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212       Practical Design Calculations for Groundwater and Soil Remediation



              •  Mixing conditions inside the reactor: Better mixing conditions will
                enhance the heat transfer and improve venting of the desorbed COCs.
              •  Volatility of the COCs: The more volatile the COCs are, the shorter the
                required retention time will be.
              •  Size of the soil particles: The smaller the soil particles, the easier the
                desorption will be.
              •  Types of soil: Clay has a stronger affinity with COCs and, thus, the
                COCs will be harder to desorb from clayey material.

             The rate of desorption or the required detention time to remediate a spe-
           cific type of soil to a permissible concentration can be best determined from
           a pilot study. The results from the pilot study should then be used for the
           preliminary design of the full-scale operation. The desorption process can
           be conducted in a batch mode or in a continuous mode. For the continuous
           mode, the reactor can be modeled as a continuous-flow stirred tank reactor
           (CFSTR) if the soil is relatively well-mixed inside the reactor. For the desorp-
           tion reaction, a first-order type of reaction is a reasonable assumption. For a
           first-order reaction, the relationship among the influent and final concentra-
           tions, reaction rate constant, and residence time are as follows (see Chapter 4
           for more detailed discussions):

              Batch reactor


                                        k
                                  C f  −τ              −τ
                                    =  e   or  C f =  ()                  (4.16)
                                                        k
                                                   Ce
                                                     i
                                  C i
              CFSTR
                                            1        1
                                      =          =                        (4.20)
                                  C out
                                                      k
                                  C in  1+ k VQ( /)  1+τ

           Example 5.35:   Determine the Residence Time for Low-Temperature
                         Heating (Batch Mode of Operation)
           A batch-type low-temperature thermal desorption reactor is proposed to
           treat soil containing 2,500 mg/kg of total petroleum hydrocarbon (TPH). A
           pilot study was conducted, and it took 25 min to reduce the concentration to
           150 mg/kg. First-order kinetics applies. If the required final soil TPH con-
           centration is 50 mg/kg, what should be the design residence time of the soil
           in the reactor?
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