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Cheatsheet: Water Treatment

1. Coagulation and Flocculation

1.1 Coagulation Fundamentals

Parameter Description
Purpose Destabilize colloidal particles by neutralizing surface charge to enable particle aggregation
Rapid Mix Time 20-60 seconds with velocity gradient (G) = 700-1000 s⁻¹
Zeta Potential Target: -5 to +5 mV for optimal destabilization
pH Range Alum: 6.0-7.5; Ferric salts: 4.0-9.0; optimal depends on coagulant

1.2 Common Coagulants

Coagulant Formula/Details
Aluminum Sulfate (Alum) Al₂(SO₄)₃·14H₂O; dose: 10-50 mg/L; produces 0.45 mg Al(OH)₃ per mg alum
Ferric Sulfate Fe₂(SO₄)₃; dose: 5-40 mg/L; wider pH range than alum
Ferric Chloride FeCl₃; dose: 5-40 mg/L; highly corrosive, effective turbidity removal
Polyaluminum Chloride (PACl) Al₁₃O₄(OH)₂₄Cl₇; lower sludge production than alum
Cationic Polymers Organic coagulants; dose: 0.5-5 mg/L; charge neutralization

1.3 Flocculation

Parameter Value/Description
Purpose Promote particle collision and growth of floc through gentle mixing
Detention Time 20-45 minutes
Velocity Gradient (G) 20-75 s⁻¹; tapered flocculation: start high, end low
Gt Product 10⁴ to 10⁵ (dimensionless); indicator of flocculation effectiveness
Tank Configuration Multiple stages (3-4) with decreasing G values

1.4 Key Equations

Equation Variables
G = √(P/μV) G = velocity gradient (s⁻¹); P = power (W); μ = dynamic viscosity (N·s/m²); V = volume (m³)
P = γQhL P = power (W); γ = specific weight (N/m³); Q = flow rate (m³/s); hL = head loss (m)
Camp Number = Gt G = velocity gradient (s⁻¹); t = detention time (s)

2. Sedimentation

2.1 Settling Types

Type Description
Type I (Discrete) Individual particles settle independently; no flocculation; dilute suspensions
Type II (Flocculant) Particles flocculate during settling; velocity increases with depth
Type III (Hindered) Interparticle forces hinder settling; particles settle as a mass
Type IV (Compression) High concentration; particles in contact; compression of lower layers

2.2 Rectangular Basin Design

Parameter Value/Criteria
Overflow Rate (vo) 500-1000 gpd/ft² (0.5-1.5 m/h); controls settling efficiency
Detention Time 2-4 hours for flocculent settling
Depth 10-15 ft (3-4.5 m)
Length:Width Ratio 3:1 to 5:1
Horizontal Velocity 0.5-1.5 ft/min (0.15-0.45 m/min); prevent scour and short-circuiting
Weir Loading Rate 10,000-20,000 gpd/ft (120-250 m³/day/m)

2.3 Circular Basin Design

Parameter Value/Criteria
Overflow Rate 400-800 gpd/ft² (0.4-1.2 m/h)
Detention Time 2-4 hours
Depth 10-15 ft (3-4.5 m)
Diameter 15-200 ft (4.5-60 m); center feed with peripheral withdrawal
Side Water Depth 7-12 ft (2-3.5 m) with sloped bottom toward center

2.4 Key Equations

Equation Variables
vo = Q/As vo = overflow rate (m/h or gpd/ft²); Q = flow rate; As = surface area
t = V/Q t = detention time (hr); V = basin volume (m³); Q = flow rate (m³/h)
vs = (g·d²·(ρpw))/(18μ) vs = Stokes settling velocity; g = gravity; d = particle diameter; ρ = density; μ = viscosity
NR = vdρ/μ NR = Reynolds number; v = velocity; d = diameter; ρ = density; μ = viscosity

2.5 Design Considerations

  • Inlet zone: distribute flow uniformly; diffusion wall or baffles
  • Outlet zone: minimize velocity; use adjustable weirs; prevent short-circuiting
  • Sludge zone: 1-2 ft depth; mechanical scrapers or sludge hoppers
  • Temperature effects: viscosity changes affect settling; design for worst case
  • Scour velocity limit: vh <>s to prevent resuspension

