Example Moisture Mass Balance Calculations

for Bioreactor Landfills
EPA-456/R-05-004

August 2005

Example Moisture Mass Balance Calculations for Bioreactor Landfills

Prepared for:

Mary Ann Warner, Project Officer

Information Transfer and Program Integration Division

Contract No. 68-D-02-0079

Work Assignment Numbers 1-03 and 2-04

U.S. Environmental Protection Agency

Office of Air Quality Planning and Standards

Information Transfer and Program Integration Division

Research Triangle Park, NC
1

1.0 INTRODUCTION

The purpose of this memorandum is to demonstrate example mass balance calculations that can

be performed to estimate the moisture content of the waste mass in a bioreactor landfill. The

Municipal Solid Waste Landfills NESHAP (40 CFR part 63, subpart AAAA) requires timely

control of bioreactor landfills. As defined in the NESHAP, a bioreactor is a MSW landfill or a

portion of a MSW landfill where any liquid, other than leachate or landfill gas condensate, is

added in a controlled fashion to accelerate the anaerobic (without oxygen) biodegradation of the

waste. The average moisture content of the waste in the area into which the liquid is added must

be at least 40 percent (by weight) for the landfill or portion of the landfill to be considered a

bioreactor. We have presented the example mass balance calculations based on the wet weight

of waste. This is consistent with the approach detailed in the book, Landfill Bioreactor Design

and Operation, by Debra Reinhart and Timothy Townsend and documented in the EPA Docket

A-98-28 (Item IV-K-9).

The only two situations where the NESHAP requires a landfill owner/operator to calculate

percent moisture content are:

1. If the landfill owner/operator adds liquids (other than leachate and condensate) and does

NOT comply with the bioreactor control requirements. In this case, they must keep a

record of calculations showing that the percent moisture content expected in the waste

mass to which the liquid is added is less than 40 percent. If the moisture content is less

than 40 percent, the landfill would not meet the definition of a bioreactor, and timely

control would not be required. See section 63.1980(g) of subpart AAAA.

2. If the landfill owner/operator chooses to begin operating the bioreactor gas collection and

control system within 180 days after achieving 40 percent moisture content instead of

within 180 days after initiating liquids addition, as allowed under section 63.1947 (a)(2)

or (c)(2). In this case, they must calculate percent moisture content to determine when

the bioreactor reaches 40 percent moisture, keep records, and submit a report within 90

days of achieving 40 percent moisture content. See section 63.1980(h) of subpart

AAAA. Note that a landfill owner/operator who adds liquids does NOT have to calculate

percent moisture content if they meet the bioreactor control requirements within 180 days

of initiating liquids addition (or by January 17, 2006 for existing landfills with

bioreactors).

The NESHAP allows moisture content to be determined using a variety of methods, as long as

the procedures and assumptions are documented and appropriate. A range of appropriate

methods exist. For example, the landfill owner/operator can perform a simple mass balance

calculation. The calculation must take into account the waste mass, moisture content of the

incoming waste, mass of liquids added to the bioreactor (including recirculated leachate),

precipitation falling on the bioreactor surface, and mass of water removed as leachate. The

landfill can perform more complex mass balances using models that take into account additional

factors such as surface runoff, landfill cover types that reduce the amount of precipitation
2

entering the waste mass, and water loss mechanisms such as evapotranspiration. Another

possible method for an established bioreactor would include sampling the moisture content of

the waste at multiple locations within the bioreactor, and performing statistical calculations to

determine the average percent moisture. However, it is expected that in most cases, a mass

balance approach will be adequate to determine whether the moisture content is above or below

40 percent and comprehensive sampling will not be needed. 

This memorandum provides two example mass balance calculation procedures, a simple method

and a more complex method. However, landfill owners/operators are free to use other methods

to take into account site-specific characteristics of their landfill. Many landfills may already

have performed moisture balance calculations, and these can be used assuming the procedures

and assumptions are documented, appropriate, and representative of current landfill conditions.

2.0 WATER BALANCE METHOD

The Water Balance Method was chosen to represent the example calculations used to model the

mass balance of moisture within a bioreactor landfill because it is a relatively basic computation. 

