567501
research-article2015
WMR0010.1177/0734242X14567501Waste Management & ResearchBagchi and Bhattacharya
Original Article Waste Management & Research 2015, Vol. 33(3) 232–240 © The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0734242X14567501 wmr.sagepub.com
Post-closure care of engineered municipal solid waste landfills Amalendu Bagchi1 and Abhik Bhattacharya2
Abstract Post-closure care is divided into perpetual care (PPC) and long-term care (LTC). Guidelines for post-closure care and associated costs are important for engineered municipal solid waste (MSW) landfills. In many states in the USA, landfill owners are required to set aside funds for 30–40 years of LTC. Currently there are no guidelines for PPC, which is also required. We undertook a pilot study, using two landfills (note: average landfill capacity 2.5 million MT MSW waste) in Wisconsin, to establish an approach for estimating the LTC period using field data and PPC funding need. Statistical analysis of time versus concentration data of selected leachate parameters showed that the concentration of most parameters is expected to be at or below the preventive action limit of groundwater and leachate volume will be very low, within 40 years of the LTC period. The gas extraction system may need to be continued for more than 100 years. Due to lack of data no conclusion could be made regarding adequacy of the LTC period for the groundwater monitoring system. The final cover must be maintained for perpetuity. The pilot study shows that although technology is available, the financial liability of maintaining a ‘Dry Tomb’ design for landfills is significantly higher than commonly perceived. The paper will help landfill professionals to estimate realistic post-closure funding and to develop field-based policies for LTC and PPC of engineered MSW landfills. Keywords Landfill, field study, leachate trend, post-closure care, perpetual care, economics, policy
Introduction Currently Wisconsin regulations require 40 years of long-term care (LTC) after closure and perpetual care (PPC) of municipal solid waste (MSW) landfills. Owner financial responsibility (OFR) funds depend on the LTC period, which must be established at the beginning of a landfill operation for estimating the disposal fee. So, a realistic LTC period is important for proper operational funding of landfills. Although the Interstate Technology and Regulatory Council (ITRC, 2006) has discussed various ideas at length regarding alternatives for optimizing postclosure care from a technological view point, we are not aware of any published literature that discusses the rationale behind choosing 30 or 40 years of LTC period or guidelines for PPC and the associated costs, which are important issues related to landfill post-closure maintenance cost and landfill economics. We undertook a pilot study using field data from the Wisconsin Department of Natural Resources (WDNR) database, and relevant programme files to address the literature gap. Additional studies involving landfills with various waste volumes and climatological locations are necessary. However, the field-based approach described in this paper will help in drawing realistic conclusions. The emphasis of this paper is on landfill economics; the paper does not address the technical issues mentioned. Further research is needed on various technical issues related to both LTC and PPC. For the pilot study we selected two ‘stand alone’ (i.e., which do not have any contiguous expansion nor have any landfills
nearby causing interference on the groundwater monitoring data) MSW landfills in Wisconsin. Basic information regarding these two landfills is included in Table 1. Leachate recirculation was not undertaken in either landfill.
Long-term care study OFR for LTC costs include maintenance of final cover, the gas extraction system, leachate collection system and ground water monitoring. Each item is discussed in the following sections.
Final cover maintenance There are two issues associated with the final cover maintenance: (1) final cover repair; (2) final cover vegetation mowing. 1. Final cover repair. Field observations indicate that final cover repair due to erosion and small-scale settlement is high
1Waste 2Blue
Management Engineer (Retired, Wis. Dept. of Natl. Res.), USA Cross Blue Shield Assoc., USA
Corresponding author: Amalendu Bagchi, Waste Management Engineer (Retired, Wis. Dept. of Natl. Res.), 222 St. Croix Ln, Madison, WI 53705, USA. Email: [email protected]
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
233
Bagchi and Bhattacharya in the first five years after construction of final cover, beyond which sporadic erosion and small-scale settlements have been observed. In addition to the sporadic settlements, it is reasonable to assume a large-scale settlement of the final cover due to waste decomposition, whereby a replacement of the entire final cover within the LTC period may become necessary. The rate of settlement is higher in bioreactor landfills than in non-bioreactor landfills (Bareither et al., 2010), which may prompt an earlier replacement of final cover in bioreactor landfills than in non-bioreactor landfills. The literature indicates that the service life (SL) of geomembrane, depending on the polymer type, may be between 55 and 125 years (Benson et. al., 2011; Rowe et. al., 2009). So, perpetual replacement of the geomembrane liner of composite final covers will be needed to maintain a ‘Dry Tomb’ design. 2. Final cover vegetation mowing. Field observations in old natural attenuation landfills indicate that yearly mowing of the final cover is essential, without which native vegetative species with deep root systems will invade the final cover. Growth of such deep root species may deteriorate the integrity of geomembrane and clay layer in the final cover system, leading to increase in water infiltration and subsequent increase in leachate generation.
Gas extraction system maintenance Currently there are no criteria as to when a gas extraction system may be stopped. The following two landfill gas emission related criteria, specified by the United States Environmental Protection Agency (USEPA) for new or existing landfills were used for the study: (i) landfills that emit total landfill gas more than 50 Mg per year must install controls to reduce emissions; (ii) landfills that emit more than 50 Mg per year of non-methane organic compounds (NMOCs) must install control to reduce emission (USEPA, 1998). The LandGEM model (USEPA, 2005) was used to estimate the number of years after closure at which the total landfill gas or NMOC would be at 50 Mg yr−1. LandGEM is based on a firstorder decomposition rate equation for quantifying emissions from MSW landfill waste. LandGEM uses the following firstorder decomposition rate equation: n
QCH4=
i
∑∑
kLo .1M i e− kt (ij ) (1)
i = j j =0.1
where QCH4 is the annual methane generation in the year of the calculation (m3 yr−1), i is the one-year time increment, n is (year of the calculation) – (initial year of waste acceptance), j is the 0.1-year time increment, k is the methane generation rate (MGR; yr−1), Lo is the potential methane generation capacity (PMGC; m3 Mg−1), Mi is the mass of waste accepted in the ith year (Mg) and t(ij) is the age of the jth section of waste mass Mi accepted in the ith year (decimal years, e.g., 3.2 years).
Table 1. Landfill information. Landfill Year ID open
Year Liner Final cover closed
LF-1
1980s 1998
LF-2
1980s 2004
5 ft. clay 5 ft. clay
Approx. waste disposal weight in million MT.
