# Chapter 3. Estimation of local effects of wastewater discharge

## Problem identification

As explained in Section 2.2.3.2 the wastewater dilution conditions in Puerto Berrío become unfavorable during the low water seasons, due to the reduction in the water level and flow. In the present, the flow and level reduction are completely related to the meteorological conditions and are a consequence of the dry seasons were there is little contribution of the precipitation to the surface runoff. However, in the near future it is expected that these low flow conditions may be accentuated by intervention activities in the river, leading to even lower water levels and flows and for an even longer period than usual.

**Figure 30 Wastewater discharge during low water season**
Source: Neotrópicos, 2008

Due to the reduction in the navigability of the Magdalena River during the past years, especially during the low water seasons, the necessity has arisen to undertake some measures that care for its recovery. This is how Cormagdalena (see Section 1.2.4) has prepared a project to carry out the so-called POEM, from the Spanish “Project of Channeling Works in the Magdalena River”. These channeling works would not be carried out all along the river, but only in the stretch between the municipalities of Puerto Berrío and Barrancabermeja (about 100 km). The project is a combination of drainage, channeling and stabilization of the river flow, in order to obtain an improved channel suitable for navigation at all times of the year. Particularly in Puerto Berrío, one of the interventions will be the construction of a 1,350 m long dike along the branch of the river previously identified as the reference points 1 and 2 (Figure 31). This intervention is expected to reduce significantly the flow of water in the branch, naturally even more during the dry seasons (Neotrópicos, 2007). Assessing the effects of the current wastewater discharges on the water quality of the river branch will help to establish and predict the assimilation capacity of this water body under varying flow and water quality conditions, leading to a vision on how the situation could be improved.

**Figure 31 Reference point 1: branch of the Magdalena River**
Source: Alcaldía Municipal de Puerto Berrío, 2008

## Stream Water Quality Modeling

One way of estimating the effects of wastewater discharges in a water body, in this case a river, is by means of a water quality model. The aim of water quality modeling is to describe and to forecast the effects of a change in a river system and to determine impacts of point and non-point sources on water quality in a receiving water body. Models are usually applied to establish the assimilative capacity of water bodies, determine the most adequate management practices and measures and to predict the time needed by the water body to recover from an alteration (EPA, 2008). For the present study, a water quality model will be used to determine the effects of the wastewater discharged by the municipality of Puerto Berrío into a branch of the Magdalena River, and especially to determine the influence of seasonal flow variations on these effects. First an introduction to the basics of water quality modeling, followed by a short overview of the models applied in the Magdalena River before will be given. Next, the model chosen for the present study, Water Quality Modeling Computer Aided Learning, will be introduced and finally the procedure and results of its application will be presented.

### Theory on stream water quality modeling

Several models applied today are extensions of two simple equations proposed by Streeter and Phelps in 1925. The first one aimed at predicting the biochemical oxygen demand (BOD) of various biodegradable constituents, and the second one at determining the resulting dissolved oxygen concentration (DO) in rivers (see page 46). For cases where more detailed and comprehensive results are desired, other complex multiconstituent models can be used. They generally require more data and computer time (Orlob, 1982).

The conditions of the system to be analyzed determine the type of model that should be used and whose results will reflect the reality in a better way. For example in cases where the water quality and quantity remain constant in time, a model that assumes steady state conditions should be used. If on the contrary, the system is dynamic and time varying, a non-steady state model is to be applied. Steady state models are usually simpler and require less computational effort. Another aspect that differentiates the types of models is the spatial dimension. One-dimensional models of river systems assume complete vertical and lateral mixing. Two-dimensional models may assume either lateral mixing, as in stratified estuaries or lakes, or vertical mixing as in relatively shallow and wide rivers (Orlob, 1982).

