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Understand the definitions of various variables in a chemical process, such as pressure, mass flow rate, specific density.
Be able to define different streams in a process.
Be able to describe the meaning of standard abbreviations and symbols used on process flow sheets.
Be able to write a description of a process flow sheet.
Be able to draw a process flow sheet from a written description using a block flow diagram.
Learning Objectives
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Process
Process Variables:Temperature, flow rate, pressure, reactor volume, heat input
Feed
Product 1
Product 2
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Density: the mass per unit volume
Specific volume: the volume occupied by a unit mass of a substance, the inverse of the density.
Densities of pure solids and liquids are essentiallyinsensitive to pressure, and vary relatively slightlywith temperature.
Mass and Volume
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Density of a pure substance can be used as a conversion factor to relate the mass and volume of a quantity of that substance.
Mass and Volume
Examples: 20 cm3 of carbon tetrachloride
20 cm3 x = 31.90 g (= 30 g)
Or 6.20 lbm of carbon tetrachloride
1.595 g1 cm3
6.20 lbm x x = 1760 cm3454 g1 lbm
1 cm3
1.595 g
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Specific gravity (SG) of a substance is the ratio of the density (ρ) of the substance to the density of a reference substance at a specific condition (ρref).
The most common reference for solids and liquids is water at 4.0°C, which has the following density:1.000 g/cm3 = 1000 kg/m3 = 62.43 lbm/ft3
The density of a liquid or solid in g/cm3 is numerically equal to the SG of that substance.
The notation SG = 0.6 signifies that the specific gravity of a substance a 20°C with reference to water at 4°C is 0.6.
Mass and Volume
20o
4o
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A thermometer uses mercury, the volume of which changes with temperature.
Coefficients of linear and cubic thermal expansion of some liquids and solids are given as empirical polynomial functions of temperature:
V (T) = V0(1 + AT + BT2)
What are the units of V0, A and B?
Mass and Volume
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Flow Rate
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The flow rate of a process stream can be expressed as a mass flow rate (mass/time) or as a volumetric flow rate (volume/time).
Density can be used as a conversion factor between massand volumetric flow rate.
The mass flow rate of n‐hexane (ρ = 0.659 g/cm3) in a pipeis 6.59 g/s. What is the volumetric flow rate of n‐hexane?
Flow Rate
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Suppose a gas is flowing through a cone‐shaped pipe.
– How do the mass flow rates of the gas at inlet and outlet compare?
– If the density of the gas is constant, how do the volumetric flow rates at these two points compare?
– What if the density decreases from inlet to outlet?
Flow Rate
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A flowmeter is a device mounted in a process line that provides a continuous reading of the flow rate in that line.
Flow Rate Measurement
Rotameter: floating ball in a conical cylinder. Use friction to lift the ball. The friction (and the height of the ball) is proportional to the velocity.Orifice meter: obstruction in the pipe creates a pressure drop. The pressure drop is proportional to the velocity.
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Atomic weight ‐‐ weight of an atom of an element on a scale by which 12C has a mass of exactly 12.
Molecular weight (MW) ‐‐ sum of the atomic weights of the atoms that constitute a molecule of the compound.
MW is a conversion factor between mass and moles for a particular compound.
Gram‐mole ‐‐ the amount of that species whose mass in grams is numerically equal to its molecular weight.
