Oxygen production
3.2.7 Input data for the DO model
The following input data are necessary for the utilisation of the Streeter–Phelps model (see Figure 3.15):
• river flow, upstream of the discharge (Qr)
• wastewater flow (Qw)
Figure 3.15. Input data required for the Streeter–Phelps model
• dissolved oxygen in the river, upstream of the discharge (DOr)
• dissolved oxygen in the wastewater (DOw)
• BOD5in the river, upstream of the discharge (BODr)
• BOD5of the wastewater (BODw)
• deoxygenation coefficient (K1)
• reaeration coefficient (K2)
• velocity of the river (v)
• travelling time (t)
• saturation concentration of DO (Cs)
• minimum dissolved oxygen permitted by legislation (DOmin)
a) River flow (Qr)
The flow of the receiving body is a variable of extreme importance in the model, having a large influence on the simulation results. Therefore it is necessary to obtain the most precise flow value, whenever possible.
The use of the DO model can be with any of the following flows, depending on the objectives:
• flow observed in a certain period
• mean flow (annual average, average in the rainy season, average in the dry season)
• minimum flow
The observed flow in a certain period is used for model calibration (adjusting the model coefficients), so that the simulated data are as close as possible to the observed (measured) data in the water body during the period under analysis.
The mean flow is adopted when the simulation of the average prevailing condi-tions is desired, such as during the year, rainy months or dry months.
The minimum flow is utilised for the planning of catchment areas, the evaluation of the compliance with environmental standards of the water body and for the allo-cation of pollutant loads. Therefore, the determination of the required efficiencies
for the treatment of various discharges must be determined in the critical condi-tions. These critical conditions in the receiving body occur exactly in the minimum flow period, when the dilution capacity is lower.
The critical flow must be calculated from the historical flow measurement data from the water course. The analysis of methods to estimate minimum flows is outside the scope of the present text, being well covered in hydrology books.
Usually a minimum flow with a return period of 10 years and a duration of the minimum of 7 days (Q7,10), is adopted. This can be understood as a value that may repeat itself in a probability of every 10 years, consisting of the lowest average obtained in 7 consecutive days. Therefore, in each year of the historical data series the 365 average daily flows are analysed. In each year a period of 7 days is selected, which resulted in the lowest average flow (average of 7 values). With the values of the lowest 7-day average for every year, an statistical analysis is undertaken, allowing interpolation or extrapolation of the value for a return period of 10 years.
Adoption of the 10-year return period in the Q7,10concept leads to small flows and frequently to the requirement of high BOD removal efficiencies, the cost of which should always be borne in mind, especially in developing countries.
For these countries, probably a shorter return period would be more realistic, especially considering that the current condition is probably already of a polluted river.
Another approach is the utilisation of percentiles, such as a 90%ile value (Q90).
In this concept, 90% of the flow values are greater than the critical flow, and only 10% are lower than it. This approach usually leads to critical flows that are greater than those based on Q7,10.
Under any flow conditions, the utilisation of the concept of the specific discharge (L/s.km2) is helpful. Knowing the drainage area at the discharge point and adopting a value for the specific discharge, the product of both leads to the flow of the water course. The specific discharge values can vary greatly from region to region, as a function of climate, topography, soil, etc., For Q7,10 conditions, the following ranges are typical: (a) arid regions: probably less than 1,0 L/s.km2; (b) regions with good water resources availability: maybe higher than 3,0 L/s.km2; and (c) in intermediate regions: values close to 2.0 L/s.km2.
b) Wastewater flow (Qw)
Wastewater flows considered in DO modelling are usually average flows, without coefficients for the hour and day of highest consumption. The sewage flow is obtained through conventional procedures, using data from population, per capita water consumption, infiltration, specific contribution (in the case of industrial wastes), etc. The calculation is detailed in Chapter 2.
c) Dissolved oxygen in the river, upstream of the discharge point (DOr) The dissolved oxygen level in a water body, upstream of a waste discharge, is a result of the upstream activities in the catchment area.
Ideally, historical data should be used in this analysis. When doing so, coherence is required: if the simulation is for a dry period, only samples pertaining to the dry period should be considered.
