Handbook_on_Material_and_Energy_Balance_Calculat1

Chapter 9 System Balances on Reactive Processes 575

Exercises

9.1. Use FREED's Reaction tool to calculate the АН°сотЪ of ammonia at 25 °C and express the
result as the HHV and LHV for one m3 (STP) of ammonia. Calculate the АЯ°геах and log Кщ for
the reaction for the formation of ammonia from the elements as a function of temperature from 25
°C to 500 °C, and plot the result. Is it possible to use FREED to calculate the ART for the reaction
between one mole of N2(g) and three moles of H2(g), initially at 25 °C, to form ammonia under
equilibrium conditions?

9.2. Calculate the heat of formation of a fuel oil that has a HHV of 43 950 kJ/kg, and a LHV of 41
460 kJ/kg. Assume the oil consists only of С and H.

9.3. Determine the AFT for combustion of propane with air as a function of the %XSA, from
stoichiometric air to 50 %XSA. Is there a simple relationship between the AFT and the % 0 2 in
the combustion gas?

9.4. Propane is burned with 120% of stoichiometric air with the intention of obtaining an AFT of
2150 °C. Calculate the air preheat temperature required.

9.5. A continuous chemical vapor deposition process (CVD) is used to prepare exceptionally pure
quartz from silane according to the reaction:

SiH4(g) + 02(g) - Si02(c) + 2H2(g)

The reactants enter at 298 K, mixed in the ratio of 1.1 mole of 02 per mole of SiH4. Any
oxygen in excess ofthat needed to oxidize silane forms H20(g). The objective is to use the АЯ°гх
to supply the heat necessary to maintain the process at 1350 K. Heat losses are estimated at 20
kJ/kg of Si02 produced. Will the process attain the desired temperature? If not, how much heat
must be added (or removed) to accomplish the goal.

9.6. An iron ore reduction process is being designed to reduce Fe203 with solid C. The reactants
are mixed and formed into briquettes, and fed (at 25 °C) continuously into a furnace kept at 1000
°C by an external source of heat. The reaction products discharge at 1000 °C. The product gas
from the reduction contains <jpCO = 0.90, balance C02. The product solids consist of a mixture of
Fe and С in a molar ratio of 10. How much heat must be provided for the process?

9.7. A reconditioned gas from a steelmaking furnace contains <pCO = 0.85, balance C02 is
available at 650 K. The gas is burned with 15% XSA to provide heat for the calcination of
limestone. The air and limestone enter the reactor at 298 К and the products leave at 1150 K. The
heat loss is 40 kJ per kg of lime produced. Calculate the fuel and process thermal efficiency.

9.8. Hydrogen can be manufactured by passing a mixture of steam and oxygen through a bed of
carbon. When operated at 950 °C, the product gases contain nearly 100 % CO and H2. Steam is
available at 400 °C, and oxygen at 80 °C. Carbon enters the furnace at 25 °C. How many tonnes
of С are required per tonne of H2 produced? Neglect heat loss. What is the AFT for the product
gas if burned with 10% XSA, and the reactants enter at 25 °C?

9.9. A blast furnace stove receives air at 30 °C with 50 %RH and heats it to a blast air temperature
of 1060 °C. Calculate the AFT of the bosh gas.

9.10. A blast furnace uses dry air heated to 1100 °C. The blast is modified by adding 40 g of CH4
(entering at 85 °C) per kg of blast air. Calculate the change in the mass of coke С consumed as a
result of the modification, and the required blast air temperature to attain the same AFT as without
any CH4.

9.11. Fuel oil having the properties described in Example 9.2 is burned with 15% XSA to generate
steam at 350 °C and 100 bar pressure. The water enters the boiler at 40 °C, and the oil and air
enter the burner at 25 °C. The combustion products leave the boiler at 475 °C. Calculate the kg of
steam that can be produced per kg of fuel oil. Use one of the steam table programs from the
internet to calculate the enthalpy of the superheated steam.

576 Chapter 9 System Balances on Reactive Processes

9.12. A shaft furnace is used to melt copper cathode. Sheets of copper are put into the top of the
furnace, and fuel oil of the type described in Example 9.4 is burned with slightly less than
stoichiometric air at the bottom. The oil and air enter at 25 °C. Molten copper is produced at 1100
°C, and the gas leaving the top of the furnace is at 750 °C. The composition of the stack gas after
drying is:

<pC02 = 14.10%; фСО = 2.79%; <pH2 = 2.95 %; <pS02 = 0.08%; balance N2.

Calculate the % of stoichiometric air used in the combustion. Calculate the mass of fuel oil
required to melt one tonne of copper.

9.13. Suppose that the stack gas from the above exercise is used to preheat the combustion air.
The stack gas can be burned directly as it leaves the furnace (without cooling and dehumidifying),
or cooled to 25 °C, with the moisture removed to the dew point at 25 °C (which also removes all
the S02), and then used as a fuel (at 25 °C). Assume the stack gas is burned with 15% XSA, and
can transfer half of its АН°сотЪ to the combustion air. Calculate the amount of fuel oil required per
tonne of copper for each type of stack gas, and determine which is preferred.

9.14. In the production of sulfur dioxide with pure 02, cool S02 must be recycled to the burner to
maintain the temperature at 740 °C (see diagram below). The S02 is cooled in a heat exchanger
that produces saturated steam. Calculate the flow of each stream. If the saturated steam is used to
melt sulfur (in a separate unit not shown below), calculate a feasible temperature and pressure for
the steam (or steam/water mixture) leaving the sulfur-melting unit. Neglect heat losses in the HX
and SPL.

S02
(130 °C)

' S02

02 (25 °C) Sulfur S02
S(liq)(120°C) burner (130 °C)
(adiabatic)
i Steam (saturated)
(180 °C)

9.15. An aqueous solution contains one mole of CuS04 and 0.5 mole of Ag2S04 dissolved in one

kg of water at 25 °C. The silver and copper are to be recovered by precipitating them by injection
of S02(g). The S02(g) dissolves quantitatively to reduce the Cu2+(aq) and Ag+(aq). The principle
the unprecipitated Cu2+(aq) and Ag+(aq), are S042"(aq),
ionic species in solution, in addition to to selectively precipitate the metals to separate them from
R+(aq), and HSOzf(ag). The objective is
each other. First S02 reduces the Ag+(aq) to Ag or Ag2S, which is then filtered from solution. It
then it reduces the Cu2+(aq) to Cu or Cu2S, which is then filtered. Determine if this is feasible, and
if virtually complete precipitation of the Ag+(aq) is feasible before any Cu2+(aq) is precipitated.
How much S02(g) is required for each metal? Calculate the pH when the last trace of Ag+(aq), and
the last trace of Cu2+(aq) is precipitated. Will there be a significant temperature change when the

process is complete? Assume the S02(g) enters at 25 °C.

Obtain data for the value of log Kf0Tm of the ionic species from the elements at 25 °C from one
of the references cited in the General References list, and write appropriate ionic reactions to
calculate the most stable Ag and Cu compound (the metals, Ag2S, or Cu2S) that will form by S02
reduction at 25 °C. Assume these values do not change significantly with temperature. Assume
ideal ionic activity, and neglect the slight amount of H20 consumed in the precipitation reactions
on solute molality.

CHAPTER 10

Case Studies

The object of the first nine Chapters was to introduce the principles of conservation of mass and
energy, and show how to apply them to a variety of practical or hypothetical processes. As a
capstone to those Chapters, we include here five case studies of materials processing processes
which are either more complex than the examples of the previous Chapters, or which bring certain
concepts together in a different way.

10.1 Material Balance for an H-Iron Reduction Process with Gas Tempering and Recycle

The material balance of the H-Iron process discussed in Section 6.5.3 omits an important part
of the process — the treatment of the spent gas (offgas) to remove moisture in a condenser so that
it can be recycled back into the FR (along with fresh H2). Also, the fresh H2 inevitably contains
some N2 as a result of the way the H2 is produced, so there must be a bleed stream to prevent N2
from accumulating in the reducing gas. This adds two additional variables to the system: the
amount of water removed in the condenser and the amount of N2 in the incoming (fresh) H2.
Figure 10.1 shows a flowsheet of a simplified version of an H-Iron process, but now with the
addition of gas tempering and gas bleed. Recall that the bleed gas is not wasted since it can be
treated elsewhere to recover most of the H2 for recycling.

Ore . Spent ■► Bleed
PR gas ^ S p l i t t e r
(Fe203) I 1

P) 10 ■ Recycle
■ PR gas

\ Mixer 7

PR oxide Condenser
(Fe304 + (CD)
FeOi.n)
13Ì
DRI (Fe +
FeOi.oe) Water |

Figure 10.1 Flowsheet for the H-Iron process with gas tempering and recycle. Solid lines
represent solid-phase streams, dotted lines represent gas-phase streams, and dashed lines represent
liquid-phase streams. Compare to Figure 6.35.

The same four reactions [6.75 - 6.78] used in Section 6.5.3 are applicable in this Section, as
are two equations relating the extent of reduction or magnetite and wustite vs. the /?H20//?H2 (gas
ratio, or GR).

The presence of N2 is not all bad, since it brings in thermal energy by virtue of its presence in (heated)
stream 4. However the <pN2 must be controlled within acceptable limits.

578 Chapter 10 Case Studies

GRpR = -7.84(XRM)2 + 8.92(XRM) - 0.04

GRFR = -7.72(XRW)2 + 13.17(XRW) - 5.18

But before tackling the material balance equations, the complexity of the flowsheet suggests
that we first step back and take an overall look at the main features of the process (please review
Section 6.5.2 and 6.5.3). Some of the process characteristics that will guide us in writing material
balance and stream constraint equations are:

• S9 is the bleed for N2, so all of the N2 entering in the new gas (SI 4) must exit via S9. S9
will also carry out H2 and H20 at GRPR.

• Streams 9 and 13 carry out all of the H20 that enters in S14 plus that produced by
reduction of hematite.

• As the extent of gas recycling increases, the N2 content of the reducing gas eventually
builds up to an unacceptable level. Therefore a practical constraint to the process might be
the level of N2 in S4.

For these and other considerations, the following seven variables are set as independent:

wFe203inSl; иН2, H20 andN2 in S14; <pH2OinS12; XRW; limit on N2 in S4.

The material balance and stream/unit constraint equations are written and solved to calculate
the flow and composition of the remaining streams. Owing to space limitations for describing the
system in this text, the only variables changed were the ntì2 in S4, XRW and the limit on N2 in S4.
A detailed setup is in workbook Recycle H-Fe.xls (folder Steel) on the Handbook CD, and can be
used to explore the effect of changing the other variables. There are four "fixed" variable values:

wFe203inSl = l; яН2<Э in S14 = 0.3; nN2 in S14 = 0.4; <pH20 in S12 = 0.03

The materials balance equations were written first. The flowsheet has seven units, and
material balance equations were written around each unit in terms of the amount of each species in
and out. The material balance equation format was similar to the previous example in Section
6.5.3. Five species balances were written around the PR, three around SP-F, five around the FR,
and three around each of MX-F, CD, MX-P and SP-P. In addition, an overall balance for O, H2
and N2 was written, for a total of 28 material balance equations.

Six system constraint equations were required. The φΗ20 in S12 was expressed in terms of
species amounts, the GRPR/A7?M relationship equation was written for S8, the GRFR/A7?W
relationship equation was written for S5, and four other stream composition equivalence equations
were written to force splitter output stream compositions to be equal. The balance and system
equations required solving 35 equations. As before, the equation format was set so that when a
solution was found, all equations would equal zero.

In addition to the system constraints, two additional Solver constraints were required to assure
a feasible solution. These constraints relate to the limits imposed on XRM by the valid range of
plant data used in deriving Equation [6.74], namely that XRM must lie between 0.60 and 0.99*.
This prevented Solver from seeking XRM values outside this range.

The first step was to determine if there were limits on %N2(S4) outside of which no feasible
materials balance could be obtained. The "fixed" variables were set as described above, for two
values of XRW: 0.98 and 0.95. The S3 (DRI) amount is always 2, and the amount of wustite
(FeOi.oó) in S3 = 2(1 - XRw). (In terms of mass fraction, the two values ofXR would produce DRI
with 0.60 and 1.50 %0). The amount of H2 consumed = 3 - 1.06xW(S3). AtXRw = 0.98, 2.9576
moles of H2 are consumed and at XRW = 0.95, 2.894 moles of H2 are consumed**.

* This is a larger range than used in Section 6.5.3. The range is expanded for example purposes.
The theoretical minimum amount of new gas H2 required is the amount consumed, but is not attainable

because the new gas has some N2 which must be bled (with some H2) via S9.

Chapter 10 Case Studies 579

SuperSolver was first used to solve the equation set for a range of ^H2(S14) between 3.2 and
3.8. A balance was sought for a maximum, then a minimum of %N2(S4). The results showed that
when minimizing %N2(S4), XRM was 0.6 if ^H2(S14) was less than about 3.33. This is the lower
limit imposed on the system by the data set used to correlate XRM and GRPR as shown by Equation
[6.73]. There was no lower limit for ^H2(S14) when maximizing %N2(S4) other than the
theoretical minimum amount of /7H2(S14) required to reduce one mole of Fe203 to the DRI. To
avoid system conditions where XRu was 0.6, the system simulations were performed only at

ftH2(S14) >3.3, with the understanding that the results at the lowest value ofrcH2(S14)at minimum
%N2(S4) may not be feasible. The results of a simulation for ^H2(S14) between 3.3 and 4 for two
values of XR^ are shown in Figure 10.2.

Figure 10.2 Simulation results for material balance on H-Iron process to determine limits of
%N2(S4) as a function of wH2(S14). Independent parameters were 1 mole of Fe203 entering, XRw
= 0.98 and 0.95, ^N2(S14) - 0.4, ^H20(S14) = 0.3, and ^H20(S12) - 0.03. The black lines are for
XRw = 0.98 and the gray lines for XR^ = 0.95. XRM at maximized %N2(S4) is not shown; it is
always 0.99.

The results show that %N2(S4) increases as ^H2(S14) decreases. This is consistent with our
earlier observation that lowering the amount of new H2 requires a greater amount of recycled gas,
which in turn causes the buildup of N2. At maximized N2(S4), XRM remains at the upper limit of
0.99 for both values of XRw, and hence is not shown on the figure. At minimized N2(S4), XRM
increases with increasing /7H2(S14).

The effect of decreased XR^ is to lower the %N2(S4) which is understandable because less
reducing gas (i.e., less gas recycle) is necessary at lower XRW. Decreasing XRW has no effect on
XRu at maximized N2, and a mixed effect at minimized N2. At both values of XR^, all variables
tend to converge with increasing <jpN2(S4). The two values of %N2(S4) appear to converge at
about «H2(S14) « 4.2, above which no feasible solution could be found.

The stream flow amounts for S4, S9, and S10 at XRW = 0.98 are shown in Figure 10.3. S4
decreases with increasing T?H2(S14) which is consistent with our earlier observation that the
amount of reducing gas should decrease as the amount of H2 in the new gas increased. Since the
T?N2(S9) remains constant at 0.4 mol (remember we "fixed" ^N2(S14) at 0.4, and all of the entering
N2 must leave via S9), the increase of S9 with /7H2(S14) is entirely due to loss of the H2 in excess
of the amount consumed by ore reduction (2.958 mol). Lowering X7?w to 0.95 (results not
displayed) greatly decreases S14 and slightly increases S9.

580 Chapter 10 Case Studies

Figure 10.3 Stream flows at maximum and minimum N2(S4). Gray lines represent stream flows
at maximized N2(S4), while black lines are for minimized N2(S4). The flow of S10 is zero at
minimized N2(S4), except at the lowest «H2(S14), which means S9 = S8 when S10 = 0. The
stream flows for minimized and maximized N2(S4) appear to converge at «H2(S14) » 4.2, which is
consistent with Figure 6.39 results. Please see worksheet Recycle H-Fe.xls for a more complete
explanation of the GR equations and the setup for SuperSolver.

