Langelier Saturation Index: Run the Number on Your RO Concentrate

Feed water LSI comes back at negative 0.1, the design looks clean, and six months later the tail elements in the second stage are scaled, differential pressure is climbing, and somebody's pricing membranes.

The calculation was fine. It described the wrong stream. The Langelier Saturation Index tells you the calcium carbonate saturation of whatever water you put into it, and the water that scales a membrane is the concentrate leaving the last element, where calcium and alkalinity have been concentrated by everything the system already pulled out as permeate. Hydranautics publishes its saturation limits against the concentrate. So does everyone else.

So this calculation has two parts. Run the index on your feed, then push your recovery through it and see where the number lands at the back of the array.

What the LSI Is Made Of

LSI is a subtraction. Measure the water's pH, calculate the pH at which it'd be saturated with calcium carbonate, take the difference.

Hach Method 8073 gives the working form as pHs = A + B minus C minus D, where A is a temperature constant, B is a total dissolved solids constant, C is the base-10 logarithm of calcium hardness in mg/L as CaCO3, and D is the base-10 logarithm of total alkalinity in mg/L as CaCO3. LSI is then your measured pH minus that pHs. Positive means the water wants to deposit calcium carbonate. Negative means it'll dissolve it.

Check which convention your calculator uses before you compare numbers with anyone. The other common form writes pHs as (9.3 + A + B) minus (C + D), and there A is the TDS term, B is the temperature term, and C subtracts 0.4 to move calcium onto an ion basis. Same index, different bookkeeping. Run the feed water below through both and you get pHs of 7.49 and 7.57. Close enough to design on, far enough apart to start an argument.

The temperature constant runs backwards from intuition: A is 2.60 at 0 °C, 2.00 at 25 °C, and 1.70 at 40 °C. Smaller A, lower pHs, higher LSI. Calcium carbonate is one of the few scales that gets less soluble as water warms, so a summer feed at 30 °C is closer to scaling than the same water in February. The TDS constant barely moves: B runs from 9.70 at zero TDS to 9.90 at 1,000 mg/L, so between a 400 and a 1,000 mg/L feed you're arguing over four hundredths of a pH unit.

The index also has a validity window most calculators don't mention. Hach limits it to waters above 40 mg/L alkalinity, with enough calcium present, between pH 6.5 and 9.5. Outside that it computes and means very little.

Recovery Is the Whole Argument

Concentration factor is the bridge between the number you measured and the number that matters. At recovery R, the concentrate carries roughly 1 divided by (1 minus R) times the feed concentration of anything the membrane rejects. WC&P put it plainly in its May 2026 design series: at 75 percent recovery, the reject stream is almost four times the feed.

Look what that does to the arithmetic. Calcium and alkalinity both multiply by the concentration factor, and both appear in pHs as logarithms that get subtracted, so pHs drops by about twice the log of CF. A rule you can run on a phone:

Work a real one. Feed at pH 7.4, 25 °C, 600 mg/L TDS, 180 mg/L calcium hardness as CaCO3, 140 mg/L alkalinity as CaCO3. That's A = 2.00, B = 9.89, C = 2.255, D = 2.146, so pHs = 7.489 and feed LSI = negative 0.09. Looks safe.

Run it at 75 percent recovery. Calcium goes to 720, alkalinity to 560, and pHs falls to 6.29. Concentrate pH is higher than feed pH in a normal brackish system, because bicarbonate and carbonate concentrate while dissolved CO2 passes through the membrane and doesn't. Call it 7.6. Concentrate LSI comes out at +1.31, a swing of 1.4 index units without anybody touching a valve, from a water that dissolves calcium carbonate to one near the ceiling of what a polymer antiscalant is rated to hold.

The hand calculation assumes complete rejection and ignores the profile inside the vessel, so treat it as direction and magnitude. Run the manufacturer's software before you commit a design.

The Limits Your Supplier Publishes

Hydranautics publishes three concentrate limits, the clearest numbers in the industry:

Technical Application Bulletin TAB111 explains negative 0.2: it puts the concentrate two tenths of a pH unit below saturation, which buys room for real-plant pH excursions. The same bulletin notes some suppliers claim efficacy to +2.5, and calls +1.8 the conservative design level. Hydranautics' alarm table lists a maximum reported LSI of +2.9 against an internal alarm at +1.8.

Worth knowing before you quote a number back to an engineer: TAB111 is inconsistent with itself on sodium hexametaphosphate. Its antiscalant section gives SHMP a maximum concentrate LSI of +1.0. Its glossary, in the same PDF, says +0.5, and the design limits sheet also says less than +0.5. If you're designing on SHMP, take +0.5 and stop arguing. It's the number that appears twice, and SHMP has enough other problems that the margin is cheap.

One more boundary. LSI's ionic strength correction stops behaving above roughly 10,000 mg/L TDS, and Hach's B table tops out at 1,000. Past that the Stiff and Davis Saturation Index takes over, same pH minus pHs structure with the saturation pH corrected for ionic strength. Hydranautics applies identical limits to both, so your thresholds don't move when you switch.

Acid, Antiscalant, or Less Recovery

Three levers move concentrate LSI. They cost different things.

