Rate Constants in Well-Stirred & Two-Zone CSTR: Determination - Prof. Annette L. Bunge, Exams of Chemistry

Download Rate Constants in Well-Stirred & Two-Zone CSTR: Determination - Prof. Annette L. Bunge and more Exams Chemistry in PDF only on Docsity! ChEN 507/Fall 2004 1 3. Correct determination of rate constants measured in constant flow stirred reactors (CSTR) requires that the reactors be well stirred. Experimental confirmation that a flow reactor really is well stirred is usually determined using a residence time analysis. A common strategy is to introduce a pulse containing a known mass of a tracer chemical into the inlet flow stream and then monitor the cumulative mass leaving the reactor. The experimental results are compared with the theoretical cumulative mass calculated from differential mass balance analysis of a well-stirred flow reactor. Consider a CSTR of volume V with steady inlet and outlet volumetric flow rate q as illustrated in the figure. Initially, the CSTR contains no chemical tracer and the inlet solute contains no chemical tracer except at t = 0, when a pulse containing a mass of tracer Mo is introduced in the inlet flow. The chemical tracer does not react. The concentration of tracer chemical C in the outlet solution is determined. The cumulative mass from the CSTR is found by integrating the mass flow rate of the chemical tracer (qC) with respect to time. a. Assume that the CSTR is well stirred. (i) Provide an expression for the inlet tracer concentration Cin describing the tracer introduced as a pulse containing a mass of tracer Mo. (Hint: What will the concentration in the reactor become if a mass of chemical Mo is introduced into a CSTR with volume V.) (ii) Derive the differential mass balance describing the concentration of the chemical tracer (C) in a well-stirred CSTR. What is the applicable initial condition. Rewrite the problem equations in terms of dimensionless concentration in the CSTR (φ) and dimensionless time (τ) defined as follows: o C M V φ = qt V τ = (iii) Solve the differential mass balance for the applicable initial condition to obtain an algebraic expression describing the dimensionless concentration of tracer chemical in the outlet solution, φ(τ). (iv) Derive an algebraic expression describing the cumulative mass out of the CSTR (M) normalized by Mo as a function of time τ. (v) Determine the dimensionless time required to clear 95% ( 95τ ) and 99% ( 99τ ) of the injected chemical mass from the reactor. (vi) The mean residence time in a reactor ( Rτ ) is calculated from: 0 1R o M d M τ τ ∞ ⎛ ⎞ = −⎜ ⎟ ⎝ ⎠∫ Determine Rτ for a well-stirred CSTR. b. A CSTR may contain zones that are less well stirred. Consider a situation in which a portion of the CSTR behaves like a second CSTR with volume V2 as shown in Figure 3.2. The volumetric flow rate to and from this reactor is q2. Remember that V = V1 + V2 and q2 < q. In V2, C2 q2 q2 q, C1 q, Cin V1, C1 ChEN 507/Fall 2004 2 most cases, the residence time in the second CSTR will be longer than the average residence (i.e., V2/q2 > V/q). (i) Derive the differential mass balances describing the concentration of the chemical tracer in the two well-stirred CSTR (i.e., (C1 and C2). Write the resulting equations in terms of the following dimensionless quantities: 1 o C M V φ = 2 o C M V θ = 2q qf q = 2V Vf V = qt V τ = (ii) Solve the differential mass balances for the applicable initial conditions using Laplace transforms to obtain an algebraic expression describing the concentration of tracer chemical in the outlet solution ( )sφ . (iii) Assuming that fq = fv = f, derive the algebraic expression describing the concentration of tracer chemical in the outlet solution φ(τ). (Hint: Mathematica may be helpful.) (iv) Derive an algebraic expression describing the normalized cumulative mass out of the CSTR (M / Mo) as a function of time τ. (Mathematica may be helpful.) (v) Plot M/Mo as a function of τ (0 < τ < 4 for the two well-stirred reactor with f = 0.2, 0.5 and 0.8 compared with the one well-stirred reactor. (vi) Determine the dimensionless time required to clear 95% ( 95τ ) and 99% ( 99τ ) of the injected chemical mass from a reactor consisting of two well-stirred reactors when f = 0, 0,2, 0.5 and 0.8. (vii) Determine Rτ for a well-stirred CSTR when f = 0, 0,2, 0.5 and 0.8. (Mathematica may be helpful.) (viii) Comment on the results in parts (v) through (vii) and why you think that the results are (or are not) reasonable. (Note: If you indicate that the results are unreasonable then explain what might be wrong in your solution.) Pfs Vv Vdc = -ge ott dg 2 -f a THO Pe! dt cok é, uso nett alinnd p0a tas pals fe) . 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