Membrane Separation Flux Calculator
Computes the required membrane area for reverse osmosis or ultrafiltration systems given flow rate, recovery, and pressure conditions. Use it when sizing membranes for water treatment, desalination, or industrial separation plants.
About this calculator
Permeate flux (J) describes the volume of fluid passing through a unit area of membrane per unit time. For pressure-driven membrane processes, flux follows the solution-diffusion or pore-flow model: J = L_p × (ΔP − Δπ), where L_p is the membrane permeability constant (L/m²·h·bar), ΔP is the transmembrane pressure (TMP), and Δπ is the osmotic pressure of the feed. The required membrane area is then: A = Q_p / J, where Q_p = Q_f × (recovery / 100) is the permeate flow rate. This calculator outputs A directly: A = [Q_f × (recovery/100)] / [L_p × max(TMP − Δπ, 0.001)]. When TMP ≤ Δπ, net driving pressure is zero and no permeation occurs. Higher permeability constants indicate more open membranes (ultrafiltration vs. reverse osmosis).
How to use
Design an RO system: feed flow Q_f = 100 m³/h, recovery = 75%, TMP = 800 kPa, osmotic pressure = 300 kPa, permeability L_p = 4 L/m²·h·bar. Convert pressures to bar: TMP = 8 bar, Δπ = 3 bar. Net driving pressure = 8 − 3 = 5 bar. Flux J = 4 × 5 = 20 L/m²·h. Permeate flow Q_p = 100 × 0.75 = 75 m³/h = 75,000 L/h. Required area A = 75,000 / 20 = 3,750 m². Divide by a standard module area (e.g., 37 m² per 8-inch element) to find the number of pressure vessels needed. This area estimate guides procurement and system layout.
Frequently asked questions
What is transmembrane pressure and how does it drive membrane flux?
Transmembrane pressure (TMP) is the pressure difference across the membrane, calculated as the average of feed and concentrate pressures minus the permeate pressure. It is the mechanical driving force that pushes solvent through the membrane against osmotic resistance. Net driving pressure (NDP = TMP − Δπ) determines actual flux; if TMP does not exceed the osmotic pressure of the solution, no permeation occurs. Engineers must set TMP high enough to achieve target flux while avoiding membrane compaction or irreversible fouling at excessively high pressures.
How does water recovery ratio affect the concentration polarization and fouling in an RO system?
Recovery ratio is the fraction of feed converted to permeate, and higher recovery means the concentrate stream becomes increasingly concentrated. This raises the local salt concentration at the membrane surface — a phenomenon called concentration polarization — which increases osmotic pressure and reduces flux. Severe concentration polarization promotes scaling (precipitation of sparingly soluble salts like CaCO₃ and CaSO₄) and biofouling. Most single-pass RO systems operate at 50–80% recovery; exceeding the design limit without antiscalant dosing or pH adjustment significantly shortens membrane life.
What is the difference between reverse osmosis and ultrafiltration membrane permeability constants?
Permeability (L_p) reflects how easily a solvent passes through the membrane and is strongly linked to pore size. Ultrafiltration (UF) membranes have pores of 0.01–0.1 μm and typical L_p values of 50–500 L/m²·h·bar, suitable for removing colloids, proteins, and bacteria at low pressures (1–5 bar). Reverse osmosis membranes are dense (near-zero pore size) with L_p of 1–10 L/m²·h·bar, requiring 5–80 bar to overcome osmotic pressure and remove dissolved salts. Nanofiltration falls between, with L_p of 5–50 L/m²·h·bar and selective rejection of divalent ions.