# Combining Mass and Enthalpy Balance Equations

## Combining Mass and Enthalpy Balance Equations

C H A P T E R 6 Combining Mass and Enthalpy Balance Equations O U T L I N E 6.1 Developing a Predictive Blast Furnace Model - Initial Steps 65 6.5 ...

C H A P T E R

6 Combining Mass and Enthalpy Balance Equations O U T L I N E 6.1 Developing a Predictive Blast Furnace Model - Initial Steps

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6.5 Altered O2(g) and N2(g) Enthalpy Values

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6.2 Benefit of Including Enthalpy

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6.6 Discussion

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6.3 Effect of Blast Temperature on Blast Air Requirement

6.7 Summary

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Exercises

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6.4 Altered Enthalpy Equation

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6.1 DEVELOPING A PREDICTIVE BLAST FURNACE MODEL INITIAL STEPS

In doing so, our objective is to move further toward a fully predictive blast furnace model. The basis for these initial steps is shown in Fig. 6.1. We begin the process (Table 6.1) by:

This chapter: 1. combines enthalpy balance equations of Chapter 5, Introduction to the Blast Furnace Enthalpy Balance, with, 2. mass balance and quantity specification equations of Chapter 4, Introduction to the Blast Furnace Mass Balance.

Blast Furnace Ironmaking DOI: https://doi.org/10.1016/B978-0-12-814227-1.00006-3

1. adding enthalpy balance Eq. (5.7) to the Table 4.3 matrix, and 2. removing O2-in-blast air specification Eq. (4.8) from the Table 4.3 matrix. Step (2) is required to avoid having more equations than variables.

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6. COMBINING MASS AND ENTHALPY BALANCE EQUATIONS

The matrix solution shows that: 1. 298 kg of O2-in-blast air per 1000 kg of Fe in product molten iron, and, 2. 1283 kg of air (mass O2 1 mass N2) per 1000 kg of Fe in product molten iron are required to keep Table 6.1 blast furnace operating at steady state.

6.3 EFFECT OF BLAST TEMPERATURE ON BLAST AIR REQUIREMENT

FIGURE 6.1 Simplified inputs, outputs, and temperatures for calculating the amounts of C-in-coke and O2-in-blast air that will give steady production of molten iron 1500 C.

Notice how Eq. (5.7) 400 5

2 ½mass Fe2 O3 in ore charge ½mass C in coke charge  ½mass O2 in blast air  ½mass N2 in blast air 1 ½mass Fe out in molten iron 1 ½mass C out in molten iron 1 ½mass CO out in top gas 1 ½mass CO2 out in top gas 1 ½mass N2 out in top gas

        

ð5:169Þ 0 1:239 1:339 1:269 (5.7) 5 ð3:836Þ ð8:844Þ 0:1099

is included in matrix Table 6.1, especially the minus signs.

An instructive use of the matrix as shown in Table 6.1 is to demonstrate the effect of blast temperature on Fig. 6.1’s steady-state O2-blast air and total blast air requirements. A specific example problem is that the temperature of the blast air, as shown in Fig. 6.1, is to be increased to 1300 C. Predict how this change will affect the blast furnace’s steady-state O2-inblast air and total blast air requirements. All other temperatures and the 400 kg C-incoke charge specification are unchanged.

6.4 ALTERED ENTHALPY EQUATION The above blast air temperature change alters Fig. 6.1’s input enthalpy Eq. (5.3) to: H  25 C   n X Fe2 O3 ðsÞ mass Fe2 O3 in  mi HiInputs 5 ore charge MWFe2 O3 i51  1

6.2 BENEFIT OF INCLUDING ENTHALPY The benefit of including enthalpy Eq. (5.7) in the matrix is that the O2-in-blast air requirement is now calculated rather than specified. So, we are half way toward our fully predictive model.

BLAST FURNACE IRONMAKING

 1  1

mass C in coke charge

mass O2 in blast air

mass N2 in blast air







H  25 C CðsÞ  MWC

H  1300  C  O2 g  MWO2 H 1300 C N2 ðgÞ  MWN2

(6.1)

TABLE 6.1 Matrix for calculating Blast Furnace O2-in-Blast air requirement for any specified Carbon-in-Coke charge

Note: enthalpy balance Eq. (5.7) in row 10; absent O2-in-blast air quantity specification Eq. (4.8); C-in-coke charge specification of 400 kg C per 1000 kg of Fe product molten iron, row 8. The matrix solution shows that steady-state operation with 400 kg of C-in-coke charge requires 298 kg of O2-in-blast air. This matrix was prepared by altering matrix Table 4.3 as described in assigned Problem 4.6. It can also be prepared from scratch. Appendix J shows how to solve it. Try it!

