(589b) Alternatives to Decline-Curve Models for Unconventional Reservoirs:  a Case for Data-Driven Discovery of Natural Laws

Unconventional resources account for an increasingly high fraction of oil and gas production in the US. The economic exploitation of such resources places significant challenges, one of which is estimation of their ultimate recovery. Decline-curve analysis is typically a tool used to predict ultimate recovery from initial production data over a relatively short period. While decline curve models, such as the celebrated Arps decline model and its variants (q(t) = qi/(1+b*Di*t)^(1/b)), work fairly well for conventional oil and gas reservoirs, they may be fairly inaccurate for unconventional reservoirs. Because production from unconventional reservoirs exhibits a long transient flow followed by boundary-dominated flow, hybrid models, combining early transient-flow models such as Duong’s and SEPD with Arps’ for boundary-dominated flow, are usually employed. This approach may produce significantly more accurate predictions than single-flow regime models. However, in unconventional reservoirs with multiphase flow these transitions are gradual and often take more than one log cycle in diagnostic plots. Further, for transition period between transient flow and boundary dominated flow, there is no consensus for what is the appropriate model structure. Therefore, a need exists for a clear-cut method that easily captures future production patterns and trends in multiphase flow unconventional reservoirs from limited initial production data. In this paper we propose such an approach.

The proposed approach completely bypasses the stipulation of an explicit formula for decline-curve analysis. Rather, a large database of available field data referring to production from unconventional reservoirs is analyzed using multivariate statistical methods, such as principal component analysis (PCA). The analysis suggests that over 96% or 99% of variability in the data can be captured with only one or two latent variables. Therefore, an appropriate model structure naturally emerges from the data, thus eliminating the need to separate production into different flow-related regimes with explicit formulas for corresponding decline curves.

Subsequently, data compression can be used to express all observed production patterns as a simple (linear or nonlinear) combination of just a few basis functions. This combination will constitute the model sought, and the coefficients in the corresponding combination will be the model parameters. In practice, these parameters would be estimated from production data over a limited time period, and the resulting model would predict production over the life of the reservoir, thus estimating ultimate recovery.

The proposed method was tested using cross-validation and found to produce comparable or better predictions than standard (equation-based) methods without the need to manually select different flow regimes for multiphase-flow reservoirs. In essence, the latent variables identified correspond to a new explicit formula that simply does not conform to standard formulas well known in mathematics (e.g. exponentials) but is tailored to describe the data. Parameter estimation using the proposed approach is also simple, as it corresponds to a linear (rather than nonlinear) least-squares problem.