Chemical Process Calculation I Material balances; Gas, vapors and liquids; Energy balances; Humidity charts 1. Introduction to engineering calculation Dimension: - Measurable extent or quantity (such as amplitude, brightness, hue, frequency, length, width, height, time, mass, volume, weight) - a measure of a physical variable Unit: - A standard amount of a physical quantity (the second is a unit of time) - A quantity chosen as a standard in terms of which other quantities may be expressed Primary (or base) unit systems: (1) SI (The International system of units or Systeme International d’Unites) Length:

meter (m)

Mass: kilogram (kg) Amount of matter: gram-mole (mol) Time: second (s) Temperature: kelvin (K) (2) CGS (The centimeter-gram-second system of units) Length:

centimeter (cm)

Mass: gram (g) Time: second (s) (3) English (or British) units (British engineering system of units) Length:

foot (ft)

Mass: pound-mass (lbm) Moles: pound-mole (lb mol) Time: second (s) Temperature: Rankine (oR)

Secondary (or derived) unit systems: quantity volume acceleration force pressure energy, work

SI unit liter (l or L) m s-2 newton (N) pascal (Pa) joule (J)

power

gram-calori (cal) watt (W)

•

CGS unit cc cm s-2 dyne erg

English unit ft3 ft s-2 pound-force (lbf) psi (lbf in-2) foot-pound (ft-lbf)

erg s-1

ft-lbf/s

Note that there are many other units. For example, power is often expressed in horsepower, Hp and energy is expressed in BTU.

Unit conversion factors: Perry’s Chemical Engineers’ Handbook •

gravitational conversion constant, gc o A constant to convert a force in the fundamental unit in Newton’s law into either a force in SI unit, N or a force in English unit, lbf. F o

ma gୡ

For SI unit,

and for English unit,

Weight: force exerted on an object by gravitational attraction Does the weight of an object vary with altitude and latitude? Does the mass of an object vary with altitude and latitude?

What is the weight of a football, 400 g in mass, at the top of Mt. Everest and at the sea level, respectively, in SI unit? Pressure: force applied perpendicular to the surface of an object per unit area

Pa, mm Hg, atm, psi, torr, bar Construct a table showing conversion factors between pressure units. Absolute pressure vs. gauge pressure Gauge pressure = absolute pressure – atmospheric pressure Dynamic pressure and static pressure: terms used for fluids. Static pressure: pressure on a body moving with the fluid ଵ

Dynamic pressure: kinetic energy per unit volume of a moving fluid (ଶ ρv ଶ ) ρ: fluid density (kg m-3) v: fluid velocity ( m s-1) Total pressure = static pressure + dynamic pressure (p଴  p

ଵ ଶ

ρv ଶ )

Bernoulli’s equation: p vଶ

z  constant ρg 2g ୮

: pressure head, m

஡୥ ୴
ଶ୥

: velocity head, m

z: elevation head, m Mechanical-energy equation for fluids: p vଶ

z h୤  constant ρg 2g h୤ : friction head Dimensional Homogeneity Quantities that are added or subtracted must have the same dimensions and units. Significant figures Digits that have meaning in measurement.

The significant figure of a number indicates the precision of the number or how precise the number is. Let’s compare a weight between 60 kg, 60. Kg, and 60.0 kg. The number of significant figure for 60 kg is one, and the real weight lies somewhere between 55 kg and 65 kg. The number of significant figure for 60. Kg is two, and the real weight lies between 59.5 kg and 60.5 kg. The number of significant values for 60.0 kg is three, and the real weight lies between 59.95 kg and 60.05 kg. Rules of thumb on significant figures: - Non-zero digits are significant. - Any zeros between two significant digits are significant - without decimal point, any trailing zeros are non-significant. - with decimal point, any trailing zeros are significant. For a number smaller than 1, the first zero to the left of the decimal point and any zeros between decimal point and the first nonzero digit that follows are non-significant. The significant figure applies to measured quantities, but not to integers. For an integer, we can say that the number of significant figures is infinite or that the given number is exact as it is. When we count students, the number of students is an integer. 10 students means that the number is exact at 10. A number can be expressed in exponential notation: 60.5 as 6.05 x 101; 0.0234 as 2.34 x 10-2. Express 1000 in exponential notation. 1 x 103 Express 1000. in exponential notation. 1.000 x 103 When you perform multiplication or division of quantities, the final result must be rounded off to have its number of significant figures equal the lowest number of significant figures among the quantities involved in the calculation. 1.25 x 3.1 = 3.875
3.9 1.25 x 3.1/4.25 = 0.91176
0.91 1.25 x 102/(4.25 x 10-2) x 3.1 x 103 = 0.91176 x 10(2-2+3)
0.91 x 103 = 9.1 x 102

