Dissolved Oxygen

The unit models the oxygen balance in the river due to the decay of organic material, the nitrification of ammonia and reaeration from the atmosphere.

Description

Dissolved oxygen concentration is often used as the main indicator of the health of a river or estuary. It represents the ability of the water body to support plant and animal life. The concentration of oxygen which can be dissolved in water is a function of temperature and salinity. For convenience, the concentration of dissolved oxygen is usually expressed as a percentage of this saturated concentration. Oxygen is utilised by the decay of organic material and the nitrification of ammonia. It can be added to the water body by reaeration.Figure 1 summarises the processes simulated in the DISSOLVED OXYGEN module.

Figure 1. The schema showing the processes simulated in the DISSOLVED OXYGEN module.

Reaeration is the process by which oxygen from the air dissolves in water. The process is limited by the saturation concentration. The rate of reaeration is proportional to the oxygen deficit, which is the difference between the saturation concentration and the actual concentration. Reaeration can be a function of temperature or alternatively be related directly to the hydrodynamics using Owen's, O'Conner and Dobbin's and Churchill's equations (see Equations below). Additional reaeration can be included at structures (see STRUCTURE).

Biochemical oxygen demand (BOD) is the potential utilisation of dissolved oxygen by aquatic microbes to metabolize organic matter. BOD is the term applied to the matter itself. BOD is commonly expressed in terms of the 5-day BOD, which is the amount of oxygen consumed by the decay of the material over 5 days. The 1D Water Quality Solver calculates oxygen demand in terms of the ultimate oxygen demand, that is the amount of oxygen that would be consumed if the material decays completely. Different types of material are metabolised at different rates. This is simulated in the 1D Water Quality Solver by using a fast rate and a slow rate. The ultimate oxygen demand is related to the 5-day BOD (see Equation below). The decay of BOD is represented in the 1D Water Quality Solver by temperature dependent, first order kinetics. BOD will decay whether the surrounding water is fully oxygenated or anoxic. In the latter case the oxygen demand is satisfied by denitrification and the reduction of sulphates.

Organic nitrogen represents nitrogen which is present in organic matter in the form of compounds such as protein and amino acids. These compounds are hydrolysed by bacteria to form ammonium compounds. As with BOD, the organic nitrogen hydrolyses at a fast and a slow rate represented by temperature dependent, first order kinetics.

Ammoniacal nitrogen represents nitrogen which exists in the form of ammonia or ammonium ions. It can be formed by the hydrolysis of organic nitrogen, as described above, but also enters a modelled system directly from industrial or sewage effluent. Ammoniacal nitrogen is oxidised to nitrite by nitrosomonas bacteria. This oxidation is modelled as a first order process which is temperature, salinity and suspended solids dependent. The process consumes dissolved oxygen. 1.14g of dissolved oxygen is required to oxidise 1g of ammoniacal nitrogen. Nitrite is in turn oxidised by nitrobacteria to form nitrate consuming more dissolved oxygen. 3.43g of dissolved oxygen is required to oxidise 1g of nitrite.

Under low oxygen or anoxic conditions the nitrification of ammonia ceases. Nitrates and nitrites are then used as a source of oxygen in order to satisfy BOD by denitrification. The nitrogen which is released during the process is released to the atmosphere and plays no further part in the model. Once all the nitrate and nitrite has been consumed BOD is then satisfied by the reduction of sulphates which leads to the formation of hydrogen sulphide. The model keeps a track of the amount of hydrogen sulphide which is formed as an indication of the severity of anoxic conditions.

