Unscrambling the Comingled Plume is Still the Allocator's Dilemna
Gary R. Walter, Ph.D., President

Allocation of responsibility for harm at federal and state Superfund sites with multiple PRPs frequently involves attempts to quantify sources of groundwater contamination. When the nature of groundwater contamination involves a commingled plume with potential contributions from various sources, "unscrambling the egg" can be quite complex. Approaches to assigning responsibility in such cases include allocation on the basis of:

• mass released,
• harm based on relative concentrations and types of contaminants,
  
• volume of contaminated groundwater from a given source, and
  
• the "stand-alone" cost of remediating the plumes attributed to given sources.

Whatever metric is selected, it should be a fair representation of the contribution to the harm to groundwater quality. The harm can be defined in various ways, but the two simplest are 1) cost to replace the lost resource and 2) cost to return the resource to its original beneficial purpose. The latter cost is usually greatest. In most cases, the remedial cost is controlled by the volume of groundwater to be restored (or controlled) and the mass of contaminant in the plume. The volume of the plume is determined by the extent of groundwater contamination that exceeds a Remedial Action Objective, usually based on the Maximum Contaminant Levels (MCLs) of the contaminants or some multiple thereof.

Fair allocation of costs requires a clear understanding of the physics of groundwater flow and transport, even if precise mathematical predictions are not possible. Without such understanding, allocation approaches may not fairly represent the contribution to harm. Consider two sources, each of which released trichloroethene (TCE) to groundwater. Source 1 released a mass (M1) sufficient to cause a maximum concentration of 4 ppb, and the second source released half the mass (M2) into an equivalent volume of groundwater resulting in a concentration of 2 ppb. Neither source has released a mass of contaminant sufficient to cause the groundwater in its plume to exceed the MCL of TCE (5 ppb) and neither plume may require remediation.

Suppose that Source 1 and Source 2 plumes overlap and commingle, as illustrated in the figure above. Is it possible for the combined releases to result in a concentration of 6 ppb, exceeding the MCL and requiring remediation? The answer is no, yet I have observed instances where the argument has been made that "but for the release from Source 2, the plume from Source 1 would not have required remediation." This argument is apparently based on the misconception that the mixing of groundwaters with differing concentrations of a contaminant can create an additive effect in the concentrations. It ignores fundamental principles of mass and volume conservation that dictate that if two volumes of water are combined, the final concentration will be less than the maximum in the two initial volumes. This principle applies whenever the contaminant is introduced in a dissolved state. It also applies to mixing that occurs by hydrodynamic dispersion. In the simplest case of mixing of two water volumes, the final concentration is given by:

where: C is the final concentration; C1 and V1 are the concentration and volume of Source 1, respectively; and C2 and V2 are the concentration and volume of Source 2, respectively. The final concentration cannot be greater than C1 or C2.

Now consider the alternative case where the two sources release the same relative masses but the releases occur in a manner as to create a single plume. This could happen where two adjacent properties released a non-aqueous phase liquid (NAPL) that entered the aquifer in a undissolved state. In this case, the plume concentrations associated with each source independently would be given by:

and

and the combined plume concentration would be:

and C is greater than either C1 or C2. Clearly, either Source 1 or Source 2 could be "the straw that broke the camel's back" by causing the combined plume concentration to exceed the MCL.

The potential violations of conservation principles described above are generally avoided when mathematical models are used to compute commingled plume concentrations. They are easy to commit, however, when making only qualitative arguments to justify allocations.