Chapter 2 Processes and Process Variables

8/13/2019 Chapter 2 Processes and Process Variables

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Processes and ProcessVariables

Chapter 2

Material and Energy Balances


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Evaluation of performance of processoperation requires the knowledge of the

amounts, composition, conditions ofmaterials that enter and leave eachprocess units.This chapter presents methods ofcalculating variables that characterize theoperation of processes and individualprocess units.


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Processes andProcess Variables

Density andSpecific Gravity

Flow rate

ChemicalComposition

Pressure

Temperature

What are in this chapter?


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Topic Outcomes

At the end of Chapter 2, you should: Explain in words the difference between density

and specific gravity, the meaning of gram-mole,lb-mole, mol and kmol, two methods of measuring

temp. and pressure, the meaning of the absolutepressure and gauge pressure and whyatmospheric pressure is not necessarily 1 atm.

Calculate the density of a liquid and solid species

from a knowledge of the specific gravity. Calculate the quantities mass, volume, and molesfrom a knowledge of the third quantity for anyspecies of known density and molecular weight.


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Topic Outcomes-cont.

Give the composition of a mixture expressed interms of mass fractions and calculate thecomposition in terms of mole fraction.

Determine the average molecular weight of amixture from the mass or molar composition ofthe mixture.

Convert pressure expressed as a head of afluid to the equivalent pressure expressed as aforce per unit area.

Convert among temperatures in K, C, F and R.


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Process

Process - any operation that cause a physical orchemical change in a substance. Can consist of

several process unit.Process streams connecting process units andform the process flow sheet .Chemical engineer is responsible to design andoperate the process.1) Design

: formation of process flow sheet/layout: specification of individual process unit: associated operating variables

2) Operate : running day-to-day process

ProcessUnitInput/Feed Output/Product

Process

Unit Output/Product


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Density

Densities of pure solids and liquids areessentially independent of pressure and varyrelatively slightly with temperature.

The density of a substance can be used as aconversion factor to relate the mass and thevolume of the substances.


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The density of CCl 4 is 1.595 g/cm 3 ; what isa) Mass of 20 cm 3 of CCl 4

b) Volume of 6.20 lb m of CCl 4

20 cm3

1.595 g = 31.9 g cm 3

6.20 lb m 454 g cm 3 = 1760 cm 3

1 lb m 1.595 g

Try This


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Specific GravitySpecific Gravity (SG)

Ratio of the density ( ) of a substance tothe density of a reference ( ref ) substance at aspecific condition:

SG = substance / ref

Density of water at 4C is used as a referencedensity; whereas the value is showed below:

ref = H2O(l) (4C) = 1.000 g/cm 3

= 1000 kg/m 3 = 62.43 lbm/ft 3

SG is a dimensionless. To get the density of asubstance, multiply the SG value to the value of

reference density, ref .


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Solution

a) = 0.5 1 g = 0.5 g/cm 3 cm 3

b)

=

0.5 62.43 lb m = 31.215 lb m /ft 3 ft 3

c) 3 cm 3 0.5 1 g = 1.5 g

cm 3

d) 18 g cm 3 = 36 cm 3

0.5 g


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Flow RateContinuous process involve movement of materials

from one point to another with certain rate.

Flow rate- the rate at which a material istransported through a process line.

Flow rate can be expressed as : mass flow rate (mass/time) volumetric flow rate (volume/time)

The mass flow rates of process streams must beknown for many process calculations, but it isfrequently more convenient to measure volumetricflow rates than mass flow rate.


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IN GROUP DISCUSSIONStatement from pg 46

[ The density of a fluid can be used to convert aknown volumetric flow rate of a process stream

to the mass flow rate of that stream or viceversa.]

Observe Eq. (3.2-1)


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Flow Rate-cont .

Flow meter is a device mounted in a processline that provides a continuous reading of theflow rate in the line.

Two commonly used flow meter are rotameter and orifice meter.


