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283294 Banana Starch Enzymatic Hydrolysis Scale-up Using a Phenomenological Model

**Abstract**

The focus of this paper is on examining the scale-up factors on reaction dynamics of the enzymatic hydrolytic reaction by using Hankel Matrix Methodology. The use of some aspects of control theory applied to the scaling of processes, specifically the concepts of controllability, observability, singular value decomposition of Hankel matrix are used. A comparison between scaled-up factors, real process conditions and operational conditions found by simulation shows that Hankel Matrix is a strong methodology for scale-up biochemical process. A kinetic model for saccharification in batch and continuous enzymatic hydrolysis of banana starch oligomers syrup was selected, from the reaction mechanism steps, to predict the rate of glucose, maltose and maltotriose production by hydrolysis of oligomers, and a mathematical modeling of how reaction kinetics of enzymatic hydrolysis is influenced by scale-up. Computational simulation based on the proposed dynamic kinetic model shows that it predicts the hydrolysis reaction well.

**1. ****Introduction**

In all industrial activity scaling is an essential task. Previous studies, calculations and pilot trials are necessary for the construction of an industrial plant. A good scaling process, especially in the chemical and biochemical knowledge requires multiple different scales factors and replicas. However, the actual small-scale replicas of a process are very costly and time consuming. Moreover, it is not possible to operate a plant in extreme conditions, safety and economic factors. Although existing methods traditionally used for scaling of a chemical process, so far not found a methodology to scale up production from lab to pilot plant or commercial scale direct, efficient and effective: because ignorance of the phenomenology of the processes, it has been necessary experiments with gradual increases in scale.

This paper presents the use of control theory in a manner analogous to scaling of processes, based on a Semiphysical Model of Phenomenological Base. Definitions are also proposed for the Point of Operation (OP) and the operating system (SO) of a process fundamental in the development of this analogy. To achieve the ranking dynamics, we applied the Hankel matrix, which is used in control theory for the pairing of manipulated and controlled variables in plant (Gomez et al, 2008). In control process, Hankel Matrix has been used as control process tool, as a result of the interaction between state variables and manipulated (controllable) variables in any chemical process. From the calculation of the Hankel matrix SO is determined according to the impact of design parameters on the dynamics of the process (index of impacted states, IIE) and with it the operating conditions of the new scale. This methodology was used previously in scale up of fermentation process (Ruiz, 2011).

**2. **** Enzymatic Hydrolysis Scale-Up**

Riedlberger et al (2012) successfully validated a scale up for the enzymatic hydrolysis of wheat straw and microcrystalline cellulose mixtures by application of a cellulase complex at a milliliter- and liter-scale reactor. They designed stirred-tank bioreactors at a 10 mL-scale, using the same particle size (~2 mm) and solid content (8–10% w/w wheat straw) as at the liter-scale.

Saethawat Chamsart, 2002, studied the enzymatic hydrolysis of starch cassava in a 10 liters hydrolysis reactor agitated together with high efficiency impellers 2 Ekato Intermig at 200, 300, and 400rpm (equivalent to power inputs of 0.07, 0.25, and 0.60 W / kg, respectively). It was found that this process is governed by the dimensionless Reynolds number. For the case of scaling a 4 liters glass reactor, 150mm diameter and 300mm height, the agitation speeds were the same for scaling to a 10L reactor with geometric similarity.

3**. ****Hankel Methodology**

For bioprocess scale up is made in nine steps as follows:

Step 1: *Process simulation and scale up variables definition*. The aim of this step is to create a semiphysical model of phenomenological based (SMPB) and to define state variables **x**. Then, the model has to be simulated in steady state. Next, after defining state variables (Operation Point ie: C_{Ao}, C_{Bo}, pH_{o}, C_{Co} and so…), control variables **u** and design variables **z**are defined as well, all of them with its corresponding to its low scale value. Minimun efficiency is also calculated in this step, and a simulation of Control Volumen vs. Desired Product concentration is required in order to define the high scale vale operation volumen.

Step 2: *Hankel Matrix Formulation*. Hankel Matrix can be formulated as H=O_{b}C_{o}.

