Suggested operation of a tap water reverse osmosis desalination system, model and SCADA

Introduction

Tap water, under sink, reverse osmosis manufacturers follow a very typical compact design concept for their products. Usually they try to reject five quantities of brine in order to produce one quantity of permeate. Is this actually happening?
Is this a correct design for every case of tap water? Is it possible for a tap water R.O. system to perform well in several circumstances in terms of quality, pressure and water temperature without any adjustment?
Designing a reverse osmosis system includes several stages for feed water prefiltration. This happens in order to reduce suspended solids, colloidal, iron, manganese etc. and absorb free chlorine which exists in feed water due to chlorination. Tap water is usually well in terms of colloidal, iron and manganese, so prefiltration is designed to further reduce suspended solids and absorb free chlorine.
In a simplified picture we would say that reverse osmosis membranes uses prefiltered feed water in one end and splits it in two streams on the other end. The permeate stream (clean water-product) has less dissolved solids (ions) than feedwater and the brine or concentrate stream (reject water) has more dissolved solids (ions) than feedwater. 
The brine stream usually passes through a hydraulic device acting as brine flow restrainer, in order to achieve standard brine flow rate,  pressure increase for the membrane and may be energy recovery. Recovery is calculated as Permeate flow divided by Feed water flow as a percentage. Tap water ro systems are designed for low recovery, so brine's dissolved solids are not very high, thus brine flow rate is pretty high, so it is not very possible to cause scaling in membrane surface. Higher recovery  rates may need chemical addition of antiscalant to feed water to prevent scaling.
After membranes, permeate stream is delivered to the post processing stages such as rehardening and sanitation etc.

What actually happens

R.O. Membranes are specified by the manufacturer by their test protocol and several design features. A known manufacturer's 1812 - 75GPD membrane is specified as follows:
•    Maximum Operating Temperature  113°F (45°C), Maximum temperature for continuous operation above pH 10 is 95°F (35°C).
•    Maximum Operating Pressure 150 psig (10 bar) 
•    Maximum Feed Flow Rate 2.0gpm (7.6lpm)
•    pH Range, Continuous Operation 2 – 11
•    Maximum Feed Silt Density Index (SDI) SDI 5 - this factor depends the success of prefiltration…
•    Free Chlorine Tolerance < 0.1 ppm - this factor depends on the success of activated carbon filters or other dichlorination means to absorb free chlorine.
This membrane is tested using the following protocol: Feed Water - softened tap water - at 50psig (3.4bar) of pressure, TDS of 250ppm, at 77°F (25°C) of temperature. In those very specific conditions membrane produced 75GPD (12lph) achieving 15% of recovery rate. Salt rejection was 99% with a minimum of 96%. 
Recovery rate 15% for brackish water membranes and 8% for seawater membranes seems to be the factor, which should be considered mostly in order to achieve long membrane life.
Another design feature which shines by absence in membrane manufacturer datasheets is the estimated lifecycle of a membrane. There is no reference about membrane lifecycle because there is no reason for a membrane to malfunction when every design limit is not exceeded. Still most of the tap water reverse osmosis manufacturers  describe a system with higher recovery usually near 20% and user obligation for yearly membrane replacement.
Membranes does not work with magic. R.O. membranes performs according to factors, in a linear response to quality and quantity of the permeate. All those factors causes changes in recovery as well. Those factors are:
1. Total disolved solids contained to the pre-filtered feed water
2. Operating Pressure
3. Operating Temperature
Due to the manufacturer test, there is a specified operating point. It is obvious that using some simple mathematics, someone can estimate another operating point and check whether this new setup is within operating limits.

Modelling Membrane Operation

Using manufacturer test results, a small amount of measurements and some easy calculus membrane performance can be estimated:
Step 1. Osmotic Pressure Correction Factor
([ppm TDS of feed water] – [ppm TDS of feed water in membrane manuf. Test]) / [100] = [O.P.C.F psi]
Ex. (815ppm-250ppm)/100=5.65psi

Step 2. Corrected Pressure
[Operation Pressure psi] – [O.P.C.F psi] = [C.P psi]
Ex. 60psi-5.65psi=54.35psi

Step 3. Pressure Compensated Flow
[Permeate flow rate in membrane manuf. test GPD]  * [C.P psi] / [membrane manuf. test feed pressure psi] = [P.C.F GPD]
Ex. 75GPD * 54.35psi / 50 psi = 81.52GPD

Step 4. Temperature Compensation
[P.C.F GPD] * [Temperature Correction Factor T.C.F] = [Actual Permeate GPD]
Ex. Feed water is 82.4°F (28°C) so T.C.F. is 1.094 (according to the Table 1)
81.52GPD*1.094=89.19GPD

Step 5. Recovery
([Actual Permeate GPD] / [Feed Flow GPD]) * 100 = [Recovery]
 Ex. On a 300 lpm (114GPD) flow restrictor
 [89.19GPD/(114GPD+89.19GPD)]*100=43.89%

Step 6. Expected Quality
[ppm TDS of feed water] * ( 100 - [salt rejection %] ) / 100 = [permeate quality TDS ppm]
Ex. For a minimum salt rejection of 96%
815ppm*(100-96)/100=32,6ppm

Step 7. Other Estimates
Brine stream quality can also be calculated solving the following equation:
[ppm TDS Feed Water] * [Feed Flow Rate GPD] = [ppm TDS Permeate] * [Permeate Flow Rate GPD] + [ppm TDS Brine] * [Brine Flow Rate GPD]
GPD, PSI, F, ppm units are used because most membrane manufacturers uses those units in datasheets.

