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# Day23 - CE 561 Lecture Notes Fall 2009 Day 23 The ideal...

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CE 561 Lecture Notes Fall 2009 p. 1 of 12 Day 23: The ideal plug flow reactor The next idealized reactor configuration we will consider is the ideal plug flow tubular reactor. In this model, we assume that the reactor is a tube in which the velocity is in the axial direction only. We further assume that the velocity and all other quantities are constant across the tube diameter, and that diffusion and conduction in the axial direction are negligible. With these assumptions, the species mole balance equations are ( ) 1 M x k ik i i d vC r dx α = = If the velocity is independent of axial position (which will be the case if density is constant), then it can be taken out of the derivative to get 1 M k x ik i i dC vr dx = = Defining a residence time τ (the time a fluid element has spent in the reactor when it reaches position x ) by x x v = this equation becomes 1 M k ik i i dC r d = = which is identical to the constant volume batch reactor equation with the clock time t replaced by the residence time . If the density in the reactor cannot be assumed to be constant (because of changes in the number of moles or changes in the temperature of a gas, for example) then the plug flow reactor balances are not identical to those for the batch reactor. However, we can still define the residence time in a similar way as , xo x v = where v x,o is the axial velocity at the inlet. Then the equation becomes , 1 M x k ik i i v d Cr dv =  =   The velocity at a given point in the reactor can be related to the density at that point using the total mass balance. For the steady-state plug flow reactor, the mass balance reduces to ( ) 0 x d v dx ρ =

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CE 561 Lecture Notes Fall 2009 p. 2 of 12 which can directly be integrated between the inlet (where the velocity is v x,o and the density is ρ o ) and some other point in the reactor to give v x = o v x,o The local velocity can often be computed from the ideal gas law using the local composition and temperature. For isothermal reaction among gases, it can be written in terms of the extent(s) of reaction (for as many linearly independent reactions as we have) and the overall change in mole number for those reactions. For a mixture of ideal gases, the velocity is ,, oo x xo p nT vv v nT p = = where T is the temperature, n / n o is the ratio of the number of moles at a particular position to the number of moles in the feed, and p is the pressure. The most direct measure of the reactor’s capability to carry out the reaction is given by the total residence time based on the inlet flow rate and total reactor volume. Froment and Bischoff designate this as θ , but most other authors (including me) use the symbol τ . , o LV vQ = = Where L is the reactor length, V is the reactor volume, and Q o is the volumetric flow rate of reactant to the reactor. In practice, reactors are often described in terms of the reciprocal of this, which is usually called “space velocity”. For catalytic reactions, it is not the volume of the
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Day23 - CE 561 Lecture Notes Fall 2009 Day 23 The ideal...

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