Estimate of solid flow rate from pressure measurement in circulating fluidized bed

Abstract

A method is described to estimate solid mass flow rate based on measurement of pressure drop in horizontal section of circulating fluid bed (CFB). A theoretical model was derived based on momentum balance equation and used to predict the solids flow rate. Several approaches for formulating such models are compared and contrasted. A correlation was developed that predicts the solids flow rate as a function of pressure drop measured in the horizontal section of piping leading from the top of the riser to the cyclone, often referred to as the cross-over. Model validation data was taken from literature data and from steady state, cold flow, CFB tests results of five granular materials with various sizes and densities in which the riser was operated in core-annular and dilute flow regimes. Experimental data were taken from a 0.20 m ID crossover piping and compared to literature data generated in a 0.10 m ID cross-over pipe. The solids mass flow rate data were taken from statistically designed experiments over a wide range of Froude number U 2 g gD ; 25-200 , load ratio Gs ρg Ug ; 0:2-23 , Euler number 2ΔP Horiz ρg U 2 g ; 2-50 , density ratio ρp −ρg ρg ; 60-2000 , Reynolds number ρg Ug dp μg ; 60-1600 , and Archimedes number ρs −ρg ð Þρgd 3 p μ 2 g ; 29-9500 ! . Several correlations were developed and tested to predict the solids mass flux based on measuring pressure drop in the horizontal section of CFB. It was found that load ratio G s ρ g U g is a linear function of the Euler number 2ΔP Horiz ρ g U 2 g! and that each of these expressions all worked quite well (R 2 N 95%) for the data within the range of conditions from which the coefficients were estimated. Published by Elsevier B.V.

Dynamic modeling of the circulating fluidized bed riser

“…When gas and solids exit the vertical riser, the particles accelerate along the horizontal pipe along with the gas. The solids concentration is usually very low in the crossover [24], [25], [26], [27]. With a dilute flow of solids existing in the crossover, it is assumed that the average particle velocity (u p,co ) attains the value of the superficial gas velocity (U g,co ) suggesting a zero slip between the gas and solids (Eq.…”

Measuring Technologies for CFB Solid Circulation Rate: A Review and Future Perspectives

“…In Yang's experiment [29], the pressure drop between the riser exit and the inlet of the cyclone was fitted to the solid circulation rate, and a different formula from Patience was obtained. Monazam et al [30] tried to use a dimensionless quantity for revising the formula. The authors showed a more detailed consideration of parameters in same momentum balance equation and proposed a formula associating dimensionless solid flux G s ρ g v gh with the Euler number Eu: G s…”

Solids circulation behaviour in a circulating fluidized bed with a concentric annular feeding mechanism

“…[ 11 ] To determine the solids circulation rate in both laboratory and commercial CFB systems, a number of devices, [ 12–15 ] techniques, [ 16–21 ] and methods [ 22–24 ] have been proposed and evaluated. The simplest method to estimate solids circulation rate is based on the measurement of pressure drops across different sections of the system, including the horizontal section between the exit of riser and the cyclone, [ 22,25 ] over the abrupt riser exit, [ 11 ] over the standpipe dense bed, [ 23 ] over the top section of the riser, [ 26 ] and over the whole riser. [ 27 ] To our knowledge, there has been no report on exploring the use of pressure drop between the riser inlet and the annulus in the bottom solids entrance region to determine G s in an a‐CFB system.…”