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CHAPTER 1- INTRODUCTION CHE243-MATERIAL AND ENERGY BALANCE AND SIMULATION
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CHAPTER 1-
INTRODUCTION CHE243-MATERIAL AND ENERGY
BALANCE AND SIMULATION
CHAPTER 1- INTRODUCTION
INTRODUCTION TO ENGINEERING CALCULATION
β’ Units And Dimensions
β’ Conversion Of Units
β’ Systems Of Units
β’ Dimensional Homogeneity
PROCESSES AND PROCESS VARIABLES
β’ Concept Of Mass, Volume, Flowrate
β’ Chemical Composition
β’ Pressure And Temperature
2.0 UNIT & DIMENSION
Proper handling of units is an essential part of being an engineer
A measured or counted quantity has a numerical value and unit, eg. 2 meter, 4.29 kilograms.
A dimension is a property that can be measured, e.g β length, time, mass or temperature, or calculated by multiplying or dividing other dimensions, such as length/time (velocity).
Measurable unit are specific values of dimensions that have been defined by convention, custom, or law, e.g β grams for mass, seconds for time and centimeters for length.
3.0 CONVERSION OF UNITS
Equivalence between two expressions of the same quantity can be defined in terms of a ratio:
Factors Conversion
mm 100
cm 1
mm 10
cm 1
centimeter 1 per milimeters 10 cm 1
mm 10
milimeters 10 per centimeter 1 mm 10
cm 1
2
2
2
To convert a quantity expressed in terms of the unit to its equivalent in terms of another unit, multiply the given quantity by the conversion factor (new unit/old unit). Example:
1 g
1000 mg
36 mg = 0.036 g
Convert an acceleration of 1 cm/s2 to its equivalent in km/yr2.
EXAMPLE 1
2
9
yr
km1095.9
CONVERSION OF UNITS
3 wk to miliseconds
554 m4/(day.kg) to cm4/(min.g)
4.0 SYSTEM OF UNITS
Base units β for mass, length, time, temperature, electrical current and light intensity.
Multiple units β defined as multiples or fractions of base units such as minutes, hours, and milliseconds, all defined in unit of seconds.
Derived units β (a) by multiplying and dividing base or multiple units
(cm2, ft/min) β preferred as compound unit.
(b) As defined equivalent to compound unit (eg. 1 lbf
32.174 lbm.ft/s2).
SYSTEM OF UNITS
SI unit β System International β meter (m) for length, kilogram (kg) for mass, seconds (s) for time and Kelvin (K) for temperature.
CGS system β Most identical to SI unit. Refer to Felder (pp. 11) Table 2.3-1.
American Engineering System β foot (ft) for length, pound-mass (lbm) for mass, seconds for time.
*Note: Refer to Felder (pp. 11)
Quantities can be added or subtracted only if their units are the same.
Rule β every valid equation must be dimensionally homogeneous; that is, all additive terms on both sides of equation must have the same dimensions.
*Note: Refer to Felder (pp. 20-22).
5.0 DIMENSIONAL
HOMOGENEITY
Consider the equation
D(ft)=3t(s)+4
1. If the equation is valid, what are the dimensions of the constants 3 and 4
2. If the equation is consistent in its units, what are the units of 3 and 4
3. Derive an equation for distance in meters in terms of time in minutes
5.0 DIMENSIONAL
HOMOGENEITY
PROCESSES AND
PROCESS VARIABLES
Chemical Process Flow Diagram
SEPARATION PROCESS
REACTION PROCESS
FEED PREPARATION
FINAL PRODUCT
You need to:
β Minimize production of unwanted byproducts
β Separate the good (product) from the bad
(byproducts)
β Recover the unused reactants
β Maximize profit, minimize energy
consumption, minimize impact on the
environment
Process: any operation or series of operations.
β’The material enters a process = Input or Feed.
β’The material which leaves the process = Output or
Product.
β’ It is common for process to consist of multiple steps.
These each steps is carried out in a process unit. Each of
process unit has associated with it a set of input and output
process stream.
β’To design or analyze a process, we need to know the
amounts, compositions & condition of materials which enter
& leave the process.
6.0 MASS AND VOLUME
Density β mass per unit volume.
Specific volume β volume occupied by a unit mass of the substance
Specific gravity β ratio of the density of the substance to the density of a reference substance ref at specific condition:
Reference most commonly used for solid and liquid is water
at 4OC 1000 kg/m3
ref
SG
Calculate the density of mercury in lbm/ft3 and the volume in ft3 occupied by 215 kg of mercury. Given SG of mercury is 13.546 and density of water is 62.3 lbm/ft3.
Density of mercuryβ¦.
392.843
ft
lbm
EXAMPLE 2
3ft5617.0
Volume of 215 kg mercuryβ¦.
β’ Flowrate- the rate at which a material is transported through a process line is the flowrate of that material
β’ Can be expressed as- mass flowrate(mass/time) or volumetric flowrate (volume/time)
β’ Volumetric flowrate can be converted to mass flowrate if density of a fluid is known
MASS AND VOLUMETRIC FLOWRATE
..
// VmVm
β’ The mass flowaret of n-hexane (π=0.659 g/cm3) in a pipe is 6.59 g/s. What is the volumetric flowrate of the hexane?
β’ The volumetric flowrate of CCl4(π=1.595 g/cm3) in a pipe is 100.0 cm3/min. what is the mass flowrate of the CCl4?
EXAMPLE 3
s
cm3
0.10
min5.159
g
7.0 CHEMICAL COMPOSITION
Atomic weight β mass of an atom.
Molecular weight β sum of atomic weights of atoms that constitute a molecule of the compound, e.g O2 = 32 g/g-mol.
