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CHEMICAL ENGINEERING

For additional information concerning transfer and Ethers fluid mechanics, refer to the HEAT TRANSFER, THER- Ethers are generally designated by naming the alkyl groups MODYNAMICS, MECHANICAL ENGINEERING or and adding the word ether. The group RO is known as an FLUID MECHANICS sections. alkoxyl group. Ethers may also be named as alkoxy For additional information concerning chemical process derivatives of hydrocarbons. control, refer to the COMPUTERS, MEASUREMENT, Carboxylic AND CONTROLS section. The name of each linear carboxylic is unique to the For additonal information concerning statistical data number of carbon atoms it contains. 1: (one carbon atom) analysis, refer to the following. Formic. 2: Acetic. 3: Propionic. 4: Butyric. 5: Valeric. 6: Confidence Intervals Caproic. 7: Enanthic. 8: Caprylic. 9: Pelargonic. 10: Capric. See the subsection in the ENGINEERING PROBABILITY Aldehydes AND STATISTICS section of this handbook. The common names of aldehydes are derived from the acids Statistical Quality Control which would be formed on oxidation, that is, the acids See the subsection in the INDUSTRIAL ENGINEERING having the same number of carbon atoms. In general the ic section of this handbook. acid is dropped and aldehyde added. Linear Regression Ketones See the subsection in the ENGINEERING PROBABILITY The common names of ketones are derived from the AND STATISTICS section of this handbook. acid which on pryrolysis would yield the ketone. A second One-Way Analysis of Variance (ANOVA) method, especially useful for naming mixed ketones, See the subsection in the INDUSTRIAL ENGINEERING simply names the alkyl groups and adds the word ketone. section of this handbook. The name is written as three separate words. SELECTED RULES OF NOMENCLATURE IN ORGANIC Alcohols Three systems of nomenclature are in general use. In the first the alkyl group attached to the hydroxyl group is named and the separate word alcohol is added. In the second system the higher alcohols are considered as derivatives of the first member of the series, which is called carbinol. The third method is the modified Geneva system in which (1) the longest carbon chain containing the hydroxyl group determines the surname, (2) the ending e of the corresponding saturated hydrocarbon is replaced by ol, (3) the carbon chain is numbered from the end that gives the hydroxyl group the smaller number, and (4) the side chains are named and their positions indicated by the proper number. Alcohols in general are divided into three classes. In primary alcohols the hydroxyl group is united to a primary carbon atom, that is, a carbon atom united directly to only one other carbon atom. Secondary alcohols have the hydroxyl group united to a secondary carbon atom, that is, one united to two other carbon atoms. Tertiary alcohols have the hydroxyl group united to a tertiary carbon atom, that is, one united to three other carbon atoms.

101 CHEMICAL ENGINEERING (continued)

Common Names and Molecular Formulas of Some Industrial (Inorganic and Organic) Chemicals

Molecular Common Name Chemical Name Formula Muriatic acid Hydrochloric acid HCl Cumene Isopropyl benzene C6H5CH(CH3)2 Styrene Vinyl benzene C6H5CH = CH2 — Hypochlorite ion OCl–1 –1 — Chlorite ion ClO2 –1 — Chlorate ion ClO3 –1 — Perchlorate ion ClO4 Gypsum Calcium sulfate CaSO4 Limestone Calcium CaCO3 Dolomite Magnesium carbonate MgCO3 Bauxite Aluminum oxide Al2O3 Anatase Titanium dioxide TiO2 Rutile Titanium dioxide TiO2 — Vinyl chloride CH2=CHCl — Ethylene oxide C2H4O Pyrite Ferrous sulfide FeS Epsom salt Magnesium sulfate MgSO4 Hydroquinone p-Dihydroxy benzene C6H4(OH)2 Soda ash Sodium carbonate Na2CO3 Salt Sodium chloride NaCl Potash Potassium carbonate K2CO3 Baking soda Sodium NaHCO3 Lye Sodium NaOH Caustic soda Sodium hydroxide NaOH — Vinyl alcohol CH2=CHOH Carbolic acid Phenol C6H5OH Aniline Aminobenzene C6H5NH2 — (NH2)2CO Toluene Methyl benzene C6H5CH3 Xylene Dimethyl benzene C6H4(CH3)2 — Silane SiH4 — Ozone O3 Neopentane 2,2-Dimethylpropane CH3C(CH3)2CH3 Magnetite Ferrous/ferric oxide Fe3O4 Quicksilver Mercury Hg 2 Heavy Deuterium oxide (H )2O — Borane BH3 Eyewash Boric acid () H3BO3 2 — Deuterium H — Tritium H3 Laughing gas Nitrous oxide N2O — Phosgene COCl2 Wolfram Tungsten W –1 — Permanganate ion MnO4 –2 — Dichromate ion Cr2O7 +1 — ion H3O Brine Sodium chloride NaCl (solution) Battery acid H2SO4

