*By C.F. ‘Chubb’ Michaud, CWS-VI*

There are two primary flow measurements used in media filtration: the superficial flow or flow per unit of surface as cubic feet, cubic meters or cubic miles. If we have a bed of GAC with a recommended EBCT of five minutes, that means that we are flowing *one BV of water through *area (gpm/ft ) and volumetric flow or volume of fluid per volume of media (gpm/ft3). From these measurements, we derive empty bed contact time (EBCT), also referred to as residence time or dwell time and loading rate (flow per unit area) (see Figure 13).

**EBCT and bed volumes (BV)**

EBCT is a volumetric rate measurement. It is called empty bed because it takes the bulk volume of the media and does not try to figure in void space. Just like gpm/ ft^{3}, it is derived from volume per volume numbers. If we express flowrate as gpm/ft^{3} and convert the gpm of water figure to ft^{3}/min of water (by dividing by 7.5 gal/ft^{3}), we have a new number that reads cubic feet of water per minute per cubic foot of media. When you divide the volume of media by the volume of water flow, you get time in minutes. A flowrate of 3 gpm/ft^{3} then translates to 3/7.5 = 0.4 ft^{3} of water/min. If that is passing through one cubic foot of media, we have a flow of 0.4 ft^{3}/min/ft^{3} of media for an EBCT of 2.5 minutes. This can be converted to flow per hour, so we have (0.4 x 60 =) 24 ft^{3}/hr of flow/ft^{3} of media. This can also now be expressed as 24 bed volumes (BV)/hr. This measurement also does not take into account voids in the bed. A bed volume can then be interpreted as cubic feet, cubic meters or cubic miles.

If we have a bed of GAC with a recommended EBCT of five minutes, that means that we are flowing one BV of water through one BV of GAC in five minutes (or one cubic foot [7.5 gallons]) of water through one cubic foot of media in five minutes) or 7.5/5 = 1.5 gpm/ft^{3}. A flowrate of 2 gpm/ft^{3} is (2 x 60 =) 120 gal per hour 3.75 minutes. One nice thing about EBCT or BV is that it removes the conventional size statement. It simply represents a relative rate of flow. 10 BV/hr can be 10 ft^{3} of flow/ft^{3} media/hr, 10 liter/liter/hr or 10 meter^{3}/meter^{3}/hr. Table 7 offers a reference chart to compare EBCT with BV/hr and gpm/ft^{3}.

If you are working with filters that have flowrates of 1 to 3 gpm/ft^{3}, you have flowrates of 8 to 24 BV/hr (gpm x 60/7.5 = BV/hr). You have EBCTs of 7.5 to 2.5 min (1 gpm/7.5 gal media = EBCT of 7.5 min). The empty bed concept takes into account only the bulk volume of the bed and makes no attempt to factor in void volume. This brings us to the concept of *half lengths*.

**Part 8, Figure 13.** Measures of dynamic flow

*Half-length reaction times*

If it takes 30 seconds for a quantity of GAC to remove 50 percent of the organics contained in the feed stream, how long does it take to remove the other half? Sounds like it should only be another 30 seconds. As the concentration of the organic is reduced, however, so is the driving force and, thus, the rate of its removal. The concept of half-length removal is that it would only remove 50 percent of the remaining 50 percent over the next 30 seconds for a total removal of 75 percent, then another 30 seconds to remove 50 percent of the remaining 25 percent and so on. From Figure 14, we can determine the number of half lengths needed to remove any particular percent of the contaminant.

We know from experience that chlorine can readily be taken out of feed water with EBCTs as low as 60 seconds. From this we could deduce that the half length for chlorine is about 10 to 12 seconds (5 to 6 half lengths per minute). It is suggested that chloramine removal (with the proper GAC) requires a minimum of five minutes EBCT; we can figure the half length is about 50 to 60 seconds. Volatile organics such as trihalomethane (THM) must usually be taken out to the tune of 95 percent or more and require 10 to 15 minutes EBCT. This would suggest a half length of 2.5 minutes. Removing ppb levels of contaminants to even lower ppb levels may take up to 30 minutes EBCT. You still have to provide some capacity for longevity (see Figure 15).

