Ejercicios Pirometalurgia

8/11/2019 Ejercicios Pirometalurgia

1/5

1) Adiabatic Flame Temperature of CH4Combustion with Excess Air

The combustion of hydrocarbon fuels is the most common way to provide heat for materials

processing needs. One of the ways to rank fuels is by their adiabatic flame temperature (AFT),

using either stoichiometric air or O2 for the oxidant. The stoichiometric amount of oxidant is

calculated by assuming complete combustion of the hydrocarbon to CO2 and H2O. (If the fuel

contains S, combustion is to SO2). This example will show how the AFT is calculated for various

amounts of air in excess of stoichiometric amounts (called XSA combustion). Air is assumed to be

79% N2and 21% O2. The units used in this example are C and kJ.

Data

Equation [1] shows the standard reaction for the combustion of methane for the formation of

water vapor as the product. The stoichiometric amount of air is 9.524 moles. For reactants

entering at 25C, the heat content of the product gases plus Hrx at 25C must equal 0 for

adiabatic conditions. Taking data from FREEDs Reaction tool:

()

()

()

()

[1]

Calculations and Results

There are at least two different ways to calculate the AFT. One way is to pick an AFT, and calculate

the % excess oxidant amount. The other is to select the oxidant amount and calculate the AFT. This

example uses the latter approach. Since we are solving for the AFT, we need an explicit equation

for the heat content as a function of temperature, where the lowercase t indicates C. An

examination of the data indicates that Cp is very close to a linear function of t above about

1200C, so the functional equation for Ht-H25is a quadratic:

Ht-H25= A (t) + B (t) + C [2]

Excels Graphics tool was used to determine values of A, B, and C for each product speciesbetween 1200 and 2000C. Figure 1 shows the results. The value of R =1, thus indicating that the

quadratic equation gives an extremely good fit to the data. The H t-H25equation parameters were

converted from J to kJ, and copied to rows 40 and 44. The mass balance relationships for various

amounts of % excess air are shown in Table I. A heat balance for combustion was written by taking

the sum of all heat effect parameter terms in cells C33:H35; the term for C includes the Hrxfor

Equation [1]. A heat balance equation was written in cells D48:I48, using an initial estimate of the

AFT of 1700 in row 47. Super Goal Seek was used to calculate the value of t for each value of %

excess air, and plotted in Figure 2. The AFT varied from about 2050C at stoichiometric air, to

1200C at double the stoichiometric air. Excels Trendline tool was used to fit a quadratic formula

to the data line in Figure 3. The equation is shown in a text box on the Figure. The value of R is0.9995, which indicates an acceptable fit for a heat balance problem. Care should be taken in

making AFT calculations above 2000C using the stoichiometry written in Equation [1]. This is

because even with excess air, some CO and H2will be present in the gas, and even small amounts

of O, H, and N. If the air is enriched with O2, the calculated AFT may be well above 2500C, but

the actual AFT will be significantly less.


2/5

Another way to calculate adiabatic reaction temperatures is to use FREEDs Reaction option. For

example, 26% XSA has 12 moles of air to one mole of CH4and produces 0.52 moles of O2and 9.48

moles of N2 (in addition to two moles of H2O and one mole of CO2). The column labeled Heat in

Table II is the sum of the heat of reaction plus the heat content of the reaction products, and will

equal zero at the AFT. Figure 3 shows a chart of the results; the heat equals zero about 1740C.

Excels Trend line tool gives the following equation (units are J):

Heat = 0.01752t2 + 463.117t854,840 [3]

The equation was solved for Heat = 0 by Goal Seek to find the AFT = 1732C. This procedure can

be repeated for each value of %XSA of interest, which generates a family of lines on the chart. You

should check this using the textbox equation in Figure 2. FREEDs Reaction tool has an even easier

way to calculate the AFTuse the Calculate feature from the floating toolbar. Enter 0 for the

value, and check the Overall Heat box, and FREED will calculate the temperature where the overall

heat is zero. You can repeat this several times, and use the set of results to create a chart like

Figure 3.

2)

Heat Balance for Calcination Furnace with Heat Exchanger

Example Description

Calcination is a process whereby a complex compound (usually a carbonate, hydroxide or sulfate)

is heated to a temperature such that the complex compound decomposes to the oxide. In this

case, MgCO3is heated in a fluidized-bed furnace heated by combustion of CH4to produce MgO.

The MgCO3and CH4enter at 25C, and the MgO and furnace gases leave at 650C. The furnace

gases pass through a heat exchanger to preheat the combustion air, thus increasing the efficiency

of the process (in terms of fuel consumption per amount of MgCO3calcined). A sketch of the

process is shown below. The objective of this example is to calculate the effect of air preheat

temperature on amount of MgCO3 calcined, and the temperature of the furnace gases leaving the

heat exchanger. The basis is 1 mole of CH4burned with 11 moles of air (15.5% excess air), and heat

losses of 60,000 J in the calcination furnace and 40,000 J in the heat exchanger,

Data


3/5

The first step is to obtain information about the heat content of the various reactions and streams

involved in the process. FREEDs Reaction tool is the best way to obtain information on the

amount of heat produced by burning CH4with 11 moles of air and by calcining MgCO3 and heating

the products to 650C. The combustion reaction is:

CH4(g) + (11)N1.58O42(g) CO2(g) + 2H2O(g) + (8.69)N2(g) + (0.31)O2(g) [1]

The reaction tool found that the sum of combustion heat plus the sensible heat of the product

gases at 650C was556,100 J. (Note we have rounded off the heat value to 4 significant figures,

which is quite adequate considering the uncertainties associated with heat losses.) A similar

calculation for MgCO3calcination plus heating the products to 650C gave an overall heat effect of

176,400 J/mol. The use of FREEDs Reaction tool is not shown on the worksheet because it was

shown before, and it is a rather straightforward FREED application.

