Flocculation

Flocculation

Introduction

Flash Mixers and Flocculators

This page is concerned with the design of flash mix and flocculation chambers.  Both devices operate in much the same way - the water flows through the tank and is mixed in the process.  The primary differences between a flash mix chamber and a flocculation chamber include the detention time and the velocity gradient. 

The detention time is the time required for a small amount of water to pass through a tank at a given flow rate.  Mathematically, detention time is given by the following formula:

Where:

 t   =  detention time
V  =  tank volume
Q  =  flow

In the case of the flash mix chamber we will consider, the optimal detention time is 30 seconds.   The detention time of a flocculator is much greater, around 30 minutes.  

The second factor, the velocity gradient, is a measurement of the intensity of mixing in the chamber.  The velocity gradient determines how much the water is agitated in the tank, and also determines how much energy is used to operate the flash mixer or flocculator.   



Size and Shape

Although the detention time and velocity gradient are the most important factors influencing the performance of a flash mixer and flocculator, the physical features of each chamber can differ greatly.  The shape of both types of mixers can vary from cylindrical to rectangular or cubical.  The water can be mixed simply by water flowing around baffles, or it can be mixed with a variety of types of paddles, turbines, and propellers.

This page is primarily concerned with determining the volume and dimensions of the tanks.  The volume depends on the amount of water being treated, and is generally much greater for a flocculator than for a flash mix chamber.  The dimensions, in turn, depend on the volume of the tank.



Power Consumption

In addition to calculating the volume and dimensions of various flash mixers and flocculators, we will be determining the amount of power which the devices require to operate.  You can use the power requirements to optimize the efficiency of the flocculators and flash mixers, or merely to predict how much operation of the devices will cost. 

Mechanical Rapid Mixer

Specifications

Each set of calculations can only be used on a certain type of device.  This set of calculations is appropriate for a mechanical rapid mixer, a type of flash mix chamber.  A diagram of the flash mixer is shown below.

Specifications: Cylindrical tank. Diameter: 3-10 ft. Depth: Less than 10 ft. Four vertical baffles. Mixing by vertical-shaft, turbine-type impeller. Flow from bottom to top. Detention time: 30 sec. Velocity gradient: 500-1000 sec.-1

A few of these specifications require explanation.  The first few specifications merely limit the physical shape and size of the mixer.  The rest are briefly explained below.

The baffles are flat boards or plates, deflectors, guides, or similar devices placed in flowing water to cause more uniform flow, to absorb energy, and to divert, guide, or agitate liquids.  You can see the baffles as four yellow rectangular shapes around the sides of the flash mixer. 

The impeller is shown in white at the center of the chamber.  A motor makes the impeller spin, which in turn agitates the water.  The arrows show the mixing action of the water.

The inlet and outlet devices are not shown in the diagram, but flow should enter from the bottom of the chamber and leave through the top of the chamber. 

Summary of Calculations

We will use the following steps to determine the flash mixer's dimensions:

1. Determine the tank volume.
2. Assume a depth.
3. Calculate the tank diameter.

Then we will calculate the power requ

irements as follows:

1. Calculate water horsepower.
2. Calculate electric horsepower.
3. Estimate power costs.

Tank Volume

The volume of the tank is calculated using the following formula:

V = Q t

Where:

V  =  volume, ft³
Q  =  flow, cfs
 t   =  detention time, sec

You should recognize this formula as a version of the formula we introduced for detention time in a previous section. 

The flow for our plant is 2 cfs and the detention time for the mechanical rapid mixer has been specified to be 30 seconds.  So the volume of the tank can be calculated as follows:

V = (2 cfs) (30 sec)

V = 60 ft³

Tank Dimensions

In order to determine the dimensions of the tank, we first assume a depth, then we calculate a diameter.  The depth can be anything within the specified range of 10 feet or less.  Here, we will assume a depth of 5 feet. 

