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Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Pena L.,Federal University of Fluminense | Pena L.,Thermodynamics and Optimization Group TOG
Journal of Petroleum Science and Engineering | Year: 2017

The capture of interfacial instabilities during water injection simulations in oil reservoirs is a challenging topic, which requires elaborate techniques, generally able to describe heterogeneities of reservoirs and phenomena associated with the flow of immiscible fluids. This article deals with simulations of viscous fingers in two-phase flows (water-oil) trough heterogeneous and anisotropic porous media, where both heterogeneity and anisotropy are modeled by the three-parameter Kozeny–Carman generalized equation, which was included in a classical model commonly used to simulate immiscible flows during waterflood operations. As main result, this paper presents a sophisticated numerical simulator, which allowed us to perform predictions of high quality, proving to be a suitable tool to describe physical aspects associated with flows in petroleum reservoirs. In fact, our simulations show that the permeability anisotropy can influence the formation and development of immiscible viscous fingering. For example, when water is injected through three different configurations, five-spot, line-drive and inverted five-spot, the results of this study indicate that this anisotropy may impose a significant degree of stabilization to the viscous fingering phenomenon, benefiting oil recoveries under water flooding processes. © 2017 Elsevier B.V.


Sacco W.F.,Federal University of Pará | 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 | De Moura Menezes A.A.,Federal University of Pará | De Moura Menezes A.A.,Thermodynamics and Optimization Group TOG | And 4 more authors.
Chemical Engineering Communications | Year: 2015

The prediction of critical points of thermodynamic systems is an important tool for modeling many high-pressure processes of theoretical and practical interest. In this article, the calculation of critical points of multicomponent mixtures is treated as a global minimization problem of a modified merit function associated with the criticality conditions obtained from the Gibbs tangent plane criterion, designed to discriminate the scale of the problem. The methodology used to solve the optimization problem is based on two versions of the particle swarm optimization (PSO), equipped with low-discrepancy sequences to prevent the sensitivity of the swarm with respect to the location of the initial population. To avoid a rapid decrease in the weight inertia, and to prevent stagnations near undesirable local minimizers, we present a modification of the PSO method, which uses different search cycles with the same inertia weight. This new version developed here is a fast and robust algorithm for solving the critical-point problem, via global optimization. © 2015, Copyright © Taylor & Francis Group, LLC.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Sacco W.F.,Federal University of Pará | 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.,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.


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 Pará | 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.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Simao G.,State University of Rio de Janeiro | Simao G.,Thermodynamics and Optimization Group TOG | And 2 more authors.
Advances in Engineering Software | Year: 2015

The development of Jacobian-free software for solving problems formulated by nonlinear partial differential equations is of increasing interest to simulate practical engineering processes. For the first time, this work uses the so-called derivative-free spectral algorithm for nonlinear equations in the simulation of flows in porous media. The model considered here is the one employed to describe the displacement of miscible compressible fluid in porous media with point sources and sinks, where the density of the fluid mixture varies exponentially with the pressure. This spectral algorithm is a modern method for solving large-scale nonlinear systems, which does not use any explicit information associated with the Jacobin matrix of the considered system, being a Jacobian-free approach. Two dimensional problems are presented, along with numerical results comparing the spectral algorithm to a well-developed Jacobian-free inexact Newton method. The results of this paper show that this modern spectral algorithm is a reliable and efficient method for simulation of compressible flows in porous media. © 2014 Elsevier Ltd. All rights reserved.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | Barufatti N.E.,State University of Rio de Janeiro | Barufatti N.E.,Thermodynamics and Optimization Group TOG | And 2 more authors.
Chemical Engineering Science | Year: 2011

This work introduces the Least Dot Products (LDP) method, a new algorithm for phase stability analysis of thermodynamic mixtures. Starting with the fact that tangent plane distance function (the objective function used in global stability tests) is, essentially, the dot product between the vector of compositions of a trial phase and the vector that describes the differences among the chemical potential of the components in the phases, our approach tries to obtain the least values of an auxiliary function that represents an appropriate dot product on a unitary sphere of the n-dimensional space, which is a good approximation for the stability test function. In agreement with the foundations of the Gibbs plane tangent criterion, the new algorithm simply tries to find points where the objective function is negative, which are not (necessarily) stationary points or global minima. Thus, our main contribution is not a new method for general nonlinear problems, or a rule-based termination criteria for a classical optimization method. Consequently, if such points do not exist, then LDP method is not capable to recognize the stability condition. To overcome this problem, we develop also a powerful safeguard algorithm, denominated Projected Simulated Annealing (PJSA) algorithm, which is obtained by projecting the Simulated Annealing algorithm onto the unitary sphere.In the present article, firstly we consider liquid-liquid equilibria at low or moderate pressures, where the excess Gibbs energy is described by NRTL or UNIQUAC models. Secondly, we address vapor-liquid equilibria at high pressures with cubic equations of state.To illustrate the performance of the new methodology, we use here 20 systems studied by other authors. Such problems possess 2-12 variables and constitute severe tests for many optimization methods. For some mixtures, we show that LDP method is capable of determining the instability condition using just two iterations. © 2011 Elsevier Ltd.


Henderson N.,State University of Rio de Janeiro | Henderson N.,Thermodynamics and Optimization Group TOG | de Sa Rego M.,State University of Rio de Janeiro | de Sa Rego M.,Thermodynamics and Optimization Group TOG | And 5 more authors.
Chemical Engineering Science | Year: 2015

Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n-dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. The purpose of this paper is two-fold. The first is a revisit to the Topographical Global Optimization method, where, for the first time, its foundations are formally described and its basic properties are mathematically proven. In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robust and efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints. The second objective is the application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering thermodynamics. Furthermore, in order to have an initial assessment of the power of this technique, first we solve 70 test problems, and then compare the performance of the method considered here with the MIDACO solver, a powerful software recently introduced in the field of global optimization. © 2015 Elsevier Ltd.


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.

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