Ultrafiltration System Design Calculation Example

Known Conditions of Ultrafiltration System Design

Design one ultrafiltration (UF) unit with a design permeate flow rate of 150 m³/h.

Design Calculations of Ultrafiltration System Design

Basic Parameters

Based on the manufacturer’s membrane selection manual:
Membrane area per module: 77 m²
Design flux: 50 LMH
Production time: 30 min
Backwash: 1 time per cycle, duration 3 min
Chemically Enhanced Backwash (CEB): Twice per day (acid CEB once every 12 operating hours, then caustic CEB once every 12 operating hours)
Duration of each CEB: 21 min

Operating Cycle

One complete operating cycle time = 30 + 3 = 33 (min)
With 2 CEBs per day (21 min each), the number of operating cycles (backwash events) per day is: (24 * 60 – 21 * 2) / 33 = 42.36 (cycles)

Required Number of Membrane Modules

Actual daily production time = 30 * 42.36 / 60 = 21.18 (h)
Since the UF system needs to provide continuous permeate flow, the flow rate must be adjusted to account for downtime (backwash, CEB):
Qc = 150 m³/h * 24 h / 21.18 h = 170 m³/h
Calculate the number of UF membrane modules (n):
n = 170 m³/h / (50 LMH * 77 m²) ≈ 44 modules
*(Note: Unit consistency: 170 m³/h = 170,000 L/h; 170,000 L/h / 77 m² / 50 L/(m²·h) ≈ 44.2)*

Ancillary Equipment Design

UF Backwash Pump (Variable Frequency Drive - VFD)

Backwash flux: 100 LMH (refer to manufacturer’s guidelines for specific requirements).
Backwash pump flow rate = 44 modules * 77 m² * 100 LMH / 1000 ≈ 339 m³/h
Head: 20 m

UF Chemically Enhanced Backwash (CEB) Dosing Pumps

Example with Hydrochloric Acid (HCl):
Dosage: 500 mg/L as HCl
32% HCl density: 1.15 g/mL
Dosing flow rate = 500 g/m³ * 339 m³/h / 32% / 1.15 kg/L / 1000 = 461 L/h
Example with Caustic Soda (NaOH):
Dosage: 500 mg/L as NaOH
30% NaOH density: 1.32 g/mL
Dosing flow rate = 500 g/m³ * 339 m³/h / 30% / 1.32 kg/L / 1000 = 428 L/h
Example with Sodium Hypochlorite (NaOCl):
Dosage: 500 mg/L as NaOCl
10% NaOCl density: 1.18 g/mL
Dosing flow rate = 500 g/m³ * 339 m³/h / 10% / 1.18 kg/L / 1000 = 1436 L/h
Note: For VFD-controlled backwash pumps, the pump frequency (and thus flow) is often reduced to approximately half during CEB. Consequently, the dosing pump flow rates should be adjusted accordingly. The chemical concentrations above are examples only; refer to the specific membrane manufacturer’s manual for final design values.

UF Cleaning (Flush/CIP) Pump

Cleaning flow rate per membrane module: 2 m³/h (refer to manufacturer’s guidelines).
Cleaning pump flow rate = 44 modules * 2 m³/h = 88 m³/h
Head: 25 m

Cleaning Tank Sizing

Volume to fill membranes (V1):
Manufacturer data: ~39 L per module.
V1 = 44 modules * 39 L / 1000 = 1.72 m³
Volume in cleaning pipeline (V2):
Pipe diameter: DN125 (0.125 m radius r = 0.0625 m)
Estimated pipe length: 50 m
V2 = 50 * π * (0.0625)² = 50 * 3.14 * 0.00390625 ≈ 0.61 m³
Volume in cartridge filter housing (V3):
Housing diameter: DN350 (radius r = 0.175 m)
Effective height: H = 1.2 m
Housing volume = 1.2 * π * (0.175)² = 1.2 * 3.14 * 0.030625 ≈ 0.12 m³
Assuming cartridges occupy ~5% of volume, net volume = 0.12 m³ * 0.95 = 0.11 m³
Calculate Cleaning Tank Volume (V):
Total system volume = V1 + V2 + V3 = 1.72 + 0.61 + 0.11 = 2.44 m³
Apply safety factor (f = 1.2 for 20% margin): V = 2.44 m³ * 1.2 ≈ 2.93 m³
Consider minimum water level for recirculation (e.g., 0.5 m³). Select a standard tank size: 4 m³

Compressed Air for Air Scour (During Backwash)

Manufacturer data: Air scour flow rate per module = 10 Nm³/h (normal conditions: 0°C, 1 atm)
Air scour duration per event: 1 minute
Given site conditions for compressed air: Gauge pressure P1 = 7 bar, Temperature T1 = 25°C (298.15 K)
Normal conditions (reference): P2 = 1 atm = 1.01325 bar, T2 = 0°C (273.15 K)
Calculate air volume required under normal conditions (V2_Nm³) for one scour event:
V2_Nm³ = (10 Nm³/h per module * 44 modules) * (1 min / 60 min/h) = 7.33 Nm³
Convert normal volume (V2) to actual volume at site conditions (V1):
Absolute pressure at site: P1_abs = 7 bar(g) + 1.01325 bar(atm) = 8.01325 bar(a)
Apply Ideal Gas Law: P1_abs * V1 / T1 = P2 * V2 / T2
Solve for V1: V1 = V2 * (P2 / P1_abs) * (T1 / T2) = 7.33 Nm³ * (1.01325 bar / 8.01325 bar) * (298.15 K / 273.15 K)
V1 ≈ 7.33 * 0.1265 * 1.0915 ≈ 1.01 m³
Conclusion: Based on the calculation, each air scour event requires approximately 1 m³ of compressed air at the site conditions (7 bar gauge pressure, 25°C).