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# Reverse osmosis pressure calculations

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## Reverse osmosis pressure calculations

(OP)
Hello All,

I'm an energy engineering student and for my master's thesis I'm building a model to simulate an RO system which includes a high pressure pump driven directly by a wind turbine via hydraulic transmission, pressure vessels with 5 RO membranes and energy recovery device (positive displacement motor directly connected to the high pressure pump by shaft).

I know the following equation for pressures:

P_netdriving = P_feed - deltaP_hydraulicloss/2 - P_permeate - P_osmotic

and

deltaP_hydraulicloss = P_feed - P_concentrate

I can assume that P_permeate is atmospheric and can calculate the losses and P_osmotic, but if I have to calculate the feed and concentrate pressure how do I proceed? I found a model that assumed the net driving pressure to be zero in the last membrane but this means no water flows though it. Are any of these usually set values?

Thanks!

### RE: Reverse osmosis pressure calculations

The quick answer is no.
You are correct in assuming that the last membrane is not at zero pressure. In fact there will be considerable pressure applied to the last membrane, with a considerable amount of pressure being dissipated by the concentrate control valve or used to drive the energy recovery device.
Those pressures depend on many things including:

1) Salinity of the water
2) Flux rate(flow rate through the membrane)
3) Type of membrane in use.
4) Degree of fouling/scaling

A number of the membrane manufacturers provide free membrane modelling programs that provide pretty useful information for what yooou are trying to do.
Here is a link to a popular program and its the one i use a lot.
http://www.dow.com/en-us/water-and-process-solutio...

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

### RE: Reverse osmosis pressure calculations

You need a better definition of the project scope. The energy usage of the RO system will depend on the salinity of the raw water. Sea water uses much more energy.

It does not sound practical to use wind power for RO. Wind power is generally not always available and water needs are constant. In fact, most water supply systems incorporate standby power systems.

### RE: Reverse osmosis pressure calculations

(OP)
Thanks for the responses.

bimr, let me explain better. This wind turbine - RO system is being developed by a start-up company and my job in my project is to try and get as much water out of the available fluctuating energy. Of course, a constant power supply would be preferred for RO but with my project I would like to explore the extent of its feasibility with a fluctuating renewable energy supply. As an energy engineer I am focusing more on the energy use side, hence my lack of RO knowledge.

More specifically I'm trying to expand the range of operation of the membranes with varying power by alternating between a single and multiple (two for now) membranes in parallel. This is also how I'm my model will work.

Thank you ashtree for the DOW document and the ROSA software. I was using IMSdesign (Hydranautics) to understand what the operation limits for an RO vessel are. The DOW document might help me indeed.

I appreciate your opinions and suggestions.

At the moment I'm trying to figure out the equations to get my model going and trying to minimise the assumptions. I'm sure it will never be as accurate as software like ROSA but most importantly I need to prove the concept of energy distribution when switching between single/multiple membranes.

### RE: Reverse osmosis pressure calculations

The fluctuating power and the swapping between one or two vessels is going to cause some headaches i suspect.

We need some clarification here. Are you using two vessels each with 5 membranes installed. Or are you using two vessels each with one membrane installed. You mention both arrangements in previous posts and it will make a lot of difference in what can and can't be achieved and the problems you will encounter.

If you have only a single membrane unless you are recirculating concentrate then recovery will be limited to about 15%. But five membranes in series with no re-circulation might give you 50% depending on the water quality(probably only 30-40% if you are doing sea water). The five membrane choice though is going to be a lot tougher to manage your sort of system because you have to maintain minimum concentrate flow rates to prevent scaling on the last membranes.

Energy recovery devices are good where you have a lot of energy to dissipate with high flow rates, high concentrate pressures or both. In a small plant and particularly if only treating lower salinity raw water the total amount of energy is relatively small. I accept that you don't have much energy available but the ERD may be a complication you don't need.

