Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.10, No.6, 2020 1 Modelling Effects of Process Variables During Fermentation of Pineapple Peels Using Yeast for Ethanol Production Using a Second Order Optimal Rotatable Design in Four Dimensions. Kabue Timothy Gichuki 1* , Koske Joseph 2 , Mutiso John 2 1. School of Pure and Applied Sciences, Mount Kenya University, Thika Kenya 2. School of Sciences and Aerospace Studies, Moi University Eldoret, Kenya * Email Address:kabuegichuki@yahoo.com Abstract The need for a cleaner environment in urban areas and the high cost of petroleum products which are becoming scarce due to unbalanced relation between supply and demand besides air pollution of sources has led to the research for other fuels to replace fossil fuels. Ethanol from biomass waste is such an alternative to petroleum products. Most studies on optimization of process variables using Response Surface Methodology apply Central Composite Designs yet other designs exist. Optimal designs have fewer trials employed with the aim of obtaining efficient designs for fitting reduced quadratic or higher order models. Coded values of a second order optimal rotatable design in four dimensions constructed using balanced incomplete block designs (BIBD) was fit into experimental data in order to study the effects of four process variables namely; time, PH, temperature and substrate concentration on fermentation of pineapples peels using Saccharomyces cerevisiae for ethanol production. Normal probability plots and Multiple R-squared of 0.9323 and Adjusted R-squared of 0.8944 which measure model fitting reliability indicated aptness of the model. Most values of Probability F were less than 0.05, confirming that the model terms were significant and only 6.8% of the total variation could not be explained by the model ensuring good adjustment of the model to experimental data. Model adequacy was also confirmed by the good agreement between the experimental data and predicted values. The design was found reliable in modeling, and studying the effects of the four factors to the processes of fermentation of pineapples peels as substrate for ethanol production using Saccharomyces cerevisiae Keywords: Ethanol, Pineapple Peels, Response Surface Methodology and Rotatable Designs. 1. Introduction Ethanol from bio-mass waste is an alternative to fossil fuels that can be used in petrol engines without modification and with the current fueling infrastructure and it is easily applicable in present day combustion engine, as mixing with gasoline Hansen et al.,(2005b).Combustion of ethanol results in relatively low emission of volatile organic compounds, carbon monoxide and nitrogen oxides compared to fossil fuels such as petrol and diesel Wyman and Hinman, (1990). Isaias et al,. (2004) observed that ethanol reduces green-house gases by between 86% to 90% while Goettemoeller and Goettemoeller, (2007) noted that many starchy wastes can be used as raw materials for ethanol production but Molasses is widely used since it is cheap and readily available for conversion with little pre-treatments as compared to other starchy materials since it’s sugars are present in fermentable form, Razmovski and Vucurovic, (2011). Tropea et al (2014) notes that 75% of the fruit processed in canneries results in peeled skin, core, and crown as the end waste products, which are rich in intracellular sugars and plant cell walls composed mainly of cellulose, peptic substances and hemicelluloses. Their dry matter content which is around 10%, is composed of about 96% organic and 4% inorganic matter Abdullah, (2007). These materials exhibit both high biochemical oxygen demand (BOD) and chemical oxygen demand (COD) values as noted by Ban-Koffi and Han, (1990) which give rise to serious pollution problems if not properly disposed. For high quality and high yield of ethanol in ethanol industry, selection of fermentative yeast is key. Saccharomyces cerevisiae is the most well-known and commercially significant yeasts that have been primarily used for bioethanol production Chandel et al., (2007). Tsuyoshi et al., (2005), records that one yeast cell ferments approximately its own weight of glucose per hour and that Sugars from sugar cane, sugar beets, molasses, and fruits are converted to ethanol directly. Choonut et al., (2014) observed that Pineapple peels, account for 29-40% (w/w) of total pineapple weight which after pretreatment with water and heat at 100 0 C for four hours, 36.25±2.87% of cellulose