The actual thermal status of a SSF wetland bed can be a very complex situation. Heat gains or losses can occur in the underlying soil, the wastewater flowing through the system, and the atmosphere. Basic thermal mechanisms involved include conduction to or from the ground, conduction to or from the wastewater, conduction and convection to or from the atmosphere, and radiation to or from the atmosphere. It can be shown that energy gains or losses to the ground are a minor component and can therefore be neglected. It is conservative to ignore any energy gains from solar radiation but is appropriate at northern sites where the temperature conditions are most critical. In the southwest, where solar radiation can be very significant on a year-round basis, this factor might be included in the calculations. Convection losses can be significant due to wind action on an open water surface, but this should not be the case for most SSF wetlands where a dense stand of vegetation, a litter layer, and a layer of relatively dry gravel are typically present. These damp out the wind effects on the underlying water in the wetland, and, as a result, convection losses will be relatively minor and can be ignored in the thermal model. The simplified model developed below is therefore based only on conduction losses to the atmosphere and is conservative. This procedure was developed from basic heat-transfer relationships (Chapman, 1974) with the assistance of experts on the topic (Calkins, 1995; Ogden, 1994).

The temperature at any point in the SSF wetland can be predicted by comparing the estimated heat losses to the energy available in the system. The losses are assumed to occur via conduction to the atmosphere, and the only energy source available is assumed to be the water flowing through the wetland. As water is cooled, it releases energy, and this energy is defined as the specific heat. The specific heat of water is the amount of energy that is either stored or released as the temperature is either increased or decreased. The specific heat is dependent on pressure and to a minor degree on temperature. Because atmospheric pressure will prevail at the water surface in the systems discussed in this book, and because the temperature influence is minor, the specific heat is assumed to be a constant for practical purposes. For the calculations in this book, the specific heat is taken as 1.007 BTU/lb-°F (4215 J/kg-°C). The specific heat relationship applies down to the freezing point of water (32°F; 0°C). Water at 32°F will still not freeze until the available latent heat is lost. The latent heat is also assumed to be a constant and equal to 144 BTU/lb (334,944 J/kg). The latent heat is, in effect, the final safety factor, protecting the system against freezing; however, when the temperature drops to 32°F (0°C), freezing is imminent and the system is on the verge of physical failure. To ensure a conservative design, the latent heat is only included as a factor in these calculations when a determination of potential ice depth is made.

The available energy in the water flowing through the wetlands is defined by Equation 7.4:

where qG = Energy gain from water (Btu/°F; J/°C).

cp = Specific heat capacity of water (1.007 Btu/lb-°F; 4215 J/kg-°C). S = Density of water (62.4 lb/ft3; 1000 kg/m3). As = Surface area of wetland (ft2; m2). y = Depth of water in wetland (ft; m). n = Porosity of wetland media (percent).

If it is desired to calculate the daily temperature change of the water as it flows through the wetland, the term AJt is substituted for As in Equation 7.4:

where qG is the energy gain during 1 d of flow (Btu/d-°F; J/d-°C), t is the hydraulic residence time in the system (d), and the other terms are as defined previously. The heat losses from the entire SSF wetland can be defined by Equation 7.6:

where qL = Energy lost via conduction at the atmosphere (Btu; J). T0 = Water temperature entering wetland (°F; °C). Tair = Average air temperature during period of concern (°F; °C). U = Heat-transfer coefficient at the surface of the wetland bed (Btu/ft2-hr-°F; W/m2-°C).

O = Time conversion (24 hr/d; 86,400 s/d). As = Surface area of wetland (ft2; m2). t = Hydraulic residence time in the wetland (d).

TABLE 7.2

Thermal Conductivity of Subsurface Flow Wetland Components

TABLE 7.2

Thermal Conductivity of Subsurface Flow Wetland Components

Material |
k (Btu/ft2hr°F) |
k (W/m °C) |

Air (no convection) |
0.014 |
0.024 |

Snow (new, loose) |
0.046 |
0.08 |

Snow (long-term) |
0.133 |
0.23 |

Ice (at 0°C) |
1.277 |
2.21 |

Water (at 0°C) |
0.335 |
0.58 |

Wetland litter layer |
0.029 |
0.05 |

Dry (25% moisture) gravel |
0.867 |
1.5 |

Saturated gravel |
1.156 |
2.0 |

Dry soil |
0.462 |
0.8 |

The rair values in Equation 7.6 can be obtained from local weather records or from the closest weather station to the proposed wetland site. The year with the lowest winter temperatures during the past 20 or 30 years of record is selected as the "design year" for calculation purposes. It is desirable to use an average air temperature over a time period equal to the design hydraulic residence time (HRT) in the wetland for these thermal calculations. If monthly average temperatures for the "design year" are all that is available, they will usually give an acceptable first approximation for calculation purposes. If the results of the thermal calculations suggest that marginally acceptable conditions will prevail then further refinements are necessary for a final system design.

