Gas-solid Fluidised Beds and Two-Phase Systems

Question 1

Gas-solid fluidised beds are usually modelled as a two-phase system, using the Eulerian Multiphase flow equations.

(a) Outline the main physical processes involved (without the equations) in such a system and discuss which processes can be ignored when flow conditions are laminar. You may assume that gas is the continuous phase, and particles are the dispersed phase. [8 marks]
(b) Considering a gas-fluidised bed is made of spherical particles of diameter 0.0005m, and density of 2660 kg m-3, using an Excel spreadsheet, plot the drag coefficient variation with respect to the Reynolds number assuming:
(i) the Arastoopour expression and (ii) the Gidaspow expression using the three different equations for the drag equations. Discuss the differences.  [17 marks]

In your calculations in part (b) you may assume the following:

Question 2

(a) Using your knowledge of two phase gas fluidisation, design a fluidised bed such that the final bed height,is 0.30 m; the incoming gas velocity is and the bubbles formed have an effective diameter,of 0.03 m.

In you design you may consider the gas to be air with densit=1.288 kg m-3 and dynamic Viscosity=1.7x10-5 Pa s-1. You may also assume that the Ergun equation applies with a void fraction. The particles density =2660 kg m-3.

In you design you will need to estimate:
(i) The initial bed height, 
(ii) The fluidising velocity 
(iii) The necessary incoming gas velocity
(iv) The particle diameter, 

(b) Consider the rise of air bubbles in a vertical water column, rising under low Reynolds number conditions. Using an Excel spreadsheet, plot the variation of the terminal velocities of bubbles with radii ranging from 0.01 to 0.3 cm.

(c) The fluidisation velocity of an aggregative fluidised bed is = 10 m/s, whilst the void fraction is = 0.45. Assume a single bubble of an effective diameter = 2 cm is rising to the top of the bed, after the inlet flow rate is terminated. Determine the rising velocity of the bubble as well as the height of the bed, if the time taken by the bubble to reach the top of the bed is 2 s.

Question 3

(a) In a bubble column, the densities for the gas and liquid phases are ρG and ρL respectively. The flow quality is x. If the gas-liquid flow is homogenous, derive the expressions of the homogenous density of the mixture ρG. [6 marks]

(b) Explain why gas-liquid stratified flow often occurs in horizontal pipe but not in vertical pipe. [5 marks]

(c) In a horizontal stratified flow, the slip ratio of gas velocity to liquid velocity is s. If the cross-sectional gas void fraction is εG, what is the gas volume fraction V? 

(d) In an oil and gas plant, a fixed volumetric flow rates of gas and liquid are mixed and then fed into a vertical pipe. A waspy annular flow was formed in the vertical pipe. Provided that the flow rates of gas and liquid and the pipe position cannot be changed, what suggestion would you make to avoid this flow pattern? Use appropriate equation to justify your suggestion.