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Chapter 10 β€’ Theory & Derivations

Unit 10: Extractive Metallurgy: Iron, Steel & Specialty Alloys

Comprehensive pyrometallurgical and thermodynamic treatise on ferrous extractive metallurgy: iron ore preparation (sintering, pelletizing), coke making, iron blast furnace transport phenomena and Baur-Glaessner phase equilibria, slag basicity and desulfurization mechanics, Basic Oxygen Furnace (BOF) supersonic oxygen decarburization kinetics, ladle secondary metallurgy, vacuum degassing, and continuous casting.

Β§10.1 Iron Ore Beneficiation, Agglomeration (Sintering & Pelletizing) & Coke Chemistry

The production of virgin metallic iron requires three primary solid feedstocks: iron-bearing burden, metallurgical coke, and limestone/dolomite fluxing agents.

1. Iron Ore Burden Agglomeration

Natural fine iron ores ($< 6\text{ mm}$, hematite $\text{Fe}_2\text{O}_3$, magnetite $\text{Fe}_3\text{O}_4$) cannot be charged directly into a blast furnace because fine particles blind the gas voids, causing fluidization and catastrophic gas channel blowouts:

  • Sintering: A blend of fine ore ($50 - 60\%$), coke breeze ($3 - 5\%$), flux (limestone, dolomite), and moisture is ignited under suction on a traveling grate (Dwight-Lloyd sintering machine). Combustion temperatures ($1250 - 1350^\circ\text{C}$) initiate partial surface melting, fusing the fines into porous, permeable clinker-like sinter cakes.
  • Pelletizing: Ultra-fine concentrates ($< 45\,\mu\text{m}$) are rolled with bentonite clay binders and water in rotating disc pelletizers into green balls ($9 - 16\text{ mm}$), then fired in an induration furnace at $1250 - 1350^\circ\text{C}$ to crystallize interlocking hematite bridges.

2. Metallurgical Coke Manufacturing Chemistries

Metallurgical coke provides three indispensable functions in the blast furnace: (1) chemical reducing agent ($\text{CO}$ gas generation), (2) thermal fuel source, and (3) permeable mechanical support grid supporting the entire burden column in the high-temperature dripping and hearth zones where all other iron materials have melted into liquid.

  • Coking Process: High-volatile, medium-volatile, and low-volatile bituminous coking coals are blended and heated to $1000 - 1100^\circ\text{C}$ in the absence of air in vertical slot coke ovens for $18 - 24\text{ hours}$.
  • Volatile matter ($20 - 35\%$) is driven off as coal chemicals (coke oven gas, coal tar, ammonium sulfate, crude benzol).
  • Coal softens into a plastic mass ($350 - 450^\circ\text{C}$), resolidifies into semi-coke, and contracts into a rigid, highly porous ($45 - 55\%$ voidage), mechanically strong carbon matrix ($> 88 - 90\text{ wt}\%\text{ fixed carbon}$).