Water quality changes in rivers are due to physical transport processes and biological, chemical, biochemical, and physical conversion processes, as explained already in Section 2.2.3. At this point it is important to review the mass conservation equation, which is the basis of all water quality models. The general word statement of the equation is (Metcalf and Eddy, 2002):

**Mass balance equation**

Or as a mathematical expression:

Equation 1 General mass balance equation

Where:
C is the concentration, the mass of the quality constituent in a unit volume of water (mass per volume ML-3)

Dx, Dy, Dz are the coefficients of dispersion in the direction of spatial coordinates x, y and z (surface area per time, L2T-1)

vx, vy, vz are the components of the flow velocity in spatial directions x, y and z (length per time, LT-1)

t is the time (T)

S(x, y, z, t) denotes external sources and sinks of the substance in concern that may vary in both time and space (mass per volume per time, ML-3T-1)

Sinternal denotes the internal sources and sinks of the substance (ML-3T-1)

The various terms of this equation will be explained more in depth in the following section as they are applied in the water quality model.

### Water quality modeling in the Magdalena River

In Colombia, during the last years mathematical river modeling has been subject to studies and research, and it has been practiced on some of the main rivers of the country. Speaking on a broad scale, the traditional Streeter and Phelps equation was applied at the national level to predict the impact of municipal wastewater discharges on the water resources, as a decision making tool in the health and sanitation sector. The result was the generation of BOD and DO maps and the division of the national water resources in critical and isolated stretches, according to their level of pollution (Barrera et al., 2002).

As specific case studies, some more complex models have been applied for large rivers in the country, such as the Bogotá, the Cauca and the Magdalena River. For the case of the Magdalena River an aggregation of flow, solute transport and water quality models has been used for the analysis on large scale of river stretches of several hundreds of kilometers, including the multilinear discrete lag cascade of channel routing, MDLC, the aggregated dead zone model, ADZ, and the Quality Simulation Along River Systems, QUASAR, with satisfactory results. (Camacho et al., 2000)

### Water Quality Modeling Computer Aided Learning: WQM CAL

The program WQM CAL version 2.0, is the second extended version of the former computer aided learning software WQM CAL version 1.1 and was made to fit into the frames of UNESCO/IHP’s “Ecohydrological” program. The program and software include following river models:

- Three BOD-DO models: the traditional oxygen sag curve and two more sophisticated versions.
- Dispersion-advection models: a one-dimensional pollutant spill model version and a 2D transversal mixing model.

According to the data and time availability and the objective of the study, the program was considered suitable. The models applied in the present study were the traditional BOD-DO model and the 2D transversal mixing model. The rest of the models included in WQM CAL, or other models, such as 3D-models, were not used due to high data requirements or inapplicable conditions. Moreover, river problems can be frequently reduced to one-dimensional (linear) or two-dimensional (longitudinal-transversal) problems, as it will be demonstrated further on (Jolánkai and Bíró, 2001).

One general specification for the applied models are the limits of BOD and DO that determine the classification of the water body into 5 classes, which are shown in the resulting graphs for a better analysis of the water quality. These limits can be adjusted in order to fit the regulations or the desired water quality to be maintained. Since the regulations for water quality found in the decree 1594 do not include limiting values for BOD and DO that allow for the classification of the water body, it is necessary to adopt them from other sources. In this case, the limits suggested by the WQM were adopted (see Figure 32).

**Figure 32 Water quality limit values as seen in WQM CAL**

### Modeling the branch

The river stretch to be modeled was divided into two reaches, each one of them with constant hydraulic characteristics, such as uniform channel slope, bottom width and side slope, which have been already presented in Section 2.3 The reach No. 1 adopts then the characteristics of the reference point No. 1 and the reach No. 2 the ones from reference point No. 2. The top and end of each reach are shown in Figure 33 and their coordinates are presented in Table 7.

**Table 7 Reaches coordinates**

**Figure 33 Reaches location**

**Figure 34 River reaches with point sources**

Since no current data about the discharge flow and exact location of the point sources to be included in the model were available, these were estimated based on the population of the sector the wastewater comes from, the network system coverage (Alcaldía Municipal de Puerto Berrío, 2000), and the observations and information from the field visit. According to this, two point sources were defined, the first one at the top of reach 1 and the second one at the top of reach 2. In reality, the first point source is made up of three smaller discharges but due to their very close location in the sector of Puerto Colombia (see Section 2.1.4) they were modeled just as one point source. Apart from the close location, the model does not allow for a separate calculation of each discharge due to the very small flow. The second point source found in Villas del Coral (see Section 2.1.4) is the main discharge in Puerto Berrío, with around 80% of the wastewater produced there. The two point sources present following characteristics:

**Table 8 Point sources description**

The characteristics of the headwater boundaries relevant for the models to be used are presented in Table 9. The river water quality for the extreme scenario is assumed to be the same as in the low water season.

