# Top Segment Mass Balance

## Top Segment Mass Balance

C H A P T E R 20 Top Segment Mass Balance O U T L I N E 20.1 Combining the Bottom and Top Segments of the Blast Furnace 191 20.5 No Carbon Oxidation...

C H A P T E R

20 Top Segment Mass Balance O U T L I N E 20.1 Combining the Bottom and Top Segments of the Blast Furnace 191

20.5 No Carbon Oxidation in the Top Segment

196

20.2 Top-Segment Calculations

20.6 Top Gas Results

196

20.7 Coupling Top and Bottom-Segment Calculations

196

20.8 Summary

198

Exercises

198

192

20.3 Mass Balance Equations 192 20.3.1 Fe Mass Balance Equation 192 20.3.2 Oxygen Mass Balance Equation 192 20.3.3 Carbon Mass Balance Equation 194 20.3.4 Nitrogen Mass Balance Equation 195 20.4 Quantity Specification Equations

195

20.1 COMBINING THE BOTTOM AND TOP SEGMENTS OF THE BLAST FURNACE Chapter 7, Conceptual Division of the Blast Furnace, examined reactions in the bottom segment of the iron blast furnace, Fig. 20.1. The principle outcome presented in Chapter 7, Conceptual Division of the Blast Furnace, was a priori calculation of carbon-incoke and oxygen-in-blast requirements for steady production at 1500 C molten iron from iron oxide ore.

Blast Furnace Ironmaking DOI: https://doi.org/10.1016/B978-0-12-814227-1.00020-8

This chapter examines reactions in the top segment of the furnace (Fig. 20.2). Our objectives are to use bottom-segment results of Chapter 7, Conceptual Division of the Blast Furnace, Table 20.1, to determine; 1. blast furnace top gas composition, and 2. the effect of blast temperature on top gas composition. Chapter 21, Top-Segment Enthalpy Balance, and Chapter 22, Top Gas Temperature Calculation, do the same for top gas enthalpy and temperature.

191

192

20. TOP SEGMENT MASS BALANCE

mass Fe in 5 mass Fe out

(20.1a)

mass O in 5 mass O out

(20.1b)

mass C in 5 mass C out

(20.1c)

mass N in 5 mass N out

(20.1d)

all per 1000 kg of Fe in product molten iron. The next four sections expand these equations to include top-segment variables of Fig. 20.2. FIGURE 20.1 Bottom segment of conceptually divided blast furnace. This is a copy of Fig. 7.3.

20.3 MASS BALANCE EQUATIONS 20.3.1 Fe Mass Balance Equation Iron enters the top segment of Fig. 20.2 as hematite, Fe2O3. It leaves in wustite, Fe0.947O. There is no Fe0.947O to Fe reduction in the top segment (Section 7.1). These specifications and Eq. (20.1a) give; "

FIGURE 20.2 Top segment of conceptually divided blast furnace. Flows of Fe0.947O, C-in-coke, CO, CO2, and N2 across the division are the same as in Fig. 20.1.

mass Fe2 O3 in

½69:9 mass% Fe in Fe2 O3   100% furnace charge " # mass Fe0:947 O descending 5 into bottom segment 

This chapter’s general conclusions are that; 1. blast furnace carbon and oxygen requirements are determined in the bottom segment of the furnace, but 2. reactions in the top segment determine top gas composition, top gas enthalpy, and top gas temperature.

or

As with all our calculations, this chapter’s calculations use steady-state mass balances and several quantity specifications. The basic top-segment steady-state mass balances are;

½76:8 mass% Fe in Fe0:947 O 100%



 mass Fe2 O3 in  0:699 furnace charge   mass Fe0:947 O descending  0:768 5 into bottom segment    mass Fe2 O3 in  0:699 subtracting furnace charge

or both sides;

 052

20.2 TOP-SEGMENT CALCULATIONS

#

 1

mass Fe2 O3 in

from



 0:699 furnace charge  mass Fe0:947 O descending into bottom segment

(20.2)  0:768

20.3.2 Oxygen Mass Balance Equation Oxygen enters the top segment in input Fe2O3. It also enters in CO and CO2 rising from the bottom segment, Fig. 20.2. Oxygen

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TABLE 20.1

Fig. 20.1 Bottom-Segment Matrix

This is the same as matrix Table 15.1. It is used here to determine (1) the masses of Fe0.947O and C descending from the top segment into the bottom segment, and (2) the masses of CO, CO2, and N2 ascending into the top segment from the bottom segment. All per 1000 kg of Fe in product molten iron.

