On the last years, there have been proposals for using supercritical conditions to produce biodiesel fuel from vegetable oils and/or animal fats without a catalyst. Different schemes have been proposed, the most popular consisting on the use of supercritical methanol as reactant. Other alternatives involve the use of methyl acetate or acetic acid as reactants. The potential of those processes may be established in terms of their total annual cost and environmental impact. Thus, in this work, the production of biodiesel fuel by using different reactants is studied. Four processes are considered: the one step supercritical methanol process (Saka process), the two steps supercritical methanol process (Saka-Dadan process), a process with methyl acetate as reactant and a process with acetic acid as reactant. Possible flowsheets for the reaction and separation stages are proposed. The processes are analyzed and compared in terms of energy consumption, pollutant emissions and total annual costs. It has been observed that, in terms of energy, the one step methanol process has the lowest energy requirements. Nevertheless, a higher temperature for the steam supplied is required; thus, that process has high values of CO2 emissions. Furthermore, methyl esters are obtained at higher temperatures, which may have a negative impact on its quality.

Abstract: "In this paper we investigate the solving of conditional models using the boundary crossing algorithm proposed by Zaher (1995). He proposed this algorithm as an alternative to using MINLP techniques for solving. This algorithm involves the execution of several well differentiated activities including logical analysis and continuous reconfiguration of the equations constituting the problem, calculation of Newton-like steps, and the calculation of subgradient steps. In this paper, we describe the practical implementation of the boundary crossing algorithm as a conditional modeling solution tool. In such an implementation, we have integrated the entities created and/or used to perform each of the activities in an object oriented solving engine: the conditional modeling solver CMS1v. Also, we describe and solve several examples of conditional models in chemical engineering. Finally we discuss the scope and limitations of the algorithm."

Abstract: "Conditional models arise in chemical engineering when modeling systems involve physicochemical discontinuities, such as phase transitions. Zaher (1993) and Grossmann and Turkay (1996) show that one can represent conditional models as an algebraic system of disjunctive equations. This work proposes a new complementarity formulation for the representation of algebraic systems of disjunctive equations. This formulation not only establishes the complementarity condition among equations belonging to different disjunctive terms but also enforces simultaneous satisfaction of all of the equations in the same disjunctive term. This approach represents an alternative to MILP formulations, avoiding discrete decisions; it also avoids the need for special procedural nonlinear techniques as required by the boundary crossing algorithm (Zaher, 1991). We identify the disadvantages associated with the proposed formulation. Solving the resulting nonlinear system of equations relies on the assumption of nondegeneracy of the solution to the complementarity equations. The proposed complementarity representation performed reliably on several example problems where the number of equations in each disjunctive term is small."

Abstract: "We identify the modeling capabilities needed for the efficient representation of conditional models in an equation-based environment and describe modeling tools for the performance of each of these tasks: conditional configuration of a model structure, conditional compilation and conditional execution of procedural statements. We also describe the details of the computer implementation of these tools and show how the expressiveness of an equation-based modeling language increases with their incorporation. Several chemical engineering examples are presented to demonstrate the scope of application of the proposed extensions."

Abstract: "Interior point methods have recently become an interesting alternative in a number of numerical applications. In particular, their performance in the solution of problems involving complementarity equations has been the subject of extensive research and their efficacy is well documented. In this paper, following a description of the fundamentals of interior point methods, we describe the globally convergent framework proposed by Wang et al (1996) for solving a constrained system of nonlinear equations by an interior point potential reduction method. Also, we show how we can apply the potential reduction algorithm and its convergence result to the complementarity formulation described in Rico-Ramirez and Westerberg (1998). Based on that observation, we then apply the algorithm proposed by Wang to solve the complementarity examples used as case studies throughout this work. Moreover, we also apply some high order strategies designed to improve convergence (Mehrotra, 1992; Gondzio, 1996), and compare the results obtained with each of the methods. All those techniques have been incorporated to the ASCENT modeling environment with the implementation of the solver IPS1v."

Abstract: "Structural analysis is applied to exploit sparsity in the solving of a system of equations (Duff et al. 1989). Zaher (1995) studied the issues involved in the structural analysis of conditional models and presented a methodology to ensure consistency in a conditional model, the complexity of such an analysis being combinatorial. In that work, Zaher considered only cases in which the number of variables and equations of all the alternatives in a conditional model are the same. In this paper, an extension to Zaher's consistency analysis is presented. This extension allows the consistency analysis to be applied to conditional models in which the number of variables and equations for each of the alternatives may not be the same. Also, we show how, by taking advantage of the structure of the problem, it is sometimes possible to reduce the effort required by such an analysis. In particular, the cases of the existence of repeated structures and common incidence pattern among alternatives are discussed."