phenomena of multiphase reactor performance

phenomena of multiphase reactor performance

1. Phenomena Affecting Multiphase (Dispersed) Reactor Performance Flow dynamics of the multi-phase dispersion - Fluid holdups & holdup distribution - Fluid and particle specific interfacial areas - Bubble size & catalyst size distributions Fluid macro-mixing - PDF’s of RTDs for the various phases Fluid micro-mixing - Bubble coalescence & breakage - Catalyst particle agglomeration & attrition Heat transfer phenomena - Liquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc. Energy dissipation - Power input from various sources ( e.g ., stirrers, fluid-fluid interactions,…) Reactor Model or Scale-Up Package

2. Chemical Processes: The Scale Issue Chemistry Chemistry + Interface Transport Chemistry + Interface Transport + Laboratory Scale Flow Patterns Chemistry + Interface Transport + Pilot Plant Scale Flow Patterns Chemistry + Interface Transport + Industrial Scale Flow Patterns Process scale-up is difficult mainly because the flow patterns (hydrodynamics) and associated transport effects are dependent on size and capacity of process This is further complicated because we do not have equally powerful flow imaging / diagnostic experimental and computational tools at different scales

3. Modeling Computational modelling is a method of representing a real world process by equations (model) Computational Modelling B E C D A Process Synthesis Retrofits R&D Equipment Design Process Improvement analysis

4. Coupling between Phases One-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. No influence of particulate phase on the gas phase. Two-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. Particulate phase reduces mean momentum and turbulent kinetic energy in fluid phase. Four-way coupling: Includes all two-way coupling. Particle-particle collisions create particle pressure and viscous stresses.

5. Gas Mean Motion Gas Fluctuating Motion Particle Mean Motion Particle Fluctuating Motion Turbulence Kinetic Theory of Granular Flow (KTGF) Drag Flux of kinetic energy Types of Interactions in Gas Solid Dispersed Flow Closure Problem

6. Multi Level Modeling Concept (Ultimate Wish) Continuum Models (Macroscopic) Large Scale Simulations Discrete particle model ( Mesoscopic ) Particle-particle interaction closure laws Lattice Boltzmann Model (microscopic) Fluid-particle interaction closure laws Experimental Validation Experimental Validation Experimental Validation

7. Models for Different Types Multiphase Flow

8. Empirical correlations Lagrangian Track Track individual point particle Particles do not interact Algebraic slip model Dispersed phase in a continuous phase. Solve one momentum equation for the mixture. Two-fluids theory (multi-fluids) Eulerian models. Solve as many momentum equations as there are phases. Discrete element method Solve the trajectories of individual objects and their collisions, inside a continuous phase. Fully resolved and coupled Increased complexity Modeling Approach

9. Algebraic Slip Model (ASM) Solves one set of momentum equations for the mass averaged velocity and tracks volume fraction of each fluid throughout domain. Assumes an empirically derived relation for the relative velocity of the phases. For turbulent flows, single set of turbulence transport equations solved. This approach works well for flow fields where both phases generally flow in the same direction.

10. Solves one equation for continuity of the mixture: Solves for the transport of volume fraction of one phase: Solves one equation for the momentum of the mixture: ASM E quations

11. Average density: Mass weighted average velocity: Velocity and density of each phase: Drift velocity: Effective viscosity: ASM Equations

12. Uses an empirical correlation to calculate the slip velocity between phases. f drag is the drag function. Slip Velocity and Drag

13. Applicable to low particle relaxation times < 0.001 - 0.01s. One continuous phase and one dispersed phase . No interaction inside dispersed phase . Volume fraction of discrete phase should be less than 10 % One velocity field can be used to describe both phases. No countercurrent flow. No sedimentation. Restrictions

14. Unstable flow in a 3-D bubble column with rectangular cross section. Bubble Column Example - ASM

15. Eulerian-Eulerian (Two Fluid) Model Solves momentum equations for each phase and additional volume fraction equations. Appropriate for modeling fluidized beds, risers, pneumatic lines, hoppers, standpipes, and particle-laden flows in which phases mix or separate. Discrete phase volume fractions from 0 to ~ 60%. Several choices for drag laws. Appropriate drag laws can be chosen for different processes. Several kinetic-theory based formulas for the granular stress in the viscous regime. Frictional viscosity based formulation for the plastic regime stresses. Added mass and lift force.

16. Granular Flow Regimes Elastic Regime Plastic Regime Viscous Regime. Stagnant Slow flow Rapid flow Stress is strain Strain rate Strain rate dependent independent dependent Elasticity Soil mechanics Kinetic theory

17. Collisional Transport Kinetic Transport Kinetic Theory of Granular Flow

18. Granular Multiphase Model: Description Application of the kinetic theory of granular flow Jenkins and Savage (1983), Lun et al. (1984), Ding and Gidaspow (1990). Collisional particle interaction follows Chapman- Enskog approach for dense gases (Chapman and Cowling, 1970). Velocity fluctuation of solids is much smaller than their mean velocity . Dissipation of fluctuating energy due to inelastic deformation. Dissipation also due to friction of particles with the fluid.

