of mass transfer for carbon dioxide is complicated by the impact of gas phase enrichment and the hydration reaction. ► Carbon dioxide can be treated as a non-reactive gas in packed columns for cold acidic waters but not for warm alkaline waters.
Introduction
Control of carbon dioxide becomes more important in aquaculture as system intensity increases. Accumulation of carbon dioxide gas can reduce the pH which, in turn, reduces the mole fraction and concentration of un-ionized ammonia (Colt and Orwicz, 1991). Therefore, it is desirable to maintain dissolved carbon dioxide gas in a range that avoids direct toxicity, but reduces un-ionized ammonia problems.
The purpose of this article is to define carbon dioxide removal parameters, determine the accuracy of common mass transfer models used for carbon dioxide, and suggest future research needs. This is part II of a 3-part article and covers development of gas transfer models. This article will present carbon dioxide models based on existing oxygen models, suggest standardized reporting parameters for carbon dioxide, and suggest approaches for correcting carbon dioxide models for gas phase enrichment. Part I covered terminology and reporting of carbon dioxide parameters (Colt et al., 2012). Part III will cover model verification. It is hoped that these articles will encourage research in critical areas and result in improved understanding of the carbon dioxide transfer in aquaculture production and hauling systems.
Section snippets
Basic gas transfer models
Gas transfer will first be discussed in terms of oxygen and then applied to carbon dioxide. The difference between the saturation concentration () and the existing concentration of a gas () is known as the driving force:The rate of oxygen transfer is generally assumed proportional to the driving force (Brown, 1979, Lewis and Whitman, 1924):where .
This equation is restricted to a simple batch system
Non steady-state parameter estimation
The non steady-state test is commonly used for surface and submerged aerators when it is not possible to clearly define influent and effluent water flows or measure gas concentrations in the liquid phase. Aerators are thus rated in a test basin under standardized conditions.
Steady-state parameter estimation
For the packed column and constant assumption, the value of can be estimated from measured values of and from Eq. (9):The value of can be significantly larger than the value based on atmospheric concentrations of carbon dioxide (see Section 3.4).
For the linear assumption (Eq. (13)), the value of is equal to:The value of r for the weir (Eq. (10)) can be based on
Non steady-state test
The following nomenclature is suggested for carbon dioxide parameters based on the ASCE oxygen parameters (ASCE, 1992):Oxygen parameter Carbon dioxide Empty Cell Term Parameter Units Standard volumetric transfer coefficient 1/h SOTR Standardized carbon dioxide transfer rate SCTR kg/h SAE Standardized stripping efficiency SSE kg/kw h
The is reported in the United States at 20 °C and 1 atm (ASCE, 1992, Stenstrom and Gilbert, 1981). The SOTR is based on standard conditions of 20 °C, 1 atm, and zero DO (ASCE, 1992)
Computation of saturation concentrations
Selection of the appropriate packed column design model must be based on the expected gas phase variation inside the column. Ideally the packed column is operated as a true counter-current flow reactor with both gas and liquid phases proceeding towards their respective discharge ends without longitudinal or axial mixing so as to maximize the driving force needed for gas desorption. Deviation from the ideal case is expected but is often ignored. Non-uniformity of the velocity profiles result
Impacts of carbon dioxide hydration/dehydration on mass transfer
Carbon dioxide gas can be formed from bicarbonate ion () by two reactions (Gavis and Ferguson, 1975):orwhere and are the forward and reverse reaction rates, respectively, for Eq. (32) and and are the forward and reverse reaction rates, respectively, for Eq. (33).
Kinetic reaction rates for are many magnitudes more rapid than for Eqs. (32) or (33) and can be assumed in equilibrium with at all times.
The
Computational approach to hydration/dehydration modeling in stripping
Within a gas transfer unit, two separate reactions are occurring: (a) removal of CO2(aq) into the gas phase and (b) formation of CO2(aq) by Eqs. (32), (33). A computational approach for a packed column segment is presented in Fig. 4. This is based on instantaneous removal of followed by a re-equilibration of the carbonate system. Larger values of (Eq. (35)) increase the performance of a packed column in comparison to smaller values. This is because Eqs. (32), (33) increase the
Summary
This article summarized mass transfer models for carbon dioxide and the computation of standardized performance parameters. Procedures were presented to estimate gas phase enrichment for both non steady-state and steady-state tests, although the best specific model for the saturation concentration remains to be determined. The assumption that carbon dioxide can be treated as a non-reactive gas in packed columns may apply for cold acidic waters but not for warm alkaline waters. How well these
Acknowledgements
This project was supported by Western Regional Aquaculture Center Grant no. 2008-38500-19230 from the USDA Cooperative State Research, Education, and Extension Service (now the National Institute for Food & Agriculture (NIFA)).
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