Qual2K: a modeling Framework for Simulating River and Stream Water Quality (Version 11)

Reaction Fundamentals

1. Biochemical Reactions

The following chemical equations are used to represent the major biochemical reactions that take place in the model (Stumm and Morgan 1996):

Plant Photosynthesis and Respiration:
Ammonium as substrate:
()
Nitrate as substrate:
()
Nitrification:
()
Denitrification:
()
Note that a number of additional reactions are used in the model such as those involved with simulating pH and unionized ammonia. These will be outlined when these topics are discussed later in this document.

2. Stoichiometry of Organic Matter

The model requires that the stoichiometry of organic matter (i.e., phytoplankton and detritus) be specified by the user. The following representation is suggested as a first approximation (Redfield et al. 1963, Chapra 1997),

()
where gX = mass of element X [g] and mgY = mass of element Y [mg]. The terms D, C, N, P, and A refer to dry weight, carbon, nitrogen, phosphorus, and chlorophyll a, respectively. It should be noted that chlorophyll a is the most variable of these quantities with a range of approximately 500-2000 mgA (Laws and Chalup 1990, Chapra 1997).
These values are then combined to determine stoichiometric ratios as in
()
For example, the amount of detritus (in grams dry weight or gD) that is released due to the death of a unit amount of phytoplankton (in milligrams of chlorophyll a or mgA) can be computed as

1. Oxygen Generation and Consumption

The model requires that the rates of oxygen generation and consumption be prescribed. If ammonia is the substrate, the following ratio (based on Eq. 58) can be used to determine the grams of oxygen generated for each gram of plant matter that is produced through photosynthesis.

()
If nitrate is the substrate, the following ratio (based on Eq. 59) applies
()
Note that Eq. (58) is also used for the stoichiometry of the amount of oxygen consumed for plant respiration.
For nitrification, the following ratio is based on Eq. (60)
()

2. CBOD Utilization Due to Denitrification

As represented by Eq. (61), CBOD is utilized during denitrification,

()

3. Temperature Effects on Reactions

The temperature effect for all first-order reactions used in the model is represented by

()
where k(T) = the reaction rate [/d] at temperature T [^oC] and ? = the temperature coefficient for the reaction.

3. Composite Variables

In addition to the model's state variables, Q2K also displays several composite variables that are computed as follows:

Total Organic Carbon (mgC/L):
()
Total Nitrogen (?gN/L):
()
Total Phosphorus (?gP/L):
()
Total Kjeldahl Nitrogen (?gN/L):
()
Total Suspended Solids (mgD/L):
()
Ultimate Carbonaceous BOD (mgO₂/L):
()

4. Relationship of Model Variables and Data

For all but slow and fast CBOD (c_f and c_s), there exists a relatively straightforward relationship between the model state variables and standard water-quality measurements. These are outlined next. Then we discuss issues related to the more difficult problem of measuring CBOD.

1. Non-CBOD Variables and Data

The following are measurements that are needed for comparison of non-BOD variables with model output:

TEMP = temperature (^oC)

TKN = total kjeldahl nitrogen (?gN/L) or TN = total nitrogen (?gN/L)

NH4 = ammonium nitrogen (?gN/L)

NO2 = nitrite nitrogen (?gN/L)

NO3 = nitrate nitrogen (?gN/L)

CHLA = chlorophyll a (?gA/L)

TP = total phosphorus (?gP/L)

SRP = soluble reactive phosphorus (?gP/L)

TSS = total suspended solids (mgD/L)

VSS = volatile suspended solids (mgD/L)

TOC = total organic carbon (mgC/L)

DOC = dissolved organic carbon (mgC/L)

DO = dissolved oxygen (mgO₂/L)

PH = pH

ALK = alkalinity (mgCaCO₃/L)

COND = specific conductance (?mhos)

The model state variables can then be related to these measurements as follows:
s = COND
m_i = TSS – VSS or TSS – r_dc (TOC – DOC)
o = DO
n_o = TKN – NH4 – r_na CHLA or n_o = TN – NO2 – NO3 – NH4 – r_na CHLA
n_a = NH4
n_n = NO2 + NO3
p_o = TP – SRP – r_pa CHLA
p_i = SRP
a_p = CHLA
m_o = VSS – r_da CHLA or r_dc (TOC – DOC) – r_da CHLA
pH = PH
Alk = ALK

2. Carbonaceous BOD

The interpretation of BOD measurements in natural waters is complicated by three primary factors:

• 
  Filtered versus unfiltered. If the sample is unfiltered, the BOD will reflect oxidation of both dissolved and particulate organic carbon. Since Q2K distinguishes between dissolved (c_s and c_f) and particulate (m_o and a_p) organics, an unfiltered measurement alone does not provide an adequate basis for distinguishing these individual forms. In addition, one component of the particulate BOD, phytoplankton (a_p) can further complicate the test through photosynthetic oxygen generation.
  