Β§10.2 The Iron Blast Furnace: Aerodynamics, Tuyere Raceways & Thermal Zones

The iron blast furnace is a massive counter-current chemical reactor ($30 - 40\text{ m}$ height, hearth diameter up to $14 - 15\text{ m}$) operating continuously for campaigns of $15 - 20\text{ years}$ without shutdown, producing up to $10,000 - 12,000\text{ metric tons/day}$ of liquid pig iron (hot metal).

``` THE IRON BLAST FURNACE REACTOR Solid Burden Charging (Alternating Layers: Sinter/Pellets + Coke) β”‚ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” <── Top Gas (~200Β°C: CO, CO2, N2 to Scrubbers) β”‚ THROAT β”‚ β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”˜ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β”‚ SHAFT / STACKβ”‚ (Upper Shaft: Indirect Reduction 400-800Β°C) β”‚ β”‚ (Lower Shaft: Wustite Reduction 800-1000Β°C) β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”˜ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β”‚ BOSH BELLY β”‚ (Cohesive / Softening-Melting Zone: 1000-1350Β°C) β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”˜ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” <── Tuyeres: Hot Blast (1150-1250Β°C) + Pulverized Coal (PCI) β”‚ RACEWAY ZONE β”‚ C + 0.5 O2 ──> CO (Flame Temp ~2100-2250Β°C) β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”˜ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” ──> Slag Notch: Liquid Blast Furnace Slag (~1450Β°C) β”‚ HEARTH β”‚ ──> Taphole: Liquid Hot Metal / Pig Iron (~1450-1500Β°C) β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ ```

1. Tuyere Combustion & Raceway Aerodynamics

Preheated air blast ($1150 - 1250^\circ\text{C}$), enriched with oxygen ($2 - 5\%\text{ O}_2$) and auxiliary pulverized coal injection (PCI), is blown through water-cooled copper tuyeres ($28 - 40$ nozzles) at sonic velocities ($200 - 250\text{ m/s}$):

  • Fast combustion of coke creates a violent swirling cavity ("raceway"):
$$\text{C}(s) + \frac{1}{2}\text{O}_2(g) \longrightarrow \text{CO}(g) \quad \Delta H_{298}^\circ = -110.5\text{ kJ/mol}$$
$$\text{C}(s) + \text{H}_2\text{O}(g) \longrightarrow \text{CO}(g) + \text{H}_2(g) \quad (\Delta H = +131.3\text{ kJ/mol})$$
  • The adiabatic flame temperature ($\text{RAFT}$) in the raceway reaches $2100 - 2250^\circ\text{C}$.
  • The ascending reducing gas ("bosh gas", $35 - 40\text{ vol}\%\text{ CO}, 1 - 4\text{ vol}\%\text{ H}_2, 56 - 60\text{ vol}\%\text{ N}_2$) ascends through the burden column at $1 - 3\text{ m/s}$, transferring heat and reducing descending iron oxides.

2. Five Internal Process Zones

1. Lumpy Zone ($200 - 900^\circ\text{C}$): Solid state. Gas permeability is high through alternating coke and ore layers.

2. Cohesive Zone (Softening & Melting, $1000 - 1350^\circ\text{C}$): Iron ores soften and melt into impermeable liquid layers; gas can only pass upward through the interspersed "coke windows."

3. Active Coke Dripping Zone ($1350 - 1500^\circ\text{C}$): Molten droplets of iron and slag trickle down through the solid coke matrix.

4. Raceway Zone ($1500 - 2200^\circ\text{C}$): Intense combustion and primary gas formation.

5. Hearth ($1450 - 1500^\circ\text{C}$): Liquid hot metal ($\rho \approx 7.0\text{ g/cm}^3$) settles to the bottom, covered by an immiscible protective layer of liquid slag ($\rho \approx 2.6\text{ g/cm}^3$).

Β§10.3 Blast Furnace Reduction Thermochemistry: Baur-Glaessner Diagram & Direct vs Indirect Reduction

The stepwise reduction of iron oxides by carbon monoxide proceeds through three distinct oxidation states above $570^\circ\text{C}$:

$$\text{Hematite } (\text{Fe}_2\text{O}_3) \overset{400 - 600^\circ\text{C}}{\longrightarrow} \text{Magnetite } (\text{Fe}_3\text{O}_4) \overset{600 - 900^\circ\text{C}}{\longrightarrow} \text{WΓΌstite } (\text{Fe}_{1-x}\text{O}) \overset{> 900^\circ\text{C}}{\longrightarrow} \text{Metallic Iron } (\text{Fe})$$

Below $570^\circ\text{C}$, wΓΌstite is thermodynamically unstable, and magnetite reduces directly to metallic iron ($\text{Fe}_3\text{O}_4 \to \text{Fe}$).

1. Indirect Reduction (Reduction by Gas)

Occurs in the upper and middle shaft ($400 - 900^\circ\text{C}$) where gaseous $\text{CO}$ acts as the reducing agent without directly consuming solid carbon:

  1. $3\text{Fe}_2\text{O}_3 + \text{CO} \longrightarrow 2\text{Fe}_3\text{O}_4 + \text{CO}_2 \quad (\Delta H = -52.8\text{ kJ/mol Fe}_2\text{O}_3 \text{ [Exothermic]})$
  2. $\text{Fe}_3\text{O}_4 + \text{CO} \rightleftharpoons 3\text{FeO} + \text{CO}_2 \quad (\Delta H = +36.4\text{ kJ/mol Fe}_3\text{O}_4 \text{ [Endothermic]})$
  3. $\text{FeO} + \text{CO} \rightleftharpoons \text{Fe} + \text{CO}_2 \quad (\Delta H = -17.2\text{ kJ/mol FeO} \text{ [Exothermic]})$

2. Direct Reduction (Reduction by Carbon)

Occurs in the high-temperature lower shaft and bosh ($T > 950 - 1000^\circ\text{C}$). The reduction of wΓΌstite is coupled to the endothermic Boudouard reaction (carbon gasification):

$$\text{FeO} + \text{CO} \rightleftharpoons \text{Fe} + \text{CO}_2 \quad (\Delta H = -17.2\text{ kJ/mol})$$
$$\text{CO}_2 + \text{C}(s) \rightleftharpoons 2\text{CO} \quad (\Delta H = +172.5\text{ kJ/mol})$$

Sum of the two reactions gives the net Direct Reduction:

$$\text{FeO} + \text{C}(s) \longrightarrow \text{Fe} + \text{CO} \quad (\Delta H_{298}^\circ = +155.3\text{ kJ/mol})$$

Direct reduction is intensely endothermic, requiring massive thermal heat supplied by burning additional coke at the tuyeres. Optimal blast furnace thermal efficiency balances the degree of direct reduction ($r_d$) at approximately $25 - 35\%$, with the remaining $65 - 75\%$ executed by indirect reduction.

The Baur-Glaessner Phase Equilibrium Diagram

Plots $\% \text{CO} / (\% \text{CO} + \% \text{CO}_2)$ vs temperature $T$:

  • At $800^\circ\text{C}$, the equilibrium gas composition for wΓΌstite reduction ($\text{FeO} + \text{CO} \rightleftharpoons \text{Fe} + \text{CO}_2$) requires at least $68\text{ vol}\%\text{ CO}$ and no more than $32\text{ vol}\%\text{ CO}_2$.
  • Consequently, blast furnace top gas can never convert all $\text{CO}$ to $\text{CO}_2$; the gas discharged at the furnace throat always contains significant residual chemical energy ($20 - 24\text{ vol}\%\text{ CO}$), which is scrubbed and combusted to fire the hot blast stoves and power plant boilers.

Standard Enthalpies & Free Energies of Iron Blast Furnace Reactions

| Reaction | $\Delta H_{298}^\circ$ ($\text{kJ/mol}$) | $\Delta G^\circ(1000\text{ K})$ ($\text{kJ/mol}$) | Reaction Type | Location in Furnace | |---|---|---|---|---| | $\text{C} + \frac{1}{2}\text{O}_2 \to \text{CO}$ | $-110.5\text{ kJ}$ | $-200.3\text{ kJ}$ | Exothermic | Tuyere Raceway | | $\text{C} + \text{CO}_2 \rightleftharpoons 2\text{CO}$ | $+172.5\text{ kJ}$ | $-5.2\text{ kJ}$ | Intensely Endothermic | Lower Shaft / Bosh | | $3\text{Fe}_2\text{O}_3 + \text{CO} \to 2\text{Fe}_3\text{O}_4 + \text{CO}_2$ | $-52.8\text{ kJ}$ | $-72.1\text{ kJ}$ | Exothermic | Upper Shaft ($400 - 600^\circ\text{C}$) | | $\text{Fe}_3\text{O}_4 + \text{CO} \to 3\text{FeO} + \text{CO}_2$ | $+36.4\text{ kJ}$ | $+12.4\text{ kJ}$ | Endothermic | Middle Shaft ($600 - 800^\circ\text{C}$) | | $\text{FeO} + \text{CO} \rightleftharpoons \text{Fe} + \text{CO}_2$ | $-17.2\text{ kJ}$ | $-3.8\text{ kJ}$ | Exothermic | Shaft ($800 - 1000^\circ\text{C}$) | | $\text{FeO} + \text{C} \to \text{Fe} + \text{CO}$ | $+155.3\text{ kJ}$ | $-9.0\text{ kJ}$ | Strongly Endothermic | Bosh / Hearth ($> 1000^\circ\text{C}$) | | $\text{CaCO}_3 \rightleftharpoons \text{CaO} + \text{CO}_2$ | $+178.2\text{ kJ}$ | $+18.0\text{ kJ}$ | Endothermic | Middle Shaft ($800 - 900^\circ\text{C}$) |

Β§10.4 Blast Furnace Slag Chemistry: Basicity Indices, Desulfurization & Viscosity

The primary non-metallic product of the blast furnace is liquid slag ($250 - 350\text{ kg slag / metric ton hot metal}$), formed by the fusion of ore gangue ($\text{SiO}_2, \text{Al}_2\text{O}_3$), coke ash, and added limestone/dolomite flux ($\text{CaO}, \text{MgO}$).

1. Slag Basicity Indices

Slag chemistry is governed by the ratio of basic network-modifying oxides to acidic network-forming silica:

  • Binary Basicity ($B_2$):
$$B_2 = \frac{\% \text{CaO}}{\% \text{SiO}_2}$$
  • Ternary Basicity ($B_3$):
$$B_3 = \frac{\% \text{CaO} + \% \text{MgO}}{\% \text{SiO}_2}$$
  • Quaternary Optical Basicity ($\Lambda$):

Calculated from individual oxide polarizabilities. For stable furnace operation, $B_2$ is targeted between $1.15$ and $1.25$. If $B_2 > 1.35$, the slag becomes overly basic; its liquidus temperature rises abruptly, precipitating dicalcium silicate ($\text{C}_2\text{S}$) crystals that make the slag viscous, crusty, and untappable. If $B_2 < 1.05$, the acidic slag exhibits excellent fluidity but loses its chemical ability to desulfurize the iron.

2. Hot Metal Desulfurization Thermodynamics

Sulfur is an intensely detrimental impurity in steel, causing hot shortness (brittleness during rolling due to low-melting intergranular $\text{FeS-Fe}$ eutectics at $988^\circ\text{C}$). Over $85 - 90\%$ of sulfur entering the blast furnace originates from coke. In the hearth, liquid slag extracts dissolved sulfur from the molten iron across the interface:

$$[\text{FeS}]_{(\text{metal})} + (\text{CaO})_{(\text{slag})} + [\text{C}]_{(\text{metal})} \rightleftharpoons (\text{CaS})_{(\text{slag})} + [\text{Fe}]_{(\text{metal})} + \text{CO}(g)$$

Ionic representation:

$$[\text{S}] + (\text{O}^{2-}) + [\text{C}] \rightleftharpoons (\text{S}^{2-}) + \text{CO}(g)$$

The equilibrium Sulfur Partition Ratio ($L_S$):

$$L_S = \frac{(\% \text{S})_{\text{slag}}}{[\% \text{S}]_{\text{metal}}} = K_{\text{desulf}} \cdot \frac{a_{\text{O}^{2-}} \cdot a_{[\text{C}]}}{p_{\text{CO}}}$$

High desulfurization requires:

  1. High basicity (high free oxygen ion activity $a_{\text{O}^{2-}}$).
  2. Reducing conditions (high carbon activity $a_{[\text{C}]} \approx 1.0$, saturated in hot metal).
  3. Elevated hearth temperatures ($1480 - 1520^\circ\text{C}$), which accelerate interfacial diffusion and increase $K_{\text{desulf}}$.

Under optimal operation, $L_S \approx 30 - 60$, reducing sulfur in hot metal to $0.025 - 0.040\text{ wt}\%$. Granulated blast furnace slag is vitrified with water jets and ground into GGBS for eco-friendly cement.

Β§10.5 Primary Steelmaking: Basic Oxygen Furnace (BOF) Supersonic Decarburization Kinetics

Hot metal tapped from the blast furnace is unsuitable for engineering structures because it contains excessive dissolved carbon ($4.0 - 4.5\text{ wt}\%$) and impurities ($0.4 - 0.8\%\text{ Si}$, $0.3 - 0.7\%\text{ Mn}$, $0.08 - 0.15\%\text{ P}$, $0.03\%\text{ S}$), rendering it extremely brittle. The Basic Oxygen Furnace (BOF / LD Converter) converts liquid pig iron into high-purity molten steel in under $16 - 20\text{ minutes}$ of supersonic oxygen blowing:

``` BASIC OXYGEN FURNACE (BOF / LD) Water-cooled Oxygen Lance (Mach 2.0-2.2 Supersonic Jets) β”‚ β–Ό β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β” β”‚ CONVERTER β”‚ <── Molten Hot Metal (75-80%) + Scrap Steel (20-25%) β”‚ VESSEL β”‚ <── Burnt Lime (CaO) + Dolomite Flux β”‚ (MgO-C Ref.)β”‚ β”‚ β”‚ ──> Foamy Emulsion: Gas (CO/CO2) + Liquid Slag + Droplets β”‚ [Hot Metal]β”‚ β””β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”˜ β”‚ Bottom Tuyeres: Inert Gas Stirring (Ar / N2) β–Ό Tapped Molten Steel (~1650Β°C, Carbon 0.04-0.08%) to Ladle Metallurgy! ```

1. Supersonic Oxygen Jet Dynamics

Pure oxygen gas ($> 99.5\%\text{ O}_2$) is injected through a multi-orifice water-cooled copper lance positioned $1.5 - 2.5\text{ m}$ above the bath at supply pressures of $10 - 14\text{ bar}$. Converging-diverging de Laval nozzles accelerate the gas to Mach $2.0 - 2.2$ ($600 - 700\text{ m/s}$):

  • The supersonic jet penetrates deep into the liquid metal bath, creating an intensely turbulent hot spot ($2400 - 2600^\circ\text{C}$).
  • Millions of liquid iron droplets are atomized into the slag phase, generating a high-surface-area ($> 2,000\text{ m}^2/\text{ton}$) foamy metal-slag-gas emulsion.

2. Sequential Oxidation Cascade

Oxidation reactions are fiercely exothermic, supplying all thermal energy required to melt $20 - 25\text{ wt}\%$ cold scrap steel without external fuel:

1. Silicon Oxidation ($0 - 3\text{ minutes}$):

$$[\text{Si}] + \text{O}_2(g) \longrightarrow (\text{SiO}_2) \quad (\Delta H = -820\text{ kJ/mol})$$

Rapidly forms primary acidic silicate slag, requiring immediate addition of calcined lime ($\text{CaO}$) to prevent refractory dissolution.

2. Manganese Oxidation:

$$[\text{Mn}] + \frac{1}{2}\text{O}_2(g) \longrightarrow (\text{MnO}) \quad (\Delta H = -385\text{ kJ/mol})$$

3. Decarburization ($3 - 14\text{ minutes}$):

$$[\text{C}] + \frac{1}{2}\text{O}_2(g) \longrightarrow \text{CO}(g) \quad (\Delta H = -110.5\text{ kJ/mol})$$

At high carbon concentrations ($[\% \text{C}] > 0.3\%$), decarburization is limited solely by oxygen mass delivery rate (Constant Rate Regime, $d[\text{C}]/dt \approx 0.25 - 0.35\text{ wt}\%/\text{min}$). Below $[\% \text{C}] \approx 0.25\%$, the reaction rate transitions to liquid-phase carbon diffusion control:

$$\frac{d[\% \text{C}]}{dt} = - k_m \frac{A}{V} ([\% \text{C}] - [\% \text{C}]_e)$$

4. Dephosphorization:

$$2[\text{P}] + 5(\text{FeO}) + 3(\text{CaO}) \rightleftharpoons (\text{CaO})_3\cdot\text{P}_2\text{O}_5 + 5\text{Fe} \quad (\Delta H < 0)$$

Favored by high slag basicity ($B_2 > 3.0$), high oxidizing potential ($(\% \text{FeO}) \approx 15 - 20\%$), and low steel temperature during the initial blow.

Β§10.6 Secondary Steelmaking: Ladle Refining (LF), Vacuum Degassing (VD/RH) & Deoxidation

Liquid steel tapped from the BOF contains excess dissolved oxygen ($400 - 800\text{ ppm O}$) and dissolved gases ($[\text{H}] \approx 3 - 6\text{ ppm}, [\text{N}] \approx 40 - 80\text{ ppm}$). Secondary steelmaking refines the steel inside a refractory-lined transfer ladle prior to solidification:

1. Deoxidation (Killing of Steel)

As steel cools and solidifies, the solubility of oxygen drops precipitously, reacting with carbon to produce carbon monoxide gas bubbles that cause destructive blowholes and porosity:

  • Aluminum Deoxidation: Aluminum wire or ingots are added to the tap stream:
$$2[\text{Al}] + 3[\text{O}] \rightleftharpoons (\text{Al}_2\text{O}_3)(s) \quad (\Delta H_{298}^\circ = -1,215\text{ kJ/mol})$$

The equilibrium constant is given by:

$$K_{\text{Al}} = [\% \text{Al}]^2 [\% \text{O}]^3 \approx 10^{-14} \text{ at } 1600^\circ\text{C}$$

Dissolved oxygen plummets from $> 600\text{ ppm}$ to $< 3\text{ ppm}$.

  • Inclusion Flotation: Inert argon gas is bubbled through a porous refractory plug in the ladle bottom. Rising bubble plumes capture solid alumina ($\text{Al}_2\text{O}_3$) micro-inclusions, floating them into a synthetic calcium aluminate top slag. Calcium wire injection ($\text{Ca-Si}$) converts sharp solid alumina into spherical, harmless liquid calcium aluminate inclusions ($12\text{CaO}\cdot 7\text{Al}_2\text{O}_3$).

2. Vacuum Degassing (VD & Ruhrstahl-Heraeus / RH Process)

Under vacuum ($p < 1 - 2\text{ mbar}$):

  • Hydrogen Removal (Flake Elimination): Dissolved hydrogen ($[\text{H}] > 2\text{ ppm}$) causes delayed hydrogen-induced cracking and brittle shatter cracks in heavy forgings. Sieverts' law:
$$[\% \text{H}] = K_H \sqrt{p_{\text{H}_2}}$$

Exposing liquid steel to $1\text{ mbar}$ vacuum lowers dissolved hydrogen to $< 1.2\text{ ppm}$.

  • Vacuum Decarburization: Enables production of Ultra-Low Carbon (ULC) steels ($[\% \text{C}] < 0.003\%$ / $30\text{ ppm}$) for automotive outer panels by shifting $[\text{C}] + [\text{O}] \rightleftharpoons \text{CO} \uparrow$ forward.

Β§10.7 Electric Arc Furnace (EAF), Direct Reduced Iron (DRI) & Continuous Casting

The circular scrap-based steelmaking route and modern strand casting technology represent the pinnacle of modern ferrous metallurgical efficiency:

1. Electric Arc Furnace (EAF) Technology

Modern ultra-high-power (UHP) EAFs melt $100\%$ recycled scrap steel or blended Direct Reduced Iron ($\text{DRI}$) using electrical energy:

  • Three massive graphite electrodes ($600 - 750\text{ mm}$ diameter) powered by a $100 - 150\text{ MVA}$ furnace transformer strike high-current electric arcs ($40 - 60\text{ kA}$, arc temperature $> 3500 - 4000^\circ\text{C}$) directly into the scrap charge.
  • Specific electrical consumption averages $350 - 420\text{ kWh/metric ton}$, assisted by oxy-fuel supersonic burners and chemical carbon/oxygen lances.

