**Calculating in KWh**

### Table of contents

## Summary

The following approximate conversion factors are used to calculate in kilowatt-hour units.

Fuel |
Factor |
---|---|

Oil | 8 kWh useful heating/liter |

Firewood | 1 000 kWh useful heating/cubic meter |

Solar panels | 400 kWh useful heating/square meter |

Woodpellets | 3.7 kWh useful heating/kg |

Wooden briquettes | 3.4 kWh /kg |

Wooden briquettes, 1 pallet | 3 300 kWh useful heating |

Using the above figures — and the assumptions underlying them — one cubic metre of firewood, not stacked neatly, corresponds to 125 litres of oil. A solar panel of 2.5 square meters also corresponds to 125 liters of oil a year.

If there are more known details, such as the type of wood or its heating efficiency, the calculations can be amended with the below formulas to generate more accurate conversion factors.

## Oil furnaces

The heating needs of a household are calculated in kilowat-hours. What if a homeowner calculates heating needs in terms of liters of oil consumed a year?

We need to be able to calculate the energy content of oil in terms of kilowatt-hours,taking into consideration the efficiency rate of the boiler. Specifically, the

For example, if we use just one liter of oil, and assume that the boiler efficiency is 0.8, then the

useful heating (kWh) = 1 liter * 0.84 kg/liter * 11.86 kWh/kg * 0.8 = 1 liter * 10 kWh/liter * 0.8 = 8 kWh

In the introduction above we stated that the expected useful heating from oil is 8 KWH/liter; this works as a rough approximation. Note that the energy content of oil pr liter is a straightforward whole number: 10 kWh/liter.

If the efficiency rate is different from 0.8, remember to substitute it into the equation. Efficiency rates usually lie in the range +/- 15% af 0.8, so the final result will also usually lie within +/- 15% af 8 kWh/liter.

For example, if a homeowner states his oil consumption as 2 000 liters a year, then theuseful heating (kWh) = 2 000 liter * 8 kWh/liter = 16 000 kWh

This number can be compared to the normal heating consumption in a house of the same size (Average single home heating consumption). The *normal* heating consumption is given effective heating (living room heating). This figure is fixed, so to facilitate comparison we have to take into account heating method and efficiency rates.

## Firewood

If a homeowner uses a private stove as a supplementary source of heating, and states annual consumption partly in terms of steres (cubic meters) of wood a year, then what?

We have to calculate the combustion value of firewood in terms of kilowatt-hours, but we also have to include the efficiency rate of the stove. Specifically, this is

Firewood is sold by volume, in *steres* (EU) or *cords* (US), but the amount of free space in a stere or cord can vary, because wood is stacked differently (Danish Institute of Technology, website on stoves). One stere corresponds to the volume of a box measuring one meter on each side (1 m height * 1 m length * 1 m width = 1 cubic meter). One stere corresponds roughly to 0.276 cords.

*Solid mass coefficient* is the fraction of the mass that is actually solid (firewood).

- Cubic meter: a cubic meter of wood; the unit cubic meter is used when considering a piece of wood, even though an average piece of wood is significantly smaller than a cubic meter. Solid fuel coefficient 1, i.e. no air pockets from wood stacking in this case.
- Stacked cubic meter: Short pieces of firewood stacked efficiently. Solid fuel coefficient of app. 0.7, i.e. 70 % solid wood and 30 % air pockets.
- Loaded cubic meter: the firewood is stacked haphazardly. The solid fuel coefficient is app. 0.45 , i.e. 45% solid mass and 55% air pockets.

The firewoods *solid mass* is the proportion of dry mass per cubic meter in one piece of firewood (kg/cbm), which depends on how much air is in the piece of firewood relative to its solid mass.

The firewoods *density* is the proportion of dry mass per cubic meter in a single piece of firewood (kg/cbm), and it depends on how large the air pockets are relative to the dry mass. This measurement is in *stere*, not cubic meters. The density depends on how fast the tree grows, so the value is dependent on the tree sprecies and the growth conditions.

The dry mass *energy content* is always 5.25 kWh/kg. Firewood with 18% moisture, equivalent to *dry* wood stored for a year, has a lower energy content, 4.2 kWh/kg.

The efficiency rate for a woodfuelled stove depends on the construction, but on average corresponds to 0.7.

