The Principles of Gravity Separation

Sept. 14, 2013

This is the first article in a three-part series on gravity separation, eventually leading to the best method for sizing basins, using field data as confirmation of the method. Gravity separation is a set of unit processes in which gravity removes settleable solids and associated pollutants, floatables, and dispersed petroleum products. Gravity separation is the primary mechanism of pollutant removal in stormwater treatment systems. Removal occurs downward for solids denser than water like sediment, and upward for solids lighter than water such as dispersed droplets of petroleum, oil, and paper. The former is sedimentation; the latter is flotation. Figure 1 conceptually displays gravity separation. The fundamental engineering principle of gravity separation is the settling velocities of particles, and recognition of two types of settling in stormwater treatment: dynamic and quiescent. Settling velocity is affected by particle size, shape, and specific gravity and by water temperature. This article discusses sedimentation, the downward removal of stormwater particles.

Settleable Solids
There is a distinction between suspended and settleable solids. Total suspended solids (TSS) are those solids captured by a laboratory filter. Some are so small they will not settle. Settleable solids are defined as those solids that settle in an Imhoff cone. An Imhoff cone is made of clear plastic or glass. Imagine a traffic cone placed upside down: That is the vision of an Imhoff cone. Settleable solids are measured by placing one liter of a thoroughly mixed sample into the cone and measuring the number of milliliters of solids accumulated at the bottom after 60 minutes (milliliters per liter). However, this definition of settleable solids understates what actually settles, because the detention time, also referred to as the hydraulic residence time (HRT), in settling basins is typically greater than one hour. The true settable solids are, in the case of wet basins, those that settle over a period of several days.

Solids are further categorized by type: organic, inorganic, biological, and chemical. The specific gravities and shape of each type and therefore settling velocities differ significantly. Organic solids are lighter than inorganic solids. Some are lighter than water, although most have specific gravities between 1.1 and 1.5. The specific gravity of most inorganic solids ranges from 1.5 to 2.65, with sand 2.45 to 2.65. Some clays have a much lower specific gravity because of entrained water, on the order of 1.5. Biological solids refer to the bacterial flocs created in wastewater treatment systems. Chemical floc is produced in coagulation processes. The engineer’s definition of clay is by size, rather than by mineral form as with soils. Hence, solids as defined in by engineers, rather than by soil scientists, likely contains organic matter.

Figure 1. Elements of gravity separation

Types of Sedimentation
There are four types of sedimentation as applied to stormwater, water, and wastewater treatment: discrete, flocculent, hindered, and compression. Only the first two are relevant to stormwater treatment. An exception may be treatment basins at construction sites in which the final two types might be relevant. For a solution where the suspension is initially relatively dilute, the suspension is considered discrete. As settling progresses, particles may flocculate as they contact each other. Near the bottom of the basin, the suspension density is sufficient to hinder settling, reducing the settling velocity. At the bottom the solids thicken by compression from the weight of the accumulation. Depending on the suspended solids, the suspension may not flocculate, moving directly from discrete to hindered settling.

The stormwater solids suspension is likely to be both discrete and flocculating. The suspension has three overlapping components: coarse materials that settle quickly as discrete particles (>50 microns), intermediate size silt that tends to naturally flocculate while settling (5 to 50 microns), and clay-size particles (<5 microns) that neither settle easily nor flocculate quickly because they are colloidal, negatively charged, and resist coagulation. Furthermore, the settling of clay-size particles is inhibited by Brownian motion. The classification system applies to vaults and basins, flotation systems, and swirl concentrators.

Determining Settling Velocities
Stormwater exhibits a distribution of settling velocities, a reflection of the complex mixture of solids of different sizes, shapes, specific gravities, and water temperatures. The settling velocity distribution is determined two ways. If the size distribution is known, the settling velocity distribution is calculated using Stokes Law and related equations. The second method is direct measurement of settling velocities. Each method has its advantages and disadvantages.

Stokes Law. Equation 1 describes the settling velocity of a spherical particle in quiescent water. The equation applies to spherical particles whether they are denser or lighter than water.