Equations

The saturated dissolved oxygen concentration is determined as a function of temperature and salinity:

                    (1)

Where:
DOS = saturated dissolved oxygen concentration (mg/l)
T = temperature (Celsius)
S = salinity (ppt)

Reaeration is represented by the equation:

                    (2)

Where:
DO = dissolved oxygen concentration (mg/l)
K_air = rate constant (s^-1)

The rate constant may be represented in one of two ways. It may be calculated from:

                    (3)

Where:
f_air = transfer velocity (m/s)
b = water surface width (m)
A = cross sectional area of flow (m²)

f_air represents the speed at which a front of oxygen penetrates through the water depth. The stronger the mixing processes are, then the higher this value will be. Typical values are in the range 0.03 - 0.1m/hour. It is also a function of temperature:

                    (4)

Where:
β = temperature adjustment constant
f_air(20) = transfer velocity (m/s) at a temperature of 20C

Alternatively the reaeration rate, K_air, can be calculated directly as a function of water depth (d) and velocity (u). This can be triggered by setting f_air to a negative value. In this case three expressions for K_air are used, depending on the hydrodynamics.

The first is Owen's equation:

for                     (5)

The second is O'Conner and Dobbin's equation:

for and                     (6)

Otherwise, Churchill's equation applies:
                    (7)

The decay of organic material in the 1D Water Quality Solver is represented by first order kinetics. This includes the decay of organic nitrogen and BOD, the hydrolysis of organic nitrogen to form ammoniacal nitrogen, the oxidation of ammoniacal nitrogen to form nitrate-nitrogen and the oxidation of nitrite to nitrite-nitrogen.

                    (8)

Where:
K = reaction rate constant (s^-1)
C = concentration of the organic material (kg/m³)

Generally the reaction rate constant is expressed as a function of temperature, θ , as shown:
                    (9)

Where:
K_θ = rate constant (s-1) at θ C
K₂₀ = rate constant (s-1) at 20C
α = temperature dependence factor

In the case of the oxidation of ammoniacal nitrogen to form nitrite, the reaction rate constant is a function of salinity and suspended solids concentration as well as temperature:
                    (10)

Where:
S₀ = reference salinity (ppt)
SS₀ = reference suspended solids concentration (ppt)
β = salinity dependence factor
γ = suspended solids dependence factor
K_{AM θ} = nitrification rate constant at θ ° C
K_{AM 20} = nitrification rate constant at 20° C

In the 1D Water Quality Solver the ultimate oxygen demand (BOD(mg/l)) is calculated. This is related to the 5-day BOD by the following equation:

                   (11)

Where:
α = proportion of slow BOD
k_f = reaction rate constant for fast BOD
k_S = reaction rate constant for slow BOD

Denitrification

It is assumed that both nitrate and nitrite can be used as sources of oxygen when oxygen concentration falls below 5% saturation. The demand of oxygen is completely satisfied by the denitrifying process. Nitrate concentration is set according to the equation:

                    (12)

And nitrite concentration is reduced according to:

                    (12)

When there is insufficient oxidised nitrogen to satisfy oxygen demand then any remaining dissolved oxygen is utilised. When all the dissolved oxygen has been used, any further demand is satisfied by the reduction of sulphates to form hydrogen sulphide. The equivalent amount of oxygen released by this process is stored in the variable 'hydrogen sulphide'. The net rate of change in dissolved oxygen concentration is given by:

                    (14)

Where:
K_NO2 : is the oxidation rate constant for nitrite.

General

The DISSOLVED OXYGEN module must be run in conjunction with the TEMPERATURE module. If oxygen balance is being simulated in an estuary or coastal situation then the SALT module must be run as well because of the impact of salinity on saturated dissolved oxygen concentrations. Otherwise the 1D Water Quality Solver will assume the model is simulating a river and the salinity is zero. If the simulation of the OXYGEN WITH SEDIMENT module is required then the DISSOLVED OXYGEN module must be included in the simulation.

The DISSOLVED OXYGEN module simulates the following transported variable names:

• Dissolved oxygen (mg/l)

• Fast BOD (mg/l)

• Slow BOD (mg/l)

• Fast nitrogen (mg/l)

• Slow nitrogen (mg/l)

• Ammoniacal nitrogen (mg/l)

• Nitrite-n (mg/l)

• Nitrate-n (mg/l)

The DISSOLVED OXYGEN module also simulates the following variable:

• Hydrogen sulphide (g)