Investigation of the Influence of Bubble-bubble Interactions on the Hydrodynamics of Bubbling Gas-solid Fluidised Beds Using the Discrete Bubble Model

To investigate the hydrodynamic behaviour of industrial scale bubbling fluidised bed reactors, a 3D Discrete Bubble Model (DBM) has been developed. In the DBM, an Euler-Lagrange model, the bubbles are treated as discrete elements and the bubble trajectories are tracked individually, while the emulsion phase is considered as a continuum and is described with the continuity and Navier-Stokes equations. The main advantage of the DBM is that it fully accounts for the two-way coupling, allowing computation of the prevailing macroscopic circulation patterns in large scale gas-fluidised beds. In this paper, we have examined the effect of bubble-bubble (wake) interactions on the macro-scale velocity profiles using the DBM. It has been found that the extent of the macroscopic circulation is significantly increased by the bubble-bubble interaction forces. NOMENCLATURE C closure [-] D distribution function [m] F force [N] g gravitational acceleration [m.s] l bubble-bubble interaction coefficient [-] m bubble-bubble interaction coefficient [-] m mass of a bubble [kg] NX number of grid cells in x-direction [-] NY number of grid cells in y-direction [-] NZ number of grid cells in z-direction [-] P pressure [Pa] R radius of bubble [m] t time [s] U emulsion phase velocity [m.s] V volume [m] v bubble velocity [m.s] x x-position [m] y y-position [m] z z-position [m] ε volume fraction [-] ρ density [kg.m] τ stress tensor [Pa ] Φ source term [N.m] Subscript b bubble d distance or drag e emulsion g gravitational p pressure tot total vm virtual mass x x-direction y y-direction z z-direction 1 leading bubble 2 tailing bubble ∞ velocity of a undisturbed bubble INTRODUCTION Bubbling gas-solid fluidised beds have found widespread application in the chemical process industries. An important process based on gas-solid fluidisation is the UNIPOL process for the production of polyolefins such as polyethylene and polypropylene. This process uses highly active and selective catalysts, resulting in an enormous heat production, which needs to be removed from the fluidised bed reactor. The temperature of the reactor is not allowed to exceed the melting temperature of the polymer, because the polymer particles will start to melt and stick together. Despite the excellent heat transfer inside a fluidised bed, the heat removal rate limits the production capacity. One of the mechanisms with which heat is removed from the reactor is convective heat transfer via the emulsion phase. The convective heat transfer is mainly governed by the macroscopic circulation patterns that are largely induced by the bubbles. Therefore, quantitative information about the macroscopic circulation patterns of the emulsion phase is needed to improve the heat removal rate from the fluidised bed. To describe the macroscopic circulation patterns prevailing in dense gas-solid fluidised bed reactors, a 3D Discrete Bubble Model (DBM) has been developed. In the DBM, an Euler-Lagrange model, the bubbles are modelled as discrete spherical elements and are tracked individually with Newton’s second law during their rise through the emulsion phase. The emulsion phase is considered as a continuum, for which the continuity and Navier-Stokes equations are solved. In this paper, the influence of bubble-bubble interactions on the macro-scale circulation patterns in the emulsion phase is studied with the DBM.