# PhD Thesis Defence: Mr. Mr. Gadi Venkat Arunchaitanya (04/08/23)

### Thesis title:

A fundamental investigation of discrete liquid, gas and fines flow in a random packed bed along with applications

### Faculty advisor(s):

Prof. Govind S Gupta

### When?

04^{th} August, 2023 (Friday), 11:00 AM (India Standard Time)

### Where

KPA Auditorium, Dept of Materials Engineering

### Abstract

The liquid flow through a packed bed is quite common in many chemical engineering applications such as distillation, stripping, catalysis, and in metallurgical processes like blast furnace, heap leaching, etc. Many researchers have modelled the liquid flow in a packed bed using continuum hypothesis for both wetting and non-wetting conditions. However, from the physical observation made by various researchers, in a non-wetting or in a low liquid flow rate (heap leaching) system, it is found that the liquid flows not as a continuous stream but as a mixture of discrete rivulet(s) or droplet(s) or combination of both. The liquid flow in any direction, in a packed bed, depends on the local void shape and size. The deterministic approach to find out the void shape and size locally, is a big challenge which is lacking currently. Moreover, the effect of gas flow on the particles and liquid phase of the packed bed, taking into account the random nature of the bed and the discrete nature of the liquid, is lacking. The liquid holdup is another parameter which affects the multiphase flow and is calculated assuming the maximum holdup between the particles which may not be the case for unsaturated bed. Therefore, fundamental understanding of the liquid-solid-gas interactions in a random bed is important to improve the processes.

To understand the effect of gas-solid interaction, a shaft-based process is considered which are common in many disciplines such as in metallurgical and chemical engineering. However, their performance suffers due to the lack of understanding in solid and gas flow thus the heat and mass transfer inside the shaft. A slow-moving packed bed, inside the reactor, has been considered. Particles are discharged from the bottom and gas is injected laterally. The gas flow has been modelled using continuum-based fluid flow equations. Spatial variation of the voids in the random bed is calculated using cube divided particle volume (DPVM) approach. It is found that gas flow is not symmetric inside the reactor due to significant variation in void sizes inside the bed. This along with gas variation also affects the residence time of each particle inside the bed.

This work is extended to the liquid flow in random bed using Discrete Liquid Flow (DLF) theory. However, it is found that DPVM approach cannot provide the void shape which is an important parameter for DLF theory. Therefore, a novel graph-based recursive Depth First Search (DFS) algorithm is developed to find the shape and size of voids in the random bed. After this, the Discrete Liquid Flow (DLF) theory is used to model the liquid flow in a randomly packed bed where the shape and size of the void are given as inputs. DLF model considers the discrete nature of the flow taking into account the local non-uniformities of the packing. Random packing has been created using the Discrete Element Method (DEM). The liquid flow behaviour has been studied in various conditions, like changing the packing size and bed height. This study confirms that the bed topology plays an important role in dictating the liquid flow behavior in a randomly packed bed. The liquid flow behaviour in multi-size packing is also studied using DLF and DFS approach.

The study is further extended to heap leaching process, where the liquid flows as droplets and rivulets due to very low liquid flow rates. The liquid flow behaviour is studied in terms of tortuosity, liquid distribution, breakthrough time, contact angle etc. The study shows that heap leaching processes can be modelled in more accurate and deterministic way using DLF theory along with DFS algorithm by avoiding the uncertain experimental parameters (like bed permeability etc). The study shows that bed topology, the local velocity of the liquid, tortuosity, and liquid dispersion affect the distribution of the liquid and the amount of liquid in a heap packing.

It is observed that liquid static holdup is an important parameter in describing the multiphase flow properly. Therefore, the liquid static holdup between the contact points of particles is calculated using Young-Laplace equation with a modified approach for its solution which not only gives the maximum static holdup but also the intermediate values of it between the particles. Using the DLF, DFS, the various phenomena, which occur in a multiphase flow packed bed, such as rupturing of rivulets, liquid hysteresis (only dynamic holdup is considered while simulating hysteresis behaviour) have been understood and explained fundamentally.

Finally, the flow behaviour of the liquid phase in a random packed bed is studied, taking into account the movement of particles due to the lateral gas and fines injection. Gas and fines phase are modelled using continuum-based momentum conservation equations. This system resembles with the dripping zone of the blast furnace, where iron ore is converted to molten iron/slag (liquid), the liquid descends over the coke bed in the form of droplets and rivulets. The hot blast of air is injected laterally, along with the pulverized coal, from the tuyere region flows counter and cross-current to the liquid flow. A cavity, known as a raceway, is formed at the tuyere region due to the gas injection. This study shows that the cavity/raceway size increases due to the liquid injection. The deviation of the liquid path due to the gas and fines drag is also captured. It is found that the deviation of the liquid path is higher for the larger particle sizes.