二元系简单蒸馏与平衡蒸馏的关系

doi:10.11949/0438-1157.20240142

摘要/Abstract

摘要：

Rayleigh方程是描述与时间相关的简单蒸馏的基础方程，广泛应用于同位素分馏等多个学科领域，但在化工分离的领域却鲜见报道。针对上述问题，基于组分净摩尔量建立了简单蒸馏的Rayleigh方程和平衡蒸馏的数学模型，并利用数学积分和差分关系，以N级串联平衡蒸馏建立了描述简单蒸馏的计算模型，从而揭示了简单蒸馏与平衡蒸馏间的理论关系。最后利用N级串联平衡蒸馏的数学模型，在N趋于无穷条件下推导出Rayleigh方程。结果表明：Rayleigh蒸馏是简单蒸馏的一种特殊操作工况，其特征为汽化率和加热速率趋于无穷小，蒸馏所需时间无限长。因此，Rayleigh蒸馏更适用于同位素分馏过程。

关键词: Rayleigh方程, 蒸馏, 简单蒸馏, 平衡蒸馏, 同位素分馏

Abstract:

The Rayleigh equation is a fundamental equation that describes time-dependent simple distillation. Despite it has extensive application in isotope fractionation related fields, its application in chemical separation related articles is few. This paper addresses this discrepancy by initially establishing the Rayleigh equation for simple distillation and the mathematical model for equilibrium distillation based on component molar flow rates. Subsequently, the theoretical relationships between integration and differentiation in mathematics are applied to build an approximate model for simple distillation using a series of N stages in equilibrium distillation, elucidating the theoretical connection between simple and equilibrium distillation. Finally, using the mathematical model of N-stage series equilibrium distillation, the Rayleigh equation is derived under the condition that N tends to infinity. The results indicate that Rayleigh distillation is a specific operational condition of simple distillation, characterized by infinitesimally small vaporization rates and heating rates, requiring an indefinitely long distillation time. It reveals that the infinite time required for Rayleigh distillation aligns more with isotope fractionation processes.

Key words: Rayleigh equation, distillation, simple distillation, equilibrium distillation, isotope fractionation

中图分类号:

TQ 021.4

刘逸群, 王超, 卢春喜. 二元系简单蒸馏与平衡蒸馏的关系[J]. 化工学报, 2024, 75(5): 1912-1919.

Yiqun LIU, Chao WANG, Chunxi LU. Relationship between simple distillation and equilibrium distillation in binary system[J]. CIESC Journal, 2024, 75(5): 1912-1919.

图/表 3

图1 单一平衡级蒸馏工艺示意图

Fig.1 Schematic diagram of single equilibrium stage distillation process

图2 简单蒸馏的N级串联平衡蒸馏工艺构建

Fig.2 A simple distillation process diagram constructed by N-stage equilibrium distillation

图3 平衡蒸馏、简单蒸馏和Rayleigh蒸馏的T-x-y相图比较

Fig.3 Comparison of T-x-y phase diagram for equilibrium distillation, simple distillation and Rayleigh distillation

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