Days20n21 - CE 561 Lecture Notes Fall 2009 Days 20 and 21:...

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CE 561 Lecture Notes Fall 2009 p. 1 of 14 Days 20 and 21: Fundamental Equations for Reactor Engineering The basis of most of reactor modeling is a set of fundamental ‘balance’ equations. These equations are mathematical statements of physical laws that require conservation of mass, energy, momentum, and quantities of particular chemical species. In general, these can be derived by selecting a control volume and writing a balance on the quantity under consideration (mass, energy, etc.) over that control volume. The control volume could be an entire reactor, a catalyst pellet, or an infinitesimally small element of volume within the reactor. This balance will have the form: + = Volume Control within Production of Rate Volume Control of out Transport of Rate Volume Control into Transport of Rate Volume Control within on Accumulati of Rate or, more simply, {accumulation = in – out + production} The separation between transport in and transport out is somewhat artificial, so it may often make sense to consider transport as a single term: Rate of Net Rate of Rate of Accumulation Transport Production within Control into Control within Control Volume Volume Volume   = +   When we are considering an infinitesimally small control volume, it often makes sense to split the transport rate into two or more mathematically separate terms. Usually we split it into a ‘convection’ term – transport due to the overall (mass-average) motion of the fluid – and a ‘diffusive term’ – motion of the particular substance under consideration (energy, momentum, or a chemical species) relative to the overall motion. The diffusive term is driven by gradients of the substance (and possibly also by gradients of other quantities). Then the general balance is Net Rate of Net Rate of Rate of Rate of Convective Diffusive Accumulation Pro Transport Transport within Control into Control into Control Volume Volume Volume =++ duction within Control Volume We will show later that application of this balance to an infinitesimally small control volume allows us to derive a general set of balance equations that can be integrated and/or simplified to describe many situations, including the prototypical reactor types (batch, plug flow, CSTR). First, however, we will apply the balance to some simple macroscopic situations.
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CE 561 Lecture Notes Fall 2009 p. 2 of 14 The Ideal Batch Reactor: Consider first an insulated, well-mixed batch reactor of volume V, with some chemical reactions (in general written as 1 0, 1, N ij j j A iM α = = = ) going on inside it. First consider a balance on the total mass inside the reactor, for which Net flow rate of mass into reactor = 0 Rate of production of mass within the reactor = 0
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Days20n21 - CE 561 Lecture Notes Fall 2009 Days 20 and 21:...

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