Fundamentals of membranes systems

Engineering memo from the SUEZ engineering department

SUEZ systems are designed to produce purified water by a process called reverse osmosis. An understanding  of this process can best be gained by a review of the process of osmosis. A simple osmosis system is shown in below.

Figure 1: Simple Osmosis System

Normal osmosis takes place when water passes from a less concentrated solution to a more concentrated solution through a semipermeable mem- brane. A semipermeable membrane will pass water molecules but will not pass a great percentage of the solute (i.e. dissolved material) – most of this material is rejected. The word most is emphasized be- cause in practice there is no such thing as a perfect membrane. 

A certain amount of potential energy exists between the two solutions on each side of the semipermeable membrane with the more dilute solution exhibiting the higher potential energy level. Water, like everything else in nature, will flow from the solution with the higher potential energy level (dilute solution) to the solution with the lower potential energy level (more concentrated solution). The highest energy level for water is pure water; as solutes (i.e. impurities) are added, the water becomes less pure and the energy level of the water is reduced.

Due to this energy difference, water will flow from the less concentrated solution to the more concentrated solution until the system is in equilibrium. Equilibrium will be reached when the differential head, ∆h is equivalent to the apparent, or differential, osmotic pressure. The state of equilibrium can be expressed as follows:

∆h = (π2 – π1) = ∆ π
π1 = Absolute osmotic pressure of less concentrated (higher energy) solution
π2 = Absolute osmotic pressure of more concentrated (lower energy) solution 

Equation 1

The absolute osmotic pressures π1 and π2 of the solutions shown in Figures 1 and 2 are defined as the potential energy difference between any solution and pure water. Keep in mind the higher the purity, the higher the potential energy. Remember that extremely pure water has a very high potential energy level and is a very aggressive material. 

Reverse osmosis (RO) is can be defined as the separation of one component of a solution from another component by means of pressures exerted on a semipermeable membrane. Usually RO is used for the separation of dissolved solids (solute) from water (solvent). Referring to Figure 2, the addition of pressure energy to the more concentrated solutions will accomplish the same thing as the differential head, and it will stop the transport of water through the membrane when the head pressure equals the ∆ π head. As more pressure is applied, the water will flow from the concentrated solution to the dilute solution, in effect, reversing normal osmotic flow. The addition of pressure has increased the energy level of the less concentrated solution. Water always flows from higher
energy to lower energy. In the case, the flow will be from the more concentrated to the less concentrated. The rate of water transport is a function of:
1. The pressure applied.
2. The apparent, or differential, osmotic pressure between the solutions. (Differential osmotic pressure is the difference between the absolute osmotic pressures of the two solutions.)
3. Area and characteristics of the membrane
4. The solution temperatures

Figure 2: Reverse “Osmosis

A reverse osmosis machine, regardless of size of complexity, can be conceptualized as the simple “black box” shown in Figure 3.

Figure 3: A conceptualized reverse osmosis machine

Definition of terminology

1. Total Dissolved Solids (TDS): The total organic and inorganic material dissolved in the water expressed as a concentration C (e.g. mg/L, ppm).

2. Feed: The solution which enters the system under pressure with solute concentration = Cfeed. Example: Cfeed = 150 mgL TDS

3. Permeate: The solution (usually purified water) which passes through the membrane and is collected for use. The solute concentration = Cperm.

4. Concentrate (brine, retentate): The solution which exits from the system which has not passed through the membrane. It is enriched in a particular rejected material. The solute concentration = Cconc.

5. Rejection: The percentage of dissolved material which does not pass through the membrane.

6. Passage: The percentage of dissolved material which does pass through the membrane.

7. Recovery: The ratio of permeate rate to feed rate: 

Equation 2


8. Concentrate Concentration: The concentration of the concentrate stream, or blow-by, as it exits the machine. It is related to feed concentration and recovery as follows: 

Equation 3

Figure 4

9. Average Concentration: The average concentration which the membrane is exposed to in the machine. It is calculated by averaging the Cfeed and Cconc.

Equation 4


Small SUEZ systems operate at relatively low recovery, typically less than 50%. The cost of higher recoveries on small systems is not justifiable, especially when the permeate quality is considered. We design the systems to operate on a flow rate, Qi, through the sepralator (membrane element), of about 5 gpm (19 lpm) in order to create turbulent flow. The basic, once-through, recover of a typical sepralator that produces 10 gph (39 lph) of permeate flow is only: 

This low recovery is increased by recirculating a percentage of the concentrate Qc that has passed over the sepralator (not through the membrane but over it) through an orifice restriction back to the pump, where it is mixed with the incoming feed solution. The amount that is recirculated is a function of the restriction in the orifice and the concentrate valve, which is an orifice-type valve that allows a predetermined amount of concentrate to flow at all times. (This is covered under SUEZ US Patent 3,716,141. This apparatus is also patented in a number of foreign countries, notably Germany, Switzerland, Canada and Japan.) 

We can also increase recovery by adding sepralators to the system, as we do in the larger unites. Recovery is increased since each sepralator removes more permeate, adding to the total permeate rate without a corresponding increase in feed rate. In actual practice, both recirculation and the addition of sepralators is used to increase recovery. On some bigger systems, very little recirculation is necessary to achieve the recovery desired, and if recycle is not used, the quality of the permeate will be higher. All SUEZ machines are manufactured so that Qi can be increased if necessary to avoid fouling the sepralators. For a given input feed rate, Qfeed, the permeate rate Qperm, obtained from a machine is a function of a number of interrelated factors. Among these are: 

1. The number sepralators used in the machine
2. The type of membrane used.
3. The operating pressure
4. The apparent osmotic pressure ∆ π, of the solution in the machine, which is a function of average concentration and solute type.
5. The temperature of the solution;
6. The condition of the membrane
To estimate the concentrate concentration (blowby) in terms of feed concentration at any given recovery, use the following method:

Equation 3


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