**Table 9 Headwater characteristics**

#### BOD-DO model

To trace the profile of pollution and natural purification of receiving waters, BOD and DO, taken together, are relied upon. The BOD identifies in a comprehensive manner the degradable load added to the receiving water or remaining in it at any time; the DO identifies the capacity of the body of water to assimilate the imposed load (Fair et al., 1968). BOD-DO models deal with the so-called self-purification process in a river, which takes place when the water equilibrium has been lost due to a wastewater discharge. The organic matter added to the water, as long as the load is not too high, is biodegraded by microorganisms that consume oxygen during this process, achieving cleaner stages as the flowing distance increases and time passes by (Uhlmann and Horn, 2001). By means of a model, such as the one included in WQMCAL, this two processes, BOD degradation and oxygen consumption, can be graphically displayed in curves that are governed by the Streeter and Phelps equations (1925) (see Table 10), including the decay and reaeration rate coefficients K1 and K2, respectively.

Other characteristics and assumptions of the BOD-DO model from WQMCAL are (Jolánkai and Bíró, 2001):

- The channel is instantaneously and well mixed, both laterally and vertically, i.e., average flow and concentrations over the cross section are assumed. The only remaining velocity component is the longitudinal velocity, vx. It is a one-dimensional model.

- A water quality constituent with concentration C is subject to internal decay processes. The process is assumed to be proportional to the concentration of the constituent and the coefficient proportionality is K, the decay rate coefficient.

- The river is considered to have steady state conditions, i.e. the flow and input material loads are not varying in time.

- Decomposition of organic matter is expressed as the “first order” decay of BOD in function of the time.

- Initial conditions are calculated using the dilution equation

- It models the carbonaceous oxygen demand, CBOD, not the nitrogenous oxygen demand, NBOD.

**Table 10 BOD-DO Model governing equations**

Where:

Lo: Initial BOD after dischargeLs: BOD in the wastewaterqs: wastewater flow Lb: BOD in the river Qb: river flow DOo: Initial DO after discharge DOs: DO in wastewater DOb: DO in the river DOsat: saturation oxygen concentration Do: initial oxygen deficit after discharge T: temperature v: flow velocity H: water depth K1: decay rate coefficient K2: reaeration rate coefficient t: time L: BOD in the river D: oxygen deficit Dcrit: critical oxygen deficit tcrit: critical time of travel Xcrit: critical distance DOcrit: critical DO concentration

**Table 11 BOD-DO Model input data**

Table 12 and Table 13 show the results obtained by the model (see also Appendix I).

**Table 12 BOD-DO model results for Reach 1 **

**Table 13 BOD-DO model results for Reach 2**

Until now only the carbonaceous BOD, and the respective sag curve have been calculated, i.e., the dissolved oxygen consumed during the degradation of organic matter. However, there are other processes taking place in the water that also consume dissolved oxygen such as the nitrification process performed by certain species of bacteria. Nitrification consists of two steps, in which ammonia (NH4-N) is oxidized to nitrite (NO2-N) and nitrite is oxidized to nitrate (NO3-N). The total oxidation reaction is as follows:

**Equation 2 Nitrification process**

Based on this reaction, the oxygen required for complete oxidation of ammonia is 4,57 g O2/gN oxidized (Metcalf & Eddy, 2002). The resulting oxygen demand is then called nitrogenous BOD, and its estimation is then done based on the content of ammonia in the water. The content of ammonia, also expressed as NH3-N, in the wastewater discharge of Puerto Berrío had already been estimated based on the guidelines RAS 2000 (See Sections 1.3 and 2.1.4). The concentration of ammonia in the stretch of the Magdalena River had to be estimated for both seasons. For the low water season, the Total Kjeldahl Nitrogen, TKN, was known and based on the relation TKN:NH3-N: org. N observed in the wastewater (1:0,7:0,3) (see Table 1), the ammonia nitrogen could be estimated. For the high water season there was no data available, neither for NH3-N, nor for TKN. In that case, the organic nitrogen was first calculated, with which the NH3-N could be estimated. Equation 3, suggested by Wolf (1974), was used for the calculation of the organic nitrogen.