The Hydrologic Evaluation of Landfill Performance (HELP) model is another, more advanced

model that can be used as an alternative to the Water Balance Method. However, the HELP

model is based on a volumetric moisture content of waste. Because the NESHAP specifies that

the 40 percent moisture content is by weight, we do not recommend using the HELP model to

conduct bioreactor mass balance calculations to meet the requirements of the NESHAP.

The Water Balance Method performs several calculations in sequence on a monthly time basis to

estimate the average moisture content of the waste. It was originally designed to measure

evapotranspiration from soils and was then adapted for landfill conditions. Our suggested

procedure for using the Water Balance Method involves a two-tiered approach. Method A is a

simplified equation that only incorporates factors which most significantly affect the average

moisture content of the waste mass. The simplified equation also assumes that all precipitation

falling directly on the landfill’s surface will become moisture in the waste mass. The primary

factors that are accounted for in the simplified equation are:

• Incoming waste moisture,

• Precipitation (only precipitation that falls directly on the landfill’s surface; assuming that

all surface runoff from adjacent areas is diverted around the landfill surface),

• Liquids addition (recirculated leachate, water, etc.), and

• Leachate production.

If landfill owners/operators are satisfied with the results of the Method A equation, then no

further calculations are needed. However, if further analysis is required, then landfill

owners/operators can proceed to Method B which comprises a more advanced set of

calculations. This more complex procedure takes into account the four factors included in the

simplified equation of Method A plus the following four elements:
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• Moisture retained in the landfill surface or cover material,

• Surface runoff,

• Surface evaporation, and

• Evapotranspiration.

A detailed description of each step is discussed in Sections 2.1 and 2.2, respectively.

2.1 Method A: Simplified Equation

The potential moisture content of the waste mass in the bioreactor landfill can be estimated using

the following simplified equation of the Water Balance Method:

PMC (Equation 1) L M P LA LCH

M LA

o

 = 

( * ) + + - 

 + P + - LCH

 * 100

Where,

PMC = estimated potential moisture content of the waste mass (% moisture content on a wet 

weight basis);

Lo = moisture entering with the waste mass (kg moisture/kg total waste mass as received);

M = total waste mass in bioreactor cell on an as received basis (kg total waste mass as received);

P = total precipitation (kg total precipitation);

LA = total liquids added to the waste mass, including recirculated leachate (kg total liquids); and

LCH = total leachate collected (kg total leachate).

If the bioreactor landfill has been at steady state (i.e., no fluctuations in any of the factors above)

since the bioreactor cell or entire bioreactor landfill opened, then M, P, LA, and LCH can be

calculated as monthly averages instead of totals. However, this scenario is not likely to occur.

When using Equation 1, landfill owners/operators must keep records of data and assumptions

used to determine values of Lo, M, P, LA, and LCH for their bioreactor landfill. The following

bullet points provide potential guidelines for determining and recording these values. 

• Lo: According to Tchobanoglous’ Integrated Solid Waste Management: Engineering

Principles and Management Issues, most MSW in the United States has a moisture

content of 15 to 40 percent, with 25% as typical. Moisture content of MSW depends

primarily on the composition of the waste, the season of the year, and the humidity and

weather conditions of the surrounding environment. For example, the moisture content

of 100 kilograms of incoming wet waste can be estimated as: [(100 kg - d)/100 kg],

where d is the total dry weight in kilograms of the solid waste components within the 100

kilograms of wet waste received.

• M: To calculate total waste mass, waste acceptance or waste placement data is needed

and should be documented accordingly.
4

• P: Total precipitation in inches of water can be obtained from precipitation

measurements at the landfill or from nearby weather station data. Convert the

precipitation from inches to kilograms of moisture using the following equation:

Total precipitation (P) = (in. of total precipitation) * (1 ft/12 in) * (ft2 of bioreactor

landfill surface) * (1 gal/0.134 ft3) * (3.78 kg/gal water)

• LA: The total amount of liquids added can be estimated using measurements currently

taken at the bioreactor site for design and operational purposes. For example, if a closedloop bioreactor with horizontal trenches uses a flow meter to measure the amount of

leachate recirculated, then flow meter reading records can be used to estimate total

leachate addition (e.g., converting the flow rate each month to kilograms of leachate per

month and then summing the monthly readings to obtain a total liquids added amount). 