The simulation reveals a number of interesting aspects about the process. Most important is
that a solution to the balance and constraint equations exists only for certain N2 and H2 amounts
because of constraints placed on the relationship between gas composition and extent of solid
reaction. For a certain set of independent variables:

• The simulation found an upper limit on the amount of new gas H2 that can be used. This
is because an upper limit was set on XRM and XR^. This doesn't mean that the process can't
be operated above the simulation limit, it just means that the GR/XR equation [6.74] would no
longer be valid.
• The simulation found that the amount of recycle gas increases rapidly as the amount of
new gas H2 approaches the theoretical minimum amount (about 2.95 moles, depending on
JL/?W). The %N2 in the reducing gas also increases. Both increases are exponential as the
theoretical minimum amount of new gas H2 is approached. This has obvious practical
implications for the process heat balance and the ability to properly operate a fluidized bed
furnace at such high gas flows. And certainly the XR/GR relationship expressed by Equation
[6.74] would not be valid at high %N2(S4).
• Other than (of course) the conservation of mass, the results are always constrained by
one of three factors: the upper or lower limit of XRM, the flow of S10, or the ^N2(S14). At
maximum %N2(S4), the upper limit of 0.99 for XRM constrains the system. At minimum
%N2(S4), the flow of S10 = 0 (it cannot be less than 0) constrains the system down to about
7?H2(S14) = 3.33. Below that, the system is constrained by the lower limit of XRM of 0.6. At
or above ^H2(S14) of «4.2 (exact value depends on set value of X7?w), the set value of
ftN2(S14) of 0.4 constrains the system because more N2 enters than can be removed by S9.
This is shown by the convergence of the maximized and minimized values of %N2(S4) at
ttH2(S14) of 4.2 forXRw = 0.98.
• The ability of Excel's Solver tool to search for process limits (i.e., maximum or
minimum values for a parameter) greatly aided the process simulation.

Chapter 10 Case Studies 581

10.2 Mass and Heat Balance Simulation for the Use of DRI in EAF Steelmaking

The objective of producing DRI is as a scrap substitute for steelmaking (usually the electric
arc furnace). If the DRI is produced as a powder, such as via the H-Iron process discussed in
Section 10.1, it must be hot-compacted into a briquette before shipping. This product is called hot
briquetted iron, or HBI, and is a preferred form because it is durable and oxidation-resistant. If the
DRI is produced in a shaft furnace, as discussed in Section 6.5.4, the porous pellets must be
completely cooled before exposure to air to prevent reoxidation . Preferred practice is to discharge
the hot pellets into a covered conveyor and charge them hot to the EAF. This decreases the
amount of electrical energy needed to melt the pellets.

An EAF operates differently when using DRI in place of scrap. First, the iron content of DRI
is less than that of scrap because of the presence of gangue, unreduced iron oxide, and carbon.
This means the fluxing practice and oxygen lancing is different. Next, the charging practice of
DRI is different because it may be charged without lifting off the roof. This may shorten the tap-
to-tap time, and thus decrease the heat loss. A mass and energy balance can quantify the effect of
DRI on the charge practice and electricity use. We developed ways of doing this in earlier
Chapters for simpler processes, and here we extend our techniques to the EAF. Our goal is to
develop a system calculation model for DRI/scrap mixtures that will simulate the effects of raw
material properties on the amount of thermal energy required to produce steel. For simplicity, we
will call this an MEB (mass and energy balance) model. The details are on workbook MEB
Program.xls (folder Steel) on the Handbook CD.

Before describing the MEB, a brief explanation of EAF steelmaking is in order. Making a
heat of steel in an EAF (100 to 180 tonnes) takes about 90 minutes from tap to tap. The charge
consists of iron units (scrap iron, DRI, etc.), flux (lime, dolomite, etc.), and often some carbon
(electrode scrap, coke, etc.). The furnace cover is lifted, and about one-third of the charge is
placed in the furnace. The lid is repositioned, and the electrodes are lowered to the top of the
charge. An arc is struck, and the electrodes melt a hole in the charge bed. Oxygen/natural gas
burners are used along the sidewalls to heat the charge. When the charge is mainly molten, the
electrodes are raised, the lid removed, and more charge is placed in the furnace. The arc is again
struck and the charge melted. This is repeated for a third time. During the last stages of
meltdown, oxygen and carbon are injected into the slag to keep it foamy, while arc heating
continues until the furnace contents reach the tap temperature, usually near 1650 °C. Throughout
the entire process, gas and fume are evolved and mix with air in the upper part of the furnace
and/or in the offtake duct. The offgas is cleaned to remove dust, and the clean offgas (C02, H20,
and N2) is discharged. When the heat specifications are reached, the furnace is tapped, and
prepared for the next heat. Some slag may be left in the furnace to protect the lining from erosion.
A sketch of an EAF is shown in Figure 10.4.

One of the goals of an EAF operator is to decrease the amount of electrical energy required to
melt the steel. Since combustion heat is cheaper than electrical heat, the goal is to use as much
combustion heat as possible, while still keeping the tap-to-tap time short. This is accomplished by
natural gas burners early in the meltdown stage, injecting carbon and burning it in the slag in a
later stage. Oxygen is injected to oxidize the bath carbon towards the end of the process, and for
post-combustion. This latter term refers to the oxidation of CO and H2 above the steel bath, as
much as possible in the foamy slag layer. Heat is transferred back to the bath by convection and
radiation heat transfer.

For simplicity, the general term "DRI" will be used to include HBI and all other forms of solid-phase iron
produced by gas-based or carbothermic reduction.

582 Chapter 10 Case Studies

electrode
water

§t-comb. lance & С
^02 inj. lance & NG
bath 02 lance
(NG burner early)

Figure 10.4 Sketch of an electric arc furnace during operation, showing principal zones. Nature
of zones and points of entry are approximate, and change with time.

Normally, the iron units to an EAF come entirely from scrap. When minor tramp element
levels are critical, DRI or HBI can be substituted for part of the scrap. The lowest levels of
interstitial elements in the steel are obtained with complete substitution of DRI for scrap.

The MEB was structured so that the mass balance was uncoupled from the heat balance. The
mass balance can be solved first, then the heat balance for melting DRI and scrap, and then an
exploration of oxygen lancing and post-combustion. The mass balance has three parts.

1. Flux mass-balance. DRI contains variable amounts of gangue, unreduced iron oxide (as
FeO), and carbon (mainly as Fe3C). Flux (lime and burned dolomite) are added to attain a
certain user-selected slag basicity, as measured by the V ratio:

%(MgO + CaO) [10.1]
V=

%(Si02+Al203)

In addition, to protect the magnesia brick furnace refractory, the slag needs to be saturated
with MgO. MEB makes a mass balance based on the user-selected V value, the amount of
gangue, and an empirical formula for the saturation limit of MgO, and calculates the
amount of each flux to use.

2. Oxygen mass balance. Oxygen is required to oxidize the DRI carbon to the user-selected
tap carbon, and to form the slag FeO. The %FeO in the slag is related to the %C at tap as
obtained from an empirical formula, which is also used in the flux mass balance.

3. Flux and oxygen mass balance on the scrap. Scrap has a narrow range of carbon levels, a
very small amount of surface oxidation (i.e., rust), and very little "dirt" (bits of concrete or
soil), so a generic scrap was selected that had typical levels of impurities, with 98.5 %Fe.
Flux and oxygen requirements were calculated for the generic scrap, based on the balance
procedures used for the DRI. The scrap composition can be changed, but was left constant
for the MEB simulations. Therefore, once the flux and oxygen requirements are calculated
for the scrap, it's not necessary to do it again.

Chapter 10 Case Studies 583

The results of a sample flux and oxygen mass balance are shown in Figure 10.5. The user-
entry data is shown in boxed cells, while the rest of the values are calculated by the MEB.

The MEB mass balance calculations involve a circular reference, which we first mentioned in
Section 4.8. A circular reference is when a formula refers back to its own cell, either directly or
indirectly. The circular reference avoided the need to use Goal Seek, so that the flux and oxygen
content could be calculated immediately after changing any user-specified data. Please use ExcePs
on-line help to understand how a circular reference works, how to trigger its use, and how to
configure its convergence and initialization. Figure 10.5 shows that for a V ratio of 2.0, nearly 50
kg of flux is required per tonne of DRI charged, and 110 kg of slag is produced.

Basis Case for DRI Flux and 02 Mass Balance

%C at tap V ratio % of total С as Fe3C 97

0.10 2 % of DRI С as Fe3C 1.65
% of DRI С as element 0.05

DRI %ofDRIFeasFe3C 23.04

% metallization 93.60 DRI gangue basicity 0.44
' Fetot 92.50 0.47
Fe++ 5.92 кg Equivalent С content of DRI, % 4.53
Fe, metal 86.58 02 req'd to blow heat to tap %C 4.91
FeO 7.62 9.44
0.005 kg 02 req'd to form slag FeO
S
Total kg O:

Chem ^ P 0.03 Lime flux Dolo flux KgFe 907.8

anal (%) Si02 2.00 0.80 4.00 Yield, % 98.14

A1203 0.70 0.20 0.80

CaO 0.80 85.00 43.00 Slag Composition
0.40
MgO 1.70 9.00 50.00 Kg %
0.20 0.40 0.20 FeO 22.1 20.0
lс 0.60 0.50
Other 100.00 4.00 1.50 CaO 42.0 38.0
LOI or VM 4.10 100.00 100.00
1.60 5.30 MgO 15.9 14.5
Total
Total Gangue A1203 7.2 6.5

Si02 21.0 19.0

Other 2.3 2.1

Flux Addit ion Slag 110.5 100.1

kg Lime kg Dolo kg Flux Flux, % of DRI charge

30.7 18.3 49.0 4.9

Figure 10.5 Results of flux and oxygen mass balance calculation from the MEB worksheet for
melting one tonne of DRI to steel in an EAF. Boxed cells represent user-entered values.

The mass balance portion of the MEB was used to explore the effect of several DRI and other
process parameters on the mass of flux required, the mass of slag produced, and the % yield.
Figure 10.6 shows that the V ratio has a significant effect on these parameters by changing the
required quantity of flux, and hence the mass of slag produced. Although the slag wFeO remains
constant at 20 % (because the tap carbon was fixed at 0.10%), the yield dropped from 98.2 % at V
= 1.8 to 97.9 % at V = 2.5. Increasing the V ratio to produce a lower sulfur steel incurs a penalty
in decreased yield. Lowering the tap carbon has very little effect on the amount of flux required,
but it has a large effect on yield because of the sharp increase in %FeO in slag as tap %C
decreases. This in turn lowers the % yield.

The flux mass required to melt one tonne of generic scrap is about half that of DRI. Only 42
kg of slag are produced per tonne of scrap melted at a tap carbon of 0.10% and a V ratio of 2.
Thus the fraction of DRI in the metallic charge is the main factor on flux requirement, mass of slag

584 Chapter 10 Case Studies
produced, yield, and amount of oxygen required to reach the tap %C. A number of other mass
balance simulations are on the Handbook CD

Flux and Slag Mass for 1 Tonne DRI

<D

<D

гEо

(0

a
x

3

2.1 2.2
slag V ratio

Figure 10.6 Effect of V ratio on flux and slag mass for melting one tonne of DRI to a tap %C =
0.10 and a slag V ratio of 2. DRI composition is shown in Figure 10.5. The % iron yield drops
from 98.2 % at V = 1.8 to 97.9 % at V = 2.5 because of the increased slag mass.

The heat balance part of the MEB was divided into two sections. The first section dealt with
the amount of electrical energy required to melt the charge, with oxygen being used only to attain
the specified %C at tap. The second section dealt with the effects of additional factors such as
oxygen lancing and post-combustion on the consumption of electrical energy.

1. Heat effect equations were written for the production of one tonne of steel using DRI and
scrap as the iron-bearing feedstock. The oxygen lance was used only to attain the tap
carbon. A 25 °C basis temperature was selected, and FREED was the source of all data
except the amount of heat required to heat the fluxes and FeO to produce slag, which came
from FACT'S Equilib program as described in Section 8.7. Reactions were carried out at
25 °C and the products heated to the tap temperature. The objective was to explore the
effect of different DRI characteristics on the amount of electrical energy required to
produce one tonne of steel at different tap temperatures. The same generic scrap was used
as in the mass balance part of the MEB, so this simplified the scrap melting heat balance.

2. The heat balance was modified by the addition of several special effects, such as natural
gas burners, oxidation of additional bath carbon, post-combustion, water from the
electrode clamps leaking into the furnace, hot-charging the DRI, and heat loss.

The steps for calculating the quantity of heat required to melt one tonne of DRI in the EAF
started with the АЯ°геах at 25 °C, using FREED data.*

Reduction of DRI FeO with Fe3C to Fe and CO: 454 kcal/kg FeO [10.2]

Oxidation of DRI Fe3C carbon by 0 2 to CO: -2700 kcal/kg С [10.3]
Oxidation of DRI С by 0 2 to CO: -2200 kcal/kg С [10.4]

Oxidation of DRI Fe by 02 to slag FeO: -1165 kcal/kg Fe [10.5]

One assumption was made in setting up these reactions. Reaction [10.2], reduction of the FeO

in the DRI, was assumed to be by Fe3C until all of the DRI FeO is reduced. The rest of the Fe3C
and elemental С are oxidized by the lance 02 according to [10.3]. If DRI contains more FeO than

These heat values will be converted later to kWh. There are 860.4 kcal in one kWh.

Chapter 10 Case Studies 585

can be reduced by the Fe3C (not common), the model should be revised. Table 10.1 shows the
mass of specified reactant and enthalpy change for the DRI composition listed in Figure 10.5.

Table 10.1 Heat of chemical reactions at 25 °C for one tonne of DRI, based on mass balance data
presented in Figure 10.5. The sum of the reaction heats is 2850 kcal/tonne DRI .

Reaction Eqn kg H, kcal

mFeO reduced by Fe3C to Fe [10.2] 76.2 34 580

mFe3C carbon oxidized by C^to CO [10.3] 2.9 -7870

mC oxidized by O2 to CO [10.4] 0.48 -1070

mFe oxidized by O2 to slag [10.5] 19.6 -22 790

The second part of the heat balance was to heat the reaction products to the tap temperature.
Over the short tap temperature range (1600 °C - 1700 °C) involved, a two-term Ht-H25 equation
was deemed suitable. Data for CO and Fe were obtained from FREED, while heat content data for
slag was obtained from FACT, as described earlier. The MEB worksheet was set up so that once
the fluxing and oxygen mass balance was performed, the mass values were automatically copied to
the heat balance worksheet, and the heat balance was calculated immediately. The results for three
tap temperatures are shown in Table 10.2.

Table 10.2 Enthalpy requirements for heating reaction products from one tonne DRI to EAF tap
temperature. CO volume at 25 °C and 1 atm.

Product kg Tap t, deg C: 1600° 1650° 1700°
CO 37.6 Nm3 kcal kcal kcal
Fe 905.4 16 700 17 280 17 860
Slag 125.8 32.81 291 730 300 650 309 570
54 110 55 990 57 880

A heat balance for melting the generic scrap was also performed by entering the scrap
composition in the DRI heat balance worksheet. Of course, the scrap charge does not involve all
of the DRI reactions. The reaction and heat content values were summed, then converted from
kcal/tonne DRI or scrap to kWh/tonne steel produced. The overall heat requirement for producing
one tonne of steel from DRI and scrap are plotted in Figure 10.7. The electrical energy required to
produce steel from DRI is significantly more than from scrap.

Theoretical Minimum Energy Required for Figure 10.7 Theoretical
minimum electrical energy
One Tonne of EAF Steel required to produce one
500 tonne of low-carbon steel
in an EAF from DRI or
0) 475 scrap steel. Data for DRI
</) listed in Figure 10.5.
ссоо Please see workbook MEB
450 DRI — o — Scrap
425
-O
400

375 1625 1650 1675 Program.xls on the
1700 Handbook CD for details
1600
beyond those given in text.
tap temperature, °C

* The A//°reax values in the text come from the MEB worksheet, where Excel used more significant figures
for the mass of reactants than displayed in Figure 10.5.

586 Chapter 10 Case Studies

Table 10.3 Special effect factors incorporated in the MEB program.

1 EAF factors (V ratio, %C at tap, etc.) 7 exit t (°C) for NG burner products
8 kg electrode cooling water + DRI water
2 kg chg & inj carbon burned to CO
9 exit t (°C) for water-based steam
3 % post comb of added carbon oxidized
from CO to C02 10 tap-to-tap time (to estimate heat loss)
11 hot charge DRI temperature, °C
4 % post comb of bath CO oxid'z. to C02 12 empirical factors (Adams 2001)

5 m3 (STP) NG burned to C02 and H20

6 % stoichiometric 0 2 for NG

Some comments are in order on these factors. Factors 3, 4 and 5 are for the post combustion
(p-c) and NG heat that is actually transferred to the bath, and thus includes an implicit heat transfer
efficiency term. Factor 9 is for the water entering via Factor 8. Factor 10 uses an empirical
equation for heat loss: 0.5 kWh/(tonne · min). Factor 12 allows for the inclusion of other
empirical factors not specifically listed (Adams 2001).