194

20. TOP SEGMENT MASS BALANCE

leaves the top segment in descending Fe0.947O and departing top gas CO and CO2. These specifications and Eq. (20.1b) give; 

" 2



½30:1 mass% O in Fe2 O3  100% furnace charge   mass CO ascending ½57:1 mass% O in CO 1  100% from bottom segment mass Fe2 O3 in

 1





mass CO2 ascending from bottom segment 

5



mass Fe0:947 O descending

1

1

mass CO2 out in top gas



mass Fe2 O3 in

#

mass CO ascending

#

 0:301 1  0:571 furnace charge from bottom segment " # mass CO2 ascending  0:727 1 from bottom segment " # mass Fe0:947 O descending 5  0:232 into bottom segment " # " # mass CO out mass CO2 out 1  0:571 1  0:727 in top gas in top gas (

subtracting

 mass Fe2 O3 in  0:3011 furnace charge

 mass CO ascending  0:571 1 from bottom segment )   mass CO2 ascending  0:727 from from bottom segment

furnace charge

#  0:301

mass CO ascending from bottom segment mass CO2 ascending

#  0:571 #

from bottom segment

 0:727

mass Fe0:947 O descending

#

(20.3)  0:232

20.3.3 Carbon Mass Balance Equation

½72:7 mass% O in CO2   100%

"

mass Fe2 O3 in

into bottom segment " # mass CO out 1  0:571 in top gas " # mass CO2 out  0:727 1 in top gas



or

or

"

into bottom segment



"

" 2

½72:7 mass% O in CO2  100%

½23:2 mass% Fe in Fe0:947 O  100%   mass CO out ½57:1 mass% O in CO 1  100% in top gas



" 052

both sides;

Carbon enters the top segment of Fig. 20.2 as C-in-coke charge and as CO and CO2 in ascending bottom-segment output gas. It leaves; 1. as unreacted C-in-coke descending into the bottom segment, and 2. as CO and CO2 in departing top gas. These specifications and Eq. (20.1c) give; 

   mass CO ascending mass C in 100% C 1  100% from bottom segment coke charge   mass CO2 ascending ½42:9 mass% C in CO 1  100% from bottom segment 2 3 mass C-in-coke ½27:3 mass% C in CO2  6 7 descending 54  5 100% into bottom segment   mass CO out ½42:9 mass% C in CO 100% C 1   100% 100% in top gas   mass CO2 out ½27:3 mass% C in CO2  1  100% in top gas

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195

20.4 QUANTITY SPECIFICATION EQUATIONS

or

or "

mass C in

#

"

mass CO ascending

 11

#

coke charge from bottom segment " # mass CO2 ascending  0:273 1 from bottom segment 2 3 mass C-in-coke 6 7 71 descending 56 4 5



 0:429

or both sides:  052

20.4 QUANTITY SPECIFICATION EQUATIONS 

subtracting





mass CO ascending  0:429 from bottom segment    mass CO2 ascending 1  0:273 from bottom segment

 mass C in 1 coke charge

1

 0 52

mass C in



  12

   mass N2 out mass N2 ascending  11 1 from bottom segment in top gas (20.5)

into bottom segment " # mass CO out 1  0:429 in top gas " # mass CO2 out 1  0:273 in top gas

or,

   mass N2 ascending mass N2 out  15 1 from bottom segment in top gas    mass N2 ascending 1 subtracting from from bottom segment

Top-segment calculations of this chapter use the following bottom-segment calculation results, all from matrix Table 20.1: 

from both sides;

mass CO ascending



 0:429 coke charge from bottom segment   mass CO2 ascending  0:273 2 from bottom segment 2 3 mass C-in-coke   mass CO out 6 7 descending 14  0:429 5 11 in top gas into bottom segment   mass CO2 out  0:273 1 in top gas (20.4)



Fe0:947 O descending 1. mass 5 1302 kg=1000 kg of Fe in into bottom segment product molten iron (from Cell C18, Table 20.1). For this chapter’s matrix calculations, this is restated as;  1302 5 

Nitrogen enters the top segment of Fig. 20.2 in ascending bottom-segment output gas. It leaves unreacted in departing top gas. These specifications and nitrogen balance Eq. (20.1d) give the equation; 



½100% N in N2   100% from bottom segment   mass N2 out ½100% N in N2   5 100% in top gas mass N2 ascending

(20.6)



descending 5 392 kg (from Cell 2. masstoC-in-coke bottom segment

C19, Table 20.1) or  392 5

20.3.4 Nitrogen Mass Balance Equation

 mass Fe0:947 O descending 1 into bottom segment

 mass C-in-coke descending 1 to bottom segment



(20.7)



mass CO ascending 5 558 kg (from Cell C24, 3. from bottom segment

Table 20.1) or  558 5 

 mass CO ascending 1 from bottom segment 

(20.8)

mass CO2 ascending 5 387 kg (from Cell C25, 4. from bottom segment

Table 20.1)

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196

20. TOP SEGMENT MASS BALANCE

or 



mass CO2 ascending 1 from bottom segment   mass N2 ascending 5 983 (from Cell from bottom segment 387 5

5.

(20.9)

C26,

Table 20.1) or  938 5

 mass N2 ascending 1 from bottom segment

(20.10)

all per 1000 kg of Fe in product molten iron.

