Combining decline-curve analysis and geostatistics to forecast gas production in the Marcellus shale

To estimate the production potential at a new, prospective field site by means of simulation or material balance, one needs to collect various forms of costly field data and make assumptions about the nature of the formation at that site. Decline-curve analysis (DCA) would not be applicable in this scenario, because producing wells need to pre-exist in the target field. The objective of our work was to make first-order forecasts of production rates at prospective, undrilled sites using only production data from existing wells in the entire play. This is accomplished through the co-Kriging of decline-curve parameter values, where the parameter values are obtained at each existing well by fitting an appropriate decline model to the production history. Co-Kriging gives the best linear unbiased prediction of parameter values at undrilled locations, and also estimates uncertainty in those predictions. Thus, we obtained production forecasts at P10, P50, and P90, and we calculated the estimated ultimate recovery (EUR) at those same levels across the spatial domain of the play. To demonstrate the proposed methodology, we used monthly gas-flow rates and well locations from the Marcellus shale-gas play in this research. Monitoring only horizontal and directional wells, the gas-production rates at each well were carefully filtered and screened. Also, we normalized the rates by perforation-interval length. We only kept production histories of 24 months or longer to ensure good decline-curve fits. Ultimately, we were left with 5, 637 production records. Here, we chose Duong's decline model (Duong 2011) to represent the production decline in this shale-gas play, and fitting this decline curve was accomplished through ordinary leastsquares (OLS) regression. Interpolation was done by universal co-Kriging while considering the correlation between the four parameters in Duong's model, which also showed linear trends (the parameters showed dependency on the x and y spatial coordinates). Kriging gave us the optimal decline-curve coefficients at new locations (P50 curve), as well as the variance in these coefficient estimates (used to establish P10 and P90 curves). We were also able to map EUR for 25 years across the study area. Finally, the universal co-Kriging model was cross validated with a leave-one-out scheme, which showed significant, but not unreasonable, error in the decline-curve-coefficient prediction. The methods proposed were implemented and did not require various costly data, such as permeability and bottomhole pressure, thus giving operators a risk-based analysis of prospective sites. While we demonstrated the procedure on the Marcellus shale-gas play, it is applicable to any play with existing producing wells. We also made this analysis available to the public in a user-friendly web application (Xi and Morgan 2018).