102 CHEMICAL ENGINEERING (continued) Often at system close to atmospheric: L sat Vapor-Liquid Equilibrium fi ≅ Pi ˆ For a multi-component mixture at equilibrium The coefficient Φi for component i in the vapor is ˆf V = ˆf L , where calculated from an equation of state (e.g., Virial). i i Sometimes it is approximated by a pure component value ˆ V fi = fugacity of component i in the vapor phase, and from a correlation. Often at pressures close to atmospheric, Φˆ = 1. The fugacity coefficient is a correction for vapor ˆ L i fi = fugacity of component i in the liquid phase. phase non-ideality. of component i in a mixture are commonly For sparingly soluble gases the liquid phase is sometimes calculated in the following ways: represented as For a liquid ˆf L = x γ f L , where ˆ L i i i i fi =xiki xi = fraction of component i, where ki is a constant set by experiment (Henry’s constant).

γi = of component i, and Sometimes other units are used besides mole L fraction with a corresponding change in ki. fi = fugacity of pure liquid component i. Reactive Systems ˆ V ˆ For a vapor f i = yi Φ i P , where Conversion: moles reacted/moles fed yi = of component i in the vapor, Extent: For each species in a reaction, the mole balance ˆ may be written: Φi = fugacity coefficient of component i in the vapor, and molesi,out = molesi,in + viξ where P = system . ξ is the extent in moles and vi is the stoichiometric The activity coefficient γi is a correction for liquid phase coefficient of the ith species, sign of which is non-ideality. Many models have been proposed for γi such negative for reactants and positive for products. as the Van Laar model: Limiting reactant: reactant that would be consumed first if −2 ⎛ A x ⎞ reaction proceeded to completion. Other reactants ⎜ 12 1 ⎟ lnγ1=A12 ⎜1+ ⎟ are excess reactants. ⎝ A21x2 ⎠ −2 , where Selectivity: moles of desired formed/moles of ⎛ A x ⎞ ⎜ 21 2 ⎟ undesired product formed. lnγ 2 =A21 ⎜1+ ⎟ ⎝ A12 x1 ⎠ Yield: moles of desired product formed/moles that would have been formed if there were no side reactions γ1 = activity coefficient of component 1 in a two- component system, and limiting reactant had reacted completely. Equilibrium γ2 = activity coefficient of component 2 in a two- component system, and For reaction A12, A21 = constants, typically fitted from experimental data. aA + bB⇋cC + dD o The pure component fugacity is calculated as: ∆G = –RT ln Ka L sat sat L sat cd fi = Φi Pi exp{vi (P – Pi )/(RT)}, where aaˆˆ ( CD)( ) νi sat K== aˆ , where aiab ∏() Φi = fugacity coefficient of pure saturated i, i (aaˆˆAB)( ) P sat = saturation pressure of pure i, i ˆ L fi vi = specific volume of pure liquid i, and âi = activity of component i = f o R = Ideal Gas Law Constant. i o fi = fugacity of pure i in its

νi = stoichiometric coefficient of component i ∆Go = standard Gibbs change of reaction

Ka = chemical

103 CHEMICAL ENGINEERING (continued)

For mixtures of ideal gases: In the conversion of A, the fractional conversion XA is o defined as the moles of A reacted per mole of A fed. fi = unit pressure, often 1 bar XA = (CAo – CA)/CAo if V is constant fˆ = y P = p i i i The gives the dependence of k on where pi = of component i.

c d c d −ERTa (pC )(pD ) c+d −a−b (yC )(yD ) kAe= , where Then K a = K p = a b = P a b ()()pA pB ()()y A yB A = pre-exponential or frequency factor,