Part clay part 2.3 composite Part clay part 2.7 composite
The model was run for both landfills for PMGCs of 100 and 170 and MGRs of 0.04 and 0.05; a uniform disposal rate over the active life period of the landfills was assumed. The results are included in Table 2. Table 2 data shows: (i) gas generation depends on waste volume and the PMGC and MGR combination; (ii) if NMOC emission criteria is used the LTC period for these two landfills varies between 40 and 60 years; (iii) if total gas emission criteria is used, the LTC period for these two landfills is more than 100 years. Thus, currently the LTC period for gas extraction is underestimated even for 2–3 million MT capacity MSW landfills. We would like to point out that a change in environment within landfills due to lack of oxygen and waste volume will greatly influence both the quality and quantity of landfill gas. The LandGEM model is not used for bioreactor landfills, because a generally acceptable MGR is not available yet. The gas generation rate in active bioreactor landfills is higher than in nonbioreactor landfills, which decrease after landfill closure (Barlaz et al., 2010). Further research is necessary for developing guidelines for specifying the allowable gas emissions criteria for both bioreactor and non-bioreactor MSW landfills. Since methane is explosive between concentrations of 5–15% in open air, chances of landfill fire, not uncommon for MSW landfills, are expected to increase several years after closure when the methane concentration becomes low. In view of this, inclusion of cost for a disaster management for landfill fire in the LTC cost merits consideration.
Leachate collection system maintenance The following issues are associated with leachate collection system maintenance. Leachate extraction and treatment: A preliminary analysis of leachate data from the two landfills indicated that after closure the concentration of monitored leachate parameters decreases with time. Ham and Anderson (1974), Pohland (1975) and Ham (1980) also observed similar decrease of leachate parameter concentration in laboratory studies. Based on the laboratory studies and field observation, we used trend analysis – a statistical modelling tool to predict future values based on current data, of selected leachate parameters from a list of parameters required by Wisconsin administrative code Ch. NR 507 (WDNR, 2012a). We analysed only those inorganic parameters in leachate that have either a Public Health Groundwater Quality Standard (PHGQS) or Public Welfare Groundwater Quality Standard (PWGQS) and a few volatile organic compounds (VOCs). The chosen VOC parameter
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
234
Waste Management & Research 33(3)
Table 2. Results of the LandGEM model study. Landfill ID
Estimated LTC period for various combinations of PMGC & MGR
100a
0.04b
Totalc
NMOCd
Totalc
NMOCd
Totalc
NMOCd
Totalc
NMOCd
LF-1 LF-2
>122 >116
33 47
119 >116
30 40
>122 >116
46 60
>122 >116
40 50
170a 0.05b
0.04b
0.05b
aPMGC. bMGR. cTotal
landfill gas (methane + carbon dioxide + NMOC) in Mg year−1. in Mg year−1. LTC: long-term care; PMGC: Potential Methane Generation Capacity; MGR: Methane Generation Rate; NMOC: non-methane organic compound.
dNMOC
list is based on field data study reported by Friedman (1988) and Battista and Connelly (1989). Since the primary purpose of leachate collection is to protect the groundwater and there are groundwater standards for the selected leachate constituents, we used Wisconsin groundwater preventive action limits (PALs) per Wisconsin administrative code Ch. NR 140 (WDNR, 2012b) for concluding whether the projected concentration of the studied leachate parameters at the end of 40-year LTC period is at or below the PAL. PAL concentrations are lower than groundwater standard. If concentration of a pollutant in groundwater reaches the PAL, the owner is notified by the regulatory agency regarding possible future exceedances of groundwater standard; PAL exceedances do not trigger enforcement action, but rather are used as an alarm bell. Leachate extraction and treatment may be stopped when leachate parameters are at or below the PAL. Statistical analysis: The study used time versus concentration data in extracted leachate for the prediction. The data cleaning technique, which is an integral part of most statistical analyses, was undertaken. Outliers were deleted or were replaced by values proportionate to neighbouring preceding and following values (Osborne, 2012). In a few data sets, to maintain uniformity of time intervals, we introduced concentration values proportionate to the previous and following values. To find the best fit three options were considered – linear, quadratic and exponential regression (Johnson and Bhattacharya, 1987). To compare the accuracy of regression fits, three measures were adopted – mean absolute percentage error (MAPE), mean absolute deviation (MAD) and mean square deviation (MSD; Bates and Watts, 1988). We compared all three measures of accuracy and chose the option with the lowest MAPE to calculate the predicted value; this measure is best suited to non-linear predictions. Although best fit curves for most concentration predictions were exponential, there were a few where the best fit curve was quadratic. All calculations for fitting models were performed using Minitab 16©. The following is a general form of exponential equations:
( )
t = A B**t (2) Z In Equation (2), Zˆt is the fit concentration at beginning of the data set, A and B are constant and t is the input time variable in years (with a fixed interval).
The following is a general form of quadratic equations:
t = C + Dt + Et 2 (3) Z In Equation (3), Zˆt is the fit concentration at the beginning of the data set; C, D and E are constant and t is the input time variable in years (with a fixed interval).
Figure 1 shows a typical exponential fit curve and Figure 2 shows a typical quadratic fit curve. Table 3 includes a list of analysed parameters, the projected concentration at the end of the LTC period, concentration in 2010, and PALs for each parameter. As the Table 3 results indicate, all organic parameters, except benzene, are likely to reach concentration below PALs within the LTC period. However, because of the upward trend for several parameters, no such conclusion may be made for inorganic parameters. For the inorganic parameters that showed an upward trend, another set of trend analyses using linear fit of the last four to five years of concentration data were done. The subsequent analysis showed that all parameters, except iron for LF-1, showed a downward trend. A separate study of groundwater data for natural attenuation landfills, closed for 20 years or more, by the first author also showed an upward trend for iron concentration in groundwater. The upward concentration trend for iron is very likely due to iron bacteria in monitoring wells. Since the subsequent analysis using linear fit showed a downward trend and a likely concentration at or below the PAL, we concluded that concentration of all analysed leachate parameters, except chloride and iron, will be at or below PALs by the end of the LTC period. However, trend analysis on leachate data from landfills closed for a longer time period (say 20–25 years) is expected to show a better picture. The predicted volumes of leachate at the end of the LTC period for LF-1 and LF-2 are 227,000 and 78,000 litres yr−1, respectively. The trend analysis showed that for both landfills the leachate volume would be very low, practically zero, in about 100 years. Sources of leachate generation, other than infiltration, are squeezing out of liquid held by waste, and liquid release due
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
235
Bagchi and Bhattacharya
Trend Analysis Plot for Sodium Growth Curve Model Yt = 3589.31 * (0.96667**t) Variable Actual Fits Forecasts
4000
Sodium
3000
Accuracy Measures MAPE 20 MAD 429 MSD 246038
2000 1000 0
08 9 8 00 3 2 20 19 / / / 2 6 21 /1 5/ 5/ 11 Sample date
Figure 1. Typical exponential fit curve.
