4094
Ind. Eng. Chem. Res. 2009, 48, 4094–4100
A Model To Predict the Concentration of Submicrometer Solid Particles in Viscous Media Confined inside Horizontal Cylindrical Channels Herbert Lorı´a* and Pedro Pereira-Almao Department of Chemical and Petroleum Engineering, Schulich School of Engineering, UniVersity of Calgary, Calgary, Alberta T2N 1N4, Canada
Carlos E. Scott In Situ Energy, UniVersity of Calgary, Calgary, Alberta T2N 1N4, Canada and Facultad de Ciencias, Escuela de Quı´mica, UniVersidad Central de Venezuela, Caracas 47102, Venezuela
As light oil reserves dwindle, the extraction and processing of heavy crude oils are becoming increasingly important. The use of ultradispersed catalysts (nanometric catalytic particles dispersed in the oil) is considered to be a promising way to upgrade these materials. To simulate such processes, mass transfer of the ultradispersed particles must be estimated. However, an adequate mathematical expression to describe the motion of these particles through viscous media in a horizontal cylindrical channel is still missing. In this paper, we developed and solved a time-dependent, two-dimensional convective-dispersive model, which simulates the transient deposition and suspension of ultradispersed particles immersed in a viscous medium, inside the cross section of a horizontal cylindrical channel in a stagnant situation. The results of the modeling are compared with a series of experiments that permit knowledge of the concentration of the ultradispersed particles inside a horizontal cylinder. These experiments were performed using particles in the submicrometer range (average sizes of 198 nm) and fluid media with diverse densities and viscosities. The effect of the fluid medium properties and the initial particle concentration in the calculation of the dispersion coefficient was also studied. The conditions needed to maintain the solid particles suspended in the liquid medium, contained in a vessel with cylindrical geometry, are also unveiled by the presented model. 1. Introduction Mass transfer and deposition of fine particles in cylindrical channels has received considerable attention for a long time, becasuse of its practical significance and direct application in industry. For example, this knowledge is helpful in aerosol classification and its deposition under electrical fields, formation of deposits in heat exchangers and pipelines, hydrodynamic field chromatography, thrombus formation in organs, on the dispersion of catalysts for heavy crude oil hydroprocessing, among others.1 A theoretical prediction of the particle deposition in such systems would be very useful for the design and optimization of these processes. The research on particle concentration profiles in vertical and horizontal channels has experienced significant advancement in the last few decades. Forney and Spielman2 investigated the phenomenon of sedimentation of particles in vertical flow and gave expressions for the sedimentation velocity of particles for a wide range of particle diameters. Continuing with the research in vertical geometries, Shah et al.3 performed work in the measurement of concentration profiles and dispersion coefficients on gas-liquid-solid column beds. Kelkar and Shah4 expanded this work by collecting experimental dispersion coefficients data for continuous three-phase bubble columns, wherein all three phases flow continuously. Laurinat and Hanratty5 took into account the motion of the particles in different directions and proposed an empirical fit to a representative deposition flux profile, as a function of the angle around the cylindrical channel cross section in horizontal flow. The determination of the driving forces present in the settling * To whom correspondence should be addressed. Tel.: +1 403 210 95 90. Fax: +1 403 210 39 73. E-mail address:
[email protected].
of particles immersed in fluids has been studied by Mols and Oliemans.6 They have modeled the dispersion and deposition as a combined process of diffusion and gravitational settling fluxes of particles in a one-dimensional problem between two horizontal plates. In the case of the conversion of heavy fractions and removal of contaminants, hydroprocessing technologies (such as hydrotreating and hydrocracking) are the most commonly used refinery processes. Hydrotreating processes are designed to remove contaminants such as sulfur, nitrogen, condensed aromatic rings, or metals, whereas hydrocracking are important conversion processes to produce high-value naphtha or distillate products from a wide range of refinery feedstocks. These technologies require elevated catalyst consumption and demands considerable amounts of hydrogen to produce highly profitable and desired fuel products. They use porous supported catalysts with particles several millimeters in diameter, which suffer from severe deactivation due to coke formation on the catalyst surface, leading to pore plugging and a reduction of active sites exposed for the reaction.7 Therefore, development of new technologies or improvement of existing ones is required for incorporating heavy crude oils to the markets. Ultradispersed catalysts are an alternative technology for heavy oil hydroprocessing, and it has been demonstrated that they are significantly more active than the conventional supported catalysts, reducing the temperatures for hydroprocessing reactions.7 Ultradispersed catalysts are formulated in reduced particle sizes (
