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# Heat losses caused by drain pipes in the PHPP

Author: Dr. Jürgen Schnieders
Passive House Institute, Rheinstr. 44/46, 64283 Darmstadt, Germany

## Scope

This article outlines a calculation method for the heat losses caused by waste water or stormwater pipes that are vented through the roof. The upper end of this type of drain pipes is open to the ambient air, the lower end is connected to the sewer. During the heating period, the air in the pipe is warmer than the ambient air, resulting in a pressure difference (stack effect) that drives air from the sewer up the drain. Since the air from the sewer is colder than the indoor air, there are heat losses from the room to the drain pipe.

PHPP 9 already contains a calculation method for these heat losses. Particularly for high-rise buildings, this method is overly conservative because it assumes a constant air temperature in the drain over its whole length. Accounting for the temperature increase in the drain is the main goal of the following considerations.

The calculation method is deliberately kept simple. In order to limit the complexity of data input, certain inaccuracies that will not affect the overall functionality of the building can be accepted. To compensate for the simplifications, conservative estimates of unknown quantities are preferred.

## Heat transfer to pipe

The drain pipe has a specific heat transfer coefficient per unit length that is denoted by Ψ and is given in W/(mK). The temperature of the incoming air at the bottom of the pipe is denoted by Tsewer. ṁcp is the capacitance rate of the airflow, Ti is the interior temperature of the building, and l is the total length of the drain pipe inside the thermal envelope.

Then, if Tdrain, the (average) temperature of the air inside the drain pipe, is known, the heat flow into the pipe is given by

$$\Large{Q = \varPsi\cdot l \cdot (T_{i} - T_{drain})}$$

There are two simply derived upper limits to the heat loss from the building to the pipe:

• The air inside the pipe may be assumed to have the sewer temperature over its whole length:

$$\Large{Q \leq \varPsi\cdot l \cdot (T_{i} - T_{sewer})}$$

• The incoming air may be assumed to be heated to room temperature before it leaves the building:

$$\Large{Q \leq \dot m c_{l} \cdot (T_{i} - T_{sewer})}$$

A more precise calculation takes the temperature increase over the length of the drain pipe into account. The temperature profile can be calculated from a simple differential equation, resulting in an exponential temperature increase.

$$\Large{T(z) = T_{i} - (T_{sewer} -T_{i}) \cdot e^ { \dfrac{-\varPsi}{\dot m c_{p}} \cdot Z}}$$

Where Z is the length in the direction of the pipe, starting at the sewer.

Averaging the temperature profile over the length l leads to the average drain temperature

$$\Large{\overline{T} = T_{i} - (T_{sewer} -T_{i}) \cdot \dfrac{\dot m c_{p}}{\varPsi l} \cdot (e^ { \dfrac{-\varPsi}{\dot m c_{p}} \cdot l} - 1)}$$

This temperature can be used to calculate the heat flow into the pipe. It always results in a smaller heat flow than the upper limits given above.

## Calculation of input data

The formula above requires a few unknown input data. Assumptions for these data are discussed in this section. The validity of these assumptions was checked by an evaluation of temperature and heat flow measurements on two drain pipes (for stormwater and waste water) in an administrative building [1] and by measurements from a single¬-family home described in [2].

### Sewer temperature

The sewer temperature depends mainly on the temperature of the water running in the sewer, whereas heat transfer to the ground and to the ambient air are of minor importance.

Many different configurations are possible, with sewers being located at different depths in the ground, carrying different water volumes, and being used either for pure waste water, pure stormwater, or a mixture. Sewers that carry only waste water are relatively warm, sewers that carry only stormwater are usually colder.

For most cases, it is a slightly conservative approximation to assume that the incoming air in the drain pipe has the annual average temperature of undisturbed ground.

### Air velocity in the pipe

In principle, one could try to calculate the air velocity in the pipe for each individual case, but such a procedure would be overly complicated for the user of the PHPP.

The evaluations described in [1] and [2] resulted in air velocities of approximately 0.5 m/s. The velocity is nearly independent of the building height (additional height adds to both the driving pressure difference and to the pressure loss), but it may be higher than measured for high-rise buildings with long, straight, vertical pipe runs where horizontal sections, bends, and elbows play a smaller part. Assuming a fixed velocity of 1 m/s is a solution that is again realistic as well as slightly conservative.

### Ψ-value of pipe

The Ψ-value of the pipe can be calculated using the formulae for air ducts in the PHPP. To calculate the interior film coefficient these formulae require the air velocity in the pipe, which was already estimated above.

