Dynamics Of Water And Membranes
Water is almost reverently referred to as the universal solvent, a marvelous combination of hydrogen and oxygen with the ability to dissolve a variety of constituents until their concentration exceeds the waters ability to hold them in solution. Pour too much sugar in a glass of lemonade and you’ll see this supersaturation phenomenon firsthand. Water treatment professionals refer to dissolved organic and inorganic molecules in terms of Total Dissolved Solids or TDS and routinely use the term “salts” when they’re actually referring to all of the compounds that make up TDS in source water. As a result, the term “salt rejection” can be all-encompassing.
Membrane technologies are applied to remove water constituents at the ionic level, and calculating membrane rejection and salt passage is critical when evaluating membrane performance and determining if a system is producing the desired product water quality. Filtration using MF and UF membranes relies on distinct pore diameters that act as a sieve to effectively separate liquids from solids and larger molecular weight constituents in a feed stream. This is commonly referred to as the “barrier layer” with the membrane acting as a barrier to allow desirable components to pass while rejecting undesirable compounds. Water molecules and a variety of dissolved species within the water are small enough to pass through the MF and UF pores. But solids larger than the pore diameter cannot pass through and remain on the surface until the membranes are backwashed, flushed, or cleaned. UF membranes have a pore diameter of 0.01 to 0.04 microns and MF membranes have a pore diameter of 0.1 to 0.2 microns. Under these specifications, MF is used to reject particulates and UF is used to reject particles and high molecular weight colloids.
RO membranes are used to remove dissolved ions in a process that does not rely on distinct pores for filtration. Instead, RO applies diffusion to allow water molecules to readily pass through a semi permeable membrane layer while rejecting constituents with a higher molecular weight. Rejection is variable but typically increases as the ionic charge and size of a molecule increases. Contemporary membranes have published rejection rates up to 99.8 percent, meaning that 0.2 percent of feedwater constituents will pass through the RO barrier layer. However, actual rejection rates rely on a number of parameters including percent recovery, feedwater temperature, pH, and the physical condition of the RO membrane. Most polyamide membranes used in RO carry a negative charge at natural water pH values, so there is also a mutual repulsion between anions and the membrane which can impede the transport of anions across a membrane.
It’s interesting to note that a rejection rate of 99.8 percent may seem impressive, but it still means that a percentage of dissolved compounds will pass through the membrane barrier into the permeate stream. Evaluating variations in published rejection rates is particularly important when dealing with exponentially high TDS values. A seawater desalination project with 33,000 ppm TDS source water might compare an RO membrane rejection of 99.5 percent vs another at 99.75 percent. While there is only a 0.25 percent, percentage difference in the rates, the expected permeate quality of the second membrane increased by 100 percent, calculated as 165 ppm vs 82.5 ppm respectively.
NF is similar to RO in that it relies on diffusion but it’s used to specifically reject dissolved divalent ions and large molecular weight compounds. NF membranes are very effective in separating water from large molecular weight compounds such as herbicides and pesticides and in removing undesirable color, typically derived from tannins.
RO Salt Passage And Rejection
A basic understanding of the RO process flow is necessary to fully appreciate salt passage and rejection. An RO membrane system is comprised of three fluid streams: the feed, permeate, and concentrate. As the feed water passes through the membranes, a resulting permeate (product water) and concentrate (reject water) are produced. Unless there are significant leaks in the system, the combined volume of permeate and concentrate will always equal the feed flow volume as shown in this calculation:
Feed Flow = Permeate Flow + Concentrate Flow
Flow designated as Q
Feed flow = Qf,
Permeate flow = Qp
Concentrate flow = Qc
Overall the mass equation is:
Qf x Cf = (Qp X Cp) + (Qc X Cc)
with C referring to the concentrations in the streams
While there is full accountability of the water volume in the RO process, the feed water constituents will also be found in either the resulting permeate or concentrate streams. The percentage of compounds that pass through the RO barrier layer and subsequently found in the permeate are described as salt “passage”. The compounds that do not pass through the RO barrier layer and found in the concentrate are considered to be “rejected”. The term “passage” is the reciprocal of the term “rejection”. Salt transport or lack of transport through the membrane barrier layer is described as “salt rejection” and it is the inverse of “salt passage”. Examples of the equations are:
Salt Passage = (Cp / Cf) X 100
Permeate TDS = Cp
Feedwater TDS is designated as Cf
Concentrate TDS = Cc
Salt Rejection = (1 – Salt Passage) x 100
If an RO feed water contains a permeate TDS of 10 ppm and a feed water TDS of 1,000 ppm:
The salt passage would be calculated as: (10 / 1000) X 100 = 1%
The salt rejection would be calculated as: (1 – .01) x 100 = 99%
Variables In Calculation Values
The values used in the salt rejection and passage calculations are not as obvious as you might expect. This is because reverse osmosis is a dynamic process. Contemporary systems are designed to house up to seven membrane elements in series within a single pressure vessel. The elements are connected via the permeate tube which captures a single product flow through the entire vessel. In this configuration, each membrane across the series removes water from the feed while rejecting salts. As a result, the TDS feeding the last element in the vessel will be much higher than the TDS feeding the first element.
To recognize this phenomenon, RO salt passage and rejection are calculated using a derived average feed and concentrate TDS. Calculating these averages appropriately considers the actual system dynamics and allows a much more accurate prediction of the membrane scaling potential. Using the example of a first stage RO operating at 50 percent recovery and a reported feed water TDS of 1,000 ppm, we would expect to have a TDS of 2,000 ppm exiting the last membranes in the system. If we ignored the unique driving forces of RO and used the reported TDS of 1,000 ppm in our calculations, we would grossly misrepresent the feed water quality to the back end of the system. In this example we would calculate:
Average Feed TDS = 1,000 + 2,000 / 2 = 1,500 ppm
Interestingly, while the terms salt rejection and passage describe the same phenomena, the calculated values of each are very different. Using the average feed concentration value outlined above:
Salt Passage = 10 / 1,500 x 100 = 0.66%
Salt Rejection = (1 – 0.0066) X 100 = 99.34%
Even though there is a significant difference between the salt passage value at 0.66% and the salt rejection value at 99.34 percent, we now understand that salt passage and salt rejection describe the same phenomena within an RO system. Combining this with the calculated average feed TDS allows operators to properly evaluate and track the performance of their membrane system.