Chap8Lecture1 - CHAPTER 8 Steady-State Nonisothermal...

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Unformatted text preview: CHAPTER 8 Steady-State Nonisothermal Reactor Design 8.1 Rationale Heat plays important role in reactions. Most industrial operations are nonisothermal . Additional equations are needed to formulate the reactor equations. Example 8-1 Additional Info Needed for Nonisothermal Reactor Design Calculate the reactor volume in a PFR. Nonisothermal, adiabatic, exothermic: T increases along the reactor. Solution : 1. Design equation: Ao A F r dV dX- = 2. Rate law: -r A = kC A 3. Stoichiometry ( liquid ) v = v o F A = C A v o F Ao = C Ao v o C A = C Ao (1-X) 4. Combine o v X k dV dX ) 1 (- = Arrhenius equation: - = T T R E k k 1 1 exp 1 1 Since T goes up along the reactor, k will also rise thus: o v X T T R E k dV dX- - = 1 1 1 exp 1 1 Then another relation is needed between T and V or T and X: Energy Balance 8.2 The Energy Balance 8.2.1 First Law of Thermodynamics Closed system : No mass crosses the system boundaries. The energy balance for a closed system: The change in the energy of the system (dE), equals the heat flow to the system (δQ) minus the work done by the system on the surrounding (δW) : W Q dt E d sys - = ˆ Open system: Mass crosses the boundaries: - + - = flow mass by system leaving energy of rate flow mass by system the to added energy of rate g surroundin the on system the by done work of rate g surroundin from system the to flow heat of rate system the within energy of ion accummulat of Rate out out in in sys E F E F W Q dt E ˆ d- +- = Figure 8-1 Energy balance on an open system. The energy balance on an open system involving many components with F i , E i : out n i i i in n i i i sys E F E F W Q dt E ˆ d ∑ ∑ = =- +- = 1 1 (8-3) 8.2.2 Evaluating the Work Term Separate the work term into i) flow work, ii) other work Flow work: work necessary to get the fluid in and out of the system. When shear stresses are negligible s out n i i i in n i i i W V ~ P F V ~ P F W + +- = ∑ ∑ = = 1 1 (8-4) where P = pressure, i V ~ = the specific volume of component i. W s = shaft work due to stirrer, turbine, etc....
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Chap8Lecture1 - CHAPTER 8 Steady-State Nonisothermal...

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