For solids âi = 1 Ea = activition energy (J/mol, cal/mol),

For liquids âi = xi γi T = temperature (K), and The effect of temperature on the equilibrium constant is R = gas law constant = 8.314 J/(mol⋅K). d lnK ∆H o For values of rate constant (ki) at two (Ti), = dT RT 2 RTT⎛⎞ k E = 12ln 1 where ∆Ho = standard change of reaction. a ⎜⎟ ()TT12− ⎝⎠ k 2 OF REACTION Reaction Order For a chemical reaction the associated energy can be defined x y If – rA = kCA CB in terms of heats of formation of the individual species ∆Hˆ o ( f ) the reaction is x order with respect to reactant A and y order at the standard state with respect to reactant B. The overall order is ˆˆoo ˆ o ( ∆=HHrf) ∑∑ υ∆−ii( ) υ∆( H f) n = x + y productsii reactants BATCH REACTOR, CONSTANT T AND V The standard state is 25°C and 1 bar. Zero-Order Reaction The heat of formation is defined as the enthalpy change – r = kC o = k (1) associated with the formation of a compound from its A A atomic species as they normally occur in nature (i.e., O2(g), – dCA /dt = k or H2(g), C(solid), etc.) CA = CAo – kt

The heat of reaction for a process using oxygen dXA /dt = k/CAo or is also known as the heat of combustion. The principal CAo XA = kt products are CO and H O . 2g()2 () First-Order Reaction CHEMICAL REACTION ENGINEERING – rA = kCA

A chemical reaction may be expressed by the general – dCA/dt = kCA or equation ln (CA/CAo) = – kt aA + bB ↔ cC + dD. dXA/dt = k (1 – XA) or The rate of reaction of any component is defined as the ln (1 – XA) = – kt moles of that component formed per unit time per unit volume. Second-Order Reaction – r = kC 2 dN A A 1 A 2 − rA = − [negative because A disappears] – dC /dt = kC or V dt A A

1/CA – 1/CAo = kt − dC A − rA = if V is constant 2 dt dXA/dt = kCAo (1 – XA) or The rate of reaction is frequently expressed by XA/[CAo (1 – XA)] = kt

–rA = kfr (CA, CB,....), where k = constant and

CI = concentration of component I.

104 CHEMICAL ENGINEERING (continued) Batch Reactor, General MASS TRANSFER For a well-mixed, constant-volume, batch reactor – rA = – dCA/dt t = −C X A dX ()− r N p ⎛ N N ⎞ D ∂p Ao ∫o A A Gas: A = A ⎜ A + B ⎟ − m A A P A A RT ∂z If the volume of the reacting mass varies with the ⎝ ⎠ conversion (such as a variable-volume batch reactor) N A ⎛ N A N B ⎞ ∂xA according to Liquid: = xA ⎜ + ⎟ − CDm A ⎝ A A ⎠ ∂z V = VX (1+ εAXA ) A=0 in which (pB)lm is the log mean of pB2 and pB1, (ie., at constant pressure), where Unidirectional Diffusion of a Gas A Through a Second V −V Stagnant Gas B (Nb = 0) X A =1 X A =0 ε A = V N A Dm P ()pA2 − pA1 X A =0 = × A RT ()p z − z then at any time B lm 2 1 in which (pB)lm is the log mean of pB2 and pB1, ⎡⎤1− X A CCAAo= ⎢⎥ Ni = diffusive flow (mole/time) of component i through ⎣⎦1+εA X A area A, in z direction, and and Dm = mass diffusivity.