I am wondering whether you may be better to use the wind turbine to drive a generator and use electricity to run the RO plant in relative conventional sense. If you used the wind turbine to charge batteries( I am assuming this plant is relatively small) the ERD could then be a simple generator as well.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

### RE: Reverse osmosis pressure calculations

It is inherent to the RO system process that the systems operate more or less continuously. You will have problems cycling the systems on/off.

As Ashtree stated, the best scenario would be to operate the RO independently with electricity.

### RE: Reverse osmosis pressure calculations

(OP)
The wind turbine/hydraulic transmission/RO combination is patented therefore it is the basis of my project. Although it may not be at all ideal I have to make do with what I was given. The membrane and vessel configuration is therefore what I can modify to exploit as much energy as possible from the wind turbine.

The pump which has a maximum delivery of about 20 m3/h would be feeding seawater to two vessels of 5 membranes each (it could be more vessels and/or less membranes if using 5 would lead to scaling in the last ones). The idea is that for the systems to operate as continuously as possible even at low wind speeds fewer vessels would operate and these can be alternated during long periods of low wind speed to avoid having to flush them too often. I'm hoping that this switching between one or more vessels gives the system more flexibility in operation and produces more permeate. Would this switching create many problems?

The energy recovery device is fixed to 60% of the pump volume therefore I've got 40% recovery to work with. And these components have already been bought for a lab experiment so I cannot change them. I'm assuming a feed pressure of around 60 bar, though this part of what I'm struggling to calculate, and a concentrate of a couple of bar less. Is this realistic?

A working pilot plant was built using a 100 kW (rated) turbine so with this power I believe 2 of the above high pressure pumps could be used in parallel (each feeding multiple RO vessels), though I want to concentrate on one for now (later I can multiply the problem by 2 ).

### RE: Reverse osmosis pressure calculations

I have run a series of projections with generic seawater just to give you a feel of the results.
This was all done with two vessels and 5 SW30-440 membranes and 40% recovery. I allowed the pressure to fluctuate as required and merely varied the flow.

5m3 hr will quickly scale the rear membranes and wreck the front ones.
10m3/hr will scale the rear membranes.
15,20 and 25m3/hr all work

Your pressure assumptions for 20m3/hr are about right 61 bar approx with a concentrate pressure around 59 bar. This plant uses about 1.3kwhr/m3 more at 25m3/hr than at 15m3/hr because of the extra system pressure required but you would recover some of that energy with an ERD.
I have attached a pdf of the 20m3/hr projections below.

You will need some good system control to alter the flow , and maintain recovery during periods where less power is available particularly if there is a lot of variation. This could obviously be done with PID control but you are potentially varying a number of factors at once.

Ideally when you drop one vessel off it should be flushed with permeate to stop scaling and bio-fouling.

You have also made no mention of any pretreatment. Even simple filtration will absorb some energy. This needs to be considered.
As bimr suggested RO prefers to operate constantly and consistently and this definitely challenges that theory.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

### RE: Reverse osmosis pressure calculations

(OP)
Ashtree, thank you for running the various projections; they give me a good indication of what I should be aiming for. The ROSA software seems more complete than IMSdesign which I had been using previously.

In terms of control for the system I thought that since I have a fixed recovery (due to the fixed pump and ERD volumes) all I can control is the operation of single or multiple vessels to ensure the membranes operate within their limits of recovery and flux. Should or could I be varying other things?

For long periods of low power during which one vessel alone would be working I thought of periodically switching between vessels in time to prevent scaling and fouling. Of course it all depends on how much power is available. Do you see problems arising in this?

You're right, I haven't mentioned pretretment at all and I probably underestimate its impact on the energy usage. I will focus on the RO and getting this model to work first as it is more important for scope of my project then may add the pretreatment if time allows. Deciphering the RO equations and finding all the constants will probably be quite tedious.