Next, we need an equation for the heat content of air and CO2. FREEDs Graphics tool and

Trendline was used to obtain a quadratic heat content equation for air, as shown in Figure 1 of the

worksheet:

Ht-H25for air = 28.44t + 0.00338t2700 (J/mol) [2]

Ht-H25for CO2= 38.43t + 0.01289t21050 (J/mol) [3]

Finally, we need a heat content equation for the products of combustion from Equation [1].

FREEDs Reaction tool is used by putting the reaction products on both sides of the re action

equation. Hrx is zero because there is no chemical change, so the Heat column simply reflects

the heat content of the products. Figure 2 on the worksheet displays the results for 12 moles of

combustion gas. A linear heat content equation appeared satisfactory for this situation:

Ht-H25for 12 moles of combustion gas = 404.42t17820 (J) [4]


We start with a heat balance around the calcinerby assuming various air preheat temperatures,

and calculate the amount of MgCO3calcined. Table I shows the results on worksheet CHX. Row 35

expresses the results in practical terms of the volume of natural gas required to produce one

tonne of MgO. Heating the combustion air to 600C cuts the natural gas consumption to about

72% of the requirement for no air preheat.

Next, we look at the heat exchanger, which operates in a counter-current mode. If the heat

exchanger operated at 100% efficiency and no heat loss, the maximum air preheat temperature

would be 650C. However, we do have heat loss, and no exchanger is 100%efficient in transferring

heat, so the highest air preheat temperature will probably be


4/5

Warm furnace gas temperature =0.551(apht) + 592 [5]

Volume of CH4 (STP m3) per tonne of MgO produced = 4.45 10-5(apht)20.124(apht) + 201 [6]

3)

The Calcination of Dolomite

Example Description

Calcination is the decomposition of complex compounds into simpler ones, plus the evolution of a

gas. This occurs when the compound is heated to a point where the decomposition products are

more stable than the original compound. The simplest case is the calcination of a carbonate to

form an oxide and CO2. Another name for calcination is thermal decomposition, because thermal

energy is the only driving force for the reaction (i.e., no reactant is necessary, just heat). The

thermal decomposition temperature is defined as the temperature where the sum of the partial

pressures of the gaseous decomposition products is 1 atm. The calcination of MgCO 3 is discussed

in Section 12.2 of the text. This example will show the procedure for calculating the decomposition

temperature for mixtures of carbonates in the CaOMgOCO2system

Data

Magnesite and calcite decompose to their respective oxides and CO2according to Equation [1]

and [2]. The calcination of dolomite could produce a mixture of CaO + MgCO3, or a mixture of

MgO + CaCO3as shown in Equations *3+ and *4+. FREEDs Reaction tool was used to obtain

thermodynamic data for Equations [1] and [2] as shown in Table I. Note that an alternative form of

CaCO3, aragonite, is not as stable as calcite.

CaCO3(calcite) CaO(lime) + CO2 (g) [1]

MgCO3(magnesite) MgO(magnesia) + CO2 (g) [2]

CaMg (CO3)2(dolomite) CaO(c) MgCO3(magnesite) + CO2 (g) [3]

CaMg(CO3)2(dolomite) CaCO3(calcite) + MgO(magnesia) + CO2(g) [4]


The calcination of dolomite CaMg (CO3)2is more complex than for a single carbonate. The CaO

MgOCO2system is effectively a 3-component system because the gas phase can be considered as

containing only CO2.*Thermal decomposition of dolomite could produce a mixture of CaO +

MgCO3, or a mixture of MgO + CaCO3. The correct situation can be determined by comparing the

Grx for Equations [3] and [4] from Table II of worksheet DOL. Alternatively, a comparison of

log(pCO2) can be made; log(pCO2) is identical to logKeq when both the carbonate and the oxide

are present. Equation [4] has a much lower G and hence is the first reaction to take place whendolomite is heated to the calcination temperature. Figure 1 shows a plot of Grxfor Equations

[1], [2], and [4]. The temperature where these lines cross the Grx= 0 line indicates athermal

decomposition temperature for dolomite of about 690 K. The thermal decomposition

temperatures for magnesite and calcite alone are about 680 and 1160 K. A more accurate

decomposition temperature can be obtained from FREEDs Reaction tool by setting logKr = 0 and

calculating T. Table III shows the results for the decomposition of dolomite; the decomposition


5/5

temperature is 419C. A similar calculation was made for the decomposition temperatures of

MgCO3and CaCO3, and the temperatures are shown on the ternary phase diagram.

The above results now permit the construction of the phase diagram for the CaOMgO

CO2system as shown below. The 3-condensed-phase fields are labeled with the temperature at

which the pCO2= 1 atm. The dashed lines emanate from the CO2apex.

Calcination of an initial mixture of magnesite and dolomite occurs along line xx. First the

magnesite decomposes at 407C (from x to x), then the dolomite decomposes according to

Equation *4+ at 419C (from xto x), and then the calcite decomposes at 891C (from xto x). A

mixture of dolomite and calcite decomposes along line yy, first by decomposition of dolomite at

419C, then calcite at 891C. Dolomite itself decomposes in the same sequence as a mixture of

dolomite and calcite.

Ejercicios Pirometalurgia

Documents

Transcript of Ejercicios Pirometalurgia