20.5 NO CARBON OXIDATION IN THE TOP SEGMENT Our final specification is that C(s)-in-coke doesn’t react at the cool temperatures in the top segment for kinetic reasons, see Section 2.8 and Eq. (7.16). This is expressed by the equation; 

 mass C in 100% C  100% coke charge   mass C-in-coke descending 100% C 5  100% into bottom segment

• 333 kg of CO, • 741 kg of CO2, and • 983 kg of N2. all per 1000 kg of Fe in the furnace’s product molten iron. This is the top gas composition. In mass percentages, it is 16.2 mass% CO, 36.0 mass% CO2, and 47.8 mass% N2 (Appendix P). In volume percentages, it is 18.6 volume% CO, 26.4 volume% CO2, and 55.0 volume% N2 (Appendix P). Top gas contains considerably more CO2(g) and commensurately less CO(g) than the ascending bottom-segment exit gas. This is the result of the overall top-segment reaction:     0:421CO g 1 0:474Fe2 O3 ðsÞ - 0:421CO2 g 1 Fe0:947 OðsÞ (20.12)

which produces CO2(g) from CO(g).

20.7 COUPLING TOP AND BOTTOM-SEGMENT CALCULATIONS

or 

   mass C in mass C-in-coke descending  15 1 coke charge into bottom segment    mass C in 1 subtracting from both coke charge

or sides:

 052

   mass C in mass C-in-coke descending  11 1 coke charge into bottom segment (20.11)

We now enter Eqs. (20.2)(20.11) into topsegment matrix Table 20.2 and calculate mass CO, mass CO2, and mass N2 in top gas per 1000 kg of Fe in product molten iron.

20.6 TOP GAS RESULTS Matrix Table 20.2 indicates that the furnace top gas contains;

Top-segment matrix Table 20.2 is readily coupled to calculated values of bottomsegment matrix Table 20.1. The most convenient coupling is with both matrices on the same spreadsheet, 26 columns apart. In the present case, the coupling instructions in matrix Table 20.2 are; Cell AC3 contains mass Fe0:947 O descending into the bottom segment; i:e:; 5 C18 Cell AC8 contains mass CO ascending from bottom segment; i:e:; 5 C24 Cell AC9 contains mass CO2 ascending from bottom segment; i:e:; 5 C25 Cell AC10 contains mass N2 ascending from bottom segment; i:e:; 5 C26 Cell AC11 contains mass C-in-coke descending into bottom segment 5 C19

Now, whenever a change is made to matrix Table 20.1, for example, blast temperature, the

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TABLE 20.2

Top-Segment Matrix for Determining Top Gas Composition

This matrix’s solution gives a top gas composition of 333 kg CO, 741 kg CO2, and 983 kg N2 (Cells AC25AC27). The Row 13 temperatures are for information only. They are not used in this chapter’s calculations. For convenience, this matrix is on the same spreadsheet as the matrix in Table 20.1—placed 26 columns to the right.

198

20. TOP SEGMENT MASS BALANCE

FIGURE 20.3 Effect of blast temperature on blast furnace top gas composition. CO, CO2, and N2 masses, per 1000 kg of Fe in product molten iron, all decrease with increasing blast temperature. This is consistent with decreasing steady-state bottom-segment C-in-coke of Fig. 7.4 and O2-in-blast air requirements with increasing blast temperature. Mass N2 in top gas also decreases because mass N2-in-air/mass O2-in-air is constant, Eq. (7.6). The lines are not exactly straight. This is the result of all our matrices’ equations. We may speculate that it is because enthalpy balance Eq. (7.15) contains two nonlinear mass 3 temperature terms, Cells F11 and G11.

top-segment matrix Table 20.2 automatically recalculates the equivalent top-segment masses. For example, this is done by changing blast temperature in Cell D13 of Table 20.1— generating the top gas compositions in Fig. 20.3.

20.8 SUMMARY Top gas composition is readily calculated by combining top-segment equations with

bottom-segment calculation results. Top gas enthalpy and top gas temperature are also calculated this way, Chapter 21, Top-Segment Enthalpy Balance and Chapter 22, Top Gas Temperature Calculation. CO, CO2, and N2 top gas masses, per 1000 kg of Fe in product molten iron, all decrease with increasing blast temperature. This is a consequence of all the equations in our bottom and top-segment matrices. We postulate that it is mainly because the amounts of C-in-coke and O2-in-blast air needed for steady production of 1500 C molten iron decrease with increasing blast temperature, Fig. 7.4. Practically, it means that gas flowrates in the blast furnace and in the top gas handling equipment can be decreased by raising blast temperature. This may be useful if, for example, top gas handling is a bottleneck in the blast furnace plant.

EXERCISES 20.1. Please calculate the top gas composition of Fig. 20.2 when the blast temperature of Table. 20.1 is 1250 C. Use Table 20.2. 20.2. Blast furnace operators of Table 20.1 have learned of a cheap source of magnetite ore. They would like to know how this ore will affect the top gas composition of Fig. 20.2, mass%. Please calculate this for them. The blast temperature is 1200 C.

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