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Using Bayesian Leave-One-Out and Leave-Future-Out Cross-Validation to Evaluate the Performance of Rate-Time Models to Forecast Production of Tight-Oil Wells
Ruiz Maraggi, Leopoldo M. (The University of Texas at Austin (Corresponding author)) | Lake, Larry W. (The University of Texas at Austin) | Walsh, Mark P. (The University of Texas at Austin)
Summary 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 (LOO) and leave-future-out (LFO) cross-validation (CV) 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 the Markov chain Monte Carlo (MCMC) algorithm, calibrate, and evaluate the robustness of the models’ inferences. Second, we evaluate the predictive accuracy of the models using the elpd accuracy metric. This metric provides a measure of out-of-sample predictive performance. We apply two different CV techniques: LOO and LFO. The results of this study are the following. First, we evaluate the predictive performance of the models using the elpd accuracy metric, which accounts for the uncertainty of the models’ estimates assessing distributions instead of point estimates. Second, we perform fast CV calculations using an important sampling technique to evaluate and compare the results of the application of two CV techniques: leave-one-out cross-validation (LOO-CV) and leave-future-out cross-validation (LFO-CV). While 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 future-time production (honoring the time-dependent structure of the data). Despite the difference in their prediction goals, both methods yield similar results on the set of tight-oil wells under study. The logistic growth model yields the best predictive performance for most of the wells in the data set, followed by the two-phase physics-based flow model. This 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 CV techniques, LOO-CV and LFO-CV. To our knowledge, the proposed approach is novel and suitable to evaluate and eventually select the rate-time model(s) with the best predictive accuracy of models to forecast hydrocarbon production.
- North America > United States > Texas (1.00)
- North America > Canada (0.94)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Performance Analysis > Cross Validation (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.88)
Averaging Predictions of Rate-Time Models Using Bayesian Leave-Future-Out Cross-Validation and the Bayesian Bootstrap in Probabilistic Unconventional Production Forecasting
Ruiz Maraggi, Leopoldo M. (The University of Texas at Austin) | Lake, Larry W. (The University of Texas at Austin) | Walsh, Mark P. (The University of Texas at Austin)
Abstract Two main limitations occur when selecting a model with the best predictive accuracy over a set of candidates to extrapolate future production of wells. First, from a Bayesian standpoint, all models are interpretations of the data and thus, they are always incomplete. Second, we could select a suboptimal model with a better bias-variance tradeoff (model selection induced bias). The goal of this work is to combine different models’ predictions to avoid the aforementioned issues. We illustrate the application of the procedure to a set of tight-oil wells of West Texas. This work aims to combine different models’ predictions using Bayesian statistics. First, we perform Bayesian inference and generate probabilistic production forecasts for four rate-time models (Arps’ hyperbolic, logistic growth, single-phase, and two-phase scaled solution of the diffusivity equation). Second, we evaluate the predictive performance of each model with production data computing the expected log predictive density (elpd) accuracy metric using leave-future-out cross-validation (LFO-CV). Third, we use the Bayesian Bootstrap to make realizations and quantify the uncertainty associated with the estimation of the elpd for each model. We compute a model's weight for the associated expectation of the elpd for each Bayesian Bootstrap realization. Finally, we calculate an average model weight including all the Bayesian Bootstrap realizations. This study shows that the present model averaging technique produces a distribution of production forecasts with reduced variance when compared to the ones derived from a single rate-time model. The procedure is suitable to integrate model uncertainty in a simple and computationally inexpensive way since it only requires using a sampling technique. The present approach is the Bayesian analog to Bagging (Bootstrap aggregating), but with the following difference: instead of assuming uncertainty in the data collection, here we are accounting for the uncertainty in model predictions. The model ensemble assigns weights to each model according to its predictive performance. This work illustrates a straightforward way to integrate the uncertainty of models’ predictions using a fully Bayesian approach combining Bayesian leave-future-out cross-validation to evaluate the predictive accuracy of rate-time models, and the Bayesian Bootstrap to account for the uncertainty in those estimates. We present the application to production data of tight-oil wells building an average predictive distribution for the estimated ultimate recovery (EUR).
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Performance Analysis (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (1.00)
Abstract A common industry practice is to select a particular model from a set of models to history match oil production and estimate reserves by extrapolation. Future production forecasting is usually done in this deterministic way. However, this approach neglects: a) model uncertainty, and b) quantification of uncertainty of future production forecasts. The current study evaluates the predictive accuracy of rate-time models to forecast production over a set of tight oil wells of West Texas. We present the application of an accuracy metric that evaluates the uncertainty of our models' estimates: the expected log predictive density (elpd). This work assesses the predictive performance of two empirical models—the Arps hyperbolic and the 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. These models are arbitrarily selected for the purpose of illustrating the statistical procedure shown in this paper. First, we perform classical regression with the models and evaluate their predictive performance using frequentist (point estimates) metrics such as R, the Akaike information criteria (AIC), and hindcasting. Second, we generate probabilistic production forecasts using Bayesian inference for each model. Third, we evaluate the predictive accuracy of the models using the elpd accuracy metric. This metric evaluates a measure of out-of-sample predictive performance. We apply both adjusted-within-sample and cross-validation techniques. The adjusted within-sample method is the widely applicable information criteria (WAIC). The cross-validation techniques are hindcasting and leave-one-out (LOO-CV) method. The results of this research are the following. First, we illustrate that the assessment of a model's predictive accuracy depends on whether we use frequentist or Bayesian approaches. This is an important finding in this work. The frequentist approach relies on point estimates while the Bayesian approach considers the uncertainty of our models' estimates. From a frequentist or classical standpoint, all of the models under study yielded very similar results which made it difficult to determine which model yielded the best predictive performance. From a Bayesian standpoint, however, we determined that the logistic growth model yielded a best match in 81 of 130 wells in our sample play and the two-phase physics-based model yielded a best match in 39 of the wells. In addition, we show that WAIC and LOO-CV present similar results for each model, a thing to expect because of their asymptotical equivalence. Finally, Our observations regarding the different models are subject to the dataset under study wherein a majority of the wells are in transient flow. The present study provides tools to evaluate the predictive accuracy of models used to forecast (extrapolate) production of tight oil wells. The elpd is an accuracy metric useful to evaluate the uncertainty of our models' estimates and compare their predictive performance since it assesses distributions instead of point estimates. To our knowledge, the proposed approach is a novel and an appropriate technique to evaluate the predictive accuracy of models to forecast hydrocarbon production.