If a molecular weight of a substance is M, then there are M kg/kmol, M g/mol, and M lbm/lb-mole of this substance.
Molecular weight can be used as a conversion factor that relates the mass and the number of moles of a quantity of the substance.
1) Conversion Between Mass and Moles
How many of each of the following are contained in 100.0 g of CO2
(M=44.01)?
(1) mol CO2 (4) mol O (7) g O2
(2) lb-moles CO2 (5) mol O2
(3) mol C (6) g O
2CO mol 273.2)1(
EXAMPLE 4
2
3 CO mole-lb 10011.5)2(
C mol 273.2)3(
O mol 546.4)4(
2O mol 273.2)5(
gO7.72)6(
2O 7.72)5( g
7.0 CHEMICAL COMPOSITION
Mass Fraction:
Mole Fraction:
Percent by mass of A is 100xA
Percent by moles of A is 100yA
2) Mass & Mole Fraction and Molecular Weight
mass total
A of massAx
moles total
A of molesAy
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
A kg 26
1) Calculate the mass of A in 175 kg of solution
EXAMPLE 5
2) Calculate the mass flowrate of A in a stream of solution flowing at a rate of 53 Ibm/h
h
AmIb8
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
min
Bmol200
3) Calculate the molar flow rate of B in stream flowing at a rate of 1000 mol/min
EXAMPLE 5 CONTβD
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
s
solution kmol140
4) Calculate the total solution flow rate that corresponds to a molar flow rate of 28 kmol B/s.
EXAMPLE 5 CONTβD
EXAMPLE 5 CONTβD
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
5) Calculate the mass of the solution that contains 300 Ibm of A.
solutionmIb 2000
7.0 CHEMICAL COMPOSITION
A set of mass fractions may be converted to an equivalent set of mole fractions by:
(a) Assuming as a basis of calculation a mass of the mixture.
(b) Using the known mass fractions to calculate the mass of each component in the basis quantity; and converting this masses to moles;
(c) Taking the ratio of the moles of each component to the total number of moles.
3) Conversion from a Composition by Mass to Molar Composition
A mixture of gases has the following composition by mass:
Component Mass %
O2 16
CO 4.0
CO2 17
N2 63
What is the molar composition?
EXAMPLE 6
Comp.
O2
CO
CO2
N2
Total
Mole fraction
(y=n/ntotal)
0.150
0.044
0.120
0.690
1.000
A researcher conducted an experiment on electrolysis of mixed brine. A mixture of gases was produced at the cathode. The composition (by weight) of the gases was as follows: 64% Chlorine (Cl2), 29% Bromine (Br2) and 7% Oxygen (O2). Using the ideal gas law, calculate the composition (by volume) of the gas mixtureβ¦.
Given Molecular weight Br2 = 159.83, Cl2 = 70.91, O2 = 32.00
7.0 CHEMICAL COMPOSITION
Average molecular weight β (mean molecular weight of a mixture), Mav
Using mole fraction:
Using mass fraction:
4) Average molecular weight
ntallcompone
iiav MyMyMyM ...2211
ntallcompone i
i
av M
x
M
x
M
x
M...
1
2
2
1
1
Calculate the average molecular weight of air:
(1) From its approximate molar composition of 79 mol% N2, 21 mol%O2
(2) From its approximate composition by mass of 76.7 wt% N2, 23.3 wt% O2
EXAMPLE 7
84.28avM
7.0 CHEMICAL COMPOSITION
5) Concentration
Solution: a mixture of substance called solutes in another substance called solvent. Solvent: a dominant substance that is present in larger amount and so it dissolves or dilutes the solutes. Solute: a substance that are present in smaller amount and dissolves or distributes in a solvent. It could be more than one solute in a solution. β’ Particles of solutes are normally distributed uniformly throughout the solvent mass.
β’ This distribution of solutes in a solvent is known as concentration (conc) of solutes in the solution.
β’ The conc of solutes could be expressed as mass conc or molar concentration (molarity).
β’ Mass concentration of a solute A in solution (g/cm3, kg/m3, Ibm/ft3).
β’ Molarity of a solute A in solution (in mol/L or M).
β’ ppm & ppb are used to express the con of trace species that is present in a very dilute amount (very small amount) relative to other components in a mixture.
β’ For a solution in liq or solid phase
Concentration of a substance A in ppm
= mass of a substance a solute A in gmol
106 unit of solution
Concentration of a substance A in ppb
β’ = mass of a substance a solute A in gmol
109 unit of solution
7.0 CHEMICAL COMPOSITION
6) Parts per Million and Parts per Billion
ppm also can be defined as
1πππ =1 π
106π π πππ’π‘πππ=
1 π
106ππΏ π πππ’π‘πππ=
1 ππ
103ππΏ π πππ’π‘πππ= 1
ππ
πΏ
β’ Pressure- ratio of a force to the area on which the force acts
β’ Unit : Ibf/in2 (psi) or dynes/cm2 or N/m2 [pascal (Pa)]
Pabsolute = Pgauge + Patmospheric
Typical value of Patmospheric at sea level are;
1atm = 14.696psi = 760mmHg = 101.325kPa
8.0 PRESSURE
AFP /
9.0 TEMPERATURE
Temperature β a measure of average kinetic energy possessed by the substance molecules.
The relationship to convert a temperature expressed in one unit to another:
15273CTKT o . 67459FTRT oO .
KT81RT O . 32CT81FT oO .
The conversion factor:
The conversion factors refer to temperature intervals, not temperatures.
K1
C1
R1
F1
K1
R81
C1
F81 O
O
OO
O
O
,,.
,.
Consider the interval from 20Β°F to 80Β°F
1. calculate the equivalent temperatures in Β°C and the interval between them
2. calculate directly the interval in Β°C between the temperatures.
EXAMPLE