Chemical Compositions
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Consider 8‐methyl‐N‐vanillyl‐trans‐6‐nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3
Conversion: Mass/Moles
Calculate the molecular weight of capsaisin
18 x 12.0107 + 27 x 1.00794 + 3 x 15.9994 + 1 x 14.0067= 216.193 + 27.2144 + 47.9982 + 14.0067 = 305.412 g/gmole C18H27NO3
C H O N
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Calculate the number of moles of capsaicin in 100 g of the substance:
Calculate the number of lb∙moles of capsaicin in 100 g of the substance:
Calculate the number of moles each element in 100 g of the substance:
Conversion: Mass/Moles
100 g C18H27NO3 x = 0.327426 gmole C18H27NO3
gmole C18H27NO3
305.412 g C18H27NO3
100 g C18H27NO3 x x = 7.218 x 10‐4
lbmole C18H27NO3
gmole C18H27NO3
305.412 g C18H27NO3
lb mole
453.6 gmole
0.327426 x 18 = 5.89367 gmole C0.327426 x 27 = 8.84051 gmole H
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Conversion: Mass/Moles
Calculate the number of grams of C in 100 g of the substance:
Calculate the number of molecules of capsaicin in 100 g of the substance:
100 g C18H27NO3 x x x
= 70.7871 g C
gmole C18H27NO3
305.412 g C18H27NO3
18 gmole C
1 gmole C18H27NO3
12.0107 g C
1 gmole C
100 g C18H27NO3 x x
= 1.97 x 1023 molecules C18H27NO3
gmole C18H27NO3
305.412 g
6.02 x 1023 molecules
1 gmole C18H27NO3
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mass fraction, xA
mole fraction, yA
Mass and Mole Fractions
XA = mass of A
total mass
yA = moles of A
total moles
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Conversion: Mass/Molar compositionA gas mixture of the mass composition:
16% O2, 4.0% CO, 17% CO2, 63% N2
The molar composition of the gas can be found assuming a 100 g basis for calculation as:
i Xi mi = Xi/mtotal Mi(g/mol)
ni = mi/Mi yi = ni/ntotal
O2 0.16 16 32 0.500 0.150
CO 0.04 4 28 0.143 0.044
CO2 0.17 17 44 0.386 0.120
N2 0.63 63 28 2.250 0.690
Total 1.00 100 3.279 1.000
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Average Molecular Weight of Mixture
i Xi yi Mi(g/mol)
xi/Mi yi Mi
O2 0.16 0.150 32 0.0050 4.8
CO 0.04 0.040 28 0.0014 1.12
CO2 0.17 0.120 44 0.0039 5.28
N2 0.63 0.690 28 0.0225 19.32
Total 1.00 1.000 0.0328 30.5
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Concentration
Mass concentration: mass of the component per unit volumeof the mixture.
Molar concentration: the number of moles of the componentper unit volume of mixture.
The molarity of a solution is the value of the molarconcentration of solute expressed in gram‐moles solute perliter of solution.
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Concentration can be used as a conversion factor between– mass/moles of component in a sample and the volume of that sample
mass/mole flow rate of a component of a continuous stream to the total volumetric flow rate of the stream
Concentration
–
5 L x = 0.1 mol NaOH0.02 mol NaOH
L
5 L mol NaOH0.02 mol NaOHLmin
xmin= 0.1
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• Parts per million (ppm), billion (ppb), trillion (ppt) are units used to express concentrations of trace species (present in minute amounts) in mixtures of gases and liquids.
• Units may refer to mass or molar ratios.
Concentration
ppmi = yi x 106
ppbi = yi x 109
ppti = yi x 1012
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Pressure: the ratio of a force to the area over which the force acts.
• SI pressure unit: pascal (Pa), which has units of N/m2.
Pressure
• Fluid pressure– Consider a fluid contained in a closed vessel or flowingthrough a pipe, and suppose a hole of area A is made in thewall of the containing vessel.
– The fluid pressure may be defined as the ratio of F/A, where F is theminimum force that would haveto be exerted on the frictionlessplug hole to contain the fluid.
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– Considering a fluid contained in a vertical column, the hydrostatic pressure is basedon the total force acting on thebottom of the container, and maybe considered as the sum of theatmospheric pressure (P0) acting onthe top of column of liquid and theweight of the column.
– Height h of a column is proportionalto the pressure, thus pressures may be expressed as an equivalent length, referred to as a head of liquid.
Pressure
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Calculate the pressure at the bottom of a 12’ deep swimming pool in which the water temperature is a uniform 82°F. The atmospheric pressure at the pool barometer reading 29.75” Hg. ρwater(82°F) = 62.198 lbm/ft3 and ρHg = 13.55 g/cm3
Calculating pressure from head
P = P0 + gh = g (HghHg + H2OhH2O)
= (32.174 ft/s2)( )[(13.55 g/cm3)( ) x
( )(29.75 in) ( ) + (62.198 lbm/ft3)(12 ft)] ( )
1 lbf32.174 lbm ft/s2
30.483 cm3
1 ft3
1 lbm453.6 g
1 ft12 in
1 ft2144 in2
1 ft2144 in2= (2097 + 746.4) (lbf/ft2)( ) = 19.74 lbf/in2
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Absolute = Atmospheric + Gauge
Absolute pressure (psia): the sum of the atmospheric contribution as well as that due to the fluid acting on a particular area.
