2.4. Experimental Design: Box–Behnken Design (BBD)

The response surface methodology (RSM) based on the Box–Behnken design (BBD) model is one of the most conventional methods for developing and optimizing the process conditions involved in any process. It is also efficient in studying the effects on the process involved, with a relatively small number of experimental runs, which saves time, labor, and cost. A three-factor Box–Behnken statistical design approach (BBD) was used to study the interactional and main effects of process conditions as well as the quadratic effect on three responses, namely, mass yield (MY), higher heating value (HHV), and energy efficiency factor (EEF) of biochar/hydrochar. BBD is usually sufficient to fit a quadratic model of the form illustrated in eq 5 and explain how the factors affect the responses.⁴⁵

where γ is the experimental responses as indicated in Table 1, α₀ is the intercept, α_j, α_jj, and α_kj are partial regression coefficients, i represents the number of process conditions, and x_j represents the three independent variables.

Two experimental designs comprising 17 experiments each, with five center points each to estimate the pure error and lack of fit, were developed to model and optimize the process conditions. The process conditions employed during torrefaction in this study were premised on other studies published in the literature for other biomass types. Similar process conditions were employed for the solvolysis experiment to create a basis for comparison between biochar and hydrochar. The process conditions and coded levels implemented in this design are shown in Table 1.

Design-Expert version 12 software was used to carry out the statistical tests and analyses to make inferences about the developed models in this study. A 95% confidence level (i.e., P = 0.05) was employed to check the significance of each model developed in this study and each variable and interactional effect present in the model equations. Several statistical tests such as P test, F test, lack of fitness (LOF) test, coefficient of determination (R²), adjusted coefficient of determination (adj. R²), and predicted coefficient of determination (pred. R²) were employed to make accurate inferences about the developed models. The model was further used to develop three-dimensional response surface plots to study the interactional effect of process conditions.