Chapter 3 ideal reactors for single reactions

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY FACULTY OF CHEMICAL ENGINEERING Chemical Reaction Engineering (Homogeneous Reactions in Ideal Reactors) Mai Thanh Phong, Ph.D FCE – HCMC University of Technology Chemical Reaction Engineering Chapter Ideal Reactors for a Single Reaction Material and energy balances The starting point for all design is the material balance expressed for any reactant (or product) Figure 3.1 Material balance for an element of volume of the reactor Thus, as illustrated in Fig 3.1, we have Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction In nonisothermal operations energy balances must be used in conjunction with material balances Figure 3.2 Energy balance for an element of volume of the reactor Thus, as illustrated in Fig 3.2, we have Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction In this chapter we develop the performance equations for a single fluid reacting in the three ideal reactors shown in Fig 3.3 We call these homogeneous reactions Figure 3.3 The three types of ideal reactors: (a) batch reactor, or BR; (b) plug flow reactor, or PFR; and (c) continuously stirred tank reactor, or CSTR Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction Batch reactor (BR) Make a material balance for any component A Noting that no fluid enters or leaves the reaction mixture during reaction, the material balance written for component A is or Mai Thanh Phong - HCMUT (3.1) Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction n n n (3.2) By replacing these two terms in Eq 3.1, we obtain n (3.3) Rearranging and integrating then gives n (3.4) If the density of the fluid remains constant, we obtain with Mai Thanh Phong - HCMUT Chemical Reaction Engineering (3.5) Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction For all reactions in which the volume of reacting mixture changes proportionately with conversion, Eq 3.4 becomes (3.6) n Continuously stirred tank reactor (CSTR) Figure 3.4 Notation for a CSTR rAf = rA Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction By selecting reactant A for consideration, material balance for a CSTR can be written as follows (3.7) As shown in Fig 3.4, if FA0 = v0CA0 is the molar feed rate of component A to the reactor, then considering the reactor as a whole we have Introducing these three terms into Eq 3.7, we obtain (3.8) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction which on rearrangement becomes (3.9) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 Chapter Ideal Reactors for a Single Reaction More generally, if the feed on which conversion is based, subscript 0, enters the reactor partially converted, subscript i, and leaves at conditions given by subscript f, we have (3.10) For the case of constant-density systems XA = – CA/CA0: (3.11) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 10 Chapter Ideal Reactors for a Single Reaction Figure 3.5 is a graphical representation of these mixed flow performance equations 3.9 3.11 Figure 3.5 Graphical representation of the design equations for CSTR Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 11 Chapter Ideal Reactors for a Single Reaction Plug flow tubular reactor (PFTR) Figure 3.6 Notation for a plug flow tubular reactor At the steady-state, the material balance for reactant A becomes (3.12) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 12 Chapter Ideal Reactors for a Single Reaction Referring to Fig 3.6, we see for volume dV that Introducing these three terms into Eq 3.12, we obtain Noting that We obtain Mai Thanh Phong - HCMUT (3.13) Chemical Reaction Engineering Apr 8, 2023 13 Chapter Ideal Reactors for a Single Reaction For the reactor as a whole the expression must be integrated Grouping the terms accordingly, we obtain Thus (3.14) For a more general expression, we have (3.15) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 14 Chapter Ideal Reactors for a Single Reaction For the special case of constant-density systems We have (3.16) Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 15 Chapter Ideal Reactors for a Single Reaction 3.14 3.16 Figure 3.7 Graphical representation of the performance equations for plug flow tubular reactors Fig 3.7 displays these performance equations and shows that the space-time needed for any particular duty can always be found by numerical or graphical Integration Mai Thanh Phong - HCMUT Chemical Reaction Engineering Apr 8, 2023 16