Water introduced at the surface of the landfill via truck could be measured using a simple

volume displacement calculation, such as: (gallons of water stored per tank truck) *

(number of tank trucks emptied onto landfill surface) * (3.78 kilograms per gallon of

water). The types of liquid addition methods vary by bioreactor landfill site, therefore,

the types of measurement methods will differ as well. We recommend that each landfill

owner/operator calculate total liquids using methods most appropriate for their bioreactor

design.

• LCH: Similar to liquids addition, the total amount of leachate produced can be estimated

using leachate collection records generated at the landfill bioreactor for design,

operational, and possibly regulatory purposes. For example, if a bioreactor landfill uses a

flow meter to measure the amount of leachate produced or collected, then flow meter

reading records can be used to estimate total leachate generation (e.g., converting the

total flow rate each month to kilograms of leachate per month and then summing the

monthly readings to obtain a total leachate amount). The leachate value used in Equation

1 should include leachate that is recirculated as well as any excess leachate that may be

treated or disposed of by other means. We recommend that each landfill owner/operator

calculate total leachate generated using methods most appropriate for their leachate

collection system design.

2.2 Method B: Advanced Set of Calculations

The following items are required inputs for Method B of the Water Balance Method calculations:

• Average monthly temperatures in degrees Fahrenheit (oF)

• Site latitude

• Average monthly precipitation in inches of water

• Landfill surface conditions

• Soil & vegetation type for final cover (if any)

The 17 calculation steps of the advanced Water Balance Method procedure are listed below. 

Steps 1 through 16 of the sequence calculate and confirm the percolation of precipitation into the
5

bioreactor landfill considering moisture contained in the landfill surface or final cover, surface

runoff, evaporation losses, and evapotranspiration. Step 17 is very similar to Equation 1 for

Method A. The only difference between Step 17 and Equation 1 is that Step 17 replaces the

amount of precipitation with the amount of moisture that percolates into the waste mass. 

Attachment B contains a Microsoft Excel spreadsheet that provides example calculations for

Steps 1 through 16. The foundation for this sequence of calculations and example spreadsheet

comes directly from McBean’s Solid Waste Landfill Engineering and Design.

Sequence of Calculations for the Advanced Water Balance Method (Method B):

Steps 1 - 5: Determine potential evapotranspiration

1. Collect average monthly temperatures (T) in oF for the area surrounding the bioreactor

landfill. Enter this information in the spreadsheet.

2. Using the monthly temperatures, determine the monthly heat index (h) for each month. 

Monthly heat indices can be determined using Table A1 in Attachment A. For months where

the temperature is less than 32 oF, set h to zero. Sum the monthly heat indices to obtain a

yearly heat index (H).

3. Using the monthly temperatures and yearly heat index, find the Unadjusted Potential

Evapotranspiration (UPET) for each month using Table A.2 in Attachment A.

4. Using the latitude at the bioreactor landfill site, find the monthly correction factor for

sunlight duration (r) in Table A.3 in Attachment A.

5. Multiply the monthly UPET by the monthly r to result in the monthly Adjusted Potential

Evapotranspiration (PET) for each month in inches of water.

Steps 6 - 9: Determine amount of precipitation that infiltrates the bioreactor landfill

6. Enter the average monthly precipitation (P) in inches of water for the bioreactor landfill site.

7. Enter the appropriate runoff coefficient (Cr/o) to calculate the runoff for each month. Table

A.4 in Attachment A can be used to determine the most appropriate runoff coefficient based

on the landfill surface conditions.

8. Multiply the monthly precipitation by the monthly runoff coefficient to obtain the runoff

(r/o) for each month in inches of water.

9. Subtract the monthly r/o from the monthly P to obtain the monthly infiltration (I) in inches of

water.

Steps 10 - 13: Calculate moisture storage in the landfill surface cover material
6

10. Subtract the monthly PET from the monthly I to determine the moisture available for storage

at the landfill surface (I - PET) in inches of water.

11. For negative (I - PET) values only, add the (I - PET) value for the preceding month to the

current month to calculate the Cumulative Water Loss (ACCWL). Begin the summation with

zero accumulated water loss for the last month having a positive (I - PET) value.

