Application of a Bayesian model to infer the contribution of coalbed natural gas produced water to the Powder River, Wyoming and Montana

The Powder River Basin (PRB) of Wyoming and Montana contains significant coal and coal bed natural gas (CBNG) resources. CBNG extraction requires the production of large volumes of water, much of which is discharged into existing drainages. Compared to surface waters, the CBNG produced water is high in sodium relative to calcium and magnesium, elevating the sodium adsorption ratio (SAR). To mitigate the possible impact this produced water may have on the quality of surface water used for irrigation, the State of Montana passed water anti-degradation legislation, which could affect CBNG production in Wyoming. In this study, we sought to determine the proportion of CBNG produced water discharged to tributaries that reaches the Powder River by implementing a four end-member mixing model within a Bayesian statistical framework. The model accounts for the ⁸⁷Sr/⁸⁶Sr, δ¹³C_DIC, [Sr] and [DIC] of CBNG produced water and surface water interacting with the three primary lithologies exposed in the PRB. The model estimates the relative contribution of the end members to the river water, while incorporating uncertainty associated with measurement and process error. Model results confirm that both of the tributaries associated with high CBNG activity are mostly composed of CBNG produced water (70-100%). The model indicates that up to 50% of the Powder River is composed of CBNG produced water downstream from the CBNG tributaries, decreasing with distance by dilution from non-CBNG impacted tributaries from the point sources to ~10-20% at the Montana border. This amount of CBNG produced water does not significantly affect the SAR or electrical conductivity of the Powder River in Montana.