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Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Brettas J.C.,Federal University of Fluminense | Brettas J.C.,Thermodynamics and Optimization Group TOG | And 2 more authors.
Advances in Engineering Software | Year: 2015

This article discusses the applicability of the three-parameter Kozeny-Carman generalized equation to trigger immiscible viscous fingers and describe it in fractal heterogeneous porous media, during numerical simulations of waterflood operations in oil reservoirs. For that purpose, for the first time this equation was incorporated into a model that describes immiscible flows of incompressible two-phase fluids in porous media. Results were generated from intensive simulations, and viscous fingers were visualized graphically for three different well patterns, typical of oil fields: Line-Drive, Five-Spot and Inverted Five-Spot. Such results suggest that this generalization of the Kozeny-Carman equation can be used in numerical simulations of oil recovery processes susceptible to hydrodynamic instability phenomena. © 2015 Elsevier Ltd. All rights reserved.


Sacco W.F.,Federal University of Para | Sacco W.F.,Thermodynamics and Optimization Group TOG | Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG
Applied Soft Computing Journal | Year: 2011

We apply a recently introduced hybrid metaheuristic to solve nonlinear systems of equations with multiple roots as an optimization problem. In this technique, first, the Luus-Jaakola random search method is used to explore the search space. Then, in order to find more than one root, the best solutions previously found are clustered using Fuzzy Clustering Means. Finally, multiple Nelder-Mead simplex instances are applied using these solutions as starting points for searching within their respective clusters' domain. Our method is compared against other methodologies using benchmarks from the literature, and shows to perform well. Moreover, we successfully apply it to a real-world nonlinear system from the field of chemical engineering: the double retrograde vaporization problem. © 2011 Elsevier B.V. All rights reserved.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Sartori J.,Federal University of Fluminense | Sartori J.,Thermodynamics and Optimization Group TOG | And 2 more authors.
Industrial and Engineering Chemistry Research | Year: 2014

This article deals with the phase stability analysis of multicomponent systems via the determination of all the stationary points of the so-called tangent plane distance function, which is known as an important but difficult problem of the thermodynamics of phase equilibrium, where high nonlinearities are inherent aspects of the different thermodynamic models commonly used in the description of this distance function. To analyze phase stability described from different models, we combine three basic procedures here that were selected in order to attack points that we deem of relevant difficulty. To this end, we encapsulate in a single iterative algorithm the following steps: (i) polarization of a merit function associated with first-order stationary conditions of the phase stability problem, in order to avoid (or at least minimize) the repetition of stationary points previously calculated; (ii) a stochastic optimization method, which (at each iteration of the encapsulation algorithm) minimizes m times the same merit function polarized with the predetermined stationary points, using m different seeds for a reliable random number generator (where m is a given integer), in order to calculate new stationary points; (iii) a change of variables designed to allow the numerical method to work in the unconstrained optimization framework, providing the location of stationary points near the boundary of the original feasible set. Using the NRTL and UNIQUAC models for liquid-liquid equilibria at low pressures and the Soave-Redlich-Kwong and Peng-Robinson cubic equations of state for vapor-liquid equilibria at high pressures, we analyze 9 multicomponent systems studied in the literature, equipped with different feed compositions, totaling 32 tested mixtures, whose component numbers ranged between 3 and 12. We show 14 new stationary points obtained here that were not detected by methods previously used by other authors. © 2014 American Chemical Society.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Sacco W.F.,Federal University of Para | Sacco W.F.,Thermodynamics and Optimization Group TOG | And 2 more authors.
Fluid Phase Equilibria | Year: 2013

Here, we follow a classification proposed by Griffiths and Widom [1], where the order of a multicritical point in a mixture is equal to the number of phases which simultaneously become identical, considering m phases and assuming that m- 1 of these phases become identical to a given test phase. Thus, employing Rolle's theorem and basic properties of the so-called tangent-plane distance function, we develop a deduction of the multicriticality conditions of mixture from Gibbs tangent plane criterion, which relies on the principle of mathematical induction, being appropriate for any m≥. 2. © 2013 Elsevier B.V.


Henderson N.,Thermodynamics and Optimization Group TOG | Henderson N.,State University of Rio de Janeiro | Sacco W.F.,Thermodynamics and Optimization Group TOG | Sacco W.F.,Federal University of Para | Platt G.M.,State University of Rio de Janeiro
Chemical Engineering Research and Design | Year: 2010

We introduce a methodology to solve nonlinear systems of equations with bound constraints, and two or more roots. In order to find more than one root, this methodology uses an appropriate global optimization algorithm together with a polarization technique. Polarization modifies (successively after the determination of a new root) a merit function associated to the nonlinear system, creating repulsive regions in the neighborhood of the previous roots. We applied successfully the proposed methodology to solve hard nonlinear systems, including the double retrograde vaporization problem for binary systems of methane. +. n-butane. © 2009 The Institution of Chemical Engineers.

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