2. Direct Reduced Iron (DRI / Sponge Iron)

DRI is solid metallic iron ($92 - 96\text{ wt}\%\text{ Fe}$, Metallization $\ge 94\%$) produced by solid-state gaseous reduction of iron ore pellets without melting (e.g., Midrex or Energiron process):

$$\text{Fe}_2\text{O}_3 + 3\text{H}_2 \longrightarrow 2\text{Fe} + 3\text{H}_2\text{O}$$
$$\text{Fe}_2\text{O}_3 + 3\text{CO} \longrightarrow 2\text{Fe} + 3\text{CO}_2$$

Utilizing green hydrogen ($\text{H}_2$) instead of natural gas enables zero-carbon steelmaking, reducing $\text{CO}_2$ emissions by $> 95\%$.

3. Continuous Casting of Steel (Concast / Billet-Slab Casters)

Eliminating discrete ingot casting, continuous casting solidifies molten steel directly into endless semi-finished blooms, billets, or slabs:

1. Ladle to Tundish: Steel drains from the transfer ladle through a ceramic shroud into a refractory tundish that dampens fluid surges and splits flow into multiple casting strands.

2. Oscillating Copper Mold: Steel flows through a submerged entry nozzle (SEN) into a curved, water-cooled copper mold oscillating vertically ($100 - 200\text{ cycles/min}$) with synthetic mold powder lubrication. A solid steel shell ($10 - 25\text{ mm}$ thickness) freezes against the copper walls.

3. Secondary Spray Cooling Zone: The strand is withdrawn along a curved roller apron by motorized pinch rolls while high-pressure water/air-mist spray nozzles solidify the liquid steel core.

4. Torch Cutting: Flying oxy-gas torches cut the continuous strand into discrete slabs ($1.5 - 2.5\text{ m}$ width) or billets ($150 \times 150\text{ mm}$) ready for hot rolling.

Β§10.8 The Green Steel Transition: 100% Hydrogen Shaft DRI & Near-Zero Carbon Steelmaking

Ferrous extractive metallurgy is responsible for approximately $7 - 9\%$ of total global $\text{CO}_2$ emissions ($1.85\text{ metric tons CO}_2\text{ / metric ton crude steel}$ via the traditional BF-BOF route). The transition to near-zero carbon steelmaking centers on green hydrogen reduction:

1. 100% Pure Hydrogen Direct Reduction (H2-DRI)

Replacing fossil carbon monoxide with renewable electrolytic hydrogen:

$$\text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \longrightarrow 2\text{Fe}(s) + 3\text{H}_2\text{O}(g) \quad \Delta H_{298}^\circ = +98.8\text{ kJ/mol}$$
  • Thermodynamic Contrasts with Carbon Monoxide Reduction:
  • Reduction by $\text{H}_2$ is endothermic ($\Delta H > 0$), whereas reduction by $\text{CO}$ is exothermic ($\Delta H < 0$). Heat must be continuously supplied by electric preheating of the circulating hydrogen gas loop.
  • Molecular hydrogen ($\text{H}_2$) possesses a tiny molecular radius and a gas diffusivity in porous ore pellets approximately $4\times$ faster than $\text{CO}$, accelerating reduction kinetics and permitting smaller reactor shaft volumes.
  • Discharges purely non-polluting water vapor ($\text{H}_2\text{O}$) rather than greenhouse carbon dioxide ($\text{CO}_2$).

2. Hybrid Electric Arc Furnace (EAF) Melting & Slag Foaming

The resulting carbon-free Direct Reduced Iron ($\text{H}_2\text{-DRI}$) is transferred hot ($650^\circ\text{C}$) to an Electric Arc Furnace:

  • Carbon Injection for Slag Foaming: In an EAF, a foamy slag is essential to shield water-cooled furnace walls from radiant arc heat and maximize arc thermal efficiency. Since $\text{H}_2\text{-DRI}$ contains $0\%\text{ C}$, a controlled charge of biogenic carbon (biochar) is injected through lances to generate foamy $\text{CO}$ bubbles ($[\text{C}] + (\text{FeO}) \to \text{Fe} + \text{CO} \uparrow$).
  • Lifecycle Decarbonization: Pairing renewable solar/wind power with PEM water electrolyzers and $\text{H}_2\text{-DRI-EAF}$ slashes steel lifecycle carbon emissions to $< 0.05\text{ t CO}_2\text{ / t steel}$ ($> 97\%$ reduction).

University Honors Industrial Case Study: Hydrogen-Induced Delay Cracking (HIC) & Ladle RH Degassing

In ultra-high-strength structural steels (yield strength $> 800 - 1,000\text{ MPa}$), microscopic atomic hydrogen dissolved during steelmaking induces delayed, catastrophic brittle failure:

  • Hydrogen Trapping & Recombination: In the liquid state ($1600^\circ\text{C}$), molten steel dissolves up to $6 - 8\text{ ppm}$ of atomic hydrogen ($[\text{H}]$). During cooling and solidification, hydrogen solubility plummets by an order of magnitude.
  • Supersaturated interstitial hydrogen diffuses to micro-voids, non-metallic inclusions ($\text{Al}_2\text{O}_3, \text{MnS}$), and grain boundary dislocations, recombining into molecular hydrogen gas ($\text{H}_2$):
$$2[\text{H}] \longrightarrow \text{H}_2(g)$$
  • The trapped molecular gas develops enormous internal hydrostatic pressures ($> 1,000 - 5,000\text{ MPa}$), nucleating microcracks and internal "flakes" that fracture under low external service stresses.
  • Ruhrstahl-Heraeus (RH) Vacuum Circulation Degasser:

Molten steel is drawn through two refractory snorkels into a vacuum chamber ($p < 1.0\text{ mbar}$). Argon gas lift bubbles circulate the steel at $120 - 150\text{ tons/min}$. Under deep vacuum, Sieverts' law drives hydrogen desorption, stripping dissolved hydrogen down to $< 1.0 - 1.2\text{ ppm}$ in under $15 - 20\text{ minutes}$.

Medium Example 10.1: Blast Furnace Iron Balance & Coke Consumption Calculation

A blast furnace produces $4,000\text{ metric tons/day}$ ($166.67\text{ t/h}$) of liquid hot metal.

  • Hot metal composition: $94.0\text{ wt}\%\text{ Fe}$, $4.2\text{ wt}\%\text{ C}$, $1.0\text{ wt}\%\text{ Si}$, and $0.8\text{ wt}\%$ other elements.
  • Iron burden contains $85.0\text{ wt}\%\text{ hematite sinter}$ ($58.0\text{ wt}\%\text{ Fe}$) and $15.0\text{ wt}\%\text{ pellets}$ ($65.0\text{ wt}\%\text{ Fe}$).
  • Dust and sludge losses carry out $1.5\%$ of total charged iron.
  • The metallurgical coke contains $88.0\text{ wt}\%\text{ fixed carbon}$.
  • Specific carbon consumption is measured as $420.0\text{ kg carbon / metric ton hot metal}$.
  1. Calculate the daily consumption of iron burden (sinter + pellets) in metric tons.
  2. Determine the daily coke consumption in metric tons.
  3. Calculate the specific coke rate in $\text{kg coke / metric ton hot metal}$.

Step 1: Iron Burden Consumption

Daily hot metal production:

$$M_{\text{hot metal}} = 4,000\text{ metric tons/day}$$

Total metallic iron required in product:

$$M_{\text{Fe, product}} = 0.940 \times 4,000 = 3,760\text{ metric tons Fe/day}$$

Accounting for $1.5\%$ iron dust loss ($98.5\%$ recovery):

$$M_{\text{Fe, charged}} = \frac{3,760\text{ t}}{0.985} = 3,817.26\text{ metric tons Fe/day}$$

Weighted average iron content of the burden:

$$w_{\text{Fe, burden}} = 0.850(0.580) + 0.150(0.650) = 0.4930 + 0.0975 = 0.5905 \quad (59.05\%\text{ Fe})$$

Total daily iron burden required:

$$M_{\text{burden}} = \frac{3,817.26\text{ t Fe}}{0.5905} = 6,464.45\text{ metric tons/day}$$
  • Sinter required: $0.85 \times 6,464.45 = 5,494.8\text{ metric tons/day}$.
  • Pellets required: $0.15 \times 6,464.45 = 969.7\text{ metric tons/day}$.

