As seen, ln([A.sub.t]/[A.sub.0]) shows a linear relation to the reaction time for three composite membranes, indicating that the reaction is in accordance with first-order reaction
Two devolatilization models were tested, single first-order reaction
and distributed activation energy, and two char conversion modes were tested: power law mode with a model constants and a constant-free model.
The algorithm transforms spectral data into c-t data according to the predefined model, i.e., the first-order reaction
. The correspondence of the extracted data to the model is visualized by the c-t curve.
The typical plot of ln ([beta]/[T.sub.m.sup.2]) vs 1/Tm depicted in Figure 6 shows that the reaction of oil shale pyrolysis can be described by a first-order reaction
model in the studied temperature range.
 studied the hydrolysis of carbonyl sulfide under medium temperature conditions and concluded that the catalytic hydrolysis of carbonyl sulfide is a first-order reaction
with respect to carbonyl sulfide, while the reaction order of water is influenced by the partial pressure of water.
The reaction kinetics equation can be described as ln([C.sub.0]/C) = 0.56891, which follows the first-order reaction
Models Equations Parameters 1st Order [C.sub.e] = [C.sub.a] [C.sub.e] = effluent x [e.sup.-k;HRT] concentration (M [L.sup.-3]); [C.sub.a] = affluent concentration (M [L.sup.-3]); Leduy and Zajic [C.sub.e] = [C.sub.r] HRT = hydraulic (1973) + (C.sub.a] - retention time (T); k [C.sub.r] x [e.sup.- = first-order reaction
k;HRT] constant ([T.sup.- 1]); Brasil et al.
For a first-order reaction
, the mean residence time is
In our calculations we assumed, that the coal and aditives oxidation is the first-order reaction
and that the effect of diffusion can be neglected under used experimental conditions.
After observing lab experiments, they proposed the hypothesis that a positive correlation exists between [sup.15]N enrichment and first-order reaction
The fitting of experimental data to first-order reaction
models will indicate the changing of desorption rate constants with respect to the different reaction periods.
The decline in long-term (seven-day) chlorine residual could be modeled as a first-order reaction
. Water samples that were both ozonated and biodegraded were able to maintain substantially higher and longer-lasting chlorine residuals than untreated water.