Chapter 9.  Energy

        Wd + MC_{w = 100.}

Therefore, the gross heating value of a pound of wet wood is obtained by adjusting HHV for the wood moisture content as follows:

        GHV  =  HHV (1 - MC_w/100).

Thus GHV represents the available potential heat at a given moisture content and is equal to HHV only
if the wood is oven-dry. Continuing the example, if this wood has HHV of 9,000 Btu/lb, then

        GHV  =  9,000 (1 - 40/100)  =  5,400 Btu/lb of oven-dry wood in the fuel.

	Species		Wood						Bark
	SOFTWOODS
	Douglas-fir	8,900					9,900
	Lodgepole pine	8,600					10,100
	Ponderosa pine	9,100					9,600
	Redwood	9,200					-
	Sitka spruce	8,100					-
	True firs	8,300					9,100
	Western hemlock	8,400					9,300
	Western redcedar	9,700					8,700
	White pine	9,600					-
	HARDWOODS
	Bigleaf maple		8,400					-
	Black cottonwood		8,800					9,000
	Oregon ash		8,200					-
	Oregon white oak		8,100					-
	Red alder		8,000					8,600

Note:  Values are averaged from multiple sources and rounded to the nearest 100 Btu/lb. For additional details on these and other species, see Ince (1979)  and Wilson et al. (1987).

Energy Losses

        GHV does not represent the amount of heat available for use because it includes all the heat that can be extracted from the products of combustion, and there are several sources of loss that must be accounted for in determining the recoverable heat. Recoverable heat (RH) is important in comparing costs of fuels and fuel systems and represents the heat energy that, for example, produces steam for industrial purposes. The literature on these losses can sometimes be confusing because authors differ on which losses to consider and how some of them are calculated.

        Losses due to the moisture content of wood are often referred to as the stack heat loss. A pound of wet fuel has a certain fraction that is oven-dry wood plus another fraction that is its water content. In the example above, there was 0.6 pound of oven-dry wood (Wd) and 0.4 pound of water (MC_w = 40%). Formulas for eight forms of heat loss, numbered H1 through H8, are discussed below (Bethel 1977; Ince 1979).

H1.  Heat used to raise the temperature of water in the wood to the boiling point. In Btus this is

          H1  =  (212 - T1)  _*  MC_w / 100

          where T1  =  ambient temperature.

H2.  Heat required to vaporize the water in the wood.  
In Btus this is

          H2  =  970  _*  MC_w / 100.

H3.  Heat required to separate the bound water (water below fiber saturation point) from the cell walls.
In Btus this is

          H3  =  136  _*   MC_b / 100

where MC_b  =  fiber saturation point (see Chapter 1) if MC_w  ≥  fsp

or MC_b   =  MC_w if MC_w < fsp.

          Usually it is assumed that  fsp = 30% MC_od or 23% MC_w.

H4.  Heat required to raise the temperature of the vaporized water to the temperature of the  exhaust gases. In Btus this is

          H4  =  0.46  _*  (T2 - 212)  _*  MC_w / 100

          where  T2 = temperature of exhaust gases.

          The average specific heat of water over the range from boiling point to exhaust temperature is about 0.46.

Losses H1, H2, and H4 are often combined and simplified into a single equation (Ince 1979):

          MC_w / 100  _*  [970 + (212 - T1)  +  0.46  _*  (T2 - 212)].

H5.  Heat required to evaporate water that forms when the  hydrogen component of wood is combusted.

          Since wood is  approximately 6% hydrogen (Table 9-1), a pound of dry wood contains about 0.06 pound of hydrogen. During combustion, one of the chemical reactions is

          2H₂ + O₂ ®2 H₂O + 61,100  Btu/lb of H₂.

          By weight, water is one part hydrogen and eight parts oxygen. Therefore, 0.06 pound of hydrogen combines with 0.48 pound of oxygen to yield 0.54 pound of water, which also escapes via the stack gases. This water incurs losses involved with raising its temperature to the boiling point, evaporating it, and then raising its temperature to that of the exhaust gases. Therefore,

          H5  =  0.54 Wd (212 - T1) + 0.54 Wd (970) + 0.54 Wd [0.46 (T2 - 212)]

          =  0.54  _*  (1 - MC_w/ 100 )[970 + (212 - T1) + 0.46   _*  (T2 - 212)].

H6.  Heat from combustion other than water vapor: dry gases. In addition to the minimum air needed for combustion reactions, there is generally some "excess" air that enters the furnace, is heated, and exits with the stack gases.

          Table 9-1 shows that oven-dry wood is about 52% carbon. The reaction to combust this is

          C + O₂ ®CO₂ + 14,100 Btu/lb of C.

          The atomic weights of carbon and oxygen are 12 and 16 respectively, hence burning 12 pounds of carbon requires 32 pounds of O₂, which yields 44 pounds of CO₂. Therefore, this process requires 32/12 or 2.7 pounds of O₂ per pound of carbon. Since one pound of oven-dry wood contains 0.52 pound of carbon, the O₂ demand is 0.52 times 2.7, or 1.4 pound per pound of oven-dry wood. It was previously calculated that 0.48 pound of O₂ is required to burn the 0.06 pound of hydrogen in a pound of oven-dry wood, hence the total O₂ demand is 1.88 pounds per pound of oven-dry wood. Since a pound of wood contains 0.40 pound of oxygen (Table 9-1), the net oxygen required from air is 1.48 pounds.

          Because air is 23.2% oxygen, it takes 4.3 pounds of air to provide one pound of oxygen. There­fore the minimum air required to burn one pound of oven-dry wood is 1.48 times 4.3, or 6.4 pounds. In addition to this theoretical mini­mum air supply to sustain combustion, some excess air is always admitted. Excess air is usu­ally expressed as a percentage of the theoretical minimum air. Thus 20% excess air means that the total air admitted to burn one pound of oven-dry wood is 6.4 times 1.20, or 7.7 pounds.