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Flow meter

Rotameter Orifice meter(based on

pressure drop)


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ChemicalComposition

Moles andMolecular Weight

Mass andMole Fractions

AverageMolecular Weight

Concentration

Parts per Million (ppm)& Part per Billion (ppb)

Chemical Composition


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Moles & Molecular Weight

Atomic weight of element- mass of an atombased on carbon isotope 12 C.

Molecular weight of compound- sum of theatomic weights of atoms that constitute a

molecule of the compound.

Moles= Mass / Molecular Weight .

Unit for moles are g-mole, kmol , lb-mole etc ( g-mole is same as mol )


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[ The molecular weight may thus be used as aconversion factor that relates the mass and the

number of moles of a quantity of the substance .]Observe Eq. (3.3-1) and (Eq. 3.3-2)


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Moles & Molecular Weight-cont.

If the molecular weight of a substance is M,then there are M kg/kmol, M g/mol, and Mlb m /lb-mole of this substance.

At 1 mol of a substance, its mass in gram isequal to its molecular weight. Eg. CO hasmolecular weight of 28. Hence, at 1 mol,mass of CO is 28 g. At 1 kmol, mass of CO is

28 kg.

One g-mole of any species contains 6.02 x10 23 (Avogadros number) molecules of that

species.


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[ The molecular weight of a species can be used torelate the mass flow rate of a continuous stream ofthis species to the corresponding molar flow rate. ]

Observe Eq. (3.3-3) and (Eq. 3.3-4)


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1. How many gram of O 2 consist in 100g of CO 2?

2. Find number of molecules of CO 2 in 100g of CO 2?

An IQ test


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Mass and Mole Fractions

Process streams consist of mixtures of liquids or

gases, or solutions of one or more solutes in aliquid solvents.

The following terms may be used to define the

composition of a mixture of substances, includinga species A.

Mass fraction: x A= mass of A / total mass

Unit: kg A/kg total; g A/g total; lb m A/lb m total

Mole fraction: y A= moles of A/ total molesUnit: kmol A/kmol total; lb-moles A/lb-mole total


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A mixture of gases has the following masscomposition:

O2 16%

CO 4%CO 2 17%N2 63%

What is the molar composition?

Try This


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4 steps to convert from mass fractions to molesfractions:

1. Assuming as a basis of calculation a mass of themixture (e.g. 100 kg or 100 lbm).

2. Using the known mass fractions to calculate themass of each component in the basis quantity.

3. Convert these masses to moles using their

molecular weights.

4. Taking the ratio of the moles of each componentto the total number of moles.


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A mixture of gases has the following masscomposition:

O2 16%

CO 4%CO 2 17%N2 63%

What is the molar composition?

Try This


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Solution

Basis: 100g of mixture

Component Mass

Fraction Mass MW Moles Mole Fraction

i x i m i Mi n i y iO2 0.16 16 32 0.500 0.152 CO 0.04 4 28 0.143 0.044

CO 2 0.17 17 44 0.386 0.118

N2 0.63 63 28 2.250 0.686 Total 1.00 100 3.279 1.000


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If 100 lb m /min of A (M A=2) and 300 lb m /minof B (M B=3) flow through pipes, find

1. Mass fractions of A and B2. Mole fractions of A and B3. Mass flow rate of A

4. Molar flow rate of B5. Total mass flow rate6. Total molar flow rate

FROM GROUP DISCUSSION


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Average Molecular Weight

The average molecular weight (or mean

molecular weight) of a mixture, (kg/kmol,lbm/lb-mole, etc.), is the ratio of the total massto the total number of moles of all species.

If y i is the mole fraction of the component i of themixture and M i is the molecular weight:

If x i is the mass fraction of the component i ofthe mixture and M i is the molecular weight:

M

componentallii2211 My.....MyMyM

componentall i

i

2

2

1

1

Mx

.....Mx

Mx

M1


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Concentration

Mass concentration (c A):

Molar concentration (C A):

Molarity :

mixtureof VolumeAof mass

cA

mixtureof VolumeAof moles

C A

Liter inmixtureof VolumeAof moles

Molarity


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[ The concentration of a substance in a mixture or

solution can be used as a conversion factor torelate the mass (or moles) of a component in a

sample mixture to the sample volume or to relatethe mass (or moles) flow rate or a component of

a continuous stream to the total volumetric flowrate of the stream. ]


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Parts per Million (ppm)&Parts per Billion (ppb)

To express the concentrations of trace species inmixtures of gases or liquids.