Vp = settling velocity of a particle
g = gravity constant
ρs = density (specific gravity) of particle
ρ = density (specific gravity) of water
d = particle diameter
CD = drag coefficient (dimensionless)

The drag coefficient (CD), related to the Reynolds Number (Re), describes the hydrodynamic condition of the fluid at the particle surface. As size increases the drag coefficient decreases. The relationship is shown in Figure 1. Shown are the three hydrodynamic conditions: laminar, transition, and turbulent.

The fluid condition described in Equation 1 is not of the water, but of the fluid boundary surrounding the particle. In the laminar zone, viscous forces dominate with small particles because of their large surface area in relation to their volume. Drag decreases linearly with increasing particle size, as the surface area of the particle decreases relative to its volume. The relationship begins to deviate from linear as the settling velocity increases because inertial forces become significant. The transition area occurs where inertial forces gradually become more significant. Eventually, inertial forces dominate and a completely turbulent condition exists around the particle. In the turbulent condition drag does not change with increasing particle size.

Equation 2, derived from Equation 1, describes the relationship between the Reynolds Number and the drag coefficient, as are values for constants b and n in Table 1. Demarcation points between the three hydrodynamic regimes are not distinct. Re is the Reynolds Number.

Stokes Law describes settling velocities only under laminar conditions. Recognizing that Re = ρVp d/µ and CD = 24/ Re for the laminar condition, Equation 1 modifies to give Stokes Law in Equation 3. The absolute viscosity is µ.

For the transition from laminar to turbulent, Stokes Law is not valid, and the values for b and n in Table 1 transform Equation 3 to Equation 4. The CD for the turbulent condition is constant at about 0.44. Equation 4 is revised to Equation 5. Both Equations 3 and 5 can be used with metric or English units. A conversion factor X is needed for Equation 4: 0.072 for metric units and 2.32 for Imperial units.

Table 1

Equations 1 through 3 assume the settling particles are spherical. Non-spherical particles experience higher drag forces, resulting in a settling velocity that is lower than the calculations from Equations 1 through 3. Equation 4 incorporates the effects of particle shape on the drag force by using a shape factor, Sf.

For a smooth spherical particle, the value of Sf is 1. For sand or silt, it is 2. Thus, sand and silt have a settling velocity about half of a spherical particle. Fall velocities of uniform shapes other than spheres have been studied. There are no shape factors for organic solids or chemical flocs. Graphite flakes have a Sf of 22, suggesting organic solids likely have a shape factor greater than that of sand, but this has not been evaluated. Organic solids settle considerably slower than inorganic solids, as does clay, given their shape factors. The effect of temperature on settling velocities is significant for stormwater given the range experienced. As temperature decreases, settling velocities decrease due to the increase in the viscosity of water. The same occurs with saline stormwater due to deicing salts. A study found that the combination of saline water and low temperature reduced the settling by about half.

Clay appears to deviate significantly from Stokes Law at very low temperatures. Stokes Law states that the settling rate decreases with decreasing temperature due to increasing water viscosity. However, forces that inhibit flocculation are reduced with decreasing temperature. According to Stokes Law, the settling rate of clay should decrease by 45% with a temperature decrease from 25 to 5°C, yet it has been observed to increase by 30%.

In contrast, a study of stormwater (Figure 2) found significant deviation from Equation 3, with the standard input of specific gravity at 2.65, beginning at about 20 microns (the upper line). The settling rate for 10 microns was only about 10% of that calculated with Equation 3. Figure 2 indicates the potential deviation of very small particles from the standard Stokes Law when a specific gravity of 2.6 is assumed for all particles. The deviation starts at 20 microns. It is often stated that settling in stormwater systems do not follow Stokes Law. This is not true. Deviations are found simply because shape factors and the inputs for specific gravity and temperature are wrong for the situation.

Figure 2. Examples of settling velocities as a function of size and specific gravity

Even for the prediction based on a specific gravity of 1.5, common for some clays and organic matter, the lower portion of the middle line overstates the observed settling rates of particles in stormwater. The difference between the middle and lower lines might be due to shape, such as the clays and fine silts appearing as more or less flat plates. For example, micaceous clay flakes have settling rates two orders of magnitude lower than a sphere of the same specific gravity. The deviation gets greater as the particle size gets smaller, as indicated in Figure 2.