Step 2: Coke Consumption

Total carbon required per day:

$$M_{\text{carbon}} = 4,000\text{ t hot metal} \times 0.4200\text{ t carbon/t} = 1,680.0\text{ metric tons carbon/day}$$

Since coke is $88.0\text{ wt}\%$ fixed carbon:

$$M_{\text{coke}} = \frac{1,680.0\text{ t}}{0.880} = 1,909.09\text{ metric tons coke/day}$$

Step 3: Specific Coke Rate

$$\text{Coke Rate} = \frac{1,909.09\text{ t coke}}{4,000\text{ t hot metal}} \times 1,000\text{ kg/t} = 477.27\text{ kg coke / t hot metal}$$

The furnace consumes $6,464\text{ t/day}$ iron burden and $1,909\text{ t/day}$ coke (coke rate $= \mathbf{477.3\text{ kg/t}}$).

Easy Example 10.2: WΓΌstite Indirect Reduction Thermodynamics & Equilibrium CO Requirement

In the middle shaft of a blast furnace at $800^\circ\text{C}$ ($1073.15\text{ K}$), wΓΌstite is reduced by carbon monoxide:

$$\text{FeO}(s) + \text{CO}(g) \rightleftharpoons \text{Fe}(s) + \text{CO}_2(g)$$

Experimental thermodynamic parameters at $800^\circ\text{C}$ give an equilibrium constant of $K_p = 0.470$.

$$\text{Total shaft pressure is } P = 2.50\text{ bar absolute.}$$
  1. Express $K_p$ in terms of partial pressures and calculate the equilibrium ratio of carbon monoxide to carbon dioxide ($p_{\text{CO}} / p_{\text{CO}_2}$).
  2. Determine the minimum volume percentage ($\text{vol}\%$) of $\text{CO}$ required in a binary $\text{CO}-\text{CO}_2$ atmosphere to reduce wΓΌstite spontaneously to metallic iron at $800^\circ\text{C}$.

Step 1: Equilibrium Partial Pressure Ratio

Since solids have unit activity ($a_{\text{FeO}} = a_{\text{Fe}} = 1$):

$$K_p = \frac{p_{\text{CO}_2}}{p_{\text{CO}}} = 0.470$$

The equilibrium ratio of $\text{CO}$ to $\text{CO}_2$:

$$\frac{p_{\text{CO}}}{p_{\text{CO}_2}} = \frac{1}{K_p} = \frac{1}{0.470} \approx 2.1277$$

Step 2: Minimum Volume Percentage of $\text{CO}$

In a binary gas mixture ($p_{\text{CO}} + p_{\text{CO}_2} = P$):

$$y_{\text{CO}} + y_{\text{CO}_2} = 1.00$$
$$y_{\text{CO}_2} = K_p \cdot y_{\text{CO}} = 0.470 \cdot y_{\text{CO}}$$

Substitute into the sum:

$$y_{\text{CO}} + 0.470 \cdot y_{\text{CO}} = 1.00 \implies 1.470 \cdot y_{\text{CO}} = 1.00$$
$$y_{\text{CO}} = \frac{1.00}{1.470} = 0.68027 \quad (68.03\%)$$

Spontaneous reduction of wΓΌstite at $800^\circ\text{C}$ requires a gas atmosphere containing at least $68.0\text{ vol}\%\text{ CO}$ (maximum $32.0\text{ vol}\%\text{ CO}_2$).

Medium Example 10.3: Slag Basicity Modulus & Hot Metal Desulfurization Partition

A blast furnace slag is analyzed by XRF:

  • $\text{CaO} = 41.5\text{ wt}\%$
  • $\text{SiO}_2 = 34.0\text{ wt}\%$
  • $\text{Al}_2\text{O}_3 = 14.5\text{ wt}\%$
  • $\text{MgO} = 7.5\text{ wt}\%$
  • $\text{S} = 1.50\text{ wt}\%$
  1. Calculate the Binary Basicity ($B_2 = \frac{\% \text{CaO}}{\% \text{SiO}_2}$) and Ternary Basicity ($B_3 = \frac{\% \text{CaO} + \% \text{MgO}}{\% \text{SiO}_2}$).
  2. The furnace produces $300\text{ kg slag}$ per metric ton of hot metal. If the sulfur partition coefficient is $L_S = \frac{(\% \text{S})_{\text{slag}}}{[\% \text{S}]_{\text{metal}}} = 45.0$, calculate the concentration of residual sulfur in the liquid hot metal ($[\% \text{S}]_{\text{metal}}$) in mass percentage and ppm.
  3. Calculate the percentage of total sulfur partitioned into the slag versus remaining in the hot metal.

Step 1: Slag Basicity Moduli

  • Binary Basicity ($B_2$):
$$B_2 = \frac{41.5\%}{34.0\%} \approx 1.221$$
  • Ternary Basicity ($B_3$):
$$B_3 = \frac{41.5\% + 7.5\%}{34.0\%} = \frac{49.0}{34.0} \approx 1.441$$

Step 2: Hot Metal Sulfur Concentration

From the definition of sulfur partition ratio:

$$L_S = \frac{(\% \text{S})_{\text{slag}}}{[\% \text{S}]_{\text{metal}}} = 45.0$$
$$[\% \text{S}]_{\text{metal}} = \frac{(\% \text{S})_{\text{slag}}}{L_S} = \frac{1.50\%}{45.0} = 0.0333\%$$

In parts per million ($\text{ppm}$):

$$[\text{S}]_{\text{metal}} = 0.0333 \times 10,000 = 333.3\text{ ppm}$$

Step 3: Sulfur Mass Distribution

Per metric ton ($1,000\text{ kg}$) of hot metal:

  • Sulfur in hot metal:
$$m_{\text{S, metal}} = 1,000\text{ kg} \times 0.000333 = 0.3333\text{ kg}$$
  • Slag produced: $300\text{ kg}$. Sulfur in slag:
$$m_{\text{S, slag}} = 300\text{ kg} \times 0.0150 = 4.500\text{ kg}$$

Total sulfur in output products:

$$m_{\text{S, total}} = 0.3333 + 4.500 = 4.8333\text{ kg}$$

Fraction partitioned into slag:

$$\% \text{ Sulfur in Slag} = \frac{4.500\text{ kg}}{4.8333\text{ kg}} \times 100\% = 93.10\%$$

The slag achieves $B_2 = 1.22$, holds hot metal sulfur to $333\text{ ppm}$, and captures $93.1\%$ of total sulfur.

Hard Example 10.4: Basic Oxygen Furnace (BOF) Charge Balance & Oxygen Requirement

A 250-metric ton Basic Oxygen Furnace (BOF) heat produces liquid steel at $1650^\circ\text{C}$.

  • Hot metal charge contains: $4.20\text{ wt}\%\text{ C}$, $0.60\text{ wt}\%\text{ Si}$, $0.50\text{ wt}\%\text{ Mn}$, $94.70\text{ wt}\%\text{ Fe}$.
  • The furnace charges $200.0\text{ metric tons}$ of liquid hot metal and $50.0\text{ metric tons}$ of scrap steel (assume scrap is $100\%\text{ Fe}$).
  • At blow completion, all silicon is oxidized to $\text{SiO}_2$, $80.0\%$ of manganese is oxidized to $\text{MnO}$, and carbon is reduced from $4.20\%$ to $0.05\text{ wt}\%$ in the steel.
  • Carbon oxidation yields $90.0\text{ mol}\%\text{ CO}$ and $10.0\text{ mol}\%\text{ CO}_2$.
  • In addition, $2.5\text{ wt}\%$ of the total iron is oxidized to $\text{FeO}$ ($71.84\text{ g/mol}$).

Atomic weights: $\text{C} = 12.01$, $\text{Si} = 28.09$, $\text{Mn} = 54.94$, $\text{Fe} = 55.85$, $\text{O} = 16.00$.

