Marcelo Castier

Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations

Knowledge of the properties of granular materials is important for efficient and safe design of industrial equipment. In this work, the Monte Carlo method is used for simulating granular systems of spherocylindrical particles. After presenting an overview of such method and of overlap detection in systems of hard spherocylinders, the application of the method for granular systems is discussed. Then, porosities, calculated for simulated monodispersed beds, are presented as functions of the particle elongation. Next, results for vibration-induced segregation of binary mixtures of spherocylinders with identical volume and density, but with different elongations, are evaluated, showing the influence of the particle shape on this phenomenon. Finally, effects of size and shape on such segregation are contrasted using results with simultaneous variation of particle volume and elongation.

Calculation of simultaneous chemical and phase equilibria in nonideal systems

Abstract A new method for the calculation of simultaneous chemical and phase equilibria at specified temperature and pressure is presented. An algorithm previously proposed for isothermal multiphase flash problems is extended and modified for systems with reversible chemical reactions. A method for the automatic selection of independent chemical reactions is improved and extended to nonideal mixtures. The iterative calculations are initialized with an accelerated direct substitution procedure. A second-order minimization algorithm is utilized for the final iterations. The differential phase stability test is applied to verify the need for adding new phases to the system. Phase removal is tried even for two-phase systems whereas, in flash problems without reaction, phase removal only needs to be attempted for systems with three or more phases. Examples that illustrate the performance of the method for mixtures with nonideal phases are presented.

Automatic implementation of thermodynamic models using computer algebra

Abstract A new package, Thermath , for the automatic implementation of thermodynamic models was developed in the Mathematica® programming language. Starting from an excess Gibbs free energy ( G E ) model or an equation of state (EOS), Thermath can be used to derive expressions for several thermodynamic properties and to analyze the structure of these expressions, generating a code that implements them in a computer language (Fortran77 is used in this paper). Using the package, procedures that implement properties derived from commonly used G E models could be rapidly generated. For EOSs, two situations occurred. Properties from simple EOSs could be readily derived and implemented. For more complex EOS, lengthy expressions may result, and their analysis can be very demanding in terms of computer time. To overcome this difficulty, a strategy to split this problem in tasks of feasible computational demand is presented. Although the applications of this paper deal with the implementation of thermodynamic models, most of the procedures developed here can possibly be used to implement models in other fields of science and engineering.

Critical points with the Wong-Sandler mixing rule—II. Calculations with a modified Peng-Robinson equation of state

Abstract This is the second of two papers in which critical point calculations in binary systems were performed utilizing cubic equations of state (EOS) combined with excess energy models using the Wong-Sandler mixing rule. In the first paper, a qualitative study of critical phase diagrams calculated using the simple van der Waals EOS combined with the NRTL model was made. In this paper, the Stryjek and Vera version of the Peng-Robinson EOS was also combined with the NRTL model and the resulting model was used in the computation of the critical loci of real systems. The binary interaction parameters of the model were estimated by correlating vapor-liquid equilibrium (VLE) data and, for some systems, successful predictions of the critical loci were obtained even when VLE data far from the critical point were used. To estimate parameters in systems for which the equation of state model may incorrectly predict a false liquid-liquid split, we used a penalty function approach based on the results of global stability tests. While the model studied here has been able to quantitatively predict the critical behavior of some non-ideal systems, involving compounds such as water, acetone and alkanols, only qualitatively correct behavior could be predicted for some highly asymmetric and non-ideal mixtures, such as water + n -dodecane.

Calculations of thermodynamic equilibrium in systems subject to gravitational fields

The objective of this work is to present a procedure for the calculation of chemical and phase equilibrium (CPE) in multicomponent mixtures subject to the effect of gravitational fields. The specifications are the total volume, initial number of moles of each species and temperature. The problem is formulated as the minimization of a modified form of the Helmholtz function that contains a term to account for the potential energy. To solve this problem, the system is divided into layers. It is assumed that each of these layers is a homogeneous part of the system, and that each phase occupies a specified number of layers. Layers in the same phase are assumed to have the same size whereas those in different phases typically have different sizes. In the minimization of the modified Helmholtz function, the independent variables are the volume fraction of each phase (thereby defining the location of the interfaces) and the number of moles of each species in each layer, taking into account the possibility of chemical reactions. The procedure is used to calculate density and pressure profiles with height for pure fluids close the critical point and composition profiles for reactive and non-reactive mixtures.

