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Process & Water Chemistry: formula sheet

Dose, treat, protect & separate · 117 formulas · metric edition 1

The full study guide: modules, problems, answer key
Module 1 · Stoichiometry at Scale
Process & Water Chemistry-1 Moles from Mass (n = m/M)
n=mMn = \frac{m}{M}
Converts a measured mass into an amount of substance by dividing by the molar mass.
Process & Water Chemistry-2 Molarity (C = n/V)
C=nVC = \frac{n}{V}
Defines molar concentration as moles of solute per volume of solution.
Process & Water Chemistry-3 Mass Percent of a Solution
c=msolutemsolution×100%c = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%
Expresses a solution's concentration as the solute's share of the total solution mass in percent.
Process & Water Chemistry-4 Particles from Moles (Avogadro's Number)
N=n NAN = n\,N_A
Converts an amount in moles into an actual particle count using the Avogadro constant NA =…
Process & Water Chemistry-5 Mole Ratio from a Balanced Equation
nB=nA ban_B = n_A \, \frac{b}{a}
Converts moles of one substance in a balanced equation into moles of another using the ratio of…
Process & Water Chemistry-6 Mass-to-Mass Stoichiometry
mB=mAMA⋅ba⋅MBm_B = \frac{m_A}{M_A} \cdot \frac{b}{a} \cdot M_B
Gives the mass of one substance produced or consumed from the mass of another, routing through…
Process & Water Chemistry-7 Dilution Equation (C1V1 = C2V2)
C1V1=C2V2C_1 V_1 = C_2 V_2
States that concentration times volume is conserved when a solution is diluted, since the moles of…
Process & Water Chemistry-8 Ideal Gas Law
PV=nRTP V = n R T
Relates pressure, volume, amount, and temperature of a gas.
Process & Water Chemistry-9 Gas Volume at STP
V=n VmV = n\,V_m
Converts between moles of an ideal gas and its volume at STP using the molar volume Vm = 22.414…
Process & Water Chemistry-10 Gas Density from Molar Mass
ρ=PMRT\rho = \frac{PM}{RT}
Gives an ideal gas's density from its molar mass, pressure, and absolute temperature using R =…
Process & Water Chemistry-11 Excess Reagent Remaining
nexcess=nB−ba nAn_{\text{excess}} = n_B - \frac{b}{a} \, n_A
Gives how much of the reactant in excess is left unreacted once the limiting reagent A has been…
Process & Water Chemistry-12 Percent Yield
% yield=mactualmtheoretical×100%\%\,\text{yield} = \frac{m_{\text{actual}}}{m_{\text{theoretical}}} \times 100\%
Compares the mass actually isolated from a reaction to the maximum mass stoichiometry predicts.
Process & Water Chemistry-13 Percent Composition of an Element
%X=a MXMcompound×100%\%X = \frac{a\,M_X}{M_{\text{compound}}} \times 100\%
Gives the mass percent an element contributes to a compound from the formula subscript and molar…
Process & Water Chemistry-14 Titration: Concentration of an Unknown
Ca=n CbVbVaC_a = \frac{n\,C_b V_b}{V_a}
Finds an analyte's concentration from the titre volume, titrant concentration, and the reaction's…
Process & Water Chemistry-15 Normality from Molarity
N=M×neqN = M \times n_{\text{eq}}
Converts molarity into normality by multiplying by the number of reactive equivalents each mole of…
Process & Water Chemistry-16 Equivalent Weight from Molar Mass and Valence
EW=Mz\mathrm{EW} = \frac{M}{z}
Gives the gram-equivalent weight of an ion or compound as its molar mass divided by the number of…
Module 2 · Chlorination & Disinfection
Process & Water Chemistry-17 Chlorine Dose, Demand and Residual
D=Cdemand+CresD = C_{\text{demand}} + C_{\text{res}}
The fundamental chlorination balance: the dose applied equals the chlorine consumed by the water's…