The diameter is calculated as follows:

Where:

D  =  diameter, ft
V  =  volume, ft³
 d  =  depth, ft

Since we know that the volume of our tank is 60 ft³ from the last section and since we've assumed a depth of 5 feet, the diameter of the tank is calculated as follows:

Power Requirements

The power requirement is the amount of energy which is needed to operate the device.  By calculating the power requirements of the flash mixer, we can determine how much it will cost to run the device.  Calculating the power requirements is done in three steps, as shown below:

1. Calculate water horsepower.  First, we calculate the amount of water horsepower used to operate the flash mixer.  To do so, we use the following formula:

P = mVG² / 550

Where:

P  =  water horse power, wHp
m  =  viscosity, lb-sec/ft²
V  =  volume, ft³
G  =  velocity gradient, sec^-1
550  =  conversion factor, ft-lb/sec Hp

The viscosity is the resistance of water to flow due to internal molecular forces.  For water, like many other liquids, the viscosity is related to the liquid's temperature.  The table below shows the viscosity of water at a variety of temperatures.

Water Temperature (°F)	Viscosity (lb-sec/ft2)
32	0.0000373
50	0.0000273
60	0.0000233
70	0.0000204
80	0.0000179
85	0.0000169
100	0.0000142
120	0.0000116
140	0.0000098
160	0.0000083
180	0.0000073
212	0.0000058

In this page, we will assume that the water temperature is 60°F, with the corresponding viscosity of 0.0000233 lb-sec/ft.²  You may choose to use other water temperatures in your calculations, especially if your source water temperature varies greatly between summer and winter. 

Using a velocity gradient of 750 sec^-1, we can calculate the water horsepower used to run our flash mixer as follows:

2. Calculate electrical horsepower.  Since motors are not 100% efficient, the amount of electricity used to power the flash mixer is greater than the water horsepower used to mix the water.  We assume a "wire to water" efficiency of 80% and use the following formula to calculate the electrical horsepower:

Where:

E  =  electrical horsepower, eHp
P  =  water horsepower, wHp

So, in the case of our example, the electric horsepower would be:

E = 1.79 eHp

3. Estimate power costs.  The final step is to estimate the daily cost of the electricity used to run the mechanical rapid mixer.  We will assume that the unit runs 24 hours per day and that the electricity cost is $0.05 per kilowatt-hour.  The following formula can be used to calculate the power cost for the mixer.

Cost = (17.9) (E) (Price)

Where:

17.9  =  conversion factor, Kw-hr/eHp-day
E  =  electrical horsepower, eHp
Price  =  electricity price, dollars/Kw-hr

In our example, the cost of running the unit for a day would be:

Cost = (17.9) (1.79) ($0.05)

Cost = $1.60

Conclusions
Our calculations show that our plant can be served by a mechanical rapid mixer with a volume of 60 cubic feet.  With a depth of 5 feet, the mixer's diameter should be 3.9 feet.
It will take a water horsepower of 1.43 to run the device, which translates to an electric horsepower of 1.79.  The flash mixer will cost about $1.60 per day to run.



Horizontal-Shaft Paddle Flocculator

Specifications
Flocculators work much like flash mix chambers, though the water is agitated at a slower rate (a lower velocity gradient) and the detention time is greater.  Here, we will calculate the tank volume, tank dimensions, and power requirements for a horizontal-shaft paddle flocculator like the one shown below.

Specifications:

• Rectangular tank
• Depth: 7-16 ft
• Width: 10-50 ft.
• Length: 2 x width
• Minimum number of stages: 2
• Minimum number of channels: 2
• Mixing by horizontal shaft paddles
• Variable speed motors for tapering mixing
• Shaft rotational speed: 60-100 rev/hr
• Paddle area: <10-20% of tank cross section
• Peripheral paddle speed: 0.5-2 ft/sec
• Detention time: 30-60 min
• Flow through velocity: 0.5-1.5 ft/min
• Velocity gradient: 30-60 sec^-1
• Mixing opportunity parameter: 10⁴-10⁵

Summary of Calculations
First we will determine the flocculator's dimensions, as follows:

1. Decide on the number of channels.
2. Calculate the flow in one channel.
3. Calculate the volume of one channel.
4. Assume a depth.
5. Calculate the width.
6. Calculate the length.

Then we will check the flow through velocity:

1. Calculate the cross-sectional area of one channel.
2. Calculate the velocity in one channel.
3. Determine whether the flow through velocity is acceptable.