**Equation 3 Organic nitrogen estimation**

The results obtained by these calculations are presented in Table 14 and Table 15.

**Table 14 NBOD in the wastewater**

**Table 15 NBOD in the river’s headwater**

Knowing the NBOD in the wastewater and in the headwater, the oxygen deficit in the river stretch could be recalculated. For this, the Streeter and Phelps equation was used, this time including the term that accounts for the oxygen consumption during the oxidation of ammonia (see Equation 4).

**Equation 4 Oxygen deficit in the stream**

Where:

D(t) = DO deficit at time t, mgO2/l Do = Initial DO deficit, mgO2/l Lo = Initial ultimate carbonaceous BOD concentration, mgO2/l No = Initial ultimate nitrogenous BOD concentration, mgO2/l K1 = Carbonaceous deoxygenation rate constant, base e, day -1 Kn = Nitrogenous deoxygenation rate constant, base e, day –1 K2 = Reaeration rate constant, base e, day -1 t = Time of travel through reach, day

The ultimate nitrogenous BOD concentration as a function of time (t) was calculated as follows:

**Equation 5 NBOD concentration as a function of time**

Where:

N(t) = Ultimate nitrogenous BOD at time, t, mgO2/l

The value of N0 is obtained by means of the dilution equation, also applied in the BOD-DO model (see Table 10). Since no value for Kn was known for the river stretch, it was assumed to be equal to the carbonaceous deoxygenation rate K1 (Thomann and Mueller, 1987) before the temperature correction. The value of K1 was obtained from the BOD-DO model and was then corrected by a temperature coefficient of θ=1,08 (Thomann and Müller, 1987) as follows:

**Equation 6 Correction of Kn**

The decay curves for the NBOD could be calculated using the BOD-DO model since the same governing equations were applied and it was possible to adjust it to the values obtained for Kn. The input data for the NBOD decay curve are presented in Table 16 (see also Appendix I) and the resulting curves in Table 17.

**Table 16 NBOD Model input data**

Where:

Ns: NBOD in the wastewater in mgO2/L Nb: NBOD in the river in mgO2/L

**Table 17 NBOD model results**

The BOD-DO model included in the WQM CAL program could not be used for the calculation of the oxygen deficit, since it does not allow for modifications in the equations. For this matter, the calculations and graphs were done in an excel worksheet. Table 18 shows the data used for the recalculation of the oxygen deficit, all of them obtained by means of the previous modeling procedures.

**Table 18 Input data for calculation of the oxygen deficit**

The resulting sag curves for the both reaches are presented in two graphs, each one including the three different scenarios (see Figure 35 and Figure 36).

**Figure 35 Oxygen sag curve for Reach 1**

**Figure 36 Oxygen sag curve for Reach 2**

All graphs obtained by the model, reflect the longitudinal variations in BOD and DO that are expected to happen in the river along many kilometers downstream of the wastewater discharges. To obtain the values of these two parameters at specific points of the river reaches, one would usually read them from the graphs, after calculating the time of travel based on the distance of the point of interest and the flow velocity. However for the reaches under study, the distances are short and the velocities high, which results in very short travel times (between 0,005 and 0,011) that cannot be precisely read from the graphs. For this reason, some extra calculations, based on the rate coefficients given by the model, the results of the dilution equation and the time of travel, were done to obtain the BOD and DO concentrations at the end of both reaches. Figure 37 and Table 19 show the results of these calculations.

**Figure 37 Reaches BOD and DO concentration**

**Table 19 Reaches BOD and DO concentration**

#### Transversal mixing model

The transversal mixing model is used to determine the spreading of a pollutant plume based on the distribution of its concentration across the river at any cross-section downstream of the effluent outfall. Some characteristics and assumptions of the transversal mixing model are (Jolánkai and Bíró, 2001):

- Vertical mixing takes place immediately

- Transversal advective transport can be neglected, since usually there is no data available for the transversal component of the flow velocity

- One single mixing term combines longitudinal and transversal dispersion

- The contaminant under analysis is considered a conservative one

- The initial concentration of the pollutant in the river is assumed to be cero.

