In this section, three different methods: Single Reaction Model, Conventional Arrhenius Method and parallel reaction model were employed to estimate the chemical kinetic parameters

Fuel	TXL	WYO	HA-PC-DB-SoilS	LA-PCDB-SepS
Moisture loss onset temperature [K]	373.09	375.71	367.45	386.19
Moisture mass [%]	24.12	20.92	4.678	8.89
Pyrolysis loss onset temperature [K]	637.93	657.15	529.23	513.6
Pyrolysis mass [%]	18.95	21.01	32.53	56.01
10% of pyrolysis mass [%]	1.895	2.101	3.253	5.601
Mass at 10% of pyrolysis mass [%]	73.985	76.979	92.069	85.509
10% pyrolysis mass loss temperature [K]	661.11	685.44	552.99	536.27
90% of pyrolysis mass [%]	17.055	18.909	29.277	50.409
Mass at 90% of pyrolysis mass [%]	58.825	60.171	66.045	40.701
90% Pyrolysis mass loss temperature [K]	748.78	759.83	1021.28	766.89
Peak pyrolysis mass [%]	61.9	66.21	45.06	81.74
Peak pyrolysis temperature [K]	698.68	702.5	697.55	749.21
FC and ash mass [%]	56.93	58.07	62.792	35.1
FC and ash loss onset [K]	774.07	786.56	1037.1	990.95
Ignition temperature [K]	544.42	571.78	509.43	526.06

Table 3.4. TGA analysis of several fuels (adopted from Lawrence, 2007).

of Biomass (Chen et al, 2012b) so that the rate of pyrolysis and time scale for pyrolysis can be determined.

3.7.1 Single reaction model: conventional Arrhenius method The single reaction model is given in the equation:

dmv

—- = k(T) ■ mv (3.17)

dt

where mv is the mass of volatiles remaining in the sample and k(T) is given by the Arrhenius expression (Annamalai and Puri, 2007):

Separating variables and integrating equation (3.17) yields the following result:

where mv is the mass of the volatiles at time t, mv 0 is the initial mass of volatiles at t = 0, B is the pre-exponential factor, E is the activation energy, R is the universal gas constant, and T is the absolute temperature.

Since the temperature change with time is constant in TGA tests, the integral on the right side of equation can be rewritten as:

ij= (E f e2X) e2(Xq)

mvo) V в) V r) l X Xq

where X = (E/RT), в is the rate of change for temperature with time (20K/min), E2, second exponential integral (Abaramovitz and Stegun, 1970) given as:

E2(X) = {exp(-X) — X ■ E1(X)},

X2 + ai • X + a2 X2 + bi • X + b2 /

where: a1 = 2.334733, a2 = 0.250621 bi = 3.330657, b2 = 1.681534

E2(X) * exp(-X)

(b: — a:) • X + (b2 — a2) X2 + b1 • X + b2

Using the expression for Ej(X), the E2(X) can also be expressed as:

Equation (3.20) presents the exact relation between mv, volatiles remaining at temperature T and heating rate for SRM. The conventional Arrhenius plot of ln(mv/mv0) vs. 1/T for extraction of E and B for the whole domain of pyrolysis is based on further approximations of equation (3.20). If T >> T0 (pyrolysis start temperature), then, X <<X0, and E2(X)/X >>>> E2(X0)/X0 and with equation (3.22), equation (3.20) becomes (Chen, 2012b):

{

(b — a1)X + b2 — a2 I X(X2 + b1X + b2) j

Here C(X) was introduced as a support vector. Taking the logarithm of equation (3.23):

l„|—1)| * .„j№/«>«№>>[_

equation (3.24) becomes:

E

ln{—ln(/)> * A — RT, (3.25)

where

/ = —

mvo

and C(X) is roughly constant. As a result, the activation energy E and pre-exponential factor B can be determined from the slope and intercept of the linear plot ln(—ln(mv/mvo). Figure 3.16 shows the Arrhenius plot for low ash partially composted separated solids dairy biomass.