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Optimisation is referred to as the method of improving the performance of a process to achieve maximum potential throughput from it. In chemical engineering, the term optimisation is generally applied to a process that produces the best response. Traditionally, the optimal conditions of a process are investigated by monitoring the influence of one factor at a time on an experimental response. One parameter at a time would be changed while the other parameters are kept constant. This optimisation technique is known as one variable at a time (Bezerra et al., 2008). The main disadvantage of using this method is it does not assess the interaction among the selected parameters. Secondly, using this method will lead to an unnecessary increase in the number of experimental runs required to perform optimisation on the experimental data. A way of overcoming these issues is by multivariate statistic techniques to perform optimisation studies. One of the most widely used multivariate techniques in optimisation studies is response surface methodology (RSM)

2.10.1. Response surface method

Over the past decade, RSM has been useful in studying the interactive effects of independent parameters for numerous chemical processes (Rajeshkannan et al., 2009; Vimalashanmugam and Viruthagiri, 2012). RSM was developed in the 50’s to model experimental responses but was then later used to model numerical responses (Bezerra et al., 2008). RSM makes use of statistical techniques to fit empirical models to experimental data. The model is then described by linear or square polynomial functions. The functions are then studied before modeling and optimisation of the conditions. According to (Bezerra et al., 2008) the methodology of optimisation via application of RSM is as follows:

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 Screening studies are used to select the independent parameters with a major effect on the system, subsequently, the definite limits of the parameters are defined by the researcher.

 Selection of experimental design and careful implementation experiments in accordance with an appropriate experimental matrix.

 Assessment of the experimental data using mathematic-statistic treatment for the fitted polynomial function.

 Evaluation of the fitness of the model.

 Locating optimum values for each parameter from the RSM plot. 2.10.2. Central composite designs

Central composite designs are common designs used for RSM for fitting second-order models. Quadratic surfaces are appropriately fitted while independent parameters are optimised using minimal experimental runs. The experimental centre points are used to assess the errors and reproducibility of the results. A comprehensive CCD with three design parameters is represented in Figure 2.8.

Figure 2. 8: Central composite design for three parameters at two levels

The CCD consists of a 2n _{factorial runs with 2n axial runs and n}

c centre runs. The number of

experiments necessary for a CCD is defined by N= 2n _{+ 2n +n}

c. There exist two types of central

composite design: uniform precision and orthogonal. The distinction relates to the number of centre points in the design and the axial values (SAS Institute Inc, 2009):

 With regards to the uniform precision, the centre points are chosen to allow the prediction variance near the centre of the design space to be flat.

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 Orthogonal designs, on the other hand, the number of centre points are selected to reduce the correlation between the second-order parameter estimates with other parameter estimates.

2.10.3. Box-Behnken designs

This method was developed by Box and Behnken (1960) as a design that allows for the accurate estimation of first and second-order coefficients of the model from the three-level factorial arrangement. The number of experimental runs for BBD is defined by N = 2n (n-1)+ nc These designs are often used for 3k designs with a large number of independent

parameters (Bezerra et al., 2008). Like to CCD, Box-Behnken Designs express the experimental design via an experimental run matrix. An advantage of BBD’s is the combinations expressed by the design matrix never result in an experimental run in which all factors are simultaneously at the highest of the lowest (Ferreira et al., 2007). The result is operation at extreme conditions is avoided. Equally, such designs are not ideal when responses at extreme conditions are required. For three factors the graphical representation is as follows:

(a) (b)

Figure 2. 9 : (a) Box-Behnken Design cube (b) three interlocking 22 _{factorial design}

Box-Behnken Designs are suitable for RSM because they allow for (Ferreira et al., 2007):

 An accurate estimation of the quadratic model

 Building of designs

 Good detection of lack of fit model

In the past, researchers have typically focussed on the optimisation of pyrolysis processes for volatile biofuel production. Issa et al. (2011) employed CCD to optimise the pyrolysis of rice husk for bio-oil production. The results from the study showed that bio-oil production was only

28 affected by the main process factors such as temperature, heating rate, particle size, holding time and gas flow rate. The interaction of these factors had no significant influence on the production of bio-oil. The authors also noted high char production at 400°C, as such bio-oil yield was reduced. No further work was done on studying the production of char in the study. Similarly, Kolokolova, (2014) optimised the production of bio-bitumen through the pyrolysis of sawdust. The author detailed maximum bio-oil yields were obtained at temperatures above 450°C. The author went further to state that by-product chars produced at 450°C had a higher calorific value to those produced at 350°C, this the author stated demonstrated char’s potential to be used as a solid fuel. The author produced char with a calorific value of 25 MJ/kg, which was higher than the 22 MJ/kg average of New Zealand coal. A noteworthy case study was by Mundike et al. (2017), who successfully employed CCD to optimise the production of chars for combustion applications through the slow pyrolysis of alien invasive plants. The study, however, did not extend to the commercial viability of the process. The current study will not only investigate the optimisation coal competitive chars but will also assess the commercial techno-economic feasibility of the process.