Difference between revisions of "Assessing Wood Fuel Supply Potentials"
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− | <span style="color: rgb(255,0,0)">NEU</span><br>[[GIZ HERA Cooking Energy Compendium| | + | = <span style="color: rgb(255, 0, 0);">NEU</span><br>[[GIZ HERA Cooking Energy Compendium|NEU]]<br> = |
− | <br> | + | == ENU == |
+ | |||
+ | === NEU === | ||
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+ | <br> | ||
= Supply Assessment<font size="2"></font> = | = Supply Assessment<font size="2"></font> = | ||
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<font size="2">The FAO have developed and implemented the ‘Woodfuel Integrated Supply/Demand Overview Mapping (WISDOM) methodology as a tool to support national wood energy planning. This is a GIS-based tool that allows the user to understand, in detail, the current spatial patterns of biomass demand and supply in a country, and to assess the sustainability of woodfuel as a renewable and widespread energy source. The methodology has been expanded to investigate the scope of urban woodfuel supply</font><font size="2">, which identifies the extent to which supply zones encroach into rural areas and forests. (The term “urban woodsheds” is analogous with the familiar geographic concept of watersheds.)</font> | <font size="2">The FAO have developed and implemented the ‘Woodfuel Integrated Supply/Demand Overview Mapping (WISDOM) methodology as a tool to support national wood energy planning. This is a GIS-based tool that allows the user to understand, in detail, the current spatial patterns of biomass demand and supply in a country, and to assess the sustainability of woodfuel as a renewable and widespread energy source. The methodology has been expanded to investigate the scope of urban woodfuel supply</font><font size="2">, which identifies the extent to which supply zones encroach into rural areas and forests. (The term “urban woodsheds” is analogous with the familiar geographic concept of watersheds.)</font> | ||
− | <font size="2">[ftp://ftp.fao.org/docrep/fao/010/i0152e/i0152e00.pdf ''WISDOM for Cities. Analysis of wood energy and urbanization using WISDOM methodology'']</font> <br> | + | <font size="2">[ftp://ftp.fao.org/docrep/fao/010/i0152e/i0152e00.pdf ''WISDOM for Cities. Analysis of wood energy and urbanization using WISDOM methodology'']</font> <br> |
{| cellspacing="0" cellpadding="0" border="1" | {| cellspacing="0" cellpadding="0" border="1" | ||
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− | | | + | | width="558" valign="top" | |
A '''WISDOM analysis''' involves five main steps: (1) selection of the spatial base, (2) development of the demand module, (3) development of the supply module, (4) development of the integration module, and (5) identification of woodfuel hot spots. | A '''WISDOM analysis''' involves five main steps: (1) selection of the spatial base, (2) development of the demand module, (3) development of the supply module, (4) development of the integration module, and (5) identification of woodfuel hot spots. | ||
At national level, the WISDOM approach has been implemented in Mexico, Senegal and Slovenia. At the subregional level, WISDOM has been implemented over the eastern and central African countries covered by the Africover Programme (Burundi, Democratic Republic of the Congo, Egypt, Eritrea, Kenya, Rwanda, Somalia, the Sudan, United Republic of Tanzania and Uganda) and over the countries of Southeast Asia (Cambodia, Malaysia, Lao People’s Democratic Republic, Thailand, Viet Nam and China, Yunnan Province) | At national level, the WISDOM approach has been implemented in Mexico, Senegal and Slovenia. At the subregional level, WISDOM has been implemented over the eastern and central African countries covered by the Africover Programme (Burundi, Democratic Republic of the Congo, Egypt, Eritrea, Kenya, Rwanda, Somalia, the Sudan, United Republic of Tanzania and Uganda) and over the countries of Southeast Asia (Cambodia, Malaysia, Lao People’s Democratic Republic, Thailand, Viet Nam and China, Yunnan Province) | ||
− | Further information can be found at: [http://www.fao.org/forestry/energy/en/ <span>http://www.fao.org/forestry/energy/en/</span>] | + | Further information can be found at: [http://www.fao.org/forestry/energy/en/ <span>http://www.fao.org/forestry/energy/en/</span>] |
|} | |} | ||
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<font size="2">As a consequence, forest resource assessments have to be complemented by legal, regulatory, institutional, and socio-economic studies that analyse the framework conditions. </font> | <font size="2">As a consequence, forest resource assessments have to be complemented by legal, regulatory, institutional, and socio-economic studies that analyse the framework conditions. </font> | ||
− | <br> | + | <br> |
= Factors for estimating woodfuel supply = | = Factors for estimating woodfuel supply = | ||