Process & Water Chemistry-18 Chemical Feed Rate (lb/day = mg/L × MGD × 8.34)
m˙=C Q\dot m = C \, Q
Converts a target chemical dose and a plant flow into a mass feed rate, the classic pounds-per-day…
Process & Water Chemistry-19 Pounds of Active Chemical in a Tank
m=V×SG×ρw×pm = V \times \mathrm{SG} \times \rho_w \times p
Gives the mass of active chemical held in a storage tank from its volume, the solution's specific…
Process & Water Chemistry-20 Hypochlorite Product Mass from Available Chlorine
mprod=mCl×100%pm_{\text{prod}} = \frac{m_{\mathrm{Cl}} \times 100\%}{p}
Converts a required mass of available chlorine into the mass of hypochlorite product to weigh out,…
Process & Water Chemistry-21 Chlorine Dose from a Weight of Product
C=m pVC = \frac{m \, p}{V}
Gives the free chlorine concentration produced by dissolving a known weight of hypochlorite product…
Process & Water Chemistry-22 Breakpoint Chlorine-to-Ammonia Ratio
R=Cl2NH3-NR = \frac{\mathrm{Cl_2}}{\mathrm{NH_3\text{-}N}}
The weight ratio of chlorine dose to ammonia nitrogen, which must reach about 7.6 to 1 to pass…
Process & Water Chemistry-23 CT Achieved (Disinfectant Residual × Contact Time)
CT=C T10\text{CT} = C \, T_{10}
The disinfection CT: the residual concentration a pathogen is exposed to multiplied by the time it…
Process & Water Chemistry-24 Effective Contact Time from Baffling Factor
T10=θ×BFT_{10} = \theta \times \mathrm{BF}
The effective contact time a basin actually delivers: its theoretical detention time multiplied by…
Process & Water Chemistry-25 Log Inactivation from Counts
LR=log⁡10 ⁣(N0N)\mathrm{LR} = \log_{10}\!\left(\frac{N_0}{N}\right)
The log reduction actually measured: the base-10 logarithm of the count before a process divided by…
Process & Water Chemistry-26 Log Reduction to Percent Kill
P=1−10−LRP = 1 - 10^{-\mathrm{LR}}
The conversion between a log reduction and a percent kill.
Process & Water Chemistry-27 Chick–Watson Inactivation
log⁡10 ⁣(N0N)=k C n t\log_{10}\!\left(\frac{N_0}{N}\right) = k \, C^{\,n} \, t
Chick's 1908 first-order disinfection law with Watson's concentration exponent: the log reduction…
Process & Water Chemistry-28 First-Order Chlorine Decay
C=C0 e−ktC = C_0 \, e^{-k t}
Free chlorine decays exponentially as it reacts with organics, biofilm and pipe wall.
Process & Water Chemistry-29 First-Order Integrated Rate Law
[A]=[A]0 e−kt[\mathrm{A}] = [\mathrm{A}]_0\,e^{-kt}
Gives the concentration remaining in a first-order reaction, the exponential decay that governs…
Module 3 · Hardness, Alkalinity & Softening
Process & Water Chemistry-30 Total Hardness as CaCO₃
TH=2.497 Ca+4.118 Mg\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}
Converts a lab report's calcium and magnesium ion results into a single total hardness expressed as…
Process & Water Chemistry-31 Ion Concentration as CaCO₃ Equivalent
CCaCO3=Cion×50.04EWC_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \frac{50.04}{\mathrm{EW}}
Restates any ion's concentration in the trade's common currency of CaCO₃ by scaling with the ratio…
Process & Water Chemistry-32 Grains per Gallon ↔ ppm Hardness
H=17.118 GH = 17.118\,G
Converts water hardness between grains per US gallon and mg/L as CaCO₃ using the exact 17.118 mg/L…
Process & Water Chemistry-33 Total Alkalinity as CaCO₃ from Species
TA=0.8202 HCO3+1.6679 CO3+2.9425 OH\mathrm{TA} = 0.8202\,\mathrm{HCO_3} + 1.6679\,\mathrm{CO_3} + 2.9425\,\mathrm{OH}
Sums bicarbonate, carbonate and hydroxide reported as their own ions into one total alkalinity…
Process & Water Chemistry-34 Acid Feed to Reduce Alkalinity
