## Completely Mixed Combined Flow

The completely mixed, combined flow, equalization system addresses the variability resulting from multiple flows from different sections of a plant. This variability often generates impulse or step input changes to the wastewater treatment facility. The primary purpose of this system is to trim impulse variance or provide a more gradual change in operating parameters.

Again, the volume of the equalization basin is determined based on the effects the change in operating parameters has on downstream systems. Because this situation is more complex, this discussion approaches the design details from the simplest perspective: time and combined flows.

Therefore, the volume of the equalization basins Ve is calculated as follows:

where:

fi = Individual flow rates, m3/min Te = Time for equalization, hr k = Conversion factor for units

For example, if three flows come into the equalization basin with flow rates of 1.98, 0.567, and 0.189 m3/min, respectively, and the required equalization time is 1 hr, the following equation applies:

= (1.98 + 0.567 + 0.189)(1 hr)(60 min/hr) = 164.16 m3 7.13(7)

From here, the environmental engineer can calculate the relative change in each operating parameter using the fol lowing formulas and converting the variability of the individual stream to the variability in the total flow:

where:

VarT = Variance in the concentration of the total stream, ppm or ppb (mg/l or /ag/l) Varpi = Variance in the concentration of the individual stream, ppm or ppb (mg/l or /g/l) fi = Flow of the individual stream, m3/min ft = Flow of the total stream, m3/min

For example, if the concentration of a pollutant in an individual stream changes by 50 mg/l, the total stream changes as follows:

This variance can be used in the calculation as a change in the concentration of the combined stream and a potential effect on the downstream system.

A typical industrial waste problem involves constant flow with wastewater concentration as the only variable. Environmental engineers can use the following method in designing facilities to reduce this kind of concentration variability. The method assumes the data are normally distributed.

For example, if a completely mixed, constant flow tank has a variable concentration input and discrete samples are collected at a uniform interval time interval At, the influent variance (s2) can be estimated as follows:

where:

Ci = Influent concentration at the i time interval C = Mean concentration n = Number of samples

The influent coefficient of variation (vo) is as follows:

An estimate of required equalization time based on the variation of concentration and sampling interval is calculated as follows:

where:

0 = Required equalization time, hr At = Sampling interval, hr vo = Influent coefficient of variation of concentration, mg/l vt = Average influent concentration, mg/l ve = Effluent variability coefficient, mg/l

Both the influent and effluent coefficients of variability are based on discrete samples collected at uniform time intervals At.

Normally, raw wastewater characteristics, providing vo and At, are the only information available. The effluent variability ve must be related to the downstream requirements and therefore is the primary design variable. The environmental engineer must select it based on subsequent treatment units and effluent standards. Where specific limits on acceptable variability do not exist, engineering judgment must be exercised.

The effluent variability Ve can be estimated as follows:

where:

(C) max = The equalization tank effluent concentration not to be exceeded C = Mean value of concentration

N = Cumulative standard normal for the re quired confidence level (confidence level is the probability that a specified concentration will not be exceeded.)

Cumulative standard N can be selected from the abbreviated Table 7.13.2. Application of this method is illustrated in the example based on data in Table 7.13.3: vt = 698 mg/l and vo = 158.6 mg/l.

If downstream conditions (for example, the next treatment unit in line) restrict effluent variability to 10% (ve = 0.1), using Equation 7.13(12) gives the required equalization time as follows:

Specific restrictions on variability are uncommon; a more realistic problem is to design an equalization tank so that the effluent does not exceed a specified value.

These analyses can ultimately produce the type of curve shown in Figure 7.13.6. This graph allows the subjective analysis of a particular tank size to determine how well it suits the requirements.

If a detention time of 3 hr has tentatively been selected based on the foregoing analysis and physical considerations at a plant, the effluent from this size tank is not expected to exceed the value of 800 mg/l approximately 5% of the time, or about eight samples per week. Reducing this expectation to fewer than two samples per week (that is, a confidence level of 99%) exceeding 800 mg/l means increasing the detention time to approximately 7 hr.

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