Comparative evaluation of multi-basin production performance and application of spatio-temporal models for unconventiona
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ORIGINAL PAPER-PRODUCTION ENGINEERING
Comparative evaluation of multi‑basin production performance and application of spatio‑temporal models for unconventional oil and gas production prediction M. E. Wigwe1 · E. S. Bougre1 · M. C. Watson1 · A. Giussani1 Received: 11 May 2020 / Accepted: 13 July 2020 © The Author(s) 2020
Abstract Modern data analytic techniques, statistical and machine-learning algorithms have received widespread applications for solving oil and gas problems. As we face problems of parent–child well interactions, well spacing, and depletion concerns, it becomes necessary to model the effect of geology, completion design, and well parameters on production using models that can capture both spatial and temporal variability of the covariates on the response variable. We accomplish this using a well-formulated spatio-temporal (ST) model. In this paper, we present a multi-basin study of production performance evaluation and applications of ST models for oil and gas data. We analyzed dataset from 10,077 horizontal wells from 2008 to 2019 in five unconventional formations in the USA: Bakken, Marcellus, Eagleford, Wolfcamp, and Bone Spring formations. We evaluated well production performance and performance of new completions over time. Results show increased productivity of oil and gas since 2008. Also, the Bakken wells performed better for the counties evaluated. We present two methods for fitting spatio-temporal models: fixed rank kriging and ST generalized additive models using thin plate and cubic regression splines as basis functions in the spline-based smooths. Results show a significant effect on production by the smooth term, accounting for between 60 and 95% of the variability in the six-month production. Overall, we saw a better production response to completions for the gas formations compared to oil-rich plays. The results highlight the benefits of spatio-temporal models in production prediction as it implicitly accounts for geology and technological changes with time. Keywords Spatio-temporal models · Data analytics · Unconventional reservoirs · Fixed rank kriging (FRK) · ST-GAMs ( ) fj xji Smooth function of covariates, xji List of symbol Ai Row of matrix for any parametric model k Basis dimension tp , cr Thin plate, cubic regression spline component ST Spatio-tempoal model s, x Space (longitude and latitude) AIC Akaike information Criteria t,r Time BAU Basic areal unit Y(s,t) True process of interest indexed in space GAM Generalized additive models and time FRK Fixed rank Kriging y(s,t), Z(x;r) Potential or observed data indexed in TOC Total organic carbon space and time MSPE Mean squared prediction error Ns Neighbors of spatial location s RMSPE Root mean squared prediction error PCV Predictive cross-validation score 𝜃D , 𝜃P , 𝜃h Model parameter for data model, process model and hyper parameter SCV Standardized cross-Validation score ( ) CRPS Continuous rank probability score g 𝜇i Function representing the model Tcf, Bcf, MMcf Trillion, billion, million cubic feet
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