化学反应工程Chapter 14.ppt

* 化 学 反 应 工 程 Chapter 14 The Tanks-In-Series Model This model can be used whenever the dispersion model is used; and for not too large a deviation from plug flow both models give identical results, for all practical purposes. Which model you use depends on your mood(心情) and taste. The tanks-in-series model is simple, can be used with any kinetics, and it can be extended without too much difficulty to any arrangement of compartments, with or without recycle. 化 学 反 应 工 程 Figure 14.1 The tanks-in-series model 化 学 反 应 工 程 14.1 PULSE RESPONSE EXPERIMENTS AND THE RTD Figure 14.1 shows the system we are considering. We also define Then and at any particular time, from Eq.11 in Chapter 11 化 学 反 应 工 程 For the first tank. Consider a steady flow ? m3/s of fluid into and out of the first of these ideal mixed flow units of volume V1. At time t = 0 inject a pulse of tracer into the vessel which when evenly(均匀地) distributed in the vessel (and it is) has a concentration C0 (C0 = M/ V1). At any time t after the tracer is introduced make a material balance, thus 化 学 反 应 工 程 In symbols this expression becomes where C1 is the concentration of tracer in tank “1.” Separating and integrating then gives or 化 学 反 应 工 程 Since the area under this C/C0 versus t curve is (check this if you wish) it allows you to find the E curve; so one may write [－] N = 1 (1) That is to say, for a single mixed flow reactor, its E function is 化 学 反 应 工 程 Separating gives a first-order differential equation, which when integrated gives [－]　 N = 2 (2) For the second tank where C1 enters, C2 leaves, a material balance gives 化 学 反 应 工 程 For the Nth tank. Integration for the 3rd, 4th,? ? Nth tank becomes more complicated so it is simpler to do all of this by Laplace transforms. The RTD’s, means and variances, both in time and dimensionless time were first derived by MacMulin and Weber (1935) and are summarized by Eq.3. 化 学 反 应 工 程 Graphically these equation