Lecture 13

Lecture Notes: Blast Furnace Ironmaking – The Rist Diagram (Operating Line)

Source: Lecture 13, Prof. Dipak Mazumdar (IIT Kanpur)

Topic: Analytical and Graphical Modeling of Blast Furnace Operations (Rist Diagram Construction & Interpretation)

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1. Introduction & Context

This lecture continues the development of a predictive mathematical model for the Blast Furnace (BF). Having previously established the material and enthalpy balance equations, the focus shifts to:

1. Solving for the three key unknowns of the BF process:

   • Top Gas Composition ($O/C$ ratio or $\%CO/\%C{O}_2$).

   • Coke Rate ($N_{AC}$, active carbon required).

   • Blast Rate ($N_{OB}$, blast oxygen required).

2. The Rist Diagram: Visualizing these equations as an Operating Line on a specific coordinate system to analyze furnace efficiency and productivity.

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2. Governing Equations (Recap & Consolidation)

The model is built upon three fundamental balance equations applied to the Bottom Segment (Wustite Reduction Zone - WRZ) and the overall furnace.

A. The Balance Equations

1. Overall Oxygen Balance $n_O^B+1.5=n_c^A(O/C{)}^g$

2. Wustite Reduction Zone (WRZ) Oxygen Balance $n_O^B+1.06=1.3n_c^A$

3. WRZ Enthalpy Balance $D^{wrz}=E_B{n}_O^B+198000n_C^A$ where

4. $D^{wrz}=330,000KJ/kg-moleofFe$

5. $D^{wrz}=E_B{n}_O^B-n_C^A[\{2-(O/C{)}^{g,wrz}\}{H}_{CO,1200K}^f+\{(O/C{)}^{g,wrz}-1\}{H}_{CO2,1200K}^f]$ $H_{CO,1200K}^f=113000KJ/mole$ $H_{CO2,1200K}^f=395000KJ/mole$

For an idealized operation (Hematite feed, no impurities), the thermal demand of the bottom zone is quantified as:

$D^{wrz}\approx 330,000\text{ kJ/kg mole Fe}$

Combined Bottom Segment Oxygen & Enthalpy Balance: $D^{wrz}=n_C^A[1.3E_B+198,0000-1.06E_B$

Components of $D_{WRZ}$ (Idealized):

1. Enthalpy to break $Fe-O$ bonds (Reduction of Wustite to Iron).

2. Enthalpy to heat Iron from $1200^{\circ }C$ (Reserve Zone temp) to $1800^{\circ }C$ (Tapping temp).

3. Enthalpy to dissolve $4.3\%$ Carbon into liquid Iron.

B. Combined Enthalpy & Oxygen Balance

To create a graphical representation, the enthalpy and oxygen balance equations are combined. The instructor derives a linear relationship containing terms related to the Heat of Formation ($\Delta H_f$) of $CO$ and $C{O}_2$.

Key Thermodynamic Values (at 1200 K):

• $\Delta H_f(CO)\approx -113,000\text{ kJ/mole}$

• $\Delta H_f(C{O}_2)\approx -395,000\text{ kJ/mole}$

Using these values, two specific constants appear in the derived equation:

• 282,000 (Derived from $\Delta H_f(C{O}_2)-\Delta H_f(CO)$)

• 169,000 (Derived from $2\times \Delta H_f(CO)-\Delta H_f(C{O}_2)$)

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3. The Rist Diagram (Operating Line Construction)

The Rist Diagram is a graphical tool that plots the Oxygen-to-Iron Ratio ($O/Fe$) against the Oxygen-to-Carbon Ratio ($O/C$).

A. Coordinate System

• Y-Axis (Ordinate): $O/Fe$ (Moles of Oxygen per Mole of Iron).

  • Range: $0$ (Liquid Iron) to $1.5$ (Hematite $F{e}_2{O}_3$).

• X-Axis (Abscissa): $O/C$ (Moles of Oxygen per Mole of Carbon in gas).

  • Range: $1.0$ (Pure $CO$) to $2.0$ (Pure $C{O}_2$).

B. The Operating Line

The Blast Furnace operation is represented by a straight line passing through two characteristic points: Point W and Point H.

1. Point W (The Pinch Point)

Represents the chemical and thermal equilibrium in the Reserve Zone (approx. $1000^{\circ }C-1200^{\circ }C$).

• Coordinates $(X_W,Y_W)$:

  • $X_W\approx 1.3$: Thermodynamic equilibrium gas composition ($O/C$) for Wustite reduction.

  • $Y_W\approx 1.06$: The atomic ratio of Oxygen to Iron in Wustite ($Fe{O}_{1.05-1.06}$).

• Note: These coordinates are fixed for an “Ideal” operation but shift slightly with real ore mineralogy.