Figure 10.8 shows the effects of oxidation of bath CO, providing the evolved heat can be
captured by the bath. The maintenance of a thick layer of foamy slag is essential in order for the p-
c heat to be transferred to the bath. Figure 10.9 shows the effect of hot charging of DRI. 17 to 20
kWh/tonne Fe are saved for every 100 °C increase in DRI charge temperature. A similar effect
occurs for scrap preheating.* Figure 10.10 shows the effect of carbon content of the steel on the
theoretical minimum electrical energy required. The electrical energy requirement decreases as tap
%C decreases because of the increased extra energy produced by oxidation of Fe to FeO in the
slag.** However, the yield also goes down.

Parameters for Post-Combustion of Charge & Inj, Carbon

-1.0 ι.ου

1.25
-1.5

1.20

О -2.0 1.15 о
-2.5
1.10 о

1.05 mb~

1.00
-3.0

0.95

-3.5 n on
0 5 10 15 20 25 30

% post-combustion

Figure 10.8 Effect of post-combustion heat on requirement of electrical energy for EAF
steelmaking. Value at 0 % p-c represents the formation of CO only from the oxidation of charge
and injected carbon. The % p-c represents the heat effect of oxidation of the CO to C02 by lance
0 2 that actually gets transferred to the bath.

The Consteel process heats scrap by post-combustion of the furnace offgas over a conveyor belt of
incoming scrap.
** The formula for % FeO in slag used by the MEB is: %FeO = 1/%C + 10.

Chapter 10 Case Studies 587

Effect of DRI Preheat on Theoretical Minimum Energy

500 I_

1 ** * - -Ο - 1700 °С tap
Ι~1 я г г л о
L^^^*480 ^ - -. — L I — IU3U \> ιαμ
'Φ 460 ^
**""°^-*. *"■--. —Δ—1600 °C tap
Li-
tt
С 440

СО

£ 420 *^

400

380
25 75 125 175 225 275 325 375 425

DRI preheat temp, °C

Figure 10.9 Effect of preheating of DRI on the electrical energy requirement to produce one tonne
of low-carbon steel. Compare to results shown in figure 10.7.

500 Theoretical Minimum Energy for DRI
130
490
"""" " ™ Ί
<D
LL - ** »ф 1600 °C tao 4скпог*а« 125

ф 480 - - . -1700 °C tap 3 slag*шшш^^-«' «■ГelЛfi 120
ос у ^ * u>
Ц 470 —„ —- — —
115 Jо«E>

110

460 105

4500.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 100
tap %C

Figure 10.10 Effect of carbon content of steel on the amount of electrical energy required to melt
one tonne of steep from DRI. Compare to results presented in Figure 10.7. The %FeO in the slag
increases as %C decreases, which explains the increased mass of slag at low %C.

The MEB model gives results in good agreement with plant data (which not unexpected), but
it cannot account for factors such as heat size, power input, and bath stirring. Its greatest value lies
in its ability to explore the effect of raw material and process changes on energy consumption. A
useful extension of the MEB would include the distribution of S, P, and Mn between the slag and
steel, and recommend flux modifications to control these species. Section 6.9 showed how
distribution coefficients can be used for this purpose.

588 Chapter 10 Case Studies

10.3 Natural Gas Combustion Control and the Wobbe Index

Some pyromaterial processes require close control of the temperature and furnace atmosphere.
Once a process is under control and operating steadily, any change in the feed rate or composition
may cause the temperature or furnace atmosphere to change in an adverse way. For example, the
austenitizing of steel requires a certain temperature to be sure all carbides have dissolved in the
austenite. And the calcination of a sulfate requires a certain gas-phase p02 to stabilize Fe203.

The temperature and furnace atmosphere of a fuel-fired furnace are controlled in two main
ways. First, by controlling the fuel input rate, which controls the rate of chemical energy entering
the furnace. Second, by controlling the quantity of air (or more correctly, the quantity of oxygen)
used for fuel combustion. The second factor is commonly expressed as a ratio of oxidant to fuel.
Section 6.3 showed how the combustion product composition was affected by the oxidant/fuel
ratio, and Section 9.2 showed how the energy input was related to the quantity of fuel. Other parts
of Chapter 9 showed how furnace temperature is affected by not only the quantity of fuel and
oxidant used, but also the thermal requirements of the process, the heat loss to the surroundings,
and the extent to which certain reactions proceed.

The most commonly-used fuel for pyromaterial processing is natural gas, which is mainly
methane, CH4. However, natural gas (called here NG) always contains other hydrocarbons, and
non-combustible species like N2, and C02. The physical and thermal properties of NG are
dependent on the nature of the constituent species. Since the main use of NG is for process fuel,
the gas utility may bill customers in "therms", which is equivalent to 100,000 Btu. Section 9.2
mentioned two ways to express the thermal energy obtainable by NG combustion: the LHV and
the HHV, depending on the physical form of the water produced as a combustion product. This
Handbook favors the use of the LHV as the most reasonable and practical measurement of the
thermal energy obtainable from combustion. In SI units, the heating value is usually expressed as
MJ/scm.

We pointed out in Chapter 9 that even if two different-composition NGs have the same LHV,
they will generally not have the same AFT, nor will they require the same amount of oxidant for
stoichiometric combustion. The operator of a pyromaterial processing operation may receive NG
of varying content, even though its LHV is nearly constant. Of even more concern is when the NG
composition fluctuates so much that the LHV varies in a non-negligible way.

The issue facing process operators is how to maintain the proper furnace temperature and
atmosphere in the face of an unpredictable NG composition and LHV. Section 9.2.2 discussed the
establishment of a constant Wobbe Index (WI) as a way to assure steady and predictable furnace
operation at excess oxidant condition. The WI relates the heating value of the NG to square root of
its specific gravity with respect to air, as shown by Equation [9.16]. This section presents a
detailed case study of the stoichiometry and heat balance for the excess-oxidant combustion of any
NG. It amplifies the material from Section 9.2.2, and develops a four-worksheet Excel workbook
(Wobbe.xls in folder NG Combust & Wobbe Index) on the Handbook CD that can calculate a wide
variety of NG combustion properties. One of the worksheets has templates for calculating the WI
of a gaseous fuel, and the amount of fuel additive that will maintain a constant WI.

10.3.1 The Stoichiometry of NG Combustion with Excess Air

Many pyroprocessing operations use NG as a source of heat, with no particularly concern
about the composition of the combustion gas products. Instead, the objective is to obtain the
greatest possible thermal efficiency commensurate with safe operation. This means operating with
a minimum amount of excess oxidant, but still leaving a small margin of safety so that the
combustion products are devoid of CO. With an efficient burner and well-mixed gases, it's
feasible to operate with a <p02 as low as 2 %. The lower the φ02, the greater the thermal efficiency
and AFT, and the lower the NOx content of the offgas. However, aiming for a too-low φ02 risks
forming non-insignificant amounts of CO in the offgas if the NG composition changes

Chapter 10 Case Studies 589

unexpectedly. The issue of careful combustion control becomes more important as the
environmental control limit for NOx becomes more stringent.

You might think that the easiest way to control the furnace operation would be to sample the
combustion products at the burner exit, and vary the oxidant or fuel input flow to keep the φ02 at
the desired value. This type of feedback control system is theoretically feasible, except for the
difficulty of sampling a gas that's often near 2000 °C. One way around the sampling difficulty is
to use a special by-pass combustor (a catalytic oxidizer) as shown in Figure 10.11.

Burner gas

Calcination -► Offgas
furnace ► MgO
(500°C)

Analysis gas

Figure 10.11 Flowsheet diagram for an air/gas regulated burner providing heat to a furnace. At
standard operation, natural gas passes through a fuel gas pressure regulator/mixer and then through
a flow-control orifice. Air is passed through a pressure regulator and flow controller. The air and
fuel gas are mixed and sent to a burner. The air/fuel mixture ignites as it leaves the burner;
combustion is complete as it passes through the furnace. Dashed lines indicate gas-phase flow,
while solid lines indicate solid-phase flow. For control purposes, a small portion of the air/gas
mixture can be diverted to a catalytic oxidizer which completely oxidizes the fuel species. This
procedure is necessary because it's nearly impossible to properly sample the combustion gas. This
is the only accurate way to assure that the air/gas ratio is correctly adjusted at the low end of a
combustion gas φ02 to give the specified %02.

If the desired combustion gas φ02 is above about 2.5 %, it's feasible to control the process by
adjusting the air blower volume and the size of the NG orifice, while taking into account the
temperature and pressure of the oxidant and NG to express measurements at STP. Fortuitously, it
turns out that the % excess air and the combustion gas φ02 have a fixed relationship over a wide
range of NG compositions. Figure 10.12 shows relationships for the combustion of three different
fuels with excess air (φ02 = 21 %).

Workbook Wobbe.xls provides two calculators for calculating the above relationships for any
NG, and for an oxidant with any φ02. The first calculator uses % 02 in the combustion flame as
the independent variable, and calculates the % excess oxidant and the oxidant/NG ratio. The
second calculator uses % excess oxidant as the independent variable, and calculates the
oxidant/NG ratio and the % 0 2 in the combustion flame. The result charts are displayed and
automatically-updated with a Trendline equation. In addition, the worksheet calculates additional
combustion parameters, such as the HHV and LHV for any NG in three different unit sets.

The calculation method is based on first calculating the stoichiometric oxidant/NG ratio for
any NG and any oxidant. Each mole of hydrocarbon constituent requires a known amount of
oxygen for stoichiometric combustion, as shown in the following table. Five species constitute the
majority hydrocarbon content of most NG; trace amounts of other hydrocarbons may be added to
one of the five with no significant error in the result.

Nat. gas component CH4 C2H4 СгН6 C3H8 С4НЮ

Stoichiometric O2 per mole of component 2 3 3.5 5 6.5

Combustion product amount formed 34 5 7 9

590 Chapter 10 Case Studies 13
Excess Air Combustion of NG
24 12
% XSA = 0.32(%O2 in CG)Z + 5.20(%O2 in CG)
11 %

2
z

cu

- + - CH4A/G ratio 3.5
— X — Rich NG A/G ratio
— O — Lean NG A/G ratio

1.5 2.0
0 2 in combustion gas, %

Figure 10.12 Relationships between the φ02 in the combustion gas, the % excess air, and the
air/NG ratio to the burner, for three different NG compositions. The lean NG has about 13 %

inerts, and the rich NG has about 9% higher-molecular-weight hydrocarbons. The dashed, dotted

and grey lines depict the relationship between the air/NG ratio and the % 0 2 in the combustion gas.
The solid black line depicts the relationship between the % excess air and the % 0 2 in the
combustion gas. The text box equation (obtained from the Trendline tool) shows that this

relationship is well-represented by one quadratic equation, which can be applied for any NG

composition.

The stoichiometric oxidant/NG ratio and the amount of combustion products depend on the

NG composition and the <jp02 in the oxidant, as shown in Equation [10.6]. Equation [10.7] shows
the amount of combustion products formed from one mole of NG.

Stoich Ox/NG = 2(%CH4) + 3.5(%C2H6) + 3(%C2H4) + 5(%C3H8) + 6.5(%C4H10) [10.6]
% 0 2 in oxidant

NG comb prod = (3(%CH4) + 5(%C2H6) + 4(%C2H4) + 7(%C3H8) + 9(%C4H10) + %inerts)/100 [10.7]

Equation [10.8] gives the relationship between the % 02 in the combustion gas (CG), the
amount of combustion products formed by NG combustion (NGcomb prod from Equation [10.7]),
and the amount of oxidant in excess of stoichiometric (XSoxidnt).

%O0inCG = - cmb prd + (%02 in oxidant)(XS oxidnt) + XS oxidnt [10.8]
NG (100 - % 0 2 in oxidnt)(St oxidnt)/100

For example, consider a furnace fired with NG of the composition listed in the top half of
Table 6.9, using an oxidant having 23 %02. According to Equation [10.6], the oxidant/NG ratio
for stoichiometric combustion is 8.867, and the NG combustion products are 3.064 moles/mole
NG. What should the oxidant/NG ratio be to attain 2.6 % 0 2 in the combustion gas? Employing
Equation [10.8] gives 1.261 moles of oxidant gas in excess of the 8.867 stoichiometric moles. The
oxidant/NG ratio is then 10.13, and the combustion process operates at 14.2 % excess oxidant
(114.2 % of stoichiometric oxidant). Workbook Wobbe.xls has calculators that automate these and
other NG combustion calculators, and make it possible to derive useful relationships between
combustion variables. The calculation strategy in the worksheet can be deduced by comparing the
above equations with the formulae in the worksheet cells.

Chapter 10 Case Studies 591

10.3.2 The Wobbe Index as a Natural Gas Combustion Control Parameter

A number of things can upset the smooth operation of a pyroprocessing operation. The raw
material being processed may change composition or temperature, air leaks in every time the
furnace door is opened to charge more material, or changes may be required in the temperature or
composition of the product. Another potentially upsetting incident is a change in the composition
of the NG supplied by the utility. Each type of upset requires a different action by the operator to
bring the process back to the aim point. When these changes are predictable or expected, the
operator has time to implement corrective action before the product properties undergo a non-
trivial change. But when the changes are unexpected, it's important to have a rapid-response
control action plan in place.

When the NG composition changes unexpectedly, the first symptom is a change in
temperature of the furnace, along with a change in the % 0 2 in the furnace atmosphere. There are
at least two possible actions to correct for a change in NG composition. First, the flow of air
and/or NG can be changed with the aim of bringing the temperature and furnace atmosphere back
to the desired set points. This requires on-line NG analysis, and accurate flow control of the air
and NG. Second, the flow of raw material can be changed in accordance with the change in heat
input. Fortunately the often massive contents of a furnace mean that there may be ample time to
take corrective action before the product properties deviate too far from their aim point.

An ideal control strategy would be to add something to the changed NG that makes it perform
as if it didn't change. This requires a control parameter that is sensitive to both the NG flowmeter
characteristic and the thermal performance of the NG. The Wobbe Index (WI) is such a parameter.
The WI contains two critical characteristics of NG: the volumetric heating value and the density.
The volumetric heating value, of course, is critical to the thermal requirements of the process. The
density is a critical parameter for the flow of a gas across an orifice flowmeter; Equation [6.45]
shows this relationship. The WI incorporates the volumetric heating value in the numerator, and a
density factor in the denominator, as was shown earlier in Equation [9.16]. It turns out that two
NGs with the same WI perform nearly identically in a heating device, whatever their composition.

__ _T Heating value of NG

WI = . —

Density of NG [10.9]
\ Density of air

The corrective action for a change in NG composition is thus to add something to the NG
upstream of the orifice flowmeter that will bring its WI back to that of the original NG. Adding a
dense inert substance like C02 lowers the WI because it lowers the numerator and raises the
denominator. Adding a dense hydrocarbon like propane (C3H8) raises the WI because although it
raises the denominator, it raises the numerator faster. The procedure for calculating the quantity of
an additive to bring a NG to any desired WI value is outlined in worksheet WICalc in workbook
Wobbe.xls. The worksheet has templates and examples for making the calculations; in some cases,
Goal Seek must be used.

As an example, suppose a process used pure CH4 as the fuel gas with sufficient excess air to
produce 3.0 % 0 2 in the combustion gas. The worksheet NGCombust template shows the air/NG
ratio to be 11.28, with 118.4 %stoichiometric air. (These values can also be read from Figure

10.12.) Worksheet WICalc shows that the LHV = 35.80 MJ/scm and the WI = 48.10. For a NG

flow of 1.00 scm/sec, the heat input is 35.80 MJ/sec.

Now suppose that a NG having 90 %CH4 and 10 %C2H6 replaces the 100 %CH4 NG with the
air flow remaining at 11.28 scm/sec. The worksheet WICalc template shows that the density of the
replacement NG is 0.7131 vs. a density of 0.6557 (g/L at 25°C). The denominator of Equation
[6.45] is thus 1.04285, so the NG flow drops to 0.9590 scm/sec. The LHV of the replacement NG
is 38.59 MJ/scm, so the furnace heat input is now 37.00 MJ/sec, or 3.4 % more than for the
original case. In addition, the combustion gas now has 2.44 %02. From worksheet WICalc, the
WI of the replacement gas is 38.59/0.7760 = 49.72.