In case that it is not possible to collect water samples at this point, the DO concentration can be estimated as a function of the approximate pollution level of the water body. If there are few indications of pollution, a DOr value of 80% to 90% of the oxygen saturation value (see item k below) can be adopted.
In the event that the water body is already well polluted upstream of the dis-charge, a sampling campaign is justified, or even an upstream extension of the boundaries of the studies should be considered, in order to include the main pollut-ing points. In such a situation, the value of DOrwill be well below the saturation level.
d) Dissolved oxygen in the wastewater (DOw)
In sewage, the dissolved oxygen levels are normally nihil or close to zero. This is due to the large quantity of organic matter present, implying a high consumption of oxygen by the microorganisms. Therefore the DO of raw sewage is usually adopted as zero in the calculations.
In case that the wastewater is treated, the following considerations could be made:
• Primary treatment. Primary effluents can be assumed as having DO equal to zero.
• Anaerobic treatment. Anaerobic effluents also have DO equal to zero.
• Activated sludge and biofilm reactors. Effluents from these systems undergo a certain aeration at the effluent weir on the secondary sedimentation tanks, enabling DO to increase to 2 mg/L or slightly more. If the discharge outfall is long, this oxygen could be consumed as a result of the remaining BOD from the treatment.
• Facultative or maturation ponds. Effluents from facultative or maturation ponds can have during day time DO levels close to saturation, or even higher, due to the production of pure oxygen by the algae. At night the DO levels decrease. For the purpose of the calculations, DOwvalues around 4 to 6 mg/L can be adopted.
• Effluents subjected to final reaeration. Treatment plant effluents may be subject to a final reaeration stage, in order to increase the level of dissolved oxygen. A simple system is composed by cascade aeration, made up of a sequence of steps in which there is a free fall of the liquid. DO values may raise a few milligrams per litre, depending on the number and height of the steps. Sufficient head must be available for the free falls. Gravity aeration should not be used directly for anaerobic effluents, due to the release of H2S in the gas-transfer operation. Section 11.10 presents the methodology for calculating the increase in DO.
Table 3.6. BOD5as a function of the water body characteristics
River condition BOD5of the river (mg/L)
Very clean 1
Clean 2
Reasonably clean 3
Doubtful 5
Bad >10
Source: Klein (1962)
e) BOD5in the river, upstream of discharge (BODr)
BOD5 in the river, upstream of the discharge, is a function of the wastewater discharges (point or diffuse sources) along the river down to the mixing point. The same considerations made for DOr about sampling campaigns and the inclusion of upstream polluting points are also valid here.
Klein (1962) proposed the classification presented in Table 3.6, in the absence of specific data.
f ) BOD5in the wastewater (BODw)
The BOD5concentration in raw domestic sewage has an average value in the order of 300 mg/L. The BOD can also be estimated through the quotient between the BOD load (calculated from the population and the per capita BOD contribution) and the wastewater flow (domestic sewage+ infiltration). For more details, see Section 2.2.5.
In case there are industrial discharges of importance, particularly from agro-industries and others with high content of organic matter in the effluent, they must be included in the calculation. These values can be obtained by sampling or through literature data. See Section 2.2.6.
For a treated wastewater, of course the BOD removal efficiency must be taken into account, since treatment is the main environmental control measure to be adopted. In this case, the BOD5in the wastewater is:
BODtw=
1− E
100
·BODrw (3.28)
where:
BODtw= BOD5of the treated wastewater (mg/L) BODrw= BOD5of the raw wastewater (mg/L)
E= BOD5removal efficiency of the treatment (%)
Table 4.9 presents typical ranges of BOD removal efficiency from various wastewater treatment systems. An overview of these systems can be found in
Chapter 4. Various other chapters of this book are dedicated to the detailed de-scription of these systems.
g) Deoxygenation coefficient (K1)
The deoxygenation coefficient can be obtained following the criteria presented in Section 3.2.4.2. It must be noted that water bodies that receive biologically treated wastewater have a lower value of K1 (see Table 3.3). For liquid temperatures different from 20◦C, the value of K1must be corrected (seer Section 3.2.4.3).
h) Reaeration coefficient (K2)
The reaeration coefficient can be obtained following the procedures outlined in Section 3.2.5.2. For liquid temperatures different from 20◦C, the value of K2must be corrected (see Section 3.2.5.3).
i) Velocity of the water body (v)
The velocity of the liquid mass in the water course may be estimated using the following methods:
• direct measurement in the water course
• data obtained from flow-measuring points
• use of hydraulic formulas for open channels
• correlation with flow
In DO simulations that can be done under any flow conditions, obtaining the velocity through the last two methods is more convenient. In other words, it is important that the velocity is coherent with the flow under consideration, since in dry periods the velocities are usually lower, with the opposite occurring in wet periods.