  1. Calculate the total moles of oxygen atoms ($\text{O}$) consumed by the oxidation of $\text{Si}$, $\text{Mn}$, $\text{Fe}$, and $\text{C}$.
  2. Determine the required volume of pure gaseous oxygen ($\text{O}_2$) at STP in $\text{Nm}^3$ ($22.414\text{ Nm}^3\text{/kmol O}_2$).
  3. If the oxygen lance blows at a volumetric rate of $800\text{ Nm}^3\text{/min}$, calculate the total oxygen blowing time in minutes.

Step 1: Oxidation Moles Calculation

In $200.0\text{ metric tons}$ ($200,000\text{ kg}$) of hot metal:

1. Silicon Oxidation:

$$m_{\text{Si}} = 0.0060 \times 200,000 = 1,200\text{ kg} \implies n_{\text{Si}} = \frac{1,200}{28.09} = 42.720\text{ kmol}$$

$\text{Si} + 2\text{O} \to \text{SiO}_2$:

$$n_{\text{O, Si}} = 2 \times 42.720 = 85.440\text{ kmol O}$$

2. Manganese Oxidation ($80.0\%$ oxidized):

$$m_{\text{Mn}} = 0.0050 \times 200,000 = 1,000\text{ kg} \implies n_{\text{Mn, ox}} = 0.80 \times \frac{1,000}{54.94} = 14.561\text{ kmol}$$

$\text{Mn} + \text{O} \to \text{MnO}$:

$$n_{\text{O, Mn}} = 14.561\text{ kmol O}$$

3. Iron Oxidation ($2.5\%$ of iron oxidized):

Total iron in heat $= 0.9470(200,000) + 50,000 = 189,400 + 50,000 = 239,400\text{ kg}$.

$$m_{\text{Fe, ox}} = 0.025 \times 239,400 = 5,985\text{ kg} \implies n_{\text{Fe, ox}} = \frac{5,985}{55.85} = 107.162\text{ kmol}$$

$\text{Fe} + \text{O} \to \text{FeO}$:

$$n_{\text{O, Fe}} = 107.162\text{ kmol O}$$

4. Carbon Oxidation:

Initial carbon $= 0.0420 \times 200,000 = 8,400\text{ kg}$. Final carbon in $\sim 235\text{ tons}$ steel $= 0.0005 \times 235,000 \approx 117.5\text{ kg}$. Carbon oxidized $= 8,400 - 118 = 8,282\text{ kg}$:

$$n_{\text{C, ox}} = \frac{8,282\text{ kg}}{12.01\text{ kg/kmol}} = 689.592\text{ kmol}$$

Since carbon produces $90\%\text{ CO}$ (1 O per C) and $10\%\text{ CO}_2$ (2 O per C):

$$n_{\text{O, C}} = (0.90 \times 1 + 0.10 \times 2) \times 689.592 = 1.10 \times 689.592 = 758.551\text{ kmol O}$$
  • Total Moles of Oxygen Atoms:
$$n_{\text{O, total}} = 85.440 + 14.561 + 107.162 + 758.551 = 965.714\text{ kmol O}$$

Step 2: Gaseous $\text{O}_2$ Volume at STP

Moles of molecular $\text{O}_2$:

$$n_{\text{O}_2} = \frac{n_{\text{O, total}}}{2} = \frac{965.714}{2} = 482.857\text{ kmol O}_2$$

Volumetric oxygen requirement at STP:

$$V_{\text{O}_2, \text{STP}} = 482.857\text{ kmol} \times 22.414\text{ Nm}^3\text{/kmol} = 10,822.76\text{ Nm}^3 \approx 10,823\text{ Nm}^3$$

Step 3: Blowing Time

$$\text{Blowing Time} = \frac{10,822.76\text{ Nm}^3}{800\text{ Nm}^3\text{/min}} = 13.528\text{ minutes} \approx 13\text{ min } 32\text{ seconds}$$

The heat requires $10,823\text{ Nm}^3$ of pure $\text{O}_2$, blown in $13.5\text{ minutes}$.

Medium Example 10.5: BOF Decarburization Diffusion Kinetics at Low Carbon

In the final stage of a BOF blow ($[\% \text{C}] < 0.25\%$), decarburization is limited by liquid-phase carbon mass transfer to the gas-metal interface:

$$\frac{d[\% \text{C}]}{dt} = - K_m ([\% \text{C}] - [\% \text{C}]_e)$$

where $K_m$ is the apparent volumetric mass transfer coefficient, and $[\% \text{C}]_e = 0.010\text{ wt}\%$ is the equilibrium carbon content.

  • At $t = 0$, carbon content enters the mass-transfer regime at $[\% \text{C}]_0 = 0.220\text{ wt}\%$.
  • After $t_1 = 2.0\text{ minutes}$, carbon content drops to $[\% \text{C}]_1 = 0.080\text{ wt}\%$.
  1. Calculate the apparent mass transfer rate constant $K_m$ in $\text{min}^{-1}$.
  2. Determine the additional blowing time required to reach the target carbon specification of $[\% \text{C}]_{\text{target}} = 0.030\text{ wt}\%$.
  3. Calculate the instantaneous decarburization rate ($d[\% \text{C}]/dt$ in $\text{wt}\%/\text{min}$) at $[\% \text{C}] = 0.050\text{ wt}\%$.

Step 1: Mass Transfer Rate Constant ($K_m$)

Integrate the first-order differential equation:

$$\ln\left(\frac{[\% \text{C}] - [\% \text{C}]_e}{[\% \text{C}]_0 - [\% \text{C}]_e}\right) = - K_m \cdot t$$

At $t_1 = 2.0\text{ min}$:

$$\ln\left(\frac{0.080 - 0.010}{0.220 - 0.010}\right) = - K_m (2.0)$$
$$\ln\left(\frac{0.070}{0.210}\right) = \ln\left(\frac{1}{3}\right) = -1.0986 = - 2.0 \cdot K_m$$
$$K_m = \frac{1.0986}{2.0} = 0.5493\text{ min}^{-1}$$

Step 2: Time to Reach $[\% \text{C}] = 0.030\text{ wt}\%$

$$\ln\left(\frac{0.030 - 0.010}{0.220 - 0.010}\right) = - 0.5493 \cdot t_{\text{total}}$$
$$\ln\left(\frac{0.020}{0.210}\right) = \ln(0.095238) = -2.3514 = - 0.5493 \cdot t_{\text{total}}$$
$$t_{\text{total}} = \frac{2.3514}{0.5493} = 4.280\text{ minutes}$$

Additional blowing time beyond $t_1 = 2.0\text{ min}$:

$$\Delta t = 4.280 - 2.000 = 2.280\text{ minutes} \approx 2\text{ min } 17\text{ seconds}$$

Step 3: Instantaneous Decarburization Rate at $[\% \text{C}] = 0.050\text{ wt}\%$

$$\frac{d[\% \text{C}]}{dt} = - K_m ([\% \text{C}] - [\% \text{C}]_e) = - 0.5493 \times (0.050 - 0.010)$$
$$\frac{d[\% \text{C}]}{dt} = - 0.5493 \times 0.040 = -0.02197\text{ wt}\%/\text{min}$$

The instantaneous decarburization rate is $-0.022\text{ wt}\%/\text{min}$.

Easy Example 10.6: Aluminum Ladle Deoxidation & Inclusion Mass Balance

A ladle of liquid steel ($M = 150.0\text{ metric tons} = 150,000\text{ kg}$) is tapped from a converter at $1600^\circ\text{C}$ containing $550\text{ ppm dissolved oxygen}$ ($0.0550\text{ wt}\%$). Pure aluminum wire ($26.98\text{ g/mol}$) is fed to deoxidize the steel according to:

$$2[\text{Al}] + 3[\text{O}] \longrightarrow \text{Al}_2\text{O}_3(s) \quad (M_{\text{Al}_2\text{O}_3} = 101.96\text{ g/mol})$$

Target specifications:

  • Reduce dissolved oxygen to $3.0\text{ ppm}$ ($0.0003\text{ wt}\%$).
  • Establish a residual soluble metallic aluminum content of $[\% \text{Al}]_{\text{sol}} = 0.035\text{ wt}\%$.
  • Aluminum recovery efficiency during wire feeding is $85.0\%$ (the remainder is oxidized by atmospheric air).
  1. Calculate the mass of oxygen eliminated from the steel in kilograms.
  2. Determine the stoichiometric mass of aluminum consumed by deoxidation.
  3. Calculate the total mass of aluminum wire that must be fed into the ladle.
  4. Calculate the mass of solid alumina inclusions ($\text{Al}_2\text{O}_3$) generated.

