Using a Bayesian Statistical Model to Determine the Amount of Coalbed Natural Gas Co-Produced Water in the Powder River, Wyoming and Montana

The Powder River Basin (PRB), Wyoming and Montana, is an area of considerable economic value because of production of coal and coalbed natural gas (CBNG). CBNG recovery is associated with large volumes of co-produced water, much of which is discharged on the surface. Montana's concern that this produced water may impact the quality of water used for irrigation led them to pass water anti-degradation legislation. This could limit Wyoming's near exponential growth in CBNG production, which has increased from just 152 CBM wells in 1994 to 13,600 in 2004, with each well producing up to 11,000 gallons of water per day.

In this study, we sought to determine the amount of CBNG co-produced water that reaches the Powder River annually using a Bayesian model implemented in WinBUGS. Strontium was selected for modeling because unlike oxygen and hydrogen isotopes, it does not fractionate in nature and it has been shown to be an effective tracer of waters of different origins. Using the ⁸⁷Sr/⁸⁶Sr ratio and strontium concentration of water collected from the Powder River at 30 locations, we created a five end-member mixing model that accounts for the ⁸⁷Sr/⁸⁶Sr ratio and strontium concentration of the different lithologies encountered in the PRB, as well as rainwater, and CBNG co-produced water. The model allows for all possible combinations of these end-members to account for the ⁸⁷Sr/⁸⁶Sr ratio and strontium concentration of the river and incorporates uncertainty in the measurements and process errors. Model results confirm that Beaver Creek is almost entirely composed of CBNG co-produced water and indicates that less than 1% of the Powder River is composed of CBNG co-produced water upstream of Beaver Creek and decreases with distance downstream. These results indicate that CBM co-produced water is volumetrically an insignificant fraction of the water carried by the Powder River.