Trend Analysis Plot for Sulfate Total Quadratic Trend Model Yt = -22.9 + 43.8*t - 2.49*t**2 300
Variable Actual Fits Forecasts
Sulfate Total
200 100
Accuracy Measures MAPE 83.18 MAD 47.20 MSD 3429.14
0 -100 -200 -300 -400
0 6 4 5 9 8 7 01 00 00 00 00 00 00 /2 4/2 6 /2 7/ 2 1 /2 2/ 2 0/2 0 /3 11 / 1 1/ 11 / 1 /1 11 / 1/1 1 11 1 Sample Date
Figure 2. Typical quadratic fit curve.
to chemical and biological reactions; leachate generation due to both is expected to be very low after 100 years. If a composite final cover is maintained properly, then it is very reasonable to assume that leachate generation beyond 100 years will be practically zero. Since, as shown by the trend analysis, the concentration of various parameters in leachate is expected to be at or below PALs, we concluded that leachate leakage through the liner will not cause groundwater standard exceedances. Based on the Table 3 data and leachate volume at the end of the LTC period, we conclude that 40 years of LTC period is adequate for 2–3 million MT capacity MSW landfills. Since peak
concentration of leachate parameters depends on volume and composition of waste, additional study is needed for bigger landfills. Although pollutants are expected to flush out more quickly in bioreactors landfills, based on a study of five bioreactor and recirculation landfills Barlaz et al. (2010) concluded that after a few years leachate generated in bioreactor landfills is not significantly different than leachate generated in non-bioreactor landfills. Leachate line cleaning
Since, for MSW landfills with composite cover, leachate collection may be stopped at the end of the LTC period, leachate
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
236
Waste Management & Research 33(3)
Table 3. Projected concentration of studied leachate parameters at the end of the long-term care (LTC) period. Sl
Parameter
1 2 3 4 5 6 7 8 9 10 11
Cadmium Chloride Iron Lead Manganese Mercury 1,1-Dichloroehane Benzene Acetone Ethylbenzene Toluene
Projected concentration at the end of LTC period (in µg l−1 except where noted)
Concentration (in µg l−1 except where noted) in 2010
PAL (in µg l−1 except where noted)
LF-1
LF-2
LF-1
LF-2
0.00 381 Upa Upa 0.00 Upa 0.00 0.2 0.0002b ~0.00 ~0.00
Upa 0.97b Upa 0.002 0.00 NDc NDc 1.8 0.07b ~0.00 1.8×10−5
0.00 2100 51b 10 940 0.68 2.2 3.1 120b 7.2 11
0.21 1700 7.2b 47 180 NDc NDc 2.1 6b 2.2 0.62
5 125 0.15b 1.5 60 0.2 85 0.5 1.8b 140 160
aThe
best fit curve showed an upward trend. in mg l−1. cNo data. PAL: preventive action limit. bConcentration
line cleaning beyond the LTC period will not be necessary. For MSW landfills with clay covers, depending on the leachate volume at the end of the LTC period, perpetual leachate line cleaning may be needed.
Groundwater monitoring Only chloride and VOCs were chosen for a preliminary study of the groundwater monitoring system. Chloride was chosen because it is highly mobile through clay (Bagchi, 2004) whereby chances of detecting chloride below clay-lined landfills are high. VOCs were chosen because in a soil-leachate system attenuation of VOCs is not expected to be high (Bagchi, 2004). In addition, based on a study of 34 engineered landfills in Wisconsin, Klett et al. (2005) concluded that the potential for groundwater contamination from VOCs is high for both clay and composite lined landfills. So, the preliminary study focused on these parameters to find out whether useful data for a trend analysis is available. The preliminary study showed: (i) PAL exceedances of chloride in several groundwater wells for both landfills; (ii) sporadic detection of several VOCs at low concentrations in quite a few groundwater monitoring wells for both landfills; (iii) near PAL concentrations of benzene in a few groundwater wells for LF-1; (iv) significant concentration of 1,1-dichloroethane, 1,1,1-trichloroehane in a few groundwater wells for LF-2; (v) PAL exceedances of acetone in a few groundwater monitoring wells for LF-2. Sample time versus concentration data for chloride is shown in Table 4 and benzene, 1,1-dichloroethane, 1,1,1-trichloroehane and acetone data are shown in Table 5. A generalized plume geometry and concentration variation within a plume of inorganic contaminants for a landfill scenario using a study of laboratory and field data has been reported by Bagchi (2004). Since groundwater monitoring points were
located within the generalized plume for inorganic contaminants, the chloride data is suitable for trend analysis. A mathematical model by Foose et al. (2002) regarding migration of VOCs through landfill shows that the migration is dependent on the thickness of soil below the base and that VOCs may take several decades to reach groundwater monitoring points. Since elapsed time between closure and this pilot study is rather short – 10 years for LF-2 and 15 years for LF-1, it is likely that large-scale migration of various VOCs is yet to occur. In addition, since generalized plume geometry and concentration variation of VOCs for the landfill scenario is not available in the literature, no conclusion could be made whether the monitoring points were correctly placed to detect VOCs. Based on these two postulates and the lack of data consistency, trend analysis for VOCs was not performed. Although significant chloride data was available for performing trend analysis, a conclusion regarding adequacy of the LTC period for groundwater monitoring based on a single parameter was not considered prudent. Hence, we refrained from drawing a generalized conclusion regarding the LTC period for groundwater monitoring. Additional research regarding VOC travel time to the monitoring points, plume geometry, concentration variation within a plume and its relevancy on data collection is necessary for a meaningful study regarding adequacy of the LTC period for groundwater monitoring.