Step 1: Mass of Oxygen Eliminated

Initial oxygen:

$$m_{\text{O, in}} = 150,000\text{ kg} \times 0.000550 = 82.50\text{ kg}$$

Final dissolved oxygen:

$$m_{\text{O, out}} = 150,000\text{ kg} \times 0.000003 = 0.45\text{ kg}$$

Oxygen eliminated:

$$\Delta m_{\text{O}} = 82.50 - 0.45 = 82.05\text{ kg}$$

Moles of oxygen eliminated:

$$n_{\text{O}} = \frac{82.05\text{ kg}}{16.00\text{ kg/kmol}} = 5.1281\text{ kmol}$$

Step 2: Stoichiometric Aluminum Consumed

From $2\text{Al} + 3\text{O} \to \text{Al}_2\text{O}_3$:

$$n_{\text{Al, deox}} = \frac{2}{3} \times n_{\text{O}} = \frac{2}{3} \times 5.1281 = 3.4187\text{ kmol}$$

Mass of aluminum consumed by deoxidation:

$$m_{\text{Al, deox}} = 3.4187\text{ kmol} \times 26.98\text{ kg/kmol} = 92.237\text{ kg}$$

Step 3: Total Aluminum Wire Required

Mass of residual soluble aluminum required in steel:

$$m_{\text{Al, sol}} = 150,000\text{ kg} \times 0.00035 = 52.50\text{ kg}$$

Net aluminum that must successfully enter the steel:

$$m_{\text{Al, net}} = m_{\text{Al, deox}} + m_{\text{Al, sol}} = 92.237 + 52.50 = 144.737\text{ kg}$$

Accounting for $85.0\%$ wire feeding recovery efficiency:

$$m_{\text{Al, wire}} = \frac{144.737\text{ kg}}{0.850} = 170.28\text{ kg}$$

Step 4: Alumina Inclusions Generated

$$n_{\text{Al}_2\text{O}_3} = \frac{n_{\text{O}}}{3} = \frac{5.1281}{3} = 1.7094\text{ kmol}$$

Mass of generated $\text{Al}_2\text{O}_3$:

$$m_{\text{Al}_2\text{O}_3} = 1.7094\text{ kmol} \times 101.96\text{ kg/kmol} = 174.29\text{ kg}$$

The operator must feed $170.3\text{ kg}$ of aluminum wire, generating $174.3\text{ kg}$ of $\text{Al}_2\text{O}_3$ inclusions to be floated into the slag.

Medium Example 10.7: Direct Reduced Iron (DRI) Metallization & Syngas Consumption

A Midrex direct reduction shaft furnace produces $150.0\text{ metric tons/h}$ of cold Direct Reduced Iron ($\text{DRI}$ / sponge iron). The DRI chemical analysis:

  • Total Iron ($\text{Fe}_{\text{total}}$): $92.0\text{ wt}\%$
  • Metallic Iron ($\text{Fe}_{\text{met}}$): $86.5\text{ wt}\%$
  • Residual Iron as WΓΌstite ($\text{Fe}$ in $\text{FeO}$): $5.5\text{ wt}\%$
  • Carbon: $2.0\text{ wt}\%$, Gangue: $6.0\text{ wt}\%$

Molar masses: $\text{Fe} = 55.85\text{ g/mol}$, $\text{FeO} = 71.85\text{ g/mol}$, $\text{Fe}_2\text{O}_3 = 159.69\text{ g/mol}$.

  1. Calculate the Metallization Degree ($\% \text{Met}$) of the DRI product:
$$\% \text{Met} = \frac{\% \text{Fe}_{\text{met}}}{\% \text{Fe}_{\text{total}}} \times 100\%$$
  1. The reducing syngas consists of $55.0\text{ vol}\%\text{ H}_2$ and $35.0\text{ vol}\%\text{ CO}$ ($10\%\text{ inerts}$). In solid-state shaft reduction, eliminating $1\text{ mole of oxygen atoms}$ from iron oxides consumes $1\text{ mole of (H}_2 + \text{CO)}$. Assuming pure hematite ($\text{Fe}_2\text{O}_3$) feed, calculate the total moles of oxygen eliminated per hour.
  2. Determine the required hourly volumetric flow rate of reducing syngas at STP in $\text{Nm}^3\text{/h}$ ($22.414\text{ Nm}^3\text{/kmol}$, assuming $40\%$ single-pass gas utilization).

Step 1: Metallization Degree

$$\% \text{Met} = \frac{86.50\%}{92.00\%} \times 100\% = 94.02\%$$

The DRI achieves a Metallization Degree of $94.0\%$ (meeting standard EAF melting grade $\ge 92\%$).

Step 2: Moles of Oxygen Eliminated

Hourly DRI production rate $= 150,000\text{ kg/h}$. Total metallic iron produced:

$$m_{\text{Fe, met}} = 0.8650 \times 150,000 = 129,750\text{ kg/h} \implies n_{\text{Fe, met}} = \frac{129,750}{55.85} = 2,323.19\text{ kmol/h}$$

Residual iron as $\text{FeO}$:

$$m_{\text{Fe, FeO}} = 0.0550 \times 150,000 = 8,250\text{ kg/h} \implies n_{\text{Fe, FeO}} = \frac{8,250}{55.85} = 147.72\text{ kmol/h}$$

Now determine initial oxygen in raw hematite ($\text{Fe}_2\text{O}_3$ has $1.5\text{ mol O per mol Fe}$):

  • For fully reduced iron: $1.5\text{ mol O}$ was eliminated per mole of $\text{Fe}$:
$$n_{\text{O, elim 1}} = 1.5 \times 2,323.19 = 3,484.78\text{ kmol/h}$$
  • For $\text{FeO}$ residue: hematite was reduced to wΓΌstite ($1.5 \to 1.0\text{ O}$, so $0.5\text{ mol O}$ eliminated per mole of $\text{Fe}$):
$$n_{\text{O, elim 2}} = 0.5 \times 147.72 = 73.86\text{ kmol/h}$$

Total oxygen eliminated from ore:

$$n_{\text{O, total elim}} = 3,484.78 + 73.86 = 3,558.64\text{ kmol O/h}$$

Step 3: Required Syngas Volumetric Flow Rate

Stoichiometric $(\text{H}_2 + \text{CO})$ consumed:

$$n_{\text{reductants, consumed}} = 3,558.64\text{ kmol/h}$$

At $40.0\%$ single-pass gas utilization:

$$n_{\text{reductants, fed}} = \frac{3,558.64\text{ kmol/h}}{0.40} = 8,896.60\text{ kmol/h}$$

Since $(\text{H}_2 + \text{CO})$ constitutes $55\% + 35\% = 90.0\text{ vol}\%$ of the syngas:

$$n_{\text{syngas, total}} = \frac{8,896.60\text{ kmol/h}}{0.90} = 9,885.11\text{ kmol/h}$$

Volumetric flow rate at STP:

$$\dot{V}_{\text{syngas, STP}} = 9,885.11\text{ kmol/h} \times 22.414\text{ Nm}^3\text{/kmol} = 221,565\text{ Nm}^3\text{/h}$$

The Midrex shaft furnace requires $221,565\text{ Nm}^3\text{/h}$ of reducing syngas to produce $150\text{ t/h}$ of sponge iron.

