A gas of density ρ = 0.9487 kg/m3 and dynamic viscosity μ = 3.1 × 10−5Pa s flows through the bed with a superficial mass flow velocity of 1.4 kg/m2 s. Determine the pressure drop in the bed….THE EQUATIONS.
| Packed bed length, ft | 60 |
|---|---|
| Density of fluid at flowing conditions, lb/ft3 | 0.413 |
| Fluid viscosity, cP | 0.0278 |
Is Ergun’s equation valid for packed bed flow?
Flow through a packed bed can be described by the Ergun Equation. It tells us the pressure drop along the length of the packed bed given some fluid velocity. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density.
How do you find the porosity of a packed bed?
The local radial porosity, εz(r), can be obtained by setting the lower and upper specific axial positions to the same particular axial location within the cylindrical packed bed. Mathematically, this is represented by the following equation, ε z ( r ) = ∑ H * f 1 H * f 1 ε ( r ) z / N z .
How do you find the superficial velocity of a packed bed?
The simplest way is by dividing the volumetric flow rate (m3/min) by the cross sectional area of the fixed bed (m2).
Is the Ergun equation empirical?
A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. The results are compared to the Ergun equation, which is empirically based on experimental measurements, and the correspondence is shown to be remarkably close.
How is Ergun equation derived?
The Ergun equation, derived by the Turkish chemical engineer Sabri Ergun in 1952, expresses the friction factor in a packed column as a function of the modified Reynolds number.
How accurate is the Ergun equation?
The Ergun equation is only able to accurately predict the pressure drop of single-phase flow over spherical particles, whereas it systematically under predicts the pressure drop of single-phase flow over non-spherical particles.
What is interstitial velocity in packed bed?
Interstitial Velocity. The convective fluid velocity between the particles of a packed bed is called the “average fluid interstitial linear velocity” or, simply, the “interstitial velocity.” Interstitial velocity is the superficial velocity adjusted for the cross-section of the actual fluid flow in a packed column.
How do you calculate superficial velocity?
The velocity of fluid moving through a pipe, defined as the volumetric flow rate of that fluid divided by the cross-sectional area. In monophasic flow, it is equal to the mean velocity of the fluid.
Is Ergun equation empirical?
The results are compared to the Ergun equation, which is empirically based on experimental measurements, and the correspondence is shown to be remarkably close.
How do you calculate interstitial velocity?
Interstitial velocity is calculated as the air volume divided by the cross-sectional area of the collection minus the cross-sectional area of the bag: What is optimal interstitial velocity?
What is the Ergun equation for flow through a bed?
This equation is commonly referred to as the Ergun equation for flow through a randomly packed bed of spheres and takes the following form: − Δ P H = 1 5 0 μ U ( 1 − ε) 2 x 2 ε 3 + 1. 7 5 ρ f U 2 ( 1 − ε) x ε 3.
How do you calculate energy loss in Ergun equation?
The original Ergun equation of the total energy loss can be rearranged as follows: ρ c = density of catalyst, lb/ft 3 ρ b = density of packed bed, lb/ft 3 For completely turbulent flow, it is assumed that fp approaches a constant value for all packed beds with the same relative roughness.
How do you calculate the pressure drop of a packed bed?
The pressure drop can be calculated from the classic Ergun equation for packed beds: (38) ∂ P ∂ Z = − ( 150 ɛ B 3 ( d p , s p φ p ) 2 ( 1 − ɛ B ) 2 η G u G + 1.75 ɛ B 3 ( d p , s p φ p ) ρ u ( 1 − ɛ B ) )
What is the relationship between Ergun and Kozeny-Carman equations?
This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation which describes laminar flow of fluids across packed beds via the first term on the right hand side.