A review of over a dozen studies found that the specific gravity of individual studies ranged from 1.1 to 2.86, with most above 2. Only three of the studies cited had values in the range of 2.6, the most common specific gravity used to calculate settling rates of particles in stormwater. One study in which the sample was mostly organic had the density of 1.1. A significant portion of the sediment can be organic, 25 to 50% in a review of six studies. Mixes used in laboratory testing such as Sil-Co-Sil 106 behave differently than sediments in stormwater. Generally, better removal is expected in laboratory studies due to the absence of materials with specific gravities less than 2.6, assuming the same particle size distribution of laboratory and stormwater sediments.

As shown in Equations 1 through 5, particle size is required to calculate settling velocity. Particle sizes are typically determined through the use of standard soil sieve tests that commonly measure particles as small as 75 microns, although sieves as small as 25 microns have been used. Sizes of smaller particles are determined using the hydrometer procedure. This method gives settling velocities directly, from which the size distribution is calculated using a modified Stokes Law as specified. For others who may use these data to recalculate settling velocities, it is important to use the equation provided in the method. The equation specifies a coefficient shape factor of about 1.75. A common error in calculating settling rate of particle sizes is to leave out the shape factor, grossly overstating the settling velocity.

Further considerations make use of Equation 3 problematic. Drying and grinding of samples prior to sieving modifies the original size distribution. In the hydrometer test, dried material is wetted with distilled water, with a significantly different chemistry than stormwater. Therefore, the results do not represent the sediment sizes present in the original stormwater sample. It is suggested that samples not be dried prior to sieving, thereby avoiding the bias of rewetting. A comparison of dry and wet sieving of street sediment samples found that dry sieving understated the fraction of particles less than 75 microns by a factor of two. Wet procedures are available.

Settling Column Method
The shortcomings of using Stokes Law and related equations are potentially overcome by measuring the settling velocity distribution directly using a settling column. The columns have a diameter of 6 to 12 inches (15 to 30 centimeters) and a height of 3 to 6 feet (1.5 to 3 meters). The settling velocity is determined by placing a stormwater sample in the column. The concentration of particles is determined by withdrawing samples at specified times and points, typically 1-foot intervals, along the column. A plot is made of removal efficiency, which is the observed concentration in each sample from the column divided by the original concentration times 100, versus depth, as illustrated in Figure 3. Note that the lines in Figure 3 are straight, indicating a discrete suspension. Clearly the settling velocity of sand cannot be measured as it immediately drops to the bottom of the column. But this does not matter, given the ease with which sand is removed. What matters is the settling velocity of silts and clays.

Figure 3. Settling column and test results

If the suspension is flocculent, the lines curve downward. This suggests that with discrete settling, the settling rate is independent of the depth of the basin, whereas with flocculent settling, the settling rate is dependent on depth and therefore the hydraulic residence time. Figure 4 presents a summation of data of settling velocity distributions observed with stormwater. Note the tremendous variability. The rates in Figure 4 are for silts and clays.

Figure 4. Settling velocity distribution data

There are potential biases with column tests. Length and temperature of sample storage affects settling velocity. Median settling velocity increased from 0.036 to 0.08 feet per minute (0.018 to 0.04 centimeter per second) between same-day and next-day testing with the stormwater stored at room temperature. Sample refrigeration further increases settling velocities. The effect is greatest with fine particles. This is consistent with observations regarding the effect of temperature on clay flocculation. Although absence of turbulence in the column allows clays to settle, it delays flocculation. Thus, absence of mild turbulence in the column as exists in stormwater basins may understate the settling rate of clay. Other devices may better mimic stormwater settling.

Settling With Intermittent Flows
Stormwater flow is intermittent. Depending on the type a basin, there are one or two settling processes. One process occurs during each storm, called dynamic settling. The second process occurs between successive storms and is called quiescent settling. Stormwater treatment systems that retain water between storms have both dynamic and quiescent settling. Examples are wet ponds, wet vaults, and constructed wetlands. Stormwater treatment systems that are dry between storms experience only the dynamic settling process. Examples are grass swales, strips, fine-media filters, and extended detention ponds.

The manner of settling is not the same with each settling process. Furthermore, the relevant design parameter that affects the efficiency of each process differs, giving rise to a potential conflict for those systems as to design with both processes.