When you perform addition or subtraction of quantities, the final result must be rounded off to have the decimal place of its last significant digit equal the decimal place of the last significant digit of the quantity lowest in precision. 1.25 + 3.1 – 4.20 = 0.15
0.2 1.25 x 103 + 3.1 x 105 – 4.20 x 104 = (0.0125 + 3.1 + 0.42) x 105 = 3.5325 x 105
3.5 x 105 When you perform logarithmic conversion of a quantity, the result must be rounded off to have the number of significant figures to the right of the decimal point equal the number of significant figures before conversion. 75 Log (75) = 1.87506
1.88 100. Log (100.) =2.000 pH = -Log[H+], where [H+] represents the molar concentration of hydrogen ion. A pH of 4.53 has two significant numbers because 4 before the decimal point indicates the exponent of the [H+] o

Most electronic instruments are good to only three significant digits. When in doubt, for most engineering analyses, three digits are usually the maximum that can be expected.

2. Measurements of Properties and Process Variables temperature, density, volume, flow rate, pressure, liquid level, concentration 2.1 Temperature Temperature is a quantitative indication of how hot or cold something is. Temperature scales: Kelvin (K), Degree Celcius (or Centigrade) (oC), Degree Fahrenheit (oF), and degree Rankine (oR) K is the SI unit. K = oC + 273.15 o F = 5/9 x oC + 32 o R = oF + 459.67 Absolute temperature: temperature in K or temperature in oR Absolute zero is the lowest temperature attainable in nature. Temperature Measuring Devices:

Glass Thermometer The principle of measuring temperature with a glass thermometer lies in the thermal expansion of the fluid that is filled in the tubular device. Mercury and alcohol are commonly used. The level of the fluid in the tube rises with increasing temperature. The tube is scaled such that it reads 0oC (or 32oF) at the freezing point of water and 100oC (or 212oF) at the boiling point of water at 1 atm. The operating range of the mercury thermometer is approximately from -38oC to 400oC and that of the alcohol thermometer is from -80oC to 100oC. Alcohol is less toxic than mercury. Thermocouple A thermocouple is a temperature measuring device based on the Seebeck effect that an electromotive force is created when there is a temperature gradient in a conductive material. When two different conductive wires are joined at an end and there exist a temperature difference between the two ends, a voltage is generated across the other end, the magnitude of which depends on the types of wire and is proportional to the temperature difference. There are various types of thermocouples dependent upon combination of conductive materials: K type with a combination of Chromel and Alumel, S type with platinum and platinum 13% in rhodium, and so on. Chromel: Alumel: The K type is the most common type and is applicable in the temperature range of -200oC to 1250oC. The temperature range can be shifted to 0oC to 1450oC with the S type, which is more expensive than the K type. A thermocouple is enclosed in a protective sheath to increase the life-time at the expense of the response time. Stainless steel (316SS) is the most common sheath material. Inconel 600 is recommended for highly corrosive environments. A thermocouple is used without a sheath where quick response matters. A thermocouple is called “grounded” when the thermocouple wires and the sheath are all welded together to form one junction at the tip of the probe. Grounded thermocouples are faster in response time, but less accurate than ungrounded thermocouples. RTD (resistance temperature detector) RTDs are based on the fact that the electrical resistance of a material varies with increasing temperature. The main materials in use are platinum, nickel and copper. In general, RTDs are more stable and accurate than thermocouples, but more expensive, slower in response time, and lower in maximum allowable temperature (750oC). Bimetallic thermometer