19. Particle velocity is decomposed into a mean local velocity and a superimposed fluctuating random velocity Analogous to the thermodynamic temperature of the gas, the ‘granular temperature’ is associated with this random fluctuation of fluctuating velocity of the solid particles. The source of the particle fluctuations come from collision with neighboring particles Granular Multiphase Model: Description k s =Kinetic Energy due to solids velocity fluctuation per unit mass

20. Gas Molecules and Particle Differences Solid particles are a few orders of magnitude larger. Velocity fluctuations of solids are much smaller than their mean velocity. The kinetic part of solids fluctuation is anisotropic. Velocity fluctuations of solids dissipates into heat rather fast as a result of inter particle collision. Granular temperature is a byproduct of flow.

21. Conservation Equations: Two-fluid Model Continuity: Phase denoted by: Density: Volume fraction: Velocity: Momentum: Solids pressure Stress-strain tensor Interphase momentum exchange coefficient Forces External body force Lift force Virtual mass force

22. Stress-Strain Tensor for Continuous Phase Dilatational Viscosity

23. Solids Stress-Strain Tensor Solids shear viscosity Collisional shear viscosity Kinetic viscosity: Syamlal Frictional Viscosity Bulk viscosity

24. Solids Pressure Lun et al Radial distribution function Granular Temperature Generation of energy by solids stress tensor Diffusion coefficient: Gidaspow, Syamlal et al Collisional dissipation of energy Coefficient of restitution

25. Interphase Momentum Exchange Coefficient Particulate relaxation time Reynolds number Terminal velocity correlation for solid phase Drag function: Syamlal-O’Brien Diameter Viscosity It is this drag function which makes different models for exchange coefficient

26. Granular Temperature k s =Kinetic Energy due to solids velocity fluctuation per unit mass Transport of solids fluctuating kinetic energy 1 2 3 4 1:Generation of energy by solid stress tensor 2:Diffusion of energy 3:Collisional dissipation of energy 4:Interphase energy exchange Kinetic Theory of Granular Flow (KTGF) Granular temperature is a flow dependent quantity as against thermodynamic temperature (Chapman and Cowling,, The Mathmatical Theory of Non-Uniform Gases (1961)) 27

27. Models for Different Types Multiphase Flow

28. 29 Eulerian-Lagrange Approach Fluid phase t reated as a “Continuum” Dispersed phase is tracked in a Lagrangian way Newton’s equation of motion is solved for dispersed phase Particle-particle collisions are included and modeled through spring dash-pot model.

29. 30 Discrete Element Modeling is an outgrowth of molecular dynamics simulations used in computational statistical physics. However , the discrete element method was independently developed by P. Cundall in the 1970’s.

30. 31 Approximate the collisional interactions between particles using idealized force models that dissipate energy. Integrate system equations of motion  Determine individual particle positions and velocities. Compute relevant transport quantities, bulk properties and analyze evolving microstructure. Basic Idea of DEM Modeling

31. 32 Initial positions, orientations and velocities Update particle link-list(find new or broken contacts) Calculate the force and torque on each particle Integrate the equation of motion to calculate the new positions, velocities and orientation Accumulate statistics to calculate transport properties Time increment: t = t + dt LOOP “F = ma” “T = I a ” Basic Flow Chart

32. 33 In contrast to the energy conservation of molecular systems-energy dissipation is a critical characteristic of granular systems, and consequently, it is necessary to employ realistic approximations to model energy loss in colliding particles. For this purpose, there are essentially two basic approaches. By considering particles to be infinitely stiff, “hard particle” models assume instantaneous, binary collisions governed by a collision operator, which is a function of particle properties (i.e., friction, normal and tangential restitution coefficients) and the pre- and post collisional velocities and spins. Such an approach is appropriate in collision-dominated systems, where continuous and/or multiple contacts are not characteristic. ‘Hard’ Particle Models ‘Soft’ Particle Models The interaction is a function of an allowed overlap between colliding particles that is intended to model the plastic deformation* at the contact.

33. 34 When particles collide, some of the kinetic energy is lost – that is, a portion of the initial kinetic energy goes into deforming the objects. Thus, a ball that is dropped and hits the ground will not rebound to the same height from which is was released. As a first approach, this energy loss is modeled through a “ coefficient of restitution ”, denoted by e . e = 1  No energy loss (perfectly elastic) e = 0  Complete energy loss (plastic) 0 < e < 1  A portion of the incident energy is loss Elementary Hard Particle Model

34. 35 The coefficient of restitution is related to the velocities of the two particles by the relation Consider a particle A of mass m A that has a velocity v A ,and collides with a stationary particle B of mass m B . What is the kinetic energy lost Δ KE during the impact? It can be shown that … A B V A V B Before collision A B After collision

35. DEM (Soft Sphere Approach) Solid Phase Gas Phase V=Volume of fluid cell 36 Contact Force Van-der Waal’s Force Drag Force

36. Modeling of Contact between Two Particles Ref:- Cundall and Strack , G é otechnique ,(1979) Soft sphere approach (Spring dashpot model) (Popularly known as ‘Distinct element method’ DEM) spring Dashpot slider F Force (N) k Spring constant [N/m] ξ Displacement [m] η Damping coefficient [Ns/m] v Velocity [m/s] μ Coefficient of friction [-] 37

37. 38 (a) (b) (c) Typical DEM Simulation for Fluidized Bed

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49. Analogy to Kinetic Theory of Gases Free streaming Collision Collisions are brief and momentarily. No interstitial fluid effect. Velocity distribution function Pair distribution function

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