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<font size="2">'''Harvest/Cutting fraction''' is the volume harvested after the percentage harvesting losses have been deducted. Harvesting losses can amount to 10% of the allowable cut.</font> | <font size="2">'''Harvest/Cutting fraction''' is the volume harvested after the percentage harvesting losses have been deducted. Harvesting losses can amount to 10% of the allowable cut.</font> | ||
− | {| cellspacing="0" cellpadding="2 | + | {| width="100%" cellspacing="0" cellpadding="2" border="1" |
|- | |- | ||
| '''Table 5: Estimating actual and potential wood supplies''' | | '''Table 5: Estimating actual and potential wood supplies''' | ||
|- | |- | ||
| width="540" | | | width="540" | | ||
− | {| cellspacing="0" cellpadding="5 | + | {| width="100%" cellspacing="0" cellpadding="5" border="1" |
|- | |- | ||
| colspan="2" | '''Supply factors''' | | colspan="2" | '''Supply factors''' | ||
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'''Sustainable harvesting:''' A x AC x FA x FF x HF | '''Sustainable harvesting:''' A x AC x FA x FF x HF | ||
− | =1000ha x 0.5 m<sup>3</sup>/ha x 0.8 x 1.0 x 0.9 = '''<u>360 m<sup>3</sup></u>''' <br> | + | =1000ha x 0.5 m<sup>3</sup>/ha x 0.8 x 1.0 x 0.9 = '''<u>360 m<sup>3</sup></u>''' <br> |
|} | |} | ||
− | <font size="2"><span | + | <font size="2"><span style="display: none;" id="1227183625767S"> </span></font><br> |
= Characteristics of woodfuel supply figures = | = Characteristics of woodfuel supply figures = | ||
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<font size="2">Wood is the major renewable resource that provides thermal energy in the world, so high conversion efficiency into energy is a key issue. Utmost care should be taken when using conversion factors, as this is the major cause of serious miscalculation. Foresters in general distinguish between ‘standing stock’ measured in solid cubic meters, and ‘harvested woodfuel’ measured in stacked cubic meters (containing air spaces between the pieces of wood), which are often called stere. A well-piled stacked cubic meter may contain 0.65 m<sup>3</sup> solid (e.g. products from plantations) whereas a poorly stacked one may only have 0.33 m<sup>3</sup> solid (e.g twisted branches of sahelian shrubs); just half as much as the well-stacked wood.</font> | <font size="2">Wood is the major renewable resource that provides thermal energy in the world, so high conversion efficiency into energy is a key issue. Utmost care should be taken when using conversion factors, as this is the major cause of serious miscalculation. Foresters in general distinguish between ‘standing stock’ measured in solid cubic meters, and ‘harvested woodfuel’ measured in stacked cubic meters (containing air spaces between the pieces of wood), which are often called stere. A well-piled stacked cubic meter may contain 0.65 m<sup>3</sup> solid (e.g. products from plantations) whereas a poorly stacked one may only have 0.33 m<sup>3</sup> solid (e.g twisted branches of sahelian shrubs); just half as much as the well-stacked wood.</font> | ||
− | <br> | + | <br> |
− | {| | + | {| width="100%" cellspacing="0" cellpadding="0" border="0" class="FCK__ShowTableBorders" |
|- | |- | ||
| | | | ||
{| cellspacing="0" cellpadding="0" border="1" | {| cellspacing="0" cellpadding="0" border="1" | ||
|- | |- | ||
− | | | + | | width="300" valign="top" colspan="3" | |
− | '''Table 2: Density (specific mass) and (net) calorific value (Heat of combustion) of some fuels''' | + | '''Table 2: Density (specific mass) and (net) calorific value (Heat of combustion) of some fuels''' |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | ''' ''' | + | ''' ''' |
− | | | + | | width="76" valign="top" | |
− | <span>density (kg/m3) </span> | + | <span>density (kg/m3) </span> |
− | | | + | | width="95" valign="top" | |
− | <span>calorific value (MJ/kg)</span> | + | <span>calorific value (MJ/kg)</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>LPG</span>''' | + | '''<span>LPG</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>560</span> | + | <span>560</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>45</span> | + | <span>45</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>Gasoline(petrol)</span>''' | + | '''<span>Gasoline(petrol)</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>720</span> | + | <span>720</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>44</span> | + | <span>44</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>Kerosene</span>''' | + | '''<span>Kerosene</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>806</span> | + | <span>806</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>43</span> | + | <span>43</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>Wood (oven dried)</span>''' | + | '''<span>Wood (oven dried)</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>650-750</span> | + | <span>650-750</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>18-19</span> | + | <span>18-19</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>Wood, (30% moisture)</span>''' | + | '''<span>Wood, (30% moisture)</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>650-750</span> | + | <span>650-750</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>12-13</span> | + | <span>12-13</span> |
