Elsevier

Aquacultural Engineering

Volume 47, March 2012, Pages 38-46
Aquacultural Engineering

Carbon dioxide stripping in aquaculture – Part II: Development of gas transfer models

https://doi.org/10.1016/j.aquaeng.2011.12.002Get rights and content

Abstract

The basic mass transfer equation for gases such as oxygen and carbon dioxide can be derived from integration of the driving force equation. Because of the physical characteristics of the gas transfer processes, slightly different models are used for aerators tested under the non steady-state procedures, than for packed columns, or weirs. It is suggested that the standard condition for carbon dioxide should be 20 °C, 1 atm, CCO2=20mg/kg, and XCO2=0.000285. The selection of the standard condition for carbon dioxide based on a fixed mole fraction ensures that standardized carbon dioxide transfer rates will be comparable even though the value of CCO2* in the atmosphere is increasing with time. The computation of mass transfer for carbon dioxide is complicated by the impact of water depth and gas phase enrichment on the saturation concentration within the unit, although the importance of either factor depends strongly on the specific type of aerator. For some types of aerators, the most accurate gas phase model remains to be determined for carbon dioxide. 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.

Highlights

► It is proposed that the standard condition for carbon dioxide stripping should be 20 °C, 1 atm, CCO2=20mg/kg, and XCO2=0.000285. ► This standard condition will ensure transfer rates will be comparable even though the value of CCO2* 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 (CO2*) and the existing concentration of a gas (CO2) is known as the driving force:Driving force(O2)=CO2*CO2The rate of oxygen transfer is generally assumed proportional to the driving force (Brown, 1979, Lewis and Whitman, 1924):dCO2dt=KLa(CO2*CO2)where KLa=volumetric transfer coefficient(1/h).

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 C* assumption, the value of KCO2 can be estimated from measured values of CCO2out and CCO2in from Eq. (9):KCO2=ln[(CCO2outCCO2*)/(CCO2inCCO2*)]zThe value of CCO2* can be significantly larger than the value based on atmospheric concentrations of carbon dioxide (see Section 3.4).

For the linear CCO2* assumption (Eq. (13)), the value of KCO2 is equal to:KCO2=ln[(CCO2outCCO2*,in)/(CCO2inCCO2*,out)]z(1m)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 parameterCarbon dioxide
Empty CellTermParameterUnits
KLaStandard volumetric transfer coefficientKLaCO21/h
SOTRStandardized carbon dioxide transfer rateSCTRkg/h
SAEStandardized stripping efficiencySSEkg/kw h

The KLa 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 (HCO3) by two reactions (Gavis and Ferguson, 1975):HCO3k2k1 CO2(aq)+OHorH2CO3k4k3 CO2(aq)+H2Owhere k1 and k2 are the forward and reverse reaction rates, respectively, for Eq. (32) and k3 and k4 are the forward and reverse reaction rates, respectively, for Eq. (33).

Kinetic reaction rates for H++HCO3H2CO3 are many magnitudes more rapid than for Eqs. (32) or (33) and HCO3 can be assumed in equilibrium with H2CO3 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 CO2(aq) followed by a re-equilibration of the carbonate system. Larger values of K (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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