Beginning of next month I'm also running an experiment on which this start-up company has decided to spend a huge amount of money (I personally can't fully justify its use). It will include the HPP and ERD connected to a variable speed motor (simulating the wind turbine) and two sets of valves representing the RO membranes and creating the membrane's pressure drop. Artificial recovery and flux limits will be set to the "pressure vessels" and these will dictate when the vessels are switched on/off. This test will be used to test whether the idea of switching between single and multiple vessels will work in practice with this set-up and whether a larger range of operation can be obtained. It should give an idea of how much "permeate" can be obtained from this system with a varying wind pattern. I have my doubts on the use of this test and how realistic it can be. Do you think this is a good/bad idea? What sort of problems could arise here? Can it be used more productively?

Many questions and doubts but thanks to all again for your advice.

### RE: Reverse osmosis pressure calculations

A couple of comments..

You have mentioned that you will have fixed recovery due to the fixed pump and ERD volumes. Maybe i have missed something but during periods of less wind power i assume that you will have less power for pumping.
This is why i suggested that you will have to control multiple parameters particularly if you intend to maintain recovery at a fixed percentage. generally what happens in practice is that if the input pump rate slows or the pressure drops the recovery goes down unless the concentrate control valve increases the back pressure. As the pressure drops you simply will not be able to maintain the same pump flows , ERD volumes and recovery. One or more of those parameters has to change.

The test rig may be able to simulate the hydraulics of the system and that is not necessarily a bad thing. What it is not simulating is the membrane performance and the chemistry associated with scaling. These will impose limiting factors outside the hydraulic limitations.

The alternating of the two vessels on line during low power events is better than doing nothing. I would still bet that you will end up with scaled membranes pretty regularly particularly if there is a change from 2 to 1 membrane after a prolonged low flow 2 membrane operation where concentrate flow rates are marginal or low.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

### RE: Reverse osmosis pressure calculations

(OP)
Sorry for the late response.
Thanks Ashtree for all your comments and advice. It's all very much appreciated.
I'll continue with the simulation and experimental preparation for now and may have some other questions in the near future.

### RE: Reverse osmosis pressure calculations

Hello, I'm the same person as "edobologna", writing with a new account as I was no longer able to log in.

I have progressed in making a model of an RO pressure vessel with 5 elements.
To calculate the feed pressure for the first element I rearranged the following equation:

Q_p = k_w*A(TMP-P_osm)

where Q_perm=pearmate flow rate, k_w=permeability, A=active area, TMP=trans membrane pressure(function of feed pressure and concentrate pressure), P_osm=osmotic pressure difference.

I applied this to calculate the feed pressure for the first element assuming that the permeate recovery fraction (40% recovery) was split equally between the elements and calculating the feed pressure of the successive elements by simply calculating the pressure drop across an element. This is wrong, however, as the changing osmotic pressure (and concentration polarisation) will mean that the recovery is not distributed equally among the elements. In fact, I got a feed pressure that was half what it should have been (according to ROSA).

My question is: how do I calculate how the permeate recovery is distributed between the elements?

I believe should apply the above equation to each element but I would have two unknowns (P_f and Q_p). Where am I going wrong?

### RE: Reverse osmosis pressure calculations

While it is admirable that you are trying to work through the RO design process, you would be better served if you talked to a RO application engineer. This calculation is not something that can be learned in a few months time.

The element to element method that you appear to be using is a complex calculation. A more practical approach is Average values are used to calculate feed pressure and permeate quality if the feed quality, temperature, permeate flow rate and number of elements are known. If the feed pressure is specified instead of the number of elements, the number of elements can be calculated with a few iterations.

http://msdssearch.dow.com/PublishedLiteratureDOWCO...

http://msdssearch.dow.com/PublishedLiteratureDOWCO...

It would be much easier to put together a few scenarios and call DOW and let them run through the calculations.