Step 3: *Hierarchy Curve and Dynamics*. At this step, it is necessary to increase the low scale control volume to desired high scale control volume and for each value of this vector, to calculate Impacted State Index (ISI) with the values of design variables **z** at low scale and then replaced them in Hankel in order to calculate Hankel Singular Values or **H=USV ^{T}** and with this components (

**U**and

**S**):

Step 4: *ISI Normalization and Operation Regimen verification*. Each sequence of ISI_{i} is divided by the maximum value reached by the ISI_{i}in the last step. In this way is determined which dynamic is dominant and which the interested dynamic is on the value of volume at the low scale.

Step 5: *ISI at all values of Control Volume. *For each value of volume from low scale to high scale, ISI is calculated and plotted vs control volume. Then, it is necessary to verify if the interested dynamic is dominant about all of them.

Step 6: *Critical Value of the Capacity Variable (CV*).*The critical value of CV has to be determined, as the value in which the highest value of ISI corresponds to the associated state with the interested dynamic. The efficiency is also verified at that CV.

Step 7: *Real ISI equation. *For each real inlets process conditions reported, ISI is calculated and an equation of ISI_{N_n}=*f*(CV) is determined.

Step 8: *Scale Up with Low and High Scale values.*For the value of VC at the low scale and taking two or three values of the VC at the high scale between VC at low and VC at high scale, scale up as follows, successively for each new value of the VC using inlets conditions of the VC immediately previous, until get the VC high scale value:

Step 9: *Scale Up verification and Results for High Scale.*With the inlets conditions for the volume at high scale, the model is solved in order to calculate the efficiency of the high scale process with the ISI vector at high scale. If the efficiency is not the desired, the Operation Point have to be checked and adjusted until desired efficiency is reached.

4**. ****References**

An-I Yeh, Yi-Ching Huang, Shih Hsin Chen. Effect of particle size on the rate of enzymatic hydrolysis of cellulose. Carbohydrate Polymers 2009)

Akerberg, C., Zacchi, G., Torto, N. and Gorton, L., 2000, A kinetic model for enzymatic wheat starch saccharification, J Chem Technol Biotechnol, 75(4): 306–314.

Bisio, a., and Kabel, r., 1985. Scale-up of chemical processes. John Wiley and Sons.

Gan, Q., Allen, S.J., Taylor, G., 2002. Kinetic dynamics in heterogeneous enzymatic hydrolysis of cellulose an overview, an experimental study and mathematical modeling. Proc. Biochem. 38, 1003–1018.

Gómez, C., Calderón, y. A. Álvarez, h., 2008. Construcción de modelos semifísicos de base fenomenológica. Caso proceso de fermentación. Biotecnología en el Sector Agropecuario y Agroindustrial. Universidad del Cauca. Colombia. Vol. 6. No. 2. pp.28-39.

Gómez, L., Amicarelli, A., Alvarez, H y diSciascio, F. (2004). El rol de los modelos en el diseño de equipos de proceso y sistemas de control. Memorias Congreso ACA. Colombia.

Ruiz-Colorado A.A, Factores de escala para la producción de Bioetanol. Tesis de Doctorado. Universidad Nacional de Colombia; Facultad de Minas (2009).

Ruiz-Colorado Angela y Álvarez Hernán. Escalamiento de Procesos Químicos y Bioquímicos basado en un Modelo Fenomenológico. Información Tecnológica Vol. 22(6), 33-52 (2011)

Margarites, a., and Zajic, J. E., 1978. Fluid Mixing Technology . Biotechnology and Bioengineering , 20, 939-1001.

Riedlberger Peter, Dirk Weuster-Botz. New miniature stirred-tank bioreactors for parallel study of enzymatic biomass hydrolysis. Bioresource Technology 106 (2012) 138–146.

S. Morales, H. Alvarez, C. Sanchez, 2008. Dynamic models for the production of glucose syrups from cassava starch. Food and bioproducts processing 86 (2008) 25–30.

Sulaiman Al-Zuhair The effect of crystallinity of cellulose on the rate of reducing sugars production by heterogeneous enzymatic hydrolysis. Bioresource Technology 99 (2008) 4078–408.

Zanin, G.M. and Moraes, F.F., 1996, Modelling cassava starch saccharification with amyloglucosidase, Appl Biochem Biotechnol, 57–58: 617–625

Zanin, G.M. and Moraes, F.F., 1998, Thermal stability and energy of deactivation of free and immobilized amyloglucosidase in the saccharification of liquefied cassava starch, Appl Biochem Biotechnol, 70–72: 383–394.

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