01.material balance complete

8/2/2019 01.Material Balance Complete

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CHAPTER ONE

MATERIAL BALANCE

OF

METALLURGICALSYSTEMS


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GROUP 1


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1.1 Dimensions and Units

A dimension is something that can bemeasured or quantified. The best known

dimensions are distance related: length, area

(length squared), and volume (length cubed).

Mass and time are also dimensions; so aremore complex variables like viscosity, tensile

strength, and electrical resistivity, etc.

Dimensions are grouped into two types:simple and derived. Derived dimensions are

those that are a function of two or more other

dimensions. Velocity, for example, is a unit

of length (miles, feet, microns, etc.) divided

by a unit of time (minutes, hours, days).


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The concept of a unit is as old as the need ofmankind to measure something: e.g. a time

interval, the distance a spear could be thrown,

the size and weight of a rock, etc.

A unit is a standard magnitude of a givendimension against which other magnitudes ofthat dimension can be compared. The width

of this page is equal to seven of a unit of

length called an inch; the thickness of this

book is equal to a few hundred of a unit

called a page.


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It is well known that there is more than oneavailable unit for nearly all dimensions; for

commonly used dimensions such as weight

and length, there are literally dozens of units.

Among the reasons for this are the

"popularity" of the particular dimension, thehistory of a dimension, convenience, and lack

of communication.

The system used most often are:The English System of Units: this system is

based on foot pound - second; therefore,

this system is called the FDS system.

The French System of Units: this system is

based on centimeter-gram-second; therefore,

this system is called the CGS system.


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The International System of Units: this

system is better known as the SI system; this

system is based on meter-kilogram-second.

1.2 Simple Units

1.Amount (numbers),2. time,3. length,4.mass and weight,5. temperature,6. electrical charge, and7. luminas intensity.


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1.3 Derived Units

as an example:Energy: the SI units of energy are kg.m

2/sec

2

which is known as (joule).

Pressure: the SI unit of pressure is the Pascal

(Pa) which equal (kg/m.sec2).

Density: it is defined as the mass per unit

volume; thus, the density SI unit is (kg/m3).

The specific gravity: it is defined as the ratio

between the density of the material to the

density of water at 25 C (1000 kg/m3

or 62.4

lb/ft3); thus the specific gravity is a unitless

number.


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1.4 Analysis

There are two types of analytical units; thoseareconcentration andcomposition.

Concentration has units similar to density(gm/lit) while composition numbers are

unitless composition values; e.g. the

fractions, the percentages, etc. could be on

weight base, volume base, mole base, etc.


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1.5 Temperature Scales


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1.6 Weight Percent and Mole Fraction

To convert from weight percent, Wi, to molefractions, Xi, we use the formula:

Xi= (Wi/Mi)/(Wi/Mi)

To convert from mole fractions to weightpercent we use the formula:

Wi = [(Xi Mi) / (Xi Mi) ]*100

where Mi is the atomic (or molecular) weight

of component i.


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1.7 Stoichiometry

Most ionic compounds are stoichiometriccompounds, i.e. one gram-mole of these

compounds consists of numbers of gram

atoms of the elements forming thiscompound according to the chemical formula

of the compounds; e.g. one gm-mole of

CaCO3 consists of one-gm atom of Ca, one

gm-atom of C and 3 gm-atoms of oxygen.

A discussion of stoichiometry begins with arelatively simple observation about most

chemical compounds; namely that the atomic

ratios of the elements in them are constant.


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The atomic ratio of calcium to oxygen incalcium oxide is always 1: 1; the atomic ratio

of magnesium to silicon in magnesium

silicide is always 2:1. Because of this, a gm-

mole of silicon added to an alloy in the form

of magnesium silicide will always bring withit two moles of magnesium; a ton-mole of

calcium oxide added to an iron blast furnace

in the form of limestone (CaCO3) will always

bring with it a ton-mole of carbon dioxide.

Such compounds are called stoichiometric,

and most ionic compounds are of this type.


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1.8 Balancing Chemical Reaction

The usefulness of compound stoichimetry inmaking mass balances lies in the fact that a

constant atomic ratio implies a constant mass

ratio of its elements as well.

This principle is the base for balancing thestoichiometric reactions; e.g. by considering

the reaction:

a Fe3O4 + b CO d FeO+g CO2

The stoichiometry of the different elements

shows the following:


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Fe: d = 3a (1)

C: b = g (2)

O: 4a + b = d +2g (3)

Let a=1 then d=3, 4 + b = 3 + 2g (4)

From equations (2) and (4) we can reach tothe following: g = 1 and b = 1; now the

previous reaction can be written as:

Fe3O4+ CO 3 FeO + CO2

1.9 The Stoichiometric Coefficient

The stoichiometric coefficient gives thelimiting values for the reagents.


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1.10 Limiting & Excess Reagents

The level of excess reagent required in anactual material-processing is given by:

% excess = [(nanR) / nR] x100

where na is the actual mass and nR is the massrequired by the reaction.

In most cases, an excess of one or morereactants will be deliberately added.