Perpetual care If PPC is not undertaken for landfills with ‘Dry Tomb’ design, then in the long run the landfill would cause both aesthetic and health-related problems. Without PPC, water infiltration through the final cover will increase, causing filling up of the ‘landfill bowl’ – from the top of the base liner to the top of the above
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
237
Bagchi and Bhattacharya ground berm – with leachate. Such build up will cause a saturated condition of the final cover base, which will lead to significant loss of final cover due to sliding of the cover materials. Depending on the elapsed time and waste composition, the landfill site would be unsanitary and may even be hazardous. Funds to undertake PPC are important for both landfill owners and regulators. Funds needed for PPC are essential for calculating waste disposal fees in landfills. Underfunding of post-closure care may force the owner to declare bankruptcy. The OFR proof amount for PPC is important for regulators, because in the case that a landfill owner declares bankruptcy, the regulatory agency needs to file a claim to the bankruptcy court for a specific amount Table 4. Sample time-concentration data for chloridea for LF-2. Chloride ESb = 250 mg l−1; PAL = 125 mg l−1 Date
Conc. mg l−1
05/23/00 11/20/00 05/23/01 11/12/01 05/08/02 11/19/02 06/02/03 12/03/03 05/20/04 11/24/04
138 143 154 136 141 130 190 150 140 210
Notes: aConcentration in leachate: Average – 2603mg l−1; maxima – 4300 mg l−1 (in 2004); minima – 1070 mg l−1 (in 2009). bES – Enforcement standard.
of money so that the agency may undertake the PPC. In addition to financial issues, administrative issues related to PPC need attention. Experience indicates that providing even 20 years of LTC oversight of landfills needs special administrative guidelines and manpower. In this era of low manpower, providing PPC oversight, unless funded properly, is likely to become administratively untenable. The PPC fund calculation is based on current costs. Future costs for various items needed for final cover construction may be much more than the nominally inflated value, whereby the estimate may not reflect the actual cost at the time of undertaking the maintenance work. It is also possible that in distant future, an item needed for construction (e.g., geomembrane) may not be available at all. So, the PPC funding estimate, based on current cost and availability, faces many uncertainties that are not possible to be accounted for at present. However, it is of upmost importance to estimate PPC funding for the reasons discussed above.
Final cover maintenance As indicated in the LTC study, the following two issues are related to the final cover maintenance. Partial reconstruction of final cover: In estimating the PPC cost it is assumed that the final cover replacement due to large-scale settlement, if needed, will be done within the LTC period. Thereafter, only the geomembrane liner of the composite final cover needs to be replaced. The rooting layer and the top soil may be salvaged prior to installing the geomembrane liner and then reused. To calculate the cost of a construction item in future, the present cost (PC) is to be multiplied by an inflation factor (I). Cost of construction of an item after one year is PC(I); after two years it is PC(I)2; after three years it is PC(I)3 and so on.
Table 5. Sample ‘time-concentration data’ for benzenea; 1,1-dichloroethaneb; 1,1,1-trichloroehanec; and acetoned. LF -1
LF-2
LF-2
LF-2
Benzene ES =5µg l−1 PAL= 0.5µg l−1
1,1-Dichloroehane ES= 850µg l−1 PAL = 85µg l−1
1,1,1-Trichloroehane ES= 200µg l−1 PAL= 40µg l−1
Acetone ES= 9mg l−1 PAL = 1.8mg l−1
Date
Conc.µg l−1
Date
Conc.µg l−1
Date
Conc. µg l−1
Date
Conc. mg l−1
05/16/01 11/21/02 05/29/02 11/21/02 05/21/03 05/13/04 11/18/04 05/24/05 05/08/06
0.2 0.24 0.53 0.46 0.47 NDe NDe 0.41 0.43
05/23/00 05/23/01 05/08/02 06/02/03 05/20/04 05/17/05 11/02/05 05/23/06 05/24/07 05/08/08
23 11 14 0.83 8.8 10 13 6.7 2.4 5.5
05/23/01 05/08/02 06/02/03 06/20/04 05/17/05 09/16/05 11/01/05 05/26/06 05/07/08 05/07/08
16 12 14 19 8.9 8.3 12 7.8 4.7 6.6
05/23/00 05/23/01 05/08/02 06/02/03 06/20/04 05/23/06 05/24/07 05/08/08
8.5 2.3 15 NDe 8 42 NDe 26.8
aConcentration
in leachate: Average – 4.45µg l−1; maxima – 9.1µg l−1 (in 2000); minima – 2.3µg l−1 (in 2010). in leachate: No data. cConcentration in leachate: No data. dConcentration in leachate: Average – 119µg l−1; maxima – 560µg l−1 (in 2005); minima – 6µg l−1 (in 2010). eNo data. bConcentration
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
238
Waste Management & Research 33(3)
Assuming a constant inflation rate of ‘F%’: I = (1 + .0 F ) (4)
However, if the money for future construction is kept in an interest-bearing account (e.g., escrow account) earning a constant interest rate of ‘G%’, and the if the inflation rate is ‘F%’, then
I = (1 + .0G )
(
(1 + .0 F )
−1
Pcr = Ccr ISL + Ccr I 2SL + Ccr I3SL + Ccr I 4SL +
1 + ISL + I 2SL + I3SL Or, Pcr = Ccr ISL 4SL + I + ……… I∞SL
Ccr I5SL + ……. Ccr I∞SL )
(6)
( ) ( ) ( )
1 + ISL + ISL 2 + SL Or, Pcr = Ccr I 3 4 ISL + ISL + ……. I∞SL
(1 + ISL + (ISL)2 + (ISL)3 + (ISL)4 +……. (ISL)∞) is an infinite geometric series, the sum of which is (1 – ISL)−1. Equation (7) has been obtained by putting the sum into Equation (6):
(
Pcr = Ccr I SL 1 − I SL
)
−1
, where I < 1 (7)
For estimating funds needed for PPC for all types of financial instruments (e.g., letter of credit), except escrow accounts, ‘I’ would consist of the inflation factor only (i.e., I = (1+ 0.0F); this factor will always be >1, which will not satisfy the necessary condition for summing up an infinite series i.e., I < 1. However, for escrow accounts I = (1+ 0.0F)((1+0.0G)−1). Since in normal economic conditions, earning rate in escrow accounts (G%) is more than the inflation (F%), I would be always
research-article2015
WMR0010.1177/0734242X14567501Waste Management & ResearchBagchi and Bhattacharya
Original Article Waste Management & Research 2015, Vol. 33(3) 232–240 © The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0734242X14567501 wmr.sagepub.com
Post-closure care of engineered municipal solid waste landfills Amalendu Bagchi1 and Abhik Bhattacharya2