Two metal strips differing in thermal expansion coefficient are joined together to a coil with one end fixed and the other end set free to move. A pointer is affixed to the moving end to indicate the temperature. Dial-type bimetallic thermocouples are frequently seen in chemical plants. Pyrometer: You can feel a fire some distance away because it gives off heat radiation in all directions. A pyrometer measures the intensity of the radiation at a distance and compares measured intensity with that of an internal heat source whose temperature is precisely known. 2.2 density The density of a substance (ρ) is defined as the mass divided by the volume. The density can be obtained from published sources, (when no data are available) by estimation, or by measurement. Published sources: Perry’s Chemical Engineers’ Handbook, Handbook of Chemistry and Physics, Journal of Physical and Chemical Reference Data, Chemical Abstract Estimation: The properties of Gases and Liquids by Reid et al. For a gaseous substance, a gas law represented by Z=PV/(nRT) holds, where Z is the compressibility factor, P is the pressure, V is the volume, n is the number of moles, and T is the temperature. The density is calculated from the gas law as follows: ρ = MP/(ZRT), where M is the molecular weight of the substance. Various empirical equations are available to estimate liquid densities in the book by Reid et al. Measurement method: Hydrometer:

(known density)(unknown density)

The gravitational force exerted by the float should be equal to the buoyancy force by the liquid in which the float is dipped. The gravitation force is mg, where m is the mass of the float and g is the gravitational acceleration. The buoyancy force of the liquid of known density (ρ1) is ρ1V1g and the buoyancy force of the liquid of unknown density (ρ2) is ρ2V2g, where V1 and V2 are the volumes of the float in the liquid, respectively. mg = ρ1V1g = ρ2V2g ρ2 = ρ1V1/V2 = ρ1V1/(V1 + A∆x) =ρ1/(1+ A∆x/V1) = ρ1/(1 + A∆xρ1/m), where A is the cross sectional area of the shaft of the float.

Pycnometer: A pycnometer is a container (usually glass flask) used for determining the density of a liquid or a powder, having a specific volume and often provided with a thermometer to indicate the temperature of the contained substance.

The volume of the pycnometer is determined by filling it with distilled water and measuring the mass of the water and converting the mass into the volume by using the density of the water. To measure the density of a liquid, the pycnometer is filled with the liquid and the mass of the liquid is determined by subtracting the mass of the pycnometer from the mass of the pycnometer and liquid. The mass of the liquid is divided by the volume of the pycnomter to give the density of the liquid. The pycnometer can be used to determine the density of a powder as well. A predetermined mass of the powder is put in the pycnometer. The pycnometer is then filled with a reference liquid of known density. The mass of the reference water is determined by subtracting the mass of the pycnometer and powder from the mass of the pycnometer, powder and reference liquid. The volume of the reference liquid is determined from the mass by using the density of the reference liquid. The volume occupied by the powder is determined by subtracting the volume of the reference liquid from the volume of the pycnometer. The density of

the powder is finally obtained by dividing the mass of the power by the volume of the powder. m  m  ρm m m  m     ρ ρ

ρ: powder density ρw: density of liquid m0: mass of pycnometer mw: mass of pycnometer and liquid ms: mass of pycnometer and powder msL: mass of pycnometer, powder and liquid

A reference gas is used instead of the reference liquid. Initially two compartments are separated by a valve. One compartment is filled with a pressurized reference gas (helium). The powder is put in the other compartment, which is then evacuated. By opening the valve the pressure is equalized between the two compartments. The volume occupied by the powder is determined from the equalized pressure and the volumes of the compartments as follows:

V  V  V 

P V P

V1: volume of compartment 1 V2: volume of compartment 2 which the powder is put in P: equalized pressure P1: initial pressure in compartment 1 The density of the powder is obtained by dividing the mass of the powder by the volume thus determined. This method of using gas as reference gives a density closer to the true density than the method with liquid as reference. 2.3 volume: Pour the liquid to be measured for its volume into a beaker, a flask, a graduated cylinder or a burette. Beakers and flasks are used only for rough measurement. Even graduated cylinders and burettes need to be calibrated for accurate measurement. How to calibrate a 100 mL mess cylinder? Put distilled water in the mess cylinder to a marked level. Transfer the water to a dry beaker and measure the mass of the water that was transferred to the beaker from the mess cylinder. By using the density of distilled water at the temperature of the water, the accurate volume is obtained and compared with the volume read from the mess cylinder. The volume of a liquid can be determined indirectly by measuring the mass and

converting the mass into a volume using the density of the liquid.

2.4 flow rate, volume per unit time Rotameter:

The rotameter is composed of a float and a tapered tube. The float stays in a position where the downward force of the float by gravity equals the upward force of the flowing fluid. Orifice flow meter:

The pressure drop across the orifice plate is related to the flow rate of the fluid. The pressure drop increase with increasing the flow rate. Venturi flow meter:

The venture meter works in a way similar to that of the orifice meter. It is often used where it is necessary with higher turndown ratio (max. flow rate/min. flow rate), or lower pressure drops, than the orifice plate can provide.

