Ergun equation is NOT applied in which one of the following unit operations to analyze gas flow behavior:
Show Hint
- Blast Furnace
- Sintering
- Roasting
- LD Converter
The Correct Option is D
Solution and Explanation
The Ergun equation gives the pressure drop of a fluid flowing through a fixed, packed bed of solid particles. It combines a viscous (laminar) friction term and an inertial (turbulent) friction term,
\[ \frac{\Delta P}{L} = \frac{150(1-\varepsilon)^2\mu U}{\varepsilon^3 d_p^2} + \frac{1.75(1-\varepsilon)\rho U^2}{\varepsilon^3 d_p} \]
where \(\varepsilon\) is the bed voidage, \(d_p\) is the particle size, \(U\) is the superficial gas velocity, and \(\mu\), \(\rho\) are the gas viscosity and density. This equation only makes sense when the gas is forced to flow through a bed made of stationary solid particles, since \(\varepsilon\) and \(d_p\) only exist for such a bed.
Step 2: Check the blast furnace.
A blast furnace is charged from the top with layers of coke, iron ore and flux, forming a deep packed bed. Hot blast gas is blown in near the bottom and rises up through this bed. The Ergun equation is the standard tool used to analyze this gas flow and the pressure drop through the burden, so it applies here.
Step 3: Check sintering.
In sintering, a bed of fine ore, coke fines and flux is laid on a moving strand, and air is drawn downward through this packed bed by suction, burning the coke fines and fusing the mix into sinter. This is again flow through a packed particulate bed, so the Ergun equation applies.
Step 4: Check roasting.
Roasting of ores, for example in a fluidized or packed bed roaster, also involves gas passing through a bed of particulate solid ore. Analyzing the gas flow and pressure drop through such a bed again calls for the Ergun equation.
Step 5: Check the LD converter.
An LD (Linz-Donawitz) converter is a steelmaking vessel where high purity oxygen is blown as a high velocity jet through a water-cooled lance directly onto or into a bath of molten metal. There is no bed of solid particles for the gas to pass through, the oxygen jet interacts with a liquid metal bath, not a packed bed of solids. Since \(\varepsilon\) and \(d_p\) have no meaning here, the Ergun equation cannot be applied to this process.
Step 6: Final Answer.
The blast furnace, sintering and roasting all involve gas flowing through a packed particulate bed, but the LD converter involves a gas jet blown into a liquid bath with no particulate bed at all.
\[ \boxed{\text{LD Converter}} \]
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