非理想流动管式反应器闭式出口边界条件的不可逆过程热力学分析

ANALYSIS OF THE EXIT BOUNDARY CONDITION OF A CLOSED TUBULAR REACTOR BY THE THEORY OF NON—EQUILIBRIUM THERMODYNAMICS

当用闭-闭式轴向返混模型模拟管式反应器中的非理想流动时,Dankwerts直觉提出的出口处浓度梯度为零的边界条件可以使模型得到唯一解。但是这个边界条件并未经过理论证明。本文将非平衡态过程热力学的最小熵增率原理用于一级不可逆反应,借助于数值计算方法,验证了零出口梯度判据和最小熵增率判据的一致性,并表明了闭-闭式轴向扩散模型在返混系数极大时,可以逼近理想全混流反应器。

In order to simulate a chemical reaction in a closed reactor with the axial dispersion model, Dankwerts(1953)proposed intuitively a boundary condition of zero gradient of concentration for the reactor outlet. Thus,a unique solution for the concentration profile and the outlet concentration for the reacting system can be decided from the mathematical model. To date no one has convincingly justified this well-known Dankwerts bondary condition, except Standart(1968) who showed that only zero gradient of concentration at the outlet garanteed the entropy production rate across the outlet non-negative, satisfying the requirement of process spontaneity. In this paper, the theory of thermodynamics of irreversible processes is applied to a closed reacting system subject to axial dispersion. The theorem of minimum entropy production for a steady state is used as the criterion to decide the outlet concentration of the reactor when more general exit boundary condition of continuity of mass flux is designated to the exit. The computational results with a first order irreversible reaction confirm that the Dankwerts boundary condition is consistent with the criterion of the minimum entropy production and with Standart's conclusion as well. It is also shown that the model of axial dispersion on a closed tubular reactor approaches an ideal mixed reactor as the extent of dispersion goes to infinity.