Turbine flow meter:

The speed of rotation of the turbine is proportional to the flow rate. Vortex flow meter:

http://www.globalspec.com/learnmore/sensors_transducers_detectors/flow_sensing/vortex_fl ow_meters In the vortex shedding flow meter, the flow path is obstructed by a bluff body (or strut) that creates the vortex swirl. The rate of vortex shedding is detected by a sensor that monitors the changes in the vortex pattern, transmitting a pulsating output signal to external readouts or data acquisition equipment. The frequency of this alternating shedding process is proportional to the velocity of the flowing stream as it passes the point of contact. The linear velocity should be high enough to create a vortex for the vortex meter to work. Electromagnetic flow meter (mag meter in short):

A magnetic field is applied to the metering tube, which results in a potential difference between the two electrodes on the sidewall of the tube. The potential difference is proportional to the volumetric flow rate. The electromagnetic flow meter measures measure the velocity of conductive liquids (conductivity >5µS/cm) in pipes, such as water, acids, caustic, and slurries. Ultrasonic flow meter:

A pair of transducers are installed on the outer surface of the pipe. pipe The propagation time of a ultrasonic sound is shorter when the sound is transmitted toward upstream than when it is transmitted toward downstream. The difference in time between the two transmissions in the opposite direction is proportional to the flow rate. ositive displacement flow meter: Positive A fixed volume of fluid is displaced by a rotating rotating or reciprocating mechanism. For example, 1 L is displaced per minute by a rotating gear: this corresponds to a flow rate of 1 L/min. The principle of the meter is analogous to holding a bucket below a tap, filling it to a set level, then quickly replacing it with another bucket and timing the rate at which the buckets are filled. filled

(gear type: a fixed volume of the fluid is passed through then meter by a rotation of the gear. Counting the revolutions totalizes the volume of the fluid.) Positive displacement flow meters are accurate and have high turndown.They .They are widely used in the custody transfer of oils and liquid fluids (gasoline) and are applied on residential home

natural gas and water metering. However, a positive displacement meter can be considerably heavier and more costly than other types such as orifice plates, magnetic or vortex flow meters.

Mass flow meter: The mass flow meter does not measure the volume, but the mass. For a fluid of constant density it is simple to convert the volume into mass. When the density changes from time to time or the fluid entrains bubbles the conversion is difficult to favor the use se of a mass flow meter. There are two types of mass flow meter: one is based on the Coriolis force created by a vibrating tube through which a fluid is flowing and the other is based on the convection of heat from a heated surface to the flowing fluid. Coriolis flow meter: https://www.youtube.com/watch?v=PvXgaDoZr1E Coriolis meters operate on the principle that a rotating motion due to the inertial force (Coriolis force) is created by vibrating a tube or tubes carrying the flow. flow By measuring the amount of inertial force or deflection, it is possible to infer the mass flow rate.

Thermal mass flow meter:

The principle of the mass flow measurement is based on two temperature sensors in close contact with the fluid. One of the two sensors is constantly heated and the cooling effect of the flowing fluid is used to monitor the flow rate. When the fluid flow increases, heat energy is drawn from the heated sensor and the temperature difference between een the sensors are reduced. The reduction is proportional to the mass flow rate of the fluid. Thermal hermal mass flow meters are used almost exclusively for gas

flow measurements and are not nearly as accurate as coriolis flow meters. 2.5 Pressure Liquid-column method: manometer A U-shaped tube is filled to the half of the length with a liquid, i.e. water and mercury. One end of the tube is connected to the region of interest and the other end is connected to a reference pressure (vacuum, atmospheric, or system). The difference in the liquid level is converted into a pressure using ∆P  ρgh, where ρ is the density of the liquid, g is the gravitational acceleration, and h is the difference in liquid level. Elastic-element method: Bourdon tube, bellow, diaphragm The elastic elements change in shape in response to the pressure of the region in question.

(Bourdon tube)

(Bellow)

(Diaphragm)

Electrical method: strain gauge The cross sectional area of a conductive wire or foil decreases with increasing applied pressure to increase the electrical resistance (Piezoresistive effect).

(strain gauge pressure element)

(wire)

2.6 Liquid level Sight glass: simple device to measure liquid level The transparency deteriorates and the seal is prone to leak.

