Nutrient availability after fertilising agricultural soils is affected by many factors, including soil moisture conditions and physicochemical properties. Herein, the availability of potassium in soil enriched with biochar is studied, considering either saturated or unsaturated moisture conditions and questioning key ion exchange approaches, such as equilibrium exchange (E.E.) and kinetic exchange (K.E.). Potassium release is simulated from a soil–biochar mixture of 0, 0.5, 1 and 2% by coupling HYDRUS-1D and PHREEQC models. The water flow, mass transport and geochemical processes are simulated for a cultivation period that imitates agronomic and environmental conditions of a common agricultural field in Northern Greece. Potassium is released gradually during the irrigation period in the case of unsaturated flow conditions as opposed to its complete release over a few days in the case of saturated flow conditions in the soil. Regarding ion-exchange processes, the soluble amount of potassium is more readily available for transport in soil solution when using the E.E. approach compared to the K.E. approach that assumes a kinetically controlled release due to interactions occurring at the solid–solution interface. The increased proportion of biochar in soil results in a doubling of available potassium. Among the four modelling schemes, although the total mass of potassium released into soil solution is similar, there is a significant variation in release time, indicating that simplified saturated conditions may lead to unrealistic estimates of nutrient availability. Further experimental work will be valuable to decrease the uncertainty of model parameter estimation in the K.E. approach.

Olive mill wastes continue to be a management challenge due to the large volumes produced, particularly due to their toxicity and impacts on the environment. Thermal conversion through pyrolysis or hydrothermal carbonization techniques can detoxify wastes while conserving nutrient contents. In this work, we produced up-to-date data on olive mill waste flows in Spain, Tunisia, and Greece and characterized representative samples in the laboratory. Assays of thermal conversion of olive mill wastewaters and solid wastes were also performed to understand biochar yields and final properties, and the total quantities of nutrients contained were estimated. Of particular note were the quantities of potassium in Tunisian wastewaters, representing 0.6% of the total mass and an annual flow of approximately 5000 t, and in the Spanish solid wastes, an average of 1.7% of the total mass is potassium, representing an annual flow of approximately 23,000 t. Concerning phosphorus, Spanish solid wastes had the highest contents (0.1%), double that of other countries’ wastes. Annually, olive mill wastes from the three countries are estimated to contain approximately 35 × 10³ tons of potassium and 2.6 × 10³ tons of phosphorus. With this resource converted to biochar, each year more than 700 km² of soils could be enriched in 0.2% carbon with biochar at an application rate of 7 t ha⁻¹.