WATER MATTERS
Cycles of Concerntration
by Bob Cavano
Author’s Note: The author has received many valuable suggestions from Fred Friar and Bill Midkiff and
thanks them for their input.
I. INTRODUCTION
"Cycles of concentration" (C) is a very useful term for describing the number of times that dissolved
minerals in a water are allowed to concentrate. It is necessary for us to have a good understanding of this
concept if we are to achieve maximum operating efficiency for recirculating cooling water systems.
Even if there are no leaks, some water will be lost — usually to evaporation or drift. But the impurities in
the make up water (calcium, magnesium, silicate), and also the added treatment chemicals remain. The
relatively pure water which is lost is replaced by fresh, less pure, water. This results in a build up of solids
which at some point must be reduced by bleed off.
We attempt to limit the amount of bleed off and thereby increase the cycles. Important cost savings can
result from as little as one additional cycle if we start at low levels of "C". The greater the number of
cycles, the less cost there will be for water and chemicals and the lower the expense for treatment of
effluent.
As cycles increase beyond a certain point, however, the savings become less and less significant. The
amount of bleed off and of the make up to replace it declines rapidly at about 4 cycles and almost levels
out at above 6 cycles, resulting in very little further reduction in water or chemical consumption.
We soon realize where the point of diminishing returns for each system is and that when it has been
reached, trying to achieve additional cycles may do more harm than good. We hope that by publishing
these results, we will partly counter inferences that each and every increase in cycles allows sizable
savings in water and chemical usage.
Among the other negative consequence of these higher concentrations is the possibility of increased
deposition and greater potential for corrosion. Precise cost/benefit analysis should be made by comparing
the savings in water and treatment to the cost of the additional chemicals needed to control this more
concentrated water.
Usually there is little that we can do about the amount of evaporation, the circulation rate or the required
reduction in the temperature of the water. All of these factors are inter-related and should impact our
conclusions, but they are almost always presented to us at pre-determined values. A thorough engineering
approach would include all of them in the design of a system and would also utilize them in determining
maintenance procedures.
The options actually available to us are simply which treatment to apply and how much bleed off to
recommend. The major concern of this paper is to learn what the consequences of our choices will be.
Computer programs (such as WaterCycle( from French Creek) can estimate fairly well the cycles possible
for such a water supply/treatment combination. The necessary data on raw materials and blends of them,
however, have not always been adequately determined by laboratory work or verified in field trials. While
these programs provide extremely useful estimates, they do not completely eliminate the necessity for
testing and vigilance.
II. TESTS
Cycles of concentration are determined by dividing the amount of any non-volatile, non-complexing
species (TDS, chlorides) in the recirculating water by the amount of the same in the make-up water.
Most commonly, chloride tests are used since chlorides are highly soluble, remain in solution, and are
easy to measure at low levels. Conductivity readings are a valuable alternative, especially where either
continuous monitoring or automatic control of bleed off and make up is desired.
Hardness comparisons are the least reliable techniques since part of the hardness precipitates as sludge or
scale and the remainder becomes a poor measure of total concentration. Tests based on treatment
chemicals which participate in film formation or precipitation reactions are also not reliable enough for
concentration comparisons
III. TERMS USED
1. Bleed Off or Blow Down (BD) in gallons per minute (gpm).
2. Evaporation Rate (ER) in gpm. Includes "windage" and "drift".
3. Make Up (MU) in gpm. Since MU = ER + BD, MU also includes windage and drift.
4. Circulation Rate (CR) in gpm.
5. Delta T ( T) in °F. Differential between incoming (~hot) water and outgoing (~cold) water.
6. Cycles of Concentration (C)
IV. DEFINITIONS
The loss of water and chemicals from the system depends upon the amount of water lost through
evaporation and drift or windage (ER), and also on whatever is purged from the system (BD). The
material balance for these factors is obvious:
1. MU = ER + BD Based on a latent heat constant of 1,000 BTU/lb., we estimate that:
2. ER = (CR)( T/1000) reflecting 1% evaporation for each 10°F. T
The best indicator of how solids concentrate in the circulating water is the ratio of the total of fresh water
added to the system divided by the total water lost to bleed off, that is:
3. C = MU/BD, where C is known as cycles of concentration. By utilizing IV-1, we obtain:
4. a) C = (ER + BD)/BD, which may also be expressed as:
b) BD = (ER)/(C-1).
