Production forecasting is usually performed by applying a single model from a classical statistical standpoint (point estimation). This approach neglects (a) model uncertainty, and (b) quantification of uncertainty of the model's estimates. This work evaluates the predictive accuracy of rate-time models to forecast production from tight-oil wells using Bayesian methods. We apply Bayesian leave-one-out and leave-future-out cross-validation using an accuracy metric that evaluates the uncertainty of the models' estimates: the expected log predictive density (elpd). We illustrate the application of the procedure to tight-oil wells of West Texas.

This work assesses the predictive accuracy of rate-time models to forecast production of tight-oil wells. We use two empirical models: the Arps hyperbolic and logistic growth models, and two physics-based models: scaled slightly compressible single-phase and scaled two-phase (oil and gas) solutions of the diffusivity equation. First, we perform Bayesian inference to generate probabilistic production forecasts for each model using a Bayesian workflow in which we assess the convergence of our Markov chain Monte Carlo algorithm, calibrate, and evaluate the robustness of our models' inferences. Second, we evaluate the predictive accuracy of models using the elpd accuracy metric. This metric evaluates a distribution to provide a measure of out-of-sample predictive performance. We apply two different cross-validation (CV) techniques: leave-one-out (LOO) and leave-future-out (LFO).

The results of this study are the following. First, we evaluate the predictive performance of models using an accuracy metric the elpd, which accounts for the uncertainty of the models' estimates assessing distributions instead of point estimates. Second, we perform fast cross-validation calculations using an importance sampling technique to evaluate and compare the results of the application of two cross-validation techniques: LOO-CV and LFO-CV. Whereas the goal of LOO-CV is to evaluate the models' ability to accurately resemble the structure of the production data, LFO-CV aims to assess the models' capacity to predict production data in future time (honoring the time-dependent structure of the data). Despite the difference in their prediction goals, both methods yield similar results on a set of tight-oil wells. The logistic growth model yields, on average, a better predictive accuracy for most of the wells in our dataset, followed by the two-phase physics-based flow model.

The present work shows the application of new tools to evaluate the predictive accuracy of models used to forecast production of tight-oil wells using: (a) an accuracy metric that accounts for the uncertainty of the models' estimates, and (b) fast computation of two cross-validation techniques; LOO-CV and LFO-CV. To our knowledge, the proposed approach is novel and suitable to evaluate the predictive accuracy of models to forecast hydrocarbon production.

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