离心萃取级联分离锂同位素的数学模型

萃取法分离锂同位素有望替代汞齐法消除汞害，但需多级萃取才能获得高丰度同位素，采用离心萃取机替代萃取澄清槽形成萃取级联系统可提升分离效率。基于萃取法分离锂同位素、离心萃取分离原理和级联理论，借鉴气体离心级联分离同位素的方法，引入分流比概念，建立了离心萃取级联分离锂同位素单级、多级的数学模型和级联的平衡时间模型，对离心萃取级联分离锂同位素进行计算分析。离心萃取级联是一种类似全回流矩形级联形式，取料量对级联级数有着很大的影响，级联存在最大取料丰度限制，级联平衡时间受到目标丰度和离心萃取机级停留时间(处理能力)影响，采用多步法级联可有效减少平衡时间。该数学模型可指导工艺的设计，为下一步的产业化应用提供理论依据。

Mathematical Model of Lithium Isotope Separation by Centrifugal Extraction Cascade

Extraction is a promising method of lithium isotopes separation, which is expected to replace the mercury method to eliminate mercury harm. The separations of lithium isotopes by solvent extraction system mainly use the difference of partition coefficients of ⁶Li and ⁷Li in two-phase solvents to separate lithium isotopes. There are several solvent extraction systems to separate lithium isotopes, mainly ethers, and crown (hole) ether extraction systems have the best separation effect whose coefficient could reach to 1.081. The solvent extraction systems for lithium isotope separation need to meet the following requirements: stable system with appropriate extraction partition coefficient for lithium; existence of obvious lithium isotope separation effect; high speed of two-phase flow contact and isotope exchange. Consequently, solvent extraction is a promising method for the separation of lithium isotopes. In order to obtain high abundance isotopes, multi-stage extraction is needed in the extraction process. Using centrifugal extractor instead of extraction clarifier to form an extraction cascade system can greatly improve the separation efficiency. Based on the principle of extraction, centrifugal extraction and cascade theory, the concept of split ratio was introduced, and the single-stage and multi-stage mathematical models and equilibrium time models of centrifugal extraction cascade separation of lithium isotopes were established. This paper is aim at isotope exchange section, which is the critical part of centrifugal extraction cascade. In the isotope exchange section, the water phase and organic phase are continuous flow in each stage. Theoretically, the ratio of organic phase to water phase and the content of lithium in each phase are exactly the same. After isotope exchanging and reclaiming, the two phases were inversed by extraction and stripping and return to the isotope exchange section. Thus, cascade’s split ratio of all stages is 0.5. In addition, the equilibrium time of cascade entirely depends on isotope exchange section which has the longest equilibrium time. The equilibrium time of isotope exchange section can be estimated by analyzing the transport rate of enriched component. Centrifugal extraction cascade is a kind of reflux rectangular cascade. The amount of feed has a great influence on the cascade stages. There is a limit of maximum feed abundance in the cascade. The equilibrium time of the cascade is affected by the target abundance and the residence time which is relied on centrifugal extractor’s processing capacity. The multi-step cascade can effectively reduce the equilibrium time. The mathematical model can guide the process design and provide a theoretical basis for the next industrial application.