The loading rate of aeration tank is based on the following four parameters: 1. Hydraulic Retention Time (HRT) 2. Volumetric BOD Loading or Volumetric Organic Loading 3. Food to Micro-Organism Ratio (F/M Ratio) 4. Mean Cell Residence Time (MCRT) or Sludge Retention Time (SRT) or Sludge Age.
Parameter # 1. Hydraulic Retention Time (HRT):
Hydraulic retention time is a loading parameter developed empirically. It may be defined as the average time for which the sewage flowing into the reactor (or aeration tank) remains in the reactor (or aeration tank), or in the entire system. Thus hydraulic retention time can be defined in the following two ways.
Parameter # 2. Volumetric BOD Loading or Volumetric Organic Loading:
Parameter # 3. Food to Micro-Organism Ratio:
Parameter # 4. Mean Cell Residence Time (MCRT) or Sludge Retention Time (SRT) or Sludge Age:
The hydraulic retention time θ may be only few hours, but the residence time θC of biological solids is much greater, and while the sewage (mixed liquor) passes through the aeration tank only once within the hydraulic retention time (HRT), the resultant biological growth and the extracted organic solids are repeatedly recycled from the secondary settling tank back to the aeration tank thereby increasing the mean cell residence time (MCRT) or sludge retention time (SRT) or sludge age.
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Generally the design of the aeration tank (reactor) is based on θC (equation 13.16) on the assumption that substantially all the substrate conversion occurs in the aeration tank. However, in systems where a large portion of the total solids may be present in the settling tank and sludge return facilities, θct (equation 13.17) can be used to compute the amount of solids to be wasted. The use of θct is based on the assumption that the biological solids will undergo endogenous respiration regardless of where they are in the system under either aerobic or anaerobic conditions.
The values of θc for the two mixing regimes viz., completely mixed flow regime and plug flow regime may be obtained as indicated below.
Completely Mixed Flow with Cellular Recycle System:
In this system, shown schematically in Fig. 13.12, the reactor contents are completely mixed, and it is assumed that there are no micro-organisms in the sewage influent. The system contains a unit in which the cells from the reactor are settled and then returned to the reactor.
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Because of the presence of this settling unit, two additional assumptions are made in the development of the kinetic model of this system:
(i) Waste stabilization by the micro-organisms occurs only in the reactor unit. This assumption leads to a conservative model, since in some systems there may be some waste stabilization in the settling unit.
(ii) The volume used in calculating the mean cell residence time for the system includes only the volume of the reactor unit (i.e., aeration tank).
The returned sludge flow rate Qr, can be determined from equation 13.25 which shows that the value of Qr depends on the volatile suspended solids concentration xr in the settling tank underflow and the mixed liquor volatile suspended solids (MLVSS) x.
A mass balance for the micro-organisms in the entire system can be written as:
Equation 13.33 indicates that the mean cell residence time θC is a function of the effluent substrate (BOD) concentration and the kinetic coefficients Y, k, Ks and kd.
The values of these coefficients may be determined from the model test data as indicated below:
For determining these coefficients, the usual procedure is to operate the units over a range of effluent substrate concentrations; therefore, several different θc‘s (at least five) should be selected for operation ranging from 1 to 10 days. Using the data collected at steady-state conditions, mean values of Q, So, S, x and rsu are determined. Equating the values of rsu given by equations 13.30 and 13.33, we get-
The values of Ks and k can be determined by plotting the term [xθ/(So – S)] versus (1/S). The slope of the straight line passing through the plotted experimental data points is equal to (Ks/k) and the intercept is equal to (1/k). The values of Y and kd may be determined using equation 13.28 (a), by plotting (1 /θc) versus (-rsu/x). The slope of the straight line passing through the plotted experimental data points is equal to Y, and the intercept is equal to kd.
Typical values of the kinetic coefficients that can be used in the solution of equation 13.33 are given in Table 13.2.
The kinetic growth equations are applicable for soluble substrate (BOD) only. Hence So and S do not represent total BOD of influent and effluent respectively, but represent only the portion of BOD which is soluble. However, in activated sludge process, which treats settled sewage only, total BOD La or BOD5 of the influent may be considered as representing the influent soluble BOD. Thus-
So = La of influent … (13.41)
or So = BOD5 of influent … (13.41a)
On the other hand BOD of effluent is attributed to that due to soluble organics escaping the treatment and that due to suspended solids or biological solids present in the effluent. Hence effluent soluble BOD S, is not equal to total BOD of effluent. The effluent soluble BOD may be estimated after giving a credit to that due to suspended solids or biological solids present in the effluent.
Out of the total suspended solids or biological solids present in the effluent only about 65% are biodegradable. Also the ultimate BOD of the cells is equal to 1.42 times the mass of cells, mg/1. Thus ultimate BOD of the effluent solids is given by-
Plug Flow with Cellular Recycle System:
The plug flow with cellular recycle system is shown schematically in Fig. 13.13. The distinguishing feature of this system is that the hydraulic regime of the reactor is of a plug-flow nature. Thus in this system it is assumed that no mixing occurs between the contents of the reactor and each element of the mixed liquor simply traverses along the length of the reactor without losing its identity.
Further in a true plug flow model, all the particles entering the reactor stay in the reactor an equal amount of time. Some particles may make more passes through the reactor because of recycle, but while they are in the reactor (i.e., aeration tank), they all pass through in the same amount of time.
In the reactor, the sewage concentration decreases along its length while the microbial mass concentration increases due to the utilization of the substrate (BOD) by the micro-organisms. Hence a kinetic model of the plug flow system is mathematically difficult.
However, Lawrence and McCarty have developed a useful kinetic model of the plug-flow reactor which is based on the two simplifying assumptions as indicated below:
(i) The concentration of micro-organisms in the influent to the reactor is approximately the same as that in the effluent from the reactor. This assumption applies only if (θc/θ) > 5. The resulting average concentration of micro-organisms in the reactor is symbolized as x̅.
(ii) The rate of substrate utilization as the sewage passes through the reactor is given by the following expression-
Integrating equation 13.44 over the retention time of the sewage in the reactor (aeration tank), and simplifying results the following expression for 0C, for this system is obtained.
Equation 13.45 is quite similar to equation 13.28 (a) which is applicable to complete-mix system. The main difference in the two equations is that in equation 13.45 θc is also a function of the influent sewage substrate concentration So. Thus θc is a function of both So and S in a plug flow cellular recycle system, while in a complete mix system θc is a function of S only.
It should be noted that in Fig. 13.13 the excess micro-organisms are essentially wasted from the reactor and not from the recycle line.
Thus θC for the plug-flow recycle system could also be defined by equation 13.20 modified as under, with the same assumptions applying:
The average hydraulic retention time of the sewage in the reactor <9 and the average hydraulic retention time of the sewage in the system 6S in the plug-flow system can also be defined using equations 13.10 and 13.10 (a). Thus in plug-flow system-
The plug-flow-recycle system is theoretically more efficient in the stabilization of most soluble wastes than the complete mix recycle system. However, in actual practice a true plug-flow regime is difficult to obtain because of longitudinal dispersion. Moreover, the plug-flow system cannot handle shock loads as well as the complete mix recycle system. On account of these factors the differences in treatment efficiency in the two systems tends to reduce.