The shaded yellow area in Figure 15 represents the steady reduction of a contaminant through a bed of GAC. As the bed exhausts, the yellow shaded area moves down the bed closer to the exit, which could be illustrated by the bed in the middle. As the bed approaches exhaustion, it would appear on the far right. The amount of bed that represents the remaining capacity is represented by brackets marked capacity. If an adsorption filter such as GAC is run at too high a flowrate for the job, it may resemble the high-flow model. Even though it removes 95 percent on day one, it may break through within a few days. Witness the standard 10-inch cartridge. These are often run at flowrates of 0.75 gpm. Since a cartridge is approximately 1/37 of a cubic foot, that is the equivalent of a flow of 27.75 gpm/ft^{3}, an EBCT of only 16 seconds. How is it that a cartridge run at almost 28 gpm/ft^{3} can do that? The answer is illustrated as the high-flow example in Figure 15. A cartridge may remove THMs for 1,000 gallons at a flow of 0.75 gpm, the equivalent of a full cubic foot of GAC treating 37,000 gallons. Under normal flowrates of 1 to 2 gpm/ft^{3}, GAC will typically function for at least five times that level—the longer the EBCT, the higher the capacity.

**Making flow determinations**

The surest way to get an accurate flow measurement is to place a bucket under a flowing tap and use a stopwatch. You can also measure the time it takes to fill a tank to a certain level or measure the rate of depth change in a tank of a given diameter. Direct measurement has no variables other than time and volume. The result is in gallons per minute or some variation of the same.

Flow measuring devices such as meters and rotameters use direct measurements of something other than flow (as gpm) and convert the measurement into flowrate. The flowing fluid turns a turbine or paddle wheel and there is a calibration that converts the signal to flow. Rotameters, which were invented in 1908, are those see-through devices with a variable area that measure the ability of the flowing fluid to suspend a shaped weight inside the column of flowing fluid. The outside of the variable area column can be calibrated to give a direct flow reading in gpm or Lpm. This is shown in Figure 16.

These devices are sufficiently accurate to be used for setting flowrates such as backwash and eductor flow, rinse and service.

**Figure 15. **An illustration of capacity versus flowrate

They have limitations, however. Examine the drag equation presented in Equation 4, where:

FD = the drag force, which is by definition the force component in the direction of the flow velocity.

*ρ *= the mass density of the fluid,

v = the velocity of the object relative to the fluid

A = the reference area and

CD= the drag coefficient, a dimensionless coefficient related to the object’s geometry and taking into account both friction and form drag.

*Equation 4. Drag dynamics*

F = ½ ** ρ**v2 C A

**Figure 16.** The Rotameter(12)

Because the column has a variable area that increases toward the top, the fluid force that suspends the float can reach a reproducible equilibrium for any given flow. The equilibrium exists between gravity, which is trying to pull the float down, and the force of the fluid that is trying to carry the float out of the column. Please note: this only works for the density (ρ) for which it was calibrated. The instruments are usually calibrated for water. They cannot be used to measure the direct flow of brine, caustic, acid or maple syrup. The results are reproducible, however; they can be used on those fluids once you have calibrated the reading with the actual flow. In other words, if a reading of 25 gpm for brine actaully was measuring the real flow of brine (which by the bucket method was determined to be 18 gpm), then it can be used to measure that particular flow for that particular concentration of brine.

*Summary*

There are two flow parameters used in designing filter beds. One is the volume of flow per volume of filter bed (used to calculate the EBCT) and the other is the surface flow of volume per area of filter, which contributes to pressure drop. Over-running too small a filter bed can result in poor removal efficiency and/ or early failure of the filter. If an EBCT of 7.5 minutes is required, the design flowrate is 1 gpm/cu ft.

*References*

*C.F. ’Chubb’ Michaud is the Technical Director and CEO of Systematix Company of Buena Park, CA, which he founded in 1982. He has served as chair of several sections, committees and task forces with WQA, is a Past Director and Governor of WQA and currently serves on the PWQA Board, chairing the Technical and Education Committees. Michaud is a past recipient of the WQA Award of Merit, PWQA Robert Gans Award and a member of the PWQA Hall of Fame. He can be reached at (714) 522-5453 or via email at **[email protected]*