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748                            Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological




                                                                          %VSS (destroyed)
                                                                            0.80 g–0.24 g
                                                                           =———–————
                                                                               0.80 g        0.56 gm
                                   =0.80%                                  =0.70
                               VSS o            0.80 gm    Digestion

                                                                            VSS=55%          0.24 gm


                                  Ash           0.20 gm                       Ash            0.20 gm
                          (a)                                         (b)
            FIGURE 23.15  Illustration of method of calculation of percent reduction in volatile suspended solids. (a) Sludge to digester and (b) sludge
            from digester.

              Example 23.4 Calculation of VSS Destroyed        oped. The approaches were empirical and experience was
                                                               assimilated in converging on guidelines and practices that
              Given                                            worked; theory had not taken hold.
              Figure 23.15a shows that VSS o   0.80 for a sludge entering a  From about 1950 to the present, theory has helped to com-
              digester. For the sludge leaving the digester, let VSS   0.55 in  plement practice. The idea of a tank as a ‘‘reactor’’ started to
              Figure 23.15b. Both were measured quantities at the plant.
                                                               emerge in the 1950s. A ‘‘golden age’’ of research occurred,
              Required                                         arguably, through the 1950s and into the 1970s, providing a
              Calculate the fraction of VSS(destroyed) by the anaerobic  knowledge base of principles. A defining break with the past
              process.
                                                               was the 1970 paper of Lawrence and McCarty (1970) that
              Solution                                         delineated these principles with guidelines for design and
                 a. Ash
                                                               operation. The 1972 Metcalf and Eddy book codified what
                   The ash mass remains constant and is 0.20 g.
                                                               had been learned in practice coupled with guidance from the-
                 b. VSS mass leaving digester
                                                               ory. Other books, e.g., by Orhan and Artan (1994), Grady et al.
                   For the sludge leaving the digester,
                                                               (1999), Rittman and McCarty (2001), added scientific ration-
                              f(VS) ¼ VSS=(ash þ VSS)          ale, essentially summarizing the state of the art gleaned from
                              0.55 ¼ VSS=(0.20 g þ VSS)        the last fifty years. In 1987 the IWA model provided a means to
                               VSS ¼ 0.24 g                    actually model the activated-sludge process and provided a
                                                               flexible framework for modeling the anaerobic process.
                 c. VSS destroyed
                                                                  Demands for a comprehensive control of pollutants during
                        VSS(destroyed) ¼ VSS o   VSS           the 1970s led to sophisticated activated-sludge and bio-filter
                                   ¼ 0.80 g   0.24 g           practices to remove nitrogen and phosphorous as well as
                                   ¼ 0.56 g
                                                               organic carbon. The anaerobic process remains less glamor-
                       f(VSS destroyed) ¼ 0.56 g=0.80 g        ous but has been understood since the 1960s as a complex
                                      0.70                     biochemical process which has been assimilated in design and
                                                               operation. Operation is understood at a different level also
              Discussion                                       than was the case through the 1960s. Plant operators run a
              Without a ‘‘tip’’ a person new to the field is likely not to
              consider the ash. Also, a sketch helps to keep the calcula-  complex chemical plant with monitoring and surveillance
              tions straight. Sampling to calculate the f(VS destroyed) is  governed by restrictive regulations; the training and profes-
              part of daily monitoring.                        sionalism has been commensurate.

            23.5 SUMMARY
                                                               23.5.2 PARAMETERS
            A perspective on the state of the art and its evolution is
                                                               The bases for most rational parameters are reaction stoichiom-
            outlined. In addition activated-sludge parameters are pro-
                                                               etry, kinetics, and reactor mass balance. From these relations a
            vided, both as a summary and as a convenience.
                                                               number of parameters may be derived. Because they are often
                                                               scattered indifferent sections ofa bookas related to their respect-
            23.5.1 STATE OF THE ART
                                                               ive presentations, they are summarizedinTable 23.10 asa matter
            Biological treatment, as a technology, is still evolving; like  of convenience for retrieval. Tchobanoglous and Burton=
            most unit processes it has not reached closure. In the first  Metcalf and Eddy (1991) was the reference used for most of
            50 years of the twentieth century technologies such as septic  the equations. In some cases the nomenclature was altered.
            tanks, Imhoff tanks for anaerobic treatment, two-stage  Also, this text used fewer defined coefficients than found in the
            digesters, activated sludge, trickling filters, etc. were devel-  literature, in order to keep a more fundamental orientation.
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