V. DETERMINATION OF COST
1. Make-up (MU). If there is no record of previous water consumption, we may, based on Formula IV1,estimate as follows:
MU = ER + BD.
2. Evaporation (ER). From previously recorded levels or calculated from estimated tonnage. This involves
multiplying tonnage by a certain factor (1.8 for example). For a 200 ton system:
ER = (200)(1.8) = 360 gallons per hour.
A further estimate of ER may be obtained from IV-2.
TABLE I
Ratio of Bleed Off Circulating rate as a function of Cycles
of Concentration where T = 10 or 40°F.
% (BD/CR) = 1/(C-1)
C C-1 1/(C-1) Difference
%Reduction 4/(C-1)
1.5 0.5 2.000
8.000
1000
50.000
2.0 1.0 1.000
4.000
0.333
33.33
2.5 1.5 0.667
2.668
0.167
25.00
3.0 2.0 0.500
2.000
0.100
20.00
3.5 2.5 0.400
1.600
0.067
16.75
4.0 3.0 0.333
1.332
0.047
14.11
4.5 3.5 0.286
1.144
0.036
12.59
5.0 4.0 0.250
1.000
0.028
11.20
5.5 4.5 0.222
0.888
0.022
9.91
6.0 5.0 0.200
0.800
TABLE 2
Ratio of Make-up to Circulating Rate as a Function of
cycle of Concentration where T = 10 or 40°F.
% (MU/CR) = C/(C-1)
C C-1 C/(C-1) Difference
%Reduction 4C/(C-1)
1.5 0.5 3.000
12.000
1.000
33.33
2.0 1.0 2.000
8.000
0.333
16.65
2.5 1.5 1.667
6.668
0.167
10.00
3.0 2.0 1.500
6.000
0.100
6.67
3.5 2.5
1.400
5.600
0.067
4.0 3.0
1.333
5.332
0.047
4.5 3.5
1.286
5.0 4.0
1.250
2.80
5.000
0.028
2.24
1.222
4.888
1.020
6.0 5.0
3.52
5.144
0.036
5.5 4.5
4.78
1.64
1.200
4.800
3. Bleed-off (BD). Based on decisions as to the number of cycles of concentration (C) we choose to carry.
Since we know from Formula IV-4 that:
BD = (ER)/(C-1), we compute at 2.5 cycles for our example:
BD = (360)/(2.5-1.0) = 240 gallons per hour.
4. Annual Make-up. Since V-1 tells us that MU = ER + BD, we combine V-2 and V-3 to obtain:
360 + 240 = 600 gallons per hour.
To cool an office building open 12 hours per day and 250 days per year, we need:
(600)(12)(250) = 1,800,000 gallons per year.
5. Cost of Water and Sewage. Estimating a cost of $1.25 per 100 cubic feet for the water received
(including costs of effluent disposal), and recalling that one cubic foot = 7.48 gallons, we have:
(1,800,000)(1.25)/(7.48)(100) = $3,008.02 per year.
In many cases, raw water costs and effluent treatment costs should be calculated separately.
6. Cost of Treatment Chemicals. Estimating a chemical cost of $10.00 per gallon and feeding at the rate of
one gallon treatment per 20,000 gallons of water, we have:
(10.00)(1)/(20,000) = $5.00 per ten thousand gallons.
or (1,800,000)(5/10,000) = $900.00 per year. Recommended treatment levels will vary with the cycles
held and with the stability of the treatment chemicals.