### Influence of wind

It might be expected that wind is creating a pressure reduction above the upper end of the drain pipe, resulting in increased airflow. However, the measurements revealed that wind does not have a relevant influence on the air velocity in the pipe.

### Cold air entering the pipe from above

Measurements in [2] assured that the airflow in the pipe is upward during the heating period. On rare occasions cold air may enter the pipe from above, so that insulation against condensation is recommended nevertheless.

For pipes that are closed at the bottom, e.g. chimneys without connection to the room air, a heat tranfer coefficient of 50 W/K per square meter of horizontal opening was estimated in earlier studies.

Water that is running down the pipe can pull air with 30 to 40 times its volume with it. This air causes an additional heat loss, albeit it may not fully be heated to the indoor temperature before it leaves the thermal envelope. The mechanism exists if the pipe is vented through the roof as well as in cases where an air admittance valve is used. For a family of 5, with a generous 100 l per person per day, the resulting airflow rate is approximately 1 m³/h, equivalent to a conductance of 0.33 W/K. This is a negligible quantity.

### Drain pipes running under suspended floors, in underground car parks, etc.

Drain pipes do not always enter the ground on leaving the thermal envelope. If there is no risk of frost, the pipes may run under a suspended floor or in an unheated basement for a while. This reduces the temperature of the incoming air at the bottom of the thermal envelope. In principle, this temperature could be calculated with the methodolgy described above. Considering the amount of additional input data required, including the temperature of the basement, the relatively small possible gain in accuracy did not appear to justify the additional user effort required.

### Influence of stormwater

There are temperature drops in stormwater drainpipes whenever cold water is running through the pipes. For the measurements in [1] this effect was already accounted for by using a sewer temperature of 11 °C, still slightly above the annual average ground temperature in the region of 10 °C. It may be concluded that the additional heat losses due to stormwater are covered by the assumption that the sewer temperature is equal to the annual average ground temperature.

### Multiple pipes that vent through a common opening

Multiple drain pipes are usually connected before they leave the building (or the basement) towards the sewer. It also happens regularly that several vent pipes are connected at the top and are vented through one common opening. Depending on the details of the installation, such reductions of the cross-section reduce the airflow rate to a different extent.

From an analysis of some examples, the following guideline was derived: if multiple pipes are connected or have varying diameters, the airflow rate can be calculated based on a reduced cross-section, provided that this cross-section is not exceeded for at least 30% of the pipe length.

It should be noted that this reduction only applies to the airflow rate, i.e. ṁcp. The specific heat losses from the building to the pipe, Ψl, still need to account for the whole pipe length, also of parallel pipes.

### Where to insulate

For pipes that are only open at the top, it is common practice to insulate only the upper 3 to 5 m of length against condensation. This is also acceptable with regard to energy efficiency.

Pipes that are open at both ends should be insulated against condensation over the entire length. The more insulation is used, the lower will be the temperatures in the higher parts of the pipes. As a general rule, it seems appropriate to insulate the whole length of the pipes evenly. Exceptions may be possible in high-rise buildings for central parts of pipes that do not carry stormwater, but no quantitative assessment is possible as of yet.

### Hot climates

If the ambient temperatures are higher than the indoor temperatures, the direction of the airflow is reversed. Hot air will fall into the drain vent and proceed down to the sewer. This air initially has the ambient air temperature, not the sewer temperature. In principle, the reduction factor that is used for the calculation of Ψ must be 1 in this case, contrary to

$$\Large{T(z) = \dfrac{T_{i} - T_{drain}}{T_{i} - T_{ambient}}}$$

for the heating case. However, such a distinction would require to provide different Ψ values for each month, or at least for winter and summer. This appears inappropriate with regard to the relative importance of the effect.

Also, cooling is required not only at ambient temperatures above the setpoint, but also below. This typically results in an average ambient temperature over the cooling period that is very close to the room temperature. A few experiments for hot climates (Jakarta, Dubai) resulted in average temperatures over the cooling period of less than 29 °C, so that the relevant temperature difference is small.

Thus, the error occuring for the cooling period due to the overly small reduction factor is acceptable.

## Conclusions

The calculation method developed above allows for an appropriate assessment of heat losses to vented drain pipes also for high-rise buildings. With a few evidence-based assumptions, the method is sufficiently simple to use for practical design applications.

## References

This article was written in the framework of the EU-funded project Sinfonia.

This project has received funding from the European Union’s Seventh Programme for research, technological development and demonstration under grant agreement No 609019.