- The model calculates ten distribution curves, each one corresponding to a distance downstream of the source. The total distance of the reach is divided into 10 equal parts.

**Table 20 Transversal mixing model governing equations**

Where:C: concentration of pollutant in the stream
Dx: coefficient of longitudinal dispersion
Dy: coefficient of lateral dispersion
K: reaction rate coefficient of non-conservative substance
vx: flow velocit
yt: time
Co: concentration of pollutant in wastewater
ey: transversal mixing coefficient
qo: wastewater rate of flow
y: distance from riverbank, across the river
o: distance of pipe outlet from riverbank
x: distance downstream of the source
d: experimental constanth: depth of water
s: slope of water surface
g: acceleration of gravity

**Table 21 Transversal mixing model input data**

Figure 38 helps for a better understanding of the model input data and results. The graphs obtained by the model are shown in Table 22 (for a better view of the graphs refer to Appendix I). Since the graphs only display the concentration of one curve at a time, the concentrations of the remaining curves are presented in Table 23.

**Figure 38 Schematic representation of the transversal mixing model**
Source: Jolánkai and Bíró, 2001

**Table 22 Transversal mixing model results**

**Table 23 Reach 1 maximum concentrations of dispersion curves**

**Table 24 Reach 2 maximum concentrations of dispersion curves**

Where:

Cmax i: concentration of the pollutant in the stream Yi: distance across the river where concentration reaches a minimum i: distribution curve

As it was mentioned before, the transversal mixing model assumes that the discharged pollutant is a conservative one, meaning that it does not undergo any reaction or process of degradation. This could make the results unrealistic, however in the case of the river stretch under study the flow velocity is so high and the analyzed distances so short that the degradation processes of BOD take place many kilometers downstream, as was already seen in the BOD-DO model results. Based on this, it can be assumed that for this particular case the BOD presents the characteristics of a conservative substance. The longitudinal variations in BOD concentrations within the river stretch were already presented in Table 19.

## Water Quality Index

With the water quality models used in the previous section, two parameters, namely BOD and DO were analyzed. These are one of the most important parameters when determining the pollution stage of a water body, since aquatic life and aquatic ecosystems depend on the presence of dissolved oxygen in the water (Jolánkai and Bíró, 2001). However, the inclusion of other parameters is important to have an overview of their influence in the water quality. For this purpose a water quality index (WQI) can be used, which is a single value derived from multiple water quality parameters, whose quantitative result points to a qualitative description of the water quality.

For the present study, the WQI from the National Sanitation Foundation was chosen (NSF, 2004). The index is calculated based on nine parameters, whose measurements are first converted into index values based on predetermined curves. For this conversion a website provided by Wilkes University (2007) offers the possibility of an online calculation. After each index is known, different weights are assigned, influencing the total water quality index in a higher or lower degree (see Table 25). The mentioned website calculates the total water quality index as well.

**Table 25 NSF WQI factors and weights**

The final index is then expressed quantitatively with values that go from 0 to 100, divided in ranges and with a respective qualitative description, as shown in Table 26.

**Table 26 Ranges of the NSF WQI**

As a complement to the results obtained by the BOD-DO model in the river branch, the water quality index was calculated for the same three scenarios with the aim of estimating the changes in the water quality of the branch before and after the wastewater discharges and also the seasonal changes in water quality (see Table 30). The water quality index was calculated for three different points: a) the headwater; b) right after the second point source; and c) the end of reach 2. The headwater characteristics for both seasons were already known (see Table 27), while for the last two points it was necessary to calculate the values of the water quality parameters.

**Table 27 Headwater quality parameters**
**Table 28 Water quality after point source 2**
**Table 29 Water quality at the end of reach 2**

The BOD and DO saturation values after the dilution and downstream could be obtained from the BOD-DO model. For the rest of the water quality parameters the dilution equation (see Table 10) was used, being the fecal coliform, the parameter that increased the most after the wastewater discharge. All parameters except for BOD and DO were assumed to be conservative due to the high velocity of the river and the short distances being analyzed. The results of the calculation of the water quality index are displayed in Table 30; for details on these see Appendix J.

**Table 30 Water Quality Index**