7. Total Cost. From Sections V-5 and V-6, we have:
$3,008.02 + $900.00 = $3908.02 as the annual chemical and water costs for this 200 ton tower operating
at 2.5 cycles.
VI. FORMULA DEVELOPMENT AND CALCULATIONS
1. Bleed-Off and Make-up Determination
Equation IV-4 when combined with IV-2 allows us to state that:
a) BD = (CR)/(100)(C-1) for every 10°F. increase in temperature.
Then the ratio of bleed off to circulating rate (in gpm) becomes:
b) BD/CR = 1/(100)(C-1), which if stated as a percentage, becomes:
c) % (BD/CR) = 1/(C-1) and from IV-3, we know that C=MU/BD and BD=MU/C, leading to:
d) % (MU/CR) = (C)/(C-1).
TABLE 3
Percentage Reduction in Water Consumption
Achieved by Increasing Cycles
Increase Cycles
(from Original "C" by:
Percent Reduction
MU/CR
Percent Reduction
BD/CR
1
2
3
4
1/C
2/(C)(C+1)
3/(C)(C+2)
4/(C)(C+3)
1/C
2/(C+1)
3/(C+2)
4/(C+3)
n/(C)(c+n-1)
n/(C+n-1)
or in general form:
n
From this we obtain the following percent reductions for MU/CR:
TABLE IV
From:
To:
% Reduction
4.0
4.5
3.52
4.0
5.0
6.25
5.0
10.0
11.11
10.0
20.0
5.26
20.0
80.0
3.80
From these formulas we calculate Tables I and II. Recall that these results are generally for a T of 10° F.
Higher values of T will, of course, increase the total amounts of water and chemical needed, but the
percentage comparisons will remain the same.
Water and chemical savings from an increase in cycles are not cumulative in that each subsequent
percentage is based on an already reduced level. Thus a change from 3 to 5 cycles results in a % (MU/CR)
savings of 16.67%, (not 17.77) and a % (BD/CR) savings of 50% (not 63.45).
For easier examination, we plot the data from Tables I and II in Graph A. The purpose of these curves is
not only to provide actual percentage values but rather to show how the curves flatten out at higher levels
of "C".
Since the relationships are of the nature y = C/(C-1) or 1/(C-1), the curve is characteristic of inverse
variation. Since "C" is always positive and greater than 1, "C-1" is always > 0 resulting in C/(C-1) being
always positive and greater than one, with 1/(C-1) always positive and greater than zero.
Bill Midkiff found that plotting the ratios between make-up or blow-down for different cycles can be
helpful in showing the amount of savings which could be obtained. Since these ratios also display inverse
variation, the asymptotic nature of the curves remains the same.
A further relationship derived from the Fifth Column of Table II is presented as Graph B. It shows the
percent reduction for MU/CR for each one-half unit increase in the number of cycles. To simplify the
calculation of the percentages for these ratios we have found the following table useful:
VII. SUMMARY
We have explored some important aspects of cycles of concentration. In doing so, we have discovered and
presented the following:
A. Positive consequences of an increase in cycles:
1. Water and Chemical Savings. In Part V we calculated the costs for a typical tower. Computing a
parallel cost for a higher concentration allow us to determine the potential savings.
2. Tables I, II, III and IV and Graphs A and B illustrate for us the extent of the savings possible based on
the range of cycles and the starting point.
3. Reduction in Discharge Cost. Increased cycles lower the amount of plant effluent and the costs for
managing it. These savings can be calculated by following the procedures demonstrated above.
C. Negative Aspects of Higher Concentrations.
1. Greater scale formation. An increase in solids brings a system closer to precipitation.
2. Increased corrosion from greater conductivity. Higher solids contribute to corrosion, especially if they
include chlorides and sulfates. As with automobile radiators, corrosion inhibitors need periodic
replacement.
3. Reduced effectiveness. Increased solids usually call for a higher level of treatment for dispersion and
for biocidal control.
GRAPH A-Ratio as Function of
cycles
back to the top
GRAPH B-Saving in Make
Up