(186e) A Two-Phase Imbibition-Drainage Model for Soils Amended with Biochars

The amendment of soils with biochar has been heralded as a sustainable method for increasing crop yield and preventing pollution problems caused by fertilizer runoff. However, the available experimental results are highly variable [1-3]. While some studies reported significant beneficial effects with up to 60% higher yield after biochar addition, other studies reported that biochar amendments either had no effect or even resulted in up to 30% lower agricultural productivity [3]. The evidence presented in these and other studies suggests that biochar my improved agricultural productivity by increasing the water holding capacities and by improving crop nutrient availability of biochar-amended soils. However, the fundamental mechanisms of these processes are still very poorly understood.

One of the most important reasons for the large variability of experimental data is that biochar is not a single entity. Dozens of biomass feedstocks are used to produce biochars in multiple types of reactors under varying temperature and oxygen conditions, leading to thousands of biochars with widely varying chemical and physical properties. To complicate things even more, soil properties, climate conditions (like rainfall and temperature), plant requirements and many other parameters vary from application to application. Clearly, much better understanding of the complex dynamic interactions among the various components of the biochar/soil/climate system is needed before we can predict the environmental performance of a biochar with specific chemical and physical properties.

To begin bridging this knowledge gap, we focused our recent research on the mechanisms that control the ability of biochars to improve crop nutrient availability, one of the main mechanisms proposed to explain crop yield increases in biochar-amended soils [2]. As a first step in this direction, we have recently developed and tested a mathematical model that uses first principles to describe nutrient transport in soils amended with biochar [4]. Simulation results demonstrated that addition of biochar can effectively slow nutrient transport through the soil if the biochar/soil ratio and crucial biochar properties (like its adsorption capacity and affinity to the sorbate) are carefully matched to the soil properties (water velocity, soil type) and the amount of rainfall or irrigation. However, that model considered just the response of biochar-amended soils to a pulse of nutrient that simulates a single fertilizer application. Continuous flow of pure water before and after the end of the fertilizer pulse was assumed.

This study presents the development and testing of a mathematical model that describes the imbibition and drainage of water and nutrients in structured soils amended with biochars. We assume a dual-porosity structured soil that consists of uniform soil aggregates and biochar particles packed in a simple cubic structure. This porous medium has three pore systems: the interstitial (fracture) pores formed between the soil aggregates and the biochar particles, the less permeable intra-aggregate pores and the intraparticle pores of the biochar. We should not here that biochars are very porous materials with total porosities as high as 0.8 and cavities connected to the exterior with micron-size mouths [5]. Water in all pore systems is assumed to be mobile.

We use the Richards’ equation to describe one-dimensional (vertical) two-phase flow in our triple-porosity medium and simulate transfer of water between the interstitial pores and the soil or biochars pores with first-order rate equations. This formulation leads to a system of coupled partial differential equations for the air and water saturations that is solved together with the appropriate boundary and initial conditions using the IMPES finite difference method.

Simulation results reveal that the water holding capacity of biochar-amended soils depends on multiple system parameters. The most important ones are the volume fraction of added biochar, the total porosity of the biochar used and its pore size distribution, and the hydraulic properties of the original dal-porosity soil system. Using sensitivity analysis we will demonstrate the critical role of the interphase mass transfer coefficients of biochar, parameters that we are currently measuring experimentally. Finally, we will demonstrate how the imbibition-drainage model can be combined with our earlier convection-dispersion-adsorption model to simulate the complete sequence of nutrient transport in biochar-amended soils.

 References:

 [1] Spokas, K. A.; Cantrell, K. B.; Novak, J. M.; et al. “Biochar: A Synthesis of Its Agronomic Impact beyond Carbon Sequestration.” J. Environmental Quality 41 (2012) 973-989.

[2] Jeffery, S; F.G.A. Verheijena; M. van der Velde; A.C. Bastos. “A quantitative review of the effects of biochar application to soils on crop productivity using meta-analysis.” Agriculture, Ecosystems and Environment 144 (2011) 175–187.

[3] Crane-Droesch, A; S. Abiven; S. Jeffery; M.S. Torn. “Heterogeneous global crop yield response to biochar: a meta-regression analysis.” Environmental Research Letters 8 (2013) 044049.

[4] Sun, S; C. E. Brewer; C. A. Masiello; K. Zygourakis. “Nutrient Transport in Soils Amended with Biochar: A Transient Model with Two Stationary Phases and Intraparticle Diffusion” Industrial and Engineering Chemistry Research, 54 (2015) 4123–4135.

[5] Brewer, C.E.; V.J. Chuang; C.A. Masiello; H. Gonnermann; X. Gao; B. Dugan; L. E. Driver; P. Panzacchi; K. Zygourakis; C.A. Davies, “Beyond Biochar Chemistry: Measuring Density Towards an Understanding of Porosity and Environmental Interactions,” Biomass and Bioenergy 66 (2014) 176-185.