X A t = −CAo ∫o dX A []()()1+ ε A X A − rA EQUIMOLAR COUNTER-DIFFUSION (GASES) (N = – N ) For a first order irreversible reaction, B A NAD= RTp×−⎡⎤ p ∆ z ⎛⎞∆V Am( ) ⎣⎦() AA12( ) kt=−ln(1 − X A ) =− ln⎜⎟ 1 − ⎝⎠εAVXA= O NADCAmAA= ( 12−∆ C) z FLOW REACTORS, STEADY STATE CONVECTION Space-time τ is defined as the reactor volume divided by the inlet volumetric feed rate. Space-velocity SV is the Two-Film Theory (for Equimolar Counter-Diffusion) reciprocal of space-time, SV = 1/τ. NA /A = k'G (pAG – pAi) Plug-Flow Reactor (PFR) = k'L (CAi – CAL) C V = K'G (pAG – pA*) Ao PFR X A dX A τ = = CAo ∫o , where = K'L (CA* – CAL) FAo ()− rA where pA*is partial pressure in equilibrium with CAL, and FAo = moles of A fed per unit time. CA* = concentration in equilibrium with pAG. Continuous Stirred Tank Reactor (CSTR) Overall Coefficients For a constant volume, well-mixed, CSTR 1/K'G = 1/k'G + H/k'L τ V X = CSTR = A , where 1/K'L = 1/Hk'G + 1/k'L C F − r Ao Ao A Dimensionless Group Equation (Sherwood) – rA is evaluated at exit stream conditions. For the turbulent flow inside a tube the Sherwood number Continuous Stirred Tank Reactors in Series 0.8 13 ⎛⎞kDmm ⎛⎞ kD ⎛⎞DVρµ ⎛⎞ With a first-order reaction A → R, no change in volume. ⎜⎟is given by: ⎜⎟= 0.023⎜⎟ ⎜⎟ ⎝⎠DDmm ⎝⎠⎝µ⎠ ⎝⎠ ρ D m τ = Nτ N-reactors individual 1 N N ⎡⎛ C ⎞ ⎤ where, = ⎢⎜ Ao ⎟ −1⎥ , where k ⎢⎜ C ⎟ ⎥ D = inside diameter, ⎣⎝ AN ⎠ ⎦ Dm = diffusion coefficient, N = number of CSTRs (equal volume) in series, and V = average velocity in the tube,

CAN = concentration of A leaving the Nth CSTR. ρ = fluid density, and µ = fluid , km = mass transfer coefficient.

105 CHEMICAL ENGINEERING (continued) Distillation Continuous Distillation (binary system) Definitions: Constant molal overflow is assumed (trays counted α = , downward) B = molar bottoms-product rate, OVERALL MATERIAL BALANCES D = molar overhead-product rate, Total Material: F = molar feed rate, F = D + B L = molar liquid downflow rate, Component A: RD = ratio of reflux to overhead product, V = molar vapor upflow rate, FzF = DxD + BxB W = total moles in still pot, x = mole fraction of the more volatile component in the OPERATING LINES liquid phase, and Rectifying Section y = mole fraction of the more volatile component in the Total Material: vapor phase. Vn+1 = Ln + D Subscripts: Component A: B = bottoms product, Vn+1yn+1 = Lnxn + DxD D = overhead product, yn+1 = [Ln /(Ln + D)] xn + DxD /(Ln + D) F = feed, m = any plate in stripping section of column, Stripping Section Total Material: m+1 = plate below plate m, L = V + B n = any plate in rectifying section of column, m m+1 n+1 = plate below plate n, and Component A: o = original charge in still pot. Lmxm = Vm+1ym+1 + BxB

ym+1 = [Lm /(Lm – B)] xm – BxB /(Lm – B) Flash (or equilibrium) Distillation Reflux Ratio Component material balance: Ratio of reflux to overhead product R = L /D = (V – D)/D FzF = yV + xL D R R Overall material balance: Minimum reflux ratio is defined as that value which results in an infinite number of contact stages. For a binary system F = V + L the equation of the operating line is

Rmin xD Differential (Simple or Rayleigh) Distillation y = x + Rmin +1 Rmin +1

⎛ W ⎞ x dx ln⎜ ⎟ = ∫ Feed Condition Line ⎜ ⎟ xo ⎝Wo ⎠ y − x slope = q/(q – 1), where When the relative volatility α is constant, heat to convert one mol of feed to saturated vapor q = y = αx/[1 + (α – 1) x] molar heat of vaporization can be substituted to give Murphree Plate Efficiency * ⎛ W ⎞ 1 ⎡ x()1− x ⎤ ⎡1− x ⎤ EME = (yn – yn+1)/( y n – yn+1), where ln⎜ ⎟ = ln o + ln o ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ y = concentration of vapor above plate n, ⎝Wo ⎠ ()α −1 ⎣ xo ()1− x ⎦ ⎣ 1− x ⎦ For binary system following Raoult's Law yn+1 = concentration of vapor entering from plate below n, and α = (y/x)a /(y/x)b = pa /pb, where * y n = concentration of vapor in equilibrium with liquid pi = partial pressure of component i. leaving plate n. A similar expression can be written for the stripping section by replacing n with m.

106 CHEMICAL ENGINEERING (continued) COST ESTIMATION Cost Indexes

Cost Indexes as Annual Averages Chemical Marshall and Swift installed- engineering plant Year equipment index for the cost index process industry, 1926 = 100 1957–1959 = 100 1950 167 79 1960 237 102 1970 301 126

1980 675 261

1990 924 356 2000 1,108 394

Other Mass Transfer Operations For additional information concerning solid/fluid separators, membrane separations, and air stripping, refer to the ENVIRONMENTAL ENGINEERING section.