The presented model has been found here [https://www.slideshare.net/mils-water/calculate-ro-performance] and it is experimentally tested for this article producing very close results.

The underlying problem on current design concept

A typical 75GPD tap water r.o. system design usually comes with a brine flow restrictor of 300 (0,3lpm)
Chios (Greek Island) tap water during the first days of September 2019 was measured at 815ppm as TDS at 28C and typical tap water pressure  was measured at 60PSI. In those conditions membrane produces 89GPD of permeate and according to flow restrictor disposes 114GPD of brine. Adding Brine and Permeate leads to a 203GPD of feed water which is 43,8% of recovery for a single membrane element, which should be working near 15%.
Recovery would be 36% for a 420 flow restrictor or 29.9% for a 550 flow restrictor. This outbound use of membrane would gradually cause quality and quantity decrease for the permeate due to membrane fouling.
In order to achieve the correct recovery for this system a flow restrainer of 1330 should have been used, this once more would not be completely correct because few days later feed water temperature, quality or pressure could change and once again the system would have to be readjusted. 
So new adjustment in inlet pressure and brine flow must occur every time in order to keep element recovery near 15%. This could benefit r.o. system owner fewer membrane element replacements and stable permeate in terms of quantity and quality.

Grater Recovery, longer membrane life – Multistage Tap Water Ro.

The demand for grater recovery may be satisfied by extra r.o. membranes in stages. This is when the brine of the first element used as feed water for a second element etc. Using two membranes in first and second stage may lead near to 30% of system recovery (15%+15%), but only when all the other operation factors are within limits. Similar to the bigger R.O. plant design concept projections could be created for tap water r.o. systems in several operating points.
Having some design concepts and many membrane elements considered, there is a nice one which seems to be working for several operating conditions of tap water feed. This design concept includes a first stage of 50GPD membrane element and a second stage of 75GPD membrane element. Using 1090ml per minute of prefiltered feed water while adjusting system pressure according to feed temperature and quality the system may produce 280-290ml per minute and a total recovery rate of 26-27%. 
The successful operation projected on spreadsheet and happened, (at least in five sets of operation) as projected, for feed water 250-2500ppm @ 18-29C by adjusting membrane inlet pressure from 2,5-4,5bar. 
Pressure adjustment could be made by taking frequent measurements for feed water TDS and temperature. Using those measurements and some consultancy from a projection graph or table of values (projections) the final user could frequently set a brine needle valve to achieve the optimum operation.
On higher inlet TDS (2000+ ppm) and continuous operation, usage of antiscalant in small dose may be needed to prevent scale formation especially in second stage, this is still under investigation.

Consultancy from SCADA software

Some extra electronic sensors and automation can be installed to make measurements pc-friendly. 
Membranes inlet pressure, feed water conductivity-temperature meter and feed water flow meter is the minimum sensor set, which can be used in order to drive R.O. by SCADA consultancy.
In the test unit, there is installed an electronic pressure transmitter before r.o. pump, another pressure transmitter after r.o. pump, an electronic paddlewheel flow meter 1-30lpm to frequency to measure feed water flow and two conductivity-temperature transmitters for feed water and permeate. The Tank Full switch is a non-contact (capacitance) liquid level detector attached at 10liters of volume.
Automation is very simple:
If Main Switch is on, Tank Full switch is off and no fault has happened the inlet valve opens to allow feed water through the system, flush valve is also open in order to flush membranes with high feed flow. After a while flush valve closes and if r.o. pump inlet pressure exists, the r.o. pump starts and operates while:
1.    R.O. pump inlet pressure is ok (otherwise fault)
2.    Membrane inlet pressure is ok (otherwise fault)
3.    Permeate tank is not full (otherwise tank full, show message and time elapsed)
4.    Main Switch is on
Stopping R.O. for any reason, is to stop R.O. Pump, close the inlet valve and open the flush valve for a while to depressurize the system. A small amount of permeate about 200ml stored in a small vessel flows by forward osmosis back to membranes and decreases salt concentration on membrane surface.
While R.O. pump is on there is a timer counting the time elapsed. Storage tank volume is known and while product consumption is stopped, time elapsed can also determine the mean permeate flow rate in order to investigate the real performance. For instance around 35minutes is needed to produce 10liters, producing 107.6GPD (0.283LPM). 
Furthermore, acquiring all measurements in a SCADA software model runs all calculations in real-time projecting the operating point. User is informed in real time about the system performance and can adjust the needle valve as often as he or she wishes to.
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Conclusions

Making projections is vital for any Reverse Osmosis System. Making projections for TW reverse osmosis systems proves that they are not plug and play products and they might not work well in any tap water out of the box. Using a fixed setups for tw r.o. systems is also wrong, but it is not impossible to provide final user a path to adjust their systems. In IoT era possibly a set of sensors can feed the model with real-time data for better performance. In cloud era manufacturer could receive performance data and provide better services. This could be a whole new product line which can become better and cheaper every year.