m˙=ΔAlk Q×EW50.04p/100%\dot m = \frac{\Delta \mathrm{Alk} \, Q \times \frac{\mathrm{EW}}{50.04}}{p/100\%}
Sizes the acid feed needed to knock a target amount of alkalinity out of a stream, correcting for…
Process & Water Chemistry-35 TDS Estimated from Conductivity (TDS = k × EC)
TDS=k×EC\mathrm{TDS} = k \times \mathrm{EC}
Estimates total dissolved solids in mg/L from a conductivity reading in µS/cm using an empirical…
Process & Water Chemistry-36 Water Resistivity and Conductivity
ρ=1σ\rho = \frac{1}{\sigma}
Relates the resistivity and conductivity of ultrapure and deionized water as exact reciprocals, the…
Process & Water Chemistry-37 Hardness Load Removed per Regeneration
m=C Vm = C \, V
Gives the mass of hardness as CaCO₃ a softener must remove between regenerations from the raw…
Process & Water Chemistry-38 Softener Resin Volume Required
V=mcapqV = \frac{m_{\text{cap}}}{q}
Sizes the ion-exchange resin bed from the hardness capacity required per regeneration and the…
Process & Water Chemistry-39 Days Between Softener Regenerations
t=mcapC Qt = \frac{m_{\text{cap}}}{C \, Q}
Gives the run time a softener achieves between regenerations from its rated hardness capacity, the…
Process & Water Chemistry-40 Flow-Weighted Blending Concentration
C=Q1C1+Q2C2Q1+Q2C = \frac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}
The concentration you land on when two streams of known flow and known strength join, each stream's…
Process & Water Chemistry-41 Salt Dose per Regeneration
msalt=D Vm_{\text{salt}} = D \, V
Gives the mass of sodium chloride a softener draws each regeneration from the resin volume and the…
Process & Water Chemistry-42 Hardness Removal Efficiency and Leakage
R=Cin−CoutCinR = \frac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}}
Gives the fraction of hardness a softener or membrane removes from the inlet and outlet…
Process & Water Chemistry-43 Lime Dose for Softening (as CaCO₃)
L=CO2+Alk+Mg+ExL = \mathrm{CO_2} + \mathrm{Alk} + \mathrm{Mg} + \mathrm{Ex}
The stoichiometric lime requirement for excess-lime softening, in mg/L as CaCO₃: every acid the…
Process & Water Chemistry-44 Soda Ash Dose for Softening (as CaCO₃)
S=TH−AlkS = \mathrm{TH} - \mathrm{Alk}
Soda ash makes up the difference between the hardness a water carries and the alkalinity it…
Module 4 · Cooling Towers & Boilers
Process & Water Chemistry-45 Cycles of Concentration (COC = M/B)
COC=MB\text{COC} = \frac{M}{B}
Cycles of concentration for a cooling tower from the makeup and blowdown flows: the master number…
Process & Water Chemistry-46 Cycles of Concentration from Conductivity
COC=σtσm\text{COC} = \frac{\sigma_t}{\sigma_m}
Cycles of concentration read straight off a conductivity meter: tower water conductivity divided by…
Process & Water Chemistry-47 Cycles of Concentration from Chloride
COC=CltClm\text{COC} = \frac{\mathrm{Cl}_t}{\mathrm{Cl}_m}
Cycles of concentration from a chloride titration: the conservative tracer that neither…
Process & Water Chemistry-48 Cooling Tower Evaporation Rate
E=0.001 R ΔTE = 0.001 \, R \, \Delta T
Evaporation loss from a cooling tower using the industry rule of 0.1% of recirculation per degree…
Process & Water Chemistry-49 Blowdown Rate from Cycles
B=ECOC−1B = \frac{E}{\text{COC} - 1}
Blowdown a cooling tower must bleed to hold a target cycles of concentration, given its evaporation…
Process & Water Chemistry-50 Cooling Tower Makeup Water Rate
M=E+B+DM = E + B + D
Total makeup water a cooling tower needs: the sum of evaporation, blowdown to drain, and drift…
Process & Water Chemistry-51 Cooling Tower Drift Loss