There are several reasons for this; those are:1. it is thermodynamically impossible for a

reaction to go to completion unless an

excess of one or more reactants is present,


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2.many reactions simply go faster if there isa large excess of one or more reactant,

and

3. in solid-state reactors, where getting goodmixing can be a problem, adding an

excess of one or more compounds canhelp ensure the reactants stay in contact

with each other .


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1.11 Systems and Processes

In order to define a system of substances, aportion of the universe is set aside by

creating system boundaries.

The form such boundaries take define: opensystems, closed systems, and isolated

systems.

An open system is the one which is capableof exchanging energy and/or mass with its

surroundings

A closed system is the one which is incapableof exchanging mass with its surroundings but

capable of exchanging heat with its

surroundings.


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An isolated system is the one which isincapable of exchanging heat and mass with

its surroundings.

A process is defined as the physical orchemical action that occurs to the feed in

materials transferring it to new forms insidethe system.

A stream is a material flowing into or out ofthe process and should be separated from the

universe.

Each process must has at least one input andone output streams.

The location into which the input streamsflow and in which they will be treated to


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generate the materials in the output streams is

known as the magic box (a reactor).

Process streams and the content of the magicbox may be characterized as homogenous or

heterogeneous.

A batch process Steel ConvertersA semi continuous Blast Furnace

A continuous process Continuous Casting


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1.12 Flow Sheets

What is a flow sheet?A flow sheet is a schematic simple drawing

showing the material streams flowing in and

out of the units (or reactors) used in a givenprocess to yield finally the required product.

A good flow sheet may contain:1. simple drawing of the process,2. properties of the process streams,3. the appropriate input and output locations of

streams entering or leaving a unit operation,

and

4. the operating characteristics of the unitoperations.


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The Total Balance Equation:

feed input output

streams streams

For batch process:mass input = mass output + accumulation

In continuous process:ss iut

uit tie

ss utut

uit tie +

uuti

uit tie

Reactor

(Accumulation)


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1.13 The Number of Degrees of

Freedom of a Reactor

The number of degrees of freedom of areactor in a system for carrying its material

balance is given by:F = CSR

where: C = number of components,

S = number of streams, and

R = number of restrictions.

The restritis, R, iits re:I. mass balance equation for each

component,

II. the total mass balance equation for thewhole system,


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III. the independent percentage given foreach component in each stream, and

IV. the atomic ratio in a compound in areactive system.

What does it mean when F has:

vue f zer e uique vue, sitive vue eugh

information, or

egtive vue set f rretvalues.


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GROUP 2


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1.14 Material Balance of Nonreactive

Systems

Mass balance equations are based on the lawof conservation of mass not only to the feed

streams and throughout streams but also to

the weight of each chemical element and

constituents .

Therefore, the mass balance equation are: feed streams mass =

thrughut stres ss

ss f eh eeet (or chemical

compound) in the feed streams =

mass of this element (or chemical

compound) in the throughout streams


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Choosing a basis: a reference amount ofgiven component should be specified as a

basis.

Focus on the consistency with units; i.e., usethe same units.

Multiple-mass balance might include: the recycled stream: where fraction of end

stream is recycled with the input stream

(iron ore sinter),

the return stream: when the whole outputstream is recycled,

the by-pass stream: when fraction or all ofthe stream by-passed the next unit,


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bleed streams: The stream passes throughpurification process then returned back to

the reactor ( purification of electrolyte ),

and

purge stream: part of the output stream ispurged out while the remainder isrecycled.


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1.15 Measures of Performances

1. Recovery: it is the fraction or percentage ofa specified component input to a system that

winds up a desired process stream.

2.

Rejection: it is the fraction or percentage ofa specified component input to a system that

winds up in the undefined process stream

(tailing).

3. Yield: the amount per batch or unit time ofsome specified output stream divided by the

amount of specified input stream.

4. Ultimate yield: yields calculated usingsystem boundaries drawn around an entire

process.


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5. Consumption: it is the inverse of yield.6. The degree of completion.7. The distribution coefficient.8. Selectivity separation factor:

SF=Mn /mN

M and m are the concentrations of thedesired component, N and n are those of

undesired components. Capital letters

indicate the desired product streams and

lower letters represent undesired stream.

9. The selectivity index (SI):SI= F /


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1.16 Thermite Welding Process


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Generating high temperature requires anamount of energy.

One of the most common processes of energyproduction is the burning of fuel.

Both organic and inorganic materials areused as fuels.

1.18Type of Organic Fuels

1.18.1 Natural Gases

Natural gases are the most commonly usedtype of gaseous fuel.


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Presence of other compounds causesproblems becausedifferent natural gases will

give off differing quantities of heat and off-

gas per unit volume when burned.

So, the amount of air needed to burn a givenvolume of different

natural gases changeswith composition.

