*3.2. Model Validation*

To evaluate the predictive power of the different models developed in Section 3.1, which are developed and trained using the training set (25 data points), they are also validated here through comparison with the testing set of data (9 data points). The performance of the different models was evaluated based on comparison of the mean squared error (MSE) and the R<sup>2</sup> values of each model with respect to the output values from the test set as shown in Table 3. It can be seen that while the full linear model can adequately predict the output for some of the predicted outputs in almost all cases, the reduced linear or quadratic models are shown to more accurately have predictions with higher R<sup>2</sup> and lower MSE values. An exception to this rule is the gas-to-fuel ratio, for which the full linear model has the best fit and where all the models are shown to have very high accuracy.

**Table 3.** Validation of models against a testing set of data showing the prediction capability of full linear and reduced linear and quadratic models.


It is also worth noting that the model for carbon monoxide (CO) shows a very poor prediction using the full linear model and appears to require a quadratic model to obtain a reasonable predictive power. Previous studies of Mirmoshtaghi et al. [15] and Pio and Tarelho [4] have also shown difficulty fitting empirical models to the CO output of circulating and bubbling fluidized bed reactors with R<sup>2</sup> values of 0.53 and 0.23, respectively. In this study, an R<sup>2</sup> value of 0.513 was found for the downdraft gasifier data used here.

The fitting of these models is also demonstrated in Figures 5 and 6, which show the comparison of experimental values plotted against model predictions for the test data set. This shows that all of the models appear to predict hydrogen mole percentage reasonably well, but there are some deviations for model predictions of carbon monoxide mole percentage. The reduced models are shown to give predictions closer to the experimental values for both of these outputs.

**Figure 5.** Parity plot of models against experimental hydrogen mole % using data from Chee [12].

**Figure 6.** Parity plot of models against experimental carbon monoxide mole % using data from Chee [12].

To assess if the models generated based on fitting to the data of Chee [12] can be used for other biomass gasifiers, the best fitting models for predicting hydrogen and carbon

monoxide are compared against experimental data from three other downdraft gasifier studies. In particular, this experimental data includes the gasification of rubberwood (nine data points) from the study of Jayah et al. [21], the gasification of sesame wood (four data points) from the study of Sheth and Babu [22], and the gasification of wood chips (two data points) from the study of Costa et al. [23].

Figures 7 and 8 show the parity plots of the reduced linear models against these three sets of data. It can be seen that the model gives a reasonable prediction of the data points from the study of Jayah et al. but has much lower accuracy for predicting the results of Costa et al. and Sheth and Babu.

**Figure 7.** Parity plot of reduced linear model against experimental hydrogen mole % for data from other downdraft biomass gasifiers using experimental data from the literature [21–23].

**Figure 8.** Parity plot of reduced linear model against experimental carbon monoxide mole % for data from other downdraft biomass gasifiers using experimental data from the literature [21–23].

Considering the reduced quadratic model, which gives the best fit to the data of Chee, when this is compared against other experimental data in Figure 9 it is shown to give poor or very poor predictions. These inaccuracies may be because of differences in the design of different downdraft gasifiers or because the conditions are outside the ranges given in Table 1. In particular, the bulk density of biomass used in all these cases are higher than those for the experiments of Chee. Additionally, these new data sources do not include grate or fan rotation speeds, so the average values from Table 1 have been assumed to utilize the reduced linear and quadratic expressions given in Table 2. Due to the second order terms in the quadratic expression, the errors associated with these assumptions lead to a much greater inaccuracy.

**Figure 9.** Parity plot of reduced quadratic model against experimental carbon monoxide mole % for data from other downdraft biomass gasifiers using experimental data from the literature [21–23].

This shows that these empirical models may only be practical for gasifiers with a similar scale and design and within the range of conditions used to build the models. This is supported by the results of Pio and Tarelho, who also found difficulty fitting empirical models to a wide range of different gasifier data sources [4], and by Baruah et al., who suggest that data must be taken from very similar scale gasifiers and with similar feedstocks [7]. However, if a large amount of data are collected from a single biomass gasifier with different conditions and feedstocks, this methodology should provide accurate models. Furthermore, due to the LASSO model reduction applied, simpler models can be obtained with much fewer parameters, which are very practical for the design of similar gasifiers.
