Paulo L.C. Lage

Experimental determination of bubble size distributions in bubble columns: prediction of mean bubble diameter and gas hold up

Bubble diameters were measured photographically in a bubble column, which was operating in the homogeneous regime with air and aqueous isopropanol solutions. The bubble size data were determined for several values of the superficial gas velocity, and used to fit bubble size distributions. The gas hold up was measured under the same conditions and its values were calculated from the bubble size distributions, using the theory for the conservation of the bubble size distribution function. The experimental results were compared to bubble size predictions given by models of bubble formation in orifices and to results from well-known correlations for the gas hold up. It has been verified that the models for bubble formation in orifices give reasonable predictions of the mean bubble diameter, while the correlations for gas hold up lead to poor agreement with the experimental data. The indirect measurement of gas hold up from the bubble size distribution was considerably more accurate.

Development and implementation of a polydispersed multiphase flow model in OpenFOAM

Abstract The two-phase flow solver implemented in the open-source OpenFOAM code was extended to a multiphase flow formulation ( n dispersed and one continuous phases) and then coupled to the population balance equation (PBE) solution by the Direct Quadrature Method of Moments (DQMOM), originating a polydispersed multiphase flow solver. Although each dispersed phase has its own velocity field, the present implementation considers only the interfacial momentum exchange between the continuous and the dispersed phases. The multiphase flow formulation was described and the details of the PBE–CFD coupling algorithms in OpenFOAM were provided. The implementation of the multiphase flow code was verified and evaluated against the original OpenFOAM two-phase flow solver for flow through a 2D backward facing step, using simplified breakage and aggregation kernels. The computational cost of both codes were compared for serial and parallel simulations.

On the numerical solution and optimization of styrene polymerization in tubular reactors

A model for the steady-state operation of styrene polymerization in a tubular reactor considering radial variation of the relevant variables was solved by the method of lines using either finite volume discretization or global spline orthogonal collocation. The finite volume solution has shown to be slightly more efficient and more robust than the orthogonal collocation solution. The former solution was used to optimize the steady-state operation of a three-section tubular reactor by selecting the wall temperature of each section. The optimization target is to obtain maximal conversion with minimum polymer polydispersity. These conflicting objectives were joined in a parametric global objective function. As it is multimodal, its global minimum for each value of the parameter was obtained by the particle swarm optimization method. The optimal operational conditions allow the production of polymers with lower polydispersity at the same conversion level obtained when uniform temperature exists at the reactor wall.

Simulating oil flow in porous media under asphaltene deposition

Abstract A simulator for one-phase flow in porous media near a wellbore is coupled with a thermodynamic model and a network model in order to predict the change in petroleum flow under asphaltene deposition. The thermodynamic model is capable of predicting the quantity of precipitated asphaltene. The network model is used to predict formation damage due to in situ asphaltene deposition. The model is qualitatively evaluated using data from literature. Results are in concordance with expected physical behavior.

On the representation of QMOM as a weighted-residual method—The dual-quadrature method of generalized moments

Abstract Quadrature-closed moment-based methods for the solution of the population balance equation were analyzed. The QMOM was shown to be a particular case of a method based on generalized moments (QMoGeM). Then, a weighted-residual method (WRM) based on the generalized moments was derived (WRMoGeM). If it is closed by the Gauss–Christoffel quadrature, the resulting method (QWRMoGeM) was shown to be identical to the QMoGeM, giving the correct representation of QMOM as a WRM. The WRMoGeM formulation was used to derive a new method (DuQMoGeM) that employs two quadrature rules, one for discretizing the particulate system and other to accurately integrate the integrals in the equations for the generalized moments. A Galerkin version of this method was implemented and used to solve several examples with known analytical solutions. The DuQMoGeM solutions for breakage and aggregation problems were shown to be more accurate than the QMOM solutions.

