Según sus características de realimentación

The need for the validity of steady-state diffusion law solutions to determine the length of the time interval was argued in Chapter 3. However, using a discrete time interval also raises a question as to the effect of reducing the size of the increment on the model

predictions. Figure 5-13 shows the effect of changing the MEA model analysis interval on the 1.33 cm pig faeces modelled data.

A

B

C

D

0.6 0.8 1.0 1.2 1.4 1.6 1.8 0 1 2 3 4 5 6 7 8 9 10 Day W /L

6 Hour 4 hour 2 Hour 1 Hour

Figure 5-13 – Four analysis intervals and their effect on the output of the MEA model using 1.33 cm particle size of pig faeces at 200C.

The divergence in the curves occurred most strongly at the peak of composting and this occurred due to a difference in the calculated oxygen penetration depth. Presumably this was because the model used substrate states at the end of the time period, shorter intervals giving a more accurate reflection of the actual time course of these states.

Chapter 6

6 RESULTS

Three sets of experimental data are analysed here with both first-order kinetics, i.e. without adjusting for aerobic proportion, and micro-environment analysis.

 Particle size trials whose impacts express entirely through the particle geometry element of micro-environment analysis noted in Chapter 4.

 Temperature trials where the observed composting time course is impacted by a wide range of effects.

 Diffusion into the pile.

The particle size and diffusion trials used the same substrate (dog sausage), but the temperature trials a different substrate (pig faeces). All used the same bulking material, that is old compost.

All data analyses, including the MEA model, were carried out in a spreadsheet.

6.1 Particle Size Trials

In addition to the experimental data with micro-environment modelled curves, this section includes aspects of the theoretical perspective which needed scrutiny as a result of

applying the theory to the experimental data:

 Rate constant multiplier.

 Fitting the growth phase.

 Modelling issues and their resolution, in particular:

o the growth phase as a special case;

o stabilisation of the model and fitting the Monod function;

o determining the diffusion coefficient.

 Explanation of the observed rewarming in terms of:

o diffusible substrate;

o oxygen flux insights into diffusible substrate;

o other electron acceptor explanations.

Five particle sizes were made by cutting dog sausage into cubical particles, 0.8 cm, 1 cm, 1.5 cm, 2 cm, 2.5 cm, (see Chapter 5). The 0.8 cm size was formed by „chopping‟ 1 cm cubical particles with the mixing shovel; thus the maximum size would be 1 cm, but a range of sizes below this maximum would dominate. The resulting size was not

measured but is assumed to be 0.8 cm. The particle size used in micro-environment analysis was based on an equivalent particle size, being the diameter of a sphere which contained the same volume of substrate (see section in Chapter 5.4.1). The calculations were based on the assumption that the dog sausage was the only active component of the mixture i.e. the energy density was based on the volume of dog sausage rather than the volume of pile solids.

The substrate based parameters (k, E, NB) were determined, in the first instance using first-order kinetics. Then the parameters from the 0.8 cm particle size time course were used in micro-environment analysis and final fitting carried out by manually adjusting the parameters Figure 6-1. 0 1 2 3 4 5 6 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Day W L -1 0.6 0.7 0.8 0.9 1.0 Aer o b ic p ro p o rt io n

Trial Data Model with fitted curve Aerobic proportion

Figure 6-1 – Measured versus modelled composting time course of the 0.8 cm cubical particle size6; and time course of the aerobic proportion.

These same parameters were then used to model the effect of changing particle size. The model output for each particle size was then compared with the experimental data. Figure 6-2 compares the 1 cm cubical particle size with the largest size (2.5 cm), while Figure 6-3 compares the two mid-sized particle sizes.

6 _{An electrical fault in the reactor coil caused the drop in composting rate in the 1 cm particle reactor (Figure} 6-2). This same fault impacted the aeration routine in the 0.8cm particle reactor (Figure 6-1), via the loggers aeration programming. The other reactors were unaffected.

0 1 2 3 4 5 6 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Day W /L (s o li d )

1 cm cubical particle Model with only size changed 2.5 cm cubical particle Model with only size changed

Figure 6-2 - Measured versus modelled composting time course of the cubical particles of size 1 cm and 2.5 cm.5 Model used the same parameters as determined for the 0.8 cm cubical particle size (Figure 6-1). The micro-environment model was run with only particle size changed.

0 1 2 3 4 5 6 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Day W /L (s o li d )

1.5 cm cubical particle Model 2 cm cubical particle Model

Figure 6-3 – Measured versus modelled composting time course of the cubical particles of size 1.5 cm and 2 cm. Model used the same parameters as determined for the 0.8 cm cubical particle size (Figure 6-1). The micro-environment model was run with only particle size changed.

The renewed burst of composting that occurs between days 9 and 14 in the three largest particle sizes (1.5 cm, 2 cm, 2.5 cm), is not explained by micro-environment analysis (Figure 6-2 & Figure 6-3). This is discussed further in Section 6.1.7, yet when

parameters are determined by first-order kinetics, then parameters (adjusted for each of the three fractions) can be made to fit, e.g. in Figure6-4. Of particular note here is that first- order kinetics contains the inherent assumption that the particle is fully aerobic and all parts contribute to the observed composting rate. This contrasts with micro-environment analysis where only the proportion of the particle that is aerobic enters the calculations. First-order kinetics therefore, should not be able to accurately model the data from a particle with substantial parts of it being anaerobic.

0 0.5 1 1.5 2 2.5 3 3.5 4 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Day W L -1

Trial data Fast fraction Slow fraction Humification fraction Sum of fractions

Figure 6-4 – Dog sausage, 2.5 cm cubical particle with first-order fractions fitted.

One can achieve a good fit to the observed data with first-order kinetics (Figure 6-4) and the slow fraction rate constant is comparable in magnitude with the k determined using micro- environment analysis. However, this fitting is achieved at the expense of the substrate density (E), where E must be substantially higher for the slow fraction to enable a fit with first-order kinetics (Table 6-1).

Table 6-1 – Dog sausage trial 2, with 2.5 cm particles and the fitted parameters for the two methods of analysis.

First-order kinetics Micro-environment analysis

Fast fraction k (W MJ-1) 1.5 2.5

E (MJ cm-3) 5.9 *10-3 4.8 *10-3

Slow fraction k (W MJ-1) 0.9 1

It can be assumed that substrate density and rate constants would be a function of the substrate and hence independent of particle size, as it is for micro-environment analysis. Putting aside for the moment the unknown effect that a diffusible substrate solution would have on the above micro-environment determination, it is hard to escape the conclusion that a first-order kinetics determination, without adjusting for aerobic proportion is insufficient for fully understanding composting – even though it may appear to fit adequately.

It is only when we adjust for aerobic proportion using micro-environment analysis (as in Figure 6-2), that we realise the limits of first-order kinetics in explaining composting in larger sized particles, and the need to look for an alternative explanation. Micro- environment analysis provides a framework by which alternative explanations can be explored. This is discussed further in Section 6.1.7.