• Gauge pressure (psig) is that contribution from the fluid, and does not include atmospheric pressure.
• Consequently, a pressure of 0 psig indicates only atmospheric pressure is acting on the gauge.
Pabsolute = Patmospheric + Pgauge
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Pressure measurement
• Elastic‐element methods– A Bourdon tube is C‐shaped and has an oval cross‐sectionwith one end of the tube connected to the process pressure.The other end issealed and connected to thepointer or transmittermechanism.
– As pressure in the systemincrease, the tube tends tostraighten, causing adeflection of the pointer.
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Pressure measurement• Liquid column pressure measurement methods– Liquid column gauges consist of a vertical column of liquid in a tube whose ends are exposed to different pressures.
– The liquid column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube.
• A manometer is a Ushapedtube partially filled with a fluid ofknown density (the manometer fluid).
• Pressure at (a) and (b)is the same.
P1 + 1gd1 = P2 + 2gd2 + fgh
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Manometer variations
P1 + 1gd1 = P2 + 2gd2 + fgh
P1 – P2 = (f ‐)gh
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Manometer Calculation
• A differential manometer is used to measure the drop in pressure between two points in a process line containing water.
Example: The specific gravity of the manometer fluid is1.05. The measured levels in each are shown in the Figure below. Calculate the pressure drop between points 1 and 2 in dynes/cm2.
P1 – P2 = (f ‐)gh= (1.05 g/cm3 – 1.00 g/cm3) x[(980.7 cm/s2) x 1 dyne/(1 g cm/s2)] x [(382 – 374) (1 cm/10 mm)]= 39.2 dynes/cm2
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• Temperature of a substance in a particular state (solid,liquid, gas) is a measure of the average kinetic energypossessed by the substance molecules.
• The energy cannot be directly measured, and thereforemust be inferred through indirect means of a physicalproperty of the substance– resistance thermometer (electrical resistance)– thermocouple (voltage at junction of 2 dissimilar metals)– pyrometer (spectra of emitted radiation)– thermometer (density change of a fluid)
Temperature
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• Temperatures can be expressed directly in terms of themeasured physical properties (i.e., ohms/cm3).
• Defined temperature scales:– Celsuis or Fahrenheit scales most common ‐‐ the scale isarbitrarily assigned two values based on the freezing (0°C or 32°F) and boiling (100°C or 212°F) points of water at 1 atmpressure.
– Absolute zero (lowest theoretical temperature attainable innature) is ‐273.15°C or ‐459.67°F.
– Kelvin and Rankine are scales equivalent to Celsius andFahrenheit, respectively, but have a value of 0 assigned toabsolute zero.
Temperature Scales
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• Derived from T(°B) = aT(°A) + b, where temperaturesrepresent arbitrarily assigned values of the scale.
• Note the interval size oftemperature on theFahrenheit (or Rankine)scale is 1.8 times the sizeof an interval on theCelsius (or Kelvin) scale.
Converting Temperature Scales
T (K) = T (oC) + 273.15
T (oR) = T (oF) + 459.67
T(oR) = 1.8 T(K)
T(oF) = 1.8 T(oC) + 32
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Measurement of temperature
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Temperature Conversion• Temperature may appear in derived units, such as the heatcapacity, Cp (BTU/lbm⋅°F), which is a function oftemperature. Consider Cp for ammonia:
• Use a dimensional analysis approach to convert:
Cp ( ) = 0.487 + 2.29 x 10‐4 T (°F)= 0.487 + 2.29 x 10‐4 (1.8 T(°C) + 32)= 0.494 + 4.12 x 10‐4 T (oC)
Btulbm oF
Cp ( ) = ( ) ( ) ( ) ( )J
g oCBtulbm oF
1.8 °F1.0 °C
1 J9.486 x 10‐4 Btu
1 lbm454 g
Jg oC
Cp ( ) = 2.06 + 1.72 x 10‐3 T (oC)
x [ 0.494 + 4.12 x 10‐4 T (oC)]
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Conversion factors refer to temperature intervals, NOT temperature!
Examples:To find number of celsium degree between 32 F and 212 F,
T (C) = (212‐32)/1.8 = 100 C
However, to find out the temperature corresponding to 32 FYou should use:
T (F ) = 1.8 T(C ) + 32
You can not use T(C) = 32 F
1.8 F1 C
A temperature A temperature interval