3. Filtration

3.1 Rapid Sand Filtration

Parameter Value/Specification
Filtration Rate 2-5 gpm/ft² (5-12 m/h); 4-6 gpm/ft² common
Media Depth 24-30 inches (0.6-0.75 m)
Effective Size (ES) 0.45-0.55 mm (d₁₀)
Uniformity Coefficient (UC) 1.3-1.7 (d₆₀/d₁₀); <1.5>
Media Grain Size 0.45-1.0 mm
Filter Run Length 12-48 hours between backwashes
Terminal Head Loss 8-10 ft (2.4-3 m)

3.2 Dual Media Filtration

Layer Specifications
Anthracite (Top) Depth: 18-24 in; ES: 0.9-1.2 mm; UC: <1.5; specific="" gravity:="">
Sand (Bottom) Depth: 9-12 in; ES: 0.45-0.55 mm; UC: <1.5; specific="" gravity:="">
Filtration Rate 4-6 gpm/ft² (10-15 m/h)
Advantages Longer filter runs; higher filtration rates; depth filtration

3.3 Multimedia Filtration

Layer Specifications
Anthracite (Top) Depth: 18-24 in; ES: 0.9-1.2 mm
Sand (Middle) Depth: 9-12 in; ES: 0.45-0.55 mm
Garnet (Bottom) Depth: 3-6 in; ES: 0.2-0.4 mm; specific gravity: 3.6-4.2

3.4 Underdrain and Support Gravel

Component Specification
Gravel Layers 4-6 layers; total depth: 18-24 in; graded from 1/8 in to 2 in
Underdrain Spacing Laterals: 6-12 in on center; manifold supports laterals
Orifice Size 1/4 to 1/2 inch diameter; prevents media passage
Modern Systems Proprietary underdrains eliminate gravel; air scour capability

3.5 Backwashing

Parameter Value
Backwash Rate 15-20 gpm/ft² (36-48 m/h); 20-50% bed expansion
Backwash Duration 5-15 minutes
Bed Expansion 25-50%; fluidize media to remove trapped particles
Water Temperature Effect Higher temperature = lower viscosity = higher expansion; adjust rate
Auxiliary Scour Air scour: 3-5 scfm/ft² (55-90 m/h) for 3-5 min before water backwash
Surface Wash Fixed or rotating; 0.5-2 gpm/ft²; during backwash to break up floc

3.6 Filter Performance

Parameter Description/Criteria
Turbidity Breakthrough End filter run when effluent turbidity >0.3 NTU or increases rapidly
Head Loss Development Terminal head loss = 8-10 ft; initial clean bed = 1-3 ft
Negative Head Avoid; causes air binding; maintain min 2 ft water above media
Filter-to-Waste 1-3 minutes after backwash to remove fines and restart

3.7 Key Equations

Equation Variables
hL = (f·L·v²)/(2g·d) hL = head loss; f = friction factor; L = depth; v = velocity; g = gravity; d = grain diameter
Carmen-Kozeny: hL = k·(1-ε)²/ε³·(v·L)/d² ε = porosity (0.4-0.45); k = constant (≈5); v = approach velocity; L = bed depth
UC = d₆₀/d₁₀ UC = uniformity coefficient; d₆₀ = 60% passing size; d₁₀ = 10% passing size (ES)
Filtration Rate = Q/A Q = flow rate (gpm); A = filter surface area (ft²)

4. Disinfection

4.1 Chlorination

Parameter Value/Description
Free Chlorine Residual 0.2-2.0 mg/L in distribution; 0.5-1.0 mg/L minimum at entry point
Contact Time (CT) CT = C × t; C = residual (mg/L); t = time (min); required CT depends on pathogen, pH, temp
Breakpoint Chlorination Cl₂:NH₃-N mass ratio = 7.6:1 to 10:1 to destroy chloramines and reach breakpoint
pH Effect Lower pH = more HOCl (stronger); higher pH = more OCl⁻ (weaker)
Temperature Effect Lower temp = longer contact time required; CT increases as temp decreases