(foil)

Float-actuated devices: The float rises and falls with the liquid level. The level is indicated on the gauge board or by a dial gauge, in response to the displacement of the float.

Hydrostatic devices: displacer, bubbler, and differential pressure transmitter Displacer: The weight of a rod immersed in a liquid varies with the liquid level due to the buoyant force based on Archimedes principle. The instantaneous weight of the rod is converted through a torque tube into a liquid level in the displacer level meter.

Bubbler: A bubble level meter operates by forcing compressed air into a bubbler tube submerged in the liquid being measured. The pressure required to force the air through the tube is measured and converted into the level of the

liquid.

Differential pressure transmitter: The differential pressure transmitter method of liquid level measurement operates by measuring the pressure at the bottom of the container of the liquid being measured. The differential pressure (∆P) between at the bottom and at the top is converted into the liquid level using ∆P = ρgh.

Time of flight devices: Ultrasonic, microwave Ultrasonic level meters operate on the basic principle of using ultrasonic sound waves to determine liquid level. The time elapsed between firing the sound and receiving the return echo is proportional to the distance between the wave emitter and the surface of the liquid.

The ultrasonic signal is strongly affected by temperature and weakly by pressure. The microwave signal is not affected by temperature and pressure. Microwave meters are generally more accurate, but expensive than ultrasonic meters.

2.7 Concentration Expression of concentration: (1) mol/L : molar concentration or molarity (number of moles per L of solution) normality (N): (2) mol/kg: molal concentration or molality (number of moles per kg of solvent) (3) wt %: percentile weight fraction (4) vol %: percentile volume fraction (5) ppm: part per million (mg/kg or mg/L) (6) ppb: part per billion (10-3 mg/kg or 10-3 mg/L) (7) ppt: part per trillion (10-6 mg/kg or 10-6 mg/L) How to measure concentration? (1) Gravimetric method: The analyte is converted from a soluble to an insoluble form or a precipitate, then weighing the precipitate. For example, Ag+ in a solution is converted into AgCl (insoluble) by adding

Cl- to the solution. Actually a salt containing Cl is added, because Cl- is not available. Another example is that a metal ion in a solution is converted into the metal electrochemically by adding a reducing agent or by applying electricity. Then mass of the metal is then measured. (2) Acid-base titration: An acid of unknown concentration is titrated with a base of known concentration or vice versa. N1V1 = N2V2 (3) Reduction-Oxidation (Redox) titration: 1 Ampere = 1 coulomb (C) per second Electrical energy (joule) = voltage x coulomb (V x C) Watt (w) = J/s = A x V The electrochemical potential of an analyte solution is measured with adding a titrant.

Titration of 0.05 F Fe2+ with 0.1 F Ce4+ Fe2+ + Ce4+ = Fe3+ + Ce3+ The equivalence point can be determined using an indicator without measuring the potential.

(4) Spectrochemical method An analyte in a solution absorbs a light of specific wavelength. The absorbance is proportional to the concentration of the analyte.

UV-visible visible spectrophotometry: spectrophotometry An analyte aborsbs a light of specific wavelength and the absorbance is proportional to the concentration. Infrared spectrophotometry: spectrophotometry A component produces unique spectra of light absorption when it is irradiated by a infrared light. light Atomic absorption spectrophometry (AAS): A sample solution is atomized by a flame, through which a light is passed. passed. The absorption of the light by an analyte (atom) is measured and interpreted to determine the concentration. concentration Inductively Coupled Plasma-Atomic Plasma Atomic Emission Spectroscopy (ICP-AES): (ICP The analyte in a sample is dissociated to form free atoms by inductively coupled plasma. The emission spectra of the excited atom are measured, measured when it drops back to the electronic ground state, state to determine the concentration. concentration Inductively Coupled Plasma-Mass Plasma Spectroscopy (ICP-MS): Inductively couple plasma is used to convert the analyte in a sample into ions. These ions are separated according to their mass-to-charge mass charge ratios. An analyte (atom) has its unique mass spectra. The concentration is determined by comparing the height of the base peak of the spectra with that of a standard concentration. concentration X-ray ray fluorescence (XRF): (XRF) It is based on the emission of characteristic "secondary" (or fluorescent) X-rays from a material that has been excited by bombarding with high-energy high X-rays. (5) Chromatography Gas Chromatography and Liquid chromatography are used to separate the components of a mixture and measure the concentration of each molecular component.