Acid injection drops feed pH, and LSI drops faster than the pH does. Mineral acid converts bicarbonate to carbonic acid on its way through, so alkalinity falls along with pH and the D term shrinks, which pushes pHs up while the measured pH comes down. Both ends of the subtraction move the same way. On the feed water above, taking pH from 7.4 to 6.9 drops alkalinity from 140 to about 119 mg/L and moves LSI 0.57 units, roughly 1.15 units of index per unit of pH, climbing past 1.2 as you dose harder. Budget acid on that, and remember that under about pH 6.5 you've left the window where the index means anything. Sulfuric costs less to operate than hydrochloric and fumes less, and TAB111 recommends it on that basis. The catch is that sulfuric adds sulfate to a stream you're about to concentrate four or five times, and calcium sulfate and barium sulfate are the scales next in the queue. Both TAB111 and WC&P point to HCl when sulfate scaling is already a concern. Solve carbonate, create gypsum: a bad trade you can make without noticing.

Antiscalant raises the ceiling instead of lowering the water. TAB111 puts typical dosing at 2 to 5 ppm. It removes no hardness and no calcium; it interferes with crystal growth so a supersaturated stream stays in solution long enough to leave the vessel.

Compute your consumption before you take a quote. A 50 gpm feed at 3 ppm runs 72,000 gallons a day, so 818 grams a day of as-supplied product. Call it 1.8 lb a day, near 80 gallons of liquid concentrate a year. Price per gallon varies enough by formulation and volume that a range here would be a guess, so bid it against that number rather than against a dose.

Dropping recovery is the lever nobody wants and the only one that attacks the mechanism. Going from 80 to 75 percent takes 0.2 index units off the concentrate and costs you feed water and pump energy. On a well with cheap water and expensive membranes, that's frequently the cheapest option on the table.

Two installation details cause more trouble than the chemistry does. Inject acid upstream of the antiscalant point and mix it in, because a concentrated pocket of low-pH acid meeting neat antiscalant destroys its efficacy. And stop the antiscalant feed during low-pressure flushes and at shutdown, because antiscalant left standing on a membrane settles onto it and becomes the foulant you were avoiding. Overdosing does the same thing. More is not safer.

Why a System Inside Its Limit Still Scales the Tail

Scaled elements turn up in racks whose paperwork says every number was in range. The bulk concentrate you sampled is a different water from the one touching the membrane.

Rejected salts pile up in a boundary layer at the membrane surface, running at a higher concentration than the stream flowing past it. WC&P calls the ratio the concentration polarization factor, always greater than 1, and membranes reject salt based on the concentration at the wall rather than in the bulk. So a concentrate comfortably under +1.8 can be supersaturated at the face of the last element and precipitate there. Suppliers carry this in their projections as the beta factor, and it climbs with recovery inside each stage.

Everything that makes polarization worse also lives at the back of the array. Feed flow has dropped, because most of the water left as permeate, so concentration peaks exactly where crossflow velocity bottoms out. That's the reason scaling shows up as differential pressure across the second stage and flow decline from the tail vessels, while the front of the system looks fine and the system-average numbers look survivable.

The fixes here are hydraulic before they're chemical. Hold minimum concentrate flow, which Hydranautics sets at 12 gpm per 8-inch vessel against a 75 gpm maximum feed, taper the array so the last stage keeps velocity up, and design at a lower flux. WC&P is explicit that lower design flux lowers the effective LSI at the membrane surface. Antiscalant mitigates the scaling polarization causes and does nothing to reduce polarization itself.

If you already have scale, an acid clean will pull calcium carbonate off. Whether it holds depends on whether you fixed the index, and how the cleaning gets run matters as much as what's in the tank.

Which Lever to Pull First

Push your feed analysis to the concentrate at the recovery you run today, and compare that number against negative 0.2, +0.5, or +1.8 depending on what you're dosing. If you're above your line, take recovery down before you add chemistry. Recovery drives the whole calculation and it's the only lever that also relieves polarization at the tail. Add antiscalant when the recovery you need requires it, and treat acid as the answer to a carbonate problem you've confirmed won't turn into a sulfate problem.

The chemistry doesn't care whose membrane is in the vessel. What the element changes is how much recovery you need in the first place. A NanoH2O (formerly LG Chem) BW 400 R G2 makes 11,500 gpd at 99.8 percent stabilized rejection on the same 400 ft² as a standard BW 400 R at 10,500 gpd and 99.6 percent. That's about 10 percent more permeate per element. Spend it on running fewer points of recovery for the same plant output and you've bought down concentrate LSI with hardware instead of chemical feed, and the low differential pressure spacer on the G2 line leaves more room before dP hits your cleaning trigger. The industry defaults to FilmTec on installed base, contractor familiarity, and a deeper US service network. Those are real reasons. None of them is a performance argument.

Enviro Membranes stocks NanoH2O 8040 elements, including the BW 400 R G2 and BW 440 R G2, at wholesale pricing with same-day US shipping. If your tail elements are scaling and you want a second read on the concentrate numbers first, send the water analysis and the recovery you're running. We're at enviromembranes.com.