Mixing in Residence Time Space

Both reactors are physically unique in that each reactor is fed with different feed concentrations (Cfj and C ), and each are associated with a different reactor volume (Vj and V2) and product volumetric flow rate (Qi and Q2). It follows that Rj and R2 must have distinct residence times, given by Ti = Vj/Qi and T2 = V2/Q2, respectively. Each reactor produces a different effluent concentration as well. The product of the two reactor effluent streams is combined to produce a mixture concentration, C and if density is assumed constant, the total volumetric flow rate is Q,ot = Qi + Q2- 

Computing the residence time of a mixture is equivalent to determining the residence time of the entire system. Let us define the residence time of the system, as the total reactor volume (the sum individual reactor volumes) divided by the combined volumetric flow rate  

Each reactor volume may be expressed in terms of the associated residence time and volumetric flow rate as follows  

When this expression is substituted into Equation 5.9, we obtain the following  

This equation is similar in appearance to the mixing expression for concentrations. If the substitution A = Qi/Qtot 

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Figure 5.21 Geometric interpretation of mixing in residence time space. Mixtures also lie on a straight line when residence time is used since residence time also obeys a linear mixing law.

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