This looks relevant to biochar nutrient management in NZ pastoral farming. No access so can’t be sure that the nutrient focus includes N.

Nutrient Transport in Soils Amended with Biochar: A transient model with two stationary phases and intraparticle diffusion

“We present the development of a rate model that simulates nutrient transport in soils amended with biochar. The model considers two stationary adsorbent phases (biochar and soil), axial dispersion, interphase mass transfer and intraparticle diffusion. Langmuir isotherms govern the local equilibria between the solute diffusing in the liquid-filled pores and adsorbed on the pore surfaces of biochar and soil particles. We demonstrate 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. Simulations can also track the spatial and temporal evolution of nutrient concentration profiles, information that is essential for analyzing and interpreting experimental data. The new model can be a valuable tool for fine-tuning the production and use of biochar.”