Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Continuous flow nanocatalysis: reaction pathways in the conversion of levulinic acid to valuable chemicals

The selective production of 2-methyltetrahydrofuran from levulinic acid has been effectively conducted using designed Cu based catalysts and compared with a commercial Pd/C system under microwave irradiation. Optimised conditions for the most active catalysts Cu-MINT (>90% conversion, 75% selectivity to MTHF) and Pd/C (78% conversion, 92% selectivity to MTHF) were further translated into a continuous flow process using the proposed catalysts to find out the deactivation of Cu-MINT under flow conditions (79 vs. 13% conversion with a switch in selectivity to products after 30 min in flow), the high stability of Pd/C (73 vs. 70% conversion at stable selectivity under analogous conditions to those of Cu-MINT) but, most importantly, different relevant pathways to valuable products from levulinic acid depending on the type of catalyst employed.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.