A closed-system model is used for predicting the δ¹⁸O of formation waters in the deep portions of the northern Green River basin, Wyoming. δ¹⁸O_calcite is calculated from this modeled water and compared with the δ¹⁸O of measured calcites to help interpret diagenesis in the basin.

The modification of ¹⁸O_water, which may be caused by diagenetic reactions at elevated temperatures, is modeled from two mass-balance equations. Three diagenetic reactions used to modify δ¹⁸O_water include: detrital limestoneå calcite cement; detrital quartz→ quartz cement; and detrital clay å authigenic illite/smectite. A weighted average δ¹⁸O_water and δ¹⁸O of calcite, quartz and illite/smectite in equilibrium with this water are calculated at 500-m increments. For a closed-system model, calculated variables at one depth are used for input variables at the next depth. An open system can be crudely simulated by adjusting the input variables at each depth.

Petrographic and hydrologic data suggest that throughout much of the basin an open hydrochemical system overlies a relatively closed system which is below 3000 m. From the surface to 3000 m deep, δ¹⁸O_calcite measured in sandstone cements deviates from calculated ¹⁸O_calcite for the closed-system model. Below 3000 m, δ¹⁸O_calcite of cement and bulk shale converge from opposite directions with increasing depth toward the calculated δ¹⁸O_calcite. Adjusting the calculated δ¹⁸O_calcite to match the measured δ¹⁸O_calcite indicates that the deviation above 3000 m results from mixing of meteoric waters with ¹⁸O-rich formation water.