- North America > United States > Texas (1.00)
- North America > Canada (0.93)
- Energy > Oil & Gas > Upstream (1.00)
- Government > Regional Government > North America Government > United States Government (0.67)
- North America > United States > Texas > Fort Worth Basin > Barnett Shale Formation (0.99)
- North America > United States > Montana > Williston Basin > Elm Coulee Field > Bakken Shale Formation > Middle Bakken Shale Formation (0.99)
- North America > United States > Texas > West Gulf Coast Tertiary Basin > Eagle Ford Shale Formation (0.94)
- (5 more...)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Performance Analysis (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (1.00)
A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight Oil Reservoirs Using a Physics-Based Two-Phase Flow Model
Maraggi, Leopoldo M. Ruiz (The University of Texas at Austin) | Lake, Larry W. (The University of Texas at Austin) | Walsh, Mark P. (The University of Texas at Austin)
Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight oil reservoirs. Nonetheless, this approach: a) omits multiphase flow effects that exist below bubble point conditions, and b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to wells of the Permian Basin of West Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation.
- Geology > Geological Subdiscipline > Economic Geology > Petroleum Geology (0.60)
- Geology > Petroleum Play Type > Unconventional Play (0.46)
- Energy > Oil & Gas > Upstream (1.00)
- Government > Regional Government > North America Government > United States Government (0.68)
- North America > United States > Texas > Permian Basin > Yeso Formation (0.99)
- North America > United States > Texas > Permian Basin > Yates Formation (0.99)
- North America > United States > Texas > Permian Basin > Wolfcamp Formation (0.99)
- (29 more...)
Bayesian Variable Pressure Decline-Curve Analysis for Shale Gas Wells
Maraggi, Leopoldo M. Ruiz (Bureau of Economic Geology, The University of Texas at Austin) | Walsh, Mark P. (The University of Texas at Austin) | Lake, Larry W. (The University of Texas at Austin) | Male, Frank R. (The Pennsylvania State University)
Abstract Decline-curve analysis (DCA) and production forecasting are usually performed from a deterministic standpoint (point estimation). This approach does not quantify the uncertainty of the model’s parameters and thus, the model’s estimated ultimate recovery (EUR). In addition, decline-curve models do not consider the variations in the bottomhole flowing pressure (BHP), which can greatly impact the accuracy of the model’s predictions. This work combines a new technique that incorporates variable BHP conditions into DCA models with Bayesian inference to improve the accuracy of production history-matches while quantifying the uncertainty of the model’s parameters and its future production prediction. We present the application of this workflow for shale gas wells. This work uses the constant-pressure solution of the pressure diffusivity equation for a compressible fluid as a decline-curve model. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: the original gas in-place and a characteristic time. Next, we apply an optimization algorithm that provides a history-match to production data subject to variable BHP. Then, this work generates the probabilistic production history-matches and forecasts using Bayesian inference treating the model’s parameters as random variables. We use an adaptive Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) algorithm for this purpose. Finally, we illustrate the calibration of the inferences through production hindcasts. This work introduces a method to efficiently perform probabilistic production history-matches and forecasts using decline-curve models while accounting for variable BHP effects. The results of the algorithm are the distributions of the model’s parameters and EUR estimates. In addition, the adaptive M-H MCMC uses information of previous iterations to improve the efficiency of the proposal distribution to accelerate the convergence of the Markov chains. Finally, incorporating variable BHP conditions into the algorithm constrains the model’s parameters and EUR distributions more than probabilistic DCA without considering BHP variations. This paper illustrates a workflow that generates probabilistic history-matches and production forecasts for any decline-curve model while incorporating variable BHP conditions. The method provides fast production history-matches and forecasts of shale gas wells and more accurately than traditional DCA while quantifying the uncertainty in the model’s parameters and EUR estimates. The main contribution of this work is the illustration of a new method for probabilistic variable pressure DCA.
- North America > United States > Texas (1.00)
- North America > Canada (0.94)
- North America > United States > Texas > Haynesville Shale Formation (0.99)
- North America > United States > Texas > Fort Worth Basin > Barnett Shale Formation (0.99)
- North America > United States > South Dakota > Williston Basin > Bakken Shale Formation (0.99)
- (9 more...)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models (0.70)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (0.69)