4.2 Chlorine Species

Species Details
Hypochlorous Acid (HOCl) Undissociated form; 80-100 times more effective than OCl⁻; dominant at pH <>
Hypochlorite Ion (OCl⁻) Dissociated form; weaker disinfectant; dominant at pH >7.5
Chloramines NH₂Cl (monochloramine), NHCl₂ (dichloramine), NCl₃ (trichloramine); combined chlorine residual
Chlorine Demand Amount consumed by organics, ammonia, Fe²⁺, Mn²⁺, H₂S before residual appears

4.3 Chlorine Forms

Form Details
Chlorine Gas (Cl₂) Liquefied under pressure; 1 lb Cl₂ = 1 lb available chlorine; 100% strength
Sodium Hypochlorite (NaOCl) Liquid bleach; 12-15% available chlorine; 1 lb Cl₂ = 7.5-8.3 lb NaOCl (12.5%)
Calcium Hypochlorite (Ca(OCl)₂) Solid/powder; 65-70% available chlorine; 1 lb Cl₂ = 1.5 lb Ca(OCl)₂ (65%)

4.4 CT Values for Disinfection

Pathogen Inactivation Requirements
Giardia 3-log (99.9%) inactivation required; CT = 35-175 mg·min/L (pH 7, 10°C, free Cl)
Viruses 4-log (99.99%) inactivation required; CT = 3-12 mg·min/L (pH 7, 10°C, free Cl)
Cryptosporidium Highly resistant to chlorine; CT >7200 mg·min/L for 3-log; use UV or ozone

4.5 Alternative Disinfectants

Disinfectant Key Characteristics
Chloramines NH₂Cl; longer residual; weaker disinfectant; Cl₂:NH₃-N = 3:1 to 5:1 mass ratio for mono
Chlorine Dioxide (ClO₂) Dose: 0.5-2 mg/L; effective against Cryptosporidium; no THM formation; pH independent
Ozone (O₃) Dose: 1-3 mg/L; powerful oxidant; no residual; CT = 0.5-3 mg·min/L for Giardia
UV Irradiation Dose: 40 mJ/cm² for 4-log virus; no chemical residual; effective for Cryptosporidium

4.6 Disinfection Byproducts

Byproduct MCL/Details
Trihalomethanes (THMs) MCL = 80 μg/L (running annual average); CHCl₃, CHBrCl₂, CHBr₂Cl, CHBr₃
Haloacetic Acids (HAA5) MCL = 60 μg/L (running annual average); 5 regulated species
Chlorite (ClO₂⁻) MCL = 1.0 mg/L; byproduct of chlorine dioxide
Bromate (BrO₃⁻) MCL = 10 μg/L; byproduct of ozonation when bromide present

4.7 Key Equations

Equation Variables
Chlorine Dose (lb/day) = Q × C × 8.34 Q = flow (MGD); C = dose (mg/L); 8.34 = conversion factor
CT = C × t C = disinfectant residual (mg/L); t = contact time (min)
log Inactivation = CTactual/CTrequired Calculate required CT from tables; compare to actual achieved CT
t₁₀ = V/(Q × baffling factor) t₁₀ = time for 10% of flow to pass; V = tank volume; baffling factor = 0.1-0.7

5. Softening

5.1 Hardness Fundamentals

Parameter Value/Description
Total Hardness Sum of Ca²⁺ and Mg²⁺; expressed as mg/L CaCO₃
Carbonate Hardness Ca²⁺ and Mg²⁺ associated with HCO₃⁻ and CO₃²⁻; temporary hardness
Noncarbonate Hardness Ca²⁺ and Mg²⁺ associated with SO₄²⁻, Cl⁻, NO₃⁻; permanent hardness
Hardness Classification Soft <60; moderately="" hard="" 60-120;="" hard="" 120-180;="" very="" hard="">180 mg/L as CaCO₃

5.2 Lime-Soda Ash Softening

Chemical Purpose/Reaction
Hydrated Lime (Ca(OH)₂) Remove CO₂, carbonate hardness; raise pH to 10.3-10.8 for Mg removal
Quicklime (CaO) CaO + H₂O → Ca(OH)₂; more economical; 1 lb CaO = 1.32 lb Ca(OH)₂
Soda Ash (Na₂CO₃) Remove noncarbonate hardness (permanent hardness)

