Fluid Dynamics Scaling of a Gas–Liquid Distributor Applied to a Commercial Ebullated Bed Hydroprocessor

Abstract

A new scaling approach for a gas–liquid distributor is proposed and experimentally validated on a commercial bubble cap geometry. The geometric similarity was achieved by matching distributor fractional opening and ratios of various critical dimensions. The dynamic similarity was attained by matching three dimensionless groups (gas–liquid density ratio, liquid Reynolds number, and gas Froude number) and bubble coalescence behavior. Two geometrically similar distributors with one and three smaller bubble caps were experimentally compared through resulting bubble size distributions to test the scaling laws. A reasonably good agreement was found at various pressures, suggesting that the scaling approach could also work at industrially relevant conditions. New models for bubble size distribution and drag coefficient were developed to explicitly account for the effect of the gas–liquid distributor and thus improve the fluid dynamics modeling of commercial ebullated bed hydroprocessors.

Fluid Dynamics Modeling of a Commercial Ebullated Bed Hydroprocessor

“…One key assumption made here is that the bubble size distribution generated at the grid is preserved through the bed and freeboard regions. For similar operating conditions and when bubble coalescence was significantly inhibited, Pjontek et al 21 found both local and global gas holdups measured in the freeboard to match those measured in a bubble column. This suggested that the bubble size distribution generated at the grid is likely preserved through the bed and freeboard regions.…”

“…Grid Distributor. Mach et al 21 proposed a scaling approach for a gas−liquid distributor and experimentally validated it on a geometrically scaled version of the industrial bubble cap grid. The scaling was based on ensuring both geometric and dynamic similitude.…”

“…To determine freeboard gas holdup, multiple bubble classes were constructed and their probability densities estimated using the bubble size distribution model presented in section 2.1.1. The drag coefficient of an individual bubble class was estimated using the model developed in the study of Mach et al 21 and presented in eq 42. The rise velocity of an individual bubble class can be determined using eq 41, which is derived from a force balance on an individual bubble in a swarm.…”

“…Mach et al 21 proposed and experimentally validated a scaling approach for a gas−liquid distributor based on the industrial bubble cap geometry. Geometrical scaling was achieved by matching the distributor fractional open area and ratios of critical dimensions.…”

“…The drag coefficient was found to decrease with increasing pressure at constant gas holdup. This effect was attributed to 21 will be used to predict phase holdups in the unit. Further, the size distribution model will be coupled with the gas−liquid separation model proposed by Lane et al 15 to better predict recycled gas and liquid flow rates and, consequently, phase holdups.…”