Group contribution equation of state based on the lattice fluid theory: Alkane–alkanol systems

Abstract A new group-contribution equation of state (EOS) is proposed and applied to phase equilibrium calculations. The EOS is based on the generalized van der Waals theory and combines the Staverman–Guggenheim combinatorial term of lattice statistics with an attractive lattice gas expression. The EOS is applied to vapor–liquid equilibrium (VLE) calculations in systems containing pure hydrocarbons, alcohols, and their binary mixtures. These systems cover a wide range of situations, including nonpolar and polar compounds of different sizes and mixtures ranging from nearly-ideal to azeotropic behavior. Using VLE data for pure substances and binary mixtures of linear hydrocarbons, the parameters of linear alkane groups (CH 3 and CH 2 ) were simultaneously fitted. For pure linear alkanes up to C 12 , calculated vapor pressures deviate less than 1.7% from the experimental values. Predicted vapor pressures of eight heavy hydrocarbons (from C 14 to C 28 ) are in satisfactory agreement with experimental data. The parameters for other groups (branched alkanes and alcohol groups) were fitted sequentially, using data for pure compounds and binary mixtures only containing the characteristic group being estimated and linear alkane groups. Satisfactory predictions of the vapor pressures of pure substances and bubble pressures of binary mixtures were obtained.

Critical points with the Wong-Sandler mixing rule—I. Calculations with the van der Waals equation of state

This is the first of two papers in which critical point calculations in binary systems were performed utilizing cubic equations of state (EOS) combined with excess energy models using the Wong-Sandler mixing rule. In this paper, the van der Waals equation of state is combined with the NRTL model in order to investigate the influence of the model parameters on the shapes of the calculated critical phase diagrams. Due to the large number of parameters in the model, it is not possible to obtain a two-dimensional global phase diagram, however the results indicate that many different types of critical phase diagrams can be obtained from the model. Due to the comparatively simple functional form of the van der Waals EOS, no attempt was made to compare the calculated critical phase diagrams with experimental data. Such a comparison is made on the second paper of this series, in which the Peng-Robinson EOS is combined with the NRTL model and the resulting model is used in the computation of the critical loci of several real systems.

Automatic implementation of thermodynamic models for reliable parameter estimation using computer algebra

Abstract An existing computer program for the automatic implementation of thermodynamic models, Thermath, was extended to allow the implementation of code compatible with the intbis / intlib package for the solution of sets of nonlinear equations using interval arithmetic. Using the extended program, we developed the scalar and interval subroutines needed to fit interaction parameters of the Wilson and UNIQUAC excess Gibbs free energy models. We could then use these codes to perform a reliable parameter estimation for these models, i.e. guaranteeing that the global minimum of the objective function was achieved inside an initially specified range for each model parameter. Our observations in the estimation of parameters for the Wilson model in binary systems confirm those of [Nonlinear parameter estimation using interval analysis, presented at FOCAPD-98, Snowbird, UT, USA (1998)] and [Fluid Phase Equilibria 168 (2000) 1], who found that the parameters presented for some systems in the Dechema Vapor–Liquid Equilibrium Data Collection [vol. I, Parts 1–8. Frankfurt/Main, Germany: DECHEMA (1977–1990)] do not correspond to the global optimum of the objective function used in that reference. Our experience with UNIQUAC allowed us to reach the same conclusion for this model.

Modeling and simulation of reactive distillation columns using computer algebra

Abstract This work presents an extension of a computer algebra (CA) program, Thermath , originally developed for the automatic implementation of physical property calculations, to generate computer codes in Fortran for the simulation of steady-state reactive distillation columns. The adopted procedure requires the simultaneous solution, using the Newton–Raphson method, of mass and energy balances, phase equilibrium equations, chemical equilibrium or rates of reaction equations and an additional equation needed to match the number of degrees of freedom. The Thermath program was used to obtain Fortran subroutines that implement these equations and their derivatives with respect to the process variables and the equation of state and/or excess Gibbs free energy model used in the simulation. The results are in excellent agreement with those available in the literature. By using Thermath , it was possible to reduce the time and effort needed to implement the mathematical models of multistage reaction–separation equipment.

Anisotropic parallel self-diffusion coefficients near the calcite surface: A molecular dynamics study

Applying classical molecular dynamics simulations, we calculate the parallel self-diffusion coefficients of different fluids (methane, nitrogen, and carbon dioxide) confined between two {101̄4} calcite crystal planes. We have observed that the molecules close to the calcite surface diffuse differently in distinct directions. This anisotropic behavior of the self-diffusion coefficient is investigated for different temperatures and pore sizes. The ion arrangement in the calcite crystal and the strong interactions between the fluid particles and the calcite surface may explain the anisotropy in this transport property.