The product gas of gasification is generally a mixture of several gases, including moisture or steam. Its composition may be expressed in any of the following ways:

• Mass fraction, mi

• Mole fraction, n

• Volume fraction, Vi

• Partial pressure, Pi

It may also be expressed on a dry or a wet basis. The wet basis is the composi­tion gas expressed on the basis of total mass of the gas mixture including any moisture in it. The dry basis is the composition with the moisture entirely removed.

The following example illustrates the relationship between different ways of expressing the product gas composition.

Example 2.2

The gasification of a biomass yields M kg/s product gas, with the production of its individual constituents as follows:

Hydrogen—MH, kg/s Carbon monoxide—MCO, kg/s Carbon dioxide—MCO2, kg/s Methane—MCH4, kg/s

Other hydrocarbon (e. g., C3H8)—MHC, kg/s Nitrogen—MN/ kg/s Moisture—MH2O, kg/s

Find the composition of the product gas in mass fraction, mole fraction, and other fractions.

Solution

Since the total gas production rate, M, is

M = Mh + Mco + Mco2 + Mch4 + Mh + MN + Mh2o Kg/s (i)

the mass fraction of each species is found by dividing the individual production rate by the total. For example, the mass fraction of hydrogen is mH = MH/M.

The mole of an individual species is found by dividing its mass by its molecular weight:

Moles of hydrogen, nH = mass/molecular weight of H2 = mH/2 (ii)

The total number of moles of all gases is found by adding the moles of i species of gases, n = X (ni)) moles. So the mole fraction of hydrogen is xH = nH/n. Similarly for any gas, the mole fraction is

Xi = n;/n (iii)

where the subscript refers to the ith species.

The volume fraction of a gas can be found by noting that the volume that 1 kmol of any gas occupies at NTP (at 0 °C and 1 atm) is 22.4 m3. So, taking the example of hydrogen, the volume of 1 kmol of hydrogen in the gas mixture is 22.4 nm3 at NTP.

The total volume of the gas mixture is V = summation of volumes of all con­stituting gases in the mixture = X[number of moles (n,) x 22.4] nm3 = 22.4 n. The volume fraction of hydrogen in the mixture is volume of hydrogen/total volume of the mixture:

VH = 22 AnHj(22.4 Ъц) = nH/n = xH

Thus, we note that

Volume fraction = mole fraction

The partial pressure of a gas is the pressure it exerts if it occupies the entire mixture volume, V. Ideal gas law gives the partial pressure of a gas component, , as

P = njRT/V Pa

The total pressure, P, of the gas mixture containing total moles, n, is

P = nRT/V Pa

So we can write

x,. = n = P = n.

n P V

Partial pressure as fraction of total pressure = mole fraction = volume fraction

The partial pressure of hydrogen is PH = xH P.

The molecular weight of the mixture gas, MWm, is known from the mass frac­tion and the molecular weight of individual gas species.

MWm = ‘L[XjMWj ] (vi)

where MWi is the molecular weight of gas component i with mole fraction xi.

Symbols and Nomenclature

ASH = weight percentage of ash (%)

C = weight percentage of carbon (%)

Cp = specific heat of biomass (J/g. K)

Cpg = specific heat of biomass at temperature в C (J/g. C)

Cw = specific heat of water (J/g. K)

dpore = pore diameter (m)

erad = emissivity in the pores (-)

FC = weight percentage of fixed carbon (%)

G(x), F(x), H(x) = functions of the cell structure and its dimensionless length of the biomass in Eq. (2.10) (-)

HR = heat of combustion or heat of reaction (kJ/mol)

HF = heat of formation (kJ/mol)

H = weight percentage of hydrogen (%)

HHV = high heating value of fuel (kJ/kg) hg = latent heat of vaporization (kJ/kg)

Kf = effective thermal conductivity of biomass (W/m. K)

Ks = thermal conductivity of the solid in dry wood (W/m. K)

Kw = thermal conductivity of the moisture in dry wood (W/m. K)

Kg = thermal conductivity of the gas in dry wood (W/m. K)

Krad = radiative contribution to the conductivity of wood (W/m. K)

LHV = low heating value of fuel (kJ/kg)

Mwet = biomass moisture expressed in wet basis (-)

Mdry = biomass moisture expressed in dry basis (-) md = moisture percentage (by weight, %)

M = weight percentage of moisture (%)

Ma = mass of surface moisture in biomass (kg)

Mi = mass of inherent moisture in biomass (kg)

Mf = mass of fuel (kg)

Mw = mass of moisture in the fuel (kg)

Mash = mass of ash in the fuel (kg) mt = mass fraction of the ith gas (-)

MW = molecular weight of gas mixture (-) n = number of moles (-)

Пі = mole fraction of the ith gas (-)

N = weight percentage of nitrogen (%)

O = weight percentage of oxygen (%)

Pi = partial pressure of the ith gas (Pa)

P = total pressure of the gas (Pa)

Q = heat content of fuel (kJ)

R = universal gas constant (8.314 J/mol. K) sp. gr = specific gravity (-)

S = weight percentage of sulfur (%)

T = temperature (K)

Wwet = weight of wet biomass (kg)

Wdry = weight of dry biomass (kg)

VM = weight percentage of volatile matter (%)

V = volume of gas (m3)

V = volume fraction of the ith gas (-)

&Hcomb = heat of combustion or reaction, kJ/mol ptme = true density of biomass (kg/m3) papparent = apparent density of biomass (kg/m3)

Ptuik = bulk density of biomass (kg/m3)

£b = bulk porosity of biomass (-)

Ep = porosity of biomass (-)

a = Steven-Boltzmann’s constant (5.67 x 10 8 W/ m2K4) в = temperature (°C)

Subscripts

ad, ar, db = subscripts representing air dry, as-received basis, and dry basis daf = dry ash-free basis td = total-dry basis i = ith component m = mixture