membrane-ro-fundamentals

What this skill does

# RO & EDI Process Fundamentals

Reference for water-treatment expertise: formulas, normative standards, vendor design envelopes, water chemistry, and bilingual terminology.

Convention markers used throughout the membrane skills:
- `⚠️` — likely bug or incorrect numerical approximation in calling code; highest priority
- `💡` — enhancement opportunity (new KPI, new model field, refined threshold)

---

## §1 — RO Process Fundamentals

All formulas in SI (LMH, bar, °C) with US field-unit (GFD, psi, °F) variant noted. Variables: `Qf` feed flow, `Qp` permeate, `Qc` concentrate, `Cf`/`Cp`/`Cc` concentrations, `Am` membrane area, `T` temperature.

### 1.1 Recovery (Water Recovery / Recupero)

```
Y = Qp / Qf
```

Typical ranges (vendor-dependent):
- SWRO single-pass: 35–50 %
- BWRO: 70–85 %
- BWRO high-recovery (w/ antiscalant): 90 %+
- Double-pass RO+RO overall: 70–80 %

Source: ASTM D6161-19; DuPont 45-D01504; Hydranautics TSB 107.

### 1.2 Concentration Factor (CF)

```
CF_ideal = 1 / (1 - Y)                          # for R = 1
CF_real  = (1 - Y·(1 - R)) / (1 - Y)            # for rejection R
```

At Y = 0.75 and R = 0.99: CF_ideal = 4.00, CF_real ≈ 3.97 (error < 1 %), so the ideal form is acceptable for SWRO/BWRO design.

Source: DuPont 45-D01591 (Design Equations).

### 1.3 Salt Rejection — three definitions

| Variant | Symbol | Formula | When used |
|---|---|---|---|
| Observed (apparent) | R_obs | `1 − Cp/Cf` | What instruments measure |
| System (log-mean) | R_sys | `1 − Cp / mean(Cf, Cc)` | Standard reporting |
| Intrinsic (at wall) | R_int | `1 − Cp / (β · mean(Cf, Cc))` | Corrected for polarization |

Concentration polarization factor:
```
β = Cwall / Cbulk = exp(0.7 · Y_element)
```
where `Y_element` is per-element recovery. FilmTec design limit: β ≤ 1.2 → Y_element ≤ 18 % (the **18 % per-element rule**). Hydranautics is more conservative at 15 %.

⚠️ A code path that confuses `R_obs` with `R_sys` will under-report rejection by 5–15 % at high recovery. Always specify which definition the calculator returns.

Sources: DuPont 45-D01591; Hydranautics *Terms and Equations of RO*.

### 1.4 Permeate Flux (Jw)

```
Jw = A · NDP · TCF · FF                          # vendor model
Jw = Qp / Am                                     # operational
```

`A` = water permeability (LMH/bar), `FF` = fouling factor (0.85 design / 0.70 EOL).

Unit conversion: **1 GFD = 1.6987 LMH** (≈ 1.70).

Typical design flux windows (vendor consensus):

| Application | GFD | LMH |
|---|---|---|
| SWRO open intake (SDI 3–5) | 7–9 | 12–15 |
| SWRO beach well (SDI < 2) | 8–10 | 14–17 |
| BWRO well (SDI < 3) | 14–18 | 24–30 |
| BWRO surface (SDI 3–5) | 10–14 | 17–24 |
| RO permeate / 2nd pass | 20–30 | 34–51 |

⚠️ A hard-coded `flux_max = 25 LMH` threshold is incorrect for SWRO (well above limit) and conservative for BWRO well (well below limit). Threshold must be water-source-aware.

Sources: DuPont 45-D01695 Rev 14 (Feb 2026); Hydranautics TSB 105; AMTA *Optimum Flux Rates*.

### 1.5 Salt Flux (Js)

```
Js = B · (mean(Cf,Cc) − Cp) ≈ B · mean(Cf,Cc)
Cp = Js / Jw                                     # key inverse relation
```

`B` is **temperature-dependent but pressure-independent** (unlike `A`). At cold feed temperature, `Jw` drops while `Js` is relatively unchanged → `Cp` rises → permeate quality degrades. Cold-water permeate TDS spikes are explained by this relation.

Source: DuPont 45-D01591; Hydranautics *Terms and Equations*.

### 1.6 Net Driving Pressure (NDP)

```
NDP = (Pf + Pc)/2 − Pp − (πw − πp)
    = mean_feed_pressure − permeate_pressure − osmotic_differential_at_wall
```

with `πw = β · π_mean(Cf,Cc)` (osmotic pressure at membrane wall, corrected for polarization).

Source: ASTM D4516-19a §6; DuPont 45-D01591.