592 Chapter 10 Case Studies

In order to bring the process back to the intended condition of 35.80 MJ/sec heat input and 3.0
%02 in the combustion gas, C02 can be added to the replacement NG upstream of the orifice plate
flowmeter. The C02-addition template on worksheet WICalc shows that adding 1.92 volumes of
C02 to 100 volumes of replacement NG brings the WI back to 48.10. The adjusted replacement
NG has 88.30 %CH4, 9.81 %C2H6, and 1.88 %C02 (difference from 100% due to roundoff). This
gas has an LHV of 37.86 MJ/scm, and a flowrate of 0.9455 scm/sec, for a heat input of 35.80
MJ/sec, the same as for the original NG of pure CH4. The air/NG ratio is now 11.93, which
according to the template in worksheet NGCombust, brings the combustion gas to 3.06 %02. Any
process can be maintained in a stable combustion mode by analyzing the NG, calculating the
additive amount necessary to bring the WI back to the original value, and making the change.

As a final check, we can use FlowBal to calculate the AFT for the combustion of pure CH4,
the replacement NG, and the replacement NG after adjustment by C02 addition. For pure CH4, the
AFT = 1815 °C when the reactants enter at 25 °C. The AFT for the replacement NG is 1864 °C,
while after C02 addition, the AFT returns to 1815 °C. The WI is therefore verified as a reliable
parameter for adjusting the composition of NG to maintain steady combustion operation in a NG-
fired process.

10.4 Reduction of Hematite to Magnetite

Hematite-rich material is available from a variety of metallurgical processes. In some cases, it
is available at "negative cost" which means that the vendor will pay to have it removed. For
example hematite residues are available from the chlorination of rutile, fines screened from iron
ore pellets, and calcined steel pickling liquor sludge. A more marketable product is magnetite, if a
process can be devised to convert hematite to magnetite. The idea is to use a gas-based reducing
process in a rotary kiln, similar to that depicted in Example 9.7. A kiln uses countercurrent flow of
gas and solid streams to minimize the consumption of gas and energy. Figure 10.13 shows a
sketch of the concept. The #1 HX zone transfers heat from the spent reducing gas to the hematite.
Hematite is reduced to magnetite in the center of the kiln at about 850 °C, and the magnetite is
cooled in the #2 HX zone. These zones are more conceptual than physical because the kiln
consists of a long horizontal pipe. Internal baffles may be used to enhance plug flow of the solid
and gas streams. In any event hematite is gradually reduced to magnetite as it passes down the
length of the kiln.

Spent #1 HX Hematite #2HX Fe3.OU 4
gas zone reduction zone zone

Fe203

= = = = = i = = = = === = = == Reducing gas

Figure 10.13 Flowsheet sketch for conceptual kiln for the reduction of hematite to magnetite.
Solid lines depict solid phase streams, while dashed lines depict gas flow.

The thermodynamics of hematite reduction require a furnace atmosphere that has just the right
amount of CO, C02, H2, and H20 to reduce the hematite completely to magnetite but not form
wustite. The thermodynamics of the Fe-0 system near 850 °C indicate that a furnace gas, after
hematite is reduced, should have a C02/CO ratio between 6 and 12. With this ratio, the hematite is
readily reduced, but magnetite is not. Methane is used as both the source of reducing agent and a
fuel to maintain the furnace contents at temperature. A heat and material balance is required to
make a preliminary evaluation of the process feasibility for the reduction of 1.9 tonnes of hematite
per hour.

Chapter 10 Case Studies 593

10.4.1 Preliminary Calculations — Single Reactor

The gradual reduction of hematite to magnetite is difficult to simulate because the gas and
solid composition change along the length of the kiln. However, the process can be approximated
by dividing the reduction zone into sections. This allows the use of a higher-CO gas in the
reduction zone closest to the magnetite discharge end, and a lower-СО gas closest to the entry
point of hematite. Since only a preliminary process analysis is requested, a two-section reduction
zone was chosen. Hematite might be suitably heated by combustion of the unused reducing gas
with air, while magnetite could be cooled by embedded boiler tubes in the #2 HX zone. Thus we
end up with a four-device process.

An experienced process engineer might be able to sketch a reasonable process flowsheet with
little effort, but the rest of us are better off with a few preliminary calculations. For example, we'd
like to know about how much methane is required to reduce 1900 kg of hematite and how much
methane must be burned to provide the necessary heat.. A simple way to do this is to make a
system balance on a single-zone reactor at 850 °C with reactants at 400 °C and products at 850°C.
This will give us a rough idea of the amount of methane and air required to close the system
balance. Figure 10.14 shows the flowsheet.

Spent gas A-- 5 Hematite H---4 --Air
Fe203 — 1 reducer - 3 --CH4
- 2 -> Fe304

Figure 10.14 Flowsheet of single-zone reactor for hematite reduction to magnetite. Gas-phase
flow is depicted by dashed lines, while solid lines are solid phase streams.

The system has four reactive elements (because we don't count N2) and eight species, so
NIRx = 4. So long as we don't use the XR tool, any four independent reactions will give the same
result. However, it's always good to select a reaction set that has some physical plausibility. For
FlowBal use, it's also nice to use a reaction set that proceeds in the written direction to prevent a
negative value for an R-R. Here, the methane and air probably react in the gas phase to form a gas
rich in CO and H2 via combined Equations [10.10] and [10.11], and these gases reduce the
hematite via Equation [10.12] (and also by CO reduction, but we don't need that reaction because
it's not independent). We assume the WGR proceeds to equilibrium in the gas phase, and since 0 2
is the limiting reactant, it is absent in the spent gas. Any remaining oxygen is therefore removed
by [10.13], with the assistance of [10.11]. The reaction set is reasonable, and written in a
somewhat plausible order (but the order is immaterial in a system balance). Figure 10.15 shows
the FlowBal starting array for the process.

CH4(g) + 02(g) - C02(g) + 2H2(g) [10.10]

C02(g) + H2(g) - CO(g) + H20(g) [10.11]

H2(g) + 3Fe203(c) - H20(g) + 2Fe304(c) [10.12]

CO(g) + V202(g) - C 0 2 ( g ) [10.13]

FlowBal wrote 10 equations for 12 unknowns, so two additional SRs are needed. We've
already mentioned that the C02/CO ratio for the reactor outgas should be between 6 and 12, so we
set the ratio to 9 for the single zone reactor. Next, we need an equation for the WGR in Celsius,
which we've already developed (see Figure 6.32). Notice that setting a certain WGR and C02/CO
ratio sets the H20/H2 ratio. As expected, the heat balance did not close; the Process net heat was a
large positive number. Repetitive Solve varied the placeholder S3 CH4 flow between 80 and 90 m3
to find that 85 m3 was required. Considering the size of stream flows and the uncertain heat loss
estimate, a net heat of ±1000 kcal is considered a "closure" value. Figure 10.16 shows the result.
A similar calculation using air enriched to 30 % 0 2 showed a system balance closure at an S3 flow
of 77 m3.

594 Chapter 10 Case Studies

P (atm) 1 1 111 850 1. CH4 + 02 -* C02 + 2H2
T(C) 400 850 25 25 Volume (m3) 2. C02 + H2 -> CO + H20
Str-unit
Spec-unit Mass (kg) Mass (kg) Volume (m3) Volume (m3)
Str-name Mass pet Mass pet Volume pet Volume pet Volume pet 3. H2 + 3Fe203 -► H20 + 2Fe304
Streams Air SpentGas 4. CO + У2О2 -► C 0 2
Hematite Magnetite Methane
Flow
1 234 5 R #1 R #2 R #3 R#4
1900
| 80 1 ? ?

CH4, (g)

CO, (g)

C02, (g)

H2, (g)

H20 ■ (g) 79 -0.5
N2 ■ (g) ?
02, (g)

Fe203, (c) -3

Fe304, (c,l) 2

Hematite Reducer (RX) Heat
Instreams Outstreams Reactions 5000

Figure 10.15 FlowBal starting array for the single-zone reduction of hematite to magnetite. The
boxed cell is a placeholder value for the amount of methane. Heat loss estimated.

P (atm) 1 1 1 1 1

T(C) 400 850 25 25 850

Str-unit Mass (kg) Mass (kg) Volume (m3) Volume (m3) Volume (m3)

Spec-unit Mass pet Mass pet Volume pet Volume pet Volume pet

Str-name Hematite Magnetite Methane Air SpentGas

Streams 1 2 3 4 5

Flow 1900 1837 85 521 2512 Figure 10.16
0 100 00
CH4, (g) 0
CO, (g) 0 0 0 0 1.27 FlowBal system
balance for single-
C02, (g) 0 0 0 0 11.47
H2, (g) 0 0 0 0 2.33 zone process for the
H20, (g) 0 0 0 0 23.16 reduction of 1900 kg

N2, (g) 0 0 0 79 61.76 of hematite to
0 21 0 magnetite. Notice
02, (9) 0 0 0 0 0 that only R #2 (the
Fe203, (c) 100 0

Fe304, (c,l) 0 100 0 0 0 WGR) is

—Heat Balance (kcal)— endothermic.

Device Instreams Outstreams Read ions
Hematite ϊ I -137,095 2 1 -264,640
329,478
5 185,701 2 23,091
Reducer 3 -1

46 3 -5,533

4 -135,230

Σ In ZOut Σ Surr Σ Rxn Device Nel
-137090 515179 5000 -382312 777

Pre>cess Net 777

R-R1 R-R2 R-R3 R-R4
3.4743 2.3469 3.9661 1.9994

Chapter 10 Case Studies 595

10.4.2 Simulation of Hematite Reduction by a Multi-Stage Process

Figure 10.17 shows a flowsheet sketch for a process involving a simple heat exchanger, a
reactive heat exchanger, and a two-reactor reduction zone. Each stage represents an arbitrary
portion of the kiln where certain reactions predominate. Dividing a single device into stages is a
common way to simulate a device that has many zones. The stage boundaries have no physical
meaning, and do not represent any particular length portion of the kiln. The objective here is to
determine if the process concept is feasible under reasonable conditions, and not to seek a "most
efficient" process. The objectives of each stage are as follows:

* Hematite preheater. The concept is to combust all remaining CO and H2 with normal air to
provide sufficient heat to bring the hematite at least part way to the #1 reduction stage
temperature. Use reactions R #2 and R #4.

* Reduction stages. The concept is to combust part of the CH4 to provide heat, and use the
rest to produce a reducing gas for the hematite. The air is enriched to 30 % 0 2 to improve
fuel economy. Stage #1 brings the hematite to the reduction temperature, and reduces part
of it. The rest of the reduction occurs in stage #2. Reactions R #1 — R #4 occur in both
stages.

* Magnetite cooler. The magnetite must be cooled to below 400 °C for packaging in closed
steel drums. Most of the sensible heat in the magnetite is removed by boiler tubes in the
kiln walls (SI7 and SI8). A nitrogen flush gas (S6) is passed through the cooler to
minimize any back-flow of reduction gas from the #2 reduction stage. Part is bled via S7,
and the rest is used as a heat carrier through the other three devices. No reactions occur in
this stage.

One way to characterize the extent of hematite reduction in stage #1 is to set a value for
X7?Fe203 for R #3. Another way is to specify the composition of S3. The latter option simplifies
the setup, so the wFe304 in S3 is set to 30%. Certain other arbitrary stream values were also set,
such as 2.2 %02 in SI6. Figure 10.18 shows the initial FlowBal array.

.-CH4
OxA

SpGas - - - - J u-J^_-J ι^ 11

F e29 ^03

'£ - - 3 ^ 4
Steam |18 17| Water

Figure 10.17 Flowsheet for the reduction of hematite to magnetite in a multi-stage kiln. The kiln
is divided into zones according to function. Gas-phase flow is depicted by dashed lines.

FlowBal identified 35 unknowns and wrote 31 equations. Two additional equations can be
inserted to specify the C02/CO ratio in SI 1 and S14 (six and twelve respectively), and Кщ for the
WGR for SI 1 and SI4. Solver initially failed to find a solution because R #4 went in the reverse
direction in reduction stage #2. Solver converged after the Assume Non-Negative box was
unchecked. An alternative would be to use the Built-in FlowBal solver, which allows the R-R
values to be negative or positive. As expected, none of the device heat balances closed, which we
must rectify by using Repetitive Solve to change the placeholder values. We do this by moving
from stage to stage until each has an adequate heat balance.

596 Chapter 10 Case Studies

P(atm) 111111111

T(C) 25 380 750 850 400 25 750 750 25

Str-unit Mass (kg) Mass (kg) Mass (kg) Mass (kg) Mass (kg) volume (m3) volume (m3) volume (m3) volume (m3)

Spec-unit Mass pet Mass pet Mass pet Mass pet Mass pet Volume pet Volume pet Volume pet Volume pet

Str-name Hematite WrmHem Hem+Mag HotMagn WrmMagn N2 BleedN2 FlushN2 #20xRchA
1 2 3 4 5 6 7 8 9
Streams

Flow 1900 ? ? ? ? 150 90 ? ?

CH4, (g)

CO, (g)

C02, (g)

H2, (g)

H20, (g)

H20, (l,g)

N2, (g) ????

02, (g) 30

Fe203, (c) ? ? 70

Fe304, (c,l) ???

I Hematite Heater (RX) #1 Hematite Reducer (RX)
Instreams Outstreams Reactions
I Instreams Outstreams Reactions Heat Heat
3000 231 5000
122 11 14 2
12 3
14 16 4 13 4

15

1111111 55

25 900 25 25 800 25 300 35 310

Volume (m3) Volume (m3) Volume (m3) Volume (m3) Volume (m3) Volume (m3) Volume (m3) Mass (kg) Mass (kg)

Volume pet Volume pet Volume pet Volume pet Volume pet Volume pet Volume pet Mass pet Mass pet

#2CH4 #2RdnGas#10xRchA #1 CH4 #1RdnGas CombAir SpentGas InWater OutSteam

10 11 12 13 14 15 16 17 18

40 40 ? | 200 | ?

?

?

? 79 ?
30 ? 2.2

I #2 Hematite Reducer (RX) I Magnetite Cooler (MX) I
Instreams Outstreams Heat I
llnstreams Outstreams Reactions Heat
5000 4 5 2000 I
341
67
8 11 2
17 8
9 3
18
I 10 4

Figure 10.18 FlowBal starting array for a multi-zone process for the reduction of 1900 kg/hr
hematite to magnetite. Boxed cells contain placeholder values for heat balance purposes. Heat
losses estimated.

Starting with the magnetite cooler, the device net heat at the S17 placeholder flow (200 kg/hr)
was about -20 000 kcal, so a greater S17 flow was needed. When the S17 flow was increased to
228 kg/hr, the net cooler heat was 80 kcal, which is a very satisfactory heat balance closure value.
We next adjust the CH4 placeholder flow into reduction stage #2 (S10). The initial device net heat
was -6160 kcal, so the placeholder value of 40 m3/hr should be decreased. The net device heat at
38.7 m3/hr was -90 kcal. Going on to reduction stage #1, the net device heat was -930 kcal, so
only a small decrease in S13 flow is required; in this case, to 38.8 m3/hr.

Chapter 10 Case Studies 597

With these changes, the net device heat for the hematite preheater is -8700 kcal, so our
placeholder value for the S2 temperature is too low. But if we raise it, the net heat for the
reduction stage #1 will require a lower S13 flow. So unlike the situation for the other three
devices, we have a connection between the material and heat balance for the hematite heater and
reduction stage #1. A little trial-and-error adjustment of the S2 temperature to 396 °C and the S13
flow to 38.6 m3/hr brings both devices into a satisfactory heat balance closure. The amount of CH4
required in each reduction stage was about the same, even though only 31 % of the hematite was
reduced in reduction stage #1. This is because much of the CH4 entering stage #1 was burned to
heat the hematite from 396 °C to 750 °C. The total CH4 requirement for the multi-stage process
was 77.4 m3/hr, which is very close to the single stage simulation.

The final system heat balance is shown in Figure 10.19. It's important not to read too much
into the heat effect of the individual reactions for each device. FlowBal uses the user-supplied
reactions to construct species balancing numbers for the material balance, and there are several
feasible four-reaction sets that FlowBal could have used to make the material balance. The only
useful number is the Σ Rxn values, which are independent of the reaction set chosen. The user-
selected reaction set is for FlowBal's convenience in solving the material balance, and does not
validate or confirm any hypothetical reaction mechanism.