5.3 Lime Softening Reactions

Reaction Stoichiometry (as CaCO₃)
Remove CO₂ CO₂ + Ca(OH)₂ → CaCO₃↓ + H₂O; 1 mg/L CO₂ requires 2.27 mg/L Ca(OH)₂
Remove Ca-Carbonate Ca(HCO₃)₂ + Ca(OH)₂ → 2CaCO₃↓ + 2H₂O; 1:1 as CaCO₃
Remove Mg-Carbonate Mg(HCO₃)₂ + 2Ca(OH)₂ → Mg(OH)₂↓ + 2CaCO₃↓ + 2H₂O; 2:1 lime to Mg as CaCO₃
Remove Mg-Noncarbonate MgSO₄ + Ca(OH)₂ → Mg(OH)₂↓ + CaSO₄; 1:1 as CaCO₃
Remove Ca-Noncarbonate CaSO₄ + Na₂CO₃ → CaCO₃↓ + Na₂SO₄; use soda ash 1:1 as CaCO₃

5.4 Softening Process Design

Parameter Value
Detention Time 1.5-4 hours in reactor basin
pH for Ca Removal 9.5-10.0; precipitate CaCO₃
pH for Mg Removal 10.8-11.2; precipitate Mg(OH)₂; requires excess lime
Practical Hardness Limit Ca: 30-50 mg/L as CaCO₃; Mg: 10 mg/L as CaCO₃; total: 75-120 mg/L as CaCO₃
Excess Lime 1.25-1.5 times stoichiometric for Mg removal
Recarbonation Add CO₂ to lower pH to 8.3-8.5; stabilize water; prevent CaCO₃ precipitation

5.5 Ion Exchange Softening

Parameter Value/Description
Resin Type Strong acid cation (SAC) resin; sodium cycle; exchange Ca²⁺ and Mg²⁺ for Na⁺
Exchange Reaction Ca²⁺ + 2Na-R → Ca-R₂ + 2Na⁺; Mg²⁺ + 2Na-R → Mg-R₂ + 2Na⁺
Operating Capacity 20,000-40,000 grains CaCO₃ per ft³ resin; 15-25 kgr/ft³ common
Service Flow Rate 2-10 gpm/ft² (5-25 m/h)
Regenerant NaCl brine; 10-15 lb NaCl per ft³ resin; 10% solution
Backwash Rate 4-8 gpm/ft² for 10-15 min; 50% bed expansion
Effluent Hardness <1 mg/l="" as="" caco₃="" achievable;="" adds="" ~50="" mg/l="" na="" per="" 100="" mg/l="" hardness="">

5.6 Key Equations

Equation Variables
Hardness (mg/L CaCO₃) = 2.5[Ca²⁺] + 4.1[Mg²⁺] Concentrations in mg/L as ion; conversion factors to CaCO₃
Lime (mg/L) = CO₂ + CH + MgCO₃ + MgNCH + Excess All as CaCO₃; CH = carbonate hardness; NCH = noncarbonate hardness
Soda Ash (mg/L) = CaNCH + MgNCH Remove only noncarbonate hardness; all as CaCO₃
Salt (lb) = (Volume ft³) × (Dosage lb/ft³) NaCl required for regeneration of IX resin

6. Advanced Treatment Processes

6.1 Membrane Filtration

Process Pore Size/MWCO/Details
Microfiltration (MF) 0.1-1 μm; 100-1000 kPa; remove suspended solids, bacteria, protozoa
Ultrafiltration (UF) 0.01-0.1 μm; 100-500 kPa; remove viruses, macromolecules, colloids; MWCO 10,000-100,000
Nanofiltration (NF) 0.001-0.01 μm; 500-1000 kPa; remove hardness, organics, divalent ions; MWCO 200-1000
Reverse Osmosis (RO) <0.001 μm;="" 1500-6000="" kpa;="" remove="" dissolved="" salts,="" tds;="" 95-99%="">

6.2 Reverse Osmosis Design

Parameter Value/Description
Operating Pressure 150-400 psi (1000-2800 kPa) brackish; 800-1200 psi (5500-8300 kPa) seawater
Recovery Rate 75-85% brackish water; 35-50% seawater; permeate/feed ratio
Flux Rate 10-20 gfd (gallons/ft²/day) or 15-30 L/m²/h
Salt Rejection 95-99% for brackish; 99.2-99.8% for seawater membranes
Pretreatment SDI <5; turbidity=""><1 ntu;="" remove="" hardness,="" fe,="" mn;="" antiscalant="">

