1 Introduction  

Pollutant trading in a watershed is a market based strategy to economically achieve environmental waste management. Trading programs allow facilities facing higher pollution control costs to meet their regulatory obligations by purchasing environmentally equivalent (or superior) pollution reductions from another source at lower cost [1]. But the added flexibility due to trading also complicates decision making for polluters such as process industries. In the presence of multiple polluters, multiple waste treatment technologies and option of trading, decisions such as if and how much to trade become difficult for the polluters. It is also important to understand the effect of trading on the final emissions and their environmental and health impacts. Finally, information about of the watershed and trading, if available while finalizing the regulation, might influence the regulation development itself.

This work uses optimization techniques to develop a decision making framework that will guide the industries in taking optimal decisions in wake of the added flexibility due to trading. The model will also guide regulators in developing optimal regulations in different situations. The proposed model is applied on a Savannah River watershed mercury waste management case study as mercury is an important concern for environmentalists.  

2 Methodology and Results  

2.1 Basic Problem Formulation  

The formulation considers that TMDL (Total Maximum Daily Load) regulation has already been developed translating into specific load allocations for each point source. Consider a set of point sources (PS_i), i=1,…N, disposing pollutant containing waste water to a common water body or watershed. Here D_i, L_i and red_i are the volumetric discharge quantity, waste load allocation and desired pollutant quantity reduction for PS_i. P_i is the treatment cost incurred by PS_i to reduce pollution when trading is not possible. Let j = 1,…,M  be the set of reduction technologies available to the point sources for implementation. TC_j is the total treatment plant cost [$/Volume] and q_j is the pollution reduction possible from the process [Mass/Volume]. Trading is possible between all point sources and a single trading policy exists between all possible pairs of point sources. Let r be the trading ratio and F be the trading transaction cost in $/Mass. The objective of the model is to achieve the desired TMDL goal at minimum overall cost. Let b_ij be the binary variables representing the point source-technology correlation. The variable is 1 when PS_i installs technology j, and 0 otherwise. Let t_ik (mass/year) be the amount of pollutant traded by PS_i with PS_k. All the parameters are on an annual basis.

The objective in the problem is to reduce the overall waste reduction cost, a function of TC_j, D_i and b_ij, by all point sources. The constraints ensure that all the targeted reduction red_i are achieved and no industry spends more while trading as compared to when not trading. The problem is a mixed integer linear programming problem (MILP). The decision variables in the problem are the binary variables b_ij and the continuous variables t_ik. The problem is quite general, applicable to any watershed and any pollutant.

For the considered case study, discharge of any mercury to the watershed is associated with some health care cost. This cost is calculated as a function of the mercury LC50 value and final total mercury discharge. It estimates the long term effects of mercury exposure on the population consuming fishes from the watershed.  

2.2 Savannah River basin case study results  

TMDL of 32.8 Kg/year of total mercury has been established for five contiguous segments of the Savannah River in Georgia, U.S. which corresponds to a water quality standard (WQS) of 2.8 ng/liter [2]. Based on the current volumetric discharge of each of the point sources, waste load allocation is carried out. In all, there are 29 significant point sources discharging mercury in the Savannah River watershed. The combined targeted reduction for point sources is taken to be 40%.

Three treatment technologies, coagulation and filtration, activated carbon adsorption and ion exchange process are considered. The cost data for the treatments is reported in [3]. The trading ratio r is 1.1 and trading transaction fee, based on the average treatment costs of the processes, is around 4x10⁸ $/Kg.

Results at 32 Kg/year TMDL indicate about 18% annual reduction (27 Million $) in the treatment cost when trading is implemented. However total mercury discharge for the trading option is higher by about 17% which results in 20% less health care costs for the technology only option. The results show a trend towards avoiding expensive technology implementations and satisfying part of the pollutant reduction through trading.

To compare the trading and technology options with respect to TMDL regulation, the problem is solved for various TMDL values between 23 Kg/year and 40 Kg/year. While reduction and total (reduction and health care) costs for trading option are consistently lower than for technology option, the variation is not always linear and appears to depend on the TMDL regulation value. For this problem trading becomes economically attractive at lower TMDL values. Also the difference between the discharge reductions for technology and trading option varies, depending on TMDL value.  

2.3 Health care cost as objective  

Health care cost is an important parameter affecting the regulatory decision. Hence optimization problem is modified to include it in the objective of minimization. This cost, previously estimated for a particular solution, is added to the existing objective function of minimization.

The modified problem is solved for Savannah River basin at various TMDL values between 23 Kg/year and 40 Kg/year. The results depend on the significance of the health care cost in the overall objective. For small compensation values, solutions do not change as compared to the original formulation. At higher values of compensation, the health care cost becomes significant and industries are made to reduce more than their load allocations by using more efficient and expensive technologies. The increased treatment costs are compensated for by reduced health care costs leading to reduced total costs.  

2.4 Chance constrained formulation  

The previous formulations assumed the data to be known deterministically which is not always true. In this work, the current discharge of mercury by each industry is considered to be uncertain, normally distributed around a mean value. This makes the parameter red_i in the problem to be normally distributed around a mean and converts the problem into a stochastic programming one. The formulation does not consider health care costs in the objective function. Equations 1-4 constitute the stochastic problem, the difference being that in stochastic case the parameter red_i is uncertain. The problem is solved by the chance constrained programming method [4]. Two different degrees of uncertainty ±15% and ±50% and various constraint satisfaction probabilities (50%, 90% and 99%) are modeled. The problem is solved for TMDL between 23 Kg/year to 40 Kg/year.

The results show that larger uncertainty and higher constraint satisfaction probability result in higher reduction but lower health care cost and the variations are not linear. The impact of uncertainty becomes more prominent at stricter regulations, sometimes resulting in infeasible problems.  

3 Results and Conclusion  

The results indicate that the advantages offered by trading in the form of reduced treatment costs should be carefully weighed against increased risk of adverse health effects of mercury. The extent of this tradeoff depends on the watershed and industry specific parameters and the regulation itself. Stochastic analysis shows that uncertainty is more pronounced as the regulations become stricter. Nonlinear dependence of the solutions on TMDL regulation indicates that consideration of trading and watershed specific details during regulation development might help develop better regulations, achieving an effective tradeoff between cost and reductions. It is important to consider all these aspects for industrial symbiosis and sustainability. The framework can thus be effectively used for sustainable industrial management.  

References  

[1] USEPA. Draft framework for watershed-based trading. Technical report, EPA 800-R-96-001. Washington, DC: United States Environmental Protection Agency, Office of Water, 1996.

[2] USEPA. Total maximum daily load (TMDL) for total mercury in fish tissue residue in the middle and lower savannah River watershed. Report, United States Environmental Protection Agency, Region 4, 2001.

[3] USDOI. Total plant costs: For contaminant fact sheets. Technical report, U.S.

Department of Interior, Bureau of Reclamation, Water treatment engineering and research group, Denver CO 80225, 2001.

[4] U.M. Diwekar. Introduction to Applied Optimization. Kluwer Academic Publishers, Dordrecht, 2003.