Heat Balance (kcal)

Device Instreams Outstreams Reactions Σ In ZOut Σ Surr Σ Rxn Dev. Net
Hematite 1 -1481 2 135,444
Heater 16 57,968 2 5028
14 -149,125
#1 Hematite 3 293,849 4 -50,733 -150,767 193,412 3000 -45,704 -60
Reducer 15 -162 14 149,125
1 -118,196
#2 Hematite 2 -135,444 4 329,478
Reducer 11 -93,549 11 93,549 2 17,035 -229,339 442,974 5000 -218,825 -190
12 -278 3 -1,700 -86
Magnetite 13 -67 5 134,966
Cooler 3 -293,849 7 5699 4 -115,965
8 -26,357 8 26,357
9 -167 18 163,009 1 -118,502
10 -67
4 -329,478 2 63 -320,440 423,027 5000 -107,673
6 -207 3 -3833
17 -2,273
4 14,599

-331,958 330,030 2000 0 72

Figure 10.19 Heat balance for the reduction of 1900 kg/hr hematite to magnetite in a multi-zone
kiln.

When looking at the results, you may notice that S17 enters as water and exits as steam (at P
= 5 atm). Both streams, of course have the same flow: 228 kg/hr. The species listed for both SI 7
and SI8 is H20, (l,g). As a reminder, FREED automatically converts this species from liquid to
gas at 100 °C, and in so doing, includes the heat of vaporization at 100 °C in the stream heat. Thus
the value of 163,009 kcal in the above heat balance table consists of the heat required to heat 228
kg of water from 25 °C to 100 °C, vaporize it at 100 °C, and heat 228 kg of steam from 100 °C to
310 °C. An alternate way to show the cooler-pipe details is to use H20, (/) as the species for SI7,
and H20, (g) as the species for SI 8. This requires writing a reaction for the vaporization of water,
which FREED calculates at 25 °C. Whichever way you do it, the net device heat will be the same.
Also, FREED data for steam assumes ideal behavior above one atm, so its results will differ
slightly from steam table results.

The results show that a hematite-to-magnetite process is indeed feasible, and they suggest
ways to decrease the amount of fuel required. First, an increase in the oxygen enrichment of the
air should be considered. Second, the warm spent gas (SI6 at 300 °C) might be used to preheat the
CH4 combustion air (a total of 320 m3/hr for S9 + SI2) to at least 100 °C.

598 Chapter 10 Case Studies

10.5 Conversion of Quartz to Cristobalite in a Fluidized Bed

Quartz, a form of silica, is a raw material for many processes. It is a reactant for the
production of ceramic materials and silicon alloys, and a flux for various nonferrous-metal-
producing processes. Quartz is also used a structural material, but has the drawback of a rather
high coefficient of thermal expansion, especially the expansion when it transforms from one
crystalline form to another at about 570 °C. This feature of quartz is particularly objectionable in
the case of foundry sand, where dimensional stability is important. However, the coefficient of
thermal expansion of cristobalite is much less than that of quartz, so this phase is preferred for such
uses. Unfortunately, cristobalite does not occur in nature to any appreciable extent, so it must be
produced by heating quartz to a temperature within the cristobalite stability range for a time
sufficient for the quartz-to-cristobalite (Q to C) transformation to occur. This example seeks to
calculate the amount of fuel (natural gas, represented as pure CH4) and air required to carry out the
conversion and to calculate the streams temperature for the offgas and converted solid. The
conversion is conveniently carried out in one or more fluidized bed reactors.

10.5.1 Process Characteristics

Silica (Si02) exists in at least three crystalline forms, depending on the temperature. The
cristobalite form is stable from about 1400 °C to 1700 °C, where it melts. The transformation rate
from quartz to cristobalite is slow but measurable, but if cristobalite is cooled rapidly, it persists
indefinitely at low temperatures.

Figure 10.20 shows a conceptual design for a 60 kg/min Q to С conversion plant. Two
fluidized bed reactors are used, with two associated fluidized bed heat exchangers for air and
quartz preheating. Bench-scale tests indicate that a 1500 °C conversion temperature was optimum
from the standpoint of reactor construction and chemical kinetics. The Q to С transformation is
first order, with к = 0.009 min-1 at 1500 °C. After transformation, the cristobalite must be cooled
rapidly to below 900 °C to prevent reversion back to tridymite or quartz. The air used for cooling
the cristobalite also preheats it for combustion. The plant aims for 80 % conversion of Q to С

Qtz 1 Д 0 _ _ ^ Offoas
= 60 kg/min r
I
!

Quartz :~9~ Quartz I Quartz Y" Air
p-heater I I reactor 2
I reactor 1 3 i ► (QR2) p-heater
(QPH) ► (QR1) «--' 4 ► (APH) 5 QtzH
2'
< - - 'I I . . . . . .►Air

«--

* ΓίΜ. *
11 12

Figure 10.20 Flowsheet for the conversion of 60 kg/min quartz to cristobalite in two same-size
fluidized bed reactors operating at 1500 °C. Dashed lines indicate gas streams, while solid lines
indicate solid phase streams. Solid flow is from left to right, with counter-current gas flow. The
quartz is preheated in the first device (QPH) by the outstream gas from QRl. The combustion air
is preheated in the fourth device (APH) while cooling the QR2 solid from 1500 °C to <900 °C.

10.5.2 Device Sizing and Heat Loss Calculation

Equations [10.14] and [10.15] express the steady-state material balance for the flow of solid
through one of the Q to С reactors:

Input flow rate of Q - output flow rate of Q - consumption of Q = 0 [10.14]
(Fng+C)(winQ) - (F°utQH:)(w0UtQ) - k(w0U{Q)(m) = 0 [10.15]

where m = the mass of solid in the conversion reactor during the process, and wQ = mass fraction
of quartz in the streams. At steady state, FnQ+C = Z^utQ+C = 60 kg/min. Equation [10.15]

Chapter 10 Case Studies 599

shows that the bed mass must be 26 700 kg for a single reactor to attain w0UtQ = 20 %. For two
reactors in series, both of which have the same bed mass, Equation [10.15] for each reactor is:

QRl: 60(100) - 60(wouiQ of QRl) - 0.009(woutß of QRl)m = 0 [10.16]

QR2: 60(woutö of QRl) - 60(20) - 0.009(20)w = 0 [10.17]

Solving, m = 8240 kg, and w0UtQ of QRl = 44.7 % quartz. The mean residence time for the
solid is about 140 min. Notice how much larger the bed mass is for a single reactor (26 700 kg)
compared to the sum of bed mass (16 500 kg) for two reactors.

Taking the density of the solid as 2400 kg/m3 (an average of that of quartz and cristobalite),
Ksolid = 3.4 m3. The fluidized bed volume will be at least double, or about 7 m3. The headspace
volume needs to be at least that much to minimize particle carryover, so each reactor will have an
inner volume of about 15m3.

For this example, the reactor is simulated as a right circular cylinder of / = 4r. Setting nr2l =
15, the inner radius of each reactor is about 1.06 m, and the inner height about 4.2 m. Suppose the
wall and roof thickness is 0.4 m, with an outside wall temperature of 250 °C. A typical
construction might be an inner abrasion-resistant layer, with a thicker outer layer of semi-
insulating brick, with an overall thermal conductivity of 1 W/(m · K). The reactor wall will have
an average circumference of about 7.5 m and a height of about 4.3 m, for a circumferential area of
about 30 m2. The roof plus bottom area will be about 8 m2, for an overall area for thermal
conductivity of about 38 m2, so the heat loss from each reactor will be about 120 kW, or 1700
kcal/min. The two heat exchangers don't need as much bed volume, and their temperature is
lower, so we estimate a heat loss of 900 kcal/min for the QPH and 1100 kcal/min for the APH.

The process has a basis time of one minute, during which 60 kg of quartz enters, and 60 kg of
Q + С exit. It's more convenient to use moles rather than mass for the balance calculations, and
we note that 60 kg of quartz is almost exactly one mole of quartz, so the quantity basis is changed
to one kg-mol/min of quartz. The material and heat balance calculations are coupled in this
example.

The first information we need concerns the chemical reactions that take place. There are two:

first, converting quartz to cristobalite, and second, burning CH4 to C02 and H20. Heat of reaction
units are kcal/kg-mol at 25 °C.

Si02(qtz) -> Si02(crst); AH° = +370 [10.18]

CH4(g) + 202(g) - C02(g) + 2H20(g); AH° = -191 760 [10.19]

It's convenient to express Equation [10.18] in terms of the extent of Si02(g/z) reaction in each
reactor. Based on Equations [10.16] and [10.17], with appropriate roundoff, the XRS\02(qtz) in

QRl and QR2 are both = 0.55. In other words, 55 % of the quartz entering a reactor is converted

to cristobalite; 0.55 kg-mol converted in QRl and 0.25 kg-mol in QR2. To obviate the presence of

CO and H2 in the gas outstreams from QPH, QRl and QR2, excess air must be used for
combustion. This means that the overall air/CH4 flow ratio must exceed 9.6. For safety purposes,
we specify that the air/CH4 ratio =10, which amounts to 5 % excess air. If we leave the amount of
excess air as "air", then the stoichiometry of the combustion reaction in each reactor is:

C02 out = C02 in + CH4 in

H20 out = H20 in + 2(CH4) in

N2 out - N2 in + 7.524(CH4) in

Air out = air in - 9.524(CH4) in

Table 10.4 summarizes what we know about the process. For a fluidized bed, the outstreams
have the same temperature, so there are only two unknown temperatures, that of S2/S10,and S5/S7.
The unknown species and stream flows can be calculated if we know the flows of S6, S10, and
SII. We find these values by making a material and heat balance around each device.

600 Chapter 10 Case Studies

Table 10.4 Basis-case stream flow and temperature for the Q to С conversion process. Time
interval is one minute.

Stream 1 2 3 4 5 6 7 8 9 10 11 12

t,°C 25 ? 1500 1500 ? 25 ? 1500 1500 ? 25 25

F, kg-mol/min 1 1 1 1 1?? ? ? ???

The material balance equations for each device were expressed in terms of the flow of each
unknown stream constituent as a function of the flow of air (S6), and CH4 (SII and S12),
according to the above four stoichiometry relationships. This gives five independent stream
unknowns in the system: two temperatures (S2/S10 and S5/S7), and three single-species stream
flows (S6, SII, and SI2).

Each device allowed one heat balance equation involving two or more of the five unknowns.
The fifth equation involved the constraint of the air flow being ten times that of the methane flow

F6 = 10(FU + Fn). [10.20]

The heat balance is made by calculating the enthalpy change for cooling each instream species
to 25 °C, calculating the heat(s) of reactions at 25 °C, and heating the outstream species. The sum
of these enthalpy changes, plus the heat loss, was set to zero. Solver was used to find values for
each unknown that would close the system balance. Table 10.5 summarizes the results of the
process simulation.

Table 10.5 Material and heat balance results for the conversion of quartz to produce a solid
containing 80 % cristobalite. Numbers in parenthesis were specified in Table 10.4.

Str 2(Q) 5 (Q+C) 6 (Air) 7 (Air) 8 9 10 (OG) 11 (NG) 12 (NG)

t,°C 717 893 (25) 893 (1500) (1500) 717 (25) (25)

F (1) (1) 1.45 1.45 1.50 1.59 1.59 0.0906 0.0543

The process requires 0.136 kg-mol/min of natural gas, and cools the cristobalite-rich solid to a
discharge temperature of 893 °C. The enthalpy of the QPH offgas (stream 10) is about 8600 kcal,
while that of the Q + C final product (S5, from the APH) is about 13 500 kcal. Additional heat
exchanger devices might be used to further lower the amount of fuel required.

Exercise

A Government agency is investigating the energy required to extract various metals from
naturally-occurring concentrates. They seek to determine, by calculation, the minimum theoretical
energy required to produce one mole of metallic product. This value will be used as a comparison
benchmark against existing processes to see which ones are the least energy-efficient, and against
which to compare hypothetical new processes that may be proposed. As a byproduct, they also
want to know the amount of carbon consumed during the selected process.

In the case of iron, the iron-bearing raw material is pure hematite, with an intrinsic energy of
zero. Possible reductants are graphite and methane, whose intrinsic energy is the enthalpy of
oxidation to C02 and H20(g). Also available is air having 21 %02, balance N2.with zero intrinsic
energy. All are at 25 °C. The iron product is one mole of solid, at 1400 °C, containing no more
than 0.06 % (С + О). The process need not be practical or even feasible, but it must conform to the
laws of thermodynamics and conservation of mass. Determine the process, the theoretical
minimum energy required, and the amount of С required.

APPENDIX

Computational Tools for Making Material and Heat Balance
Calculations

The material balance calculations in earlier chapters relied extensively on the computational
assistance provided by a spreadsheet, namely Excel. In later chapters we moved to more complex
systems which combined material and heat balances, and explored the effects of two or three
variables on a system's performance. Even with Excel, flowsheet calculations can be difficult and
time-consuming. Accordingly, a number of Excel-based programs were developed to aid these
calculations. This Appendix summarizes the important aspects of these programs, all of which are
on the CD that accompanies this Handbook. Each program has a guide and examples that give
details on its installation and use. Please read the guides before trying to use the programs.

Brief mention is also made of other's programs for making calculations involving steam and
air/water vapor. The vendors who sell or offer on-line versions of the programs have other useful
programs which are described on their web site. You are also encouraged to search for other
useful calculational tools on the web.

A.l U-Converter

Unit conversions are a common and vexing problem in making material and energy balances.
For example, material balance calculations are often easier when all units are in moles, but the data
and final answer may be in mass or volume units. U-Converter (U-C for short) is an Excel add-in
for making a large variety of unit conversions. The necessary U-C files are in the Unit
Conversions folder on the CD. A brief mention of this program was given in section 1.4, which
you may want to refer to. In addition to making unit conversions, U-C also calculates a conversion
factor or equation that can be used elsewhere in the worksheet to make conversions without using
U-C. For unique conversions that are not one of the 904 units in the U-C program, new
conversions can be added by the user. U-C can also perform reciprocal conversions for one-
dimensional units. For example, suppose that flow values are in gallons (U.S.) per minute
(gal/min) but wanted in gallons per hour (gal/h). This conversion (which is not in U-C) can be
made with U-C's reciprocal units feature that converts 1/min values into 1/h values. This
automatically creates the reciprocal conversion formula to convert gal/min values into gal/h values.

One example will suffice to give an idea of how U-C works. Suppose a metal production
process is developed in the laboratory with the objective of determining the energy requirement to
produce one pound of metal. The energy is expressed as BTUth/lb, and for scale-up purposes,
should be expressed in kWh/tonne (which is equivalent to W · h/kg). Five different experiments
were performed using slightly different techniques, and the energy analysis was done in an Excel
worksheet. The following results were obtained:

Experiment Number 1 2 3 4 5
Energy required, Btuth/lb 420 466 423 477 469

U-C was used to convert the energy requirement from Btuth/lb to W · h/kg by following the
on-screen prompts to select the "From" and "To" energy units, and clicking on "Convert". The
results are shown below.

Btu,h/lb 420 466 423 477 469

602 Appendix

W - h/kg | 271.2 1 300.9 | 273.1 | 308.0 1 302.8

Other unit conversion tools are available from various web sites. For example, see
http://www.joshmadison.com/software/convert/. However, none of the web programs is as
extensive as U-C, and they may contain conversion factors that are not traceable to NIST values.

A.2 Thermophysical Properties of Steam and Air

In many material and energy balance calculations, assuming that gases are ideal gives
satisfactory accuracy. But when high accuracy is needed, or at elevated pressure when a gas
deviates significantly from ideal, real-gas data is needed. Data for most gases can be found in
published handbooks or from the web. Detailed thermophysical properties of air as derived from
NIST are in theAir folder on the Handbook CD.

A.2.1 Steam Calculators

The ChemicaLogic Corporation provides a variety of programs among which is a steam
calculator (http://www.chemicalogic.com/steamtab/companion/download.htm. This program is
capable of calculating 21 different properties of water and steam. You may download this
program, or purchase a more elaborate program. Megawatsoft provides a free on-line version of
their steam calculator (http://www.steamtablesonline.com/steam97web.aspx), which includes
steam calculations relating to turbines and flash evaporators. The Engineering Toolbox provides
steam calculators, along with many other useful programs at:
http://www.engineeringtoolbox.com/saturated-steam-table-d_812.html. Folder Charts on the
Handbook CD contains a table for the vapor pressure of steam and expanded vapor pressure
equations.