Abstract Post-closure care is divided into perpetual care (PPC) and long-term care (LTC). Guidelines for post-closure care and associated costs are important for engineered municipal solid waste (MSW) landfills. In many states in the USA, landfill owners are required to set aside funds for 30–40 years of LTC. Currently there are no guidelines for PPC, which is also required. We undertook a pilot study, using two landfills (note: average landfill capacity 2.5 million MT MSW waste) in Wisconsin, to establish an approach for estimating the LTC period using field data and PPC funding need. Statistical analysis of time versus concentration data of selected leachate parameters showed that the concentration of most parameters is expected to be at or below the preventive action limit of groundwater and leachate volume will be very low, within 40 years of the LTC period. The gas extraction system may need to be continued for more than 100 years. Due to lack of data no conclusion could be made regarding adequacy of the LTC period for the groundwater monitoring system. The final cover must be maintained for perpetuity. The pilot study shows that although technology is available, the financial liability of maintaining a ‘Dry Tomb’ design for landfills is significantly higher than commonly perceived. The paper will help landfill professionals to estimate realistic post-closure funding and to develop field-based policies for LTC and PPC of engineered MSW landfills. Keywords Landfill, field study, leachate trend, post-closure care, perpetual care, economics, policy
Introduction Currently Wisconsin regulations require 40 years of long-term care (LTC) after closure and perpetual care (PPC) of municipal solid waste (MSW) landfills. Owner financial responsibility (OFR) funds depend on the LTC period, which must be established at the beginning of a landfill operation for estimating the disposal fee. So, a realistic LTC period is important for proper operational funding of landfills. Although the Interstate Technology and Regulatory Council (ITRC, 2006) has discussed various ideas at length regarding alternatives for optimizing postclosure care from a technological view point, we are not aware of any published literature that discusses the rationale behind choosing 30 or 40 years of LTC period or guidelines for PPC and the associated costs, which are important issues related to landfill post-closure maintenance cost and landfill economics. We undertook a pilot study using field data from the Wisconsin Department of Natural Resources (WDNR) database, and relevant programme files to address the literature gap. Additional studies involving landfills with various waste volumes and climatological locations are necessary. However, the field-based approach described in this paper will help in drawing realistic conclusions. The emphasis of this paper is on landfill economics; the paper does not address the technical issues mentioned. Further research is needed on various technical issues related to both LTC and PPC. For the pilot study we selected two ‘stand alone’ (i.e., which do not have any contiguous expansion nor have any landfills
nearby causing interference on the groundwater monitoring data) MSW landfills in Wisconsin. Basic information regarding these two landfills is included in Table 1. Leachate recirculation was not undertaken in either landfill.
Long-term care study OFR for LTC costs include maintenance of final cover, the gas extraction system, leachate collection system and ground water monitoring. Each item is discussed in the following sections.
Final cover maintenance There are two issues associated with the final cover maintenance: (1) final cover repair; (2) final cover vegetation mowing. 1. Final cover repair. Field observations indicate that final cover repair due to erosion and small-scale settlement is high
1Waste 2Blue
Management Engineer (Retired, Wis. Dept. of Natl. Res.), USA Cross Blue Shield Assoc., USA
Corresponding author: Amalendu Bagchi, Waste Management Engineer (Retired, Wis. Dept. of Natl. Res.), 222 St. Croix Ln, Madison, WI 53705, USA. Email: [email protected]
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
233
Bagchi and Bhattacharya in the first five years after construction of final cover, beyond which sporadic erosion and small-scale settlements have been observed. In addition to the sporadic settlements, it is reasonable to assume a large-scale settlement of the final cover due to waste decomposition, whereby a replacement of the entire final cover within the LTC period may become necessary. The rate of settlement is higher in bioreactor landfills than in non-bioreactor landfills (Bareither et al., 2010), which may prompt an earlier replacement of final cover in bioreactor landfills than in non-bioreactor landfills. The literature indicates that the service life (SL) of geomembrane, depending on the polymer type, may be between 55 and 125 years (Benson et. al., 2011; Rowe et. al., 2009). So, perpetual replacement of the geomembrane liner of composite final covers will be needed to maintain a ‘Dry Tomb’ design. 2. Final cover vegetation mowing. Field observations in old natural attenuation landfills indicate that yearly mowing of the final cover is essential, without which native vegetative species with deep root systems will invade the final cover. Growth of such deep root species may deteriorate the integrity of geomembrane and clay layer in the final cover system, leading to increase in water infiltration and subsequent increase in leachate generation.
Gas extraction system maintenance Currently there are no criteria as to when a gas extraction system may be stopped. The following two landfill gas emission related criteria, specified by the United States Environmental Protection Agency (USEPA) for new or existing landfills were used for the study: (i) landfills that emit total landfill gas more than 50 Mg per year must install controls to reduce emissions; (ii) landfills that emit more than 50 Mg per year of non-methane organic compounds (NMOCs) must install control to reduce emission (USEPA, 1998). The LandGEM model (USEPA, 2005) was used to estimate the number of years after closure at which the total landfill gas or NMOC would be at 50 Mg yr−1. LandGEM is based on a firstorder decomposition rate equation for quantifying emissions from MSW landfill waste. LandGEM uses the following firstorder decomposition rate equation: n
QCH4=
i
∑∑
kLo .1M i e− kt (ij ) (1)
i = j j =0.1
where QCH4 is the annual methane generation in the year of the calculation (m3 yr−1), i is the one-year time increment, n is (year of the calculation) – (initial year of waste acceptance), j is the 0.1-year time increment, k is the methane generation rate (MGR; yr−1), Lo is the potential methane generation capacity (PMGC; m3 Mg−1), Mi is the mass of waste accepted in the ith year (Mg) and t(ij) is the age of the jth section of waste mass Mi accepted in the ith year (decimal years, e.g., 3.2 years).
Table 1. Landfill information. Landfill Year ID open
Year Liner Final cover closed
LF-1
1980s 1998
LF-2
1980s 2004
5 ft. clay 5 ft. clay
Approx. waste disposal weight in million MT.
