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TECHNICAL ASSISTANCE TEAM FOR EMERGENCY RESPONSE REMOVAL AND PREVENTIONI-PA CONTRACT 68-01-6669 MEMORANDUM

TO: Gerry Heston, OSC, U.S. EPA, Region III

THRU: Richard Habrukowich, TATL, Region III

FROM: Mark Tucker, TAT, Region III /" f

SUBJECT: Freundlich Isotherms and Estimates of Carbon Efficiency

DATE: August 19, 1986

The following is background information useful in interpreting carbon efficiencyand time to breakthrough.

Freundlich Isotherms

Carbon efficiency can be estimated using "Freundlich isotherms". The isothermsrelate the concentration of specific contaminants in water to the adsorptioncapacity of carbon expressed as the amount of contaminant adsorbed per weight ofcarbon. Plotted isotherms are mathematically expressed by "Freundlichequations" of the form:

X - K C1/nM

where X = mg of contaminant adsorbed per gram of carbonM

C = the equilibrium concentration at saturation, or for ourpurposes the influent or well concentration

1/n and K = Freundlich isotherm constants specific to variouscontaminants

Freundlich isotherms have the following form:

log XM

m=l/n^

log C

Roy F. Weston, Inc. /IP/ n n nSPILL PREVENTION & EMERGENCY RESPONSE DIVISION w •» H (J 0 Q Q {In Association with ICF Inc., Jacobs Engineering Group Inc.. C.C. lohnson & Associates. Inc.. nn<«

ORIGINAL

Freundlich Isotherms and Estimates of Carbon EfficiencyPage -2-

Isotherms for various organic contaminants are derived experimentally. In theseexperiments values of X/^ are found by introducing a known amount of carboninto water spiked with a known concentration of contaminant. The mixture isallowed to equilibrate and the amount of contaminant adsorbed is determined.Isotherms give the amount of contaminant adsorbed at total saturation for variousconcentrations.

Figures 1, 2, and 3 (attached) give isotherms experimentally derived fortrichloroethylene, trichloroethane, and benzene. It can be seen from theisotherms that there is a logarithmic decrease in carbon efficiency withdecreasing concentrations.

Figure 4 (attached) shows the same isotherms redrawn onto one sheet, along withFreundlich equations describing them mathematically. The values for theisotherm constants K and 1/n were taken directly from the curves.

Estimating Carbon Efficiency

Isotherms can be used to estimate the length of time to total saturation forvarious systems. Parameters which must be known are the concentration ofcontaminant in the water to be treated, the water usage in gallons per day, theamount of carbon contained in the filters, and the isotherm constants for thecontaminant of concern.

For example, suppose you wish to estimate the life expectancy of 1.5 cubic feetof carbon which is treating 100 ug/1 of TCA at 200 gallons/day. The time indays to total saturation can be found following the following steps:

1. What is the weight of carbon in grams?

M - 1.5 ft3 X 25 Ib. X 454 gm - 1.7 X 10 4 gmi Ft3 Ib.

2. What is the contaminant loading rate in mg per day?

100 ug X 10-3 mg_ X 200 gal X 3.8 1 -1 ug day gal

3. What is carbon efficiency in X/M for this concentration?

A. Reading directly from the isotherms (attached):X/M m 1.3 mg adsorbed per gram of carbon

B. Or by using the equation X/^ - KCVn wherefor TCA K = 0.23 and 1/n - 0.32, X/M = 1.25

Freundlich Isotherms and Estimates of Carbon EfficiencyPage -3-

4. What is the total amount of contaminant adsorbed for this amountof carbon and this concentration?

1.25 mg_ X 1.7 X 10 4 gm = 2.12 X 104 raggm

5. And finally, how long will the carbon last?

2.12 X 104 mg X day = 279 days76 mg

More simply stated, the length of time to saturation can be determinedusing the equation:

t = MKC1/" -13.8 X 1CT3F

where: t = time to saturation in daysM = mass of carbon in gramsK and ^'n = isotherm constants for the contaminant ofconcern

C = influent concentrationF = flow in gallons per day

The relationship of days to saturation for various contaminant concentrationsand carbon filter sizes can also be presented graphically. Figures 5 and 6(attached) show the relationships for TCA and TCE. These plots are based on1.5 cubic feet of carbon and show days to total saturation for various flowrates in gallons per day.

Precautions L^'

The time in days derived from any of the above techniques gives the time tototal saturation. For many of our applications it is advisable to plan carbonchanges well in advance of total saturation. From past case studies it has beenrecommended that to avoid breakthrough, carbon should be changed at half thetime to saturation.

Contact time is another important consideration. Effective adsorption requiresthat contaminants have a sufficient residence time within the filters. A"superficial contact time" can be found by dividing the volume of carbon by theflow rate. Various writers recommend that a superficial contact time of atleast 10 minutes is required for efficient adsorption.

MT:ah

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