PROCESS DESIGN AND CONTROL Batch Fermentation Networks Model for Optimal Synthesis, Design, and Operation Gabriela Corsano, † Pı ´o A. Aguirre,* ,† Oscar A. Iribarren, ‡ and Jorge M. Montagna ‡ INGAR, Instituto de Desarrollo y Disen ˜ o, Avellaneda 3657, (3000) Santa Fe, Argentina This paper addresses an integral optimization of fermentation processes. The behavior of the fermentors is described by a set of algebraic and differential equations written as finite-difference equations in an equation-oriented environment. Unconventional constraints related to the number of batch items and connections among them, detailed kinetic models and operating costs corresponding to inoculum, and different available substrates are included in the model. The optimal number of units to be used in the process, their optimal operation policy (i.e., connected in series or in parallel working out of phase), as well as the optimal volume and operation of each unit, are determined simultaneously. The model is formulated as a sequence of nonlinear programming (NLP) problems. 1. Introduction In recent years, there has been significant growth in chemical industry in the use of batch fermentors because of the demand for a large number of specialty chemicals. Genetically engineered microorganisms pro- duce complex molecules of higher quality more ef- ficiently than does chemical synthesis. Fermentation isalso useful in the case of less sophisticated products, as it allows their production starting from chemically complex but rather inexpensive raw materials that are byproducts or even wastes from agricultural processes. In general, batch processing is used in manufacturing low-volume, high-value products. Thus, even a moderate increase in product yield can lead to a considerable improvement in profitability. For this reason, it is important to address the modeling and optimization of these batch processes. 1 There is abundant literature on batch process syn- thesis and design with batch stages described by fixed time and size factors as in refs 2-5. The papers by Reklaitis and co-workers 2,3 resorted to algorithmic solu- tion procedures, whereas the latter works used the mixed-integer nonlinear programming (MINLP) ap- proach: for batch processes in general in Ravemark and Rippin 4 and for processes that specifically include fermentation stages in Montagna et al. 5 This approach allows for the optimization of plant decision variables, including batch sizes and operating times of semi- continuous items, as well as the structure of the plant, i.e., the number of units in parallel and the provision of storage tanks between stages. However, the use of constant time and size factors requires that the units’ process decision variables, e.g., reaction extents, be fixed, thus preventing better solu- tions for these problems. A first level of detailed description of the units’ performance depending on these process variables consists of using algebraic models. Such an approach was first proposed by Salomone and Iribarren 6 and applied to fermentation processes by Pinto et al. 7 This approach allows for the simultaneous optimization of the units’ process variables and the plant decision variables. The process performance models are additional algebraic equations describing the time and size factors as functions of the units’ process variables, so that the global problem formulation is still an MINLP. A more detailed description of the performance of batch stages requires that they be modeled with dif- ferential equations. First Barrera and Evans 8 and later Salomone et al. 9 proposed that this simultaneous opti- mization should be approached by integrating the batch plant model with dynamic simulation modules for the batch units. This approach does succeed in performing the optimization, but it entails a great computational effort. The global problem is no longer just an MINLP. It has dynamic simulation blocks interacting with it, and therefore, this requires algorithmic solution proce- dures. Incidentally, the approach in ref 9 proposes an algorithm whose resolution sequence overcomes the unfeasibility problems reported in ref 8. One way of incorporating the units’ dynamic models without losing the MINLP nature of the global problem is to discretize the differential equations to convert them into algebraic constraints of the program. This was the approach used by Bathia and Biegler 10 for simple process examples, and it is used here for a complex fermentation network. One of the main motivations for using a detailed model for the fermentation network was to be able to optimize the consumption of complex substrate mixtures that can be fed at different locations of the network. This issue arises in our case study, which is a fermentation * To whom correspondence should be addressed. Tel.: 54-342-4534451. Fax: 54-342-4553439. E-mail: paguir@ ceride.gov.ar. † Universidad Nacional del Litoral. ‡ Universidad Tecnolo ´gica Nacional. 4211 Ind. Eng. Chem. Res. 2004, 43, 4211-4219 10.1021/ie030549h CCC: $27.50 © 2004 American Chemical Society Published on Web 06/24/2004