(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.