|- | |- | ||
− | | valign="top" nowrap="nowrap | + | | width="130" valign="top" nowrap="nowrap" | |
− | '''<span>Charcoal</span>''' | + | '''<span>Charcoal</span>''' |
− | | valign="top" nowrap="nowrap | + | | width="76" valign="top" nowrap="nowrap" | |
− | <span>180</span> | + | <span>180</span> |
− | | valign="top" nowrap="nowrap | + | | width="95" valign="top" nowrap="nowrap" | |
− | <span>30</span> | + | <span>30</span> |
|- | |- | ||
− | | | + | | width="300" valign="top" colspan="3" | |
− | '''<span>NB.: Values are approximate, since fuels vary in composition which affects both the density and calorific value.</span>''' | + | '''<span>NB.: Values are approximate, since fuels vary in composition which affects both the density and calorific value.</span>''' |
|} | |} | ||
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{| cellspacing="0" cellpadding="0" border="1" | {| cellspacing="0" cellpadding="0" border="1" | ||
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− | | | + | | width="177" valign="top" colspan="2" | |
− | '''Table 3: Influence of wood moisture on calorific value''' | + | '''Table 3: Influence of wood moisture on calorific value''' |
|- | |- | ||
− | | | + | | width="92" valign="top" | |
− | '''Moisture content %''' | + | '''Moisture content %''' |
− | | | + | | width="85" valign="top" | |
− | '''MJ/kg''' | + | '''MJ/kg''' |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">0</font> | + | <font size="2">0</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">19.0</font> | + | <font size="2">19.0</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">10</font> | + | <font size="2">10</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">16.9</font> | + | <font size="2">16.9</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">20</font> | + | <font size="2">20</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">14.7</font> | + | <font size="2">14.7</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">30</font> | + | <font size="2">30</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">12.6</font> | + | <font size="2">12.6</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">40</font> | + | <font size="2">40</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">10.4</font> | + | <font size="2">10.4</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">50</font> | + | <font size="2">50</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">8.2</font> | + | <font size="2">8.2</font> |
|- | |- | ||
| width="92" | | | width="92" | | ||
− | <font size="2">60</font> | + | <font size="2">60</font> |
| width="85" | | | width="85" | | ||
− | <font size="2">6.1</font> | + | <font size="2">6.1</font> |
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Energy content is proportional to the dry-weight of wood; so higher density woods have higher calorific values. The reportedrange in wood densities is between 100 kg/m<sup>3 </sup> and 1200 kg/m<sup>3</sup>. Species used as woodfuel are generally from 650 kg/m<sup>3 </sup>to 750 kg/m<sup>3</sup>. The moisture content plays a crucial role in determining the calorific value (Table 3). The moisture content of wood is around 50 % (of total weight) when first harvested, whereas air-dried wood contains between 12% to 20% of moisture yielding a calorific value between 14 MJ/kg and 16 MJ/kg. To evaporate one kilogram of water takes about 2.5 MJ. In the case of charcoal, the calorific value is around 30 MJ/kg. In its statistics, the FAO uses a conversion factor of 165 kg of produced charcoal from one cubic meter of fuelwood (see also chapter on charcoal). | Energy content is proportional to the dry-weight of wood; so higher density woods have higher calorific values. The reportedrange in wood densities is between 100 kg/m<sup>3 </sup> and 1200 kg/m<sup>3</sup>. Species used as woodfuel are generally from 650 kg/m<sup>3 </sup>to 750 kg/m<sup>3</sup>. The moisture content plays a crucial role in determining the calorific value (Table 3). The moisture content of wood is around 50 % (of total weight) when first harvested, whereas air-dried wood contains between 12% to 20% of moisture yielding a calorific value between 14 MJ/kg and 16 MJ/kg. To evaporate one kilogram of water takes about 2.5 MJ. In the case of charcoal, the calorific value is around 30 MJ/kg. In its statistics, the FAO uses a conversion factor of 165 kg of produced charcoal from one cubic meter of fuelwood (see also chapter on charcoal). | ||
− | <br> | + | <br> |
{| cellspacing="0" cellpadding="0" border="1" | {| cellspacing="0" cellpadding="0" border="1" | ||