Heat and mass transfer modeling during the formation and ascension of superheated bubbles

A previously developed model for the heat and mass transfer of a single superheated bubble during the ascension stage was extended to include the formation stage. It allows variable properties and bubble radius changes, solving the gas conservation equations coupled to a bubble dynamics model. Its results were used to predict the existing experimental data in a direct contact evaporator with good agreement. A correction factor for isothermal gas hold-up correlations can be fully calculated by the model enabling good prediction of gas hold-up. The constant property assumption overestimates the gas hold-up and should not be used. Experimental data for steam bubbling process could be reasonably simulated using the superheated bubble model with some additional assumptions.

The quadrature method of moments for continuous thermodynamics

A new pseudo-component characterization method was developed. It is based on a Gaussian quadrature rule whose weight function is the molar fraction distribution of the complex mixture. Due to its accuracy, this quadrature was shown to be more adequate than the conventional Gaussian quadrature rules to obtain polynomial approximations of any molar fraction distribution function and to calculate any property of the corresponding mixture. A new method was proposed for the solution of continuous thermodynamics flash and mixing operations. It can be applied to continuous or discrete molar fraction distributions and it is adaptive in the sense that the pseudo-component characterization evolves according to the compositional changes. It was shown to be more accurate than the conventional Gaussian quadrature discretization method. Being based on the conservation of the moments of the distributions, it can be called the quadrature method of moments (QMOM) for continuous thermodynamics.

Comparison of the accuracy and performance of quadrature-based methods for population balance problems with simultaneous breakage and aggregation

Simulations of polydisperse multiphase flows must include the effects of particle breakage and aggregation, which requires the solution of the population balance equation (PBE). Therefore, the analysis of the existing numerical techniques to solve the PBE regarding their efficiency and accuracy is paramount to their implementation in CFD codes. This work focused on analyzing the three quadrature-based methods available in the literature (QMOM, DQMOM and PPDC) in terms of efficiency and accuracy and against the classical method of classes. Analytical solutions were used to derive test cases from dominant breakage to dominant aggregation. The methods were evaluated in terms of moment accuracy and convergence. The computational costs were evaluated for all cases. It was verified that PPDC has poor convergence and is not adequate. For all cases, the QMOM and DQMOM solutions presented similar accuracy, but the DQMOM was the most efficient method.

Towards a polydisperse molecular thermodynamic model for asphaltene precipitation in live-oil

A polydisperse molecular thermodynamic model is developed to predict the asphaltene precipitation in crude oil under reservoir conditions. Asphaltenes are characterized as a continuous family that follows a distribution function taken from the fractal aggregation theory. Discretization of the continuous family is made by using collocation points chosen as the roots of an orthogonal polynomial. It is assumed that the asphaltenes form a pseudo-liquid phase, free of other components. The parameters of the model were adjusted to fit experimental data available from the literature. A satisfactory representation of these data was obtained, showing a better agreement than the earlier models. A sensitivity analysis is performed in order to evaluate the influence of the model parameters on predicted values.

Kinetic Rates of the Fischer Tropsch Synthesis on a Co/Nb2O5 Catalyst

Abstract The kinetics of the Fischer-Tropsch reaction over a Co/Nb 2 O 5 catalyst in a fixed bed reactor was investigated experimentally. Experiments were carried out under isothermal and isobaric conditions ( T =543 K, P =2.1 MPa) and under different conditions of several H 2 /CO feed molar ratio (0.49–4.79), space velocities (0.2–3.8 h −1 ), mass of catalyst (0.3–1.5 g), and CO conversion (10%–29%). Synthesis gas conversion was measured and data were reduced to estimate the kinetic parameters for different Langmuir-Hinshelwood rate expressions. Differential and integral reactor models were used for the nonlinear regression of kinetics parameters. One of the rate equations could well explain the data. The hydrocarbon product distributions that were experimentally determined exhibited an unusual behavior, and a possible explanation was discussed.