Finally, we will calculate the power requirements:

1. Calculate the volume of the entire flocculator.
2. Calculate water horsepower for the flocculator.
3. Calculate electric horsepower for the flocculator.
4. Estimate power costs for the flocculator.

Tank Volume

The tank volume is calculated just as it was for the flash mix chamber.  However, the flocculation basin is typically divided into two or more channels, as shown below.

Since the water must be divided between the various channels in the flocculator, the flow is similarly divided.  To find the flow in one channel, we use the following formula:

Q_c = Q/n

Where:

Q_c =  flow in one channel
Q   =  total flow
 n   =  number of channels

In our example calculations, we will use the same treatment plant which we used for the flash mix chamber calculations.  The flow of this plant, as you will remember, is 2 cfs.
We want to determine the volume of one channel of a two-channeled horizontal-shaft paddle flocculator.  The detention time is given as 30 minutes.  First we find the flow in one channel:

Q_c = 2 cfs/2

Q_c = 1 cfs

Then we determine the volume of the channel:

V = (1 cfs) (30 min) (60 sec/min)

V = 1,800 ft.³

When calculating the volume, we used the same formula used for the flash mix chamber, but added in a conversion since detention time was given in minutes rather than seconds.


Tank Dimensions
The tank dimensions of the flocculator channel are calculated in the same manner that was used for the flash mix chamber.  However, since the flocculator is a rectangle rather than a cylinder, the formulas used are different.
First we choose a depth within the specified range.  We will use a depth of 10 feet here.
The flocculator specifications note that the length should be equal to twice the width.  So we can find the width using the following formula:

Where:

W =  width, ft
V  =  volume, ft³
 d  =  depth, ft

In the case of our example, the width is calculated as follows:

The length can be calculated using the following formula:

L = 2 W

Where:

L  =  length, ft
W =  width, ft

So the length of our basin would be:

L = 2 (9.5 ft)

L = 19 ft

Check Velocity
The velocity of water flowing through the flocculation basin must be within a very specific range, designed to gently mix the water without breaking apart the floc.  In the case of our basin, the specifications list the flow through velocity as between 0.5 and 1.5 ft/min.
To check whether the flow through velocity of the basin we've designed is within these limits, we used the following formula:

v = 60 Q_c/A_x

Where:

v   =  velocity, ft/min
Q_c =  flow in one channel
60  =  conversion from seconds to minutes
A_x =  cross-sectional area, ft², calculated as follows:

A_x = W d

In our example, first we calculate the cross-sectional area of one of our channels:

A_x = (9.5 ft) (10 ft)

A_x = 95 ft²

Then we calculate the velocity of water flowing through the channel:

v = 60 (1 cfs)/(95 ft²)

v = 0.63 ft/min

This velocity is within the acceptable range, so we can use the tank dimensions calculated above to design our flocculation basin.  If the velocity had been too high, we would have assumed a greater number of channels and then chosen new dimensions.  If the velocity was too low, we would have repeated the calculations using a smaller depth or only one channel.


Power Requirements
The power requirements are calculated just as they were for the flash mix chamber, except that you must be sure to calculate the power requirements for the entire flocculator rather than for just one channel.  We will assume a water temperature of 60°F and a velocity gradient of 45 sec.^-1  Our calculations are shown below:

1. First, the volume of the entire flocculator is calculated:
   
   
   Flocculator volume = (Channel volume) (Number of channels)
   
   Flocculator volume = (1,800 ft³) (2)
   
   Flocculator volume = 3,600 ft³
   
   
2. Next, the water horsepower is calculated:
   
   
   
   
   
3. Then the electrical horsepower is calculated:
   
   
   
   
   
4. Finally, the cost is calculated:
   
   
   Cost = (17.9) (0.376) ($0.05)
   
   Cost = $0.34

Notice that the cost to run the flocculator is much less than the cost to run the flash mix chamber.  This smaller cost is due to the much less vigorous mixing occurring in the flocculator.



Conclusions

Our plant requires a two channel, horizontal-shaft paddle flocculator with a total volume of 3,600 ft.³  Each channel will have a volume of 1,800 ft³, a depth of 10 ft, a width of 9.5 ft, and a length of 19 ft.

The flow through velocity in each channel will be 0.63 ft/sec.  The power cost for the entire flocculator will be $0.34 per day. 

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