6.3 Activated Carbon Adsorption

Parameter Value/Description
GAC Contact Time 10-30 minutes EBCT (empty bed contact time)
GAC Loading Rate 2-10 gpm/ft² (5-25 m/h)
Bed Depth 4-10 ft (1.2-3 m)
Backwash Rate 12-20 gpm/ft²; 50% bed expansion; 10-15 min duration
Regeneration Thermal at 800-900°C; or replace with virgin carbon
Applications Remove taste, odor, THMs, synthetic organics, pesticides

6.4 Air Stripping

Parameter Value/Description
Purpose Remove volatile organic compounds (VOCs), radon, H₂S, CO₂
Air-to-Water Ratio 20:1 to 100:1 for VOC removal
Tower Height 15-25 ft (4.5-7.5 m) packed tower
Loading Rate 20-60 gpm/ft² (50-150 m/h)
Packing Material Plastic media; 20-40 ft²/ft³ surface area

6.5 Advanced Oxidation Processes (AOP)

Process Description
O₃/H₂O₂ Generate hydroxyl radicals (•OH); oxidize refractory organics; H₂O₂:O₃ = 0.3-0.5 mg/mg
UV/H₂O₂ UV photolysis of H₂O₂; dose 3-10 mg/L H₂O₂; UV >400 mJ/cm²
O₃/UV Enhance ozone decomposition; produce •OH radicals
Applications Degrade pesticides, pharmaceuticals, endocrine disruptors, taste/odor compounds

6.6 Corrosion Control

Method Details
pH Adjustment Raise pH to 7.5-8.5 with lime, soda ash, or NaOH to reduce corrosivity
Alkalinity Addition Increase buffering capacity; reduce pH swings; target 30-100 mg/L as CaCO₃
Corrosion Inhibitors Orthophosphate: 1-3 mg/L as PO₄; zinc orthophosphate; polyphosphates
Langelier Index (LI) LI = pH - pHs; LI > 0 supersaturated (scaling); LI < 0="" unsaturated="" (corrosive);="" target="">
Calcium Carbonate Saturation Maintain slight supersaturation; protective CaCO₃ film on pipes

6.7 Fluoridation

Chemical Details
Target Concentration 0.7 mg/L F⁻; dental health benefits
Hydrofluosilicic Acid H₂SiF₆; 23% F⁻; liquid; most common; 1 mg/L F⁻ requires 4.3 mg/L H₂SiF₆
Sodium Fluoride NaF; 45% F⁻; powder or liquid; 1 mg/L F⁻ requires 2.2 mg/L NaF
Sodium Fluorosilicate Na₂SiF₆; 61% F⁻; powder; 1 mg/L F⁻ requires 1.6 mg/L Na₂SiF₆

7. Sludge Handling and Disposal

7.1 Sludge Production

Source Sludge Quantity
Coagulation/Flocculation 0.2-0.5% of water treated by volume; 2-4% solids concentration
Alum Sludge 3.5 mg sludge per mg alum added (dry weight basis)
Lime Sludge 2.6 mg sludge per mg hardness removed as CaCO₃ (dry weight)
Filter Backwash 2-5% of plant flow; 100-500 mg/L TSS

7.2 Thickening

Method Details
Gravity Thickening Increase solids from 1-3% to 4-8%; detention time: 12-24 hr; alum/iron sludge
Dissolved Air Flotation Increase solids to 3-6%; A/S ratio 0.02-0.06; good for alum sludge
Centrifuge Increase solids to 10-20%; bowl speed 1000-4000 rpm; high polymer dose

7.3 Dewatering

Method Cake Solids/Details
Belt Filter Press 15-25% solids; polymer dose 2-10 lb/ton; low energy; alum sludge 12-18%
Plate and Frame Press 30-50% solids; batch operation; high pressure; polymer conditioning required
Centrifuge 12-25% solids for alum; 15-30% for lime; continuous operation; high speed
Sand Drying Beds 30-40% solids; area: 1-2 ft²/capita; 4-6 week drying; climate dependent
Freeze-Thaw Cold climate; natural freezing improves dewaterability

