Lecture 09

1. Introduction & Process Overview

The Iron Blast Furnace (BF) is a counter-current reactor designed to reduce iron oxides to metallic iron.

• Structure: A tall vertical shaft where solid charge descends and gases ascend.

• Counter-Current Flow:

  • Descending Phase: Solid burden (Iron ore, Coke, Flux) charged from the top.

  • Ascending Phase: Reducing gases ($CO$, $N_2$) generated at the bottom tuyeres by combustion of coke with preheated blast ($O_2$, $N_2$).

• Interaction: Intense heat and mass transfer occur between the ascending hot gases and the descending solids.

  • Solids undergo heating, reduction, melting, and carburization.

  • Gases undergo cooling and oxidation ($CO\to C{O}_2$).

Schematic of Inputs and Outputs

Plaintext

                  Off-Gas (Top Gas)
                  (CO, CO2, N2)
                       ^
                       |
            +---------------------+
            |     Charge Input    |
            | (Iron Ore, Coke)    |
            |                     |
            |    BLAST FURNACE    |
            |                     |
            |  (Reaction Zone)    |
            |                     |
   Blast -> |      Tuyeres        | <- Blast
 (O2, N2)   |                     |    (O2, N2)
            +---------------------+
                       |
                       v
                Liquid Outputs
           (Hot Metal + Liquid Slag)

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2. Modeling Philosophy: Steady State Assumption

To control and understand the furnace, we develop a mathematical model. While complex models (aerodynamic, kinetic, granular flow) exist, this lecture focuses on a Simplified Steady State Material and Enthalpy Balance.

• Steady State Definition: The furnace operates continuously. Averaged over a significant time period (e.g., monthly), inputs equal outputs. There is no accumulation of mass or energy within the control volume.

  • Mathematical implication: $\text{Input Rate}=\text{Output Rate}$.

• Model vs. Law: Laws (e.g., thermodynamics) are exact. Models are approximations based on assumptions.

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3. Simplifying Assumptions for the Model

To make the system solvable, several idealizations are made:

1. Pure Materials:

   • Iron Ore is pure Hematite ($F{e}_2{O}_3$).

   • Coke is pure Carbon ($C$).

   • Blast is pure Oxygen and Nitrogen mixture.

   • Note: No gangue ($Si{O}_2$, $A{l}_2{O}_3$) implies no slag formation in the ideal case (relaxed later).

2. Product Purity:

   • Hot Metal: Contains only $Fe$ and dissolved Carbon ($C$). No $Si,Mn,S,P$.

   • Slag: Contains no Iron ($Fe$) and no Carbon ($C$).

3. No Losses:

   • No material loss via dust.

   • No heat loss through furnace walls (Adiabatic).

4. Oxygen Distribution:

   • No Oxygen in Hot Metal (Carbon saturation prevents dissolved $O$).

   • All Oxygen from Ore and Blast manifests in the Off-Gas.

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4. Material Balance Formulation

Basis of Calculation:

All calculations are performed per 1 kg-mole of Fe product in the hot metal.

$n_{Fe}^{product}=1\text{ kg-mole}$

4.1. Iron (Fe) Balance

Since there is no Fe loss to slag or dust:

$n_{Fe}^{in(Ore)}=n_{Fe}^{out(Metal)}=1$

• Implication for Hematite ($F{e}_2{O}_3$): To get 1 mole of Fe, we need 0.5 moles of $F{e}_2{O}_3$.

4.2. Carbon (C) Balance & Distribution

Carbon input comes from Coke. It splits into two streams inside the furnace:

1. Passive Carbon ($n_C^{passive}$):

   • Dissolves in the hot metal.

   • Does not participate in reduction or combustion reactions.

   • Leaves the furnace in the liquid metal.

2. Active Carbon ($n_C^{active}$):

   • Participates in combustion and reduction.

   • Leaves the furnace in the Off-Gas (as $CO$ or $C{O}_2$).

   • Instructor Note: This is the quantity we aim to minimize to lower the Coke Rate.