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− | | | + | | width="550" valign="top" | |
'''<font size="2">Table 4: Calculation for replacement value of one stere of wood by LPG</font>''' | '''<font size="2">Table 4: Calculation for replacement value of one stere of wood by LPG</font>''' | ||
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<br><font size="2">To harmonize definitions and conversion factors for adequate data collection and estimation, the FAO has published a ‘Unified Bioenergy Terminology’ located at:</font> | <br><font size="2">To harmonize definitions and conversion factors for adequate data collection and estimation, the FAO has published a ‘Unified Bioenergy Terminology’ located at:</font> | ||
− | [ftp://ftp.fao.org/docrep/fao/007/j4504e/j4504e00.pdf <span style="color: rgb(0,0,255)"><font size="2">ftp://ftp.fao.org/docrep/fao/007/j4504e/j4504e00.pdf</font></span>] | + | [ftp://ftp.fao.org/docrep/fao/007/j4504e/j4504e00.pdf <span style="color: rgb(0, 0, 255);"><font size="2">ftp://ftp.fao.org/docrep/fao/007/j4504e/j4504e00.pdf</font></span>] |
<font size="2">When estimating actual or potential wood supplies, an important distinction has to be made between (i) clear felling (often limited to plantations) and (ii) sustainable harvesting. The calculation is straightforward (see Table 5). </font> | <font size="2">When estimating actual or potential wood supplies, an important distinction has to be made between (i) clear felling (often limited to plantations) and (ii) sustainable harvesting. The calculation is straightforward (see Table 5). </font> | ||
− | <br> | + | <br> |
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− | <font size="2"></font> | + | <font size="2"></font> |
− | <br> | + | <br> |
[[Category:Cooking_Energy_Compendium]] [[Category:Cooking]] [[Category:Wood_Energy]] | [[Category:Cooking_Energy_Compendium]] [[Category:Cooking]] [[Category:Wood_Energy]] |
Revision as of 12:31, 28 August 2011
NEU
NEU
ENU
NEU
Supply Assessment
Sound information on baseline forest resources is a precondition for shaping woodfuel supply strategies on national and/or sub-national level. Theoretically there are two main sources of woodfuel information: forestry services, and energy agencies; their approaches differ significantly. Analyzing information from these sources is challenging as there are often discrepancies in the reported values: definitions are seldom consistent; measurement units are different; conversion factors needed are not always available etc.. Deficiencies of data, coupled with the failure to prioritise forest energy at policy level, frequently result in the absence of legislation on sectoral wood energy.
The process of collecting and verifying facts and figures is a laborious, costly and time-consuming undertaking, requiring properly trained and qualified personnel.
To alleviate these constraints, FAO published a guide outlining simple rapid methods to verify existing data, to fill gaps in the information chain, and to conduct more reliable surveys
(A guide for woodfuel surveys EC-FAO PARTNERSHIP PROGRAMME (2000 - 2002)).
The FAO have developed and implemented the ‘Woodfuel Integrated Supply/Demand Overview Mapping (WISDOM) methodology as a tool to support national wood energy planning. This is a GIS-based tool that allows the user to understand, in detail, the current spatial patterns of biomass demand and supply in a country, and to assess the sustainability of woodfuel as a renewable and widespread energy source. The methodology has been expanded to investigate the scope of urban woodfuel supply, which identifies the extent to which supply zones encroach into rural areas and forests. (The term “urban woodsheds” is analogous with the familiar geographic concept of watersheds.)
WISDOM for Cities. Analysis of wood energy and urbanization using WISDOM methodology
A WISDOM analysis involves five main steps: (1) selection of the spatial base, (2) development of the demand module, (3) development of the supply module, (4) development of the integration module, and (5) identification of woodfuel hot spots. At national level, the WISDOM approach has been implemented in Mexico, Senegal and Slovenia. At the subregional level, WISDOM has been implemented over the eastern and central African countries covered by the Africover Programme (Burundi, Democratic Republic of the Congo, Egypt, Eritrea, Kenya, Rwanda, Somalia, the Sudan, United Republic of Tanzania and Uganda) and over the countries of Southeast Asia (Cambodia, Malaysia, Lao People’s Democratic Republic, Thailand, Viet Nam and China, Yunnan Province) Further information can be found at: http://www.fao.org/forestry/energy/en/ |
Woodfuel problems are not always simply a gap between demand and supply. They are increasingly regarded as a reflection of more systemic, and often locally site-specific, deficiencies in land tenure, in fiscal and incentive policies, in urban energy markets, and in misallocation of forests and cropland.
