In hydrothermal valorization of black liquor (BL) from the Kraft process, the separation of inorganic salts is pivotal to prevent them from fouling downstream equipment such as reactors and for the cost-efficient recycling of salts into pulp cooking chemicals. In this work, the phase behavior of the inorganic salts present in BL was studied in supercritical water and the conditions for the separation from BL were optimized. A high-pressure differential scanning calorimetry study indicated the concomitant precipitation of salts and the formation of a second salt-rich liquid-like phase. The potassium-to-sodium ratio was found to strongly impact the phase behavior of the salt mixture. Potassium was found to prevent salt precipitation and to lead to the formation of a second liquid-like phase alone. At K/(K + Na) >= 0.4, a steady salt separation could be achieved, enabling the continuous extraction of up to 96% of the salts in a concentrated brine effluent.