12. Determine the monthly Soil Moisture Storage (ST) in inches of water for the landfill surface

by following the steps outlined below:

a. Determine the initial ST for the soil depth and type. Table A.5 can be used to

configure the initial ST (retention) value.

b. Assign the initial ST value to the months having a positive (I - PET) value, prior to

months that have a negative (I - PET) value.

c. Determine the ST for each subsequent month having a negative (I - PET) value. Use

the monthly ACCWL values and Table A.6 to obtain the ST.

d. For subsequent months having an (I - PET) value greater than or equal to zero, add

the (I - PET) value for each month to the preceding month’s ST. Be careful not to

exceed the soil field capacity (i.e., fraction of water in the soil based on the dry

weight of the soil). Enter the soil field capacity for monthly soil moisture storage if

the sum exceeds the field capacity.

13. Calculate the change in the ST, or )ST, for each month in inches of water by subtracting the

ST for the preceding month from the current month’s ST.

Steps 14 - 16: Calculate actual evapotranspiration and percolation of moisture into the

bioreactor landfill waste mass

14. Calculate the Actual Evapotranspiration (AET) by following the steps outlined below:

a. For wet months where the (I - PET) value is greater than or equal to zero, set the AET

equal to the PET.

b. For dry months where the (I - PET) value is negative, use the following equation for

the AET: AET = PET + ((I - PET) - )ST). This equation represents the fact that the

evapotranspired amount is the amount potentially evapotranspired plus that available

from excess infiltration that would otherwise add to soil moisture storage plus that

available from previously stored soil moisture.

15. Calculate the monthly percolation (PERC) as follows:
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a. For wet months where the (I - PET) value is greater than or equal to zero, use the

following equation for the PERC: PERC = ((I - PET) - )ST).

b. For dry months where the (I - PET) value is negative, set the PERC equal to zero.

16. As a check for Steps 7 through 15, calculate the average monthly precipitation (P) in inches

of water to be sure they match the original precipitation values entered in Step 6. The

precipitation calculation is as follows: P = PERC + AET + )ST + r/o.

Step 17: Estimate moisture content of the waste mass in the bioreactor landfill

17. Convert PERC from inches of moisture to kilograms of moisture per kilogram of waste (e.g.,

[PERC (in) * (1 ft/12 in) * (ft2 of bioreactor landfill surface) * (1 gal/0.134 ft3) * (3.78 kg/gal

water)] / (total kg wet waste mass in bioreactor)). Then, estimate the potential moisture

content of the waste mass, on a monthly wet weight basis, using the following equation:

PMC = Lo + PERC + LA - LCH (Equation 2)

Where,

PMC = estimated potential moisture content of the waste mass (kg moisture/kg wet waste);

Lo = average amount of moisture in the initial waste added each month (kg moisture/kg wet 

 waste);

PERC = monthly percolation (kg moisture/kg wet waste);

LA = amount of liquids added to the waste each month, including recirculated leachate

 (kg liquids/kg wet waste); and

LCH = amount of leachate produced each month (kg leachate/kg wet waste).

Lo, LA, and LCH should be estimated and documented similarly to Method A procedures

described under Equation 1 in Section 2.1. The difference between Equations 1 and 2 is that Lo,

LA, and LCH are monthly values per kilogram of waste in Equation 2, not total values. 

Therefore, for Equation 2, monthly values will need to be determined and then divided by the

amount of waste added each month.
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3.0 REFERENCES

1. McBean, E.A., Rovers, F.A., and Farquhar, G.J. Solid Waste Landfill Engineering and

Design. Prentice-Hall: New Jersey, 1995. Chapter 7 and Appendix C.

2. Tchobanoglous, G., Theisen, H., and Vigil, S. Integrated Solid Waste Management:

Engineering Principles and Management Issues. McGraw-Hill: New York, 1993. pp.