• 
  Nitrogenous BOD. Along with the oxidation of organic carbon (CBOD), nitrification also contributes to oxygen depletion (NBOD). Thus, if the sample (a) contains reduced nitrogen and (b) nitrification is not inhibited, the measurement includes both types of BOD.
  

• 
  Incubation time. Short-term, usually 5-day, BODs are typically performed. Because Q2K uses ultimate CBOD, 5-day BODs must be converted to ultimate BODs in a sensible fashion.
  

We suggest the following as practical ways to measure CBOD in a manner that accounts for the above factors and results in measurements that are compatible with Q2K.

Filtration. The sample should be filtered prior to incubation in order to separate dissolved from particulate organic carbon.
Nitrification inhibition. Nitrification can be suppressed by adding a chemical inhibiting agent such as TCMP (2-chloro-6-(trichloro methyl) pyridine. The measurement then truly reflects CBOD. In the event that inhibition is not possible, the measured value can be corrected for nitrogen by subtracting the oxygen equivalents of the reduced nitrogen (= r_on ? TKN) in the sample. However, as with all such difference-based adjustments, this correction may exhibit substantial error.
Incubation time. The model is based on ultimate CBOD, so two approaches are possible: (1) use a sufficiently long period so that the ultimate value is measured, or (2) use a 5-day measurement and extrapolate the result to the ultimate. The latter method is often computed with the formula
()
where CBODFNU² = the ultimate dissolved carbonaceous BOD [mgO₂/L], CBODFN5 = the 5-day dissolved carbonaceous BOD [mgO₂/L], and k₁ = the CBOD decomposition rate in the bottle [/d].
It should be noted that, besides practical considerations of time and expense, there may be other benefits from using the 5-day measurement with extrapolation, rather that performing the longer-term CBOD. Although extrapolation does introduce some error, the 5-day value has the advantage that it would tend to minimize possible nitrification effects which, even when inhibited, can begin to be exerted on longer time frames.
If all the above provisions are implemented, the result should correspond to the model variables by
c_f + c_s = CBODFNU
Slow versus Fast CBOD. The final question relates to discrimination between fast and slow CBODU. Although we believe that there is currently no single, simple, economically-feasible answer to this problem, we think that the following 2 strategies represent the best current alternatives.
Option 1: Represent all the dissolved, oxidizable organic carbon with a single pool (fast CBOD). The model includes parameters to bypass slow CBOD. If no slow CBOD inputs are entered, this effectively drops it from the model. For this case,
c_f = CBODFNU
c_s = 0
Option 2: Use an ultimate CBOD measurement for the fast fraction and compute slow CBOD by difference with a DOC measurement. For this case,
c_f = CBODFNU
c_s = r_ocDOC ­– CBODFNU
Option 2 works very nicely for systems where two distinct types of CBOD are present. For example, sewage effluent and autochthonous carbon from the aquatic food chain might be considered as fast CBOD. In contrast, industrial wastewaters such as pulp and paper mill effluent or allochthonous DOC from the watershed might be considered more recalcitrant and hence could be lumped into the slow CBOD fraction. In such case, the hydrolysis rate converting the slow into the fast fraction could be set to zero to make the two forms independent.

For both options, the CBODFNU can either be (a) measured directly using a long incubation time or (b) computed by extrapolation with Eq. 75. In both situations, a time frame of several weeks to a month (i.e., a 20- to 30-day CBOD) is probably a valid period in order to oxidize most of the readily degradable organic carbon. We base this assumption on the fact that bottle rates for sewage-derived organic carbon are on the order of 0.05 to 0.3/d (Chapra 1997). As in Figure , such rates suggest that much of the readily oxidizable CBOD will be exerted in about 20 to 30 days.

Figure Progression of CBOD test for various levels of the bottle decomposition rate.
In addition, we believe that practitioners should consider conducting long-term CBOD tests at 30^oC rather than at the commonly employed temperature of 20^oC. The choice of 20^oC originated from the fact that the average daily temperature of most receiving waters and wastewater treatment plants in the temperate zone in summer is approximately 20^oC.
If the CBOD measurement is intended to be used for regulation or to assess treatment plant performance, it makes sense to standardize the test at a particular temperature. And for such purposes, 20^oC is as reasonable a choice as any. However, if the intent is to measure an ultimate CBOD, anything that speeds up the process while not jeopardizing the measurement's integrity would seem beneficial.
The saprophytic bacteria that break down nonliving organic carbon in natural waters and sewage thrive best at temperatures from 20°C to 40°C. Thus, a temperature of 30^oC is not high enough that the bacterial assemblage would shift to thermophilic organisms that are atypical of natural waters and sewage. The benefit should be higher oxidation rates which would result in shorter analysis times for CBOD measurements. Assuming that a Q₁₀ ? 2 is a valid approximation for bacterial decomposition, a 20-day BOD at 30^oC should be equivalent to a 30-day BOD at 20^oC.

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