Total Coke Rate ($n_C^{total}$):

$n_C^{total}=n_C^{active}+n_C^{passive}$

Molar Ratio in Metal ($C/Fe{]}_m$):

This represents the passive carbon.

$(C/Fe{)}_m=\frac{\text{Moles of C in Metal}}{\text{Moles of Fe in Metal}}$

• For saturation (approx 4.3 wt% C), $(C/Fe{)}_m\approx 0.21$.

• For 4.0 wt% C, $(C/Fe{)}_m\approx 0.20$.

• Formula: $(C/Fe{)}_m$ is a fixed parameter based on hot metal chemistry.

4.3. Oxygen (O) Balance

Convention: Moles of Oxygen are expressed as atomic Oxygen ($O$), not molecular ($O_2$).

Input Sources:

1. Iron Ore: Oxygen combined with Iron.

   • Parameter: $(O/Fe{)}_x$ = Moles of $O$ per mole of $Fe$ in ore.

   • For Hematite ($F{e}_2{O}_3$): $(O/Fe{)}_x=1.5$.

   • For Magnetite ($F{e}_3{O}_4$): $(O/Fe{)}_x=1.33$.

2. Blast: Gaseous Oxygen injected ($n_O^{blast}$).

Output:

• Entire Oxygen output is in the Off-Gas (as $CO$ and $C{O}_2$).

4.4. Off-Gas Analysis ($O/C$ Ratio)

The composition of the top gas indicates furnace efficiency. We analyze the Carbonaceous Portion ($CO+C{O}_2$).

Define $(O/C{)}_{gas}$ as the molar ratio of Oxygen to Carbon in the top gas.

$(O/C{)}_{gas}=\frac{n_O^{gas}}{n_C^{gas}}=\frac{n_{CO}+2n_{C{O}_2}}{n_{CO}+n_{C{O}_2}}$

Mole Fractions:

Let $x_{C{O}_2}$ and $x_{CO}$ be mole fractions in the carbonaceous gas mixture.

$x_{C{O}_2}=\frac{n_{C{O}_2}}{n_{CO}+n_{C{O}_2}}$

Derivation of Composition from $(O/C{)}_{gas}$:

$(O/C{)}_{gas}=\frac{1\cdot n_{CO}+2\cdot n_{C{O}_2}}{n_{CO}+n_{C{O}_2}}=\frac{(n_{CO}+n_{C{O}_2})+n_{C{O}_2}}{n_{CO}+n_{C{O}_2}}$

$(O/C{)}_{gas}=1+x_{C{O}_2}$

Therefore:

$x_{C{O}_2}=(O/C{)}_{gas}-1$

$x_{CO}=2-(O/C{)}_{gas}$

• Range: $1\le (O/C{)}_{gas}\le 2$

  • $(O/C{)}_{gas}=1⟹100\%\text{ CO}$ (Low Efficiency)

  • $(O/C{)}_{gas}=2⟹100\%{\text{ CO}}_2$ (High Efficiency)

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5. Summary of Model Variables

To solve the system, we identify variables and required equations.

Known Parameters (4):

1. $n_{Fe}^{in}$ (Input Fe = 1)

2. $n_{Fe}^{out}$ (Output Fe = 1)

3. $(C/Fe{)}_m$ (Metal composition, ~0.21)

4. $(O/Fe{)}_x$ (Ore stoichiometry, 1.5 for hematite)

Unknown Variables (The “Big Three” Performance Indicators):

1. Blast Rate: Amount of Oxygen/Air required.

2. Coke Rate ($n_C^{active}$): Carbon required for reaction.

3. Top Gas Composition ($O/C$ ratio): Efficiency of the process.

Instructor’s Conclusion:

We have established the variables. To have a fully predictive model, we need 3 Characteristic Equations involving these unknowns. These will be derived in the next lecture based on:

1. Overall Oxygen Balance.

2. Heat/Enthalpy Balance.

3. Chemical Equilibrium (Efficiency constraints).