Spiral-Wound Test Planner

Element. 1-D plug flow along the feed channel, 60 cells per element. Mass transfer from Schock & Miquel (1987), Sh = 0.065 Re^0.875 Sc^0.25 with Re on the interstitial velocity and the spacer hydraulic diameter; channel friction λ = 6.23 Re^−0.3. Film model c_m = c_p + (c_b − c_p) e^J_v/k with c_p = (1 − R_int) c_m. Osmotic pressure by van't Hoff (dilute solutions; for concentrated aqueous electrolytes use the Pitzer-based CP Calculator). Feed-channel cross-section A_ch = A·h / 2L from the active area, element length and spacer thickness.

Cartridge. Concentration polarisation from the buoyancy-driven model of Geraldes et al. (2026), k = 0.28 U* 𝒢^1/4 Sc^−1/4, at the run-mean pressure and bulk concentration. The planner solves for the cartridge feed concentration whose run-mean wall concentration c_m equals the area-mean c_m of the element at the same ΔP. The same membrane at the same ΔP and c_m gives the same flux, so the cartridge flux is taken equal to the element mean flux.

Properties. Solvent density and viscosity from handbook data (Andrade fit, 10–50 °C). Solute diffusivity by Stokes–Einstein with the molecular radius from molar mass and solute density; density contrast β = (1 − ρ_solvent/ρ_solute)/ρ_solvent (volume-additive mixture). Both can be overridden by measured values.

Validity. The O-CMF correlation is dimensionless: it applies to any Newtonian solvent whenever the buoyancy parameter 𝒢, the Schmidt number and J_v/k lie in the ranges over which it was established (𝒢 7×10⁻⁹–5×10⁻⁶, Sc 700–2200, J_v/k ≤ 1.5). The planner checks each run and flags any group outside its range; Sc enters only as Sc^−1/4, so a modest excursion in Sc is a short extrapolation. The property inputs — β (volume-additive mixture) and D (Stokes–Einstein) — are estimates: replace them by measured values when you have them. A quick in-system check: two runs at the same speed with feed concentrations differing by a factor of 3 should show the observed rejection rising with C₀ as k ∝ C₀^1/4 predicts. Solvents denser than the solute (DCM, chloroform, DMSO with most solutes) give β ≤ 0: the retained layer is stably stratified, the buoyancy model does not apply and the planner stops.

Rejection. A membrane's intrinsic rejection can depend on c_m. That is why the planner reproduces c_m instead of transferring a rejection measured elsewhere. When the element spans a wide range of c_m (high recovery, several elements in series), the programme adds inlet, mid-length and outlet runs so the membrane is tested across that range.