## 1 Introduction  
Ethanol, a two-carbon aliphatic alcohol, can be produced from various renewable carbon resources such as rice hulls [1], tea processing wastes [2, 3], carob pods [4, 5, 6, 7], rice straw [8], barley husk, wheat bran, rye bran [9], waste potato mask [10, 11, 12], sugarcane [13], corn grain [14]. Among them, carob has been suggested to be an attractive raw material in the production of bioethanol from renewable sources due to its high carbohydrate content including sucrose, glucose, and fructose [5]. Bioethanol produced from these sources can be used as a fuel with high octane. Besides, it is a biodegradable product that is less toxic than methanol; its combustion causes a reduction in CO\({}_{2}\) emissions and is associated with a lower risk of ozone formation than gasoline and diesel [15]. Therefore, it creates an alternative low-cost attractive energy source that can replace fossil fuels [4]. The annual ethanol production in the worldwide is above 80 billion litters [16] and the majority of this (90%-95%) is produced by fermentation [17]. Therefore, it is also a remarkable fuel as it can be used alone or with 10%-22% mixture with gasoline in recent years, especially in Brazil and the U.S. [18]. The most widely used and effective microorganisms for bioethanol production are _Saccharomyces cerevisiae_, _Scheffersomycess stititis_, _Zymomonas mobilis_, and _Candida_ species, either using fermentation of biomass rich in fermentable sugars or using lignocellulosic biomass and polysaccharides, which require several pre-treatment steps to obtain hydrolysate sugars. Almost 12% of the bioethanol produced by fermentation is beverage alcohol, 20% for various industries uses and the remaining 68% is used as fuel ethanol [4; 19; 20]. Biofilms are the forms of natural cell immobilization and can be employed in bioreactors [21; 22]. Thereby, biofilm reactors can be defined as the reactors in which microbial cells are attached to the support materials to occur the biofilms [5]. Biofilm reactors have been widely used to generate the added-value products such as industrial enzymes, ethanol, vitamins, antibiotics, and biopolymers, since they provide unique environment and advantages including long-term fermentation, higher biomass accumulation, higher production yield, elimination of re-inoculation, time loss prevention (washing, sterilization of bioreactor, etc. ), operation stability, additional nutrient releasing from plastic composite support material, high resistance to the microorganisms at the extreme conditions of pH and temperature, contaminations, shear force, hydraulic shocks, antibiotics and toxic substances, decreasing of medium viscosity (especially filamentous microorganisms) and increasing of nutrient and oxygen transfer (especially filamentous microorganisms) [21; 22]. Kinetic models can capture information about the kinetic-metabolic nature of a fermentation process, and also assist the control and optimization of the fermentation process. Predictions of product formation and sugar consumption based on cell growth would be valuable for practical and scale-up purposes [23]. Various attempts have been made to develop a model describing the growth of a product producer, product formation and substrate consumption [24; 25; 26; 27; 28; 29]. However, no kinetic modeling of ethanol fermentation based on the cell growth in carob extract-based biofilm reactor has been made. Therefore, the logistic model was originally used to describe cell growth and also to calculate the kinetics of microbial growth. The Luedeking-Piret (LP) model was used to correlate product formation with biomass growth and substrate consumption while a modified Luedeking-Piret (MLP) model was employed to describe the substrate consumption corresponding with cell growth. Cost-effective ethanol production from renewable resources is essential since it primarily depends on the cost of the carbon sources and nutrients used in the fermentation media [30].