The hydraulic formulas are presented in pertinent literature. The most adequate friction factor should be chosen as a function of the river bed characteristics (see Chow, 1959).
The flow-correlation method should follow a methodology similar to the one described in Item 3.2.5.2c for the reaeration coefficient. The model to be obtained can have the form v= cQd, where c and d are coefficients obtained from regression analysis.
j) Travel time (t)
In the Streeter–Phelps model, the theoretical travel time that a particle takes to complete a certain river reach is a function of the velocity and the distance. This is because the model assumes a plug-flow regime and does not consider the effects of dispersion. Therefore, knowing the distances and having determined the velocities in each reach, the residence time is obtained directly from the relation:
t= d
v· 86, 400 (3.29)
where:
t= travel (residence) time (d) d= distance (m)
v= velocity in the water body (m/s) 86,400= number of seconds per day (s/d) k) DO saturation concentration (Cs)
The saturation concentration of the oxygen can be calculated based on theoretical considerations, or through the use of empirical formulas. The value of Cs is a function of water temperature and altitude:
• The increase in temperature reduces the saturation concentration (the greater agitation of molecules in the water tends to make the dissolved gases pass to the gas phase)
• The increase in altitude reduces the saturation concentration (the atmo-spheric pressure is lower, thus exerting a lower pressure for the gas to be dissolved in the water).
There are some empirical formulas in the literature (the majority based on regression analysis) that directly supply the value of Cs(mg/L) as a function of, for example, the temperature T (◦C). A formula frequently employed is (P¨opel, 1979):
Cs= 14.652 − 4.1022 × 10−1.T + 7.9910 × 10−3.T2− 7.7774 × 10−5.T3 (3.30) The influence of the altitude can be computed by the following relation (Qasim, 1985):
fH=Cs
Cs
=
1−Altitude 9450
(3.31)
where:
fH= correction factor for altitude, for the DO saturation concentra-tion (−)
C s= DO saturation concentration at the altitude H (mg/L) Altitude= altitude (m above sea level)
Salinity also affects the solubility of oxygen. The influence of dissolved salts can be computed by the following empirical formula (P¨opel, 1979):
γ = 1 − 9 × 10−6· Csal (3.32)
where:
γ = solubility reduction factor (γ = 1 for pure water) Csal= dissolved salts concentration (mg Cl−/L)
Table 3.7. Saturation concentration for oxygen in clean water (mg/L) Altitude (m)
Temperature (◦C) 0 500 1000 1500
10 11.3 10.7 10.1 9.5
11 11.1 10.5 9.9 9.3
12 10.8 10.2 9.7 9.1
13 10.6 10.0 9.5 8.9
14 10.4 9.8 9.3 8.7
15 10.2 9.7 9.1 8.6
16 10.0 9.5 8.9 8.4
17 9.7 9.2 8.7 8.2
18 9.5 9.0 8.5 8.0
19 9.4 8.9 8.4 7.9
20 9.2 8.7 8.2 7.7
21 9.0 8.5 8.0 7.6
22 8.8 8.3 7.9 7.4
23 8.7 8.2 7.8 7.3
24 8.5 8.1 7.6 7.2
25 8.4 8.0 7.5 7.1
26 8.2 7.8 7.3 6.9
27 8.1 7.7 7.2 6.8
28 7.9 7.5 7.1 6.6
29 7.8 7.4 7.0 6.6
30 7.6 7.2 6.8 6.4
Table 3.7 presents the saturation concentrations for oxygen in clean water at different temperatures and heights.
l) Minimum allowable dissolved oxygen concentration in the water body (DOmin)
The minimum levels of dissolved oxygen that need to be maintained in the water body are stipulated by the legislation applicable in the country or region. In the absence of specific legislation, it is usual to try to maintain DO concentrations in the water body equal to or above 5.0 mg/L.