RO separation models and performance metrics

There are two main models which attempt to characterise the RO separation process, one is the porous model of the membrane. The porous model of the membrane assumes that the flow through the membrane “occurs through the pores, which have a characteristic size distribution [48]”. The alternative model that is widely accepted for RO systems is the

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solution-diffusion model. This model assumes that each component of the high-pressure solution “diffuses through the membrane in response to the concentration and pressure difference” (originally from [56] in [48]).

The performance of an RO unit depends on many factors, including most importantly, suitable feed water pre-treatment. To assure final product water quality, UPW plants are designed to complement the incoming feed water characteristics to the RO unit so that performance capabilities are not compromised. This pre-treatment is essential to minimise fouling and scaling effects. Once the feed water is suitably pre-treated, the performance is generally measured in terms of several important metrics, (1) the permeate water flux, (2) the percentage salt rejection, and (3) the percentage recovery. The permeate water flux can be defined as the quantity of permeate water attained per unit area of membrane per unit time (m³/m²/s); in imperial units, this is commonly referred to as gfd (gallons per square foot per day). The water flux Jw through the membrane is represented in its most simple form by (2.1).

( )

w Tr F

J =A P − Π (2.1)

In (2.1) A is the membrane permeability coefficient (experimentally calculated for various membranes, it characterises the membrane’s resistance to flow), PTr is the trans-membrane pressure, and Π_F is the osmotic pressure of the feed water. As (2.1) illustrates, for a given membrane, the permeate flux is proportional to the difference between the trans-membrane pressure and the osmotic pressure of the feed water. The osmotic pressures dealt with in UPW plants are not significant when compared to seawater, and therefore, the permeate flux is primarily a function of the trans-membrane pressure. So, because the energy

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required for the RO process is electrical pump energy, there is a necessary trade-off between the operating pressure of the pump and the permeate flux rate; the lower the operating pressure, the lower the permeate flux. Hence, the efficiency of the pump is very important to energy efficient RO. Therefore, in order to maintain the same permeate flux rate at a lower operating pressure, raising the membrane permeability coefficient A is necessary.

The salt flux through the membrane is given by (2.2).

( )

s F P

J =B C −C (2.2)

Equation (2.2) shows that the flow of salt across the membrane is independent of pressure but is a function of the difference in concentration across the membrane where B is the membrane permeability coefficient for the salt, CF is the concentration of the salt in the feed and CP is the concentration of the salt in the permeate. The second important performance metric, and particularly important for UPW applications, is the percentage salt rejection, see (2.3). concentration of the permeate divided by the concentration of the feed water. The recovery metric is defined according to (2.4) as the volumetric flow rate of the permeate water divided by the flow rate of the feed water.

27 polarisation, as a consequence, salt rejection increases and permeate flow decreases. [43, 52]

Other main factors affecting performance include operating parameters such as temperature, pressure, recovery and feedwater concentration. These factors are shown in Figure 2-9 where the direction of each arrow (within each of the four plots) indicates the relationship between the relevant performance metric and the independent variables. The feed concentration is controlled as much as possible by suitable pre-treatment. Therefore, regarding RO operating parameters, and specifically RO system performance, the areas of influence include pressure, temperature and recovery rates. As Figure 2-9 illustrates, increased pressure, is beneficial to both permeate flux and salt rejection. Higher operating temperatures increase the permeate flux but have a detrimental effect on salt rejection. The operation of RO systems at higher recoveries has a negative effect on both the percentage salt rejection and the permeate flux, this negative effect increases dramatically after a certain percentage recovery. Feed concentration increases have a negative effect on both percentage salt rejection and permeate flux, although salt rejection performance decreases steadily initially and then experiences a more dramatic decline in performance; permeate flux falls off sharply initially and then more steadily. Figure 2-9 shows the complexity involved in parameter set-up, and importantly, how this set-up often entails a trade-off between permeate flux and percentage salt rejection. Also, two of these parameters,

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temperature and pressure are explicitly related to plant energy consumption. The temperature affects the viscosity of the water, reduced viscosity means greater permeate flux. However, in order to increase the temperature of the water, energy must be expended, again involving a trade-off between the energy required to heat the water and the increased permeate flux as a result of this increased permeate flow rate, but also with an added caveat that increased temperature also increases salt passage. Pressure increases appear to be a win-win situation with respect to permeate flux and salt rejection, but increased pressure also has an associated energy cost. The influence of pressure on permeate flux can be seen clearly from (2.1), what is not obvious is the non-linear mathematical relationship between salt rejection and pressure. The reason the percentage salt rejection increases with increased pressure is that increased pressure causes increased permeate flux, however, due to the fact that salt flux is independent of pressure, see (2.2), the salt flux does not change and becomes more diluted leading to higher percentage salt rejection [57].

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Figure 2-9: RO performance parameters [52]