As a consequence, forest resource assessments have to be complemented by legal, regulatory, institutional, and socio-economic studies that analyse the framework conditions.
Factors for estimating woodfuel supply
The most important factors necessary to estimate woodfuel supply include:
'Forest' area is a land area of more than 0.5 hectares, with a tree canopy cover of more than 10%, which is not primarily under agricultural or other specific non-forest land use. In the case of young forests or regions where tree growth stunted by climate, the trees should be capable of reaching a height of 5 m in situ, and of meeting the canopy cover requirement. Forest land may include grassland, shrub land, tree land, wetland, and/or barren land.
Mean stock density per hectare is the average total volume of wood in cubic metres per hectare
Mean annual increment (MAI) is the total increase in volume (of wood) of a stand per hectare per year. Except for plantations, the MAI is often estimated as 2.5 percent of the forest stock density.
Allowable cut is the amount of wood that may be harvested annually (or over a given period) per hectare, according to the governing rules. In overexploited stands this figure is often significantly below the MAI, in order to rehabilitate the stand.
Accessible area fraction is the share of forest area accessible for exploitation. Generally, parts of a forest are subject to legal restrictions (protected areas, ownership rights etc.) or are physically inaccessible or economically non-viable, and are therefore not considered for exploitation. On a regional level, a factor of 40-50% is often applied, depending on the population density.
Fuelwood fraction is the share of wood volume destined for woodfuel production. Forest owners are eager to increase their profits by selling their produce as lumber or poles etc. as these often achieve much higher prices on the market than fuelwood.
Harvest/Cutting fraction is the volume harvested after the percentage harvesting losses have been deducted. Harvesting losses can amount to 10% of the allowable cut.
Table 5: Estimating actual and potential wood supplies | ||||||||||||||||||||||||||||||||
Example of stock and yield estimation: Clear felling: A x D x FF x HF (for clear felling , 100% of land accessibility is assumed) =1000ha x 30 m3/ha x 1.0 x 0.9 = 27 000 m3 Sustainable harvesting: A x AC x FA x FF x HF =1000ha x 0.5 m3/ha x 0.8 x 1.0 x 0.9 = 360 m3 |
Characteristics of woodfuel supply figures
Wood is the major renewable resource that provides thermal energy in the world, so high conversion efficiency into energy is a key issue. Utmost care should be taken when using conversion factors, as this is the major cause of serious miscalculation. Foresters in general distinguish between ‘standing stock’ measured in solid cubic meters, and ‘harvested woodfuel’ measured in stacked cubic meters (containing air spaces between the pieces of wood), which are often called stere. A well-piled stacked cubic meter may contain 0.65 m3 solid (e.g. products from plantations) whereas a poorly stacked one may only have 0.33 m3 solid (e.g twisted branches of sahelian shrubs); just half as much as the well-stacked wood.
|
|
Energy content is proportional to the dry-weight of wood; so higher density woods have higher calorific values. The reportedrange in wood densities is between 100 kg/m3 and 1200 kg/m3. Species used as woodfuel are generally from 650 kg/m3 to 750 kg/m3. The moisture content plays a crucial role in determining the calorific value (Table 3). The moisture content of wood is around 50 % (of total weight) when first harvested, whereas air-dried wood contains between 12% to 20% of moisture yielding a calorific value between 14 MJ/kg and 16 MJ/kg. To evaporate one kilogram of water takes about 2.5 MJ. In the case of charcoal, the calorific value is around 30 MJ/kg. In its statistics, the FAO uses a conversion factor of 165 kg of produced charcoal from one cubic meter of fuelwood (see also chapter on charcoal).
Table 4: Calculation for replacement value of one stere of wood by LPG Assuming a mean value for 1 stere of wood = 0.5m3 and average density of 700kg/m3 Weight of 1 stere of wood : 700 kg/m3 x 0.5 (stere/volume conversion)= 350 kg Energy content of 1 stere: 350 kg x 13 MJ/kg = 4,550 MJ
Assuming energy output of 1 kg of LPG =45MJ (see Table 2) and density of LPG is 0.056Kg/litre Equivalent weight of LPG for 1 stere of wood =
|
To harmonize definitions and conversion factors for adequate data collection and estimation, the FAO has published a ‘Unified Bioenergy Terminology’ located at:
ftp://ftp.fao.org/docrep/fao/007/j4504e/j4504e00.pdf
When estimating actual or potential wood supplies, an important distinction has to be made between (i) clear felling (often limited to plantations) and (ii) sustainable harvesting. The calculation is straightforward (see Table 5).