(749a) Transient Multicomponent Models for Simulating Water and Nutrient Flow Through Soils Amended with Biochar

Biochar is charcoal generated for intentional soil amendment by pyrolyzing sustainable biomass feedstocks.  In addition to providing an easily deployable method for carbon sequestration, properly “engineered” charcoals can increase the water holding and cation exchange capacities of soils, improving the ability of plants to survive under drought conditions and reducing fertilizer runoff into watersheds.  Fertilizer runoff has become a serious problem, because as much as 70% of fertilizer applied to crop fields is leached into the groundwater or lost to streams and rivers, eventually leading to large hypoxic “dead” zones in the world’s oceans (including the Gulf of Mexico).

We present here the development and testing of mathematical models that allow us to evaluate the environmental performance of biochars used for soil amendment. Our earlier work (1-2) has established that both the pore structure and the surface chemistry of biochars can vary widely depending on the composition of the biomass feedstocks and on the pyrolysis conditions employed during biochar production.  The work presented here will demonstrate how these biochar properties affect the ability of soil/biochar mixtures to adsorb, retain and release water and nutrients.  Our ultimate objective is to develop a comprehensive theoretical framework that can guide us to engineer biochars with optimal properties for every field application.

The first model describes the dynamic adsorption/elution of a model fertilizer (ammonium nitrate) in columns packed with mixtures of biochar and soil and perfused with aqueous solutions of the fertilizer.  This model can be used to simulate a fertilization event that is followed by irrigation/rain events that elute the fertilizer adsorbed in the solid column.  The dynamic model accounts for all the important processes occurring in this system: convection and dispersion of the aqueous solution through the bed, external mass transfer between the fluid phase and the soil and biochar particles, intraparticle diffusion and adsorption of the solute on the pore surface area of the sorbents.  To our knowledge, this is the first model that accounts explicitly for the presence of two solid phases with widely different pore structures, surface chemistries and, therefore, nutrient holding capacities. It also accounts for the complicated pore structure of biochars that consists of interconnected networks of large macropores, mesopores and micropores.  The transient mass balances lead to a system of partial differential equations that are discretized using orthogonal collocation on finite elements.  The resulting differential equations are approximated by backward differentiation formulae and the nonlinear systems at each time-step are solved by Newton's method.

We will first discuss the approach used to determine the optimal mode of applying a given amount of fertilizer (e.g. 100 kg N per hectare).  The solution of this optimization problem determines the flow rate and inlet solute concentration that maximizes the loading of solute in our column, or, equivalently, minimizes fertilizer runoff.  The solute adsorbed on sorbent particles will then be released slowly during the subsequent irrigation or rain events.  We then carry out a systematic parametric study to determine how the dynamic loading and elution processes are affected by the amount of biochar added to the mixture, the size, porosity and pore size distributions of biochar particles, and the adsorption equilibrium constants for the solute or the kinetic constants of solute adsorption.  As expected, simulations predict that higher biochar amendment levels improve the ability of the soil/biochar mixture to retain nutrients and release them over a longer period of time.  Simulation results also reveal that smaller biochar particles accelerate both the adsorption and the desorption of nutrients, while lower biochar porosities both increase the amount of nutrient adsorbed and prolong its subsequent release.  The adsorption kinetic constants also play a prominent role in determining both the nutrient loading and the dynamics of the adsorption/elution processes.

Fertilization, irrigation and rain events are intermittent processes. Therefore and in order to complete our theoretical framework, we have also developed a model that describes the dynamics of water saturation and drainage for a column packed with soil/biochar mixtures.  This model is important to describe the transients that precede and follow each nutrient adsorption or elution event described by the previous model.  A systematic parametric study is also carried out to evaluate the importance of the hydraulic conductivity and capillary pressure of the biochar particles on the duration of the saturation and drainage transients.  Simulation results show that these transients are short and do not affect significantly the dynamics of the nutrient adsorption/elution processes.

1)    Hao Sun, W.C. Hockaday, C.A. Masiello and Kyriacos Zygourakis*, “Multiple Controls on the Chemical and Physical Structure of Biochars,” Industrial and Engineering Chemistry Research, 51, 3587−3597 (2012) dx.doi.org/10.1021/ie201309r.

2)    T.J. Kinney, C.A. Masiello, B. Dugan, W.C. Hockaday, M.R. Dean, K. Zygourakis and R.T. Barnes, “Hydrologic properties of biochars produced at different temperatures,” Biomass and Bioenergy (2012), doi:10.1016/j.biombioe.2012.01.033