(a) G = 0.050
kg·m-2·s-1, (b) G = 0.126
kg·m-2·s-1, (c) G = 0.214
kg·m-2·s-1
Besides, according to the visual observations, the movement of particles
would break up the liquid pockets or plugs between particles, and
inhibited the formation of local liquid blockages. Above all, the
movement of particles affected the formation of local liquid blockages
in three ways:
(1) The voidage increased with the solid flow rate,
(2) The dynamic liquid holdup decreased with the solid flow rate,
(3) The movement of particles would destroy the liquid pockets or plugs
between particles.
As a result, some pulse flow in the trickle bed shifted to trickle flow
when particles started to move because the movement of particles
inhibited the formation of local liquid blockage. Meanwhile, the liquid
mass flow rate required to form the local liquid blockage and initiate
the pulse was increased, and the transition boundary from trickle flow to
pulse flow in the three-phase moving bed shifted rightwards at a higher
solid flow rate as shown in Figure 4.
Prediction of the trickle-to-pulse transition
boundary
Previous studies have shown that the hydrodynamics are different in each
flow regime.
Therefore,
it is important to predict flow regime boundary accurately for the
design and scale-up of the three-phase moving bed. It can be seen from
Figure 4 that the trickle and pulse flow still exist in the three-phase
moving bed, which have the same characteristics as those presented in
the trickle bed. Thus, the models developed for the prediction of the
transition between the trickle flow and the pulse flow in the trickle
bed can work as a basis for the prediction in the three-phase moving
bed.
Although researchers have conducted model research on flow regime
transition for many years, estimation of the trickle to pulse flow
regime transition in the trickle bed is still not very
accurate44. Earlier models attempted to relate the
inception of pulse flow to a pore-scale phenomenon, which assumed that
the pulsing inception was due to the liquid pockets blocked the
interstices between particles45. While recent models
considered it as a macroscopic scale phenomenon, which assumed that the
pulsing inception was related to the instability in the liquid film due
to the gas shear46. Though macroscopic models were in
good agreement with the experimental data, the pore-scale physical
phenomenon was also important in the inception of the pulse flow. Up to
now, the understanding of the inception of pulse flow is limited, so
theoretical prediction of flow regime transition is difficult. In
summary, although researchers have tried to establish a mechanism model
for the prediction of flow regime transition in trickle bed, the
published models are still mainly empirical based on the correlations of
experimental data. Considering that in the three-phase moving bed the
multi-phase interactions will be more complex due to the movement of
particles, the empirical approach is still used in this work to
establish a model for the estimation of transition boundary in the
three-phase moving bed.
Wammes attempted to develop models based on the physical understanding
of the transition40. In his opinion, the mean
thickness of the liquid film on the particle surface was proportional to
the dynamic liquid holdup. When the thickness of the liquid film was
enough to collapse in the interstices between particles, the pulses
would be formed. A correlation had been derived based on a criterion
that assumed the transition occurring at some critical dynamic holdup
and it related the operating parameters as follows:
where, C =0.27 for water-N2 and 0.32 for 40%
ethylene glycol-N2, 𝛽t,tr is the
total liquid holdup at the transition and ugdenotes
the
superficial gas velocity.
In the trickle bed, the trickle-to-pulse flow transition boundary of the
system in this work was obtained and shown in Figure 2(c). Based on
equation (2), the prediction model for the trickle bed in this work
could be fit as follows:
In the three-phase moving bed, considering that the dynamic liquid
holdup decreased with the increase of the solid flow rate, we first
tried to just introduce the effect of solid flow rate on the dynamic
liquid holdup into equation (3) to develop a model for the prediction of
trickle-to-pulse transition. The dynamic liquid holdup in three-phase
moving bed was correlated with the gas and liquid Reynolds numbers and
the solid flow rate. The coefficients were obtained by multiple
regression techniques, and it could be expressed as equation (4). The
equation (4) could describe the dynamic liquid holdup at the flow regime
transition with an average relative error of 1.99%.
By combining equation (3) and (4), equation (5) was acquired, which
related the parameters governing the flow regime transition and
described the hydrodynamic condition at the transition.
Using equation (5), the corresponding transition boundary can be
acquired at the given solid flow rate, which is compared with the
experimental results in Figure 7. It can be seen from Figure 7 that when
only introducing effects of the solid flow rate on the dynamic liquid
holdup into the model of the trickle bed, it can roughly describe the
experimental trend at a lower solid flow rate
(us ≤2 mm/s), but at a larger solid flow rate
(us ≥3 mm/s), the predicted value and the
experimental value will show a large deviation. This result proves the
above explanation that the effect of the particle moving on the flow
regime transition is not only caused by the decreasing dynamic liquid
holdup but also caused by the increasing voidage and the destruction of
liquid pockets. Effects of the last two aspects are particularly
important at a larger solid flow rate.