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6. COMBINING MASS AND ENTHALPY BALANCE EQUATIONS

where the last two lines are different from those in Eq. (5.7).

6.5 ALTERED O2(g) AND N2(g) ENTHALPY VALUES H

 1300  C  O2 g

H

1300 C N2 ðgÞ

The values of MW and MW are calculated from Appendix J’s O2(g) and N2(g) enthalpy versus temperature equations. They are: O2

N2

HT½ C   O2 g 5 0:001137  T ½ C 2 0:1257 MWO2

1. 292 kg of O2-in-blast air per 1000 kg of Fe in product molten iron, and, 2. 1255 kg of air (mass O2 1 mass N2) per 1000 kg of Fe in product molten iron are required to keep Table 6.2 blast furnace operating at steady state. These are noticeably lower than with 1200 C blast, Section 6.1. Figs. 6.2 and 6.3 confirm these results.

6.6 DISCUSSION Section 6.1 suggests that we are now half way to a fully predictive blast furnace model. Unfortunately, this is not quite true because Fig. 6.1 specifies that the top gas temperature is 130 C. In reality, top gas temperature is a dependent variable. So, we are only a third of the way toward our fully predictive objective. Chapters 710 will show how this objective is attained.

HT½ C

N2 ðgÞ 5 0:001237  T ½ C 2 0:1450 MWN2

from which: H 1300 C   O2 g 5 1:352 MWO2 H 1300 C

N2 ðgÞ 5 1:463 MWN2

where the units are all MJ per kg of substance. These values are now inserted into Eq. (5.7), which becomes 2400 5 2 ½mass Fe2 O3 in ore charge  ½mass C in coke charge  ½mass O2 in blast air  ½mass N2 in blast air 1 ½mass Fe out in molten iron 1 ½mass C out in molten iron 1 ½mass CO out in top gas 1 ½mass CO2 out in top gas 1 ½mass N2 out in top gas

        

as shown in matrix Table 6.2. The matrix solution shows that;

ð25:169Þ 0 1:352 1:463 1:269 5 ð3:836Þ ð8:844Þ 0:1099

(6.2)

6.7 SUMMARY This chapter shows how to combine the enthalpy balance of Chapter 5, Introduction to the Blast Furnace Enthalpy Balance, with the mass balance and quantity specification equations of Chapter 4, Introduction to the Blast Furnace Mass Balance. The variables are the same - so, the equations are easily combined into an Excel matrix. The combined equations indicate that raising blast temperature decreases the steady-state blast furnace O2-in-blast air and air requirements, all else being constant.

BLAST FURNACE IRONMAKING

TABLE 6.2 Matrix Table 6.1 but with 1300 C blast. Only Cells F10 and G10 are altered. The steady state O2-in-blast air requirement is lowered from 298 to 292 kg by increasing blast temperature from 1200 to 1300 C

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6. COMBINING MASS AND ENTHALPY BALANCE EQUATIONS

FIGURE 6.2 Effect of blast temperature on steady-state

FIGURE 6.3 Effect of blast temperature on steady-state

O2-in-blast air requirement. The requirement decreases appreciably with increasing blast temperature. This is because hotter air brings more enthalpy into the furnace— decreasing the amount of C that must be exothermically oxidized to CO2(g).

blast air requirement. The requirement decreases appreciably with increasing blast temperature.

EXERCISES All masses are kg per 1000 kg of Fe in product molten iron. 6.1. Matrix Table 6.1’s carbon charge is lowered to 380 kg per 1000 kg of Fe in product molten iron. Predict what this operation’s steady-state O2-in-blast and

total blast air requirements will be with this decreased carbon charge. Assume that the top gas temperature remains at 130 C. 6.2. Matrix Table 6.1’s stoves are under repair so that they can only attain 1100 C blast. What is the blast furnace’s steady-state O2in-blast air requirement with this cooler blast? The C-in-coke charge is 400 kg per 1000 kg of Fe in product molten iron.

BLAST FURNACE IRONMAKING