2. Point H (The Enthalpy/Heat Balance Point)

This theoretical point is derived from the enthalpy balance. Its coordinates depend on the heat demand ($D_{WRZ}$) and the heat supplied by the blast ($E_B$).

Derived Coordinates for Point H $(X_H,Y_H)$:

$X_H=\frac{169,000}{282,000+E_B}$

$Y_H=\frac{1.06\cdot D_{WRZ}+1.06\cdot E_B}{282,000}$

(Note: The exact form of $Y_H$ involves the algebraic manipulation of the $D_{WRZ}$ and enthalpy terms shown on the board.)

C. Properties of the Line

• Slope ($N_{AC}$): The slope of the line connecting H and W represents the Coke Rate (Active Carbon per mole Fe).

  • Steeper Slope $\to$ Higher Coke Rate (Less Efficient).

  • Flatter Slope $\to$ Lower Coke Rate (More Efficient).

• Intercepts: Extrapolating the line gives the Top Gas Composition (at $Y=1.5$) and the Blast Rate.

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4. Visual Representation (Board Work Reconstruction)

Below is a reconstruction of the Rist Diagram as drawn on the board, showing the Operating Line and the shift directions for efficiency.

Plaintext

      Y-Axis (O/Fe)
        ^
    2.0 +
        |
    1.5 +--------- Top Gas Composition (Exit)
        |         \
        |          \  <-- Operating Line
    1.06+           \ W (Pinch Point: ~1.3, 1.06)
(Wustite)|            \
        |             \
    0.0 +--------------\-------------------->
(Liq Fe)|               \
        |                \
   -Nob +                 \ H (Enthalpy Point)
        |                  \
        +---------+---------+---------+----> X-Axis (O/C)
       1.0       1.5       2.0       (Gas Composition)
      (CO)               (CO2)

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5. Factors Affecting Blast Furnace Efficiency

The power of the Rist Diagram lies in visualizing how operational changes “move” Points W and H, thereby changing the slope (Coke Rate).

A. Blast Temperature (Enthalpy $E_B$)

• Effect: Increasing Blast Temperature increases the enthalpy input ($E_B$).

• Movement on Graph: Point H moves upward/left (towards the Y-axis).

• Result: The operating line becomes less steep.

• Benefit: Lower Coke Rate and Higher Productivity.

• Limitation: Practical limits on stove materials restrict blast temp (typically max $\sim 1200-1300^{\circ }C$).

B. Thermal Demand ($D_{WRZ}$)

• Effect: Reducing the thermal demand (e.g., using better quality ore with less gangue/slag, lower heat losses).

• Movement on Graph: Point H moves down/right (favorable direction).

• Result: The operating line becomes less steep.

• Benefit: Lower Coke Rate.

• Note: Large furnaces have lower surface-area-to-volume ratios, reducing heat loss components of $D_{WRZ}$.

C. Ore Quality & Impurities (Point W)

• Effect: Presence of impurities (Silica, Alumina, Phosphorus) or metalloids requiring reduction changes the initial oxygen ratio.

• Movement on Graph: Point W shifts (specifically, the Y-intercept $1.06$ increases to e.g., $1.16$ or $1.17$).

• Result: The pivot point W moves up, forcing a steeper slope.

• Penalty: Higher Coke Rate (Lower Efficiency).

• Mitigation: Charging metallic iron (scrap) lowers the effective input $O/Fe$, moving W down (beneficial).

D. Oxygen Enrichment

• Effect: Reduces Nitrogen volume, alters enthalpy carried by blast, and changes gas transport.

• Movement: Moves Point H favorably.

• Benefit: Increases Productivity significantly.

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6. Productivity & Blast Rate

The instructor defines a specific relationship for productivity based on blast volume:

$\text{Productivity}\propto \frac{1}{\text{Blast Rate per Ton of Hot Metal}}$

• Goal: Minimize the Blast Rate ($N_{OB}$) required to produce a ton of iron.

• Mechanism: Any parameter change (High Blast Temp, Low $D_{WRZ}$) that flattens the operating line reduces the required blast volume per unit iron, thereby increasing the daily production rate (TPD).

  $\text{Productivity}\propto \frac{\text{Total vol of blast supplied in a day}}{\text{Blast Rate per Ton of Hot Metal}}$

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7. Summary & Instructor’s Closing Remarks

• The “Operating Line” is a straight line passing through the Reserve Zone equilibrium point (W) and the Heat Balance point (H).

• To Improve Efficiency (Lower Coke Rate, Higher Productivity):

  1. Maximize Blast Temperature.

  2. Minimize Thermal Demand ($D_{WRZ}$) (e.g., control slag volume, reduce heat loss).

  3. Control Burden Chemistry (minimize impurities that raise the W point).

• The Rist Diagram analytically solves the three simultaneous balance equations without needing iterative numerical calculation, providing a powerful visual guide for process engineers.