D=d100 RD = \frac{d}{100} \, R
Drift (windage) loss from a cooling tower as a percentage of the recirculation rate, the fraction…
Process & Water Chemistry-52 Cooling Tower Range
ΔT=Th−Tc\Delta T = T_h - T_c
Cooling tower range: the temperature drop the tower achieves between the hot water returning from…
Process & Water Chemistry-53 Cooling Tower Approach
A=Tc−TwbA = T_c - T_{wb}
Cooling tower approach: how many degrees the cold basin water sits above the ambient wet-bulb…
Process & Water Chemistry-54 Cooling Tower Heat Rejection
Q=500 R ΔTQ = 500 \, R \, \Delta T
Heat a cooling tower rejects from flow and range using the trade constant 500 = 8.34 lb/gal × 60…
Process & Water Chemistry-55 Chemical Feed Rate from Dose
W=C Q ρwW = C \, Q \, \rho_w
Chemical feed rate in pounds per day from a ppm dose and a water flow, using the trade density of…
Process & Water Chemistry-56 Dose Achieved from Chemical Added
C=mV ρwC = \frac{m}{V \, \rho_w}
Concentration reached in a system of known volume after adding a measured mass of chemical, at 8.34…
Process & Water Chemistry-57 Product Dose from Active Strength
Dp=100 DaAD_p = \frac{100 \, D_a}{A}
Converts a required active-ingredient dose into the as-supplied product dose when the drum is only…
Process & Water Chemistry-58 Closed Loop Slug Dose Volume
Vp=C Vs ρwρpV_p = \frac{C \, V_s \, \rho_w}{\rho_p}
Volume of liquid product needed for a one-shot slug dose to hit a target ppm in a closed loop of…
Process & Water Chemistry-59 Holding Time Index
HTI=ln⁡2  VB\text{HTI} = \frac{\ln 2 \; V}{B}
Holding time index: the half-life of a chemical in a bled system, the time for half the treatment…
Process & Water Chemistry-60 System Volume from Turnover Time
V=R tV = R \, t
System water volume estimated from the recirculation rate and the measured turnover time: the field…
Process & Water Chemistry-61 Boiler Cycles of Concentration
COC=TDSbTDSfw\text{COC} = \frac{\text{TDS}_b}{\text{TDS}_{fw}}
Cycles of concentration in a steam boiler: boiler water TDS divided by feedwater TDS, since steam…
Process & Water Chemistry-62 Boiler Blowdown Percent
%B=TDSfwTDSb×100\%B = \frac{\text{TDS}_{fw}}{\text{TDS}_b} \times 100
Boiler blowdown as a percentage of feedwater, set by the ratio of feedwater TDS to the maximum TDS…
Process & Water Chemistry-63 Boiler Blowdown Rate from Steam Rate
B=SCOC−1B = \frac{S}{\text{COC} - 1}
Continuous blowdown a steam boiler must carry, in pounds per hour, from its steam production rate…
Process & Water Chemistry-64 Condensate Return Percentage
%CR=ScS×100\%CR = \frac{S_c}{S} \times 100
Percentage of generated steam that comes back to the boiler house as condensate: the headline…
Process & Water Chemistry-65 Boiler Makeup from Condensate Return
M=S(1−%CR100)M = S\left(1 - \frac{\%CR}{100}\right)
Fresh makeup water a steam plant must treat, from the steam production rate and the fraction of…
Process & Water Chemistry-66 Flash Steam Percentage
%F=hf1−hf2hfg2×100\%F = \frac{h_{f1} - h_{f2}}{h_{fg2}} \times 100
Percentage of hot condensate that flashes to steam when let down to a lower pressure, from the…
Module 5 · Corrosion & the Water Quality Indices
Process & Water Chemistry-67 Langelier Saturation Index (LSI)
LSI=pH−pHs\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}
The classic calcium-carbonate scaling index: measured pH minus the saturation pH, positive for…
Process & Water Chemistry-68 Saturation pH (pHs) for Langelier's Index
pHs=(9.3+A+B)−(C+D)\mathrm{pH_s} = (9.3 + A + B) - (C + D)
Computes the pH at which water is saturated with calcium carbonate from its TDS, temperature,…
