| 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 |
| 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 |
| 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 |
| 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) |
| 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 |
| 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) |
| 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 |
| 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·(ρp-ρw))/(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 |
| 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>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) |
| Layer | Specifications |
|---|---|
| Anthracite (Top) | Depth: 18-24 in; ES: 0.9-1.2 mm; UC: <1.5; specific="" gravity:="">1.5;> |
| Sand (Bottom) | Depth: 9-12 in; ES: 0.45-0.55 mm; UC: <1.5; specific="" gravity:="">1.5;> |
| Filtration Rate | 4-6 gpm/ft² (10-15 m/h) |
| Advantages | Longer filter runs; higher filtration rates; depth 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 |
| 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 |
| 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 |
| 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 |
| 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) |
| 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 |
| 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 |
| 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%) |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 CaCO₃60;> |
| 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) |
| 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 |
| 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 |
| 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="">1> |
| 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 |
| 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%="">0.001> |
| 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="">5;><1 ntu;="" remove="" hardness,="" fe,="" mn;="" antiscalant="">1> |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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) |
| 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 |
| 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 |
| 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 |
| 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 |