A computational procedure for identifying the minimal set of metabolic reactions capable of supporting various growth rates on different substrates is introduced and applied to a flux balance model of the Escherichia coli metabolic network. This task is posed mathematically as a generalized network optimization problem. The minimal reaction sets capable of supporting specified growth rates are determined for two different uptake conditions: (i) limiting the uptake of organic material to a single organic component (e.g., glucose or acetate) and (ii) allowing the importation of any metabolite with available cellular transport reactions. We find that minimal reaction network sets are highly dependent on the uptake environment and the growth requirements imposed on the network. Specifically, we predict that the E. coli network, as described by the flux balance model, requires 224 metabolic reactions to support growth on a glucose-only medium and 229 for an acetate-only medium, while only 122 reactions enable growth on a specially engineered growth medium.

Following a model-centric strategy in the development of a manufacturing process for a new medicine empowers the simultaneous study of a large number of process parameters, which is large enough to exceed the capability of a graphic representation of the interactions across them. This work presents a discussion regarding the identification, description, and communication of multidimensional design spaces of high order. It introduces the reader to mathematical tools developed by the process systems engineering community that become relevant in the challenge to replace graphics as a means to describe and communicate a design space. Concepts like process f lexibility are discussed and illustrated. The paper also introduces geometric projection as a way to capture and describe the shape of the design space in an easier form (than that of the complete mechanistic model) that can be communicated to the regulator. An assessment is presented regarding the key elements communicated by a graphical representation of a design space, and alternate ways of conveying the same information using mathematics are suggested. These ideas are illustrated by applying them to the identification and definition of a design space for a chemical reaction step and the digital risk assessment for a packed bed adsorption step.

To increase manufacturing flexibility and system understanding in pharmaceutical development, the FDA launched the quality by design (QbD) initiative. Within QbD, the design space is the multidimensional region (of the input variables and process parameters) where product quality is assured. Given the high cost of extensive experimentation, there is a need for computational methods to estimate the probabilistic design space that considers interactions between critical process parameters and critical quality attributes, as well as model uncertainty. In this paper we propose two algorithms that extend the flexibility test and flexibility index formulations to replace simulation-based analysis and identify the probabilistic design space more efficiently. The effectiveness and computational efficiency of these approaches is shown on a small example and an industrial case study.

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The optimal synthesis of the refrigeration configuration and the selection of the best refrigerants that satisfy a set of process cooling duties at different temperatures is addressed. This approach simultaneously selects refrigerants and synthesizes refrigeration structures by minimizing a weighted sum of in®estment and operating costs. A superstructure representation considers the majority of refrigeration cycle features encountered in real complex multistage refrigeration cycles such as economizers, multiple refrigerants, and heat integration. A no®el theoretical treatment of modeling representations and algorithmic impro®ements is introduced. Results, for example, in®ol®ing multiple refrigerants, cooling loads, and heat sinks are obtained. Complex, nonintuiti®e topologies typically emerge as the optimal refrigeration configurations that are better than those obtained when refrigeration synthesis is performed after refrigerant selection. IntroductionThe need for efficient utilization and recovery of energy in chemical processes has been firmly established on both economic and environmental grounds. Refrigeration systems in chemical process plants are complex, energy, and capital intensive utility systems which remove heat from low-temperature process streams and reject it to streams at higher temperature or cooling water at the expense of mechanical work. Most research work in refrigeration systems addresses the refrigeration cycle synthesis problem in isolation of the refrigerant selection. In this work we show that significant cost reduction can be realized by encompassing both objectives within the same unified framework.A simple vapor compression refrigeration cycle consists of a sequence of evaporation, compression, condensation, and expansion steps. In most cases, refrigeration needs to arise simultaneously for multiple loads at different temperature ranges. This necessitates the need for staged refrigeration cycles with multiple compressors and evaporators to meet the process cooling loads. Even for a single refrigeration load, in many cases, a single refrigeration stage cannot span the entire temperature range between the evaporator and the condenser, either because the required compression ratio is too high or the critical pressure is reached in the condenser. This explains why design alternatives typically need to be explored Correspondence concerning this article should be addressed to C. D. Maranas. involving complex multistage refrigeration cycles utilizing multiple refrigerants for different temperature ranges. This complexity of the topology of refrigeration cycles and the diversity in the selection of refrigerant molecules coupled with the high investment and energy intensive nature of refrigeration cycles motivates the need for the development of systematic procedures for the efficient synthesis of refrigeration cycles.One of the earlier works addressing the problem of synthesizing minimum cost cascade refrigeration systems is that of Ž . Barnes and King 1974 . They identified and standardi...