          The quantity of heat that escapes in stack gases due to dry gases and excess air (EA) is calcu­lated by

          H6  =  (T2 - T1)(1 - MC_w / 100) [1.44 EA /100 + 1.56].

H7.  Heat required to raise the temperature of wood to the combustion temperature. In Btus this is

          H7  =  Wd (T3 - T1)[0.226 + 0.000322 (T1 + T3 - 64)]

          where T3  =  combustion temperature.

H8.  Other heat losses.  Otherlosses occur from radiation, conduction, and convection of heat, incomplete combustion and so forth, and have been estimated as 3 to 4 % (Corder et al. 1970; Miller and Hansen 1951). This can be estimated as

       H8  =  0.04 GHV.

          This percentage of loss may be appropriate for a well-operated system burning the type of fuel for which it was designed but could be higher with an improperly operated system or fuels that have improper size particles or excessive moisture.

Recoverable Heat and Combustion Efficiency

        The recoverable heat (RH) is obtained by subtracting the sum of these eight losses from the gross heating value.

RH  =  GHV - (H1 + H2 + H3 + H4 + H5 + H6 + H7 + H8).

        Combustion efficiency (CE) is the ratio of recoverable heat to available potential heat:

CE (%)  =  (RH / GHV) _* 100.

With current technology, combustion efficiency of wood fuels ranges from about 80% for dry fuels to

about 60% for wet fuels. Unfortunately, many wood fuels are received in a relatively wet condition. See Example 1.

Lower Heating Value

        The terms lower heating value  and net heating value  are used in combustion engineering and reflect the net heat available in a fuel after the various losses associated with wood moisture content and water formed during combustion are subtracted from HHV (Harris et al. 1986).

Heating Values per Unit Volume

Calculating Btus per Cubic Foot of Solid Wood

        Suppose it is desired to estimate the heat value per cubic foot of a conifer under the following conditions:

        HHV   =  9,000 Btu/oven-dry lb

        MC_od =  67%  (MC_w = 40%)

        SG_g     =  0.40.

        Chapter 1 presents the definitions of moisture content and specific gravity. Table 1-2 indicates that a cubic foot of this wood weighs nearly 41.9 pounds. Of this, 40% is water, hence there are 16.8 pounds of water and 25.1 pounds of oven-dry wood in this cubic foot. The weight of oven-dry wood per cubic foot can also be obtained by looking up the value in Table 1-2 at the intersection of SG_g = 0.40 and MC_od = 0. The difference between the 25.0 in the table and the above calculation is rounding.

Assumptions
Higher heating value (Btu/lb)	9,000
Moisture content (% MCw)	40
Combustion temperature, T3 (°F)	450
Ambient temperature, T1 (°F)	70
Fiber saturation point, wet basis (%)	23
Exhaust temperature, T2 (°F)	470
Excess air (%)	20
Other losses (%)	4

Losses	H1	57
	H2	388
	H3	31
	H4	47
	H5	399
	H6	444
	H7	85
	H8	216
	Total	1,667

  Recoverable heat (RH) is 3,733 Btu/lb oven-dry wood in the fuel. Combustion efficiency (CE) is 69%.

        Using the data from Example 1:

        HHV/ft³  =  25.1 _* 9,000  =  225,900 Btu

        GHV/ft³  =  25.1 _* 5,400  =  135,540 Btu

        RH/ft³     =  25.1 _* 3,949  =  99,120 Btu.

Calculating Btus per Cord

        Select the appropriate cubic feet per cord from Table 3-1 or 3-2 and multiply by HHV, GHV, or RH per cubic foot calculated above.

        If a standard cord of the above species contained 80 cubic feet of wood, then

HHV/cord  =  18,072,000 Btu

GHV/cord  =  10,843,200 Btu

RH/cord     =  7,929,600 Btu.

Calculating Btus of Chips and Hog Fuel

        When the chips or hog fuel are in weight units,  first deduct weight that corresponds to the moisture content and then apply HHV, GHV, or RH per pound of dry wood in the fuel.

        When the chips or hog fuel are in volumetricunits, use the residue to solid wood expansion factors in Table 7-1 or 7-2 to convert the chip or hog fuel volume to solid wood equivalent. Then apply HHV, GHV, or RH per cubic foot calculated above.

        For example, if a unit (200 cubic feet) of hog fuel is obtained for the species conditions outlined earlier, first convert the 200 cubic feet of hog fuel to a solid equivalent. Assuming an expansion factor of 2.5 cubic feet of hog fuel per cubic foot of solid wood, a unit becomes

        200 / 2.5  =  80 ft³ of solid wood.

Multiply this by either of the three heating values per cubic foot as desired.

Working with Mixtures of Wood and Bark

        This involves obtaining a weighted average higher heating value, a weighted average moisture content, and a weighted average specific gravity. See Example 2.

Suppose western redcedar hog fuel has 40% bark and that wood and bark have an MC_od of 60 and 100% respectively. Also, Tables 1-1 and 7-5 indicate that cedar wood and bark have an SGg of 0.31 and 0.37 respectively. Weighted averages are

      HHV:    0.4 _* 8,700 + (1 - 0.4)  _*  9,700  =  9,300 Btu / oven-dry lb.

      MC_od:  0.4 _* 100 + (1 - 0.4)  _*  60     =   76%.

      SG_g:  0.4 _* 0.37 + (1 - 0.4)  _*  31    =   0.34.

Use these values to calculate GHV, HV, and other measures in the preceding sections.

Heating Values of Conventional Fuels

        Table 9-3 presents heating values of fossil fuels that often compete with wood.