70-73, 421-424.
A-1

Attachment A

Reference Tables for Water Balance Method Calculations
A-2

Table A.1. Monthly Values of Heat Indices Corresponding to Monthly Mean Temperatures
A-3

Table A.1. Monthly Values of Heat Indices Corresponding to Monthly Mean Temperatures

(Continued)
A-4

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values
A-5

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-6

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-7

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-8

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-9

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-10

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-11
A-12

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-13

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-14

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-15

Table A.2. Values of Unadjusted Daily Potential Evapotranspiration (in.) for Different Mean Temperatures and I Values

(Continued)
A-16

Table A.3. Mean Possible Monthly Duration of Sunlight in the Northern Hemisphere (12 hours)
A-17

Table A.3. Mean Possible Monthly Duration of Sunlight in the Northern Hemisphere (12 hours)

(Continued)
A-18

Table A.4. Runoff Coefficients
A-19

Table A.5. Provisional Water Holding Capacities for Combinations of Soil and Vegetation
A-20

Table A.6. Soil Moisture Retention Table for Various Amounts of Potential Evapotranspiration for

a Root Zone Water-Holding Capacity of Four Inches (Continued)
A-21

Table A.6. Soil Moisture Retention Table for Various Amounts of Potential Evapotranspiration for

a Root Zone Water-Holding Capacity of Four Inches (Continued)
A-22

Table A.6. Soil Moisture Retention Table for Various Amounts of Potential Evapotranspiration for

a Root Zone Water-Holding Capacity of Four Inches (Continued)
A-23

Table A.6. Soil Moisture Retention Table for Various Amounts of Potential Evapotranspiration for

a Root Zone Water-Holding Capacity of Four Inches (Continued)
B-1

Attachment B

Microsoft Excel Spreadsheet Showing Method B Water Balance Example Calculation
TECHNICAL REPORT DATA

(Please read Instructions on reverse before completing)

1. REPORT NO.

 EPA-456/R-05-004

2. 3. RECIPIENT'S ACCESSION NO.

4. TITLE AND SUBTITLE

Example Moisture Mass Balance Calculations for Bioreactor

Landfills

5. REPORT DATE

 August 2005

6. PERFORMING ORGANIZATION CODE

7. AUTHOR(S)

Amy Alexander

Eastern Research Group, Inc. 

8. PERFORMING ORGANIZATION REPORT NO.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Office of Air Quality Planning and Standards

Mail Drop E143-02

Research Triangle Park, NC 27711

10. PROGRAM ELEMENT NO.

11. CONTRACT/GRANT NO.

68-D-02-0079 

12. SPONSORING AGENCY NAME AND ADDRESS

 U.S. Environmental Protection Agency

 Office of Air Quality Planning and Standards

 Research Triangle Park, NC 27711 

13. TYPE OF REPORT AND PERIOD COVERED

Final Report

14. SPONSORING AGENCY CODE

EPA/200/04

15. SUPPLEMENTARY NOTES

To be published at: http://www.epa.gov/ttn/atw/landfill/landflpg.html

16. ABSTRACT

This document contains example mass balance calculations for estimating the moisture content of the waste

mass in a bioreactor landfill. Under the National Emission Standards for Hazardous Air Pollutants for

Municipal Solid Waste Landfills (landfills NESHAP), a portion of a landfill operated as a bioreactor has

timely control requirements. The landfills NESHAP allows moisture content to be determined using a variety

of methods, as long as the procedures and assumptions are documented and appropriate. Although a range of

appropriate measures exist, a mass balance approach is expected to be adequate in determining whether the

moisture content of the waste is above or below 40 percent. Two example mass balance calculations are

presented, a simple method and a more complex method. The simplified equation incorporates factors such

as incoming waste moisture, liquids addition, and leachate production, which most significantly affect the

average moisture content of the waste mass. The more complex procedure accounts for additional factors

such as moisture retained in the landfill, surface runoff and evaporation, and evapotranspiration. 

17. KEY WORDS AND DOCUMENT ANALYSIS

a. DESCRIPTORS b. IDENTIFIERS/OPEN ENDED TERMS c. COSATI Field/Group

Bioreactor landfill

Air pollution

Clean Air Act

NESHAP

Moisture content

Air Pollution control

Nonmethane organic compounds

Methane

18. DISTRIBUTION STATEMENT

 Release Unlimited

19. SECURITY CLASS (Report)

 Unclassified

21. NO. OF PAGES

36

20. SECURITY CLASS (Page)

 Unclassified

22. PRICE

EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION IS OBSOLETE
United States Office of Air Quality Planning and Standards Publication No

Environmental Protection Information Transfer and Program Integration Division August 2005Agency Research Triangle Park, NC