### RE: Reverse osmosis pressure calculations

From a practical perspective i totally agree with bimr's comments. But just looking at your attempts at the maths i can see a couple of things that are potentially incorrect. However i am only working with what you have written here.

TMP or transmembrane pressure is normally the difference between the feed pressure and the permeate pressure not TMP=trans membrane pressure(function of feed pressure and concentrate pressure) as you have written. The concentrate from membrane 1 becomes the feed for membrane 2 etc and in a perfect world all membranes see the same feed pressure. However the world is not perfect and there is a thing called friction and because of the design of the membrane and with biofouling, particulate fouling there is a pressure differential across each element from one end to the other. DOW specifies a maximum of about 50kpa (7psi) per element. New or clean elements operating at reasonable flow rates probably have a pressure differential of about 50-60% of that value. These values may need to be added to your calculation , but is already included in the ROSA projection.

ROSA also considers that there will be some fouling on the membranes as it is a fact of life and allows the user to set the fouling index. Typically 0.85 is used but you may not have made any allowance for that in your model.

I am not sure how you have dealt with the concentrate pressure. Back pressure is normally applied to the concentrate stream ensure that each membrane has adequate pressure to produce permeate. As you have alluded to each membrane in a 5 element array sees increasing salinity but slightly reducing pressure because of the pressure loss due to friction as you move down the array. By throttling the concentrate the impact of this pressure loss is reduced and it ensure that all elements have enough pressure, it ensures that flow to the elements is reasonably evenly distributed and the permeate production is relatively balanced between all the elements. Almost for certain though the tail end element will have a lower recovery than the front elements because of the increasing salinity.

This does result in having a significant amount of concentrate pressure to be burn't off through an ERD or across the control valve.
On the other unless practicing permeate throttling the permeate comes off the membranes at quite low pressure.

Hope this helps your understanding.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

### RE: Reverse osmosis pressure calculations

Thanks for the responses.

I am doing this model so that I can simulate a pilot project of an RO system directly powered by a wind turbine, therefore having varying feed pump power with time and, as a result, varying feed flow with time. This is to say that I am not considering the fouling or other factors that as I would just like to prove the operation of the system and make some variations to test different options. It is not necessary for me to calculate the permeate production or quality as precisely as ROSA or similar software, nor to calculate the lifetime of membranes. I would however like to get the main mechanism correct so I get round about the same figures as in professional software for a fixed flow rate.

I went through an extensive calculation for the pressure drop on the feed-concentrate side of each element. I realised later that for the purpose of my simulation I could have just assumed a value since it is quite small (e.g. 0.2-0.3 bar) but now that is done.

In practice the concentrate would end up in an ERD therefore there would be a back pressure.

My only concern was exactly how to calculate the distribution of the permeate production as this depended on the feed side pressure of a particular element and the osmotic pressure difference, which itself will depend on the concentrate flow from the previous element and therefore the permeate flux of the previous element. Essentially I end up with two unknowns in my equation (feed pressure and permeate flow).

Today I made some progress: what I have done so far is calculated the feed pressure assuming the array as a single element. In this case I have all the variables I need (40% recovery means I know my permeate flow). I use this pressure for the feed of the first element. I reduce the feed pressure of the following elements by the pressure drop of each (which actually also depends on the feed flow of each element and thus requires me to know the permeate distrebution, but thats a smaller problem. Assuming a fixed value for now). What remains unknown is the osmotic pressure which also depends on feed flow of an element, therefore needing to know the permeate distribution...here we go again.

I imagine the permeate distribution calculation requires a sort of iterative process, which on time varying simulation like mine can be quite complex, otherwise I wouldn't be able to explain how such calculations are done. Is there an easier way for this?

### RE: Reverse osmosis pressure calculations

You are correct in that it requires a series of iterations. It can be done long hand but basically it is what ROSA does in the background.

If you come up with wide variations in the recovery between the different elements than you have done something wrong in your maths or the design is wrong , probably having insufficent pressure.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

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