Dynamic Settling. With dynamic settling of discrete solids, the sole determinant of removal efficiency is the hydraulic loading rate (HLR). The HLR is the rate of flow into the treatment system divided by the surface area of the wet basin. The HLR has the units of ft3/ft2/day (m3/m2/day).

The common reason given for how vortex separation works in stormwater vaults is that the swirling motion (vortex) results in a longer flow path for the particle and in turn detention time: increased detention time for the particle, not the water. However, in the context of gravity separation, as opposed to vortex separation, this view is incorrect, as the velocity of the entering water in a vortex separator is too low. Vortex separators are more aptly described as swirl concentrators. Hence, the relevant design criterion is the hydraulic loading rate, the principles of which were first established in 1904, and shown in Equation 5.

HLR = hydraulic loading rate
L = basin length
W = basin width
Q = flow rate

Note that Equation 5 does not contain the parameters of volume, depth or hydraulic residence time (HRT). With discrete settling these are not relevant factors in determining efficiency. Derivation of Equation 5 with the help of Figure 5 demonstrates this point.

Figure 5. Removal of the design particle

The fraction of particles removed is a function of HRT/td where td is the time required for the particle of interest, or design particle, to reach the bottom of the basin at the outlet end (line A in Figure 5). All particles with settling velocities equal to or greater than the settling rate of the design particle (Vd) are captured. Some of the particles with lower settling velocities also are removed because as the water enters, the solids distribute across the vertical cross-section of the basin at the inlet. HRT and td are defined by:

Hence, the design HLR is the settling velocity of the target particle to be captured, Vd. The relationship is recognized when realizing the units for the HLR are ft3/ft2/day, the same for settling velocity of feet per day. This analysis indicates that two basins with the same volume, but different depths, have different removal efficiencies if both have the same hydraulic efficiency. The basin with the shallower depth and therefore greater surface area has the greater removal efficiency. Ignoring the potential for resuspension of settled sediments, a very shallow flat basin represents the optimal condition. The relationship between HLR and settling of TSS solids has been established.

Quiescent Settling
With quiescent settling, the relevant design parameter is the volume of the wet pool rather than its surface area. This is understood intuitively. The larger the volume of the wet pool in relationship to the incoming storm volume, the greater the fraction of the storm volume retained by the basin, and in turn, the greater the percentage of the settleable solids retained for settling during the quiescent period. This relationship in its simplest form is described for a wet basin by Equation 6.

Equation 6 indicates that the fraction of particles removed depends on the fraction of inflow volume retained by the settling basin. Stated differently, it represents the fraction of particles present in the event volume that is retained by the basin. If the settling time for the particle of interest is less than the time to the next event, all of the solids of that size or smaller will reach the bottom before the next event.

However, if the settling time for the particle of interest is greater than the time to the next event, only a fraction of the particles trapped in the basin will reach the bottom.
Equation 6 assumes ideal hydraulic conditions; that is, a complete exchange occurs between the volume of the incoming water and an equal volume present in the basin prior to the event. The equation says that basins that retain water between storms have a greater removal efficiency than basins that are dry between storms, if all other factors such as size and hydraulic efficiency are the same.

Factors Affecting the Relative Significance of Each
The comparison of the two settling periods, dynamic and quiescent, raises the question of which period is dominant in wet basins and therefore which design parameter, volume or surface area, is most relevant.

The relative importance of each type of settling is determined by whether the settling is discrete or flocculent, the settling velocity distribution of the particles in the stormwater, the volume of the basin relative to the volume of the storm, and the treatment efficiency goal.

If the suspension is discrete, surface area is more significant. If the suspension is flocculent, basin depth and therefore volume become significant. The greater the fraction of fine solids (with low settling velocities), the less significant the dynamic period, and the more significant the quiescent period. The issue of clays is relevant only when there is a significant amount of clay, say on the order of 10 to 20%.

Given that a significant percentage of settleable solids in stormwater are small and have low settling velocities, as well as that most stormwater suspensions appear to be flocculent, it is likely that volume is the more relevant design parameter. The greater the volume of the wet pool relative to the volume of the storms, the more significant the quiescent period.

