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264079 Modeling and Dynamic Optimization of Fuel-Grade Ethanol Fermentation Using Fed-Batch Process

Ethanol produced from fermentation of biomass-derived sugar is increasingly being used as a fuel for transport, either neat or in petrol blends. The main advantage of fuel-grade ethanol is that it can be produced from plants such as maize, sugar cane and sweet sorghum, thereby balancing the amount of greenhouse gases produced during the combustion process by absorption during photosynthesis. Also, gasoline additives are not necessary and the combustion is more complete when fuel-grade ethanol is used [1].

As the world’s largest biofuel producer, the U.S. will produce over 57 billion liters of ethanol in 2012, and 136 billion liters in 2022 [2]. Most of the ethanol in U.S. is produced from maize-based plant, and more than 90% of the plants make use of the dry mill process, which involves four steps: milling, liquification, simultaneous saccharification and fermentation (SSF), and distillation. The SSF process is the most important step, where dextrin is broken down into fermentable dextrose by glucoamylase and dextrose is converted into ethanol by yeast. The theoretical maximum yield of ethanol from maize starch indicates that the ethanol concentration after SSF process can be over 160 (g/L) in the batch fermenter [3]. Currently, the most advanced commercial plants can produce approximately 150 (g/L), however, the average yield from the plants using traditional techniques produce less than 140 (g/L). Therefore, improving the operations of the SSF process based on current facilities is undoubtedly the most economic approach to increase ethanol yield. However, optimization of SSF operations requires a good understanding of the process, usually represented by data and models.

Models of the SSF process usually consist of dynamic balances of components such as yeast, dextrose, and ethanol. Models of different complexities have been developed, ranging from relatively simple models [4] to quite detailed ones [5-7]. The main differences of the degree of complexity results from addition of intermediate steps in the saccharification process, use of more appropriate kinetics reflecting growth rate and inhibition term, and inclusion of correlations of the temperature influence on enzyme and yeast activity.

One significant challenge for the use of SSF models in commercial plants is the lack of data, since yeast, active yeast, and dead yeast cannot be measured independently. In addition, fed-batch fermenters are operated as a “black box” for the majority of the operating time. Dextrose and ethanol concentrations can be measured only every few hours and other intermediate substances are difficult to measure. The one process variable that is measured often in commercial plants is the process temperature, however, an energy balance is required if these temperature data are to be used for parameter estimation or monitoring other quantities. Unfortunately, none of the existing models for SSF include an energy-balance equation as SSF is a complex process and an energy balance includes a significant number of parameters and relationships to describe the thermo-physical properties.

Another challenge for operating ethanol plants is that ethanol fermentation is an exothermic process and temperature changes will significantly affect enzyme and yeast activity. Glucoamylase has an optimum activity at 140 ℉ in the saccharification process, while the optimal temperature for yeast growth and ethanol fermentation is in the range of 84-94℉. These competing optimal process temperatures for the SSF highlight the complexity of selecting an optimal temperature profile over the course of a batch. It should be noted that most commercial plants hold the temperature constant between 86-90℉.

The model developed in this work is based upon existing work [5-11], however, the model has been updated to address the challenges mentioned above: reformulate the flowrate equation which reduces the stiffness of the system and simplifies numerical solution of the model; substitute Monod kinetics expression with Haldane kinetics expression to enhance the synergistic substrate and product inhibition; expand the existing model to also include an energy balance with new parameters that are estimated from available data. Furthermore, this work addresses the above mentioned challenges by:

- Establishing the relationship between cooling water flowrate, temperature, and active yeast concentration, so that temperature data can be used to estimate unknown parameters arising from both mass-balance equations and energy-balance equations;
- Computing optimal input profiles for a fermenter used for ethanol fermentation by using the developed model and a simultaneous approach for solving the dynamic optimization problem.

The parameter estimation algorithm presented here is based on a Trust-Region approach with a fixed-step Runge-Kutta method. The simulation results fit the original experimental data well for both the training and testing set. In the dynamic optimization problem, both the input profile and the model are discretized using a three-point Radau collocation on finite elements [12]. Then, the optimization problem is implemented in AMPL [13], and is solved using nonlinear solver IPOPT [14]. It is shown that modifications of the input profiles for the cooling rate and the glucoamylase addition lead to an approximately 10% increase in ethanol yield. These are promising results, even though these findings will ultimately need to be validated during real plant operations.

**Reference**

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