Part clay part 2.3 composite Part clay part 2.7 composite
The model was run for both landfills for PMGCs of 100 and 170 and MGRs of 0.04 and 0.05; a uniform disposal rate over the active life period of the landfills was assumed. The results are included in Table 2. Table 2 data shows: (i) gas generation depends on waste volume and the PMGC and MGR combination; (ii) if NMOC emission criteria is used the LTC period for these two landfills varies between 40 and 60 years; (iii) if total gas emission criteria is used, the LTC period for these two landfills is more than 100 years. Thus, currently the LTC period for gas extraction is underestimated even for 2–3 million MT capacity MSW landfills. We would like to point out that a change in environment within landfills due to lack of oxygen and waste volume will greatly influence both the quality and quantity of landfill gas. The LandGEM model is not used for bioreactor landfills, because a generally acceptable MGR is not available yet. The gas generation rate in active bioreactor landfills is higher than in nonbioreactor landfills, which decrease after landfill closure (Barlaz et al., 2010). Further research is necessary for developing guidelines for specifying the allowable gas emissions criteria for both bioreactor and non-bioreactor MSW landfills. Since methane is explosive between concentrations of 5–15% in open air, chances of landfill fire, not uncommon for MSW landfills, are expected to increase several years after closure when the methane concentration becomes low. In view of this, inclusion of cost for a disaster management for landfill fire in the LTC cost merits consideration.
Leachate collection system maintenance The following issues are associated with leachate collection system maintenance. Leachate extraction and treatment: A preliminary analysis of leachate data from the two landfills indicated that after closure the concentration of monitored leachate parameters decreases with time. Ham and Anderson (1974), Pohland (1975) and Ham (1980) also observed similar decrease of leachate parameter concentration in laboratory studies. Based on the laboratory studies and field observation, we used trend analysis – a statistical modelling tool to predict future values based on current data, of selected leachate parameters from a list of parameters required by Wisconsin administrative code Ch. NR 507 (WDNR, 2012a). We analysed only those inorganic parameters in leachate that have either a Public Health Groundwater Quality Standard (PHGQS) or Public Welfare Groundwater Quality Standard (PWGQS) and a few volatile organic compounds (VOCs). The chosen VOC parameter
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
234
Waste Management & Research 33(3)
Table 2. Results of the LandGEM model study. Landfill ID
Estimated LTC period for various combinations of PMGC & MGR
100a
0.04b
Totalc
NMOCd
Totalc
NMOCd
Totalc
NMOCd
Totalc
NMOCd
LF-1 LF-2
>122 >116
33 47
119 >116
30 40
>122 >116
46 60
>122 >116
40 50
170a 0.05b
0.04b
0.05b
aPMGC. bMGR. cTotal
landfill gas (methane + carbon dioxide + NMOC) in Mg year−1. in Mg year−1. LTC: long-term care; PMGC: Potential Methane Generation Capacity; MGR: Methane Generation Rate; NMOC: non-methane organic compound.
dNMOC
list is based on field data study reported by Friedman (1988) and Battista and Connelly (1989). Since the primary purpose of leachate collection is to protect the groundwater and there are groundwater standards for the selected leachate constituents, we used Wisconsin groundwater preventive action limits (PALs) per Wisconsin administrative code Ch. NR 140 (WDNR, 2012b) for concluding whether the projected concentration of the studied leachate parameters at the end of 40-year LTC period is at or below the PAL. PAL concentrations are lower than groundwater standard. If concentration of a pollutant in groundwater reaches the PAL, the owner is notified by the regulatory agency regarding possible future exceedances of groundwater standard; PAL exceedances do not trigger enforcement action, but rather are used as an alarm bell. Leachate extraction and treatment may be stopped when leachate parameters are at or below the PAL. Statistical analysis: The study used time versus concentration data in extracted leachate for the prediction. The data cleaning technique, which is an integral part of most statistical analyses, was undertaken. Outliers were deleted or were replaced by values proportionate to neighbouring preceding and following values (Osborne, 2012). In a few data sets, to maintain uniformity of time intervals, we introduced concentration values proportionate to the previous and following values. To find the best fit three options were considered – linear, quadratic and exponential regression (Johnson and Bhattacharya, 1987). To compare the accuracy of regression fits, three measures were adopted – mean absolute percentage error (MAPE), mean absolute deviation (MAD) and mean square deviation (MSD; Bates and Watts, 1988). We compared all three measures of accuracy and chose the option with the lowest MAPE to calculate the predicted value; this measure is best suited to non-linear predictions. Although best fit curves for most concentration predictions were exponential, there were a few where the best fit curve was quadratic. All calculations for fitting models were performed using Minitab 16©. The following is a general form of exponential equations:
( )
t = A B**t (2) Z In Equation (2), Zˆt is the fit concentration at beginning of the data set, A and B are constant and t is the input time variable in years (with a fixed interval).
The following is a general form of quadratic equations:
t = C + Dt + Et 2 (3) Z In Equation (3), Zˆt is the fit concentration at the beginning of the data set; C, D and E are constant and t is the input time variable in years (with a fixed interval).
Figure 1 shows a typical exponential fit curve and Figure 2 shows a typical quadratic fit curve. Table 3 includes a list of analysed parameters, the projected concentration at the end of the LTC period, concentration in 2010, and PALs for each parameter. As the Table 3 results indicate, all organic parameters, except benzene, are likely to reach concentration below PALs within the LTC period. However, because of the upward trend for several parameters, no such conclusion may be made for inorganic parameters. For the inorganic parameters that showed an upward trend, another set of trend analyses using linear fit of the last four to five years of concentration data were done. The subsequent analysis showed that all parameters, except iron for LF-1, showed a downward trend. A separate study of groundwater data for natural attenuation landfills, closed for 20 years or more, by the first author also showed an upward trend for iron concentration in groundwater. The upward concentration trend for iron is very likely due to iron bacteria in monitoring wells. Since the subsequent analysis using linear fit showed a downward trend and a likely concentration at or below the PAL, we concluded that concentration of all analysed leachate parameters, except chloride and iron, will be at or below PALs by the end of the LTC period. However, trend analysis on leachate data from landfills closed for a longer time period (say 20–25 years) is expected to show a better picture. The predicted volumes of leachate at the end of the LTC period for LF-1 and LF-2 are 227,000 and 78,000 litres yr−1, respectively. The trend analysis showed that for both landfills the leachate volume would be very low, practically zero, in about 100 years. Sources of leachate generation, other than infiltration, are squeezing out of liquid held by waste, and liquid release due
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
235
Bagchi and Bhattacharya
Trend Analysis Plot for Sodium Growth Curve Model Yt = 3589.31 * (0.96667**t) Variable Actual Fits Forecasts
4000
Sodium
3000
Accuracy Measures MAPE 20 MAD 429 MSD 246038
2000 1000 0
08 9 8 00 3 2 20 19 / / / 2 6 21 /1 5/ 5/ 11 Sample date
Figure 1. Typical exponential fit curve.
