Page 220 - Elements of Chemical Reaction Engineering Ebook
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Sec. 4.7   Unsteady-State Operation of  Reactors               191


                                                                                            (4-54)

                               with the initial condition V  = Vo at t  = 0, integrating for the case of constant
                               Vo yielcls
                     Semibatch
                        reactor
                    volume as a                                                             (4-,55)
                 function of  time
                               Substituting Equation  (4-54) into  the  right-hand  side of  Equation (4-52) and
                               rearranging gives us
                                                                     Vdc,
                                                      - uoC, + Vr, = -
                                                                       dt
                               The balance of A.  [i.e. Equation (4-52)] can be rewritten as
                                                        - 1

                Mole balance on A                                                           (4-56)

                                                         ~
                               A mole balance of B that is fed to the reactor at a rate FBo is


                                                                                            (4-57)

                                                 dVCB  dV       VdCB  = rBv+FBo
                                                 - -cB+-
                                                  dt   =  dt     dt
                               Substituting Equation (4-55) in terms  of  V  and  differentiating, the mole  bal-
                               ance on  B becomes


                Mole balance on B                                                            (4-58)

                               If  the  reaction  order  is  other  than  zero-  or  first-order, or  if  the  reaction  is
                               nonisotliermal, we must use numerical techniques to determine the conversion
                                as  a function of  time. Equations  (4-56)  and  (4-58) are easily  solved with  an
                                ODE solver.


                                  Exaniple kll Isothermal Semibatch Reactor with Second-Order Reaction

                                  The production of methyl bromide is an irreversible liquid-phase reaction that fol-
                                  lows an elementary rate law. The reaction
                                                    CNBr + CH,NH, + CH,Br + NCNH,

                                  is carried out isothermally in  a semibatch reactor. An  aqueous solution of  melthyl
                                  amine (B) at a concentration of 0.025 g mol/dm3 is to be fed at a rate of 0.05 drn3/s
                                  to an aqueous solution of  bromine cyanide (A) contained in a glass-lined reactor.
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