A.2.2 Moist Air Calculator

The air used in materials processes always contains some moisture, and the potential exists for
some of this moisture to condense if the air temperature is lowered or the pressure increased. The
Linric Corporation has a student edition of their PsyCalc program for making relative humidity and
moist air calculations: (http://www.linric.com/studentpsycalc.htm). You may also want to try their
on-line psychrometer (http://www.linric.com/webpsysi.htm). Also, search the web for other
psychrometry programs.

A.3 Stream Units Conversion Calculator (MMV-C)

MMV-C stands for Mole-Mass-Volume Converter, and is used when stream quantity or
composition units are given in one set of units but are needed in another. MMV-C.xla is in folder
"FlowBal and MMV-C" on the handbook CD. We know that material balance calculations can be
easier using mole units, but often the stream and process data are given in mass units. Suppose a
blast furnace requires 3 tonnes of humidified air per minute, which is made by mixing 160 kg of
steam with 2840 kg of dry air. MMV-C can calculate the volume and volume fraction of each
species in the mixture. We take the composition of dry air listed in Chapter 1, in terms of volume
fraction:

<pN2 = 0.780; φ02 = 0.210; фАг = 0.010

MMV-C then converts this to mass fraction. Each mass fraction is multiplied by 2840 (using
Excel) to obtain the mass of each species. 160 kg of H20 is then added to the other species mass,
from which MMV-C calculates the volume of each species at STP and at the actual blast condition
of 1200 К and 1.85 atm.

Appendix 603

Species Mol Fract Mass Fract Mass, kg Vol. STPm3 Voi actual m
N2 0.780 0.754 2142 1714 4070
0 2 0.210 0.232 659 461 1096
Ar 0.010 0.014 39 22 52
H20 0 0.00 160 199 473

MMV-C has other conversion features, such as combining multiple streams into one stream.
It also generates an Excel workbook with cells renamed such that entering a formula containing an
element displays the atomic mass of the element. MMV-C is useful in converting a FlowBal
output stream from amounts to any other unit set. For that, be sure MMV-C.xla is in the same
folder as FlowBal.

A.4 Extension of Excel Tools for Repeat Calculation

Excel's Goal Seek and Solver tools are good ways to obtain iterative solutions to flowsheets
with one or more unknown variables. But often one wants to calculate a mass or energy balance
for a variety of conditions. Both of these tools have been modified to do repetitive solving while
systematically modifying one primary and one secondary variables. The number of solves is the
product of the number of primary times the number of secondary variables. Both of these
programs and supporting guides are on the Handbook CD in folders "SuperGoalSeek" and
"SuperSolver".

SuperGS.xla is an Excel add-in program based on Goal Seek. SuperGS is set up to select a
range of variables to change instead of a single cell. In a heat balance, we may wish to calculate
the adiabatic flame temperature as a function of several air preheat temperatures, and as a function
of the amount of excess air. Suppose the air preheat temperature is selected as the primary
variable, and the amount of excess air the secondary variable. SuperGS will first calculate the
AFT for a range of air temperatures and one of the air amount values. It will next calculate the
AFT for the same range of air temperatures but for the next excess air amount. A new worksheet
is created for each excess air amount. Please see the Help Text and SuperGS examples in the
SuperGS workbook. The convergence limit for Goal Seek can be set by going to <Tools>
<Options> <Calculations>.

SuperSolver.xla is an Excel program based on Excel's Solver tool, which may not be
automatically installed when you install Office. Solver is an add-in tool that finds a solution to a
set of equations, based on a starting estimate for each variable. The main application of Solver in
this Handbook is to calculate system balances on processes that have equation sets that cannot be
reduced to a single equation. Please read your Excel manual for basic information about the Solver
tool.

SuperSolver (SS) was developed so that multiple calculations could be made on an equation
set, then changing a primary initial variable, and repeating the solve. In addition, a secondary
variable can be selected for each set of primary variables. A worksheet can be arranged to display
the results of a range of input conditions. Consider the reforming of natural gas with steam. The
material balance contains Keq equations that are non-linear in both partial pressure of species and
temperature, and the heat balance contains quadratic temperature terms. The entire system
equation set may contain over eight equations.

Suppose we were interested in a system balance as a function of the ratio of natural gas to
steam into the reformer (the primary variable), and also as a function of the system pressure (the
secondary variable). You must first make a single Solver calculation to create the SS model on the
worksheet. It's always a good practice to provide a reasonable set of starting estimates, and format
the equation set so that all equations are set to equal zero. Avoid using expressions that have an
unknown in the denominator, or as a square root. Check the Options box to Assume Non-
Negative, and Use Automatic Scaling. If Solver converges, you are ready to use SuperSolver.

604 Appendix

SS first calculates the system balance for all of the specified steam/NG ratios, then changes
the pressure, and repeats the solving process. The total number of solves is the product of the
number of primary variables times the number of secondary variables. Please see the SS User's
Guide on the Handbook CD for examples and hints.

A. 5 Thermodynamic Database Programs

Material and heat balance calculations require a database of molecular mass and
thermodynamic properties of the elements and compounds. FREED is such a database, and was
used extensively throughout the Handbook. Also, FlowBal uses FREED as the database for all of
its calculations. FREED is in folder "Thermodynamic Database" on the Handbook CD. FREED
contains data on about 2450 species, which includes elements, compounds of invariant
stoichiometry, and substances of variable composition. FREED has features to view the data as
abbreviated datafiles, tables, or charts. It also has several computational tools that extend the
database to material and heat balance applications. Specifically, the Reaction tool allows the data
for individual species to be aggregated to groups of reactants and products, and calculates the
change in thermodynamic properties when these substances react.

FREED is structured for people who have a basic knowledge of thermodynamics and some
experience in applying it to practical problems. The User's Guide (FreedGuide.rtf) is a detailed
description of FREED's features. It contains a description of the examples that are in workbook
Freed-xmpls.xls.

There are also a number of print, web-based, and commercial database programs that serve
the same purpose. Please consult the General References section for information on these
programs.

A.6 Flowsheet Simulation and System Balancing

The Handbook makes extensive use of FlowBal, an Excel-based program for making material
and heat balances on steady state multiple device processes. FlowBal is in folder "FlowBal and
MMV-C" on the Handbook CD. FlowBal uses a non-sequential species balance method for
material balances. The heat balance is calculated after the material balance calculation. The
thermodynamic database program FREED supplies atomic mass data for material balances and
enthalpy data for heat balances.

FlowBal is started by entering the number of streams, number of reactions, and number of
species. The species may be entered via the keyboard, or selected from a database worksheet
derived from Freed.xls. Next, devices are entered, and assigned streams and reactions. FlowBal
offers two ways to include constraints on the system. First, you may define an extent of
consumption of a reactant species. Second, you may enter equations that relate stream variables,
such as an equilibrium constant expression. FlowBal uses either Excel's Solver to solve the set of
material balance equations, or a built-in Newton-Raphson solver. The Repetitive Solve tool
calculates multiple system balances at different stream variables. The tool also includes a Target
feature, which assigns a value to a system variable. The tool's results are used to generate a linear
or quadratic equation from which Excel calculates the value of the variable that reports the target
value.

The FlowBal User's Guide has hyperlinks to the Examples workbook, and all of FlowBal's
features are explained by context-sensitive help text. FlowBal is not intended for use independent
of this Handbook, except for experienced process engineers. The FlowBal User's Guide text is
based on the assumption that you have access to the Handbook and are familiar with the
fundamentals of material and heat balance principles.

GENERAL REFERENCES

1. General Chemistry
Zumdahl, S. S, and Zumdahl, S. A., Chemistry, 7th Edition, Houghton Mifflin, 2007.

2. Thermophysical and Thermodynamic Data
Haynes, William M., Ed., CRC Handbook of Chemistry and Physics, 91st Edition, CRC Press,

2010.
Speight, James, Lange 's Handbook of Chemistry, 70th Anniversary Edition, McGraw-Hill

Professional, 2005.
Green, Donald W. and Perry, Robert H., Perry's Chemical Engineers ' Handbook, 8th Edition,

McGraw-Hill Professional, 2007.
NIST Chemistry WebBook, http://webbook.nist.gov/.

3. Encyclopedias
Encyclopedia of Materials Science and Technology, Elsevier, 2001.
Ulimann 's Encyclopedia of Industrial Chemistry, 6th Edition, Wiley-VCH, 2002.
Kirk-Othmer Encyclopedia of Chemical Technology, 5th Edition, John Wiley & Sons, Ine,

2001.

Wikipedia contributors, Wikipedia, The Free Encyclopedia, December 2010.
http://en.wikipedia.org/wiki/Main_Page.

4. Material and Energy Balances
Schlesinger, Mark E., Mass and Energy Balances in Materials Engineering, Prentice Hall,

1996.
Oloman, Colin, Material and Energy Balances for Engineers and Environmentalists

(Advances in Chemical and Process Engineering), Imperial College Press, 2009.
Himmelblau, David M., and Riggs, James В., Basic Principles and Calculations in Chemical

Engineering, 7th Edition, Prentice Hall, 2003.
Felder, Richard M. and Rousseau, Ronald W., Elementary Principles of Chemical Processes,

3rd Edition, with Integrated Media and Study Tools and Student Workbook, Wiley, 2005.
Reklaitis, G. V., Introduction to Material and Energy Balances, Wiley, 1983.

5. Computerized Databases and Thermodynamic Calculation Programs
Bale, C. and Pelton, A., FactSage Program for Computational Thermochemistry, CRCT,

http://www.factsage.com. 2010. FactWeb Programs, www.crct.polymtl.ca/factweb, 2010..
Roine, Antti, HSC Chemistry, www.Outotec.com/hsc, 2009.
Thermo Cale Software, www.thermocalc.com, 2010.
MTDATA thermodynamic and phase equilibria software.

www.npl.co.uk/advanced-materials/measurement-techniques/modelling/mtdata
CompuTherm/PanDat phase diagram calculator, www.computherm.com, 2008.

6. Computational Software for Material and Energy Balance Calculations
METSIM process simulator, www.metsim.com, 2010.
SysCAD plant simulation by Kenwalt, www.syscad.net, 2010.
Wiseman, David, Limn flowsheet processor, www.davidwiseman.com.au/, 2010.
HSCSim flowsheet designer, www.Outotec.com/hsc, 2009.

INDEX

The Index entries refer to pages in the text where the term is mentioned in a significant way.
If the term is mentioned on a succeeding page, the second page is not cited. Also, index terms are
not listed when they appear in the end-of-Chapter exercises.

A oxygen enriched, 283, 326, 329, 528,
544? 546, 548
Absolute pressure (see Pressure) preheated, 328, 338, 437, 474. 477, 502,
Absolute temperature (see Temperature) 520, 528, 544, 546, 553, 560, 574, 598
Absorber (see Devices) stoichiometric, for reaction, 324, 332,
Absorption (see Process) 337, 406, 448, 454, 469, 475, 478, 514,
Accepted (see Units) 516,518,544,547,552,592
Acceleration of gravity, 4, 5, 6 Alumina, 162,288,502
Acceleration, unit of, 2, 4, 5, 414 Aluminum, 5, 21, 157, 177, 221, 454, 468,
Accuracy (see also Statistics), 78, 83, 86-92, 474? 478, 499, 502, 547
Ammonia, 246, 260, 262, 372, 405, 449, 575
170,175,425,431 Amount of substance (mole), 2, 4, 11, 13, 17,
Activity, activity coefficient (see also 248
Amount of substance fraction (mole fraction)
Solutions), 46, 231, 371, 390, 395, 441 (see Composition)
Acid Ampere, 2,20,571
Analysis (see also Statistics)
acetic, 244, 565 chemical, 18, 157, 328, 329, 332, 325,
boric, 181,288 344,369,517
carbonic, 47 Aqueous (see Solutions)
hydrochloric, 197, 202, 293, 393, 397, Area, 2, 5, 9, 72, 82
402, 444, 498 Array, FlowBal, 217-223, 280, 309, 312, 314,
sulfuric, 25, 202, 208, 217, 245, 268, 338, 355, 489-492, 494, 534, 537, 539,
289, 368, 382, 393, 395, 397, 444, 449, 544,595,597
498,525,567,571,573 Ash, coal, 310,328,516
Acid - base reactions, 392 Atmosphere (see also Air), 1,3,10
Adiabatic controlled, 277, 329, 333, 340,343, 346,
process, 412, 414, 417, 436, 444, 458, 371,515,547,589,592
462, 470, 499, 502, 517, 523, 566 protective, 257,260,372,531
compression, 438 Atomic mass, 12, 17, 245, 253, 604
expansion, 434, 447 Atomic weight (see Atomic mass)
flame temperature, 448, 517, 519, 528, Atomization, 241,459,466,494
551,573 Avogadro's number, 2,12,248
reaction, 440
reaction temperature, 441, 449, 506, 531, В
573
AES system of units (see Units) Balances (see Heat, Material, System)
Agglomeration, agglomerate, 362, 369 Bar (see Pressure)
Air (see also Humidity, Psychrometry, Barometer, 10
Oxygen, Nitrogen, Nitrogen oxide) Base (see Acid - base, Units)
composition, 18, 25, 44, 160, 178, 249, Basic oxygen furnace (BOF) (see Device)
322,431 Basis, for balances (see Heat balance,
compressibility, 32, 44, 432
density, 13, 18,30,44,52 Material balance)
equation of state, 105,432 Batch process (see Process)
expansion, 434,448
molar mass, 18, 31

Index 607

Bauxite, 162 273-275, 279, 284-287, 293, 297, 302,
Bayer, 162 305, 309, 328, 352, 390-394, 402,411,
Benzene, 248,511,543 420,426, 437, 440, 505, 555
Blast furnace {see Device) balancing, 253,283
Boiling, boiling point, 36, 38, 41, 44, 418, extent of (XR), 155, 256, 258, 261, 265-
269, 271, 274, 278-281, 297, 313, 315-
428,492,512 321, 338, 341, 343, 350-355, 394, 526,
Boric acid {see Acid) 578,581,599
Boundary {see Phase, System) formation, 49, 251, 259, 261, 263, 266,
Boyle's law, 30 270, 336, 338, 371, 391, 420, 441, 444,
British thermal unit (Btu), 4, 7, 70-74, 322, 498, 516, 521, 526, 531, 539, 561, 570
independent, NIRx, 28, 29, 274-276, 278,
413,417,513 294-300,305,316
Bulk density, 15 oxidation, 217, 257, 258, 281, 283, 284-
286, 306, 316, 318-321, 326, 330, 341,
С 344, 360, 367, 369, 394, 506-510, 524-
527,562,567-569
Calcine, calcination, 147, 266, 292, 345-348, oxidation-reduction 284, 345, 392
367, 369, 407, 510, 542,552-557 parallel, 260,290
reduction, 58, 114-116, 235, 252, 255-
Calcium, 146,241,249 257, 269-271, 275-277, 284, 291, 302,
Calcium compounds 340, 345, 348-352, 355-366, 421, 439,
531-533, 539-542, 558-561, 578-580,
calcium carbonate, 249, 398 593-598
calcium hydroxide, 266, 345, 399 reversible, 266-268, 270, 275, 278, 287,
calcium oxide, 49, 266, 293-296, 374, 297, 306, 341, 411, 521, 526, 571, 573
385, 399, 408,552-557, 539-542 sequential, 273,280,316,352
calcium sulfate, 49 spontaneous, 263, 266-268, 272, 276,
Calculations, 21, 86, 151, 154-160, 174-181, 280, 287, 290, 297, 306, 325, 334, 344,
195-201, 216-218, 256, 275-277, 306- 346, 367, 369, 399, 402,411, 438, 440,
309, 333, 371, 377, 422-427, 451, 462, 506,518,534,536,565,567
505,512,602 standard reactions, 263, 439, 521, 553,
Calorie, 3,7,413 562
Calorific power, value {see Fuel) stoichiometric reactions, relationships,
Calorimeter, 77,92,418-420 28, 161, 274, 268, 248, 252, 268, 286,
Carbon {see also Graphite), 12, 248,251,311, 327,513
328, 343, 370-378, 386, 442, 536, 539- water-gas shift reaction (WGR), 277,
542 287, 311-313, 316-318, 341-345, 360,
Carbon potential, 344, 370 363, 365, 427, 523, 545, 594
Catalyst, 29,93, 120, 122-125, 131, 197,225, Chemical kinetics, rate processes {see also
260, 263, 278, 290, 306, 316, 318-320, Rate of reaction), 27, 110, 114, 258-263,
340-343, 525 322, 339, 350, 362, 371, 384, 398, 402
CH4 and CH4 reactions, 254, 279, 316, 322, Chemical vapor deposition (CVD), 305
331, 341-344, 363,458, 512-515, 518, Chlorine, chlorination, 250, 309, 319, 427,
547, 589-592
C-0 reactions, 253-255, 265, 272-274, 280- 536
283, 296, 437-440, 521-523, 528, 582- Clapeyron equation, 42
588 Coal, 284, 310-314, 321, 327-329, 511, 516
C-O-H reactions, 235, 243, 251, 274, 277- Coke, 322, 327, 374-376, 528-530, 542, 557
279, 313, 316, 321-326, 337-345, 370, Coke oven gas, 542
464,513-523,547,589,594 Combustion, 148, 254, 258, 266, 282, 314,
Celsius {see Temperature)
Centigrade {see Temperature) 321, 373,403,437,492,511,549-555,
Charge {see Electrical) 560, 573, 589, 599
Charles' law, 30
Chemical equations/reactions {see also
Decomposition, and specific reactants),
28, 144, 148, 151, 156, 248, 251-266,