Trend Analysis Plot for Sulfate Total Quadratic Trend Model Yt = -22.9 + 43.8*t - 2.49*t**2 300
Variable Actual Fits Forecasts
Sulfate Total
200 100
Accuracy Measures MAPE 83.18 MAD 47.20 MSD 3429.14
0 -100 -200 -300 -400
0 6 4 5 9 8 7 01 00 00 00 00 00 00 /2 4/2 6 /2 7/ 2 1 /2 2/ 2 0/2 0 /3 11 / 1 1/ 11 / 1 /1 11 / 1/1 1 11 1 Sample Date
Figure 2. Typical quadratic fit curve.
to chemical and biological reactions; leachate generation due to both is expected to be very low after 100 years. If a composite final cover is maintained properly, then it is very reasonable to assume that leachate generation beyond 100 years will be practically zero. Since, as shown by the trend analysis, the concentration of various parameters in leachate is expected to be at or below PALs, we concluded that leachate leakage through the liner will not cause groundwater standard exceedances. Based on the Table 3 data and leachate volume at the end of the LTC period, we conclude that 40 years of LTC period is adequate for 2–3 million MT capacity MSW landfills. Since peak
concentration of leachate parameters depends on volume and composition of waste, additional study is needed for bigger landfills. Although pollutants are expected to flush out more quickly in bioreactors landfills, based on a study of five bioreactor and recirculation landfills Barlaz et al. (2010) concluded that after a few years leachate generated in bioreactor landfills is not significantly different than leachate generated in non-bioreactor landfills. Leachate line cleaning
Since, for MSW landfills with composite cover, leachate collection may be stopped at the end of the LTC period, leachate
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
236
Waste Management & Research 33(3)
Table 3. Projected concentration of studied leachate parameters at the end of the long-term care (LTC) period. Sl
Parameter
1 2 3 4 5 6 7 8 9 10 11
Cadmium Chloride Iron Lead Manganese Mercury 1,1-Dichloroehane Benzene Acetone Ethylbenzene Toluene
Projected concentration at the end of LTC period (in µg l−1 except where noted)
Concentration (in µg l−1 except where noted) in 2010
PAL (in µg l−1 except where noted)
LF-1
LF-2
LF-1
LF-2
0.00 381 Upa Upa 0.00 Upa 0.00 0.2 0.0002b ~0.00 ~0.00
Upa 0.97b Upa 0.002 0.00 NDc NDc 1.8 0.07b ~0.00 1.8×10−5
0.00 2100 51b 10 940 0.68 2.2 3.1 120b 7.2 11
0.21 1700 7.2b 47 180 NDc NDc 2.1 6b 2.2 0.62
5 125 0.15b 1.5 60 0.2 85 0.5 1.8b 140 160
aThe
best fit curve showed an upward trend. in mg l−1. cNo data. PAL: preventive action limit. bConcentration
line cleaning beyond the LTC period will not be necessary. For MSW landfills with clay covers, depending on the leachate volume at the end of the LTC period, perpetual leachate line cleaning may be needed.
Groundwater monitoring Only chloride and VOCs were chosen for a preliminary study of the groundwater monitoring system. Chloride was chosen because it is highly mobile through clay (Bagchi, 2004) whereby chances of detecting chloride below clay-lined landfills are high. VOCs were chosen because in a soil-leachate system attenuation of VOCs is not expected to be high (Bagchi, 2004). In addition, based on a study of 34 engineered landfills in Wisconsin, Klett et al. (2005) concluded that the potential for groundwater contamination from VOCs is high for both clay and composite lined landfills. So, the preliminary study focused on these parameters to find out whether useful data for a trend analysis is available. The preliminary study showed: (i) PAL exceedances of chloride in several groundwater wells for both landfills; (ii) sporadic detection of several VOCs at low concentrations in quite a few groundwater monitoring wells for both landfills; (iii) near PAL concentrations of benzene in a few groundwater wells for LF-1; (iv) significant concentration of 1,1-dichloroethane, 1,1,1-trichloroehane in a few groundwater wells for LF-2; (v) PAL exceedances of acetone in a few groundwater monitoring wells for LF-2. Sample time versus concentration data for chloride is shown in Table 4 and benzene, 1,1-dichloroethane, 1,1,1-trichloroehane and acetone data are shown in Table 5. A generalized plume geometry and concentration variation within a plume of inorganic contaminants for a landfill scenario using a study of laboratory and field data has been reported by Bagchi (2004). Since groundwater monitoring points were
located within the generalized plume for inorganic contaminants, the chloride data is suitable for trend analysis. A mathematical model by Foose et al. (2002) regarding migration of VOCs through landfill shows that the migration is dependent on the thickness of soil below the base and that VOCs may take several decades to reach groundwater monitoring points. Since elapsed time between closure and this pilot study is rather short – 10 years for LF-2 and 15 years for LF-1, it is likely that large-scale migration of various VOCs is yet to occur. In addition, since generalized plume geometry and concentration variation of VOCs for the landfill scenario is not available in the literature, no conclusion could be made whether the monitoring points were correctly placed to detect VOCs. Based on these two postulates and the lack of data consistency, trend analysis for VOCs was not performed. Although significant chloride data was available for performing trend analysis, a conclusion regarding adequacy of the LTC period for groundwater monitoring based on a single parameter was not considered prudent. Hence, we refrained from drawing a generalized conclusion regarding the LTC period for groundwater monitoring. Additional research regarding VOC travel time to the monitoring points, plume geometry, concentration variation within a plume and its relevancy on data collection is necessary for a meaningful study regarding adequacy of the LTC period for groundwater monitoring.
