In the field of water treatment, various types of ion exchangers are commonly used. Whether softeners, demineralizers, or desalination units, they all rely on the same principle of ion exchange. While their mode of operation is relatively simple, understanding how to size these systems can sometimes be complex.

So, how do you size ion exchangers?

To begin with, adjusting the treatment flow rate of an ion exchanger is done by modifying the diameter of the resin bed. Intuitively, a tank with a larger diameter will allow for a higher flow rate.

As for the flow rate in relation to the necessary contact time, it is adjusted by modifying the volume of resin in the tank. The more resin there is in the tank, the longer the water will remain in contact with the resins. Depending on the type of resin and its processing speed, the amount of resin will affect the permissible flow rate.

In other words, the flow rate is adjusted through the diameter of the resin bed, while the contact time depends on the volume of resin or the "depth" of the resin bed.

To understand the possible flow rate based on diameter:

Ion exchanger tanks are made up of several internal components for water treatment. However, regarding the possible flow rate, the diameter of the tank is the main aspect to consider. This is crucial because an increase in pressure would impact the flow rate of water through the tank. Thus, when calculating the necessary diameter to achieve a specific flow rate in gallons per minute, the resin processing speed is taken into account.

The calculation used for this step is as follows:
 


Where:
   - D is the diameter of the softener resin bed (in units of length, for example, inches or centimeters).
   - Q is the required water flow rate in gallons per minute (GPM).
   - V is the resin processing speed (in gallons per minute per square foot).
   - π is a constant, approximately equal to 3.14159.

A suitable resin processing speed is essential to ensure optimal ion exchange efficiency. Too low a speed can result in resin bypass by water (preferential path), while too high a speed can reduce the contact time between water and resin, compromising ion exchange efficiency. Generally, resins offer permissible flow rates ranging between 1 and 4 GPM per square foot.

Let's take a concrete example: suppose a required water flow rate of 10 gallons per minute (GPM) and a resin processing speed of 5 gallons per minute per square foot (GPM/ft²). Applying these values to the formula to find the resin bed diameter:



In this case, the tank diameter should be at least 1.59 feet to allow for the necessary flow rate.

A quick note before moving on: resin processing speed is typically a range. Since the calculation doesn't account for this, some discrepancies may occur. For example, in this situation, we would suggest a tank with an 18-inch diameter.

Understanding the possible flow rate based on contact time and the number of cubic feet of resin:

The flow rate must also be adjusted based on the amount of resin and the levels of contaminants in the water, due to the contact time required for the resin to remove these contaminants. It is noted that the contact time varies according to many factors, but generally, the optimal flow rate per cubic foot of resin is typically around 3 gallons per minute (GPM).

Next, consider the resin treatment capacity, usually measured in grains per cubic foot. The main categories of resins include anionic, cationic, and mixed bed resins, each with a different average treatment capacity.

   - Anionic resin: 20,000 to 25,000 grains per cubic foot
   - Cationic resins: 20,000 to 25,000 grains per cubic foot
   - Mixed bed resins: 10,000 to 15,000 grains per cubic foot

Normally, instead of talking about 20,000 grains, the term "KGR" is used to define kilograms of grain. So, it would be stated as 20 KGR.

Calculation:

Let's take a concrete example: if a cationic resin has a exchange capacity of 24,000 grains per cubic foot of resin, it means it can exchange 24,000 positive ions per cubic foot before becoming saturated.

Now, if the water to be treated contains 10 grains per gallon (gpg) of CaCO3 (calcium carbonate), we first need to convert this measure into grains per cubic foot (gpc).

   1 gallon of water = approximately 7.48 cubic feet of water

So, 10 gpg * 7.48 = 74.8 grains per cubic foot (gpc) of CaCO3.

Now, if the exchange capacity of the cationic resin is 24,000 grains per cubic foot, we divide this number by the amount of grains per cubic foot of CaCO3 to get the volume of water that the resin can treat before becoming saturated:

   - Resin exchange capacity / Grains per cubic foot of ions in water = Volume of treated water

So, 24,000 grains per cubic foot of resin / 74.8 grains per cubic foot = approximately 320 cubic feet of water treated before saturation.

This means that for each cubic foot of resin, an ion exchanger can treat about 320 cubic feet of water with a hardness of 10 gpg of CaCO3 before needing to be regenerated. This is equivalent to about 2,393.77 gallons of water.

Treatment capacity:

It is important to note that increasing the number of cubic feet of resin is generally done with the aim of spreading out the intervals between regenerations. To revisit the previous example, an ion exchanger with 1 cubic foot of resin should be regenerated every 2,393.77 gallons of water treated. By increasing the number of cubic feet to 2, it should be regenerated every 4,787.2 gallons of water treated.

Scenario:

By reusing the examples used above, here's a brief scenario. After previously testing your water and defining your treated water needs, you have the following requirements:
   - 10 GPM for 8 hours a day
   - You need to remove 10 gpg of cation or anion.

At 10 gallons per minute for 8 hours a day, that equates to 14,400 gallons of water per day.
(10 gallons x 60 minutes) x 8 hours

To avoid regeneration every 76.8 minutes, we will increase the amount of resin present in the tank.

2393 gallons (capacities) / 14,400 gallons (demand) = 0.16
8 hours = 480 minutes
0.16 x 480 = 76.8 minutes

For optimal operation in this system, 5 cubic feet of resin would be required. This would treat approximately 12,000 gallons of water. Regeneration would then occur once per day.

In summary, to achieve 10 gallons per minute while removing 10 gpg of CaCo3, a system

with an 18-inch diameter and 5 cubic feet of resin would be optimal.

The relationship between GPM per square foot and GPM per cubic foot

The relationship between flow rate in gallons per minute per square foot (GPM/ft²) and flow rate in gallons per minute per cubic foot of resin (GPM/ft³) is crucial in the planning and optimization of ion exchange systems. In addition to the characteristics mentioned earlier, it is crucial to consider this relationship to avoid issues such as resin breakage. 

Indeed, when the resin bed is too thick or if the pressure difference (Delta P) increases significantly, resin beads can crack. To simplify, a general rule is followed: with a few exceptions where thickness up to 60 inches is tolerated, resin beds should not exceed a thickness of 48 inches. Typically, resin bed thicknesses range between 36 and 48 inches.

Conclusion:

As the expression goes, this is just the tip of the iceberg. After properly sizing the system, it's important to calculate the necessary regenerant quantities as this can be expensive in the long run. Next come the types of resins; even though we talk about mixed bed resins, cationic resin, and anionic resin, there are a plethora of resins offering different treatment capacities. One might think of better processing speed, higher grain capacity, emphasis on certain stubborn contaminants, special capabilities, specific uses, etc.

In short, these calculations can help you size the system you need and set your expectations, but other aspects must be considered. Not to mention that these calculations can be complex to perform.

That's why, although we prefer to lay it all out for you, we always suggest reaching out to Durpro experts to get a system that truly meets your needs.