The conductance (U) value in Equation 7.6 is the heat-conducting capacity of the wetland profile. It is a combination of the thermal conductivity of each of the major components divided by its thickness as shown in Equation 7.7:

Conductance (Btu/ft2-hr-°F; W/m2-°C). Conductivity of layers 1 to n (Btu/ft2-hr-°F; W/m-°C). Thickness of layers 1 to n (ft; m).

Values of conductivity for materials that are typically present in SSF wetlands are presented in Table 7.2. The conductivity values of the materials, except the wetland litter layer, are well established and can be found in numerous literature sources. The conductivity for a SSF wetland litter layer is believed to be conservative but is less well established than the other values in Table 7.2.

Example 7.1

Determine the conductance of a SSF wetland bed with the following characteristics: 8-in. litter layer, 6 in. of dry gravel, and 18 in. of saturated gravel. Compare the value to the conductance with a 12-in. layer of snow.

Solution

1. Calculate the U value without snow using Equation 7.7:

U = 1/[(0.67/0.029) + (0.5/0.867) + (1.5/1.156)] = 0.040 Btu/ft2-hr-°F

2. Calculate the U value with snow:

U = 1/[(1/0.133) + (0.67/0.029) + (0.5/0.867) + (1.5/1.156)] = 0.031 Btu/ft2-hr-°F

The presence of the snow reduces the heat losses by 23%. Although snow cover is often present in colder climates, it is prudent for design purposes to assume that the snow is not present.

The change in temperature due to the heat losses and gains defined by Equation 7.5 and Equation 7.6 can be found by combining the two equations:

Tc = qjqo = (T - Tail)(U)(c)(As)(t)/(cp)(8)(As)(y)(n) (7.8)

where Tc is the temperature change in the wetland (°F; °C), and the other terms are as defined previously.

The effluent temperature (Te) from the wetland is:

T = T0 - (T0 - Tair)[(U)(o)(t)/(cp)(5)(y)(n)] (7.10)

The calculation must be performed on a daily basis. The T0 value is the temperature of the water entering the wetland that day, Te is the temperature of the effluent from the wetland segment, and Tair is the average daily air temperature during the time period.

The average water temperature (Tw) in the SSF wetland is, then:

This average temperature is compared to the temperature value assumed when the size and the HRT of the wetland were determined with either the biochemical oxygen demand (BOD) or nitrogen removal models. If the two temperatures do not closely correspond, then further iterations of these calculations are necessary until the assumed and calculated temperatures converge.

Further refinement of this procedure is possible by including energy gains and losses from solar radiation and conduction to or from the ground. During the winter months, conduction from the ground is likely to represent a small net gain of energy because the soil temperature is likely to be higher than the water temperature in the wetland. The energy input from the ground can be calculated with Equation 7.6; a reasonable U value would be 0.056 Btu/ft2-hr-°F (0.32 W/m2-°C), and a reasonable ground temperature might be 50°F (10°C).

The solar gain can be estimated by determining the net daily solar gain for the location of interest from appropriate records. Equation 7.12 can then be used to estimate the heat input from this source. The results from Equation 7.12 should be used with caution. It is possible that much of this solar energy may not actually reach the water in the SSF wetland because the radiation first impacts on the vegetation and litter layer and a possible reflective snow cover, so an adjustment is necessary in Equation 7.12. As indicated previously, it is conservative to neglect any heat input to the wetland from these sources:

where qsolar = Energy gain from solar radiation (Btu; J).

s = Fraction of solar radiation energy that reaches the water in the SSF wetland, typically 0.05 or less.

If these additional heat gains are calculated, they should be added to the results from Equation 7.4 or Equation 7.5 and this total used in the denominator of Equation 7.10 to determine the temperature change in the system.

If the thermal models for SSF wetlands predict sustained internal water temperature of less than 33.8°F (1°C), a wetland may not be physically capable of winter operations at the site under consideration at the design HRT. Nitrogen removal is likely to be negligible at those temperatures.

Constructed wetlands can operate successfully during the winter in most of the northern temperate zone. The thermal models presented in this section should be used to verify the temperature assumptions made when the wetland is sized with the biological models for BOD or nitrogen removal. Several iterations of the calculation procedure may be necessary for the assumed and calculated temperatures to converge.

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