Process & Water Chemistry-69 Ryznar Stability Index (RSI)
RSI=2 pHs−pH\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH}
An empirical scaling index scaled so that values below about 6 predict scale and values above about…
Process & Water Chemistry-70 Puckorius (Practical) Scaling Index
PSI=2 pHs−pHeq,pHeq=1.465 log⁡10Alk+4.54\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}\mathrm{Alk} + 4.54
A Ryznar variant that replaces measured pH with an equilibrium pH derived from alkalinity, giving a…
Process & Water Chemistry-71 Larson–Skold Index
LS=Cl35.45+SO448.03Alk50.04\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}
Ratio of aggressive chloride and sulphate equivalents to protective bicarbonate alkalinity,…
Process & Water Chemistry-72 Dissolved Oxygen Saturation with Temperature
ln⁡Cs=−139.34411+1.575701×105T−6.642308×107T2+1.243800×1010T3−8.621949×1011T4\ln C_s = -139.34411 + \frac{1.575701 \times 10^5}{T} - \frac{6.642308 \times 10^7}{T^2} + \frac{1.243800 \times 10^{10}}{T^3} - \frac{8.621949 \times 10^{11}}{T^4}
How much oxygen fresh water can hold at saturation, falling from about 14.6 mg/L at freezing to 7.6…
Process & Water Chemistry-73 Corrosion Rate from Coupon Weight Loss
P=m Yρ A tP = \frac{m \, Y}{\rho \, A \, t}
Uniform corrosion rate as metal thickness lost per year, from a coupon's weight loss, density,…
Process & Water Chemistry-74 Wall Penetration and Remaining Life
L=T−TrPL = \frac{T - T_r}{P}
How many years of wall are left: the metal above the retirement thickness divided by the…
Process & Water Chemistry-75 Penetration Rate from Corrosion Current Density
P=i Mn F ρP = \frac{i \, M}{n \, F \, \rho}
Faraday's law applied to a corroding metal: a corrosion current density converted into the…
Process & Water Chemistry-76 Galvanic Driving Voltage
ΔE=Ec−Ea\Delta E = E_c - E_a
The potential difference between two metals coupled in the same electrolyte: the noble one's…
Process & Water Chemistry-77 Sacrificial Anode Mass for a Required Life
W=I tC uW = \frac{I \, t}{C \, u}
How much anode metal a cathodic protection system has to carry to supply its current for the design…
Process & Water Chemistry-78 Anode Current Output
I=ΔERI = \frac{\Delta E}{R}
What a galvanic anode actually delivers: the driving voltage between the anode and the polarized…
Process & Water Chemistry-79 Cathodic Protection Current Demand
I=A i fI = A \, i \, f
The total current a cathodic protection system has to supply: the structure's surface area times…
Process & Water Chemistry-80 Pitting Resistance Equivalent Number (PREN)
PREN=%Cr+3.3 %Mo+16 %NPREN = \%Cr + 3.3\,\%Mo + 16\,\%N
The single index that ranks stainless steels for resistance to pitting and crevice attack in…
Module 6 · Clarifiers, Filters & the Sludge Line
Process & Water Chemistry-81 Hydraulic Detention Time
t=VQt = \frac{V}{Q}
Theoretical detention time of a tank, clarifier or contact basin: the working volume divided by the…
Process & Water Chemistry-82 Surface Overflow Rate
vo=QAv_o = \frac{Q}{A}
Surface overflow (surface loading) rate of a settling basin: flow divided by plan area, reported…
Process & Water Chemistry-83 Clarifier Solids Loading Rate
SLR=(Q+Qr) XA\text{SLR} = \frac{(Q + Q_r) \, X}{A}
Solids applied to a secondary clarifier per unit of surface area, in kg of MLSS per square metre…
Process & Water Chemistry-84 Weir Loading Rate (Weir Overflow Rate)
WL=QLwW_L = \frac{Q}{L_w}
Flow divided by the total length of weir crest it leaves over: the loading on a clarifier's…
Process & Water Chemistry-85 Stokes Settling Velocity
