Teorías de Proceso

C

o n c l u s io n s

A detailed chemical model describing the oxidation o f n-heptane has been developed and applied to a low-pressure batch reactor. The results o f the numerical simulations are tested against the previous experimental work o f Laughlin (1967). The model is able to reproduce the phenomenological and kinetic features discussed in Chapters Two (Phenomenology) and Three (Chemistry) respectively to varying degrees o f success. With respect to phenomenological features, the comparison o f the variation o f induction time and o f the variation o f pressure rise during the first cool flame with initial pressure and initial temperature between numerical simulation and experiment are satisfactory. The induction time to a cool flame is dependent upon the initial conditions (ie temperature, pressure and reactantroxidant ratio), and, from the numerical simulations, is also influenced by the rate parameters assigned to the chain-branching reaction o f the ketoheptylhydroperoxide species (0= Q 00H ):

Chapter Nine Conclusions

0 = Q 0 0 H 0 = Q 0 + OH (9.1)

where the rate coefficient for reaction (9.1), kg.i = I.lxl0^^.exp(-21901AT) or 7.0xl0^^exp(-20894/T) for an hydroperoxide group attached to a 1° or 2° C-atom site respectively.

The chemical explanation for the induction time to a cool flame may be found by considering the rate o f formation/decomposition o f the 0 = Q 0 0 H species. The rate o f change in the concentration o f the 0 = Q 0 0 H species (d[0=Q 00H ]/dt, eqn. (9.3)) is governed by reaction (9.1) and reaction (9.2):

HOOQOOH ^ 0 = Q 0 0 H + OH (9.2)

^ ^ ^ = k , 2 [ H 0 0 Q 0 0 H ] - k , , [ 0 = QOOH] (9-3)

For positive values o f d[0=Q 00H ]/dt, ketoheptylhydroperoxide is being formed at a rate faster than it decomposes, while for negative values 0 = Q 0 0 H decomposes at a rate faster than it is produced, resulting in chain-branching. When conditions are amenable for cool flame propagation a change from positive values to negative values in d[0=Q 00H ]/dt is observed just prior to the appearance o f the cool flame, implying the accumulation o f ketoheptylhydroperoxide to some critical concentration. Since the rate o f formation/destruction o f 0 = Q 0 0 H are explicitly governed by reactions (9.1) and (9.2), one might expect that suitable adjustment o f either, or both, sets o f rate parameters for the two reactions will provide adequate control over induction time. However, the results from the sensitivity analysis show that reaction (9.1) is by far the most influential reaction occurring at all times during the induction period to a cool flame and it is accurate rate data for this reaction that should be applied to a chemical model.

That reaction (9.1) should be so influential conforms with the general agreement (Morley, 1987; Sahetchian et al., 1990) that the chain-branching agent in alkane combustion is a carbonyl alkylhydroperoxide. Furthermore, o f the possible chain- branching agents included in the chemical model, the relatively large concentrations o f the two species 2-ketoheptyl-4-hydroperoxide and 4-ketoheptyl-2-hydroperoxide calculated from numerical simulations leads to the suggestion that these specifically are the chain-branching agents. Support is given to this claim from the sensitivity analysis

results showing that key reactions leading to their formation, as well as their decomposition reactions (of the form o f reaction (9.1)), to be o f greatest influence.

The success o f the chemical model to reproduce the kinetic features observed experimentally is varied. In general an underprediction is made by the numerical simulations in the concentrations o f the chemical species, although in some cases (e.g. butanal, pent-l-ene, n-heptane) fairly good agreement may be found. The large disparities encountered between numerically simulated concentrations and experimentally measured ones may lie in some o f the rate parameters assigned to reactions in the chemical model. Most o f the reactions leading up to formation o f the chain-branching agent 0 = Q 0 0 H have been studied by other workers and values o f the rate parameters for these reactions are fairly well documented. Relatively little information regarding the reactions following the chain-branching o f ketoalkylhydroperoxides exists at present and future work in this area would be beneficial. However, to apportion the blame o f underprediction by the numerical simulations on inaccurate rate parameters does not explain why the calculated concentration o f only one particular compound in an homologous series compares well with experiment, e.g. butanal o f all the aldehydes included or pent-l-ene o f all the alkenes included.

Alternatively, one may suggest that chemical reactions not included in the proposed chemical model, due to size restrictions, may account for the wild variations between numerical prediction and experimental measurement. Further homogeneous reactions that may be added to the model are reactions involving compounds formed such as alkenes, aldehydes and cyclic ethers. However, while the inclusion o f such reactions would make the chemical model more complete, the influence o f those reactions, particularly in the low-temperature regime, would probably be minimal due to the relatively low concentrations predicted from the numerical simulations.

With a reactor length o f 8.96 cm and volume 330 cm^ used in the numerical calculations, leading to a reactor radius o f 3.4 cm, the internal surface area o f the cylindrical reactor modelled is 266 cm^. Thus the surface to volume ratio o f the reactor, SW is 0.81 cm'% and one may well consider that surface reactions may be an important feature overlooked in the chemical model. As is expanded in Fish’s review (1968) the nature o f the reaction vessel surface is an influential factor, in low pressure batch reactors; the main chain-terminating steps occurring heterogeneously. However, inclusion o f an heterogeneous reaction in the model (reaction (9.4)), diffusion o f the

Chapter Nine Conclusions

hydroxyl radical to the reactor to form (assumed) inert products, had no influence on the behaviour o f the model. However, data for such heterogeneous reactions is rather scant and the inclusion o f such reactions invariably have not been included in chemical models.

OH -> inert products (9.4)

Cool flame multiplicity observed in experiment and numerical simulation arises from the coupling o f chemical kinetics and heat transfer. Investigation o f the effect o f heat loss showed that, for a given set o f initial conditions, the number o f cool flames predicted numerically varied with the mode o f heat loss, or more significantly with the magnitude o f the rate o f heat loss. As was discussed in Chapter Seven, the validity o f applying steady-state heat transfer correlations to an unsteady-state system was questioned, although a more correct and proper description is unrealistic with a detailed chemical model.

While the proposed chemical model is detailed it cannot include every possible reaction that may occur due to a necessary compromise between reaction mechanism size and computer processing performance. Also, that spatial variations across the reactor are likely to exist, particularly with the occurrence o f ignition, suggests that due consideration should be made when attempting to model such a system. However, the detailed chemical description afforded by a zero-dimensional approach is, with current computer capabilitites, immediately sacrificed by accounting for spatial distributions. Compromises and assumptions will always be necessary in the modelling o f chemical systems while current computer technology restricts the detail o f any model (whether solely chemical or solely physical or a combination o f both) and while knowledge o f the system being modelled remains incomplete.