By Laurence A. Belfiore

ISBN-10: 0471202754

ISBN-13: 9780471202752

This graduate textbook methods the layout of chemical reactors from microscopic warmth and mass move rules. Belfiore (Colorado nation college) describes the layout of packed catalytic tubular reactors, analyzes mass move and chemical reactions in isothermal catalytic pellets, and develops quantitative ways to estimate diffusion and axial dispersion coefficients. Annotation (c)2003 booklet information, Inc., Portland, OR

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Hence, this variable contribution to the inlet stream of all reactors, except the first, is accounted for by −1 along the diagonal below the main diagonal in A described above. As a preliminary to the solution of (2-37) it is instructive to solve a similar inhomogeneous ODE for x(ω) without matrices: dx + ax = xinlet dω x(ω = 0) = xinitial (2-39) (2-40) 43 ANALYSIS OF A TRAIN OF FIVE CSTRs where xinlet and xinitial are constants. The homogeneous solution is obtained by ignoring xinlet and solving dx + ax = 0 dω (2-41) which has the following solution via separation of variables: dx = −a d ω x x(ω)homogeneous = (constant) exp(−aω) (2-42) (2-43) Since xinlet is constant, the particular solution is obtained by choosing a constant for xparticular .

By definition, each extent of reaction is zero at the inlet to the reactor, where V = 0. The similarities between the two approaches return when one relates molar densities, partial pressures, and mole fractions as Ci = yi p RT (1-5) and the mole fraction of component i is yi = Fi j Fj 1 ≤ j ≤ total number of components (1-18) The final task, before solving the coupled ODEs for the extents of reaction ξ1 , ξ2 , and ξ3 is to express component molar flow rates in terms of the extents of reaction.

0 0 2 4 6 8 Variable time/average residence time 10 Figure 2-3 Transient molar density response for reactant A in a series configuration of five equisized CSTRs that operate at the same temperature, with simple first-order chemical kinetics. The numerical solution of these five coupled ODEs is illustrated in Figure 2-3. Solution (b) Steady-State Solution. The steady-state response for each CSTR is obtained by neglecting the accumulation term in the generic mass balance from part (a): d CAk = CA,k−1 − (1 + β)CAk = 0 d (t/τk ) (2-21) Hence, the steady-state recurrence formula is CAk = CA,k−1 1+β (2-22) which suggests that CAk should be of the following form: CAk = σ = k = 1 1+β σ k−1 1+β (2-23) (2-24) ANALYSIS OF A TRAIN OF FIVE CSTRs 41 The constant σ is determined from the molar density of reactant A in the feed stream to the first reactor: CA0 = σ ◦ =σ (2-25) CA0 (1 + β)k (2-26) The steady-state solution is (CAk )steady state = Laplace Transform Analysis.

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