608 Index

Combustion gas, 149, 292, 295, 314, 325, Density (mass), specific gravity, 2, 11, 13-18,
329-333, 337, 454, 468, 475,492, 514, 34, 105, 195, 208, 228, 323, 331, 432,
519,542,548,553,589 514,589,592

Components, 16, 27, 29, 159-161, 164, 167, Dependent variable (see Variables)
179,294-296,300,441 Derivative control (see Controllers)
Derived units (see Units)
Composition, 16-19, 26-29, 44-47, 94, 145, Desulfurization, 256, 314, 378, 385-389
157-165, 239, 249, 296-298, 300, 328, Device, 146-150, 155, 160, 167, 172, 179,
389, 410,441, 451, 515-518, 606
197, 205, 217, 223, 234, 239, 296, 300,
Compressibility, 32, 40, 105, 432 418, 451, 466, 469, 483, 488, 533
Concentration, 2,4, 13, 16, 19, 49, 110, 211- basic oxygen furnace (BOF), 377, 379,
381
215,390,444 blast furnace, 348, 357, 373-376, 489,
Condensation (see also Humidity, Dew point), 528,575
continuously stirred tank, 223
30,35-39, 41, 153, 219,463-465, 486- control, controller, 62, 67, 149, 234, 238,
488 514,590
Condenser (see Device) dryer, 40, 183, 187, 190, 219, 246, 233,
Conductivity, thermal, 3, 600 465
Conservation, (see Mass, Energy) filter, filtering, filtrate, 150, 166, 187-
Constraint, 29, 176, 185, 196, 234, 268, 296, 191,202-204,347,398,567
320,371,402,452,579 flash furnace, 382,443
thermal, 505 fluid bed, 147, 223, 225, 275, 349, 351,
Consumption (see Fuel, Energy) 355, 357, 368, 507, 521, 552, 559, 599
Continuously stirred reactors (see Device) heat exchanger, 149, 459, 474, 480, 491,
Control volume, 144,415 500, 533, 536, 548, 552, 557, 558, 561,
Controller (see Device) 596, 599
Convergence, 155,286,318,334,604 mixer, 148, 153, 205, 217, 385-388, 590
Conversion of units (see Units) mixer-settler, 205, 208, 211
Conversion of material, 254, 260, 269, 272, reactor, 149, 197, 220, 223, 225, 257,
445,599 260, 271, 276, 294, 349, 359, 373, 505,
Copper, 9,46, 48, 55, 60, 86, 89, 91, 205, 594, 600
208-217, 244, 284,367,381-385, 395- recuperator (see also Heat exchange),
398, 443,459-462, 533-535, 567-570, 469
571-573 roaster, 187, 367-369, 508-511, 533,
chalcopyrite, 250, 367, 533, 567-570 561-565
Coulomb (see also Faraday), 3, 20, 392 scrubber, 179, 187, 198-202, 314, 395,
Counter-current (see Process) 479,484, 489
Coupled (see Process) separator, 148,150,162,206,241
Critical point, 35, 38,429 shaft (furnace), 348, 359-366, 373,474,
Critical temperature, (see Temperature) 555
Current efficiency, 20, 572 splitter, 148, 161, 167, 201, 217-223,
Cyanide, 285 236, 320, 332, 385
thickener, 206,221,484
D Dew point, dpt (see also Humidity), 38, 50,
177,323, 328, 333, 344, 436, 462-465
Dalton's law (see Pressure) Diffusion, 262
Decomposition, thermal, 260-262, 266, 297, Dimension, 1, 4, 7, 12, 16, 18, 20, 602
Dimension equation, 11
300,345,371 Distribution coefficient, 233, 377, 381-386
Degree of Freedom (DOF), 29, 35, 156, 158- DRI (see Iron)

173, 177,179-184, 189, 213, 217, 222, Dry bulb temperature (dbt), 40
239, 294,296-309, 403, 452-456, 508 Dulong, 517
subsidiary relation (SR), 161, 164, 169,
173, 181, 189, 214, 236, 271, 276, 280,
296, 300, 302, 305, 347

Index 609

E Equations
independent, 156-159,164,239,306
Efficiency (see also Current efficiency) solving, 85,96, 103, 106, 154-156, 165,
energy, 211 174-177, 184, 194-196, 216, 218, 239,
material, 202, 205, 208, 215, 239, 269, 283,318,451,532,604
349, 360-363
thermal, 148, 197, 321, 325, 337, 468- Equilibrium constant (Keq), equilibrium
500, 542, 546, 553, 562, 587, 589 position, 27, 29, 35, 42, 44,46, 48, 213,
229, 258, 260, 263, 266-274, 276, 283,
Electric 287, 294, 299, 307, 316, 335-340, 342,
charge, 20 349, 360, 370, 382, 385, 391,428, 519,
current, 1,20,389,571-573 547,566
energy (see Energy)
furnace, 348,474, 495, 539, 571. 582- Equilibrium (mechanical), 27
588 Equilibrium (thermal), 27
potential, emf, 3, 20, 568, 573 Errors, non-statistical (see also Statistics,
power, 3, 6, 20, 327
resistance, 3, 20, 571 error), 21, 157, 223, 238, 305, 373, 395,
419,451,459,565
Electrochemical processes Ethane, 316,322
electrorefining, 205, 571-573 Evaporation (see Process)
electrowinning, 137, 211-214, 567-570, Excess reactant (see Reactant)
572 Exothermic reaction, process, 341, 346, 367,
electrochemistry, 20, 212, 283, 389-391, 369, 428, 438,444, 498, 507, 517, 526,
444,496-498,566,571-573 529, 531, 533, 536, 558, 565, 572
Expansion, gas, 417,433-435
Electromotive force (see Electric, potential) Expansion
Electrons, 12, 20, 284-286, 389, 392, 498, 571 thermal, 34,599
Element, 12,25,248,284 free, 433-435
Element (atomic) balance, 152, 155, 159, 176, Extraction, 146, 205, 211-215, 463, 536, 567,
572
178, 218, 242, 251-254, 284, 286, 296,
300-307, 310, 324, 328, 332, 342-345, F
369-371, 377, 386, 422, 509, 604
Endothermic reaction, process, 341, 343, 440, Fahrenheit temperature, 1, 8
444, 517, 529, 572 Faraday constant, 20, 392
Energy Faraday's law, 571
electrical, 20, 327, 572, 582, 586 Feedback control (see Device)
heat (Enthalpy) Please search for this Feed-forward control (see Device)
term in the Table of Contents. Filter (see Device)
First law of thermodynamics, 410-416, 445,
internal, 412-414,431,445,450
kinetic, 6,412,416,445,501 505
potential, 6,412,416,445 Fixed carbon, 328
work, 3,6,144,411-417,433,445 Flow
Energy balance (see also Heat balance), 26,
44, 54, 235, 369, 410,424,437, 445, 450, flowrate control (see Device)
602 measurement, 10, 31, 40
Energy efficiency (see Efficiency) FlowBal, Please see Table of Contents and
Energy, conservation of, 413,450 List of Examples for this term.
Enthalpy , enthalpy change (and heat/heat Flowsheets, 146-151, 155, 163, 197, 222, 239,
change). Please search for these and 655
related terms in the Table of Contents and Flue gas (see Stack gas)
List of Examples. Fluid, 10, 14, 27, 38, 204, 385, 418, 471-474,
478
Environment, environmental, 171, 187,339, Fluid bed (see Device)
478,525,590 Foot (dimension) (see Length)
Force, 2-7,9, 11,20,25,411-414
Equation of state, 26, 28, 32, 50,94,105, 195, Formation reaction (see Chemical reaction)
411,431

610 Index

Formula weight (see Molecular mass) Heat balance, 437-440. (see also System
Formula balance). Please also search for this term
in the Table of Contents and List of
chemical, 18, 220, 248, 252, 258, 260, Examples for Chapters 8-10
284,327,360,516 overall heat balance, 410, 421, 438-440,
empirical, 18, 159, 248, 253, 327, 516 442-444, 451, 462, 464, 467, 488, 495,
FREED, 12, 144, 216, 264, 278-280, 299, 499, 517, 524, 559, 566, 570, 586
306, 391, 421-431, 437-442, 446, 451-
455,459, 462,511-516, 536, 598, 605 Heat capacity, 2, 9, 77, 99, 110, 416-418, 426,
Fuel 432, 435, 439, 443
calorific power, 511
gross (higher) heating value, HHV, 512 Heat content, 416-428, 445, 451-454, 458,
net (lower) heating value, LHV, 512 463, 500, 507
process fuel equivalent, 547
Fuel oil, 159, 258, 321, 327, 332, 417, 511, Heat exchange (see also Device), 469-471,
516,519,523,542 474, 478

G Heat loss, 54, 450-455, 458, 468, 490, 505-
507,517,599
Gallon (dimension), (see Volume)
Galvanic cell (see Electrochemical) Heat of formation, 7, 418, 420, 424, 427, 429,
Gas constant R, 30, 33, 105, 417, 432, 439 517,570
Gas, gases (see also Compressibility, and
Heat of mixing, solution, 441-443, 494
specific gas) Heat of reaction, 420, 426-428, 512
ideal, 18, 28, 30, 32, 36, 43, 411, 415- Heat of transformation, 425, 418, 421, 428
417,445 Heat transfer (see Heat exchange)
non-ideal, 32-34,50,411 Hematite (see Iron, compounds)
vanderWaals, 32-34,36 Hess'law, 421,488,516
Gasification, gasifier, 310-313, 462 Homogeneous (see System)
Gibbs phase rule, 27, 35, 159, 195, 294, 423 Hour (dimension) (see Time)
Glass, 27,233,411 Heating value (.see Fuel)
Goal Seek, Super Goal Seek, 33, 56, 174, 186, Humidity (see also Dew point, Psychrometry),
194, 216, 232, 237, 332, 485, 496, 604
Gold, 9, 146, 285 38, 50, 103, 194, 246, 323, 333, 344, 452,
Grade, 233 603
Grain (dimension) (see Mass) Hydrochloric acid (see Acid, Hydrochloride)
Gram (dimension) (see Mass) Hydrogen, hydrogen reactions, 22, 48, 114,
Gram equivalent, 571 211, 229, 230, 260, 266, 275, 278, 285,
Gram formula weight, 12 302, 321, 327, 349, 355, 362, 427, 462,
Grammole, 12 498,521,558,560,572
Granular solid, 15,223,225,561
Graphite (see also Carbon), 371,442,601 I
Gravity, 4-6,27
Gravimetric factor, 249-251, 286, 305, 376, Ice, 29,35-37,42, 151,503
379, 386 Ideal (see Gas, Solutions, Statistics)
Gross heating value (see Fuel) Inch (see Length)
Independent equation (see Equations)
H Independent reaction (see Chemical reactions)
Independent variable (see Variables)
Head, metallostatic, 11 Inert species, 27, 29, 42-44, 149, 192, 229,
Heat (see Enthalpy)
253, 264, 267, 286, 300, 330, 346, 506,
592
Instreams (see Streams)
Integral control (see Device)
Intensive property (see Property)
Interaction (see Statistics)
Internal energy (see Energy)
International Practical Temperature (see
Temperature)
Interpolation, 44,61,74,472,458

Index 611

Iron, 6, 11, 44, 48, 101, 230, 233, 442, 544 M
compounds, 142, 202, 211, 248, 284,
346,367,383,391,395,567 Magnetite {see Iron, compounds)
DRI, 256, 340-342, 348, 352, 355-365, Manometer, 11
507,539,579,582-588 Mass (dimension), {see also Atomic mass),
oxide reduction, 146-148, 150, 235, 253, 1-8, 11, 16,248,581
266, 340, 348, 359, 373, 381, 463, 474,
507,531,539,578,593 kilogram, gram, 2-5, 12, 16
pyrite, 219, 250, 284, 328, 367, 394, 569 ounce, 89
wustite, 159, 248, 253, 348-354, 357- pound, 1, 7, 602
364,539,578 ton, 3, 7, 8
tonne, 3, 6-8, 15
J Mass balance {see Material balance)
Mass density {see Density)
Joule, 2-4,6,20,413,425,515 Mass, conservation of, 144, 151, 157, 239,
Joule-Thomson coefficient, 433 251,294,413
Mass fraction {see Composition)
К Mass, thermal, 470-479, 483, 551, 556-558,
562
Kelvin {see Temperature) Material balance, 11 {see also System
Kilogram (dimension) {see Mass) balance)
Kilogram calorie {see Calorie) atomic species method, 294, 300-304,
Kilowatt hour (kWh), 6 {see also Energy, 309,311,332
molecular species method, 294-297, 299-
electrical) 303,305,309,316
Kinetics {see Chemical kinetics) overall, 151, 179-183, 185, 194, 203,
Kinetic energy {see Energy) 206, 209, 213, 222, 264, 272, 284, 291,
Kirchhoff equation, 426-430,451 328, 351, 360, 372, 376, 383, 440
Kroll {see Process) McCabe-Thiele diagram, 213-215
Measurements {see Statistics)
L Metallostatic head {see Head)
Metallothermic {see Process)
Latent heat of transformation {see Heat of Metastable, 27,402,411,421
transformation) Meter {see Length)
Methane {see CH4)
Law of {see specific item) Methanol, 344,511
Ledgers, 152, 154, 156, 163, 170, 239, 317, Millimeter of mercury {see Pressure)
Mineralogy, 250, 367, 369, 509
332, 370, 373 Minute {see Time)
Length, dimension, 1-3, 6, 11, 20, 25, 34, 86, Mixer {see Device)
Mixer-settler {see Device)
322 Mixture, 13, 16, 18, 26, 29, 31, 38, 44, 156,
Lime, limestone, 49, 256, 266, 293, 295, 314,
162, 167, 241, 249, 258, 294, 369, 411
377, 385, 399-401, 539-542, 555-557, MMV-C, 144, 174, 178, 187, 202, 249, 286,
567,583
Limiting reactant {see Reactant) 310,323,335,367,417,603
Liquid {see Fluid) Model {see also Statistics), 155, 196, 238,
Liter {see Volume)
Lower heating value, LHV {see Fuel) 246, 319, 357, 381, 389, 394, 444, 449,
Lignite, 327, 517 582,588
Linear functions {see also Statistics), 9,15, Molality, 4, 16, 48, 105, 110, 389, 393, 444,
30, 34, 35, 50, 156, 196, 208, 218, 228, 498, 565
262,331,417,419,425,429,435 Molarity, 4, 16,49,389
Loading, 211 Mole {see Amount of substance)
Mole fraction {see Composition)
Mole ratio method, 400
Molecular mass, 12, 156, 248, 286, 517, 605

612 Index

Molecule, 12, 149, 211, 230, 248, 252, 286, Performance, measures of, 193, 208, 213, 232,
300,398,410-413 240,271-273,373,592