If the desirable treatment efficiency is modest in the case of a pretreatment wet basin, the dynamic period becomes more significant. If the treatment efficiency goal is high in the case of a wet basin that serves as the primary unit operation, quiescent settling increases in importance.

It is commonly believed that wet basins should be sized based on a specified hydraulic residence time during the storm period. However, the above discussion establishes that hydraulic residence time during the storm is not a relevant design parameter, regardless of which settling period is dominant.

A more relevant hydraulic residence time is that between the storms, or the average annual hydraulic residence time. It represents the average time water resides in the wet basin over a year. The average hydraulic residence time provides an indication of the time available for settling during the quiescent period. It is the total annual runoff divided by the depth of the mean annual runoff event multiplied by 365 to give the units of days.

Resuspension of previously settled sediments or organic matter during extreme events is a concern in basins and swales. The condition may be exacerbated by narrowing basins to improve hydraulic efficiency, thereby increasing the longitudinal velocity. Except for wind, resuspension is likely to occur only in the inlet and outlet areas.

A study found little resuspension in a sedimentation basin with a depth of 3 feet (1 meter). The general guideline to keep sand from resuspending is to keep the water velocity below 1 foot per second (30 centimeters per second). Higher velocities are allowed for smaller particles, in the range of 50 to 100 microns or less, due to their cohesive nature. Because of their feeding habits, ducks and swans will cause resuspension of bottom sediments.

The force required to resuspend a particle is related to the force keeping it down, which in turn is related to the settling velocity of the particle and the cohesiveness between particles. Methods of analysis for calculating resuspension velocities are available from water and wastewater treatment engineering, river engineering, and mining engineering. Equation 7, drawn from water and wastewater treatment engineering, is applicable to low-density organic solids.

Vr = resuspension water velocity
f = Darcy-Weisbach friction factor, taken as English: 0.025 units
Vp = settling velocity of the particle

Vp represents the original settling velocity of the particle that is not to be resuspended. Resuspension velocity, Vr, is the average forward water velocity through the basin that will cause resuspension. For example, assume a settling velocity of 0.1 foot (3 centimeters) per second for the particle of interest. The resuspension velocity is about 1.8 feet per second. Average forward velocity in an in-line wet basin during extreme events may reach this value in small vaults. The assumed settling velocity represents organic particles 100 to 300 microns.

Equation 7 does not recognize that depth affects the value of Vr, which decreases with decreasing water depth. As the equation was developed for water and wastewater settling basins with depths of 10 to 15 feet (3.3 to 5 meters), the resuspension velocity for the same particle in stormwater wet basins might be considerably lower than indicated by Equation 7.

Equation 7 assumes that Vr decreases as particle size decreases through the entire size spectrum. This is a reasonable assumption for organic sediments. However, with inorganic sediments, Vr decreases as the particle size decreases only to a diameter of about 200 microns.

With inorganic particles less than 200 microns, Vr increases rather than decreases due to increasing cohesiveness of the sediment. For example, at 10 microns the critical velocity is about twice that of a 200-micron particle, although, based on Stokes Law it ought to be about one-fifth. These observations suggest that clays and silts are not likely to be resuspended during extreme events, except near the inlet, to the extent that the cohesive condition of the sediments are reestablished.

A field study of resuspension of deposited silts and clays in mine tailing ponds lead to Equation 8, which therefore may be most applicable to stormwater ponds and wetlands for inorganic sediments. The equation defines the minimum depth necessary to avoid resuspension by wind, not incoming water.

For a depth of 3 feet (1 meter), a pond of about 1,000 feet (330 meters) in the direction of the wind can withstand a wind velocity of 55 miles per hour (17 meters per second) before resuspension. According to this method, wetlands with depths less than 0.5 foot should experience resuspension of inorganic sediments if the basin length exceeds a few hundred feet. However, the effect should be moderated by the vegetation.

Resuspension by wind has been observed in wet ponds with depths less than 3 feet (1 meter). Bacteria in the water column ponds were observed to increase in the presence of wind, implying resuspension of sediments. Various equations for estimating resuspension potential have been studied. Other relationships have been developed on this topic.

About the Author

Gary Minton

Gary R. Minton, Ph.D., P.E., is a consultant on stormwater treatment and the author of the book Stormwater Treatment: Biological, Chemical, and Engineering Principles.

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