Water does not "burn"* so every percent of water mass present in a given mass of moist timber results in a reduction in the percentage of combustible material.
So, simplistically Energy Wet = Energy dry x (100-M)/100 where M is moisture percentage of mass.Due to the temperature of 'flu gases' being well above the boiling temperature of water at 100C$\rm100^\circ C$, water leaving a fire will usually be in the form of 'steam' - water vapour at > 100 C$\,100^\circ C$. The combustion process has had to bthboth heat the water to boiling point and then to supply the latent heat of vaporisation to turn it to steam. For typical moisture contents the energy required to do this is significant but relatively small compared to the energy loss due to fuel replacement.
eg assume 6 kWh/kg for a sample of dry wood.
10% moisture would displace 10% x 6000 Wh = 600 Wh$\rm10\% \times 6000\,Wh = 600\,Wh$ from a 1kg mass.
600 Wh = 600 x 3600 = 2$\rm600\,Wh = 600 \times 3600 = 2.16\,MJ$.16 MJ
Energy to heat 100g100 g water 10C10$^\circ$C say to 100C ~= 4
$\rm100\,^\circ C \simeq 4.3\,J/^\circ C/g \times (100\,^\circ C-10\,^\circ C) \times 100\,g \simeq 40\,kJ$.3 J/C/G x (100c-10c) x 100g =~ 40 kJ
Energy to vaporise 100g of water from 100C
$100\,^\circ\,\rm C$ to steam = 2260 J/g x 100g = 226 kJ$\rm2260\,J/g\times100\,g = 226\,kJ$
Total energy loss due to vapourising 10% water = 266 kJ =$266\,\rm kJ$ = 11%
Loss of energy from water replacing wood = 2160 kJ= $2160\,\rm kJ$ = 89%.
Total loss to water = 2.426 MJ$2.426\,\rm MJ$.
Energy loss % in 1 kg wood due to 10% moisture = 2.426 MJ / 21.6 MJ
=$\rm2.426\.MJ/21.6\,MJ$ = 11.2%
- Not taken into account is the "watergas" process whereby passing water vapour over hot carbon results in breakdown of the water into Hydrogen and Oxygen and re-re action to form CO and CO2CO$_2$. The net energy effects of this process vary immensely with circumstance and are ignored here.
Page 5 - Wood - open fire
0.4–0.6 m3 /100 kWh$\rm0.4–0.6\,m^3/100\,kWh$ delivered;
125–200 kg/100 kWh delivered$\rm125–200\,kg/100\,kWh delivered$.