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A new slurry pH model accounting for effects of ammonia and carbon dioxide volatilization on solution speciation

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Nutrient Cycling in Agroecosystems Aims and scope Submit manuscript

Abstract

Ammonia (NH3) emissions from manure constitute a significant loss of fixed nitrogen (N) from agricultural systems and contribute to air pollution and ecosystem degradation. Accurate models of such NH3 emissions will improve our understanding of the factors that control the emissions and allow appropriate mitigation actions to be identified and quantified. Although the importance of manure pH on ammonia emission has been recognized for decades, the physical and chemical interactions that control pH are not fully understood. Here we present a novel mathematical model that includes the dynamic and crucial pH changes in the surface of stored slurry or slurry applied in the field. In the model, slurry pH is calculated by simultaneously determining: (1) speciation of the acid–base reactions, (2) diffusion of each buffer species, and (3) emission of NH3 and CO2. New features of the model include a reduced variable that combines time and location and an analytical approach to solving the resulting system of equations using Mathematica. To evaluate the model, we made measurements of pH at a resolution of 0.1 mm in the top 30 mm of an ammonium bicarbonate solution. These measurements show the creation of a large pH gradient (>1 pH unit in <30 mm after 20 h) and its change over time due to simultaneous NH3 and CO2 emission from aqueous solutions. The model was able to accurately predict the development of pH gradients over time, suggesting that our understanding of the factors controlling pH is correct. New developments presented in the model should be useful for future work on understanding and predicting NH3 emission from manure.

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Abbreviations

D X :

Diffusion coefficient of chemical species X in water (cm2 s−1)

D X,Air :

Diffusion coefficient of chemical species X in air (cm2 s−1)

F X :

Constant determining how quickly the species X is transported from water to air through the water–air surface (mol L−1 cm s−1/2). The cumulative mass transported to the air through area A over time t is given by the expression \(A\sqrt t F_{x}\)

\(H_{X} = \frac{{[X]_{0} }}{{[X]_{0,Air} }}\) :

Henry´s law constant for the chemical species X (dimensionless)

K X :

Equilibrium constant for the chemical reaction of the species X

z :

Depth in solution or height in the air, always positive (cm)

t :

Time since stirring, always positive (s)

\(w = \frac{z}{\sqrt t }\) :

Reduced variable, always positive (cm s−1/2)

[X]:

Concentration of chemical species X in water (mol L−1)

[X] Air :

Concentration of chemical species X in air (mol L−1)

[X]0 :

Concentration of chemical species X in water at the water–air surface (mol L−1)

[X]∞ :

Concentration of chemical species X in water at infinite depth (bulk value) (mol L−1)

[X]0,Air :

Concentration of chemical species X in air at the water–air surface (mol L−1)

[X]∞,Air :

Concentration of chemical species X in air at infinite height (bulk value) (mol L−1)

TAN:

Total Ammonia Nitrogen: [TAN] = [NH3] + [NH4 +] (mol L−1)

TIC:

Total Inorganic Carbon: [TIC] = [CO2] + [HCO3 −] + [CO −23 ] (mol L−1)

α x :

Ionization fraction for TAN or TIC: [X] = α x [TAN] or [X] = α x [TIC]. It is a polynomial fraction which depends only on [H3O+] and has values between 0 and 1 (dimensionless)

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Acknowledgments

We thank Grønt udviklings- og demonstration program for the financial support (Gylle—IT), Ministeriet for Fødevarer, Landbrug og Fiskeri - NaturErhvervstyrelsen. We thank Lars B Pedersen, Preben Sørensen, and and Niels Peter Revsbech (Aarhus University, Bioscence - European Research Council, Grant No. 267233) for constructing the hock formed temperature sensors and pH electrodes, Steen Bennike Mortensen (NovoZymes) for providing us with the carbonic anhydrase and Henrik Midtiby for valuable comments to the model development.

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Authors and Affiliations

  1. Faculty of Engineering, Institute of Chemical Engineering, Biotechnology and Environmental Engineering, University of Southern Denmark (SDU), Odense M, Denmark

    V. Petersen, S. D. Hafner & S. G. Sommer

  2. Department of Bioscience, Microbiology, Aarhus University, Aarhus, Denmark

    R. Markfoged

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  1. V. Petersen
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  2. R. Markfoged
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  3. S. D. Hafner
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  4. S. G. Sommer
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Correspondence to S. D. Hafner.

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Petersen, V., Markfoged, R., Hafner, S.D. et al. A new slurry pH model accounting for effects of ammonia and carbon dioxide volatilization on solution speciation. Nutr Cycl Agroecosyst 100, 189–204 (2014). https://doi.org/10.1007/s10705-014-9637-6

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