(545ab) Fluid Flow and Nutrient Retention in Biochar Amended Soils

Zygourakis, K., Rice University
Chen, Y., Rice University
Scope and Significance: Over the past several decades, food production has kept pace with human population growth only because of the successful development of new high-yielding crop varieties grown with the help of fertilizers. Thus, vast amounts of energy are consumed every year to produce the approximately 200 Mt of ammonia needed to make the nitrogen (N) fertilizers used by farmers around the globe. Unfortunately, more than half of the N fertilizer applied to a field is not available for plant growth due to losses caused by surface runoff, leaching into surface and ground water, or volatilization. These losses cause serious water pollution problems ranging from the hypoxic zone in the Gulf of Mexico to the contamination of wells and groundwater with nitrates. In addition, fertilizer losses trigger the release into the atmosphere of large amounts of nitrous oxide (a major greenhouse gas) and NOx.

The amendment of soils with biochar has been heralded as a sustainable method for preventing pollution problems caused by fertilizer losses and, at the same time, increasing crop yields. However, the available experimental data are highly variable. While some field studies report significant beneficial effects with up to 60% higher yield after biochar addition, other studies report that biochar amendments either have no effect or even result in lower agricultural productivity [1-2]. A major source for the variability of experimental data is the fact that biochar is not a single entity. Dozens of biomass feedstocks are used to produce biochars in different types of reactors under widely varying temperature programs and pyrolysis atmospheres. Thus, biochars have a very broad spectrum of chemical and physical properties. To further complicate things, 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 specific biochar.

Our Earlier Work in this Area: To begin bridging this knowledge gap, our recent research we focused on understanding the mechanisms that control the ability of biochars to improve crop nutrient availability and mitigate fertilizer leaching. First, we developed and tested a mathematical model that describes nutrient transport in soils amended with biochar[3]. Simulation results showed that biochar is effective in increasing nutrient availability for plants and minimizing fertilizer losses through leaching, but only if the biochar/soil ratio and some key biochar properties (like its adsorption capacity and affinity to the nutrient) are carefully matched to the soil properties (water velocity, soil type) and the amount of rainfall or irrigation.

A subsequent publication focused on the adsorption/desorption dynamics within biochar particles [4]. While it confirmed our original hypothesis that a biochar’s ability to retain nutrients is influenced by the differential in adsorption and desorption rates, the second study revealed a more complicated dynamic behavior that originally envisioned. The ability of a biochar to adsorb and then slowly release the fertilizer is determined by a complex interplay of external mass transfer, intraparticle diffusion (occurring through either pore or surface diffusion), and adsorption dynamics. Biochar particle size and porosity modulate the interactions between adsorption/desorption and intraparticle or external mass transfer. And, fast surface diffusion improves the ability of a biochar to act as a slow release medium at high water interstitial velocities, pointing out that biochars with fast intraparticle transport rates are good candidates for high-permeability fields or high rainfall areas. These findings explain why biochars with similar properties can have widely different impacts on crop yields, as reported in the literature.

However, both these publications considered the response of biochar-amended soils to a single pulse of nutrient that simulates a single application. Continuous flow of water before and after the end of the fertilizer pulse was assumed.

Fluid Flow in Biochar-Amended Soils: This study presents the development and testing of a mathematical model that provides a much more realistic description of fluid flow in structured soils amended with biochars. We assume a triple-porosity structured soil that consists of uniform soil aggregates and biochar particles packed in a simple cubic structure. This structured soil has three pore systems: (i) the interstitial pores formed between the soil aggregates and the biochar particles; (ii) the less permeable intrapores of soil aggregate pores; and (iii) the intraparticle pores of the biochar. Water in all pore systems is assumed to be mobile. We should note 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].

The solution of the flow equation of water in soils requires the water retention curve (WRC) that describes the relationship between the volumetric water content, or water saturation, and the capillary pressure. We used the van Genuchten and lognormal Kosugi models to fit the available experimental data for the WRC of (a) sandy soils and (b) soils amended with biochars having different particle size distributions. While the bimodal van Genuchten model provided very good approximations for the WRC of soils, the trimodal Kosugi model did a better job fitting the experimental data for biochar-amended soils. Because of the semi-empirical nature of the van Genuchten model parameters, bimodal and trimodal Kosugi models were used to fit the WRC of all porous media considered in this study.

Richards’ equation was used to describe two-phase flow in our triple-porosity medium with water as the invading fluid. Water transfer between the interstitial pores and the pores of soil aggregate or biochar particles was modeled with first-order rate equations. The pressures of both fluids in the three pore systems were assumed to be equal at each spatial position (local equilibrium). We also assumed constant densities and viscosities, and negligible gravity effects. With these assumptions, we obtained a system of coupled partial differential equations for the air and water saturations that was solved together with the appropriate boundary and initial conditions using the IMPES finite difference method. A full parametric study was conducted to select the time step and grid sizes that satisfy the stability criterion and minimize mass balance errors. In all cases, the PDEs were integrated for long enough times to describe the wetting and drying dynamics, as well as the temporal evolution of water velocities in the topsoil. As is well known, only the top approximately 30 cm of soil are critical for nutrient transport and crop uptake.

Simulation results with the WRC obtained experimentally for (a) sandy soils and (b) soils amended with 2 wt% biochar show that the addition of biochar increases only slightly either the time required to fully saturate the topsoil (about 12 hours in both cases) or the water holding capacity of the amended soil. Small effects on the topsoil saturation times were also observed with biochar/soil ratios as high as 5 wt% and 0.5-0.8 total biochar porosities [5], the typical range of these parameter values for field applications. Clearly, the beneficial effect of biochar comes primarily from its ability to adsorb and slowly release nutrients (fertilizer).

Having computed the temporal evolution of water velocities in the top soil during wetting and drying events, we revisited our earlier model to study the adsorption/desorption dynamics of biochar-amended soils with realistic velocity profiles. We will present simulation results describing how the way in which the fertilizer is applied (flow rate, nutrient concentration etc.) affects the initial spatial distribution of nutrient in the topsoil and how this distribution changes over time in response to irrigation or rain events and dry periods. These simulations confirm our earlier results regarding the benefits of biochar amendments and provide guidelines for rational management of fertilizer use.


[1] Spokas, K. A.; Cantrell, K. B.; Novak, J. M.; et al. “Biochar: A Synthesis of Its Agronomic Impact beyond Carbon Sequestration.”J. Environmental Quality41(2012) 973-989.

[2] Crane-Droesch, A; S. Abiven; S. Jeffery; M.S. Torn. “Heterogeneous global crop yield response to biochar: a meta-regression analysis.” Environmental Research Letters8(2013) 044049.

[3] 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.

[4] Zygourakis, K. “Biochar soil amendments for increased crop yields: How to design a “designer” biochar,” AIChE J., 63(2017), 5435-5437.

[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 Bioenergy66(2014) 176-185.