vs=g(ρs−ρ)d218μv_s = \frac{g (\rho_s - \rho) d^2}{18 \mu}
Terminal settling velocity of a small sphere in laminar flow by Stokes' law: the grit chamber and…
Process & Water Chemistry-86 Filtration Rate (Filter Loading Rate)
vf=QAv_f = \frac{Q}{A}
Filtration rate through a granular media filter: flow divided by filter bed area, the approach…
Process & Water Chemistry-87 Backwash Water Volume
Vbw=vb A tV_{bw} = v_b \, A \, t
Water consumed by one filter backwash, from the backwash rise rate, the filter bed area and the…
Process & Water Chemistry-88 Percent Backwash Water
%BW=VbwVf×100\%BW = \frac{V_{bw}}{V_f} \times 100
Share of a filter's production consumed by its own backwash, the housekeeping ratio that flags…
Process & Water Chemistry-89 Jar Test Dose Scale-Up
D=Vst CstVsD = \frac{V_{st} \, C_{st}}{V_{s}}
Converts millilitres of stock solution added to a jar test beaker into the equivalent plant dose in…
Process & Water Chemistry-90 Alkalinity Remaining After Alum
Af=A0−0.45 DA_f = A_0 - 0.45 \, D
Alkalinity left after coagulation, since each mg/L of alum destroys 0.45 mg/L of alkalinity as…
Process & Water Chemistry-91 Mass Loading: BOD, Solids or Metals
W=Q CW = Q \, C
Mass of BOD, COD, solids or a dissolved metal carried per unit time by a flow at a concentration,…
Process & Water Chemistry-92 BOD Removal Efficiency
E=Ci−CeCi×100E = \frac{C_i - C_e}{C_i} \times 100
Percent removal across a treatment unit or a whole plant, from the influent and effluent…
Process & Water Chemistry-93 Population Equivalent
PE=WwPE = \frac{W}{w}
Population equivalent of a waste stream: its pollutant load divided by the load one person…
Process & Water Chemistry-94 Food-to-Microorganism (F/M) Ratio
FM=Q S0V X\frac{F}{M} = \frac{Q \, S_0}{V \, X}
Food-to-microorganism ratio: BOD applied per day divided by the mass of mixed liquor solids holding…
Process & Water Chemistry-95 Mean Cell Residence Time (Sludge Age)
SRT=V XQw Xw\text{SRT} = \frac{V \, X}{Q_w \, X_w}
Solids retention time of an activated sludge plant: the mass of solids under aeration divided by…
Process & Water Chemistry-96 Sludge Volume Index (SVI)
SVI=SV30X\text{SVI} = \frac{SV_{30}}{X}
Sludge volume index in mL/g: the volume a gram of mixed liquor solids occupies after settling…
Process & Water Chemistry-97 Return Activated Sludge Rate
Qr=Q XXr−XQ_r = \frac{Q \, X}{X_r - X}
Return sludge flow needed to hold a target mixed liquor concentration, from a solids balance around…
Module 7 · Separations & Absorption
Process & Water Chemistry-98 Raoult's Law
P=x P0P = x \, P^{0}
Gives the vapour pressure of a solvent above an ideal solution as its mole fraction times the pure…
Process & Water Chemistry-99 Henry's Law (Gas Solubility)
C=H PC = H\,P
At a fixed temperature the concentration a gas reaches in a liquid is proportional to its partial…
Process & Water Chemistry-100 Relative Volatility (Binary)
α=y(1−x)x(1−y)\alpha = \frac{y\left(1 - x\right)}{x\left(1 - y\right)}
The single number that says how easy a binary mixture is to distil: the ratio of the light…
Process & Water Chemistry-101 Column Material Balance (Distillate and Bottoms Split)
D=F zF−xBxD−xBD = F\,\frac{z_F - x_B}{x_D - x_B}
How much of the feed leaves overhead and how much out the bottom, from nothing but the three…
Process & Water Chemistry-102 Reflux Ratio
R=LDR = \frac{L}{D}
The liquid sent back down the column divided by the product drawn off the top.
Process & Water Chemistry-103 Boilup Ratio
VB=VBV_B = \frac{V}{B}
The vapour the reboiler raises divided by the bottoms drawn off beneath it.