7.4 Disposal Methods

Method Details
Landfill Most common for alum/iron sludge; non-hazardous; meet solids content requirements
Land Application Lime sludge; agricultural benefit; soil amendment; metal content limits apply
Discharge to Sanitary Sewer Return backwash water; coordinate with WWTP; increase BOD/TSS loading
Lagoon Storage Temporary or long-term; 1-3 year accumulation; area-intensive
Recovery of Coagulants Acid dissolution of alum sludge; recover Al₂(SO₄)₃; pH 2-3; reuse after neutralization

7.5 Key Equations

Equation Variables
Sludge Volume (gpd) = Q × SS × 8.34 / (ρ × % solids) Q = flow (MGD); SS = suspended solids (mg/L); ρ = sludge density (lb/gal); % solids as decimal
Solids Loading (lb/day) = Q × SS × 8.34 Q = flow (MGD); SS = suspended solids concentration (mg/L)
% Solids = (Dry Weight / Wet Weight) × 100 Measure moisture content and calculate solids percentage

8. Water Quality Parameters and Standards

8.1 Physical Parameters

Parameter Standard/Criteria
Turbidity ≤0.3 NTU (95% of samples); ≤1.0 NTU (max) for filtered water; measured by nephelometry
Color ≤15 color units (CU); true color vs. apparent color
Temperature Affects disinfection, chemical reactions, viscosity; design for 1-25°C range
Total Dissolved Solids (TDS) Secondary MCL = 500 mg/L; aesthetic concern

8.2 Chemical Parameters

Parameter MCL/Limit
pH 6.5-8.5 (secondary standard); affects corrosion and disinfection
Iron (Fe) 0.3 mg/L (secondary); staining, taste issues
Manganese (Mn) 0.05 mg/L (secondary); staining, taste issues
Sulfate (SO₄²⁻) 250 mg/L (secondary); laxative effect
Chloride (Cl⁻) 250 mg/L (secondary); corrosion, taste
Fluoride (F⁻) 4.0 mg/L (primary MCL); 2.0 mg/L (secondary); dental fluorosis
Nitrate (NO₃⁻-N) 10 mg/L (primary MCL); methemoglobinemia in infants
Nitrite (NO₂⁻-N) 1 mg/L (primary MCL)

8.3 Inorganic Contaminants (Primary MCLs)

Contaminant MCL
Arsenic (As) 10 μg/L; carcinogen
Lead (Pb) Action Level = 15 μg/L; 90th percentile at tap
Copper (Cu) Action Level = 1.3 mg/L; 90th percentile at tap
Chromium (Cr) 100 μg/L (total)
Barium (Ba) 2 mg/L
Cadmium (Cd) 5 μg/L
Mercury (Hg) 2 μg/L (inorganic)
Selenium (Se) 50 μg/L

8.4 Organic Contaminants

Contaminant MCL
Total THMs 80 μg/L (annual running average)
HAA5 60 μg/L (annual running average)
Benzene 5 μg/L
Vinyl Chloride 2 μg/L
PCBs 0.5 μg/L
Atrazine 3 μg/L

8.5 Microbiological Parameters

Parameter Standard
Total Coliform No more than 5% positive samples per month (systems taking ≥40 samples)
E. coli MCL = 0; indicates fecal contamination; acute health risk
Heterotrophic Plate Count ≤500 CFU/mL; distribution system integrity indicator
Giardia 3-log (99.9%) removal/inactivation required
Viruses 4-log (99.99%) removal/inactivation required
Cryptosporidium Removal credit based on source water concentration; filtration essential

8.6 Drinking Water Treatment Goals

Parameter Typical Goal
Turbidity After Filtration ≤0.1 NTU (for optimal pathogen removal)
Chlorine Residual 0.2-2.0 mg/L free Cl₂ in distribution system
pH (Distribution) 7.0-8.5; optimize for corrosion control
Alkalinity 30-100 mg/L as CaCO₃; adequate buffering
Hardness 75-150 mg/L as CaCO₃; acceptable range
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