Heat Loss Calculation According to DIN EN 13941

Heat losses in buried district heating pipes range from 5 to 40 % of the energy fed in, depending on the network type, and are calculated according to DIN EN 13941 using thermal resistances of cylindrical layers (pipe, insulation, soil). The main levers are insulation thickness, medium temperature and soil conditions — lowering the supply temperature from 90 to 70 °C alone reduces losses by approximately 25 %.

Physical Fundamentals

The heat loss of a buried pipe is governed by heat conduction. The hot medium inside the pipe releases heat via the pipe wall, the insulation and the surrounding soil to the ground surface. The driving force is the temperature difference between the medium and the surroundings.

For a single, concentric pipe system (medium — pipe — insulation — casing — soil), the linear heat loss $q$ (in W/m) is:

The total thermal resistance $R_{tot}$ is made up of the individual resistances of the layers.

Thermal Resistances of Cylindrical Layers

For a cylindrical layer (e.g. the thermal insulation), the thermal resistance per metre of pipe length is calculated as:

with the thermal conductivity $\lambda$ of the material and the outer and inner diameters $d_a$ and $d_i$ of the respective layer. The thermal resistance of the insulation layer usually dominates the total resistance, since the thermal conductivity of the insulation ($\lambda \approx 0{.}024$ — $0{.}030$ W/(m$\cdot$K) for PUR foam) is many times lower than that of the soil or the pipe material.

Thermal Resistance of the Soil

The surrounding soil represents an additional thermal resistance. For a single, horizontally buried pipe in homogeneous soil, DIN EN 13941 gives:

Here, $h$ is the cover depth (distance from the pipe centre to the ground surface), $d_c$ is the outer diameter of the casing pipe and $\lambda_{soil}$ is the thermal conductivity of the soil. Typical values for $\lambda_{soil}$ lie between 1.0 and 2.0 W/(m$\cdot$K), depending on soil type and moisture content.

Characteristics of Twin-Pipe Systems

In the common practice of laying supply and return pipes next to each other in the same trench, the warmer supply pipe influences the cooler return pipe and vice versa. This effect of thermal coupling must be taken into account in the calculation.

DIN EN 13941 introduces a coupling resistance $R_{12}$ which describes this mutual interaction. The heat losses of the supply and return lines then follow from a coupled system of equations:

Thermal coupling results in the supply line losing slightly more heat than an isolated single pipe, while the return line loses slightly less (or, at very low return temperatures, even absorbs heat from the soil). The total loss of the system is slightly higher due to the coupling than for pipes placed far apart.

Influencing Factors for Heat Losses

Insulation Thickness

The insulation thickness has the greatest influence on the heat losses. Pre-insulated bonded pipes (KMR) according to DIN EN 253 are available in various insulation classes (Series 1, 2 and 3). The differences are considerable: a DN 100 pipe of Series 1 (standard insulation) has a heat loss of approximately 18 W/m at 80 °C medium temperature, while Series 3 (reinforced insulation) has only about 12 W/m.

Medium Temperature

The heat loss is directly proportional to the temperature difference between the medium and the ground surface. Lowering the supply temperature from 90 °C to 70 °C reduces the heat loss by approximately 25 %. This is one of the main advantages of low-temperature networks.

Burial Depth

A greater cover depth increases the soil resistance and thus reduces heat losses. At the same time, however, the soil temperature at burial depth rises, which partially offsets the effect. Typical burial depths are between 0.6 and 1.2 m (top of pipe). In practice, the choice of burial depth is driven more by frost protection requirements and excavation costs than by heat loss optimisation.

Soil Temperature

The soil temperature fluctuates seasonally. In central Europe, the undisturbed ground temperature at 1 m depth varies between approximately 3 °C in February and approximately 17 °C in August. An annual mean of approximately 10 °C can be assumed. In winter, heat losses are therefore higher than in summer — at the same time, heat demand is at its peak, which increases the relative loss share.

Soil Moisture Content

Moist soil conducts heat better than dry soil. The thermal conductivity of dry sand is approximately 0.4 W/(m$\cdot$K), while that of water-saturated sand is approximately 2.4 W/(m$\cdot$K). In areas with a high groundwater level, heat losses can therefore be considerably higher than computed using standard values.

Typical Loss Ranges

The following guide values provide an orientation for the relative heat losses of different network types:

For cold district heating, the effect is reversed: since the network temperature is below the soil temperature, the network absorbs heat from its surroundings. The pipes then act as a linear heat source.

Annual Heat Losses

For economic evaluation, not the instantaneous losses but the annual heat losses are decisive. These result from integrating the hourly losses over the entire year while accounting for the varying medium and soil temperatures. As a simplification, the annual heat loss per metre of route can be estimated as:

where $q_{mean}$ is the mean linear heat loss taking into account the annual profile of the temperatures. For a typical local district heating network with a supply temperature of 80 °C and standard insulation (DN 100), the result is approximately 140 kWh/(m$\cdot$a) of total losses for supply and return combined.

Conclusion

Heat loss calculation according to DIN EN 13941 provides the tools to quantify the thermal efficiency of buried pipes. The main levers are the insulation thickness, the medium temperature and the soil conditions. For a realistic assessment, the thermal coupling in twin-pipe systems and the seasonal variations must be taken into account. The results feed directly into the economic calculation and form an essential basis for the choice of network type and operating temperatures. In VICUS Districts, heat losses according to DIN EN 13941 are automatically calculated for every time step and included in the overall energy balance of the network.

Further reading: Network Temperatures in District Heating Networks — how temperature levels drive heat losses, Linear Heat Density — the economic context in which losses must be evaluated, Pipe Dimensioning in District Heating Networks — insulation class and pipe sizing decisions, Economic Analysis According to VDI 2067 — how heat losses translate into operating costs.

References and Standards

• DIN EN 13941 — District heating pipes — Design and installation of pre-insulated bonded pipe systems
• AGFW FW 401 Part 10 — Installation and Structural Analysis of Pre-insulated Pipes — Thermal Calculation
• AGFW FW 309 — Energy Evaluation of District Heating and Cooling