ASTM D4189 Reverse-Osmosis SDI-15 & Plugging Formula

Crystal-clear 0.3 NTU turbidity feedwater can still carry sub-micron colloidal silica that spikes SDI-15 past 5.0—blinding lead-element RO feed spacers and voiding membrane warranties!

Optical nephelometers (`NTU`) barely scatter light off `< 0.5` um colloidal clay, iron oxyhydroxide, and bacterial EPS—yet those exact colloids cake spiral-wound **Polyamide Reverse-Osmosis (`RO`) Lead Elements**! **ASTM `D4189`** therefore measures dead-end filtration decay across a `47`-mm, **`0.45`-um cellulose nitrate membrane disk regulated at `207` kPa (`30.0` psi)**: timing **`t_i` (`seconds` to collect the initial `500` mL)** and **`t_f` (`seconds` to collect a second `500` mL after `T = 15` minutes of continuous flow)** yields **Membrane Plugging Factor `PF = (1 - (t_i / t_f)) * 100%`** and **Silt Density Index `SDI_T = PF / T`** (`%/min`)! Spiral-wound RO manufacturers mandate **`SDI_{15} < 3.0`** for low-fouling operation and **`SDI_{15} <= 5.0` absolute warranty ceiling** (furthermore, if `PF > 75%` during a `15`-min run, ASTM `D4189` invalidates linear `SDI_{15}` and requires switching to `T = 5` min `SDI_5`)!

Verify on Ultrafiltration (`UF`)-Pretreated Seawater RO Feed—Initial_`500mL`_Time `t_i` = 28.5 s (B2), Final_`15min`_`500mL`_Time `t_f` = 46.2 s (B3), and Elapsed_Interval `T` = 15.0 min (B4): Flow-Retention Ratio `t_i / t_f` equals `0.617` (E2), `0.45`-um Plugging Factor `PF` equals `38.31%` (`<= 75%` valid ASTM linear range! E3), **`SDI_{15}` equals `2.55`** (`< 3.0` clean RO feed! E4), utilizing just **`51.1%` of the `5.0` RO warranty ceiling** (E5)!

ASTM D4189 0.45-um Dead-End Membrane Plugging & SDI-15 Formula

Validate `Initial_Time t_i` in `[10, 120]` s, `Final_Time t_f >= t_i` up to `1,200` s, and `Test_Interval T` in `[5, 15]` min!

=LET(ti_s, B2, tf_s, B3, tm_m, B4, pf_p, (1 - (ti_s / tf_s)) * 100, sd_i, pf_p / tm_m, IF(OR(ti_s < 10, ti_s > 120, tf_s < ti_s, tf_s > 1200, tm_m < 5, tm_m > 15), "Invalid SDI Input", ROUND((sd_i / 5) * 100, 1)))

Broken UF Fiber / Coagulant Under-Dose (`t_f = 168` s -> `SDI_15 = 5.54`) RO Blinding Check

Snap hollow-fiber UF capillaries or lose ferric chloride coagulant during a spring runoff event so final `500`-mL collection drags out to `B3 = 168.0` s: Plugging Factor E3 hits **`83.04%`** (`> 75%` -> re-test as `SDI_5`!) while `SDI_{15}` E4 climbs to **`5.54`** (**`110.7%` of the `5.0` RO warranty max** in E5)—commanding automatic feed diversion before irreversible colloidal cake locks lead RO vessels!

=IF(ISTEXT(E5), E5, ROUND(((1 - (B2 / B3)) * 100) / B4, 2))

Further reading

• Arte Sheets Lesson — Bohart-Adams BDST Activated-Carbon Service Time Formula
• Arte Sheets Lesson — Coe-Clevenger Continuous Thickener Area & Solids Flux