Perpetual care If PPC is not undertaken for landfills with ‘Dry Tomb’ design, then in the long run the landfill would cause both aesthetic and health-related problems. Without PPC, water infiltration through the final cover will increase, causing filling up of the ‘landfill bowl’ – from the top of the base liner to the top of the above
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
237
Bagchi and Bhattacharya ground berm – with leachate. Such build up will cause a saturated condition of the final cover base, which will lead to significant loss of final cover due to sliding of the cover materials. Depending on the elapsed time and waste composition, the landfill site would be unsanitary and may even be hazardous. Funds to undertake PPC are important for both landfill owners and regulators. Funds needed for PPC are essential for calculating waste disposal fees in landfills. Underfunding of post-closure care may force the owner to declare bankruptcy. The OFR proof amount for PPC is important for regulators, because in the case that a landfill owner declares bankruptcy, the regulatory agency needs to file a claim to the bankruptcy court for a specific amount Table 4. Sample time-concentration data for chloridea for LF-2. Chloride ESb = 250 mg l−1; PAL = 125 mg l−1 Date
Conc. mg l−1
05/23/00 11/20/00 05/23/01 11/12/01 05/08/02 11/19/02 06/02/03 12/03/03 05/20/04 11/24/04
138 143 154 136 141 130 190 150 140 210
Notes: aConcentration in leachate: Average – 2603mg l−1; maxima – 4300 mg l−1 (in 2004); minima – 1070 mg l−1 (in 2009). bES – Enforcement standard.
of money so that the agency may undertake the PPC. In addition to financial issues, administrative issues related to PPC need attention. Experience indicates that providing even 20 years of LTC oversight of landfills needs special administrative guidelines and manpower. In this era of low manpower, providing PPC oversight, unless funded properly, is likely to become administratively untenable. The PPC fund calculation is based on current costs. Future costs for various items needed for final cover construction may be much more than the nominally inflated value, whereby the estimate may not reflect the actual cost at the time of undertaking the maintenance work. It is also possible that in distant future, an item needed for construction (e.g., geomembrane) may not be available at all. So, the PPC funding estimate, based on current cost and availability, faces many uncertainties that are not possible to be accounted for at present. However, it is of upmost importance to estimate PPC funding for the reasons discussed above.
Final cover maintenance As indicated in the LTC study, the following two issues are related to the final cover maintenance. Partial reconstruction of final cover: In estimating the PPC cost it is assumed that the final cover replacement due to large-scale settlement, if needed, will be done within the LTC period. Thereafter, only the geomembrane liner of the composite final cover needs to be replaced. The rooting layer and the top soil may be salvaged prior to installing the geomembrane liner and then reused. To calculate the cost of a construction item in future, the present cost (PC) is to be multiplied by an inflation factor (I). Cost of construction of an item after one year is PC(I); after two years it is PC(I)2; after three years it is PC(I)3 and so on.
Table 5. Sample ‘time-concentration data’ for benzenea; 1,1-dichloroethaneb; 1,1,1-trichloroehanec; and acetoned. LF -1
LF-2
LF-2
LF-2
Benzene ES =5µg l−1 PAL= 0.5µg l−1
1,1-Dichloroehane ES= 850µg l−1 PAL = 85µg l−1
1,1,1-Trichloroehane ES= 200µg l−1 PAL= 40µg l−1
Acetone ES= 9mg l−1 PAL = 1.8mg l−1
Date
Conc.µg l−1
Date
Conc.µg l−1
Date
Conc. µg l−1
Date
Conc. mg l−1
05/16/01 11/21/02 05/29/02 11/21/02 05/21/03 05/13/04 11/18/04 05/24/05 05/08/06
0.2 0.24 0.53 0.46 0.47 NDe NDe 0.41 0.43
05/23/00 05/23/01 05/08/02 06/02/03 05/20/04 05/17/05 11/02/05 05/23/06 05/24/07 05/08/08
23 11 14 0.83 8.8 10 13 6.7 2.4 5.5
05/23/01 05/08/02 06/02/03 06/20/04 05/17/05 09/16/05 11/01/05 05/26/06 05/07/08 05/07/08
16 12 14 19 8.9 8.3 12 7.8 4.7 6.6
05/23/00 05/23/01 05/08/02 06/02/03 06/20/04 05/23/06 05/24/07 05/08/08
8.5 2.3 15 NDe 8 42 NDe 26.8
aConcentration
in leachate: Average – 4.45µg l−1; maxima – 9.1µg l−1 (in 2000); minima – 2.3µg l−1 (in 2010). in leachate: No data. cConcentration in leachate: No data. dConcentration in leachate: Average – 119µg l−1; maxima – 560µg l−1 (in 2005); minima – 6µg l−1 (in 2010). eNo data. bConcentration
Downloaded from wmr.sagepub.com at University of Birmingham on May 29, 2015
238
Waste Management & Research 33(3)
Assuming a constant inflation rate of ‘F%’: I = (1 + .0 F ) (4)
However, if the money for future construction is kept in an interest-bearing account (e.g., escrow account) earning a constant interest rate of ‘G%’, and the if the inflation rate is ‘F%’, then
I = (1 + .0G )
(
(1 + .0 F )
−1
Pcr = Ccr ISL + Ccr I 2SL + Ccr I3SL + Ccr I 4SL +
1 + ISL + I 2SL + I3SL Or, Pcr = Ccr ISL 4SL + I + ……… I∞SL
Ccr I5SL + ……. Ccr I∞SL )
(6)
( ) ( ) ( )
1 + ISL + ISL 2 + SL Or, Pcr = Ccr I 3 4 ISL + ISL + ……. I∞SL
(1 + ISL + (ISL)2 + (ISL)3 + (ISL)4 +……. (ISL)∞) is an infinite geometric series, the sum of which is (1 – ISL)−1. Equation (7) has been obtained by putting the sum into Equation (6):
(
Pcr = Ccr I SL 1 − I SL
)
−1
, where I < 1 (7)
For estimating funds needed for PPC for all types of financial instruments (e.g., letter of credit), except escrow accounts, ‘I’ would consist of the inflation factor only (i.e., I = (1+ 0.0F); this factor will always be >1, which will not satisfy the necessary condition for summing up an infinite series i.e., I < 1. However, for escrow accounts I = (1+ 0.0F)((1+0.0G)−1). Since in normal economic conditions, earning rate in escrow accounts (G%) is more than the inflation (F%), I would be always