May refer to mass ratios (usual for liquids) or moleratios (usual for gases). How many parts (in gram ormoles) of the species are present per million or billionparts of the mixture.

ppm i= y i x 10 6

ppb i = y i x 10 9


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IN GROUP DISCUSSIONExample given from pg 53

[ Air in the area of a power plant is said to contain

15 ppm SO 2 .]


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Pressure

A pressure is the ratio of a force to the area onwhich the force acts (P= F/A).

Pressure units: N/m 2 , dynes/cm 2 , lb f /in 2 , psi, Pa.


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IN GROUP DISCUSSIONStatement on page 54

[ The fluid pressure may be defined as the ratio

F/A, where F is the minimum force that wouldhave to be exerted on a frictionless plug in the

hole to keep the fluid from emerging. ]Observe Figure (3.4-1)


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[as a head of a particular fluid-that is, as theheight of a hypothetical column of this fluid thatwould exert the given pressure at its base if the

pressure at the top were zero .]Observe Eq. (3.4-2)


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The fluid pressure may be defined as the ratioF/A, where F is the minimum force that wouldhave to be applied on a frictionless plug in thehole to keep the fluid from emerging.

F (N)P (N/m 2 ) A (m

2 )

P (N/m 2 )

F (N)

A (m 2)

Pressure-cont.


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Atmospheric, Absolute & Gauge Pressure

The atmospheric pressure can be thought ofas the pressure at the base of a column offluid (air) located at the point measurement(e.g. at sea level).

A typical value of the atmospheric pressure atsea level, 760.0 mm Hg , has been designatedas a standard pressure of 1 atmosphere .


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The fluid pressure is referred as absolutepressures . In a perfect vacuum, the pressure iszero.

Pressure-measuring devices give gauge pressure

of fluid. A gauge pressure of zero indicated that theabsolute pressure (fluid pressure) is equal toatmospheric pressure.

Relationship between absolute pressure andgauge pressure is:

Atmospheric, Absolute & GaugePressure-cont.

atmopheric gaugeabsolute P P P


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Fluid Pressure Measurement

Common pressure- measurement devices-Bourdon gauge and monometer.

Monometer- U-shaped tube partially filled with

fluid of known density.

Manometer gives the measurement of pressure inpressure difference , P ( P 1- P 2 ).

Manometers are used in several ways ( Figure3.4-4). Most common ways is differentialmonomer. In each diagram P 1 is higher than P 2 .


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[ In particular, the pressure at the height of the

lower surface of a monometer fluid is the same inboth arms of the monometer.]

Observe Figure 3.4-5 and Eq. (3.4-5)


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Equation for general manometer;

As fluids 1 and 2 are the same, 1 = 2= . Theequation is reduced to where d 1 - d 2= h :

If P 2 is atmospheric pressure, the pressure atpint 1 is the difference in the levels of themanometer fluid, h .

gh gd P gd P f 222111

P gh P P f 21

h P P atm 1


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IN GROUP DISCUSSIONExample 3.4-3 on page 59


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Temperature of a substance in a particularstate of aggregation (solid, liquid, or gas) is ameasure of the average kinetic energypossessed by the substance molecules.

Some temperature measuring devices:resistance thermometer , thermocouple ,pyrometer and thermometer .

Temperature


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The following relationship may be used toconvert a temperature expressed in onedefined scale unit to its equivalent in another;

Temperature-cont.

328.1

8.1

67.459

15.273

C T F T

K T RT

F T RT

C T K T


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Consider the interval from 20 F to 80 Fa) Calculate the equivalent temperature in C

and the interval between them.

C33.36.7)(26.6TTT

C26.6C1.8

3280F)(80T

C6.7C1.8

3220F)(20T

1.832F)T(C)T(

12

2

1

Try This

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Chapter 2 Processes and Process Variables