Traditionally, in order to estimate the production potential at a new, prospective field site via simulation or material balance, one needs to collect various forms of expensive field data and/or make assumptions about the nature of the formation at that site. Decline curve analysis would not be applicable in this scenario, as producing wells need to pre-exist in the target field. The objective of our work is 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 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 can obtain production forecasts at P10, P50, and P90, as well as calculate 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. Looking only at 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 kept only production histories of 24 months or longer in duration to ensure good decline curve fits. Ultimately, we were left with 5,637 production records. Here, we chose Duong’s decline model to represent production decline in this shale gas play, and fitting of this decline curve was accomplished through ordinary least square regression.
Interpolation was done by universal co-kriging with consideration to correlate the four parameters in Duongs’ model, which also showed a linear trend (the parameters show 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 across the study area. Finally, the co-kriging model was cross-validated with leave-one-out scheme, which showed significant but not unreasonable error in decline curve coefficient prediction.
We forecasted potential gas production in the study area using co-kriging. Heat maps of decline curve parameters as well as EUR were constructed to give operators a big picture of the production potential in the play. The methods proposed are easy to implement and do not require various expensive data like permeability, bottom hole pressure, etc., giving operators a risk-based analysis of prospective sites. We also made this analysis available to the public in a user-friendly web app.