Molybdenum, molybdenum compounds, 255, Phase {see also Gas)
275,318 boundary, 37, 262, 267, 360
condensed, 27, 29, 34, 47, 50, 266, 268,
N 275
rule {see Gibbs phase rule)
Natural gas (see CH4 and CH4 reactions, Fuel) transformation, 42, 144, 149, 219, 251,
Net heating value (see Fuel) 279, 418, 422, 428, 445, 490, 536, 599
Newton (see Force)
Newton's law, 4, 111-115 Placeholder, 457, 489-494, 501, 508, 526,
Newton-Raphson method, 365, 605 533-538, 541, 544-546, 594-598
NIST 605, 1,4, 11, 22, 44, 54, 57, 105, 116,
Potential {see Electric potential)
137,431-433,603 Potential energy {see Energy)
Nitrogen, nitrogen reactions (see also Pound-force {see Units, Force)
Pound-mass {see Units, Mass)
Ammonia), 229, 248, 266, 272, 285, 297, Pound-mole {see Units, Amount of substance)
300, 308, 344, 376,459, 596 Powder, 223-227, 275, 459-462, 465, 494,
Nitrogen oxides (NOx), 266, 328, 335-337,
339,478,548,551,589 582
Non-linear functions (see also Statistics), Power {see Electric)
156, 184, 199, 306, 358, 453, 525, 604 Poynting, 42
Non-reactive (see Systems) Pressure
Number of independent reactions (NIRx) (see
Chemical reactions) absolute, 9, 30-33,
Dalton's law, 31
О gage, 9-11
partial, 31, 35, 40, 43-45, 47, 50, 192,
Ohm (dimension), 3, 20 199, 229, 239, 246, 263, 250, 267, 277,
Oil {see Fuel oil) 282, 294, 299, 301, 307, 312, 345, 270,
Optimization {see Process, Statistics) 527,552
Organic, 205,211-215,322,511 pitottube, 10
Orifice, 331,514,590-593 torr,
Ounce {see Mass) saturation {see also Dew point), 35-38,
Outstream {see Stream) 41,316
Oxidizing agent, 284 vacuum, 9,34, 153, 187,230
Oxygen, oxygen reactions, 101, 230, 251, vapor, 29, 35-37,40-47, 151, 153, 161,
177, 187, 189, 197, 231, 429, 436, 482,
255, 268, 272, 274, 284, 296, 323, 325, 486, 490, 493
329, 333, 340, 343, 346, 355, 367, 370, Process
377, 386, 394, 516, 519, 523, 539-541, absorption, 197-199,295,309,408
5449 547? 573? 582-586, 590 accumulation, 144, 151-154,223,239,
Oxygen enrichment {see Air) 413,450
Oxygen potential, 321, 340, 361, 370, 547 batch, 145, 151, 153, 155, 223, 239, 260,
262, 309, 372, 384, 387, 542
Parts per million (ppm) {see Concentration, calcination {see Calcine)
Composition) constrained, unconstrained, 155
counter current, CCCD, 171, 197, 205,
Pascal {see Pressure) 207, 239, 245, 359, 373, 469, 475, 483,
Peat, 327 542, 548, 552, 555, 599
Pellet, 348, 359, 439, 474, 539, 558, 582 decant, decantation, 162, 168, 181, 207,
Percentage {see Concentration) 221,243
distillation, 43, 151, 154, 180
drying, 183,219,246,465
evaporation, vaporization, 35, 37, 192,
219, 230, 251, 279, 412, 418, 428, 432,
435, 452, 479, 486, 492, 530, 562, 598

Index 613

Process (com) Quadratic equation (see also Statistics), 218,
filtration, 166-168, 187, 191-194, 202- 231, 283, 314, 417-420, 425-428, 457,
204, 244, 246, 567 464,472,474,485,559,591
hydrometallurgical. Please search for
this process type in the Table of Contents Quartz (see Silica)
and List of Examples.
R
isobaric, 37, 262, 412, 414, 416, 432,
445,450,517 Rankine (see Temperature)
isochoric, 37, 260-262,412, 414, 445, Raoult's law (see Solutions, ideal)
517 Rate of reaction (R-R term) (see also
isothermal, 30, 37, 469, 260, 264, 412,
414,418,517 Chemical kinetics), 29, 219, 258-261,
iterative approximation, 230, 240, 384, 282,299,312
436 Reactant
Kroll, 257,531 excess, 255, 256-258, 266, 269, 272, 280,
leaching, 157-162, 167, 171, 174, 177, 291, 324-327, 330-334, 341, 346, 367-
205,212,221,239,245,394, 398, 402, 370, 478, 518-520, 544, 564-567, 589-
435, 496, 567 592
liquid-liquid extraction, 211-216 limiting, 256, 266, 270-274, 280, 287,
metallothermic, 145,257,531 352, 367, 438
models (see Model, Statistics) stoichiometric amount of, 252, 256-258,
optimization (see also Statistics, 268, 274-277, 294-297, 299, 304, 323-
optimum), 161, 207, 225, 232, 308, 398 327, 330, 370, 437, 511, 532, 566
overspecified (see Degree of freedom) Reactions (see Chemical reactions)
precipitation, 181, 203, 318, 392, 398- Recovery of
402 heat (see Heat exchange, Device)
pyrometallurgical. Please search for this substances, 162, 166, 182, 184, 194, 210,
process type in the Table of Contents and 215, 221, 232, 244, 256, 318, 389
List of Examples. Recuperator (see Device)
Recycle (see Stream)
refining, 144, 152-154, 181,230,322, Red mud, 162-164
571-573 Reducing agent, 257, 269, 284, 302, 531, 593
reforming, 273, 316-319, 340-345, 359, Reducing gas, 235, 256, 269-275, 278, 292,
364, 523-525 311-313, 340, 343, 348,351-356, 359-
roasting, 146, 366-369, 508-511, 533- 366, 371, 403, 463,516,521-523, 525,
535, 561-565 529,578-581,593-596
scrubbing, 49, 179, 187-189, 197-202, Reduction (see Chemical equations)
314,478,483-486,489-491 Reference state, 47, 390,411,437,444
sintering Reference temperature, 392,416,418,422,
smelting, 148,367,381-385,443 431,445,450,459,472,512
solvent extraction (see liquid-liquid). Refining (see Process)
steady state, 145, 152, 155, 159, 163, Relative humidity (see Humidity)
223, 231, 296, 372, 415, 450, 470, 599 Repetitive solving, 194, 218, 283, 306, 313,
transient, time-varying, 145, 223, 384 318, 335, 338, 356-358, 365, 384, 489,
underspecified (see Degree of freedom) 491,529,538,541,594,604
Resistance (see Ohm)
washing, 162-164, 166, 168, 171, 174, Restrictions (see Degree of freedom)
204-211,568 Retention time, 223-228, 270, 274, 337, 349,
Process fuel equivalent (see Fuel) 350, 360
Productivity, 269,359 Roasting (see Process)
Property Rounding of numbers (see Significant figures,
Statistics)
extensive, 26-29, 144
intensive, 26-28, 144, 195,553
Proportional control (see Device)
Psychrometry, 39, 436, 603
Purge stream (see Stream)

614 Index

s Steady-state (see Process)
Steam, 32-39,44, 195,278,311,316,341-
S - О reactions, 187-194, 217-219, 251, 253, 344, 364,431-439, 455, 463, 466, 471-
258, 266, 268, 297-304, 306, 314, 323, 473, 486, 508, 521-525, 528-530, 536,
329,333-335, 346, 369, 383, 5069,525- 603
528,533
Steam table, 36,44, 195, 422, 431, 437,446,
Sankey diagram, 499 451,500,536,598
Saturation pressure {See Pressure)
Second (see Time) Stoichiometry (see also Chemical reactions),
Selectivity, 234, 269, 272 50, 248, 274, 299, 324, 346, 367, 396,
SI (see Units) 399, 511, 522, 526, 565-569, 589, 600
Significant figures (see also Statistics), 4, 6,
Stream, 54, 144, 146, 149-151, 156-161, 163-
12, 21, 36, 159, 167, 170, 432, 451, 458, 174, 183-186, 197,205,211,223,228,
491,511,535,540 232, 234, 262, 307, 331, 359, 371, 385,
Siemens process, 304 590-592
Sieverts' law (see Solutions, condensed
phase) bleed, 205, 348, 365, 493, 571, 578
Silica, Si02, 250, 311, 367, 375, 378, 380, 383 bypass, 197-204,235,237,239,245,
Silicon reactions, 250, 304, 309, 375, 379 335,385, 564
Slurry, 14, 157, 160, 162, 166-171, 177, 181, plug flow, 223, 226, 593
184,187-190,205-211,221-223,227, purge (see Stream, bleed)
462,484, 489, 494-497 recycle, 145, 155, 197, 202-205, 239,
Solubility limit, 48-50 318-321, 364-366, 548-552, 578
Solubility product, 49, 391 Statistics
Solutions, condensed phase, absolute values, 96, 105, 117
aqueous, 29, 181, 197-202,211-214 accuracy, 78, 83, 86, 89, 92
(see also ionic) adjusted R2, 102,107,126
gas-liquid, 47, 197-202, 398 analysis, statistical and regression, 54,
Henry's law, 47, 390, 398, 402 75,81,89, 103, 106, 113, 123, 138
ideal, 44,51, 390,394,441,498,565 array, 61, 91
ionic, 20, 49, 283, 285, 389-398, 402, average, (see also mean and median),
444, 497-499, 565-570 60, 70, 78, 83, 87, 90, 96, 98, 115, 117,
regular, 44,46,231,441 122,238,350,460
Sieverts' law, 48, 229 bias, 54,80,87,90, 135
Solvent extraction, (see Process, liquid-liquid) causation (see Statistics, curve fitting)
Solver, Super Solver, 101-107, 112, 130, 174- central limit theorem (CLT), 78-85, 90
178,184-187, 194, 196, 199, 202, 207, coefficient of determination (R2), 67-70,
210, 214, 216, 239, 277, 298, 306-308, 74, 80, 97-100, 102, 107, 125-127
311, 316, 332, 343, 345, 353, 362, 379, correlation (see Statistics, curve fitting)
387-389,400, 457, 480, 524-527, 559- confidence, confidence interval, 77, 82,
561,579-581,604 89, 114,129
Species balance (see Material balance) cumulative distribution function (cdf),
Split fraction (see Device, splitter) 64, 70, 72
Specific gravity (see Density) cumulative percentage, 63,71
Specific heat (see Heat capacity) curve fitting (see also Trendline), 95
Splitter (see Device) data analysis, 54, 103, 114, 122, 137
Stack gas, 217, 314, 328, 332, 335-338, 403, descriptive, 54-56,86,137
difference plot 113
454, 465-469, 474-478, 514, 542-544, dispersion, 59
553 distribution plot 66-70, 73-75, 79-81, 90,
Standard state, 263, 371, 390, 411, 418, 108,128
420-422,433, 444-446, 498 error, random, 75, 87, 92-95
Standard temperature and pressure (STP), 3, error, systematic, 67,75,81,86-95
18, 30-32, 50 experimental design, 76, 117, 119-136
State property, 414,421,445,453 extrapolation (see curve fitting)
factorial experimental design, 120-130

Index 615

Statistics (coni) System
format, 60,97, 105, 110 boundary, 26, 144, 162, 171, 179,410-
fractional factorial design, 122, 130-136 415
frequency distribution, 56-58,63, 139 non-reactive, 27-29, 151, 156, 159,279,
FTEST, 90-92 294, 450-452, 478
histogram, 56-58, 61-68, 70-74, 78-82 constrained, 155
hypothesis testing, 108-110, 118, 129 open, 27,36,144,410,413,415
independence, 75-77, 108,111 closed, 27, 36, 144, 410, 413-416, 445,
inference, 77 458
interactions, 123, 125, 127, 131-136 homogeneous, 26, 28, 203, 260, 410, 418
lag plot, 76, 108, 111 isolated, 27,144,410,413,458
mean, 59-61, 70-73, 75-88, 90, 92, 98, surroundings, 27, 144, 149,410-414,
108, 117-119, 122 420, 433, 445, 450, 490, 505, 510
median, 60, 64
models, 54, 62-74, 94, 99-119, 123-131, System balance, 450, 466, 475-477, 488, 501,
136 505, 549, 559, 602
model, empirical vs. phenomenological, sequential modular method, 155
110, 116,239 simultaneous solution method, 155
normal distribution, 62, 70-75, 78-85,
90, 108,128 Temperature, 1, 4, 26-30, 111, 426, 437
OFAT (see Statistics, experimental absolute, 8
design) Celsius, 3, 8
optimization, optimum, 54, 120-123, conversion, 8
128-130 critical, 32,431,435,547
outliers, 111,117-119 Fahrenheit, 8
p-value, 108, 110, 125-130, 136 Kelvin, 2,4,21
percentile, 60-62, 66, 70, 73 Rankine, 21
Plackett-Burman (see Statistics,
experimental design) Thermal conductivity (see Conductivity)
population, 55, 59, 63-65, 70, 73, 75-83, Thermal decomposition (see Decomposition)
87,90, 100,113 Thermal efficiency (see Efficiency)
precision, 21, 62, 65, 78, 84-87, 90-92 Thermal expansion (see Expansion)
probability density function (pdf), 65, 70- Thermal mass (see Mass)
73,82 Thermite, 531
random, 62, 64, 69, 75, 91, 135 Thermodynamic data (see FREED)
rational function, 116 Time (units of), 1, 6
sampling, 8, 18, 54, 59, 61, 67, 76, 78- Time series (see Statistics)
86, 89-91, 96, 111, 157-160, 329, 333- Titanium (see also Process, Kroll), 34, 257,
335,505,590
significance, 67, 88-93, 108, 110, 114, 531
125, 127-129, 135 Titanium oxide, 100, 117, 168, 536
significant figures, 60-65, 86, 97-100 Torr (see Pressure)
skew, 62, 80, 130 Trendline (see also Statistics, curve fitting),
standard deviation, 59, 70-73, 77, 79, 82-
85,87,90-94,108, 117, 138, 141 67, 74, 80, 96, 99-101, 103, 106, 111,
sum of squared distance (SSD), 97, 105, 115,117, 195, 198, 225, 228, 232, 237,
432 262, 277. 283, 308, 331,338, 357, 389,
time series, 110 417,425,435,459,523,590
uniform distribution, 62-69, 71, 73, 78 Triple point, 4,8,28,35,512
variance, 59,75,91,93,98
и
Subsidiary relation (see Degree of freedom)
Sulfur oxidation (see S - О reactions) Units
Sulfuric acid (see Acid) AES, 1,4,6,8, 13,482
Supercooling, 411, 429-431 derived, 1-5,8,22

616 Index

Units {coni) z
SI, 1-5,8, 11-13,20
table {see inside cover) Zinc, zinc compounds, 41, 146, 151-154,
228, 230, 252, 276, 368, 418, 429,
Unit conversion, 4, 6-13, 16-19, 21, 23, 486-488, 508
178, 187, 209, 307, 413, 602, 603 zinc oxide reduction, 252, 276
dimension table, 7, 10, 13, 16
factor, 4, 6-9, 11
U-Converter, 1, 4, 6, 8, 11, 30, 602

Uranium, 412, 531-533

V

Vacuum {see Pressure)
Vapor-liquid equilibrium (VLE), 28, 35-38,

40, 46, 196, 431, 463, 472,481, 485,487
Vapor pressure {see Pressure)
Variables {see also Statistics)

independent, 28, 158, 165, 174, 223, 259,
308, 314, 410, 414, 442, 445, 453
dependent, 28, 157, 161, 174, 178, 331,
352, 358, 399,490, 492, 510, 524, 563
Volt {see also Electric, potential), 3, 20
Volume, unit, 1, 13-16, 18, 26-38, 40, 48, 50,
208, 224, 228, 230, 260-262, 264, 268,
331,411-417,429,512,590-593
cubic foot, 16, 18, 30, 70, 229, 322
cubic meter, 2-4,13-17,30-33,40
gallon, 1,227,246,602
liter, 1-3, 17, 323

w

Water, 4, 8, 13-15, 17, 34-39, 42, 48, 144,
398,481,492

water vapor (лее also Steam), 18,28,35,
40, 43, 99, 267, 295, 350, 437,455, 462,
479-485,492,512,603
water vapor pressure, 35-37, 40, 43
Water gas shift reaction (WGR) {see
Chemical reactions)
Washing {see Process, washing)
Watt, kWh {see Electric, power)
Weight, 4-6, 11-13,208,230
Work {see Energy, work)

Y

Yield, 95-100, 120-126, 129, 233, 269,
271,380,584