Process & Water Chemistry-104 Fenske Equation (Minimum Stages)
Nmin=ln⁡ ⁣[xD1−xD⋅1−xBxB]ln⁡αN_{min} = \frac{\ln\!\left[\frac{x_D}{1 - x_D}\cdot\frac{1 - x_B}{x_B}\right]}{\ln \alpha}
The number of theoretical stages a distillation column would need at total reflux: the absolute…
Process & Water Chemistry-105 Overall Column Efficiency
Eo=NtNaE_o = \frac{N_t}{N_a}
The bridge from the calculation to the hardware: theoretical stages divided by the actual trays…
Process & Water Chemistry-106 Gilliland Correlation (Actual Stages)
N−NminN+1=1−exp⁡ ⁣[(1+54.4X11+117.2X) ⁣(X−1X)],X=R−RminR+1\frac{N - N_{min}}{N + 1} = 1 - \exp\!\left[\left(\frac{1 + 54.4X}{11 + 117.2X}\right)\!\left(\frac{X - 1}{\sqrt{X}}\right)\right],\quad X = \frac{R - R_{min}}{R + 1}
The empirical bridge across the middle of column design: given the two unbuildable limits (Fenske's…
Process & Water Chemistry-107 Rectifying Operating Line (McCabe–Thiele)
y=RR+1 x+xDR+1y = \frac{R}{R + 1}\,x + \frac{x_D}{R + 1}
The straight line above the feed that ties the vapour rising off a stage to the liquid falling onto…
Process & Water Chemistry-108 Stripping Operating Line (McCabe–Thiele)
y=VB+1VB x−xBVBy = \frac{V_B + 1}{V_B}\,x - \frac{x_B}{V_B}
The straight line below the feed, written in terms of the boilup ratio.
Process & Water Chemistry-109 Feed Line (q-Line)
y=qq−1 x−zFq−1y = \frac{q}{q - 1}\,x - \frac{z_F}{q - 1}
The line the feed's thermal condition draws on a McCabe–Thiele diagram.
Process & Water Chemistry-110 Packed Column Height from HTU and NTU
Z=HOG NOGZ = H_{OG} \, N_{OG}
A packed column's height split into the two things that set it: how hard the separation is, and how…
Process & Water Chemistry-111 Transfer Units for Dilute Absorption
NOG=ln⁡[y1y2(1−1A)+1A]1−1AN_{OG} = \frac{\ln \left[ \dfrac{y_1}{y_2} \left( 1 - \dfrac{1}{A} \right) + \dfrac{1}{A} \right]}{1 - \dfrac{1}{A}}
The number of transfer units a dilute absorber demands: the packed-column counterpart of a stage…
Process & Water Chemistry-112 Absorption Factor
A=LmVA = \frac{L}{m V}
The single number that decides whether an absorber can do its job: the liquid's capacity to carry…
Process & Water Chemistry-113 Kremser Equation for Absorption Stages
N=ln⁡[y1y2(1−1A)+1A]ln⁡AN = \frac{\ln \left[ \dfrac{y_1}{y_2} \left( 1 - \dfrac{1}{A} \right) + \dfrac{1}{A} \right]}{\ln A}
How many theoretical stages a tray absorber needs, from the recovery demanded and the absorption…
Module 8 · Thermal Kill: D, z and F
Process & Water Chemistry-114 D-Value (Decimal Reduction Time)
D=tLRD = \frac{t}{\mathrm{LR}}
The decimal reduction time: how long at a fixed temperature it takes to reduce a population by one…
Process & Water Chemistry-115 z-Value (Thermal Resistance Constant)
z=T2−T1log⁡10D1−log⁡10D2z = \frac{T_2 - T_1}{\log_{10} D_1 - \log_{10} D_2}
The z-value: the temperature change that moves the D-value by a factor of ten.
Process & Water Chemistry-116 F-Value (Equivalent Time at Reference Temperature)
F=t×10 (T−Tref)/zF = t \times 10^{\,(T - T_{ref})/z}
The F-value: time spent at one temperature expressed as the equivalent time at a reference…
Process & Water Chemistry-117 Pasteurisation Units (PU)
PU=t×10 (T−Tref)/7\mathrm{PU} = t \times 10^{\,(T - T_{\mathrm{ref}})/7}
One pasteurisation unit is one minute held at 60 °C, and every other temperature is converted to…