### 1.7 Osmotic Pressure (π)

**Rigorous Van't Hoff:**
```
π = i · M · R · T                                # i ≈ 1.8–2.0 for NaCl
                                                 # R = 0.08314 L·bar/(mol·K)
                                                 # T in Kelvin
```

**Engineering shortcut (industry standard at 25 °C):**
```
π [psi] ≈ 0.0085 · TDS [ppm]
π [bar] ≈ 0.000586 · TDS [ppm]
```

Shortcut accuracy:
- ±3 % for NaCl-dominated brackish (1 000–10 000 ppm)
- ±5 % for seawater (32 000–40 000 ppm) — agrees with Pitzer model up to 70 g/L NaCl
- Diverges > 10 % for sulfate-rich or hardness-dominated brines — use OLI/PHREEQC instead

Seawater rule of thumb: 35 000 ppm → π ≈ 25–28 bar bulk; ≈ 32–35 bar at wall with β = 1.15.

⚠️ A formula returning π ≈ 8 bar for seawater under-estimates by 3–4× — verify constants and unit handling. The correct order of magnitude for seawater is **25–35 bar**.

Source: Pitzer comparison (Tandfonline 2019); Stark-Water RO Working Principle Guide; FilmTec 45-D01591.

### 1.8 Temperature Correction Factor (TCF)

ASTM D4516-19a normalizes flux to a 25 °C reference. General exponential form:

```
TCF = exp[ Ke · (1/298 − 1/(273 + T)) ]
```

Membrane-chemistry constants (Hydranautics TSB 107.28 Apr 2025; FilmTec 45-D01616 Rev 10 Feb 2022):

| Membrane type | Ke | Regime |
|---|---|---|
| FilmTec BW30 / SW30 (T ≥ 25 °C) | **3 020** | Hot |
| FilmTec BW30 / SW30 (T < 25 °C) | **2 640** | Cold (flux drops faster) |
| Hydranautics CPA / ESPA | 2 500–3 480 | Element-specific (TSB 107) |
| Hydranautics SWC seawater | ~3 020 | |

Practitioner shortcut: TCF ≈ 1.03 per °C around 25 °C; doubles every ~25 °C rise.

### 1.9 Normalized Permeate Flow (NPF) — ASTM D4516-19a §7

```
NPF = Qp_meas · (NDP_std / NDP_actual) · (TCF_std / TCF_actual)
```

Action thresholds (industry consensus):
- NPF drop **10 %** vs baseline → schedule CIP
- NPF drop **15 %** → CIP mandatory
- NPF drop **30 %** → autopsy / replacement evaluation

⚠️ NPF cannot be computed without a baseline. Code paths declaring `NPF` as a field but never populating it because `calculate_kpis()` receives no baseline are silently broken.

### 1.10 Normalized Salt Passage (NSP) — ASTM D4516-19a §8

```
NSP = SP_meas · (mean_C_std / mean_C_actual) · (EPF_actual / EPF_std) · (STCF_std / STCF_actual)
```

where `SP = Cp / mean(Cf, Cc)` and `STCF` is the salt-passage temperature factor (different exponent constant: `Ks ≈ 2 200`).

Action threshold: NSP rise **15 %** → integrity check via ASTM D6908 VDT or ASTM D3923 leak test.

### 1.11 Element / Vessel / Stage / Train Hierarchy

```
Train (skid)
└── Stage 1                  ┐ array typically 2:1 or 3:2:1
    ├── Pressure Vessel       │
    │   ├── Element 1         │ standard 8"×40" or 4"×40"
    │   ├── Element 2         │ 6–8 elements per vessel
    │   └── …                 │ typical per-vessel Y = 8–15 %
    └── Stage 2 / 3            reuses concentrate as feed
```

Per-stage recovery rule of thumb:
- Stage 1 (8 elements, single pass): Y₁ ≈ 50 %
- 2-stage train: `Ysys = 1 − (1−Y1)·(1−Y2) ≈ 75 %`
- 3-stage train: 85–90 % for high-recovery BWRO

Per-element max: Y_element ≤ 18 % (FilmTec) or ≤ 15 % (Hydranautics).

---

## §2 — Authoritative Standards Reference

| Standard | Title | Edition | When to invoke |
|---|---|---|---|
| **ASTM D4516-19a** | Standardizing RO Performance Data | 2019 | Normalize NPF, NSP — any commissioning, surveillance, warranty claim |
| **ASTM D3923** | Detecting Leaks in RO and NF Devices | 2023 (also 2018) | New-element acceptance; suspected O-ring / glue-line failure |
| **ASTM D3739-19** | Calculation of the Langelier Saturation Index for RO | 2019 | CaCO₃ scaling prediction; valid for concentrate TDS 10–10 000 mg/L |
| **ASTM D4582** | Stiff & Davis Stability Index | current | CaCO₃ scaling at TDS > 10 000 mg/L |
| **ASTM D4194-23** | Operating Characteristics of RO and NF Devices | 2023 | Short-term (< 24 h) factory or commissioning test — not for plant design |
| **ASTM D4195** | Water Analysis for RO/NF Application | 2014 (withdrawn 2023, still authoritative for scope) | Feedwater characterization scope |
| **ASTM D6161-19** | Terminology for Membrane Separation | 2019 | Definitive glossary; ci