107 CHEMICAL ENGINEERING (continued) Cost Segments of Fixed-Capital Investment

Component Range

Direct costs Purchased equipment-delivered (including fabricated equipment and process machinery 100 such as pumps and compressors) Purchased-equipment installation 39–47 Instrumentation and controls (installed) 9–18 Piping (installed) 16–66 Electrical (installed) 10–11 Buildings (including services) 18–29 Yard improvements 10–13 Service facilities (installed) 40–70 Land (if purchase is required) 6 Total direct plant cost 264–346

Indirect costs Engineering and supervision 32–33 Construction expenses 34–41 Total direct and indirect plant costs 336–420 Contractor's fee (about 5% of direct and 17–21 indirect plant costs) Contingency (about 10% of direct and 36–42 indirect plant costs) Fixed-capital investment 387–483 Working capital (about 15% of total 68–86 capital investment) Total capital investment 455–569

108 CHEMICAL ENGINEERING (continued) Scaling of Equipment Costs The cost of Unit A at one capacity related to the cost of a similar Unit B with X times the capacity of Unit A is approximately Xn times the cost of Unit B. n ⎛⎞capacityof Unit A Cost of Unit A = cost of Unit B ⎝⎠⎜⎟capacityof Unit B

TYPICAL EXPONENTS (n) FOR EQUIPMENT COST VS. CAPACITY

Equipment Size range Exponent Dryer, drum, single vacuum 10–102 ft2 0.76 Dryer, drum, single atmospheric 10–102 ft2 0.40 Fan, centrifugal 103–104 ft3/min 0.44 Fan, centrifugal 2 × 104 –7 × 104 ft3/min 1.17 Heat exchanger, shell and tube, floating head, c.s. 100–400 ft2 0.60 Heat exchanger, shell and tube, fixed sheet, c.s. 100–400 ft2 0.44 Motor, squirrel cage, induction, 440 volts, 5–20 hp 0.69 explosion proof Motor, squirrel cage, induction, 440 volts, 20–200 hp 0.99 explosion proof Tray, bubble cup, c.s. 3–10 ft diameter 1.20 Tray, sieve, c.s. 3–10 ft diameter 0.86

CHEMICAL PROCESS SAFETY Threshold Limit Value (TLV) TLV is the lowest dose (ppm by volume in the atmosphere) the body is able to detoxify without any detectable effects. Examples are: Compound TLV 25 Chlorine 0.5 Ethyl Chloride 1,000 Ethyl Ether 400 Flammability LFL = lower flammability limit (volume % in air) UFL = upper flammability limit (volume % in air) A vapor-air mixture will only ignite and burn over the range of between LFL and UFL. Examples are: Compound LFL UFL Ethyl alcohol 3.3 19 Ethyl ether 1.9 36.0 Ethylene 2.7 36.0 Methane 5 15 Propane 2.1 9.5

109 CHEMICAL ENGINEERING (continued) Concentrations of Vaporized Liquids

Vaporization Rate (Qm, mass/time) from a Liquid Surface sat Qm = [MKASP /(RgTL)] M = molecular weight of volatile substance K = mass transfer coefficient AS = area of liquid surface sat P = saturation vapor pressure of the pure liquid at TL Rg = ideal TL = absolute temperature of the liquid

Mass Flow Rate of Liquid from a Hole in the Wall of a Process Unit ½ Qm = AHCo(2ρgcPg)

AH = area of hole Co = discharge coefficient ρ = density of the liquid gc = gravitational constant Pg = gauge pressure within the process unit

Concentration (Cppm) of Vaporized Liquid in Ventilated Space 6 Cppm = [QmRgT×10 /(kQVPM)] T = absolute ambient temperature k = nonideal mixing factor QV = ventilation rate P = absolute ambient pressure Concentration in the Atmosphere See "Atmospheric Dispersion Modeling" under AIR POLLUTION in the ENVIRONMENTAL ENGINEERING section. Sweep-Through Concentration Change in a Vessel

QVt = Vln[(C1 – Co)/(C2 – Co)]

QV = volumetric flow rate t = time V = vessel volume Co = inlet concentration C1 = initial concentration C2 = final concentration

110