Example: The amount of air required tocompletely burn one standard cubic meter of

Alaskan natural gas (99.6% CH4 and

0.4%N2) at standard state can be get by :

(1/22.4)*1000= 44.615 gm-mole

A chemical reaction for Alaskan gas can bewritten as:

(a CH4 + b N2 ) + (cO2 + d N2) =

e CO2 + f H2O + g N2


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By inspection, a=e and f=2a=89.23, the

values of a=44.44 and b=0.18,

Knowing e and f sets up an oxygen balance:

c= (2e+f) = 88.87 moles O2

This amount of oxygen can be divided by

0.21 to get 423.2 gm-mole of air needed to

burn one standard cubic meter of Alaskan

natural gas.

Converting this to Kg-moles and multiplying

by 22.414 m3/Kg mol gives 9.49 m

3for the

volume of the required air.


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1.18.2 Fuel Oils

Carbonaceous liquid fuels are better knownas fuel oils and they consist of a large number

of hydrocarbon compounds.

In addition to C and H, most fuel oils containa little sulfur, which burns to form SO2.

Example:fuel oil contains 86.4% C, 11.6% H, and

2.0% S, how many standard cubic feet of off-

gas will we have to handle when one u.s

gallon of this osil with 10% burn excess air?

Its specific gravity is 0.910.

Since density of water in English units is 62.4

lb/ft3

at room temperate, multiplying this


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value by 0.910 gives a density for the oil of

56.78 lb/ft3.

Using conversion constants: thus, the weight

of a gallon = 56.78 (lb/ft3) 6.1337

(ft3/gallon) = 7.59 (lb/gallon)

ie the fue i t be serted it itscompounds, we will use a materials balance

based on its elemental composition.

Setting up the equation:

(a C + b H + c S ) + (d O2 + e N2 ) =

f CO2 + g H2O + h SO2 + j O2 + kN2

multiplying the 7.59 pounds of fuel oil in a

gallon which was just calculated by the massfractions of C, H, and S; and dividing by their

atomic mass, yields h=c and


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a = 0.546, b = 0.874, c = 0.00474; and since

f=a, 2g=b, and d = f + g + h + j

If j = 0, 0.769 lb-moles of O2 are required,

multiplying this by 1.1 produces an actual

input of d = 0.846

Multiplying (d) by 79/21 results in

e=k=3.183 lb-moles of N2 which gives an

actual value of j = 0.077.

Adding f, g, h, j, and k determines the totalquantity of off - gas produced by burning the

fuel oil, 4.248 lb-molls, multiplying this by

the 359 standard ft3/lb-mol produce 1525

standard ft3 off-gas per gallon of fuel oil

burned.


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1.18.3 Solid Fuels

There are a lot of solid carbonaceous fuels as:wood, charcoal, manure, etc.

The Ash: it is the xides tht dt bur rvaporize when the coal is set on fire such as

alumina, hematite, lime, silica, magnesia, etc.

Volatile matter: it is the unfixed carbonwhich is chemically bonded to other elements

that tends to form gaseous compounds when

the coal is heated in absence of air.

Coking: it is the process of driving off thevolatile matter in coal by heating in absence

of air.


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1.19Working Backward

The previous examples had something incommon, that the specified inputs to given

process determined what came out.

I rtie it seties dest wrk thisway, as limitations on composition or

properties of the products will dictate the

input.

This problem may be solved by choosing theproducts as basis, so the solution is worked

backward.


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In the process of roasting pyrite the input is aconcentrate 75 %( FeS2) and 25% Silica and

the roosting reaction is:

4 FeS2 +11 O2=2 Fe2O3 +8 SO2

Some of pyrite might react to form ferricsulphate:

2 FeS2 +7 O2=Fe2(SO4)3 + SO2

To keep the volume percentage of SO2 in theoff-gas below 6.3%, we must solve the

material balance of the reaction:

[a FeS2+b SiO2] + [c O2+d N2] =

[e Fe2O3 + b SiO2] + [f O2 + d N2 + g SO2]

There is no need to use more than onevariable for silica and nitrogen.

Assume one ton of pyrite concentrate:


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Starting with 6.3 Kg-moles of SO2 in the off

gas, so:

Fe: a=2e,

O: 2c=3e +2f +2g, and

S: 2a=g.

By using the ratio O2:N2 =21:79, the problemcan be solved to obtain the needed air to roast

certain amount of pyrite by considering:

C/D =79/21

The base equation is: f + d + g=100


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1.20 The Use of Ledger

The following figure is a schematic drawingof the blast furnace for the manufacture of

pig iron.

As shown in the figure we have four processstreams entering the blast furnace ,those are:

1. an ore containing iron oxide,2. coke,3. flux (mainly limestone), and4. blast air.


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Three process streams leaving; those are1. top gas,2. slag, and3. hot metal.

Example:


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w we eed t write whts gig i dwhts ig ut s hei reti:

[hfFe + hsSi + hmMn + haAl + hhH + hoO] +

[cc C+ caAl + csSi + cfFe + cuS + coO] +

[llCa + lcC + lmMg + lsSi + loO] +

[boO + bbH + bnN] =[pfFe + pcC + psSi + pmMn] +

[sfFe + sfCa + ssSi + saAl + suS + smMn + soO] +

[tcC+thH+tnN+toO]

Each variable is separately identified with afirst letter that defines the particular stream,

and a subscripted letter identifying the

element.


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01.material balance complete

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