轴向扩散模型—闭式模型中的示踪过程与停留时间分布

THE AXIAL DISPERSION MODEL—TRACER EXPERIMENTS AND RESIDENCE TIME DISTRIBUTION IN A CLOSED REACTOR

本文采用严格满足质量守恒的卷积型出口边界条件(uc-D^(c)/x=u integral from 0 to t c0(t-θ)E(L,θ)dθ,x=L),正确描述了闭式模型中纯物理的暂态示踪过程.与[1]类似,这也是一种未知边界问题。本文用传递函数概念给出第二种新解法.结果同样证明:对示踪过程,著名的 Danckwerts出口边界条件(c/x=0,x=L)也仅当模型长度 L→∞时才严格成立,对有限长的模型也是不恰当的。将两种解作了对比.还证明了:模型中示踪物的暂态浓度分布与 L 无关;D→∞时,E(L,t)→δ(t),→0,这与一个=0的全混流模型等价。

In this paper,the convolutional boundary condition at exit which represents both the total mass conservation between entrance and exit as well as the flux conservation at exit is proposed by the author.Thus the tran- sient tracer experiment of a closed model is rigorously formulated. For such a boundary value problem in domain of the Laplace transforma- tion parameter it is proved that at any arbitrary point x′(0≤x′<L),the transfer function H^(x′,s)=(x′,s)/(0,s)is independent of the length of of the model,namely dH^(x′,s)/dL=0 This decouples the transient concentration distribution of tracer from the residence time distribution,and the RTD density function,transient concentration distribution and exact solution of the exit concentration are easily solved.Theoretically,these solutions apply to any extent of back- mixing. The result of this paper strictly proves that the Danckwerts boundary condition at exit (c/x=0,x=L)only holds under the limit L→∞ and is not appropriate when the length of the model is finite.Based on this condi- tion,the solution in time-parameter space obtained by Brennet (1962)is only useful for weak backmixing.When D→∞(Pe→0),the RTD density fun- ction of this model E(L,t)→δ(t),simply equivalent to CSTR at t=0.