Tutorial Modeling of monolith reactors

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Continuum converter models • Classical porous media models treat the domain as a continuum containing fluid and solid phases. • The common term for developing the resulting equations is called volume averaging – the balances are made on a representative elemental volume that contains both fluid and solid • Each node in the computational domain represents both a fluid and a solid – the spatial identity is lost. • The conservation equations are then fairly classical: Zygourakis, K. (1989). Chemical Engineering Science, 44, 2075-2086. 54
Momentum balance equation Velocity and pressure are obtained from the Volume Averaged Navier- Stokes equation and the equation <strong>of</strong> continuity: ⎡ ( ) ( T ( ) ) ⎛2η ⎞ ⎤ ρ vi∇ v = ∇i⎢− pI + η ∇ v + ∇v − ⎜ −κ⎟( ∇ iv) I + S i 3 ⎥ ⎣ ⎝ ⎠ ⎦ ( v) 0 ∇i ρ = The velocity is the superficial velocity. The source term S accounts for the porous inertia. The Brinkman equation is a classical version <strong>of</strong> the VANS ⎛ μ 1 S i = − ⎜ v i + C2 ρ 2 f v ⎝ K v i ⎞ ⎟ ⎠ K is the permeability. For laminar flow, the second term is zero. 55
Page 1 and 2:
Introduction to Monolith Reactor Mo
Page 3 and 4: Why use computer modelling? • Exp
Page 5 and 6: Observations • The problem involv
Page 7 and 8: Model Scales Micro scale: At the at
Page 9 and 10: Mathematical formulation • The fu
Page 11 and 12: Basic models in common use • Sing
Page 13 and 14: The 3D SCM • The real monolith do
Page 15 and 16: The 2D approximate SCM • The 2D m
Page 17 and 18: The 2D SCM • All of the physical/
Page 19 and 20: Modelling the fluid domain Velocity
Page 21 and 22: Modelling the washcoat domain • T
Page 23 and 24: Diffusion in the washcoat • Diffu
Page 25 and 26: Modelling the substrate domain The
Page 27 and 28: Comparing 2D and 3D models • The
Page 29 and 30: Comparing 2D and 3D models • The
Page 31 and 32: Comparing 2D and 3D models Percenta
Page 33 and 34: Review of boundary layer flow Flow
Page 35 and 36: Boundary layers in a tube • At th
Page 37 and 38: Heat and mass transfer • Heat and
Page 39 and 40: 1D SCM mass balances The fluid phas
Page 41 and 42: 1D SCM energy balances The fluid ph
Page 43 and 44: Nusselt and Sherwood numbers • Fo
Page 45 and 46: Nusselt and Sherwood numbers • Ho
Page 47 and 48: Nusselt and Sherwood numbers • Ho
Page 49 and 50: Simplified 1D models • Dispersion
Page 51 and 52: Models for the converter • In rea
Page 53: Discrete converter models • A pas
Page 57 and 58: Energy balances The fluid phase ene
Page 59 and 60: Continuum model • In effect, the
Page 61 and 62: Model validation • All models mus
Page 63 and 64: Model validation - Example Heating
Page 65: Advertising supplement R.E. Hayes a
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Tutorial Modeling of monolith reactors

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