6. process variables

8/14/2019 6. Process Variables

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Process Variables

To design or analyze a process, we need to know the

amounts, compositions, and condition of materials

entering, leaving, and within the process.

The quantities used to describe a process are called

process variables. These must be measured or

computed.

In this class we will be concerned with a number of

process variables, including:

y Mass and Volume

y Flow Rate

y Chemical Composition

y Pressure

y Temperature


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MASSAND VOLUME

Density

Density is the mass per unit volume of a substance

kg/m3,g/cm3, lbm/ft3 (symbolized by the Greek letterV)

Density relates mass and volume of a substance.

density = (mass)/(volume) m =V V

EXAMPLE:Determine the mass of 200 cm3

ofCCl4and the volume (in cm

3) of 6.20 lbm ofCCl4

(=1 595kg/m3)

Gas/vapor densities depend heavily on Pressure and

Temperature -V(P,T). Liquid and solid densities cannormally be looked up in a table.

Densities of pure solids

and liquids also vary

when pressure and

temperature change, butmuch less.

Solid and liquid densities

are often treated as

constants.


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In most applications assume the density of water as

1.0 g/cm3- strictly true only for a specific temperature.

Specific Volume

The specific volume of a substance is the volume perunit mass, the reciprocal of the density.

Specific Gravity

The specific gravity is the ratio of the density of a

substance to that of a reference substance. - a dimensionless quantity.Usually reference for solids and liquids is water at 4

oC

V = 1.000 g/cm3

= 1 000 kg/m3

= 62.43 lbm/ft3

For gases usual reference density is air.

Since density varies with temperature- specify the

temperatures involved:

e.g.

this means "the specific gravity of the substance at

20oC is 0.73 times that of water at 4

oC".

In CGS the numerical values of the density and s.g.

are the same

s.g. = 0.6 = 0.6 g/cm3

1V

!


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EXAMPLE: If dibromopentane has a sg of 1.57, what

is the density in a) g/cm3

b) lbm/ft3

c) kg/m3

EXAMPLE:A drum contains 8.00 liters of toluene.

What is the mass of the liquid?

EXAMPLE:A drum 700 lbm of a liquid mixture of

benzene and toluene. The density of the mixture is

measured to be 0.850 g/ml. Estimate the mass andvolumes of the two hydrocarbons in the drum


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Flow Rates

Expressed as

y the mass flow rate, , mass per unit timey the molarflow rate, , moles per unit timey the volumetric flow rate, , volume per unit time

m = mass kg

n = moles kg V = volume m

3

volumetric flow rate can be converted to mass flow

rate by using the density:

Vm V!

Most industrial flow measurement devices measure

the flow velocity. The volumetric flow rate is then

calculated from the velocity and the cross-sectionalarea of the pipe:

vAV !


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Chemical Composition

Moles

AMole is a measure of the number of particles(6.02x10

23) or quantity of substance.

Agram-mole (mol, gmol) of a substance is the amount

of a substance that contains as many elementary

entities as there are atoms in 0.012 kg of carbon 12.

A substance whose mass in grams is numerically the

same as its molecular (or atomic) weight contains

6.02x1023

particles and thus equates to one mole of the

substance.

Carbon Dioxide has a molecular weight of 44, so

1 mol ofCO2 contains 44 grams and 6.02x1023

molecules ofCO2

EXAMPLE:1.505x10

24

molecules of a substance has amass of 34.5 grams. What is the molecular weight of

the substance?


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Kilogram-moles (kgmol) andpound-moles (lbmol,

mole) are also used. These are defined the same way

but using different mass units.

1 gmol ofCO contains grams1 lbmol ofCOcontains grams

Ifthe molecular weightofa substance is M,then there

are Mgrams pergram-mole. This means you can use

the molecular weight as a conversion factor for goingfrom mass to moles.

EXAMPLE: How many a) lb moles and b) gmol in

2.00 pounds ofNaOH?


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Use the same conversion factors for the different units

of mole as for converting mass units

(1 lbmole = 454 g-mole, etc.).

The molecular weight is used to convert from mass tomoles, so it is logical that it is also used to convert

between mass and molar flow rates:

MW

mn

!

Most material streams in process units are mixtures of

compounds. Composition of streams can be described

in various ways.

Composition Fractions

Composition fractions can be based on mass (x) or on

moles (y).

mass fractionxi

Ax or or

!

mole fraction yi

Ay or or

!


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Convert from "fraction" to "percent" by multiplying

by 100.

The units of mass measurement used don't make a

difference, as long as the top and bottom of the ratiouse the same units:

0.25 0.25 0.25 0.25

Ax etc! ! ! ! !

EXAMPLE:A stream contains 20 g of oxygen gas, 70

g of nitrogen, 5 g of helium, and 5 g of hydrogen.

Find the mass and mole fractions and the mass and

mole percent compositions.


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Parts per Million (PPM) and

Parts per Billion (PPB)

A concentration unit often seen in environmental

usage isparts permillion orppm. For solids andliquids it is the grams of solute in 1 million grams of

solution. For gases it is the number of particles

(moles). PPM (or ppb) is a special kind of mass (or

mass) fraction

Used to express the concentration oftrace species

Signifies how many parts (grams, moles) of the

species are present per million or billion parts (grams,

moles) of the mixture.

Parts perMillion (ppm) = xA*106 or yA*106Parts per Billion (ppb) = xA*10

9or yA*10

9

EXAMPLE: The current OSHA 8 hour limit for HCN

in air is 10.0 ppm. Convert to mg HCN/kg air


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Given a mass composition in percentorfraction form

convertto molar composition or vice-versa

assume a basis of 1 kg, 100 mol, etc.

E.G.:Air is 78 mole% nitrogen, 21 mole% oxygen,and 1 mole% argon. What is its mass composition?

Basis:

Component moles mol wt mass mass fraction

The Average MolecularWeightof a mixture is

computed from the molar composition and the

molecular weight. It is a weighted average -- themolecular weights are averaged using the mole

fractions as weights.

!!compnentsall

iiMyMyMyM -

1111

and, using mass fractions

!!componentsall

i

i

Mx

Mx

Mx

M.

2

2

1

11

EXAMPLE:Calculate the average molecular weight of

air.


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Do NOT try to calculate average densities or average

specific gravities using a weighted arithmetic mean,

use a weighted harmonic mean.

Concentration

composition and concentration used interchangeably.

Concentration is based on volume and is one way of

expressing composition. The mass concentration is

the mass of a component per unit volume, similarly

molar concentration is the moles per unit volume.

The following are some ways to expressconcentration, where the numerator signifies the solute

and the denominator signifies the solution.

Mass Concentration: g/cm3, lbm/ft

3, kg/in

3

MolarConcentration: kmol/m3, lb-mol/ft

3, g-mol/L

The last molar concentration listed, g-mol/L is the

Molarity of the solute in the mixture.

Molarity of component A, MA = g-molA/Ltotal


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6. process variables

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