Abstract
The application of a volume average Navier-Stokes equation for the prediction of pressure drop in packed beds consisting of uniform spherical particles is presented. The development of the bed permeability from an assumed porous microstructure model is given. The final model is quasi-empirical in nature, and is able to correlate a wide variety of literature data over a large Reynolds number range. In beds with wall effects present the model correlates experimental data with an error of less than 10%. Numerical solutions of the volume averaged equation are obtained using a penalty finite element method.
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Abbreviations
- d :
-
length of a representative unit cell
- d e :
-
flow length in Representative Unit Cell
- d p :
-
characteristic pore size
- D T :
-
column diameter
- D P :
-
equivalent particle diameter
- e v :
-
energy loss coefficient for elbow
- f app :
-
apparent friction factor
- f v :
-
packed bed friction factor, defined by Equation (30)
- F :
-
term representing impermeability of the porous medium
- I :
-
integral defined by Equation (3)
- L :
-
length of packed column
- N :
-
Number of RUC in model microstructure
- P :
-
pressure
- P ∈ :
-
interstitial pressure
- P′:
-
pressure deviation
- Rep :
-
Reynolds number,v p ρd p/μ
- Res :
-
Reynolds number,v s ρd/gm
- Reb :
-
Reynolds number,v s ρD p/μ
- S fs :
-
fluid solid contact area
- T :
-
tortuosity
- v :
-
fluid velocity
- v′:
-
velocity deviation
- v p :
-
velocity in a pore
- v s :
-
superficial velocity in the medium
- v ∈ :
-
interstitial velocity
- V o :
-
total volume of representative unit cell
- V ∈ :
-
pore volume of representative unit cell
- Δ:
-
change in indicated property
- u :
-
normal vector onS fs
- ε :
-
porosity
- μ :
-
viscosity
- ρ :
-
density
- η :
-
coefficient in unconsolidated permeability model
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Hayes, R.E., Afacan, A. & Boulanger, B. An equation of motion for an incompressible Newtonian fluid in a packed bed. Transp Porous Med 18, 185–198 (1995). https://doi.org/10.1007/BF01064677
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DOI: https://doi.org/10.1007/BF01064677