Fig. 1 Estimated solid fuelcoefficient: 0.45. |

Fig. 2 Estimated solid fuelcoefficient: 0.70. |

Fig. 3 Estimated solid fuelcoefficient: 0.80 (assuming a dense core). |

useful heating (kWh) = 1 stere * 0.55 cbm/stere * 620 kg/cbm * 4.2 kWh/kg * 0.7 = 1 000 kWh

The conversion factor used here is equivalent to the one at the top of page (Summary). It depends on several assumptions, so if the actual figures for solid fuel coefficients, density, combustion values and efficiency rates are known, the average of 1 000 kWh/kg can be modified.

Table 1 contains modified conversion factors for wood from different tree species. The figures in the table range between +/- 10% of the average estimate of 1 000 kWh/stere.

**Table 1.** Useful heating in firewood (data from Energy Service Denmark, spreadsheet *Estimates of wood*). Assumption: moisture 18%, efficiency rate 0.7, solid fuel coefficient 0.55, efficient heating 4.2 kWh/kg.

Tree species |
Density (kg/cbm) |
Useful heating (kWh/stere) |
---|---|---|

Beech | 710 | 1 150 |

Oak | 700 | 1 130 |

Ash | 700 | 1 130 |

Elm | 690 | 1 120 |

Maple | 660 | 1 070 |

Birch | 620 | 1 000 |

Mountain fir | 600 | 970 |

Willow | 560 | 910 |

Alder | 540 | 870 |

Forest fir | 520 | 840 |

Larch | 520 | 840 |

Small-leaved lime | 510 | 820 |

Pine | 450 | 730 |

Poplar | 450 | 730 |

Deciduous trees | 680 | 1 100 |

Spruce trees | 593 | 960 |

## Solar heating (Solar panels)

Solar panels consist of a piping system containing water and anti-freeze solution. The pipes are black, so that they can absorb as much sun as possible, and they are encapsulated in a box with a glass or plastic surface to minimize loss due to wind.

The yearly production varies with the number of sunlight hours in the geographic area, but estimated production is app. 400 kWh per square meter solar panel, with deviations of app. +/- 25% (Danish Technological Institute, Life cycle estimates, p. 25, table 5.5). A panel on a house is typically 2 - 3 square meters.

The efficiency of a solar panel depends on its placement relative to the sun, as well as the outside temperature.

## Woodpellets

An average woodpellet boiler has an efficiency rate of 0.75, and the combustion value for woodpellets is 4.9 kWh/kg. Thus the conversion factor is 4.9 kWh/kg * 0.75 = 3.7 kWh/kg.

## Wood bricquettes

Wood bricquettes consist of glue-free sawdust, shavings and bark which is pressed into bricquettes.

The moisture content is normally around 6 - 8% in bricquettes, unless they have been exposed to moisture. Assuming a moisture content of 6%, the energy content is 4.9 kWh/kg (Figure 4), equivalent to woodpellets. With a boiler efficiency of 0.7, the conversion factor becomes 4.9 kWh/kg*0.7 = 3.4 kWh/kg.

One pallet of wood bricquettes weighs 960 kg, so the useful heating at 6% moisture content is 3.4 kWh/kg * 960 kg = 3 264.

## Moisture

The higher the moisture content in wood, the lower the energy content, because the boiler will waste energy on heating up the water to boiling point and then evaporating it. Figure 4 shows that the energy content drops to less than half if there is 50 % moisture in the fuel (e.g. newly lumbered logs)

Fig. 4 Wood energy content. The more moisture, the less energy. |

The energy content for one kg of wood is reduced by the heat needed for evaporatation and for heating the water to boiling point

`energy content = energy content dry mass - evaporation heat loss - heating loss`

If the moisture content is *f*, then the formula for one kg of fuel at living room temperature 20 degrees C,

`energy content [kWh] = 5.25*(1-(f*0.01)) - 0.6274*f*0.01 - 0.001163*f*0.01*(100-20)`

5.25 is the energy content for dry mass (kWh), the value 0.6274 is the thermal energy needed to evaporate a kg of water, and the value 0.001163 is the thermal energy in kWh required to heat one kg of water by one degree. The difference 100 - 20 = 80 is the number of degrees the wood has to be heating to reach boiling point.