Medium Example 10.8: 100% Pure Hydrogen Direct Reduction (H2-DRI) Gas Consumption & Water Vapor Balance

A green steel plant operates an industrial shaft furnace utilizing $100\%$ electrolytic green hydrogen ($\text{H}_2$, $2.016\text{ g/mol}$) to reduce pure hematite pellets ($\text{Fe}_2\text{O}_3$, $159.69\text{ g/mol}$) to metallic sponge iron ($\text{Fe}$, $55.85\text{ g/mol}$). The endothermic shaft reduction reaction is:

$$\text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \longrightarrow 2\text{Fe}(s) + 3\text{H}_2\text{O}(g) \quad \Delta H_{298}^\circ = +98.8\text{ kJ/mol Fe}_2\text{O}_3$$
  • The plant produces $\dot{m}_{\text{DRI}} = 100.0\text{ metric tons/h}$ of metallic iron ($1,790.5\text{ kmol/h Fe}$).
  • In the shaft furnace, thermodynamic equilibrium and gas channeling limit single-pass hydrogen conversion to $\alpha_{\text{pass}} = 30.0\%$. Unreacted gas is cooled, condensed to remove water, reheated, and recycled.
  • Latent heat of condensation of water is $\Delta H_{\text{vap}} = 2,260\text{ kJ/kg}$.
  1. Calculate the stoichiometric consumption of pure hydrogen gas per hour in $\text{kg/h}$ and STP volumetric flow rate ($\text{Nm}^3\text{/h}$, $22.414\text{ Nm}^3\text{/kmol}$).
  2. Determine the total circulating hydrogen gas feed rate entering the shaft tuyeres ($\text{Nm}^3\text{/h}$).
  3. Calculate the hourly generation rate of water vapor in metric tons per hour and the heat released when this water is condensed from the recycle gas loop ($\text{MW}$).

Step 1: Stoichiometric Hydrogen Consumption

Hourly iron production:

$$\dot{n}_{\text{Fe}} = \frac{100,000\text{ kg/h}}{55.85\text{ kg/kmol}} = 1,790.51\text{ kmol/h}$$

Stoichiometric $\text{H}_2$ required ($1.5\text{ mol H}_2\text{ / mol Fe}$):

$$\dot{n}_{\text{H}_2, \text{consumed}} = 1.5 \times 1,790.51 = 2,685.77\text{ kmol/h}$$

Mass of pure hydrogen consumed:

$$\dot{m}_{\text{H}_2} = 2,685.77\text{ kmol/h} \times 2.016\text{ kg/kmol} = 5,414.5\text{ kg/h} \approx 5.415\text{ metric tons/h}$$

Volumetric consumption at STP:

$$\dot{V}_{\text{H}_2, \text{STP}} = 2,685.77\text{ kmol/h} \times 22.414\text{ Nm}^3\text{/kmol} = 60,198.8\text{ Nm}^3\text{/h} \approx 60,200\text{ Nm}^3\text{/h}$$

Step 2: Circulating Hydrogen Gas Flow

At $30.0\%$ single-pass conversion:

$$\dot{V}_{\text{H}_2, \text{circ}} = \frac{60,198.8\text{ Nm}^3\text{/h}}{0.300} = 200,662.7\text{ Nm}^3\text{/h} \approx 200,663\text{ Nm}^3\text{/h}$$

Step 3: Water Vapor Generation & Condensation Enthalpy

From stoichiometry, moles of $\text{H}_2\text{O}$ vapor produced equals moles of $\text{H}_2$ consumed:

$$\dot{n}_{\text{H}_2\text{O}} = 2,685.77\text{ kmol/h}$$

Mass of water produced:

$$\dot{m}_{\text{H}_2\text{O}} = 2,685.77\text{ kmol/h} \times 18.015\text{ kg/kmol} = 48,384.1\text{ kg/h} \approx 48.38\text{ metric tons/h}$$

Latent condensation heat duty:

$$\dot{Q}_{\text{cond}} = 48,384.1\text{ kg/h} \times 2,260\text{ kJ/kg} = 1.0935 \times 10^8\text{ kJ/h}$$

In thermal megawatts ($\text{MW}$):

$$\dot{Q}_{\text{thermal}} = \frac{1.0935 \times 10^8\text{ kJ/h}}{3,600\text{ s/h}} = 30,374.5\text{ kW} \approx 30.37\text{ MW}$$

The furnace consumes $5.42\text{ t/h}$ of $\text{H}_2$, circulates $200,663\text{ Nm}^3\text{/h}$ of gas, and produces $48.38\text{ t/h}$ of clean water, releasing $30.37\text{ MW}$ of recoverable condensation heat.

Medium Example 10.9: Electric Arc Furnace (EAF) Dynamic Slag Foaming Kinetics

In an Electric Arc Furnace melting DRI and scrap, biochar fines ($90.0\text{ wt}\%\text{ fixed carbon}$, $12.01\text{ g/mol}$) and gaseous oxygen are co-injected into the liquid slag at $1600^\circ\text{C}$ to generate a thick foaming slag that shields the water-cooled furnace walls. The foaming reaction with dissolved wΓΌstite in the slag is:

$$\text{C}(s) + (\text{FeO})_{(\text{slag})} \longrightarrow \text{Fe}(l) + \text{CO}(g)$$
  • Biochar is injected at a rate of $\dot{m}_{\text{char}} = 18.0\text{ kg/min}$ ($16.2\text{ kg carbon/min}$).
  • Carbon gasification efficiency is $85.0\%$.
  • Ideal gas law applies to $\text{CO}$ at $T = 1600^\circ\text{C}$ ($1873.15\text{ K}$) and $P = 1.0\text{ bar}$.
  • The slag has a mean gas bubble residence time (foaming retention time) of $\tau = 45.0\text{ seconds}$ ($0.75\text{ min}$).
  • The cross-sectional bath area of the furnace shell is $A = 28.0\text{ m}^2$.
  1. Calculate the generation rate of carbon monoxide gas in $\text{kmol/min}$ and actual cubic meters per minute ($\text{m}^3\text{/min}$).
  2. Determine the steady-state volumetric holdup of gas trapped inside the foamy slag ($V_{\text{gas}}$ in $\text{m}^3$).
  3. Calculate the average height expansion of the foaming slag ($\Delta h_{\text{slag}}$) in meters.

Step 1: Carbon Monoxide Generation Rate

Moles of carbon reacted per minute:

$$\dot{n}_{\text{C}} = \frac{0.850 \times 16.2\text{ kg/min}}{12.01\text{ kg/kmol}} = 1.1465\text{ kmol/min}$$

Stoichiometric $\text{CO}$ generated:

$$\dot{n}_{\text{CO}} = 1.1465\text{ kmol/min}$$

Actual volumetric gas generation rate at $T = 1873.15\text{ K}$, $P = 1.0\text{ bar} = 100\text{ kPa}$ ($R = 8.314\text{ kPa}\cdot\text{m}^3\text{/(kmol}\cdot\text{K)}$):

$$\dot{V}_{\text{CO}} = \frac{\dot{n}_{\text{CO}} \cdot R \cdot T}{P} = \frac{1.1465 \times 8.314 \times 1873.15}{100} = 178.55\text{ m}^3\text{/min}$$

Step 2: Steady-State Gas Holdup ($V_{\text{gas}}$)

Using the dynamic holdup relation $V_{\text{gas}} = \dot{V}_{\text{gas}} \times \tau$:

$$V_{\text{gas}} = 178.55\text{ m}^3\text{/min} \times 0.750\text{ min} = 133.91\text{ m}^3$$

The foamy slag holds $133.9\text{ m}^3$ of trapped $\text{CO}$ gas bubbles.

Step 3: Slag Height Expansion ($\Delta h_{\text{slag}}$)

Across furnace hearth area $A = 28.0\text{ m}^2$:

$$\Delta h_{\text{slag}} = \frac{V_{\text{gas}}}{A} = \frac{133.91\text{ m}^3}{28.0\text{ m}^2} = 4.782\text{ m}$$

Accounting for gas bubble escape and froth void fraction ($\epsilon \approx 0.75$, physical foam height):

$$\Delta h_{\text{foam}} \approx 1.2 - 1.5\text{ meters above calm bath}$$

The injected biochar generates a $1.2 - 1.5\text{ m}$ thick stable protective foaming slag, shielding furnace sidewalls from electric arc radiation.

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