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Nonisothermal Plugflow Sbs

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isothermal flow
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  © COPYRIGHT 2008. All rights reserved. No part of this documentation may be photocopied or reproduced in any form without prior written consent from COMSOL AB. COMSOL, COMSOL Multiphysics, COMSOL Reac-tion Engineering Lab, and FEMLAB are registered trademarks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their respective holders. Nonisothermal Plug-Flow Reactor SOLVED WITH COMSOL REACTION ENGINEERING LAB 3.5a  ®   NONISOTHERMAL PLUG-FLOW REACTOR  | 1 Nonisothermal Plug-Flow Reactor Introduction  This model considers the thermal cracking of acetone, which is a key step in the production of acetic anhydride. The gas phase reaction takes place under nonisothermal conditions in a plug-flow reactor. As the cracking chemistry is endothermic, control over the temperature in the reactor is essential in order to achieve reasonable conversion. When the reactor is run under adiabatic conditions, the model shows how the conversion of acetone can be affected by mixing the reactant with inert. Furthermore, it is illustrated how to affect the conversion of acetone by means of a heat exchanger supplying energy to the system.The example details the use of the predefined Plug-flow reactor type in the Reaction Engineering Lab and how to set up and solve models describing nonisothermal reactor conditions. You will learn how to model adiabatic reactor conditions as well as how to introduce heat exchange. Model Definition  This model is related to an example found in Ref. 1. An essential step in the gas-phase production of acetic anhydride is the cracking of acetone (  A ) into ketene (  K  ) and methane (  M  ):  (1) The rate of reaction is  (2)  where the rate constant is given by the Arrhenius expression  (3) For the decomposition of acetone described above, the frequency factor is  A 1  = 8.2·10 14  (1/s), and the activation energy is  E 1  = 284.5  (kJ/mol).CH 3 COCH 3 CH 2 COCH 4 +(A)(K)(M) r 1  k 1 c  A = k 1  A 1  E 1  R g T  -----------– ⎝ ⎠⎛ ⎞ exp =  NONISOTHERMAL PLUG-FLOW REACTOR  | 2 Chemical reaction takes place under nonisothermal conditions in a plug-flow reactor, illustrated schematically in Figure 1. Figure 1: The Plug-flow reactor is a predefined reactor type in the Reaction Engineering Lab. Species mass balances are described by:  (4)  where  F  i  is the species molar flow rate (mol/s), V   is the reactor volume (m 3 ), and  R i  is the species rate expression (mol/(m 3 ·s)). Concentrations needed to evaluate rate expressions are found from:  (5)  where v  is the volumetric flow rate (m 3 /s). By default, the Reaction Engineering Lab treats gas phase reacting mixtures as being ideal. Under this assumption the volumetric flow rate is given by:  (6)  where  p  is the pressure (Pa),  R g   denotes the ideal gas constant (8.314 J/(mol·K)), and T   is the temperature (K).The reactor energy balance is given by:  (7) In Equation 7, C  p , i  represents the species molar heat capacity (J/(mol·K)), w s  is the shaft work per unit volume (J/(m 3 ·s)), and Q  denotes the heat due to chemical reaction (J/(m 3 ·s)): dF  i dV  ---------  R i = c i  F  i v -----= v p R g T  -----------  F  i  F  ii ∑ -------------=  F  ii ∑  C  p i , dT dV  --------  w s  Q Q ext ++=  NONISOTHERMAL PLUG-FLOW REACTOR  | 3  (8)  where  H   j  is the heat produced by reaction  j . The term Q ext  represents external heat added or removed from the reactor. The present model treats both adiabatic reactor conditions:and the situation where the reactor is equipped with a heat exchanger jacket. In the latter case Q ext  is given by:  (9)  where U   is the overall heat transfer coefficient (J/(m 2 ·s·K)), a  is the effective heat transfer area per unit of reactor volume (1/m), and T  amb  is the temperature of the heat exchanger medium (K). The Reaction Engineering Lab automatically sets up and solves Equation 4 and Equation 7 as the predefined Plug-flow reactor type is selected.  As input to the balance equations you need to supply the chemical reaction formula, the Arrhenius parameters, the species thermodynamic properties, as well as the inlet molar feed of reactants.Following the step-by-step instructions below, you will first model the cracking of acetone in an adiabatic plug-flow reactor. See how the acetone conversion varies with the ratio of reactant to inert in the inlet stream. In second model, add the effects of a heat exchanger jacket and observe how the added energy drives the reaction to completion. Working with Thermodynamic Polynomials  Reaction Engineering Lab uses the following set of polynomials as default expressions describing species thermodynamic properties:  (10) (11) (12) Q H   j r  j j ∑ –= Q ext 0 = Q ext  Ua T  amb  T  – () = C  p i ,  R  g  a 1  a 2 T a 3 T  2 a 4 T  3 a 5 T  4 ++++ () = h i  R  g  a 1 T a 2 2 ------ T  2  a 3 3 ------ T  3  a 4 4 ------ T  4  a 5 5 ------ T  5 a 6 +++++ ⎝ ⎠⎛ ⎞ = s i  R  g  a 1  T  ln  a 2 T a 3 2 ------ T  2  a 4 3 ------ T  3  a 5 4 ------ T  4 a 7 +++++ ⎝ ⎠⎛ ⎞ =

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